sikSaKNnaeRKOgbgÁúMGMBIEdk

LRFD STEEL DESIGN

GñkniBn§³ WIILIAM T. SEGUI

bkERbeday³ etg qay
viTüasßanCatiBhubec©keTskm<úCa
mhaviTüal½ysMNg;sIuvil

qñaM 2010
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

matika
Contents

I. esckþIepþIm (Introduction)
1>1> karsikSaKNnaeRKOgbgÁúM (Structural Design) ..............................................................1
1>2> bnÞúk (Loads)...............................................................................................................4
1>3> Building Codes .......................................................................................................... 5
1>4> Design Specifications ..................................................................................................5
1>5> eRKOgbgÁúMGMBIEdk (Structural Steel) ...............................................................................6
1>6> rUbragmuxkat;bTdæan (standard Cross-sectional Shapes) ............................................11

II. eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁÁúMEdk (Concepts in Structural Steel Design)

2>1> TsSnviC¢akñúgkarsikSaKNnamuxkat; (Design Philosophies) ...................................... 20
2>2> American Institute of Steel Construction Specification ......................................... 22
2>3> emKuNersIusþg; nigemKuNbnÞúkEdleRbIR)as;enAkñúg AISC Specification
(Load and Resistance Factors Used in the AISC Specification) ............................. 23
2>4> mUldæanRbU)ab‘ÍlIetrbs; Load and Resistance Factors
(Probabilistic Basis of Load and Resistance Factors) ............................................. 25
2>5> Manual of Steel Construction ................................................................................. 30

III. eRKOgbgÁúMrgkarTaj (Tension Members)

3>1> esckþIepþIm (Introduction) ......................................................................................... 30
3>2> ersIusþg;KNna (Design strength) ............................................................................. 31
3>3> RkLaépÞmuxkat;suT§RbsiT§PaB (Effective net area) .................................................... 36
3>4> karteRmobtamEbbqøas; (Staggered fasteners) ......................................................... 43
3>5> Block shear ............................................................................................................. 50
3>6> karKNnaGgát;rgkarTaj (Design of tension members) .......................................... 52
3>7> EdksrésEdlmaneFμj nigExSkab (Threaded rods and Cables)................................ 59
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3>8> Ggát;rgkarTajenAkñúgdMbUl (Tension members in roof trusses) ............................... 61

3>9> Ggát;EdltPa¢b;edayknøas; (Pin-Connection Members) ........................................... 70
IV. eRKOgbgÁúMrgkarsgát;
Compression Members
4>1> esckþIepþIm (introduction) .......................................................................................... 73
4>2> RTwsþIssr(Column Theory) ....................................................................................... 73
4>3> tRmUvkarrbs; AISC (AISC Requirements) ............................................................ 82
4>4> karKNnamuxkat; (Design) ......................................................................................... 89
4>5> esckþIbEnßmsRmab;RbEvgRbsiT§PaB (More on Effective Length) .............................. 92
4>6>karekagedayrmYl nigedayBt;-rmYl (Torsional and Flexural-Torsional Buckling) . 105
4>7> Built-up Member .................................................................................................... 112

V. Fñwm
Beams
5>1> esckþIepþIm (Introduction) ........................................................................................ 120
5>2> kugRtaMgBt; nigm:Um:g;)øasÞic (Bending Stress and the Plastic Moment) ...................... 121
5>3> lMnwg (Stability) ...................................................................................................... 127
5>4> cMNat;fñak;rbs;rUbrag (Classification of Shapes) ..................................................... 129
5>5> Bending Strength of Compact Shapes .................................................................. 130
5>6> Bending Strength of Noncompact Shapes............................................................. 140
5>7> Summary of Moment Strength ............................................................................. 144
5>8> ersIusþg;kmøaMgkat;TTwg (Shear Strength) ................................................................. 145
5>9> PaBdab (Deflection) ............................................................................................... 152
5>10> karKNnamuxkat; (Design) ................................................................................... 154
5>11> rn§RbehagenAkñúgFñwm (Holes in Beam).................................................................. 165
5>12> Open-Web Steel Joists ....................................................................................... 167
5>13> bnÞHRTFñwm nigbnÞH)atssr (Beam Bearing Plates and Column Base Plate) ...... 171
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5>14> Biaxial Bending ................................................................................................. 182

5>15> ersIusþg;m:Um:g;Bt;rbs;rUbragepSg² (Bending Strength of Various Shape) .............. 190
VI. Fñwm-ssr
Beam-Columns
6>1> esckþIepþIm (Introduction) ....................................................................................... 197
6>2> smIkarGnþrkmμ (Interaction Formulas) .................................................................. 198
6>3> m:Um:g;bEnßm (Moment Amplification) .................................................................... 201
6>4> Web Local Buckling in Beam-Columns .............................................................. 204
6>5> eRKagBRgwg nigeRKagGt;BRgwg (Braced versus Unbraced Frame).............................. 206
6>6> Ggát;enAkñúgeRKagEdlBRgwg (Members in Braced Frames) ....................................... 207
6>7> Ggát;enAkñúgeRKagEdlminBRgwg (Members in Unbraced Frames) .............................. 217
6>8 KNnamuxkat;Fñwm-ssr (Design of Beam-Column) ................................................ 224
6>9> Trusses With Top Chord Loads Between Joints ................................................... 234
VII. tMNsamBaØ
Simple Connections
7>1> esckþIepþIm (Introduction) ..................................................................................... 241
7>2> Bolted Shear Connections: Failure Mode ............................................................ 244
7>3> Bearing Strength, Spacing and Edge-distance Requirements ............................. 246
7>4> b‘ULúgFmμta (Common Bolts) ................................................................................ 253
7>5> b‘ULúgersIusþg;x<s; (High-Strength Bolts)................................................................... 256
7>6> Shear Strength of High-Strength Bolts ................................................................. 258
7>7> Slip-Critical Connections ..................................................................................... 261
7>8> b‘ULúgersIusþg;x<s;rgkarTaj (High-Strength Bolts in Tension) ............................... 277
7>9> kmøaMgpÁÜbrvagkmøaMgTaj nigkmøaMgTajenAkñúgb‘ULúg (Combined Shear and Tension in
Fasteners) ............................................................................................................ 287
7>10> tMNpSar (Welded connections)........................................................................... 293
7>11> Fillet Welds........................................................................................................ 295
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VIII. tMNcakp©it
Eccentric Connections
8>1> ]TahrN_sMrab;tMNcakp©it (Examples of Eccentric Connections) .......................... 306
8>2> tMNcMNakp©itedayb‘ULúg³ EtkmøaMgkat; (Eccentric Bolted Connections:
Shear only) .......................................................................................................... 307
8>3> tMNcMNakp©itedayb‘ULúg³ kmøaMgkat;bUknwgkmøaMgTaj
Eccentric Bolted Connections: Shear Plus Tension .......................................... 319
8>4> tMNcMNakp©itedaypSar³ EtkmøaMgkat;
Eccentric Welded Connections: Shear only........................................................ 323
8>5> tMNcMNakp©itedaypSar³ kmøaMgkat; nigkmøaMgTaj
Eccentric Welded Connections: Shear and Tension ........................................... 333
8>6> tMNTb;m:Um:g; (Moment-Resisting Connection)......................................................... 339
8>7> Column Stiffeners and other Reinforcement ...................................................... 348
8>8> End Plate Connection.......................................................................................... 361
8>9> esckþIsnñidæan (Concluding Remarks) ................................................................. 369
IX. eRKOgbgÁúMsmas
Composite Construction
9>1> esckþIepþIm (Introduction)........................................................................................ 370
9>2> karsagsg;edaymankarTb; nigedayminmankarTb;
Shored Versus Unshored Construction .............................................................. 382
9>3> TTwgsøabRbsiT§PaB (Effect Flange Width ) ............................................................ 384
9>4> Shear Connectors ................................................................................................. 387
9>5> karKNnamuxkat; (Design) ....................................................................................... 390
9>6> PaBdab (Deflections) .............................................................................................. 395
9>7> FñwmsmasCamYynwgkRmalBum<Edk (Composite Beams with Formed Steel Deck) .... 399
9>8> taragsRmab;karviPaK nigkarKNnaFñwmsmas
Tables for Composite Beam Analysis and Design.............................................. 412
9>9> FñwmCab; (Continuous Beams).................................................................................... 419
9>10> ssrsmas (Composite Columns) ....................................................................... 421

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X. rtEdkbnÞH
Plate Girder
10>1> esckþIepþIm (Introduction) .................................................................................... 428
10>2> karBicarNaTUeTA (General Considerations ) .......................................................... 429
10>3> tRmUvkarrbs; AISC (AISC Requirements) ...................................................... 433
10>4> ersIusþg;rgkarBt; (Flexural Strength) ..................................................................... 435
10>5> ersIusþg;kmøaMgkat; (Shear Strength) ........................................................................ 438
10>6> GnþrGMeBIénkarBt; nigkmøaMgkat; (Interaction of Flexural and Shear) ..................... 444
10>7> Bearing Stiffeners .............................................................................................. 445
10>8> kaKNnamuxkat; (Design) ...................................................................................... 457
Appendix A. karKNna nigkarviPaKedaylkçN³)aøsÞic
Plastic Analysis and Design
A>1> esckþIepþIm (Introduction) ..................................................................................... 478
A>2> AISC Requirements.............................................................................................. 480

A>3> karviPaK (Analysis) ............................................................................................... 481

A>4> karKNnamuxkat; (Design) ....................................................................................... 488

A>5> karsnñidæan (Conclusion Remark)........................................................................... 490

Appendix B. karKNnaeRKOgbgÁúMEdkedayQrelIkugRtaMgGnuBaØat
Structural Steel Design Based on Allowable Stress

B>1> esckþIepþIm (Introduction) ...................................................................................... 491

B>2> Ggát;rgkarTaj (Tension members) ...................................................................... 493

B>3> Ggát;rgkarsgát; (Compression members) .............................................................. 494

B>4> Fñwm (Beams) ............................................................................................................ 498

B>5> Beam-Columns...................................................................................................... 505

B>6> snñidæan (Concluding Remarks) ............................................................................... 510

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I. esckþIepþIm
Introduction

1>1> karsikSaKNnaeRKOgbgÁúM Structural Design

karsikSaKNnaeRKOgbgÁúMsMNg;GKar eTaHCaeRKOgbgÁúMGMBIEdk b¤GMBIebtugBRgwgedayEdkk¾

eday KWeKtRmUv[kMNt; nigeRCIserIsmuxkat;smrmürbs;Ggát;eRKOgbgÁúMTaMgGs; edIm,ITb;Tl;nwg bnÞúk
xageRkATaMgGs;EdlmanGMeBImkelIeRKOgbgÁúM. kñúgkrNICaeRcIn sßabtükrmantYnaTIrcnam:UtGKar
edayrYmmankarerobcMcMnYnCan;rbs;GKar nigkarerobcMbøg;tamCan;nImYy² ehIyvisVkreRKOgbgÁúMRtUveFVI
karkñúgEdnkMNt;énkarrcnaenH. CakarEdlRbesIrbMputKW visVkr nigsßabtükrRtUvshkarKñakñúgdMeNIr
karrcna nigsikSaKNnaeRKOgbgÁúMenHedIm,IbBa©b;KMeragedayTTYl)aneCaKC½y. dMeNIrkarénkarsikSa
KNnaeRKOgbgÁúMRtUv)ansegçbdUcteTA³ sßabtükrCaGñksMercnUvesaP½NPaBrbs;GKar ehIyvisVkr
CaGñksikSaKNnamuxkat;rbs;eRKOgbgÁúMRbkbedaylkçN³esdækic© nigedayFananUvsßirPaBdl;sMNg;
GKar. visVkreRKOgbgÁúMRtUvKitCacMbgnUvsuvtßiPaB bnÞab;mkKWkareRbIR)as; niglkçN³esdækic©. lkçN³
esdækic©enAkñúgsMNg;KW sMedAelIkareRbIR)as;nUvsmÖar³ nigkmøaMgBlkmμy:agmanRbsiT§PaB.
karsikSaKNnad¾l¥KWTamTarnUvbøg;eRKagy:ageRcIn edayrYmmankarteRmobGgát; nigkartP¢ab;
Ggát;tamEbbEpnxus²Kña ehIyeFIVkareRbobeFobnUvlkçN³esdækic©rbs;va. sRmab;bøg;eRKagnImYy²
EdlRtUveFVIkarGegát eKRtUvsikSaKNnamuxkat;rbs;Ggát;nImYy². edIm,IeFVIVdcU enH)an CadMbUgeKRtUv
karsikSaviPaKeRKOgbgÁúM ehIyKNnakmøaMg nigm:Umg: ;Bt;rbs;Ggát;nImYy². CamYynwgTinñn½yTaMgenH
GñksikSaKNnaeRKOgbgÁúMGaceRCIserIsmuxkat;)any:agsmRsb. b:uEnþ munnwgeFVIkarsikSaviPaKRKOg
bgÁúM eKRtUvsMercCadMbUgnUvsmÖar³sRmab;eRbIR)as;kñúgeRKOgbgÁúM EdlCaTUeTAmanebtugBRgwgedayEdk
eRKOgbgÁúMGMBIEdk nigbnSMénsmÖar³TaMgBIr. CakarRbesIbMput eKKYrerobcMnUvCeRmIsénkarsikSaKNna
BIsmÖar³TaMgenH.
enAkñúgesovePAenH manEtkarENnaMBIkarsikSaKNnamuxkat;eRKOgbgÁúMGMBIEdk nigkartP¢ab;
rbs;vaEtb:ueNÑaH. visVkreRKOgbgÁúMRtUveRCIserIs nigepÞógpÞat;RbB½n§eRKOgbgÁúMTaMgGs;edIm,ITTYl)annUv
karsikSaKNnaRbkbedaylkçN³esdækic© nigsuvtßiPaB.
munnwgerobrab;BIeRKOgbgÁúMGMBIEdk eyIgcaM)ac;RtUvsÁal;RbePTGgát;nImYy²rbs;eRKOgbgÁúMCamun
sin. rUbTI 1>1 bgðajBI truss CamYynwgkmøaMgcMcMNucbBaÄrEdlGnuvtþRtg;tMNénGgát;xagelI. eday
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mhaviTüal½ysMNg;sIuvil NPIC

rkSanUvkarsnμt;énkarviPaK truss ¬tMN pinned nigkmøaMgGnuvtþEtelItMN¦ Ggát;rbs; truss CaGgát;

rgkmøaMgBIr (two-force member) EdlrgkmøaMgsgát; b¤kmøaMgTajtamG½kS. sRmab; truss TRm
samBaØEdlrgbnÞúkdUcbgðajkñúgrUb 1>1 Ggát;xagelICaGgát;rgkarsgát; ehIyGgát;xageRkamCaGgát;
rgkarTaj. Ggát;RTnugGacCaGgát;rgkarTaj b¤rgkarsgát;edayGaRs½yeTAelITItaMg TisTRmuy nig
TItaMgrbs;bnÞúk.

RbePTepSgeTotrbs;Ggát;RtUv)anbgðajCamYynwgeRKagtMNrwg (rigid frame) enAkñúgrUbTI

1>2. Ggát;rbs;eRKagenHRtUv)antP¢ab;y:agrwgedayTwkbnSar nwgGacsnμt;CaeRKOgbgÁúMCab;. enARtg;
TRm Ggát;RtUv)anpSarP¢ab;eTAnwgbnÞHctuekaNEdlP¢ab;edayb‘ULúgeTAnwgRKwHebtug. edaydak;eRKag
enHRsb²Kña ehIyP¢ab;BYkvaedayGgát;bEnßm EdlbnÞab;mkRtUv)anRKbedaysmÖar³dMbUl nigbiT)aMg
edaysmÖar³CBa¢aMgedIm,IbegáIt)anCaRbB½n§sMNg;TUeTA. karlMGitsMxan;minRtUv)anerobrab;eT b:uEnþGKar
BaNiC¢kmμxñattUcRtUv)ansagsg;tamlkçN³EbbenH. karsikSaKNnaeRKOgbgÁúM nigkarsikSaviPaK
eRKagnImYy²rbs;RbB½n§cab;epþImCamYynwgeRKagkñúgbøg;dUcbgðajenAkñúgrUbTI 1>2 b. cMNaMfa TRm
RtUv)anbgðajCaTRmsnøak; (hinges or pinned) minEmnTRmbgáb; (fixed). RbsinebIeCIgtagman
lT§PaBrgmuMrgVilsþÜcesþIg b¤RbsinebIkartP¢ab;manlkçN³bt;Ebn (flexible) RKb;RKan;edIm,IGnuBaØat
[manmuMrgVil enaHeKcat;TukvaCaTRmsnøak; (pinned). karsnμt;enAkñúgviFITUeTAénkarsikSaviPaKeRKOg
bgÁúMKW kMhYcRTg;RTaymantémøtUc Edlmann½yfamMurgVild¾tictYcrbs;TRmGaceFVI[TRmmanlkçN³Ca
tMNsnøak; (pinned) )an.
enAeBlEdleKTTYl)annUvragFrNImaRtrbs;eRKag niglkçxNÐTRmehIy eKGackMNt;kardak;
bnÞúk)an. karkMNt;bnÞúkenHTak;TgnwgkarEckrMElkbnÞúksrubTaMgGs;eTAeRKagnImYy². RbsinebI
eRKagEdlBicarNargbnÞúkdMbUlBRgayesμI enaHeRKagnImYy²EdlTTYlnUvcMENkrbs;bnÞúkenHnwgman
TRmg;CabnÞúkBRgayesμIEdlmanlkçN³CabnÞat;dUcbgðajenAkñúgrUbTI 1>2 b.
T.Chhay 2 Introduction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

sRmab;kardak;bnÞúkEdlbgðajenAkñúgrUbTI 1>2 b eRKagnwgxUcRTg;RTaydUcbgðajenAkñúgrUb

edayExSdac;. Ggát;nImYy²rbs;eRKagRtUv)ancat;cMNat;fñak;edayGaRs½yeTAelIRbePTénkareFVIkar
EdlsMEdgedayrUbragEdlxUcRTg;RTay. Ggát;edk AB nig BC rgkarBt;begáag (bending or
flexure) RtUv)aneKehAfaFñwm (beam). Ggát;bBaÄr BD Edlrgm:Um:g;KU (couple) EdlbBa¢ÚnBIFñwm

nImYy² ¬b:uEnþsRmab;eRKagsIuemRTIdUcbgðaj vamantémødUcKña EtTisedApÞúyKña¦ dUcenHeKGacecal

m:Um:g;KU (couple) enH)an. dUcenH Ggát; BD rgEtkmøaMgsgát;tamG½kSEdl)anBIbnÞúkbBaÄr. enA
kñúgsMNg; Ggát;rgkarsgát;bBaÄrdUcGVIEdl)anerobrab;RtUv)aneKehAfassr (column). cMENkGgát;
bBaÄrBIrepSgeTot AE nig CF minRtwmEtRTnUvkmøaMgsgát;tamG½kSb:ueNÑaHeT b:uEnþvaEfmTaMgTb;Tl;
nwgkarBt;begáagEdlmantémøFMeTotpg. Ggát;EbbenHRtUv)aneKehAfa beam-column. Cak;Esþg
RKb;Ggát;TaMgGs; eTaHCaRtUv)ancat;cMNat;fñak;CaFñwm b¤ssrk¾eday k¾vaenAEtrgbnÞúktamG½kS nig
m:Um:g;Bt;Edr b:uEnþenAkñúgkrNICaeRcIn eKGacecal\T§iBlNaEdlmantémøtUc)an.
bEnßmBIelIRbePTGgát;Edl)anBN’naxagelI esovePAenHnwgerobrab;BIkarKNnakartP¢ab; nig
Ggát;Biess²dUcteTA³ composite beam, composite column nig plate girder.

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mhaviTüal½ysMNg;sIuvil NPIC

1>2> bnÞúk Loads

kmøaMg (force) EdlmanGMeBIelIeRKOgbgÁúMRtUv)aneKehAfabnÞúk (load). bnÞúkRtUv)anEckecj

CaBIrRbePTFM²KW³ bnÞúkefr (dead load) nigbnÞúkGefr (live load). bnÞúkefrCabnÞúkEdlsßitenACa
GciéRnþy_EdlrYmmanTm¶n;rbs;eRKOgbgÁúMxøÜnÉg EdleK[eQμaHfabnÞúkpÞal;xøÜn (self-weight). bEnßmBI
elIbnÞúkpÞal;xøÜn (self-weight) bnÞúkefr (dead load) enAkñúgGKarrYmmanTm¶n;rbs; nonstruc-tural
component EdlmandUcCa floor covering, partition nig suspended ceilings ¬CamYynwgRbB½n§

GKÁisnI smÖar³emkanic nigRbB½n§Twk¦. RKb;bnÞúkEdl)anerobrab;CabnÞúkEdlTak;TgeTAnwgTMnajEpn

dIehIyRtUv)aneKehAfa gravity loads. bnÞúkGefrEdlGacCa gravity load CabnÞúkEdlminenAsßit
esßrdUcbnÞúkefreT. vaGac b¤minGacmanGMeBIelIeRKOgbgÁúMRKb;eBl ehIyTItaMgrbs;vak¾minCab;lab;
Edr. bnÞúkGefrrYmman eRKOgsgðarwm smÖar³ Tm¶n;rbs;mnusSEdlrs;enAelIGKar. CaTUeTAeKminGac
kMNt;TMhMrbs;bnÞúkGefr (live load) )anCak;lak;dUcbnÞúkefr (dead load) eT dUcenHTMhMrbs;vaCa
TMhM)a:n;sμan. kñúgkrNICaeRcIn eKRtUveFVIkarGegáteTAelIGgát;eRKOgbgÁúMsRmab;TItaMgepSg²rbs;bnÞúk
Gefr (live load) EdlkareFVIEbbenHeKnwgminemIlrMlgBIlkçxNÐ)ak;d¾eRKaHfñak;eLIy.
RbsinebIeKGnuvtþbnÞúkGefreTAelIeRKOgbgÁúMyWt² edaymindkecj b¤dak;eLIgvijsarcuHsar
eLIg enaHeKviPaKeRKOgbgÁúMCalkçN³sþaTic. RbsinebIeKGnuvtþbnÞúky:agelOn dUckñúgkrNIeRKOgbgÁúM
RT]bkrN_sÞÚccl½t eKRtUvKitbBa©Úl\T§iBlTgÁic. RbsinebIbnÞúkRtUv)andak; nigdkcuHeLIg²eRcIndg
kñúgmYyCIvitrbs;eRKOgbgÁúM fatigue stress nwgkøayCabBaðaEdleKRtUvykmksikSa. bnÞúkTgÁicekItman
cMeBaHGKarkñúgkMrittictYc dUcCaGKar]sSahkmμ cMENkÉ fatigue load KWkMrnwgekItmanNas; eRBaHmun
nwg fatigue køayCabBaða luHRtaEtvdþénkardak;bnÞúkmanrab;Ban;dg. edaymUlehtuenH RKb;lkçxNÐ
bnÞúkTaMgGs;EdlmanenAkñúgesovePAenHRtUv)aneKKitCabnÞúksþaTic ehIyeKminBicarNaBI fatigue eT.
edaysarFmμCatiminzitefrrbs;xül;bk;xÞb; nigbWtenAelIépÞxageRkArbs;GKar eKcat;Tukxül;
kñúgCMBUkbnÞúkGefrEdr. b:uEnþedaysarkarKNnabnÞúkxül;manlkçN³sμúKsμaj eKcat;TukvakñúgCMBUk
dac;edayELk. edaysarbnÞúkxag (lateral load) man\T§iBly:agxøaMgcMeBaHGKarx<s;² dUcenH xül;
manlkçN³minsMxan;cMeBaHGKarTab²eT b:uEnþ uplift énRbB½n§dMbUlRsalGacmaneRKaHfñak;. eTaHbICa
xül;manvtþmanRKb;eBlk¾eday k¾eKminBicarNavaCajwkjykñúgkarsikSaKNnaEdr ehIyeKk¾mincat;
TukvaCa fatigue load eT.

T.Chhay 4 Introduction
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bnÞúkrBa¢ÜydICaCMBUkBiessmYyeTotEdleKcaM)ac;BicarNaBIvasRmab;EtTItaMgPUmisaRsþNaEdl
GacekItmanrBa¢ÜydIb:ueNÑaH. karsikSaviPaKeRKOgbgÁúMEdlrg\T§iBlrBa¢ÜydITamTarkarsikSaviPaK
structure’s response eTAnwgclnarbs;dIEdlbegáIteLIgedayrBa¢ÜydI. eBlxøHeKeRbIviFIgayRsYl

Edl\T§iBlrBa¢ÜydIRtUv)an simulate edayeRbIRbB½n§kmøaMgedk EdlmanlkçN³dUcCasm<aFxül;eday

dak;va[manGMeBItamCan;nImYy²rbs;GKar.
RBwlCaRbePTbnÞúkGefrmYyEbbeTotEdlRtUvKitkñúgCMBUkdac;edayELk. RBwlGacKrCaBMnUk.
bnÞúkGefrepSgeTotk¾RtUv)ancat;TukkñúgCMBUkdac;edayELkEdr dUcCasm<aF hydrostatic nig
sm<aFdI.

1>3> Building Codes

GKarRtUv)ansikSaKNna (design) nigsagsg;edayGaRs½yelIGVIEdl)anEcgenAkñúg building

code EdlCaÉksarc,ab;EdlmantRmUvkarTak;TgeTAnwgsuvtßiPaBrbs;eRKOgbgÁúM suvtßiPaBelIGKÁIP½y

karerobcMRbB½n§Twk karerobcMRbB½n§xül; nigkarsMrYlkareRbIR)as;dl;CnBikar. Building code min)an

pþl;nUvlMnaMsikSaKNna (design) eT b:uEnþvakMNt;nUvtRmUvkarkñúgkarsikSaKNna (design). lkçN³
sMxan;sRmab;visVkreRKOgbgÁúMKWbBaØtþBIbnÞúkGefrGb,brmaEdlmanGMeBIelIGKar.
bc©úb,nñ eKman building code mYyEdlGacsMrYldl;kargarrbs;visVkrEdlsikSaKNnaeRKOg
bgÁúMTaMgenAshrdæGaemric k¾dUcbNþaRbeTsepSg²KW International Building Code (IBC).

1>4> Design Specifications

pÞúyBI building code, design specification pþl;nUvkarENnaMlMGitsRmab;karsikSaKNna

Ggát;eRKOgbgÁúM nigkartP¢ab;rbs;va. Design Specification tMNag[karGnuvtþvisVkmμd¾l¥EdlQr
elIkarsikSaRsavRCavcugeRkaybMput. vaRtUv)anEksMrYl nigeFVI[kan;EtRbesIreLIgtamxYb. dUcKña nwg
building code Edr design specification RtUv)aneKsresreLIgkñúgTRmg;c,ab;edayGgÁkarEdlmin

rkplcMeNj.
Specification EdlvisVkreRKOgbgÁúMcab;GarmμN_eRcInKW specification Edle)aHBum<pSayeday

GgÁkardUcxageRkam³

esckþIepþIm 5 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

!> American Institute of Steel Construction (AISC): Specification enHpþl;[sRmab;

sikSaKNnaeRKOgbgÁúMGMBIEdk nigkartP¢ab;rbs;va. vaCa Specification cMbgEdlykcitþ
Tukdak;edayesovePAenH (AISC, 1993).
@> American Association of State Highway and Transportation Officials (AASHTO):
Specification enHRKbdNþb;elIkarsikSaKNnas<an highway nigeRKOgbgÁúMTak;TgepSg²

eTot. vapþl;RKb;smÖar³TaMgGs;EdleRbICaTUeTAsRmab;s<anEdlmandUcCa Edk ebtugBRgwg

edayEdk nigeQI (AASHTO, 1992, 1994).
#> American Railway Engineering Association (AREA): ÉksarenHRKbdNþb;elIkar
sikSaKNnas<ansRmab;rfePøIg nigeRKOgbgÁúMEdlTak;TgepSgeTot (AREA, 1992).
$> American Iron and Steel Institute (AISI): specification enHedaHRsayCamYynwg cold-
formed steel Edlmanerobrab;enAkñúgkfaxNÐ 1>6 kñúgesovePAenH (AISI, 1996).

1>5> eRKOgbgÁúMGMBIEdk Structural Steel

eKeRbIR)as;EdkdMbUgbg¥s;sRmab;smÖar³tUc²taMgBIRbEhl 4000qñaMmunRKisþskraC
(Murphy, 1957). smÖar³enHmanTRmg;Ca wrought iron EdlplitedaykardutEr:EdkenAkñúgePøIg.

enAkñúgGMLúg cugstvtSr_TI 18 nigedImstvtSr_TI 19 cast iron nig wrought iron RtUv)aneRbIsRmab;

sMNg;s<an. EdksMNg; (steel) CasMelah³én iron nigkarbUn. Edkmansar³FatuminsuT§ nigkabUn
ticCag cast iron EdlRtUv)aneKeRbIsRmab;sMNg;Fn;F¶n;dMbUgkñúgstvtSr_TI 19. CamYynwgkarmk
dl;énkarEkERbrbs; Bessemer enAkñúgqñaM 1855 Edkcab;epþImCMnYs wrought iron nig cast iron kñúg
sMNg;.
lkçN³rbs;EdkEdlvisVkreRKOgbgÁúMcab;GarmμN_xøaMgCageKKWdüaRkaménlT§plEdkTaj. Rb
sinebIsMNakKMrUBiesaFn_rgkmøaMgtamG½kS P dUcbgðajenAkñúgrUbTI 1>3 a enaHkugRtaMg (stress) nig
bERmbRmYlrageFob (strain) GacRtUv)ankMNt;tamrUbmnþdUcxageRkam³
ΔL
f =
P
A
ni g ε=
L
Edl f = kugRtaMgkmøaMgTajtamG½kS
A = RkLaépÞmuxkat;

ε = strain tamG½kS
T.Chhay 6 Introduction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

L= RbEvgrbs;sMNakKMrU
ΔL = kMhUcRTg;RTay

RbsinebIeKbegáInbnÞúkBIsUnüeTAdl;cMNucdac; (fracture) ¬kugRtaMg nig strain RtUv)aneKKNna

tamCMhannImYy²¦ ExSekagTMnak;TMngrvagkugRtaMg nigbERmbRmYlrageFob (stress-strain curve)
RtUv)anbgðajenAkñúgrUbTI 1>3 b. ExSekagenHsRmab;RbePTEdksVit (ductile, mild or steel) .
TMnak;TMngrvagkugRtaMg nig strain manlkçN³CabnÞat;BIcMNucsUnürhUtdl;EdnkMNt;smamaRt
(proportional limit) EdlkñúgcenøaHenHsmÖar³eKarBtamc,ab;h‘Uk (Hook’s law). bnÞab;mkvaeTA

dl;cMNuc yield xagelIy:agelOnrYcFøak;mkcMNuc yield xageRkam. bnÞab;BI enaHkugRtaMgenArkSa

témøefr eTaHbICa strain enAEtbnþekIneLIgk¾eday. enARtg;tMNak;kalénkardak;bnÞúkenH sMNak
KMrUBiesaFn_enAEtbnþlUtEvg eTaHbICaeKminbegáInbnÞúkk¾eday ¬EtbnÞúkk¾minRtUv)andkEdr¦. tMbn;kug
RtaMgefrenHRtUv)aneKehAfatMbn;)aøsÞic (plastic range or yield plateau). enARtg; strain Edlman
témøRbEhl 12dgén strain enAtMbn; yield, strain hardening cab;epþImekItman ehIyeKRtUvkar
esckþIepþIm 7 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

bnÞúkbEnßm ¬b¤kugRtaMgbEnßm¦ edIm,IeFVI[mansac;lUtbEnßm ¬b¤ strain¦. eRkayeBl vaeTAdl;cMNuc

kugRtaMgGtibrma sMNakKMrUcab;epþIm neck down EdleFVI[kugRtaMgcab;epþImfycuH Et strain enAEtbnþ
ekIneLIgdEdl ehIyekItman fracture.
eTaHbICamuxkat;RtUv)ankat;bnßykñúgGMLúgeBldak;bnÞúkk¾eday (Poisson effect) k¾eKenAEt
eRbIRkLaépÞmuxkat;edImedIm,IKNnakugRtaMgTaMgGs;. kugRtaMgEdl)anBIkarKNnatamviFIenH RtUv)an
eKsÁal;faCa engineering stress. RbsinebIeKeRbIRbEvgedImedIm,IKNna strain enaHvaRtUv)aneKehA
fa engineering strain.
EdkEdlRtUv)aneKBiesaFedIm,ITTYl)andüaRkamdUcbgðajkñúgrUbTI 1>3 b Ca ductile eRBaHva
man lT§PaBrgkMhUcRTg;RTayFMmunnwgeFVIkardl; fracture. eKGacvas;PaBsVit (ductility) edayeRbI
sac;lUt (elongation) EdlkMNt;edayrUbmnþ
L f − Lo
e= ×100 (1.1)
Lo
Edl e= sac;lUt ¬KitCaPaKry¦
L f = RbEvgrbs;sMNakKMrUenAeBldac;

Lo = RbEvgedIm

EdneGLasÞic (elastic limit) rbs;smÖar³CakugRtaMgEdlsßitenAcenøaHEdnsmamaRt nigcMNuc

yeild xagelI. smÖar³EdlrgkugRtaMgkñúgtMbn;enH sMNakKMrUnwgminmankMhUcRTg;RTayeRkayeBl

eKdkbnÞúkeT. KnøgénkardkbnÞúknwgsßitenAtamKnøgénkardak;bnÞúk ehIyvaminman permanent

strain eT. tMbn;rbs; stress-strain diagram enH RtUv)aneK[eQμaHfa EdneGLasÞic (elastic rage).

eRkABI elastic limit KnøgénkardkbnÞúknwgsßitenAelIExSRtg;EdlRsbeTAnwgKnøgénkardak; bnÞúk

ehIyvanwgman permanent strain. ]TahrN_ RbsinebIeKdkbnÞúkRtg;cMNuc A kñúgrUbTI 1>3 b
KnøgénkardkbnÞúknwgsßitenAelIExS AB Edlpþl;nUv permanent strain OB .
rUbTI 1>4 bgðajBIkMENd¾l¥rbs; stress-strain curve. Proportional limit, elastic limit,
upper nig lower yield point KWsßitenAelIcMNucEtmYyEdleKehAfa yield point EdlkMNt;edaykug

RtaMg Fy . cMNucmYyeTotEdlvisVkreRKOgbgÁúMRtUvcab;GarmμN_KWkugRtaMgGtibrma EdleK[eQμaHfa

ultimate tensile strength Fu . rUbragrbs;ExSekagenHCaKMrUsRmab; mild structural steel TaMgGs;

EdlvaxusKñaBImYyeTAmYyedaytémø Fy nig Fu . pleFobkugRtaMgelI strain kñúgEdneGLasÞic

T.Chhay 8 Introduction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RtUv)ankMNt;eday E EdleKehAfa young’s modulus or modulus of elasticity. E mantMé;lesμI

29,000ksi ≈ 2 ⋅ 10 MPa sRmab;RKb;eRKOgbgÁúMEdkTaMgGs;.
5

rUbTI 1>5 bgðajBIRbePT stress-strain curve sRmab; high-strength steels EdlmanPaBsVit

tUcCag mild steels. eTaHbIvamanEpñk linear elastic nig tensile strength k¾eday Etvaminman yield
point b¤ plastic plateau eT. edIm,IeRbI higher strength steel enH[dUcnwgkareRbIR)as; ductile steel

eKRtUvkartémøkugRtaMg Fy dUcenHeKGaceRbIdMeNIrkar nigrUbmnþdUcKñasRmab;RKb;RbePTEdkTaMg Gs;.

dUcEdl)anbgðajBImun sRmab;EdkEdlrgkugRtaMgeRkABItMbn; elastic limit enAeBleKdkbnÞúk
vanwgsßitenAelIKnøgExSEdlRsbnwgKnøgdak;bnÞúk EtvamineTAdl;cMNuc strain esμIsUnüeT. dUcenHva
man residual strain b¤ permanent strain eRkayeBldkbnÞúk. Yield stress sRmab;EdkCamYy
nwgRbePT stress-strain curve EdlbgðajenAkñúgrUbTI 1>5 RtUv)aneKehAfa yield strength Edl
RtUv)ankMNt;Ca kugRtaMgRtg;cMNucénkardkbnÞúkEdlRtUvnwg permanent strain énbrimaNkMNt;Na
mYy. eKeRCIserIs yk strain esμInwg 0.002 ehIyviFIénkarkMNt; yield strength enHRtUv)aneKehAfa
0.2% offset method. dUcEdl)anerobrab;BImun CaTUeTAeKRtUvkarlkçN³BIrsRmab; structural

strength design KW Fy nig Fu edayminKitBIrUbragrbs; stress-strain curve nigminKitBIrebob

EdlTTYl)an Fy eT. sRmab;mUlehtuenH eKeRbItYTUeTA yield stress ehIyvaGacmann½yCa yield

point b¤ yield strength.

lkçN³epSg²rbs;eRKOgbgÁúMEdkEdlrYmbBa¢ÚlTaMg strength nig ductility RtUv)ankMNt;eday

smasFatuKImI (chemical composition). Edk (steel) CasMelah³EdlFatupSMcMbgrbs;vaCa iron.
esckþIepþIm 9 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

sarFatupSMrbs;eRKOgbgÁúMEdkTaMgGs; ¬eTaHCakñgú brimaNtictYck¾eday¦ KWkabUnEdlCasarFatucUlrYm

kñúgkarbegáIn strength b:uEnþvakat;bnßy ductility. karekIneLIgénPaKrykabUnKWbegáIn strength
Etkat;bnßy ductility EdleFVI[karpSarmankarBi)ak. sarFaturYmpSMdéTeTotrbs;EdksMNg;rYm
mans<an; (copper), manganese, nickel, chromium, molybdenum nig silicon. eRKOgbgÁúMEdk
RtUv)anerobcMCaRkumEdlGaRs½yeTAnwgsarFatupSMrbs;vadUcxageRkam³
!> Plain carbon steel: EdlPaKeRcInCa iron nigkabUnticCag 1%
@> Low-alloy steel: man iron nigkabUn EdlrYmpSMCamYynwgsarFatuepSgeTot ¬CaTUeTAtic
Cag 5% ¦. sarFatubEnßmKWedIm,IbegáInersIusþg; Etvanwgkat;bnßyPaBsVit.
#> High-alloy or specialty steel: mansarFatupSMRsedogKñanwg low-alloy steel Edr Etman
sarFatubEnßmeRcInPaKryCag. EdkenHmanersIusþg;FMCag plain carbon steel nigman
KuNPaBBiessdUcCakarkarBarERcH.

Graderbs;EdksMNg; (structural steel) RtUv)ankMNt;eday American Society for Testing

and Material (ASTM). GgÁkarenHbegáItbTdæanedIm,IkMNt;smÖar³eTAtamsarFatupSM lkçN³ nigkar

eFVIkarrbs;va (ASTM, 1996a). EdkeRKOgbgÁúMEdleKcUlcitþeRbIsBVéf¶Ca mild steel EdlsMKal;Ca

ASTM A36 b¤sresry:agxøI A36 . vaman stress-strain curve dUcbgðajenAkñúgrUbTI 1>3 b nig 1>4

ehIymanlkçN³rgkarTajdUcxageRkam³
Yield stress: Fy = 36 Ksi ≈ 250 MPa

Tensile strength: Fu = 58ksi ≈ 400 MPa eTA 80ksi ≈ 550MPa

T.Chhay 10 Introduction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Edk A36 RtUv)ancat;fñak;Ca plain carbon steel ehIyvamansarFatupSM ¬eRkABI iron¦ dUcxageRkam³
Carbon: 0.26% ¬Gtibrma¦

Phosphorous: 0.04% ¬Gtibrma¦

Sulfur: 0.05% ¬Gtibrma¦

PaKryenHCatémøRbhak;RbEhl témøCak;EsþgGaRs½ynwgTRmg;énkarplitEdk. Edk A36 Ca

ductile steel Edlmansac;lUt (elongation) EdlkMNt;edaysmIkar 1.1 KW 20% edayQrelIRbEvg

edIm Lo = 8in. ≈ 200mm .

eKRtUvplitEdk A36 edayeKarBtambTdæanrbs; ASTM. témø yield strength nig tensile
strength Edl)anbgðajCatRmUvkarGb,brma EtvaGacFMCagtémøenH. Tensile strength RtUv)aneK

[enAkñúgcenøaHtémømYy eRBaHlkçN³enHminGacTTYl)anedaysuRkitdUc yield strength eT.

CaTUeTA EdkEdlman yield stress FMCag 36ksi ≈ 250MPa RtUv)anKitCa high-strength
steel. High-strength steel EdleKniymeRbI eRcInCaRbePTEdkEdlman yield strength

50ksi ≈ 345MPa nigman tensile strength 65ksi ≈ 450MPa b¤ 70ksi ≈ 480 MPa ehIyeKk¾man

EdkEdlman yield strength 100ksi ≈ 690MPa . Ca]TahrN_ ASTM A242 Ca low-alloy,

corrosion resistant steel Edlman yield strength 42ksi ≈ 290MPa / 46ksi ≈ 320MPa nig

50ksi ≈ 345MPa CamYynwg tensile strength EdlRtUvKñanwg 63ksi ≈ 435MPa / 67 ksi ≈ 460 MPa

nig 70ksi ≈ 480MPa . cMENksmasFaturYmpSMKImIrbs;vamandUcxageRkam³

Carbon: 0.15% ¬Gtibrma¦

Manganese 1.00% ¬Gtibrma¦

Phosphorus: 0.15% ¬Gtibrma¦

Sulfur: 0.05% ¬Gtibrma¦

Copper: 0.20% ¬Gtibrma¦

Edk A242 minEmn ductile dUc A36 . sac;lUtEdlQrelIRbEvgedIm 8in. ≈ 200mm esμInwg 18%
ebIeRbobeFobCamYysac;lUtrbs; A36 EdlmantémøesμInwg 20% .

1>6> rUbragmuxkat;bTdæan (Standard Cross-sectional Shapes)

eKalbMNgcMbgkñúgkarsikSaKNnaeRKOgbgÁúMEdkKWkareRCIserIsmuxkat;EdlsmRsbsRmab;
esckþIepþIm 11 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Ggát;nImYy². CaTUeTA kareRCIserIsenHtRmUv[eRCIserIsrUbragmuxkat;tambTdæanEdleRbIR)as;y:ag

TUlMTUlayCagkartRmUv[plitrUbragEdlmanxñat niglkçN³Biess. kareRCIserIsrUbragEdkEdl
manRsab; (off-the shelf) CaCMerIsEdlmanlkçN³esdæikc©Cag eTaHbICavaeRbIsmÖar³eRcInCagbnþicbnþÜc
k¾edaykþI. RbePTénrUbragbTdæanEdlFMCageKRtUv)anplitedaykarhUtekþA (hot-rolling). enAkñúg
dMeNIrplitkmμEdleFVIeLIgenAkñúgeragcRkplitEdk (mill) EdkEdlrlayEdl)anBILsøEdkRtUv)an
cak;cUleTAkñúgRbB½n§Bum<EdlCab; edayTuk[EdkeLIgrwg b:uEnþeKminGnuBaØat[vaRtCak;eBj eljeT.
EdkekþAqøgkat; roller Caes‘rI EdlKab[eTACarUbragEdlcg;)an. karhUtEdkkñúgeBlEdlvaenAekþA
GnuBaØat[vaxUcrUbragedaymin)at;bg; ductility rbs;va dUckrNIhUtRtCak;eT. kñúgGMLúgeBlhUt
Ggát;EdllUtRbEvgehIyRtUv)ankat;tamRbEvgbTdæan EdlCaTUeTAmanRbEvgGtibrma BI 65 ft ≈ 20m
eTA 75 ft ≈ 23m ehIyEdlvaRtUv)ankat;CabnþbnÞab;eTAtamRbEvgrbs;eRKOgbgÁúMenA eragCageTAtam
karkMNt;rbs;bøg;.

T.Chhay 12 Introduction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

muxkat;xøHrbs; hot-rolled shape EdlRtUv)aneRbICaTUeTARtUv)anbgðajenAkñúgrUbTI 1>6. xñat

nigkMNt;sMKal;rbs;rUbragbTdæanRtUv)ankMNt;enAkñúg ASTM standard (ASTM, 1996). W-shape
EdleKGacehA)anfa rUbragsøabTUlay (wide flange shape) EdlpSMeLIgedaysøabBIrEdlEjk
edayRTnugmYy. rUbragenHmanG½kSsIuemRTIBIr. kMNt;sMKal;KMrUrbs;vaKW W 18 × 50 Edl W bgðajBI
RbePTrUbrag/ elx 18 Ca nominal depth EdlRsbeTAnwgRTnug nig 50 CaTm¶n;rbs;EdkkñúgmYy
ÉktþaRbEvg. W-shape én nominal size TaMgGs;RtUv)andak;CaRkumEdlmankm<s;BIsøabxagkñúgeTA
søabxagkñúgdUcKña b:uEnþmankMras;søabxusKña.
American Standard b¤ S-shape KWRsedogKñaeTAnwg W-shape Edr edaymansøabBIrRsbKña

RTnugmYy nigmanG½kSsIuemRTIBIr. PaBxusKñarbs;vaKWsmamaRtrbs;muxkat;³ søabrbs; W FMCagRTnug

cMENkÉsøabrbs; S tUcCagRTnug. elIsBIenH épÞxagkñúg nigépÞxageRkArbs;søabén W-shape man
lkçN³RsbKña EtépÞxagkñúgénsøabrbs; S-shape eTrEdleFVI[kMras;xagcugtUcCagkMras;enAEk,r
RTnug. kMNt;sMKalrbs; S-shape KW S18 × 70 Edl S bgðajBIRbePTrbs;rUbrag nigelxTaMg
BIrtYCakm<s; nigTm¶n;kñúgmYyÉktþaRbEvg erogKña. rUbragenHRtUv)aneKehAfa I-beam.
EdkEkg (angle shape) GacmaneCIgesμI b¤eCIgminesμI. kMNt;sMKal;KMrUKW L6 × 6 × b¤ 3
4

L6 × 3 × 5 8 . elxTaMgbItYKW RbEvgeCIgTaMgBIrrbs;vaEdlvas;BIcugeTAEkgxageRkA nigkMras;rbs;va.

kñúgkrNIEdkEkgEdlmaneCIgminesμI eCIgEvgRtUv)ansresrmun. kMNt;sMKal;rbs;EdkEkgmin)an

R)ab;BITm¶n;eT.
American Standard Channel b¤ C-shape mansøabBIr nigRTnugmYy EtmanG½kSsIuemRTIEt

mYy. kMNt;sMKal;KMrUrbs;vaKW C 9 × 20 . nimitþsBaØaenHKWRsedogKñanwg W- nig S-shape Edr Edl

manelxmYytYtMNag[km<s; nigmYytYeTottMNag[Tm¶n;kñúgmYyÉktþaRbEvg. b:uEnþsRmab; channel
km<s;manRbEvgCak;EsþgCag. épÞxagkñúgrbs;søabKWdUcKñanwg S-shape Edr. eKenAman
Miscellaneous Channel EdlCa]TahrN_ MC10 × 25 KWRsedogKñanwg American Standard

Channel Edr.

Structural Tee RtUv)anpliteLIgedaykat; W-, M- b¤ S-shape Rtg;km<s;Bak;kNþal.

eBlxøHeKehArUbragenHfa split-tee. buBVbTénnimitþsBaØarbs;rUbragenHKW WT, MT b¤ ST GaRs½y

eTAelIrUbragedImrbs;vamuneBlkat;. ]TahrN_ WT18 × 115 man nominal depth 18in. nigmanTm¶n;
115lb / ft ehIyvaRtUv)ankat;ecjBI WT 36 × 230 . dUcKñasRmab; ST- nig MT-shape.

esckþIepþIm 13 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

edaymin)anbgðajkúñgrUbTI 1>6 eKenAman hot-rolled shapes EdlmanlkçN³RsedogeTAnwg

W-shape EdrKW³ HP- nig M-shapes. eKeRbI HP shape sRmab;ssrRKwH EdlvamanépÞsøabRsbKña

nigmanTTwgesμInwgkm<s; ehIykMras;søabdUcKñanwgkMras;RTnug. GkSr M tMNag[ Miscellaneous

¬epSg²¦ EdlrUbragenHminRtUvKñanwgRbePTrUbragén W, HP b¤ S eT. TaMg M- nig HP-shape
RtUv)ansMKal;kñúgTRmg;dUcKñanwg W-shape Edr ]TahrN_ M 14 × 18 nig HP14 × 117 .
rUbragEdlRtUv)aneKeRbICajwkjab;Edr RtUv)anbgðajenAkñúgrUbTI 1>7. Edkr)ar (bar) Gac
manmuxkat; mUl kaer nigctuekaNEkg. RbsinebITTwgrbs;muxkat;ctuekaNEkgmanRbEvgtUcCag
8in. ≈ 20cm eKcat;TukrUbragenHCaEdkr)ar (bar) ehIyvaRtUv)ansMKal;edayTTwgmunkMras; ( 8× 3 4 )

EtpÞúymkvijvaRtUv)ancat;TukCaEdkbnÞH (plate) ehIykMNt;sMKal;rbs;vaRtUv)annaMmuxedaykMras;

munTTwg ( 12 × 10 ). Edkr)ar (bar) nigEdkbnÞH (plate) RtUv)anpliteday hot-rolling.

rUbTI 1>7 k¾bgðajBImuxkat;RbehagEdr EdlGacplitBIEdkbnÞH (plate) EdlRtUv)anBt;eTACa

rUbragEdlcg;)anehIypSartamefñr b¤eday hot-working edIm,IplitrUbragEdlKμanefñr. rUbragenH
RtUv)ankt;sMKal;eday HSS sRmab;muxkat;EdkRbehag. muxkat;RbehagrYmman TIbmUl nigTIbRCug
EdlmanrUbragkaer nigctuekaN.
eKenAmanrUbragepSg²eTot b:uEnþeyIgelIkykEtrUbragEdleKniymeRbICaTUeTAmkbgðaj
b:ueNÑaH. kñúgkrNICaeRcIn rUbragbTdæanmYynwgbMeBjtRmUvkarsRmab;karsikSaKNna. Rbsinvamin
manrUbragbTdæanEdlRtUvnwgkarsikSaKNnaeT eKcaM)ac;eFVI built-up section dUcbgðajenAkñúgrUbTI
1>8. eBlxøH standard shape RtUv)anbEnßmeday cross-sectional element dUckrNIEdleKpSar
cover plate P¢ab;eTAnwgsøabmYy b¤søabTaMgBIrrbs; W-shape. kareFVI built-up section CaviFId¾man

T.Chhay 14 Introduction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RbsiT§PaBkñúgkarbegáInlT§PaBRTRTg;rbs; standard shape. eBlxøHeKRtUveRbI built-up shape

edaysarKμan standard rolled shape NaEdlmuxkat;rbs;vamanRkLaépÞ b¤m:Um:g;niclPaBFMlμm. enA
kñúgkrNIEbbenH eKeRbI plate girder EdlGacmanrUbragCa I-shaped section EdlmansøabBIr nig
RTnugmYy b¤muxkat;RbGb; EdlmansøabBIr nigRTnugBIr. eKGacpSarFatupSMbBa©ÚlKñaedayrcnaedIm,I
TTYl)annUvlkçN³Edlcg;)an. eKGacbegáIt built-up shape edayP¢ab; standard rolled shape BIr
b¤eRcInbBa©ÚlKña. bnSMénrUbragEdleRbICaTUeTAKWEdkEkgDubEdlRtUv)andak;xñgTl;xñg ehIyRtUv)an
P¢ab;tamcenøaHénRbEvgrbs;va.

RbePTepSgeTotrbs;EdksRmab;eRKOgbgÁúMKW cold-formed steel. Structural steel RbePTenH

RtUv)anbegáIteLIgedaykarBt;snøwkbnÞHEdkesþIgedaymineRbIkMedA. muxkat;KMrURtUv)anbgðajenAkñúgrUb
TI 1>9. Cold-formed shape RtUv)aneRbIsRmab;RTTm¶n;Rsalb:ueNÑaH. Cold-working nwgbegáIn
yield point b:uEnþvanwgkat;bnßyPaBsVitrbs;Edk nigeRkamlkçxNÐCak;EsþgeKGaceRbIvakñúgkarsikSa

KNna (AISI, 1993). KuNsm,tþirbs;vaKWrUbragrbs;vagayRsYlkñúgkarbegáIt. edaysarmuxkat;

rbs;vaesþIg instability CaktþacMbgkñúgkarsikSaKNna cold-formed structure.

esckþIepþIm 15 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

II. eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁÁúMEdk
Concepts in Structural Steel Design

2>1> TsSnviC¢akñúgkarsikSaKNnamuxkat; Design Philosophies

karsikSaKNnaGgát;eRKOgbgÁúMtMrUvnUvkareRCIserIsmuxkat;EdlmansuvtßiPaB nigmanlkçN³
esdækic© edIm,ITb;Tl;nwgkmøaMgEdlGnuvtþBIxageRkA. CaTUeTA lkçN³esdækic©mann½yfabrimaNEdk
Gb,brma. brimaNenHRtUvnwgmuxkat;EdlmanTm¶n;kñúgmYyÉktþaRbEvgRsalCageK ehIyRtUvnwgmux
kat;EdlmanRkLaépÞtUcCageKpgEdr. edIm,ITTYl)annUveKalbMNgenH visVkreRKOgbgÁúMk¾RtUvsMerc
eFVIy:agNaeGayvamanlkçN³suvtßiPaBpgEdr. eKmanviFIkñúgkarKNnabIsMxan;xus²KñaKW³
!> sRmab; allowable stress design eKRtUveRCIserIsGgát;EdlmanlkçN³muxkat;dUcCa RkLa
épÞ nigm:Um:g;niclPaBFMRKb;RKan;edIm,IkarBarkugRtaMgGtibrmakMueGayFMCagkugRtaMg
GnuBaØat. kugRtaMgGnuBaØatKWsßitenAkñúgtMbn;eGLasÞicrbs;smÖar³ ehIyvamantémøtUcCag
yield stress Fy ¬emIlrUbTI 1>4¦. témørbs;kugRtaMgGnuBaØatGacesμInwg 0.6 Fy . eKTTYl

)ankugRtaMg GnuBaØatedayEck yield stress Fy b¤ ultimate tensile stress F CamYynwg

u

emKuNsuvtßiPaB. eKGacehAviFIkñúgkarKNnaenHfa elastic design b¤ working stress

design. Working stress CakugRtaMgEdl)anBIbnÞúkeFVIkar (working load or service

load). Ggát;Edl)anKNnarYcehIy GacrgkugRtaMgmineGayFMCagkugRtaMgGnuBaØatenAeBl

rgbnÞúkeFVIkar.
@> Plastic design KWQrelIkarsnμt;lkçxNÐ)ak; (failure) CaglkçxNÐbnÞúkeFVIkar. Ggát;
RtUv)aneRCIserIsedayeRbIlkçxNÐvinicä½yeGayeRKOgbgÁúM)ak;eRkambnÞúkEdlFMCagbnÞúkeFVI
kar. kar)ak; (failure) k¾mann½yfavamanPaBdabFMelIslub. eKeRbIBakü plastic enATI
enHeRBaH enAeBl)ak; Epñkrbs;Ggát;nwgrg strain FM EdlvamantémøFMRKb;RKan;edIm,I eGay
Ggát;sßitenAkñúgtMbn;)aøsÞic ¬emIlrUbTI 1>3 b¦. enAeBlEdlmuxkat;TaMgmUlrbs;Ggát;
køayeTACa)aøsÞicenATItaMgRKb;RKan; plastic hinge nwgekIteLIgenATItaMgenaH Edl
begáIt)anCa collapse mechanism. edaysarbnÞúkCak;EsþgtUcCag failure load
edaymanemKuNsuvtßiPaBEdleKsÁal;faCa emKuNbnÞúk (load factor). Ggát;EdlKNna

T.Chhay 16 Concepts in Structural Steel Design

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

tamviFIenH nwgmansuvtßiPaB eTaHbICakarKNnaQrelIGVIEdlekItmanenAeBl)ak;k¾eday.

dMeNIrkarénkarsikSaKNnaenHRtUv)ansegçbdUcteTA³
KuN working load b¤ service load CamYynwgemKuNbnÞúkedIm,ITTYl)an
z

failure load.

kMNt;lkçN³muxkat;EdlcaM)ac;edIm,ITb;Tl; failure eRkamGMeBIénbnÞúkem

z

KuN. Ggát;EdlmanlkçN³EbbenHKWmanersIusþg;RKb;RKan; ehIyvanwgCit²

nwg)ak; enAeBlEdlGgát;rgbnÞúkemKuNEbbenH.
eRCIserIsrUbragmuxkat;EdlRsalCageKEdlmanlkçN³EbbenH.
z

Ggát;EdlKNnaedayRTwsþI)aøsÞicnwgeTAdl;cMNuc)ak;eRkamGMeBIbnÞúkemKuN Etvamansuvtßi-
PaBeRkamGMeBIbnÞúkeFVIkarCak;Esþg.
#> Load and resistance factor design (LRFD) manlkçN³RsedogKñanwg plastic design
Rtg;eKKitlkçxNÐeBl)ak;. eKGnuvtþemKuNbnÞúkeTAelIbnÞúkeFVIkar ehIyeKRtUveRCIserIs
Ggát;EdlmanersIusþg;RKb;RKan;edIm,IkarBarbnÞúkemKuN. elIsBIenH ersIusþg;Edl)anBIRTwsþI
RtUv)ankat;bnßyedaykarGnuvtþemKuNersIusþg;. lkçN³vinicä½yEdlRtUvbMeBjkñúgkareRCIs
erIsGgát;enHKW³

bnÞúkemKuN (factored load) ≤ ersIusþg;emKuN (factored strength) (2.1)

CaTUeTA enAkñúgsmIkarenH bnÞúkemKuNCaplbUkénbnÞúkeFVIkarTaMgGs;EdlRtUv)anTb;Tl;

edayGgát;eRKOgbgÁúM edayKuNnwgemKuNbnÞúkeTAtamRbePTbnÞúk. Ca]TahrN_ bnÞúkefr
RtUv)anKuNedayemKuNbnÞúkEdlxusBIbnÞúkGefr. ersIusþg;emKuNCaersIusþg;RTwsþIEdl
KuNCamYynwgemKuNersIusþg;. dUcenHeKGacsresrsmIkar 2.1 dUcxageRkam³

∑ ¬bnÞúk × emKuNbnÞúk¦ ≤ ersIusþg; × emKuNersIusþg; (2.2)

bnÞúkemKuNCa failure load EdlmantémøFMCagbnÞúkeFVIkarsrubCak;Esþg dUcenHCaTUeTAem

KuNbnÞúkEtgEtFMCag 1.0. b:uEnþ ersIusþg;emKuNRtUv)ankat;bnßy dUcenHemKuNersIusþg;
eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁúMEdk 17 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

EtgEttUcCag 1.0. bnÞúkemKuNCabnÞúkEdlnaMeGayeRKOgbgÁúM b¤Ggát;eTAdl;cMNucEdn

kMNt;. kñúgn½ysuvtßiPaB sßanPaBkMNt;GacCa fracture, yielding b¤ buckling
ehIyersIusþg;emKuN CaersIusþg;EdlmanRbeyaCn_rbs;Ggát;Edlkat;bnßyBIersIusþg;RTwsþI
edayemKuNersIusþg;. sßanPaBkMNt;k¾GacCasßanPaBkMNt;énkareRbIR)as; dUcCaPaBdab
GnuBaØatGtibrma.

2>2> American Institute of Steel Construction Specification

sRmab;karsikSaKNnamuxkat;Ggát;rbs;eRKOgbgÁúMGMBIEdk nigkartP¢ab;rbs;va specification

of the American Institute of Steel Construction Ca design specification Edlmansar³sMxan;.

vaRtUv)aneKsresr nigeFVIkarEkERbtamsm½ykaleday AISC committee EdlrYmmanvisVkreRKOg

bgÁúM GñksikSaRsavRCavBIsMNg;Edk plitkr nigGñksagsg;sMNg;Edk. Allowable stress design
CaviFIdMbUgEdlRtUv)aneKeRbIsRmab;sMNg;EdleFVIBIeRKOgbgÁúMEdktaMgBIkare)aHBum<pSayrbs; AISC
Specification elIkTImYy kñúgqñaM 1923. enAqñaM 1986 AISC )ane)aHpSay specification dMbUg

sRmab; load and resistance factor design sRmab;sMNg;GMBIEdk rYmCamYynwg Manual of Steel
Construction. eKalbMNgénÉksarTaMgBIrKWpþl;nUvCeRmIssRmab;karKNnatam allowable stress

design eGay)aneRcIndUc karKNnatam plastic design. kare)aHBum<elIkTIBIrrbs; Manual (AISC,

1994) rYmman AISC Specification 1993.

Load and resistance factor design minEmnCaKMnitfμIeT. taMgBIqñaM 1974 vaRtUv)aneKeRbIenA

RbeTskaNada EdlenATIenaHeKehAviFIenHfa limit state design. ehIyvak¾CaeKalkarN_rbs;

European building code pgEdr. enAshrdæGaemric LRFD CaviFIénkarKNnaEdlRtUv)anGnuBaØat

sRmab;ebtugBRgwgedayEdkCaeRcInqñaMmkehIy ehIyvaCaviFIdMbUgEdlGnuBaØatenAkñúg American

Concrete Institute’s Building Code EdlvaRtUv)aneKsÁal;Ca Strength design (ACI, 1995).

Highway bridge design standard pþl;eGayTaMg allowable stress design (AASHTO, 1992) nig

load and resistance-factor design (AASHTO, 1994).

T.Chhay 18 Concepts in Structural Steel Design

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

2>3> emKuNersIusþg; nigemKuNbnÞúkEdleRbIR)as;enAkñúg AISC Specification

Load and Resistance Factors Used in the AISC Specification
smIkar 2.2 GacRtUv)aneKsresreGaykan;EtmanlkçN³suRkitEfmeTotdUcxageRkam³

∑γ Q i i ≤ φRn (2.3)

Edl = bnÞúk ¬kmøaMg b¤m:Um:g;¦

Qi

γ = emKuNbnÞúk
i

R = nominal resistance or strength

n

φ = emKuNersIusþg;
φR RtUv)aneKehAfa ersIusþg;KNna (design strength). GgÁxageqVgénsmIkar 2.3, ∑ γ Q KWCa
n i i

plbUkéncMnYnbnÞúkKNna ¬bnÞúkemKuN¦ TaMgGs;EdlmanGMeBIelIeRKOgbgÁúM. emKuNbnÞúk γ GaRs½y

eTAnwgRbePTbnÞúk nigkarbnSMbnÞúk (load combination). bnÞúkemKuN RtUv)anykeTAeFVIkarsikSa
KNnasRmab;témøEdlFMCageKkñúgcMeNamsmIkarpSMbnÞúkTaMg ^ xageRkam. xageRkamCakarbnSMbnÞúuk
EdleGayeday “General Provision” enAkñúgCMBUk A
1 .4 D ¬A$-!¦
1.2 D + 1.6 L + 0.5( L orSorR )
r ¬A$-@¦
1.2 D + 1.6( L orSorR) + (0.5 Lor 0.8W )
r ¬A$-#¦
1.2 D + 1.3W + 0.5 L + 0.5( L orSorR )
r ¬A$-$¦
1 .2 D ± 1 .0 E + 0 .5 L + 0 .2 S ¬A$-%¦
0.9 D ± (1.3Wor1E ) ¬A$-^¦
Edl D = bnÞúkefr (Dead load)
L = bnÞúkGefr (Live load)

L = bnÞúkdMbUlGefr (Roof live load)

r

S = bnÞúkRBwl (Snow load)

R = bnÞúkePøóg b¤Twkkk (Rain or ice load)

W = bnÞúkxül; (Wind load)

E = bnÞúkrBa¢ÜydI (Earthquake load)

eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁúMEdk 19 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

eyIgeXIjfa smIkar A$-@/ γ sRmab;bnÞúkGefr L esμI 1.6 EtsRmab;smIkar A$-@ vij

γ = 0.5 . mUlehtuKWbnÞúkGefr RtUv)aneKepþatsMxan;sRmab;smIkar A$-@ ÉbnÞúkmYykñúgcMeNam
bnÞúkTaMgbI L / S b¤ R RtUv)aneKepþatsMxan;sRmab;smIkar A$-#.
r

ÉemKuNersIusþg; φ mantémøenAcenøaHBI 0.75 eTA 1.

]TahrN_ 2>1³ ssr ¬Ggát;rgkarsgát;¦ enACan;xagelIrbs;GKarrgbnÞúkdUcxageRkam³

bnÞúkefr (Dead load): 485kN

bnÞúkGefrelIkRmal (Floor live load): 205kN

bnÞúkGefrelIdMbUl (Roof live load): 84.5kN
bnÞúkRBwl (Snow): 89kN

a. kMNt;karbnSMbnÞúktam AISC Edllub nigtémøbnÞúkemKuNEdlRtUvKña

b. RbsinebIemKuNersIusþg; φ = 0.85 . etI nominal strength EdlRtUvkaresμIb:unμan?
dMeNaHRsay³
a. bnSMbnÞúkEdllubCabnSMbnÞúkEdlbegáItbnÞúkemKuNFMCageK. eyIgnwgBinitüsmIkarnImYy²
EdlmanBak;B½n§nwgbnÞúkefr D / bnÞúkGefrEdl)anBI]bkrN_ smÖar³ nigmnusSEdlmanGMeBI
elIkRmal L / bnÞúkGefrEdlmanGMeBIelIdMbUl Lr nigbnÞúkRBwl S .
(A4-1): 1.4 D = 1.4(485) = 679kN
(A4-2): 1.2 D + 1.6 L + 0.5( Lrb¤ S b¤ R) . eday S > Lr ehIy R = 0 dUcenHeyIg
caM)ac;sikSakarbnSMbnÞúkEtmþgKt; edayeRbI S
1.2 D + 1.6 L + 0.5S = 1.2(485) + 1.6(205) + 0.5(89 ) = 954.5kN
(A4-3): b¤ S b¤ R) + (0.5L b¤ 0.8W )
1 .2 D + 1 .6 ( L r

sRmab;bnSMbnÞúkenH eyIgeRbI S CMnYseGay Lr ehIy R = W = 0

1.2 D + 1.6 S + 0.5 L = 1.2(485) + 1.6(89 ) + 0.5(205) = 826.9kN
(A4-4): b¤ S b¤ R) . smIkarenHRtUv)ankat;bnßymk
1.2 D + 1.3W + 0.5 L + 0.5( Lr

Rtwm 1.2D + 0.5L + 0.5S ehIytamkarGegÁt eyIgeXIjfasmIkarenHpþl;nUv

lT§pltUcCagbnSM (A4-2) nig (A4-3).

T.Chhay 20 Concepts in Structural Steel Design

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

(A4-5): . edaysar E = 0 dUcenHsmIkarenHRtUv)ankat;

1 .2 D ± 1 .0 E + 0 .5 L + 0 .2 S

bnßymkRtwm 1.2D + 0.5L + 0.2S EdllT§plTTYl)anBIsmIkarenHtUcCag

lT§plEdlTTYl)anBIsmIkar (A4-4).
(A4-6): 0.9 D ± (1.3W b¤ 1.0 E ) . smIkarenHmanemKuNbnÞúkefrtUcCagsmIkard¾éT

naMeGaylT§plrbs;smIkarenHtUcCaglT§plrbs;smIkard¾éT.
cemøIy³ bnSMbnÞúkEdllubKW (A4-2) ehIybnÞúkemKuNKW 954.5kN .
b. RbsinebIeKCMnYsbnÞúkemKuNxagelIeTAkñúgsmIkar 2.3 eyIgTTYl)an

∑ λi Qi ≤ φRn

954.5 ≤ 0.85Rn

Rn ≥ 1123kN
cemøIy³ nominal strength EdlRtUvkarKW 1123kN .

2>4> mUldæanRbU)ab‘ÍlIetrbs; Load and Resistance Factors

Probabilistic Basis of Load and Resistance Factors
TaMgemKuNbnÞúk TaMgemKuNersIusþg;EdlkMNt;eday AISC KWQrelIeKalkarN_RbU)ab‘ÍlIet.
emKuNersIusþg;karBarPaBminCak;lak;énlkçN³rbs;smÖar³ RTwsþIénkarsikSaKNna nigkarsagsg;.
Tinñn½yénkarBiesaFRtUv)anbgðajkñúgTMrg; histogram b¤ bar graph dUcbgðajenAkñúgrUbTI 2>1
EdlmanG½kSGab;sIustMNageGaytémørbs;sMNakKMrU b¤RBwtþikarN_ (event) nigG½kSGredaentMNag
eGaycMnYnsMNakKMrUEdlmantémøCak;lak; b¤PaBjwkjab; (frequency) énkarekIteLIgéntémøCak;
lak;. r)ar (bar) nImYy²GactMNageGaytémøsMNakKMrUmYy² b¤EdnéntémømYy. RbsinebIGredaen
KitCaPaKry RkaPicnwgtMNageGaykarEbgEck relative frequency. kñúgkrNIEbbenH plbUkrbs;
GredaennwgesμI 100% . RbsinebIG½kSGab;sIusCaRBwtþikarN_ ehIyeRbInUvsMNakKMrURKb;RKan; Gredaen
nImYy²GacsMEdgCaRbU)ab‘ÍlIetedaysresrCaPaKryéntémøsMNakKMrU b¤RBwtþikarN_EdlekItman.
Relative frequency k¾GacsresrCaTMrg;TsSPaKpgEdr EdlmantémøenAcenøaHBI 0 nig 1.0 . dUcenH

plbUkrbs;GredaennwgesμI 1.0 ehIyRbsinebIr)ar (bar) nImYy²manTTwgÉktþa dUcenHRkLaépÞsrub

rbs;düaRkamk¾nwgesμI 1.0 pgEdr. lT§plenHbBa¢ak;faRbU)ab‘ÍlIetEdlesμInwg 1.0 nwgnaMeGayRBwtþi-
karN_sßitenAkñúgEdnkMNt;rbs;düaRkam. elIsBIenH Rb)ab‘ÍlIeténtémøCak;lak;EdltUcCag Edlnwg

eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁúMEdk 21 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

ekIteLIgnwgesμIRkLaépÞrbs;düaRkamEdlenAxageqVgrbs;témøenaH. RbU)ab‘ÍlIeténRBwtþkarN_Edl
mantémøsßitenAcenøaH a nig b enAkñúgrUbTI 2>1 esμInwgRkLaépÞrbs;düaRkamenAcenøaH a nig b .

munnwgdMeNIrkarsikSaKNna eyIgRtUvsÁal;BIrUbmnþxøH²EdleRbIenAkñúgRbU)ab‘ÍlIet. mFümPaK

(mean) x énsMnMutémøsMNakKMrU b¤ population CatémømFümnBVnþEdl

1 n
x= ∑ xi
n i =1

Edl xi CatémøsMNakKMrU ehIy n CacMnYnrbs;témø. Median CatémøkNþalrbs; x ehIy mode

CatémøEdlekItmanjwkjab;CageK. Variance v CaxñatEdlvas;BIbERmbRmYlénTinñn½yTaMgGs;BI
mean ehIyRtUv)ankMNt;dUcxageRkam³

v=
1 n
(
∑ xi − x
n i =1
)2

Standard deviation s Cab¤skaerén variance

s=
1 n
(
∑ xi − x
n i =1
)2

dUcKñanwg variance Edr standard deviation CargVas;énbERmbRmYlTaMgmUl b:uEnþvamanxñat niglMdab;én

GaMgtg;sIuetCa data. Coefficient of variation V CaplEckrvag standard deviation elI mean.
s
V =
x

T.Chhay 22 Concepts in Structural Steel Design

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RbsinebIeKCMnYskarEbgEck frequency Cak;EsþgedayGnuKmn_Cab;tamRTwsþIEdlesÞIrEtesμIKñanwgTinñ-

n½y (data) enaHeKehAGnuKmn_enHCa probability density function. GnuKmn_EbbenHRtUv)an
bgðajenAkñúgrUbTI 2>2. GnuKmn_RbU)ab‘ÍlIetRtUv)anKNnaedayeGayRkLaépÞsrubEdlenABIeRkam
ExSekagesμIcMnYnÉktþa. sRmab;GnuKmn_ f (x)
+∞
∫− ∞ f (x )dx = 1.0

Edlmann½yfaRbU)ab‘ÍlIeténtémøsMNakKMrU b¤RBwtþikarN_EdlnwgekIteLIgesμInwg 1.0 . RbU)ab‘ÍlIetén

RBWtþikarN_enAcenøaH a nig b enAkñúgrUbTI 2>2 esμInwgRkLaépÞeRkamExSekagcenøaH a nig b
∫a f (x )dx
b

enAeBlEdleKeRbI probability density function eKsnμt;eRbInimitþsBaØaxageRkam

μ = mean
σ = standard deviation

eKalkarN_RbU)ab‘ÍlIetrbs;emKuNbnÞúk nigemKuNersIusþg;EdleRbIeday AISC RtUv)anbgðaj

enAkñúg ASCE structural journal (Ravindra and Galambos, 1978). \T§iBlbnÞúk Q nigersIusþg; R
CaGBaØat ehIyvaGaRs½yeTAnwgemKuNCaeRcIn. eK)a:n;sμan nigTTYl)anbnÞúkBIkarvas;eRKOgbgÁúMCak;
Esþg ehIyersIusþg;RtUv)anKNna nigkMNt;edaykarBiesaF. Q nig R RtUv)anbMEbkeGaydac;BIKña

eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁúMEdk 23 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

ehIy GacbgðajCa frequency distribution histogram b¤bgðajCa theoretical probability density

function.

RbsinebIeKsg;düaRkamén probability density sRmab;\T§iBlbnÞúk Q nigersIusþg; R enAelI

RkaPicEtmYy dUcenAkñúgrUbTI 2>3 tMbn;EdlRtUvKñanwg Q > R bgðajBI failure ehIy Q < R bgðajBI
survival. RbsinebIkarEbgEck Q nig R RtUv)andak;bBa©ÚlKñaeTAkñúgGnuKmn_EtmYy témøviC¢manén

R − Q RtUvKñanwg survival. dUcKña RbsinebIeKeRbI probability density function R / Q ¬emKuN

suvtßiPaB¦ survival RtUv)ansMEdgedaytémø R / Q FMCag 1.0 . RbU)ab‘ÍlIetEdlRtUvKñanwg failure

CaRbU)ab‘ÍlIetEdl R / Q tUcCag 1.0 .
⎡⎛ R ⎞ ⎤
PF = P ⎢⎜⎜ ⎟⎟ < 1⎥
⎣⎝ Q ⎠ ⎦

edaydak;elakarItenEBeTAelIGgÁsgxagénvismIkarxagelIeyIgTTYl)an
⎡ ⎛R⎞ ⎤ ⎡ ⎛R⎞ ⎤
PF = P ⎢ln⎜⎜ ⎟⎟ < ln1⎥ = P ⎢ln⎜⎜ ⎟⎟ < 0⎥
⎣ ⎝Q⎠ ⎦ ⎣ ⎝Q⎠ ⎦

ExSekagEbgEck frequency én ln(R / Q ) RtUv)anbgðajenAkñúgrUbTI 2>4. eKGackMNt;TMrg;Edlman

lkçN³sþg;daénGBaØat ln(R / Q ) Ca
⎛ R ⎞ ⎡ ⎛ R ⎞⎤
ln⎜⎜ ⎟⎟ − ⎢ln⎜⎜ ⎟⎟⎥
⎝ Q ⎠ ⎣ ⎝ Q ⎠⎦ m
U=
σ ln (R / Q )

T.Chhay 24 Concepts in Structural Steel Design

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

⎡ ⎛ R ⎞⎤
Edl ⎢ln⎜⎜ ⎟⎟⎥ = témømFüm (mean value) én ⎛⎜⎜ QR ⎞⎟⎟
⎣ ⎝ Q ⎠⎦ m ⎝ ⎠

σ ln (R / Q ) = standard deviation én ⎛⎜⎜ QR ⎞⎟⎟

⎝ ⎠

eyIgGacsresrRbU)ab‘ÍlIetén failure Ca
⎡ ⎛R⎞ ⎤ ⎛ ⎧⎪ ⎡ ⎛ R ⎞⎤ ⎫⎪ ⎞
PF = P ⎢ln⎜⎜ ⎟⎟ < 0⎥ = P⎜ ⎨Uσ ln ( R / Q ) + ⎢ln⎜⎜ ⎟⎟⎥ ⎬ < 0 ⎟
⎣ ⎝Q⎠ ⎦ ⎜⎪ ⎣ ⎝ Q ⎠⎦ m ⎪⎭ ⎟
⎝⎩ ⎠

⎧ ⎡ ⎛ R ⎞⎤ ⎫ ⎧ ⎡ ⎛ R ⎞⎤ ⎫
⎪ ⎢ln⎜⎜ ⎟⎟⎥ ⎪ ⎪ ⎢ln⎜⎜ ⎟⎟⎥ ⎪
⎪ ⎣ ⎝ Q ⎠⎦ m ⎪ ⎪ ⎣ ⎝ Q ⎠⎦ m ⎪
= P ⎨U < − ⎬ = Fu ⎨− ⎬
⎪ σ ln (R / Q ) ⎪ ⎪ σ ln( R / Q ) ⎪
⎪ ⎪ ⎪ ⎪
⎩ ⎭ ⎩ ⎭

Edl Fu Ca cumulative distribution function én U b¤CaRbU)ab‘ÍlIetEdl U minFMCag argument

rbs;GnuKmn_. RbsinebIeyIgyk
⎡ ⎛ R ⎞⎤
⎢ln⎜⎜ ⎟⎟⎥
⎣ ⎝ Q ⎠⎦ m
β= (2.4)
σ ln (R / Q )

⎡ ⎛ R ⎞⎤
enaH ⎢ln⎜⎜ ⎟⎟⎥ = βσ ln ( R / Q )
⎣ ⎝ Q ⎠⎦ m

eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁúMEdk 25 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

eKGacbgðajGBaØat β CacMnYnén standard deviations BIeKalén mean value ln(R / Q ) . edIm,I

suvtßiPaB/ mean value RtUvEttUcCagsUnü ehIyCavi)ak β RtUv)aneKehAfa safety index b¤
reliability index. témøenHkan;EtFM kMritsuvtßiPaBkan;EtFM. enHmann½yfaRbU)ab‘ÍlIetén failure Edl

bgðajedayépÞqUtenAkñúgrUbTI 2>4 nigmankMNt;sMKal; PF nwgmantémøtUc. Reliability index

CaGnuKmn_én\T§iBlbnÞúk Q nigersIusþg; R . kareRbI reliability index dUcKñasRmab;RKb;RbePTGgát;
EdlrgRKb;RbePTbnÞúk dUcKñanwgkarpþl;eGayGgát;nUversIusþg;RKb;RbePTEdr. témøkMNt; (target
value) rbs; β EdlbgðajenAkñúgtarag 2>1 RtUv)aneRCIserIs nigeRbIenAkñúgkarKNnaemKuNbnÞúk

nigemKuNersIusþg;sRmab; AISC Specification EdlQrelIkaresñIeLIgeday Ravindra and

Galambos (1978) ehIyk¾)anbgðajfa

Rm − 0.55βV R
φ= e (2.5)
Rn

Edl énersIusþg; R
Rm = mean value

Rn = nominal resistance b¤ersIusþg;tamRTwsþI

VR = emKuNbERmbRmYlrbs; R

smIkar 2.5 CasmIkarsRmab;emKuNersIusþg; φ EdleGayenAkñúg Commentary to the

Specification.

tarag 2>1 Edntémø (target value) rbs; β

lkçxNÐbnÞúk
RbePTeRKOgbgÁúM
b¤
D + (L S ) D+L+S D+L+E
Ggát; 3.0 2.5 1.75

tMN 4.5 4.5 4.5

2>5> Manual of Steel Construction

manBIrPaK EdlPaKTImYymancMNgeCIgfa “Structural Members, Specifications

Manual

and Codes” man 7Epñk Edlerobrab;BIkarKNnaGgát; ehIyPaKTIBIrmancMNgeCIg “connections”

T.Chhay 26 Concepts in Structural Steel Design

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

man 5Epñk EdlniyayBIkarKNnatMN. esovePAenHepþatCasMxan;eTAelIPaKTImYyEdlEckecjCa

7Epñk.

Part1. Dimensions and Properties: EpñkenHmanB½t’manlMGitBI standard rolled-shapes,

pipe nig structural tubing EdlrYmmanTMhMmuxkat; niglkçN³sMxan;²TaMgGs; dUcCaRkLaépÞ

nigm:Um:g;niclPaB. EdkEdlmanerobrab;enAkñúg manual enHRtUv)anGnuBaØateday AISC

Specification sRmab;eRbIR)as;enAkñúgsMNg;GKarEdlrYmmandUcxageRkam³

ASTM A36: Carbon structural steel

ASTM A529: High-strength, carbon-manganese structural steel
ASTM A572: High-strength, low-alloy structural steel
ASTM A242: Corrosion-resistant, high-strength, low-alloy structural steel
ASTM A588: Corrosion-resistant, high strength, low-alloy structural steel
ASTM A852: Quenched and temped low-alloy structural plate
ASTM A514: High-strength, quenched and tempered alloy structural steel plate

Part2. Essentials of LRFD: EpñkenHENnaMy:agsegçbBImUldæanrbs; load and resistance

factor design rbs;eRKOgbgÁúMEdk nigman]TahrN_CaelxbgðajpgEdr.

Part3. Column Design: EpñkenHmantaragCaeRcInsRmab;sRmYlldl;karKNnaTaMgGgát;

rgkarsgát;tamG½kS nig beam-columns. taragPaKeRcInKWsRmab;EdkEdlman yield stress

36ksi ≈ 250 MPa nig 50ksi ≈ 345MPa .

Part4. Beam and Girder Design: EpñkenHk¾dUcEpñkTI 3EdrKWvaman design aid CaeRcInrYm

mantarag nigRkaPic. Design aid PaKeRcInmanniyayBItMrUvkarrbs; AISC Specification

b:uEnþ design aid xøHdUcCa Beam diagrams and Formula KWTak;Tgnwg structural analysis.
kñúgEpñkenHk¾manerobrab;BIdMeNIrkarKNnaFñwm nig girder ehIyman]TahrN_bgðajBIkarsikSa
KNnaeTotpg.
Part5. Composite Design: EpñkenHerobrab;BIeRKOgbgÁúMsmas EdlCaTUeTACaFñwm b¤ssr.

eRKOgbgÁúMsmaspSMeLIgedaysmÖar³BIrRbePTKW EdkeRKOgbgÁúM nigebtugGarem:. CaFmμta eK

eRbIFñwmsmasenAeBlEdlRbB½n§FñwmRsbRTkMralxNÐebtugGarem:. enAkñúgkarGnuvtþ element
EdlpSarP¢ab;eTAnwgsøabxagelIRtUv)anbgáb;enAkñúgebtugedIm,IP¢ab;smÖar³TaMgBIr. ssrsmas
eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁúMEdk 27 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

GacCaEdkeRKOgbgÁúMbgáb;enAkñúgebtugGarem: b¤EdkRbehagEdlbMeBjedayebtug. EpñkenH

man design aid nig]TahrN_bgðajpgEdr.
Part6. Specifications and Codes: EpñkenHman AISC Specification nig Commentary,

specification sRmab;b‘ULúgersIusþg;x<s; (RCSC, 1994) nigÉksardéTeTot.

Part7. Miscellaneous Data and Mathematical Tables: EpñkenHniyayBI wire, sheet

steel niglkçN³epSg²rbs;Edk nigsmÖar³sMNg;déTeTot. ehIyk¾manrYmbBa©ÚlTaMgrUbmnþ

KNitviTüa nigemKuNsRmab;bMElgxñat.
PaKTIBIr ¬EdlpSMeday 5Epñk¦ mantaragsRmab;CYykñúgkarKNnakartP¢ab;edaykarpSar
nigedayb‘ULúgCamYynwgtaragEdlpþl;eGayy:aglMGitelI standard connection.
AISC Specification RKan;EtCaEpñkd¾tUcmYyrbs; Manual. Bakü nigtémøefrCaeRcInEdleRbI

enAkñúgEpñkxøHrbs; Manual RtUv)anbgðajedIm,IsRmYldl;dMeNIrkarsikSaKNna ehIyvaminmansresr

enAkñúg specification eT.

T.Chhay 28 Concepts in Structural Steel Design

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

cMeNaT
cMNaM³ bnÞúksmμtikmμTaMgGs;CabnÞúkeFVIkar (service load).

@>#>!> ssrenACan;xagelIrbs;GKarrgbnÞúksgát;Edl)anBI³ bnÞúkefr = 137kN / bnÞúkGefr = 7.5kN /

bnÞúkGefrEdlmanGMeBIelIdMbUl = 85kN nigbnÞúkRBwl = 90kN .
k> kMNt;karbnSMbnÞúkEdlmanlkçN³lub nigbnÞúkemKuN.
x> RbsinebIemKuNersIusþg;esμInwg 0.85 . etI nominal strength tRmUvkarrbs;ssrmantémøb:unμan?
@>#>@> ssrrgbnÞúkEdl)anBI³ bnÞúkefr = 115kN / bnÞúkGefr = 67kN / bnÞúkGefrEdlmanGMeBIelI
dMbUl = 22kN / bnÞúkRBil = 35kN / bnÞúkePøóg = 22kN nigbnÞúkxül; 35kN . bnÞúkTaMgGs;CabnÞúk
sgát;elIkElgEtbnÞúkxül;EdlGacCabnÞúkTaj b¤bnÞúksgát;.
k> kMNt;karbnSMbnÞúkEdlmanlkçN³lub nigbnÞúkemKuN.
x> RbsinebIemKuNersIusþg;esμInwg 0.85 . etI nominal strength tRmUvkarrbs;ssrmantémøb:unμan?
@>#>#> bnÞúkenAelIFñwmdMbUlrYmmanbnÞúkGefr 2.9kN / m / bnÞúkGefrEdlmanGMeBIelIdMbUl 1.9kN / m
nigbnÞúkRBwl 2.0kN / m . kMNt;bnÞúkemKuNEdleKeRbIsRmab;sikSaKNnaFñwmenH. etIbnSMbnÞúkmYy
NaEdllub?
@>#>$> eKnwgsikSaKNnaFñwmsRmab;RbB½n§dMbUl nigRbB½n§kRmalsRmab;GKarkariyal½y. kMNt;bnSM
bnÞúkEdllub nigbnÞúkemKuNsRmab;krNIxageRkam³
k> dMbUl³ bnÞúkefr 1.4kN / m / bnÞúkefrEdlmanGMeBIelIdMbUl 1.0kN / m / bnÞúkRBil 1.0kN / m
2 2 2

nigbnÞúkTwkePøógEdl)anBIkm<s;Twk 10cm .
x> kRmal³ bnÞúkefr 3.0kN / m nigbnÞúkGefr 3.8kN / m
2 2

@>#>%> CaerOy² eKEtgsikSaKNnasMNg;GKarGMBIEdkCamYynwgRbB½n§BRgwgGgát;RTUg (diagonal

bracing system) edIm,ITb;Tl;nwgbnÞúkxag ¬kmøaMgtamTisedkEdlekItBIbnÞúkxül; nigbnÞúkrBa¢ÜydI¦.

kMNt;bnSMbnÞúk nigbnÞúkemKuNEdllubsRmab;bnÞúkEdl)anBI³ bnÞúkefr = 59kN / bnÞúkGefr = 31kN /

bnÞúkGefrEdlmanGMeBIelIdMbUl = 5.8kN / bnÞúkRBil = 5.8kN bnÞúkxül; = 670kN nigbnÞúkrBa¢ÜydI
= 717 kN .

cMeNaT 29 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

III. eRKOgbgÁúMrgkarTaj
Tension Members
3>1> esckþIepþIm (Introduction)
eRKOgbgÁúMrgkarTaj CaeRKOgbgÁúMsMNg;EdlrgkmøaMgTajtamG½kS. vaRtUv)aneKeRbIsRmab;
eRKOgbgÁúMeRcInRbePT rYmbBa©ÚlTaMgeRKOgbgÁúM truss ExSkabsRmab; suspension bridge nig cable-
stayed bridge, RbB½n§BRgwgGKar nigs<an ExSkabsRmab;RbB½n§dMbUlBüÜrpgEdr. sRmab;Ggát;rg

karTaj RkLaépÞmuxkat;CaGñkkMNt;lT§PaBTb;Tl;eTAnwgkmøaMgxageRkA. EdkEdlmanmuxkat;mUl

nig EdkEkghUtekþA (rolled angle shape) RtUv)aneKeRbICaTUeTA. eBlxøH muxkat; built-up BI
muxkat;hUtekþA (rolled shape) b¤muxkat;pSMKñaBImuxkat;hUtekþACamYynwgEdkbnÞH (plate) RtUv)aneK
eRbIR)as;kñúgkrNITb;Tl;CamYybnÞúkFM. muxkat; built-up PaKeRcInCa double-angle section ¬rUb
TI3>1¦ CamYynwgmuxkat;KMrUepSg²eTot. edaysarEtkareRbIR)as;muxkat;enHmanPaBTUlMTUlay
taraglkçN³énbnSMmuxkat;Ekg (combinations of angles) epSg²k¾RtUv)anbB©ÚaleTAkñúg AISC
Manual of steel Construction.

Figure 3.1

kugRtaMgenAkñúgGgát;rgkarTajtamG½kSKW
P
f =
A

RbsinebIRkLaépÞmuxkat;rbs;Ggát;rgkarTajERbRbYltamRbEvg enaHkugRtaMgnwgERbRbYltam
muxkat;Edr. CaFmμta eRKOgbgÁúMrgkarTajEdlP¢ab;edayb‘ULúg EtgEtmanRbehag. vtþmanrbs;Rb
T.Chhay 30 Tension Members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

ehagEtgman\T§iBleTAelIkugRtaMg. enAkñúgkrNIenH eKecalmuxkat;Rbehag. RkLaépÞmuxkat;suT§

(net area b¤ net section) Camuxkat;suT§EdlminKitmuxkat;Rbehag ÉRkLaépÞeBj (gross area) Camux

kat;eBjEdlKitrYmTaMgmuxkat;Rbehag. CaerOy² Ggát;rgkarTajEtgP¢ab;edayb‘ULúgenAxagcug ¬rUb

TI3>2¦.
Figure 3.2

karsikSaKNnaeRKOgbgÁúMrgkarTaj KWCakareRCIserIsGgát;Edlmanmuxkat;RKb;RKan; edIm,ITb;

Tl;nwgkugRtaMgEdl)anBIbnÞúkemKuN. kñúgkrNIEdleKsÁal;muxkat;Ggát; eKGacKNnaersIusþg;KNna
(design strength) ehIyeKeFVIkareRbobeFobvaCamYybnÞúkemKuN. CaTUeTA karsikSaviPaK (analysis)

CadMeNIrkarKNnaviPaK ÉcMENkkarsikSaKNnamuxkat; (design) CadMeNIrkarKNnasarcuHsareLIg

ehIyRtUvkarkarsakl,g nigmankMhusecosminput.

3>2> ersIusþg;KNna (Design strength)

eRKOgbgÁúMrgkarTajGacminCab;edaysßanPaBkMNt; (limit state) BIry:ag³
- kMhUcRTg;RTayelIslb; (excessive deformation)³ edIm,IkarBarsßanPaBEbbenH bnÞúkenAelI
muxkat;eBj (gross section) RtUvEtmantémøtUcRKb;RKan; EdlnaM[kugRtaMgenAelImuxkat;
eBj (gross section) man témøtUcCagkugRtaMgyal (yield stress) F .y

Pn < Fy Ag

eRKOgbgÁúMrgkarTaj 31 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Edl Pn = nominal strength in yielding

Fy = yield strength
Ag = gross section area

- kardac; (fracture)³ edIm,IkarBarsßanPaBEbbenH kugRtaMgenAelImuxkat;suT§ (net section) RtUv

EtmantémøtUcCagersuIsþg;dac; (tensile strength) F . u

Pn < Fu Ae

Edl Pn = nominal strength in yielding

Fu = tensile strength
RkLaépÞmuxkat;suT§RbsiT§PaB (effective net area). kñúgkrNIxøH A mantémø
Ae = e

esμIRkLaépÞmuxkat;suT§ (net section) A EtkñúgkrNIxøHvamantémøtUcCag A .

n n

eTaHbICa enAelImuxkat;suT§ (net section) ekItmanyal (yield) munk¾eday EtkMhUc

RTg;RTayenAelIRbEvgéntMNmantémøtUcCagkMhUcRTg;RTayenAelIEpñkrgkarTajEdlenAsl;.
mUlehtuKWsac;lUtsrub (total elongation) CaplKuNrvagRbEvgedIm nigsac;lUteFob (strain)
¬GnuKmn¾eTAnwgkugRtaMg¦. sßanPaBkMNt; (limit state) seRmc[muxkat;eBj (gross section)
rgkugRtaMgyal (yield stress) KWedaysarEtsac;lUtsrubmantémøFMCag minEmneday
sarkaryal (yielding) muneT.
emKuNersIusþg; φ = 0.9 sRmab;karyal (yielding)
t

emKuNersIusþg; φ = 0.75 sRmab;kardac; (fracture)

t

BIsmIkar !># eyIgGacsresr

∑γ Q i i ≤ φt Pn

b¤ Pu ≤ φt Pn

Edl P CabnSMbnÞúkemKuNEdlmantémøFMCageK.
u

edaysareKmansßanPaBkMNt; (limit state) cMnYnBIr dUcenHsßanPaBTaMgBIrRtUvbMeBjlkçxNÐ

xageRkam³
T.Chhay 32 Tension Members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Pu ≤ 0.9 Fy Ag sRmab;;muxkat;eBj (gross section)

Pu ≤ 0.75 Fu Ae sRmab;muxkat;suT§ (net section)
témøtUcCageKkñúgcMeNamtémøTaMgBIrCaersIusþg;KNnarbs;Ggát;rgkarTaj.
RkLaépÞBitR)akdEdldkecjBIRkLaépÞmuxkat;eBj (gross area) edaymanvtþman
RbehagKWGaRs½yeTAnwgdMeNIrkarplit. sRmab;karGnuvtþTUeTA rn§EdlecaHedaylkçN³bTdæan
drill or punch oversized holes eKRtUvbUkbEnßm 2mm eTAelIGgát;p©itrbs;b‘ULúg. sRmab; drill or

punch standard holes eKRtUvbUkbEnßm 4mm eTAelIGgát;p©itrbs;b‘ULúgEdleKeRbIR)as;. sRmab;

rn§RTEvg (slotted holes) eKRtUv)aneKbUkbEnßm 2mm eTAelIGgát;p©itrbs;b‘ULúg. xageRkamCatarag

bgðajBIGgát;p©itb‘ULúg nigGgát;p©itrn§.
Nominal Hole Dimensions, mm
Ggát;p©itb‘ULúg xñatRbehag Hole Dimensions
Bolt Diameter Standard Oversize Short-Slot Long-Slot
(Dia.) (Dia.) (Width × Length) (Width × Length)
M16 18 20 18×22 18 ×40
M20 22 24 22×26 22×50
M22 24 28 24×30 24×55
M24 27 [a] 30 27×32 27×60
M27 30 35 30×37 30×67
M30 33 38 33×40 33×75
≥ M36 d+3 d+8 (d + 3)×(d + 10) (d + 3)× 2.5d
[a]Clearance provided allows the use of a 1-in. bolt if desirable. ( RtUvKña 25mm )

]TahrN_3>1³ r)arEdkm:ak A36 Edlmanmuxkat; 125 ×12.5mm RtUv)aneRbICaGgát;rgkarTaj.

2

vaRtUv)antP¢ab;eTAnwg gusset plate CamYynwgb‘ULúg M16 cMnYn 4 RKab; ¬rUbTI3>3¦. edaysnμt;fa

effective net area A esμInwg net area cUrkMNt;ersIusþg;KNna (design strength).
e

eRKOgbgÁúMrgkarTaj 33 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Figure 3.3

dMeNaHRsay³
EdkEdlmanm:ak A36 man F = 250MPa nig F
y u = 400MPa

sRmab; yielding én gross section

Ag = 125 × 12.5 = 1562.5mm 2

ersIusþg; nominal
Pn = Fy Ag = 250 × 1562.5 = 390kN

ersIusþg;KNna (design strength)

φt Pn = 0.9 × 390 = 351kN
sRmab; fracture én net section
An = Ag − Aholes
= 1562.5 − 2 × (12.5 × 20) = 1062.5mm 2
Ae = An = 1062.5mm 2 ¬sRmab;Et]TahrN_enHb:ueNÑaH¦
ersIusþg; nominal
Pn = Fu Ae = 400 × 1062.5 = 425kN
ersIusþg;KNna (design strength)
φt Pn = 0.75 × 425 = 348.75kN
dUcenH ersIusþg;KNna (design strength) φ Pt n = 348.75kN ¬témøtUcCagCacemøIy¦

\T§iBlénkugRtaMgpþúM (stress concentration) minRtUv)aneKBicarNakñúgkrNIenHeT EtFatuBit

kugRtaMgenARtg;rn§mantémøRbEhlbIdgkugRtaMgmFümEdlekItmanenAelI net area ehIykugRtaMgenA
T.Chhay 34 Tension Members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Rtg; fillet énmuxkat;hUtekþA mantémøFMCagkugRtaMgmFümelIsBIrdg. edaysarEtPaBsVit b¤PaB

hUtlYs (ductile) rbs;EdkEdlTItaMgEdlman overstress RtUv)anecalsRmab;karKNnaTUeTA.
eRkamlkçxNÐCak;Esþg EdkGac)at;bg;PaBsVitrbs;va ehIy stress concentration GaceFVI[r)ar
dac;Pøam². sßanPaBenHrYmman fatigue loading nigeRkamsItuNðPaBTabEmnETn.
Figure 3.4

]TahrN_3>2³ r)arrgkarTajmuxkat;EkgeTal L89 × 89 × 9.5 Rtv)anP¢ab;eTAnwg gusset plate

CamYynwgb‘ULúg M22 cMnYn 3 RKab; ¬rUbTI3>4¦. r)arEdkenH manm:ak A36 . bnÞúkefr DL = 155kN
nigbnÞúk LL = 67kN . viPaKmuxkat;enH edaysnμt; effective net area A esμIeTAnwg 85% rbs; net
e

area .

dMeNaHRsay³
bnSMbnÞúk (load combination)
(A4-1): 1.4 DL = 1.4 × 155 = 217 kN
(A4-2): 1.2 DL + 1.6 LL = 1.2 × 155 + 1.6 × 67 = 293.2kN > 217 kN

⇒ Pu = 293.2kN

ersIusþg;KNna (design strength)

gross section: Ag = 1610mm 2
φt Pn = φt Fy Ag = 0.9 × 250 × 1610 = 362.25kN
net section: An = 1610 − (9.5 × 26) = 1363mm 2
Ae = 0.85 × 1363 = 1158.55mm 2
φt Pn = φt F y u Ae = 0.75 × 400 × 1158.55 = 347.57 kN < 362.25kN

eRKOgbgÁúMrgkarTaj 35 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

eday P < φ P
u t n (293.2kN < 347.57kN ) dUcenH r)armansuvtßiPaBedaybMeBjlkçxNÐ.

enAkñúg]TahrN_xagelIenH eyIgeXIjfabnSMMbnÞúk (A4-2) RtUv)anykmkeFVIkarKNna. enA

eBlmanEtbnÞúkefr nigbnÞúkGefreFVIGMeBIelIeRKOgbgÁúM ehIybnÞúkefr tUcCagbnÞúkGefr *dg enaHeKeRbI
bnSMbnÞúk (A4-2) edIm,IeFVIkarKNna. sRmab;]TahrN_xagmux eyIgnwgmineFVIkarepÞógpÞat;bnSMbnÞúk
1.4 D (A4-1) eT edaysarEtvaminGacFMCagbnSMbnÞúk (A4-2)eT.

3>3> RkLaépÞmuxkat;suT§RbsiT§PaB (Effective net area)

kñúgcMeNamktþaCaeRcInEdlman\T§iBleTAelIkareFVIkarrbs;r)arrgkarTaj rebobénkartP¢ab;
CaktþamYyEdlsMxan;CageK. tMNPaKeRcInEtgEteFVI[r)arcuHexSay karKNnanUv\T§iBlrbs;vaRtUv
)aneKehAfa Joint efficiency . ktþaenHCaGnuKmn_eTAnwgPaBsVitrbs;smÖar³ (ductility of material)
KMlatrbs;eRKOgP¢ab; (fastener spacing) kugRtaMgpþúMenARtg;Rbehag (stress concentra-tion) TRmg;
énkarplitrYmTaMg)atuPUtEdleKsÁal;faCa shear leg. ktþaTaMgenHnaM[mankarkat;bnßyRbsiT§PaB
rbs;r)ar b:uEnþ shear lag CaktþamYyEdlsMxan;CageK.
Shear lag ekItmanenAeBlEdlmuxkat;r)arTaMgmUlminRtUv)antP¢ab; dUcCaenAeBlEdleCIg

mçagrbs;EdkEkgRtUv)anP¢ab;edaysarb‘ULúgeTAnwg gusset plate ¬rUbTI3>5¦. sar³sMxan;rbs;kart

P¢ab;edayEpñk eFVI[Epñkrbs;r)arEdltP©ab;rgbnÞúkFM (overload) ehIyEpñkEdlmintP¢ab;minrg
kugRtaMgeBjelj. karbnøayRbEvgtMbn;tP¢ab;CyY kat;bnßy\T§iBlenH. karRsavRCavEdleFVIeLIg
eday Munse nig Chesson (1963) )ansMNUmBr[Kit shear lag kñúgkarkat;bnßy net area.
edaysarEt shear lag man\T§iBleTAelIkartP¢ab;edayb‘ULúg nigkartP¢ab;edaykarpSar enaH effec-
tive net area RtUv)aneKGnuvtþcMeBaHtMNTaMgBIrRbePTenH.

Effective net area sRmab;tMNb‘ULúg

Ae = UAn

Effective net area sRmab;tMNpSar

Ae = UAg

T.Chhay 36 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Figure 3.5

U CaemKuNkat;bnßyRbsiT§PaB (reduction factor)

x
U = 1− ≤ 0.9 (AISC Equation B3-2)
L
x CacmøayBITIRbCMuTm¶n;rbs;mxu kat;eTAbøg;énkartP¢ab;.
L CaRbEvgénkartP¢ab;.

RbsinebIr)artP¢ab;edaymanlkçN³sIuemRTI x RtUveRCIserIsyktémøtUcCageK ¬rUbTI3>6¦.

Figure 3.6

CaRbEvgtP¢ab;tamTisedAbnÞúkeFVIGMeBI ¬rUbTI3>7¦. sRmab;tMNb‘ULúg L RtUv)aneKvas;BI

L

cugmçagrbs;G½kSb‘ULúg eTAcugmçageTotrbs;G½kSb‘ULúg. sRmab;tMNpSar L RtUv)anvas;BIcugtMNmçag

eTAtMNmçag. RbsinebI kMNat;EdlpSarmanRbEvgtamTisedAkmøaMg RbEvgkMNat;EdlmanRbEvgEvg
CagRtUv)anykmkKNna.
eRKOgbgÁúMrgkarTaj 37 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Figure 3.7

témømFüm Lx sRmab;kartP¢ab;edayb‘ULúgsRmab;Ggát;rgkarTajepSg² Commentary to

AISC B3 [témø U CMnYs[karKNna 1 − . témømFüm U sRmab;tMNb‘ULúgmanBIrRbePT³
x
L
sRmab;kartP¢ab;eday fastener BIrkñúgmYyCYrtamTisedAbnÞúkeFVIkar nigsRmab;karP¢ab;eday fastener
bIb¤ eRcInkñúgmYyCYr. eK[témø U bIepSgKña EdleKaeBtamlkçxNÐxageRkam³
!> sRmab;EdkEdlmanmuxkat; W, M, S EdlmanpleFobTTwgelIkm<s;y:agtic 2
3

¬nigsRmab; muxkat; T Edlkat;ecjBImuxkat;TaMgbIxagelI¦ ehIyRtUv)anP¢ab;enAnwgsøabCamYynwg

fastener y:agticbIkúñgmYyCYrtamTisedAbnÞúkeFVIGMeBI

U = 0 .9
@> sRmab;RKb;TRmg;muxkat;epSgeTot ¬rYmTaMgmuxkat; built-up¦ CamYynwg fastener y:agtic
bIkúñgmYyCYr
T.Chhay 38 Tension Members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

U = 0.85
#> sRmab;RKb;Ggát;TaMgGs; CamYynwg fastener y:agticBIrkúñgmYyCYr
U = 0.75
rUbxageRkamnwgbgðajnUv beRmIbRmas;c,ab;TaMgenH ¬rUbTI3>8¦.
eKk¾GaceRbIR)as;témø U mFümsRmab;tMNpSarEdr. ebIeTaHCamin)anbriyaykñúg Com-
mentary k¾eday EtvaCaectnarbs; ¬AISC, 1989b¦. c,ab;enHdUcKña EtelIkElgsRmab;karpþl;[

EdleqøIytbeTAnwg fastener BIrminRtUv)anGnuvtþ. témømFüm U sRmab;tMNpSarmandUcxageRkam³

!> sRmab;EdkEdlmanmuxkat; W, M, S EdlmanpleFobTTwgelIkm<s;y:agtic ¬nig 2
3

sRmab;muxkat; T Edlkat;ecjBImuxkat;TaMgbIxagelI¦ ehIyRtUv)anP¢ab;enAnwgsøab

U = 0 .9
@> sRmab;RKb;TRmg;muxkat;epSgeTot
U = 0.85

krNIBiesssRmab;kartedaykarpSar
AemantémøtUcCag A enAeBlEdlmuxkat;rbs;Ggát;xøHb:eu NÑaHminRtUv)antP¢ab;. sRmab;
n

Ggát;rgkarTajdUcCa bnÞHEdk b¤r)ar ¬dUcbgðajkñúg]TahrN_3>1¦ effective net area RtUv)anyk

eBj dUckarKNna net area. EteTaHCay:agNa vamankrNIelIkElgsRmab;c,ab;enH³ sRmab;bnÞH
Edk b¤Edkr)arEdltP¢ab;edaykarpSartambeNþay (longitudinal weld) Epñkxagcugrbs;va ¬rUbTI
3>9¦ .
Ae = UAn

Edl U =1 sRmab; l ≥ 2w
U = 0.87 sRmab; 1.5w ≤ l < 2w
U = 0.75 sRmab; w ≤ l < 1.5w
l= RbEvgkarpSar > w
w = cmøaycenøaHkarpSar ¬EdlGacykTTwgrbs; plate b¤ bar¦

eRKOgbgÁúMrgkarTaj 39 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

AISC B3k¾[nUvkrNIBiessmYysRmab;Ggát;edaykarpSarEt transverse weld b:ueNÑaH

A = RkLaépÞmuxkat;EdlpSar
e

Figure 3.8

T.Chhay 40 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Figure 3.9

¬rUbTI3>10¦ bgðajBIPaBxusKñarvagkarpSartambeNþay (longitudinal weld) nigkarpSar

tamTTwg (transverse weld). karEdlpSarEt transverse weld CakarxusFmμta EdleKmineRbIkñúg
plitkmμeT.

Figure 3.10

]TahrN_TI3>3³ kMNt; effective net area sRmab;Ggát;rgkarTaj ¬rUbTI3>11¦.

dMeNaHRsay³ A = A − An g holes

An = 3.72 × 10 −3 − (12.7 × 20) × 2 × 10 −6 = 3.212 × 10 −3 m 2

eCIgEtmçagb:ueNÑaHrbs;mxu kat;RtUv)anP¢ab; dUcenH net area RtUvEtkat;bnßy. BItaraglkçN³
kñúgEpñkTI1 rbs; Manual cmøayBITIRbCMuTm¶n;eTAépÞxageRkAéneCIgrbs; L152 × 152 × 12.7 KW
x = 4.25 × 10 −2 m
RbEvgtP¢ab;KW L = 75 × 2 = 150mm

eRKOgbgÁúMrgkarTaj 41 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Figure 3.11

42.5
U = 1− = 0.717 < 0.9
150
Ae = UAn = 0.717 × 3.212 ⋅ 10 −3 = 2.3 ⋅ 10 −3 m 2
eKGaceRbItémømFüm U BI Commentary . edaysarEtmuxkat;minEmn W, M, S b¤ GkSr T
ehIymanb‘ULúgeRcInCagBIrkñúgmYyCYrtamTisbnÞúkeFVIGMeBI U = 0.85
Ae = 0.85 × 3.212 ⋅ 10 −3 = 2.73 ⋅ 10 −3 m 2
témø U TaMgBIrGacTTYlyk)anTaMgBIr Ettémø U Edl)anBIkarKNnatam AISC Equation
B3-2 mantémøsuRkitCag. EteTaHCay:agNak¾eday k¾témømFüm U manRbeyaCn_sRmab;karKNna

dMbUg (preliminary design) enAeBlEdlmuxkat;BitR)akd nigB½t’manlMGitGMBIkarpSarminTan;RtUv

)andwgenaH.

]TahrN_TI3>4³ RbsinebIGgát;kñúg]TahrN_TI3>3 RtUv)anpSardUcbgðajkñúgrUbTI3>12 cUrkMNt;

effective net area
dMeNaHRsay³ dUckñúg]TahrN_TI3>3 manEtEpñkmuxkat;tP¢ab; nig reduced effective net area
RtUv)aneRbI. karP¢ab;RtUv)aneFIVeLIgCamYynwgkarpSartambeNþay nigtamTTwg dUcenHvaminEmnCa
krNIBiesssRmab;Ggát;pSareT.
⎛x⎞ ⎛ 42.5 ⎞
U = 1− ⎜ ⎟ = 1− ⎜ ⎟ = 0.7 < 0.9
⎝L⎠ ⎝ 140 ⎠
cemøIy³ A e = UAg = 0.7 × 3.72 ⋅ 10 −3 = 2.604 ⋅ 10 −3 m 2

T.Chhay 42 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Figure 3.12

3>4> karteRmobtamEbbqøas; (Staggered fasteners)

RbsinebIkartP¢ab;Ggát;eFIVeLIgCamYynwgb‘ULúg enaH net area nwgmantémøGtibrmakñúgkrNI
EdleRKOgP¢ab; (fastener) RtUv)andak;EtmYyCYr. eBlxøH edaysarEtKMlatRtUv)ankMNt; dUcCaTMhM
a enA kñúgrUbTI3>13 (a) caM)ac;eFVI[eKRtUvEteRbIeRKOgP¢ab;eRcInCagmYyCYr. RbsinebIdUcenH kar

kat;bnßyRkLaépÞmuxkat;RtUv)ankat;bnßy RbsinebIeRKOgP¢ab;RtUv)anteRmobtamEbbqøas; staggered

pattern dUcbgðaj. eBlxøH Staggered fasteners RtUv)aneKtRmUv[erobtamlkçN³FrNImaRtdUc

bgðajkñúgrUbTI13 (b). kñúgkrNIepSgeTot muxkat;xøHEdlkat;tamrn§nwgkat;tamrn§EdlmancMnYntic

CagRbsinebIeRKOgP¢ab;minRtUv)anteRmobtamEbbqøas;eTenaH.
RbsinebIcMnYnén stagger mancMnYnticlμm enaHkarP¢ab;Gacdac;tamExSKnøg abcd dUckñúgrUbTI
3>13 (c). kñúgkrNIEbbenH eKminGacGnuvtþTMnak;TMng f = P A )aneT ehIykugRtaMgenAkñúgmuxkat;
tamExSeRTt bc KWCabnSMénkugRtaMgTaj nigkugRtaMgkmøaMgkat;. viFIsaRsþRbhak;RbEhl (approxi-
mate) CaeRcIn RtUv)aneKesñIeLIgedIm,IBnül;GMBIRbsiT§PaBrbs; staggered hole. elak Cochran

(1922) )anesñInUvkar eRbIR)as;RkLaépÞsuT§ (net area) EdlesμInwgplKuNrvagkRmas;bnÞH nig

TTwgsuT§ (net width). karKNnaRkLaépÞRtUv)aneFVIeLIgdUcteTA³ kMNt;ExSdac;EdlGacekIteLIg)an

edIm,IeFVIkarGegát nig[TTwgsuT§ (net width) esμInwgTTwgdk[
s2
d'= d − (2-1)
4g
sRmab;muxkat;dac;tam staggered hole b¤dk d sRmab;muxkat;dac;tam unstaggered hole. d Ca
Ggát;p©itRbehag s (pitch) CaRbEvgKMlatrvagrn§BIrCitKñatamTisedARsbnwgbnÞúk nig g (gage) Ca
eRKOgbgÁúMrgkarTaj 43 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

RbEvgKMlatRbehagtamTTwg. AISC specification k¾eRbInUvviFIsaRsþdUcKñaenHEdr b:uEnþkñúgTRmg;xus

Kñabnþic. Epñk B2 tRmUv[TTwgsuT§RtUv)anKNnaedaydkplbUkGgát;p©itRbehagBITTwg ehIybUk
2
bEnßmExSeRTt tamCYrmYy²Edlmantémø 4s g .

Figure 3.13

s2
wn = w g − ∑ d + ∑
4g

enAeBlEdlkardac;GacekIteLIgtamTRmg;eRcIn eKRtUveFVIkarGegátRKb;lT§PaBénkardac;TaMg
Gs; ehIy (net width) EdlmantémøtUcCageKbMputRtUv)anykmkeRbI. cMNaMfa viFIsaRsþenHmin)an
pþl;nUvTRmg;nwgkardac;CamYyExSRsbeTAnwgTisedAbnÞúkeFVIGMeBIenaHeT.

]TahrN_TI3>5³ KNna net area EdltUcbMputsRmab;bnÞHEdlbgðajkñúgrUbTI3>14 . RbehagTaMg

Gs;sRmab;b‘ULúgGgát;p©it 25mm .

T.Chhay 44 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Figure 3.14

dMeNaHRsay³ Ggát;p©itRbehagRbsiT§PaB (effective hole diameter) KW 30mm

sRmab;ExSbnÞat; abcd
wn = 410 − 2(30) = 350mm
sRmab;ExSbnÞat; abcde
2(75) 2
wn = 410 − 3(30) + = 341.6mm < 350mm
4(130)
cemøIy³ A n = twn = 20 × 341.6 = 6832mm 2

edaysarEteRKOgP¢ab; (fastener) nImYy²Tb;Tl;kmøaMgesμI²Kña ¬karsnμt;EdleRbIenAkñúgkar

KNnatMNsamBaØ kñúgCMBUkTI 7¦ sñamExSdac;EdlmanlkçN³epSgKña GaceFVI[muxkat;Rtg;kEnøg
dac;rgkmøaMgepSgKña. ]TahrN_ ExS abcde kñúgrUbTI3>14 muxkat;rbs;Ggát;Rtg;kEnøgdac;rgkmøaMg
eBj 100% EdlExS ijfh eFVI[muxkat;rbs;Ggát;Rtg;kEnøgdac;Tb;Tl;Et 8 / 11 énkmøaMgEdl Gnuvtþ.
mUlehtuKW kmøaMg 3 / 11 EdlbBa¢ÚnBIGgát;RtUv)anTb;edayeRKOgP¢ab; munnwg ijfh TTYlbnÞúk.
enAeBlEdl eRKOgP¢ab; (fastener) RtUv)anP¢ab;CaCYrenAelIeCIgTaMgBIrrbs;EdkEkg ehIykar
P¢ab;manlkçN³qøas; (staggered) KñaeTAvijTAmk enaHedIm,ITTYl)anRkLaépÞ net area dMbUgeKRtUv
BnøatEdkEkgedIm,ITTYl)anbnÞHEdksmmUl. bnÞHEdkenHRtUv)anviPaKdUcbnÞHEdkdéTeTotEdr.
karBnøatRtUv)aneFVIeLIgtamRTnugEdkEkgEdlpþl;[nUvTTwgEdkbnÞHesμIeTAnwgplbUkRbEvgeCIgrbs;
eRKOgbgÁúMrgkarTaj 45 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

vadknwgkRmas;EdkEkg. AISC B2 kMNt;faRbEvg g Edlkat;tamRTnugEkgrbs;EdkEkgRtUv)andk

edaykRmas;EdkEkg. dUcenH RbEvg g enAkñúgrUbTI3>15 EdlRtUv)anykeTAeRbIkñúgtY s 2 / 4 g nwgman
témøesμInwg 75 + 50 − 12 = 113mm .

Figure 3.15

]TahrN_TI3>6³ cUrrk design tensile strength rbs;EdkEkgdUcbgðajkñúgrUbTI 3>16. Edk A36

RtUv)aneKykmkeRbIEdlmanRbehagsRmab;b‘ULúg 22mm.
dMeNaHRsay³ KNna net width
wg = 203 + 152 − 12.7 = 342.3mm

Ggát;p©itRbehagRbsiT§PaB effective hole diameter esμI 28mm

sRmab;ExSbnÞat; abdf w = 342.3 − (2 × 28) = 286.3mm
n
2
sRmab;ExSbnÞat; abceg w = 342.3 − (3 × 28) + 4(×3863) .5 = 263.98mm
n

Figure 3.16

T.Chhay 46 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

edaysarEt bnÞúk 1 / 10 RtUv)anepÞrBIGgát;edayeRKOgP¢ab;enARtg;cMNuc d enaHExSrdac;

potential failure line enHRtUvEtTb;nwgbnÞúkEt 9 / 10 . dUcenH net width 263.98mm RtUvEtKuNnwg

10 / 9 edIm,ITTYl)an net width EdlGaceRbobeFobCamYynwgExSbnÞat;EdlTb;nwgbnÞúkeBj 100% .

dUcenHExSbnÞat; abceg man w = 263.98 ×10 / 9 = 293.31mm

n

sRmab;ExSbnÞat; abcdeg
g cd = 76 + 57 − 12.7 = 120.3mm
(38) 2 (38) 2 (38) 2
wn = 342.3 − (4 × 28) + + + = 243.74mm
4 × 63.5 4 × 120 4 × 76
eday net width Edldac;tamExS abcdeg mantémøtUcCageK dUcenHkrNIenHRtUv)aneKykmk
KNna net area
An = 12.7 × 243.74 = 3095.5mm 2
edaysarEteCIgTaMgBIrrbs;EdkEkgRtUv)anP¢ab; dUcenH
Ae = An = 3095.5mm 2
ersIusþg;KNnaKW
φt Pn = 0.75Fu Ae = 0.75 × 400 × 3095.5 = 928.65kN
φt Pn = 0.5Fy An = 0.9 × 250 × 4390 = 987.75kN
cemøIy³ ersIusþg;KNnaKW 928.65kN

cMNaMfa plKuNrvag gross width nwgkRmas;EdkEkgKWCa gross area krNIRtwmRtUvRbsinebI

eCIgrbs;EdkEkgmanragctuekaNEkg. mUlehtuKWfa eKGacTTYl)anragctuekaNEkgedaydképÞ
enARtg;rbt;Ekg nigbUkbEnßmépÞenARtg;cugEdkEkg.
AISC Specification min)anpþl;karENnaMsRmab;karerobeRKOgP¢ab;tamEbbqøas;enAelI

rolled shape eRkABIEdkEkgeT. bnÞHEdksmmUlmanPaBsμúKsμajedaysarkRmas;Ggát;manPaBxus

Kña dUckrNIEdk channel nig wide flange . enAkñúgkrNIEbbenH eKesñI[eRbIRkLaépÞ ¬RbesIrCag

TTWg¦ nigdkGgát;p©itrn§ Edl[edaysmIkar (2-1).
enAkñúg]TahrN_TI3>7 RKb;rn§RbehagTaMgGs;sßitenAEtmYyEpñkénmuxkat;.

eRKOgbgÁúMrgkarTaj 47 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

]TahrN_TI3>7³ kMNt;RkLaépÞmuxkat;suT§Gb,brma (smallest net area) sRmab;Edk American

Standard Channel dUcbgðajenAkñúgrUbTI3>17. RbehagsRmab;b‘ULúgEdlmanGgát;p©it 16mm.

dMeNaHRsay³ A n = Ag − ∑ t w × (d b¤ d')

d = 20mm
ExSbnÞat; abc
An = Ag − t w d = 2460 − 11.1 × 20 = 2238mm 2

ExSbnÞat; abcd
An = Ag − t w (d sRmab;RbehagRtg; b) − t w (d ' sRmab;RbehagRtg; c)
⎡ 50 2 ⎤
= 2460 − 11.1 × 22 − 11.1 × ⎢22 − ⎥ = 2064.1mm
2

⎣⎢ 4 × 75 ⎦⎥
cemøIy³ RkLaépÞmuxkat;Gb,brma (smallest net area) KW 2064.1mm 2

enAeBlEdlEpñkCaeRcInrbs;muxkat;manRbehag eKeRbIviFIsaRsþedaHRsayxusKñabnþic. eTaHbICa

EdkEdlmanrUbragepSgBIEdkEkgminGacBnøattamviFIEdlEdkEkgBnøatk¾eday k¾eKmanviFIsaRsþ
epSgeTotkñúgkarBnøatrUbragEdkTaMgenaHEdr. viFIsaRsþkñúgkarBnøatEdkTaMgenaHRtUv)anbgðajkñúgrUbTI
3>18 nigkñúg]TahrN_TI3>8.

T.Chhay 48 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Figure 3.18

]TahrN_TI3>8³ kMNt;ersIusþg;KNnarbs;Edk S-Shape dUcbgðajkñúgrUbTI3>19. RbehagKWsRmab;b‘U

LúgEdlmanGgát;p©it 20mm . eRbIEdk A36 .

Figure 3.19

dMeNaHRsay³ KNnaRkLaépÞ net area

A = A − ∑ (t × Ggát;p©itRbehag )
n g

Ggát;p©itRbehagRbsiT§PaB = 24mm
sRmab;ExS ad
An = 9470 − 4 × 24 × 15.8 = 7953.2mm 2
2
sRmab;ExS abcd RbEvg g sRmab;eRbIenAkñúgtY 4s g KW
eRKOgbgÁúMrgkarTaj 49 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

g t 89 14
+ g1 − w = + 70 − = 107.5mm
2 2 2 2
edayKitRbehagRtg; b nigRtg; c CaRbehagEdlerobqøas; eKTTYl)an
⎛ 382 ⎞⎟
An = 9470 − 4 × 15.8 × 24 − 2 × 14 × ⎜ 24 − = 7375.23mm 2
⎜ ⎟
4 × 107.5 ⎠
⎝
kardac;tamExS abcd mantémøtUcCageK. edaysarRKb;EpñkTaMgGs;rbs;muxkat;RtUv)anP¢ab; dUcenH
Ae = An = 7375.23mm 2
sRmab; net section
φt Pn = 0.75Fu Ae = 0.75 × 400 × 7375.23 = 2212.57kN
φt Pn = 0.5Fy An = 0.9 × 250 × 9470 = 2130.75kN
cemøIy³ ersIusþg;KNnaKW 2130.75kN

3>5> Block shear

sRmab;rUbsNæanénkartP¢ab;xøH kMNat; b¤bøúkénsmÖar³enAxagcugénGgát;GacrEhk. ]Ta-
hrN_ kartP¢ab;rbs;Ggát;ragEkgeTalrgkarTaj dUcbgðajkñúgrUbTI3>20 gayrg)atuPUtEbbenH Edl
eK[eQμaHfa block shear ¬kardac;TaMgbøúk¦. sRmab;krNIEdl)anbgðajkñúgrUb épÞEdlqUtGac
dac;edaykmøaMgkat;TTwg (shear) tammuxkat;beNþay ab nigkmøaMgTaj (tension) tammuxkat;TTwg
bc. RbFanbT enHmin)anbgðajy:agc,as;kñúg AISC Chapter D (“Tension Members”) eT

b:uEnþkfaxNÐdMbUg )anENnaMeyIgeTAkan; Chapter J (“Connections, Joints, and Fasteners”),

Section J4.3 (“Block Shear Rupture Strength”).

nitiviFIKWQrenAelIkarsnμt;fa muxkat;dac;mYyKWdac;eday fractures nigmYyeTotdac;eday

yielding. enHmann½yfa muxkat;EdlrgkugRtaMgTaj yield naM[muxkat;EdlrgkugRtaMgkmøaMgkat;

TTwg fracture b¤pÞúymkvij. muxkat;TaMgBIrenH naMmknUvPaBFn;srub ehIyersIusþg;rbs; block shear

KWCaplbUkénPaBFn;énmuxkat;TaMgBIr.
PaBFn;Fmμta (nominal strength) enAkñúgGgát;rgkarTajKW Fu Ant sRmab; fracture nig
Fy Agt sRmab; yield Edl Ant KWCa net area nig Agt KWCa gross area tambeNþaymuxkat;rgkar

Taj ¬ bc enAkñúgrUbTI3>20¦. edayykkugRtaMg yield sRmab;møaMgkat; nigkugRtaMg ultimate sRmab;

T.Chhay 50 Tension Members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Figure 3.20

kmøaMgkat;esμI 60% énkugRtaMgkmøaMgTaj enaHersIusþg;dac;Fmμta (nominal fracture strength) sRmab;

kmøaMgkat;KW 0.6Fu Anv nigersIusþg; yield sRmab;kmøaMgkat;KW 0.6Fy Agv Edl Anv KWCa net area nig
Agv KWCa gross area tambeNþaymuxkat;rgkmøaMgkat; ¬ ab enAkñúgrUbTI20¦.

eKGacmanTRmg;énkardac;Ca2rebob.
sRmab;kmøaMgkat; yield nigkmøaMgTaj fracture ersIusþg;KNnaKW
φRn = φ[0.6 Fy Agv + Fu Ant ] (AISC Equation J4-3a)

sRmab;kmøaMgTaj yield nigkmøaMgkat; fracture ersIusþg;KNnaKW

φRn = φ[0.6 Fu Anv + Fy Agt ] (AISC Equation J4-3a)

sRmab;krNITaMgBIr φ = 0.75 . BIeRBaH sßanPaBkNt; (limit state) KW fracture smIkarEdl

lub KWsmIkarNaEdlmantY fracture FMCag.
]TahrN_TI3>9³ kMNt;ersIusþg; block shear rbs;Ggát;rgkarTajdUcbgðajenAkñúgrUbTI
3>21. rn§RbehagRtUv)aneRbIsRmab;Ggát;p©it 22mm nigEdkRbePT A36RtUv)aneRbI.
dMeNaHRsay³
RkLaépÞmuxkat;kmøaMgkat;KW
Agv = 9.5 × 190 = 1805mm 2

eRKOgbgÁúMrgkarTaj 51 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Figure 3.21

edaysarEtman 2.5 Ggát;p©itrn§

Anv = 9.5 × [190 − 2.5 × 28] = 1140mm 2
RkLaépÞmuxkat;kmøaMgTaj
Agt = 9.5 × 39 = 370.5mm 2

Ant = 9.5 × [39 − 0.5 × 28] = 237.5mm 2

edayeRbI AISC Equation J4-3a eKTTYl)an
φRn = φ[0.6 Fy Agv + Fu Ant ]

= 0.75 × [0.6(250 )(1805) + 400 × 237.5]

= 0.75 × [270750 + 95000] = 274.3kN

edayeRbI AISC Equation J4-3b eKTTYl)an
φRn = φ[0.6 Fu Anv + Fy Agt ]

= 0.75 × [0.6(400 )(1140 ) + 250 × 370.5]

= 0.75 × [273600 + 92625] = 274.7kN

smIkarTI 2 mantY fracture FM ¬tYEdlman F ¦ dUcenHsmIkarTI 2 lub.
u

cemøIy³ ersIusþg;KNnasRmab; block shearKW 274.7kN .

3>6> karKNnaGgát;rgkarTaj Design of tension members

karKNnaGgát;rgkarTaj KWkarKNnark gross area nig net area RKb;RKan;sRmab;Ggát;Edl
rgkarTaj. RbsinebIGgát;enaHRtUv)anP¢ab;edaytMNb‘ULúg enaHeKRtUvkarnUvmuxkat;smRsbsRmab;Rk
T.Chhay 52 Tension Members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

LaépÞEdl)an)at;bg;edaysarrn§tMN. sRmab;Ggát;Edlmanmuxkat;ctuekaNEkg karKNnaman

lkçN³RsYlCag. RbsinebImuxkat; rolled shape RtUv)aneRbImuxkat;EdlRtUvkat;bnßyminGacRtUv)an
BüakrN_TukCamun)an BIeRBaHkRmas;rbs;muxkat;enARtg;cMNucrn§minRtUv)andwg.
karBicarNabnÞab;kñúgkarKNnaGgát;rgkarTajKW PaBrlas; (slenderness). RbsinebIGgát;
rbs;eRKagbgÁúMmanmuxkat;tUceFobeTAnwgRbEvgrbs;va enaHGgát;enaHmanlkçN³Rsav (slender). kar
KNnaEdlmanlkçN³suRkit KWpleFobrlas; (slenderness ration) RL Edl L CaRbEvgrbs;Ggát;
nig r Ca kaMniclPaB (radius of gyration) énRkLaépÞmuxkat;Gb,brma. kaMniclPaB (radius of
gyration) Gb,brma KWRtUvKñanwgG½kS minor principal énmuxkat;. témørbs; radius of gyration

RtUv)anerobCataragsRmab;muxkat; rolled shape TaMgGs;enAkñúgtaraglkçN³ (properties tables)

enAkñúgEpñkTI1 én Manual.
sRmab;Ggát;rgkarsgát; slenderness mansar³sMxan;sRmab;ersIusþg; (strength) b:uEnþ slender-
ness minsUvCasMxan;sRmab;Ggát;rgkarTajb:unμaneT. eTaHCay:agNak¾eday enAkñúgsßanPaBxøH vaCa

karRbesIrsRmab;karkMNt;nUv slenderness sRmab;Ggát;rgkarTaj. RbsinebIbnÞúkcMG½kSenAkñúg Ggát;

rgkarTajRsav (slender tension member) ehIyrgbnÞúktamTTwg (transverse load) eTaHtUckþI
k¾rMjr½EdleKminR)afñacg;)an b¤PaBdabnwgekItmaneLIg. Ca]TahrN_ krNIenHGacekIteLIgsRmab;
EdkBRgwg (bracing rod) EdlmanlkçN³mintwgRbQmnwgkmøaMgxül;. sRmab;krNIenH AISC B7
)anesñInUv slenderness ratio GtibrmaesμInwg 300. témøenHRKan;EtCatémøesñI (commended value)
BIeRBaH slenderness minmanPaBsMxan;sRmab;Ggát;rgkarTajeT ehIytémøenHGacRtUv)anykFMCag
enHenAeBlEdlkal³eTs³BiessGnuBaØat[. EdntémøenHminRtUv)anGnuvtþeTAelIExSkabeT ehIy
specification k¾)anelIkElgcMeBaHEdksrésEdr.

bBaðasMxan;kñúgkarKNnaRKb;muxkat;TaMgGs; rYmbBa©ÚlTaMgkarKNnaGgát;rgkarTaj KWkarrk

muxkat; EdlplbUkbnÞúkemKuNTaMgGs;mni RtUvelIsersIusþg;rbs;Ggát;. Edl
∑ γQ ≤ φRn

sRmab;Ggát;rgkarTaj smIkarenHmanrag

eRKOgbgÁúMrgkarTaj 53 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Pu ≤ φt Pn b¤ φt Pn ≥ Pu

Edl Pu KWCaplbUkbnÞúkemKuN. edIm,IKNna yielding

0.9 Fy Ag ≥ Pu b¤ Ag ≥
Pu
0.90 Fy

edIm,IeCosvag fracture
0.75Fu Ae ≥ Pu b¤ Ae ≥
Pu
0.75Fu

Slenderness ratio RtUv)anbMeBjRbsinebI

L
r≥
300

Edl r Ca radius of gyration Gb,brma nig L CaRbEvgGgát;.

]TahrN_TI3>10³ Ggát;rgkarTajEdlmanRbEvg 1750mm RtUvTb;nwgbnÞúkefreFVIkar (service dead

load) 80kN nigbnÞúkGefreFVIkar (service live load) 233kN . eRCIserIsGgát;Edlmanmux

kat;ctuekaNEkg. eRbIEdk A36 nigtMNRtUv)ansnμt;eRbIb‘ULúgEdlmanGgát;p©it 24mm mYyCYr.

dMeNaHRsay³
Pu = 1.2 × 80 + 1.6 × 233 = 468.8kN
468.8 ⋅ 103
muxkat;caM)ac; A g =
Pu
0.9 Fy
=
0.9 × 250
= 2083.6mm 2

.8 ⋅ 10 3
muxkat;caM)ac; A = 0.75P F = 468
e
u
0.75 × 400
= 1562.7mm 2
u

edaysarEt A = A sRmab;Ggát;enH gross area EdlRtUvKñanwg muxkat;caM)ac; net area

e n

enHKW
Ag = An + Ahole

= 1562.7 + 28 × t

T.Chhay 54 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

sakl,g t = 25mm
Ag = 1562.7 + 28 × 25 = 2262.7mm 2

edaysarEt 2262.7 > 2083.6 dUcenHmuxkat;caM)ac;KW 2262.7mm 2

Ag 2262.7
wg = = = 90.5mm
t 25
sakl,gmuxkat; 25 × 92
epÞógpÞat; slenderness ratio
92 × 253
I min = = 119791.7mm 4
12
A = 25 × 92 = 2300
BI I = Ar eyIgTTYl)an
2

I min 119791.7
rmin = = = 7.22mm
A 2300
L 1750
= = 242.4 < 300 (OK)
r 7.22
cemøIy³ eRbIEdkEdlmanmuxkat; 25 × 92 .

Ggát;enAkñúg]TahrN_TI3>10 manTTwgtUcCag 20mm EdlRtUv)aneKcat;fñak;vaCaEdkr)ar

(bar) CaCagEdkbnÞH (plate). Edkr)arKYrRtUv)ankMNt;eday[TTwgrbs;vaERbRbYlmþg 5mm nig

kRmas;rbs;vaERbRbYlmþg 2mm ¬RbB½n§cMNat;fñak;Cak;lak;RtUv)anpþl;[kñúgEpñkTI1 én Manual

eRkamcMNgeCIg “Bars and Plates”.
RbsinebIEdkEkgRtUv)aneRbICaGgát;rgkarTaj ehIykartP¢ab;RtUv)aneFVIeLIgedayeRbIb‘ULúg
enaHvacM)ac;RtUvmanépÞ ¬TMhM¦ RKb;RKan;sRmab;b‘ULúg. vaGacekItmanbBaðaenAeBlEdleKeRbIb‘ULúgBIr
CYrenAelIeCIgmYy. rn§RbehagRtUv)aneKecaHenATItaMgdUcbgðajenAkñúgrUbTI3>22 (a) sRmab;karplit
TUeTA eday)andkecjBIrUbTI 9-5 enAkñúgEpñkTI9 én Manual (VOL. II). cmøayKMlat Rbehag
tamTTwg gage g1 RtUv)aneKeRbIenAeBlEdleKmanb‘ULúgmYyCYr ehIy g 2 nig g3 RtUv)aneKeRbIenA
eBlEdleKmanb‘ULúgBIrCYr. rUbTI3>22 (b)bgðajfaeCIgEdkEkgRtUvmanRbEvgy:agxøIbMput 127mm
edIm,IGnuBaØat[eRbIb‘ULúgBIrCYr)an.

eRKOgbgÁúMrgkarTaj 55 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Figure 3.22

KMlatRbehagtamTTWgsRmab;EdkEkg (mm)
Leg 203 178 152 127 102 89 76 64 51 44 38 35 32 25
g1 114 102 89 76 64 51 44 35 26 25 22 22 19 16
g2 76 64 57 51
g3 76 76 64 44

(b)

]TahrN_TI3>11³ KNnaGgát;rgkarTajEdlmanmuxkat;EdkEkgeCIgminesμIKña (unequal-leg angle)

RbEvg 4.6m Tb;nUv service dead load 155kN nig service live load 310kN . eRbIEdkRbePT
A36 . kartRtUv)anbgðajenAkñúgrUbTI23.

Figure 3.23

dMeNaHRsay³
bnÞúkemKuN (factored load) P
u = 1.2 D + 1.6 L = 1.2(155) + 1.6(310) = 682kN

T.Chhay 56 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

nigmuxkat;caM)ac; Ag =
Pu
=
682
φt Fy 0.9(250)
= 3031.1mm 2

ehIymuxkat;caM)ac; A = φPF = 0.75682(400) = 2273.3mm

e
u 2
t u

kaMniclPaB (radius of gyration) KYrmantémøy:agtUcbMput

L 4600
r= = = 15.33mm
300 300
edIm,IrknUvmuxkat;RsalbMputsRmab;bMeBjlkçxNÐTaMgenH eyIgrkEdk (unequal-leg angle) Edlman
RkLaépÞeBj (gross area) EdlGacTTYlyk)anmantémøtUcbMput rYcehIyepÞógpÞat; effective net
area. kaMniclPaB (radius of gyration) k¾GacRtUv)anepÞógpÞat;edaykarRtYtBinitüpgEdr. eday

sarkarteFVIeLIgedaymanb‘ULúgBIrCYr enaHeCIgEdlRtUv)aneFVIkartP¢ab;RtUvmanTTwgtUcbMput 127mm

¬emIlkñúgtaragKMlatRbehagtamTTWgsRmab;EdkEkg rUbTI3>22¦. eyIgcab;epþImBItaraglkçN³
sRmab;EdkEkgeTal (table of properties for single angle) enAkñúgEpñkTI1 én Manual nigerobnUv
muxkat;EdkRsalCageKtamlMdab;BItUceTAFM ¬minEmnlMdab;dUcKñaenAkñúgtarageT¦. muxkat;xageRkam
GacRtUv)anerob.
L152 × 102 × 12.7 : A = 3060mm nig r = 22.1mm
g
2
min

L127 × 89 × 15.9 : A = 3180mm nig r = 20mm

g
2
min

L 203 × 102 × 11.1 : A = 3300mm nig r = 22.1mm

g
2
min

L178 × 102 × 12.7 : A = 3400mm nig r = 22.15mm

g
2
min

¬cMNaMfa sRmab;EdkEkg G½kS X nig Y Edl)anbgðajenAkñúgtaragminEmnCaG½kSem (principal

axes)eT EtG½kS Z eTIbCaG½kSem (principle axis) r = r . EtsRmab;EdkEkgDub (double-angle
min z

shape) G½kS X nig Y KWCaG½kSem.¦

sakl,g L152 × 102 × 12.7 . muxkat;enHman gross area EdlRtUvKñaBitR)akdeTAnwgRkLaépÞcaM)ac;

¬RbesIrCagmuxkat;bIeTot RkLaépÞrbs;vaRtUv)an[enAkñúgtarag¦.
An = Ag − Aholes = 3060 − 2(24)(12.7 ) = 2450.4mm 2

edaysarRbEvgtminRtUv)andwg AISC Eq. B3-2 minGacRtUv)aneKeRbIedIm,IKNna shear lag factor

U . dUcenH eyIgeRbI U = 0.85 / témømFümEdl)anBI Commentary. ¬]TahrN_TI8 kñúgCMBUkTI 7

tMNsamBaØbgðajlMGitGMBItMN nigtémø U mFümGacRtUv)aneKeRbIedIm,ITTYl)annUvmuxkat;sakl,g

eRKOgbgÁúMrgkarTaj 57 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

bnÞab; témø U BI AISC Eq. B3-2 GacRtUv)aneKKNna¦.

Ae = UAn = 0.85 × 2450.4 = 2082.84mm 2 < 2273.3mm 2 ¬minl¥ N.G.¦
sakl,g L127 × 89 × 15.9
An = 3180 − 2(24)(15.9) = 2416.8mm 2
Ae = 0.85 × 2416.8 = 2054.28mm 2 < 2273.3mm 2 ¬minl¥ N.G.¦
eTaHbICamuxkat;enHman gross area FMCagmuxkat;munk¾eday Etvamin)anbegáIn net area eT. mUlehtu
KWRkLaépÞEdlRtUvdksRmab;rn§mantémøFM edaysarEtkRmas;eCIg.
sakl,g L203 × 102 × 11.1
An = 3300 − 2(24)(11.1) = 2767.2mm 2
Ae = 0.85 × 2767.2 = 2352.12mm 2 > 2273.3mm 2 (OK)
cemøIy³ muxkat;enHbMeBjRKb;lkçxNÐtRmUvkar dUcenHeRbI L203 × 102 × 11.1 ttameCIgEdlman
RbEvg 203mm .

enAeBlEdlEdkrag (structural shape) b¤EdkbnÞHRtUv)aneRbIedIm,IpÁúMCa built-up shape vamin

RtwmEtRtUv)anpÁúMenAEtxagcugGgát;b:ueNÑaHeT b:uEnþvak¾RtUv)anpÁúMenAcenøaHtamRbEvgbeNþayrbs;vapg
Edr. eKminRtUvkarkarpÁúMEdlmanlkçN³Cab;rhUteT. karpÁúMEbbenHRtUv)aneKehAfa stitching ehIy
eRKOgP¢ab;rbs;vaRtUv)aneKehAfa stitch bolts. karGnuvtþTUeTAKWkMNt;TItaMg stitching Edl L / r sM
rab;EpñkpÁúMnImYy² minelIs L / r sRmab;muxkat; built-up. AISC D2 ENnaMfa Edkrag built-up Edl
EpñkpÁúMrbs;vaRtUv)anEckeday filler EdlRtUv)aneRbIsRmab;P¢ab;enAcenøaH filler enaH témøGtib,rma
L / r sRmab;EpñkmYy²minRtUvelIs 300. Edkrag built-up EdlekIteLIgedayEdkbnÞH b¤edaykarpÁúM

rvagEdkbnÞH nigEdkragRtUv)aneBalenAkñúg AISC Section J3.5 of Chapter J (“Connections joints,

and Fasteners”). CaTUeTA KMlatrbs;eRKOgP¢ab; b¤karpSarminKYrelIs 24dg énkRmas;EpñkesþIgbMput

rbs;bnÞHEdk b¤ 300mm . RbsinebIGgát;CaEdk weathering EdlsßitenAkñúgbriyakasgayrgERcHsIu

enaHKMlatGtibrmaKW 24dg énkRmas; b¤ 175mm .

T.Chhay 58 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

3>7> EdksrésEdlmaneFμj nigExSkab Threaded rods and Cables

enAeBl slenderness minRtUv)anBicarNaEdksrés rod Edlmanmuxkat;mUl nigExSkab
(cable) RtUv)aneKeRbIR)as;CaTUeTAsRmab;Ggát;rgkarTaj. Edksrés nigExSkabxusKñaRtg; Edk

sréstan; EtExSkabekItBIExSlYskabCaeRcInv½NÐbBa©ÚlKñaehIymanrUbragdUcExSBYr. Edksrés nig

ExSkab RtUv)aneKeRbICaerOy²sRmab;RbB½n§dMbUlBüÜr k¾dUcCa hanger nig suspension member
sRmab;s<an. Edksrésk¾RtUv)aneRbIenAkñúgRbB½n§ bracing enAkñúgkrNIxøH vaRtUv)aneKeFVIeRbkugRtaMg
edIm,IkarBarvaBIPaBrlg; (slack) enAeBlEdlbnÞúkxageRkARtUv)andk. rUbTI3>24 bgðajBIviFItEdk
srés nigExSkabKMrU.
enAeBlcugmçagrbs;EdksrésRtUv)aneFVI[maneFμj (thread) eBlenaH upset end RtUv)an
eRbI. EpñkEdlmaneFμjRtUv)ankat;ecjedIm,IBRgIkmuxkat;. enAkEnøgeFμj muxkat;EdkRtUv)ankat;
bnßy EtkareFVI upset end )anbegáInmuxkat;Edk[FM. tambTdæan upset end EdlmaneFμj CaTUeTA
man net area enARtg;kEnøgeFμj eRcInCagRtg;EpñkEdlKμaneFμj. eTaHCa upset end mantémøéføk¾
eday EteKk¾mincaM)ac;eRbIvaRKb;krNIeT.
RkLaépÞmuxkat;RbsiT§PaB (effective cross-sectional area) enARtg;EpñkeFμjRtUv)aneK[
eQμaHfa stress area ehIyvaCaGnuKmn_eTAnwgGgát;p©it unthreaded nigcMnYneFμjkñúg 1inch . pleFob
rvag stress area nig nominal area ERbRbYl b:uEnþvamantémøtUcbMputRbEhl 0.75 . dUcenH ersIusþg;
rgkarTaj nominal rbs;Edk threaded GacRtUv)ansresrdUcxageRkam³
Pn = As Fu

= 0.75 Ab Fu

Edl As = stress area

Ab = nominal (unthreaded) area
smIkarenHpþl; nominal strength EdlRtUv)anbgðajenAkñúgtarag Table J3.2 enAkñúg Section
J3.6 én AISC Specification. emKuNersIusþg; (resistance factor) enAkñúgkrNIenH φt = 0.75 .

RbsinebI upset end RtUv)aneKeRbI enaHlT§PaBrgkarTajenAGgát;eFμjEdlFMRtUvFMCag Fy KuNnwg

unthreaded body area (AISC Table J3.2, footnote c).

eRKOgbgÁúMrgkarTaj 59 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Figure 3.24

]TahrN_TI3>12³ Edk threaded RtUv)aneKeRbICaGgát;sRmab;BRgwgEdlRtUvEtTb;Tl;nwg

service tensile load EdlbnÞúkefr 9kN nigbnÞúkGefr 26.5kN . etIGgát;p©itEdkTMhMb:uNÑaRtUv)aneRbI

RbsinebIeKeRbI A36?
dMeNaHRsay³ bnÞúkemKuN (factored load)
Pu = 1.2(9) + 1.6(26.5) = 53.2kN
edaysar φ P ≥ P
t n u

φt (0.75Fu )Ag ≥ Pu

muxkat;caM)ac; A g =
Pu
=
53.2
φt (0.75)Fu 0.75(0.75)400
= 236.44mm 2

BI A = πd4
2
g

Ggát;p©itcaM)ac; d = 4 × 236
π
.44
= 17.35mm

cemøIy³ eRbIEdk threaded EdlmanGgát;p©it 18mm (A g = 254.47mm2 ).

edIm,IkarBarkarxUcxatkñúgeBlsagsg; EdksrésminRtUvRsav b¤rlas; (slender) eBkeT.

eTaHbIminmankarTamTarBI specification k¾eday EtsRmab;karGnuvtþTUeTA Ggát;p©itGb,brmaEdlRtUv
eRbI RtUvmantémø 16mm .
T.Chhay 60 Tension Members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

ExSkabkñúgrUbragCa strands b¤ wire rope RtUv)aneKeRbIenAkñúgkarGnuvtþEdlTamTar high

strength EtPaBrwg (rigidity) minmanlkçN³sMxan;eT. bEnßmBIelIkareRbIR)as;vaenAkñúgRbB½n§s<anBüÜr

nigdMbUl vak¾RtUv)aneKeRbIenAkñúgeRKOgelIkdak;dUcCa hoist nig derrick EdleKeRbIvadUcCaExSeyag

sRmab;GKarx<s;² nigsRmab;BRgwgtambeNþayenAkñúgGKarEdleFVIBIEdk. PaBxusKñarvag strand nig
wire rope KWbgðajenAkñúgrUbTI3>25. Strand CakarrYmpSMKñaénsréslYsCaeRcInrMuv½NÐKña ehIy wire

rope CakarrYmpSMKñaén strand CaeRcInrMuv½NÐKña.

kareRCIserIsExSkabEdlRtwmRtUvsRmab;bnÞúkEdl[CaTUeTAQrenAelIkarBicarNaGMBI ersIu
sþg; (strength) nigkMhUcRTg;RTay (deformation). bEnßmBIelIsac;lUteGLasÞicFmμta karlUtdMbUg
EdlbNþalmkBI seating b¤ shifting énsréslYsmYy² EdlCalT§plvaeFVI[ExSkabmankarlUt
Gcié®nþy_. sRmab;mUlehtuenH CaTUeTAExSkabRtUv)aneKTajBnøÚtmun (prestretched). Wire rope
nig strand RtUv)aneKpliteLIgBIEdkEdlmanesIusþg;x<s;CagEdksMNg;Fmμta ehIyminmanEcgenAkñúg
AISC Specification eT. ersIusþg;dac;rbs;ExSkabnImYy² k¾dUcCakarlMGitBIkarttMNr GacTTYl)an

BI manufacturer’s literature. Tinñn½ymanRbeyaCn_sRmab;RbePTenHmanenAkñúg Cable Roof

structures (Bethlehem Steel, 1968).

3>8> Ggát;rgkarTajenAkñúgdMbUl Tension members in roof trusses

Ggát;rgkarTajCaeRcInEdlvisVkrKNna CaeRKOgbgÁúM trusses. enAeBleRKOgbgÁúM trusses
RtUv)aneRbIR)as;enAkñúgsMNg; CaTUeTAvamannaTIcbM gkñúgkarRTRbB½n§dMbUlEdleKRtUvkarElVgEvg. va
RtUv)aneKykmkeRbIenAeBlEdléfø nigTm¶n;Fñwmmantémøx<s;. ¬eRKOgbgÁúM trusses RtUv)anKitCaFñwm
CeRmA (deep beam) EdlykecjnUvEpñénRTnugy:ageRcIn¦. dMbUl trusses RtUv)aneRbICaerOy²enAkñúg
eRKOgbgÁúMrgkarTaj 61 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

sMNg;shRKas eTaHbICasMNg;RbePTenHRtUvkareRKagrwg (rigid frame) k¾eday. dMbUl trusses KMrU

EdlRTeday load-bearing wall RtUv)anbgðajenAkñúgrUbTI 3>26. sMNg;RbePTenH CaTUeTA cugmçag
rbs; trusses EdlP¢ab;eTAnwgCBa¢aMgRtUv)aneKKitCaTRm pinned nigTRmmçageTotRtUv)aneKKitfaCa
TRm roller. dUcenH trusses GacRtUv)aneKviPaKCaeRKOgbgÁúMsþaTickMNt;. CBa¢aMgEdlCaTMrGaceFVIBI
ebtugBRgwgedayEdk bøúkebtug \dæ b¤bnSMénsmÖar³TaMgenH.
CaFmμta dMbUl trusses EtmanKMlatesμIKñatambeNþayGKar nigcgP¢ab;KñaeTAvijeTAmkeday
sarFñwmbeNþayEdleKehAfa édrENg (purlin) nigedayEdkExVg (X-bracing). tYnaTIcMbgrbs;éd
rENgKWbBa¢ÚnbnÞúkeTAGgát;xagelI (top chord) rbs; trusses b:uEnþvak¾GaccUlrYmedayEpñkxøHkñúgkar
BRgwgRbB½n§. CaTUeTAEdkBRgwg (bracing) RtUv)andak;enAkñúgbøg;énGgát;xagelI nigGgát;xageRkam
b:uEnþvamincaM)ac;enARKb;ElVg (bay) TaMgGs;eT edaysarkmøaMgxag (lateral forces) GacRtUv)anbBa¢ÚnBI
ElVgEdlTb;mYyeTAElVgEdlTb;mYyeTot edaysarédrENg.
vaCakarRbesIrbMputEdlédrENgRtUv)andak;enAelItMNrbs; trusses. dUenH trusses Gac
RtUv)anKitCaeRKOgbgÁúMtMNsnøak; (pin-connected structure) EdlRTbnÞúkEtRtg;tMN. EteBlxøH
kRmaldMbUlminGaclatsn§WgelIcmøayrvagtMN dUcenHeKRtUvkarédrENgkNþal (intermediate
purlin). enAkñμúgkrNIEbbenHGgát;xagelInwgrgm:Um:g;Bt;FM k¾dUcCakmøaMgsgát;tamG½kS (axial
compression) ehIy vaRtUv)aneKKNnaedayKitCa Fñwm-ssr (beam-column) EdlmanBnül;kñúg

CMBUkTI6.
Sag rod CaGgát;rgkarTajEdlRtUv)aneRbIedIm,Ipþl;TRmxagsRmab;édrENg. bnÞúkPaKeRcIn

EdlGnuvtþmkelIédrENgmanTisQr dUcenHvanwgmanbgÁúMkmøaMgRsbeTAnwgmMuCMraldMbUlEdlnwgeFVI
[édrENgekagenAkñúgTisedAenaH ¬rUbTI 3>27¦. Sag rod GacRtUv)andak;enAcMNuckNþal b¤
cMNucmYyPaKbI b¤GacjwkenAtambeNþayédrENg GaRs½yeTAnwgcMnYnTRmEdlRtUvkar. KMlatrbs;
sag rod CaGnuKmn_eTAnwgKMlat trusses, mMuCMralrbs;Ggát;xagelI/ ersuIsþg;rbs;édrENgTb;nwg

karBt;RbePTenH ¬rUbragPaKeRcInrbs;EdkEdleRbICaédrENgmanlkçN³exSayNas;sRmab;karBt;
tamTisenH¦ nigcMnYnTRmEdlpþl;edaydMbUl. RbsinebIeKeRbI bnÞHEdk CaTUeTAvaRtUv)aneKP¢ab;y:ag
rwgCamYyédrENg dUcenHeKmincaM)ac;RtUvkar sag rod eT. EteBlxøH EtTm¶n;pÞal;rbs;édrENgKWva
RKb;RKan;kñúgkarbgábBaðaenH dUcenHeKcaM)ac;dak; sag rod edIm,IRT kñúgGMLúgeBlsagsg;muneBldak;
T.Chhay 62 Tension Members
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kRmaldMbUl.

eRKOgbgÁúMrgkarTaj 63 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

RbsinebIeKeRbI sag rod eKcaM)ac;KNnavaedIm,IRTbgÁMúbnÞúkdMbUlEdlRsbeTAnwgdMbUl. Ggát;

nImYy²cenøaHédrENgRtUv)ansnμt;[RTGVI²TaMgGs;BIxageRkamva dUcenHGgát;xagelIRtUv)anKNna
sRmab;bnÞúkenAelIépÞdMbUlEdlmanGMeBIelIGgát;enaH BIcugdMbUldl;kMBUldMbUldUcbgðajenAkñúg rUbTI
3> 28. eTaHbICakmøaMgenAkñúgGgát;nImYy²xusKñak¾eday EtCakarGnuvtþTUeTAeKeRbITMhMEtmYysRmab;
RKb;Ggát; sag rod enaH. kareRbIR)as;nUvmuxkat;dUcKñasRmYldl;kargarsagsg; ÉbrimaNEdkelIs
minCaFMb:unμaneT.

rUbTI 3>29 a bgðajBIkarcgP¢ab;édrENgenARtg;RBMdMbUl. Tie rod cenøaHédrENgxagRtUvTb;

nwgbnÞúkBIRKb; sag rod TaMgGs;EdlenAsgçagsøabdMbUl. kmøaMgTajenAkñúgGgát;edkmYyCabgÁúMkmøaMg
rbs;Ggát; sag rod EdlenAxagelI. düaRkamGgÁesrI (free-body diagram) rbs;édrENgkMBUl
RtUv)anbgðajenAkñúgrUbTI 3>29 b .

]TahrN_TI3>13³ Fink trusses EdlmanKMlat 6m KitBIG½kSeTAG½kS ehIyRTédrENg

W 150 × 0.18 dUcbgðajenAkñúgrUbTI 3>30 a. édrENgRtUv)anRTeday sag rod enAcMNuckNþal.

edayeRbIEdk A36 KNna sag rod nig tie rod enAédrENgkMBUlsRmab;bnÞúk service load dUcxag
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eRkam³
kRmaldMbUlEdk (metal deck)³ 0.1kN / m 2

Built-up roof: 0.25kN / m 2

RBwl³ 0.85kN / m elIbøg;edk
2

Tm¶n;édrENg³ 0.18kN kñúgmYyEm:RtRbEvg

dMeNaHRsay³
KNnabnÞúk³
TTwgrgbnÞúksRmab; sag rod nImYy² = 6m / 2 = 3m
RkLaépÞrgbnÞúksRmab;kRmaldMbUl nig Built-up roof = 3 ×14 = 42m 2

bnÞúkefr ¬kRmaldMbUl nig Built-up roof¦ = (0.1 + 0.25) × 42 = 14.7kN

Tm¶n;édrENgsrub = 0.18 × 3 × 9 = 4.86kN
bnÞúkefrsrub = 14.7 + 4.86 = 19.56kN
épÞrgbnÞúkRBwl = 3 ×13.6 = 40.8m 2

bnÞúkRBwlsrub = 34.68kN
eRKOgbgÁúMrgkarTaj 65 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

RtYtBinitübnSMbnÞúk³
(A4-2)³ 1.2 D + 0.5S = 1.2 × 19.56 + 0.5 × 34.68 = 40.8kN

(A4-3)³ 1.2 D + 1.6 S = 1.2 × 19.56 + 1.6 × 34.68 = 79kN

bnSMbnÞúk A4-3 lub. ¬tamkarGegát A4-1, A4-4 nig A4-5 nwgminmantémøFMeT¦.

sRmab;bgÁMúkmøaMgRsbeTAnwgépÞdMbUl ¬rUbTI 3>30 b¦
3.6
T = 79 = 20.3kN
14

muxkat;EdkEdlRtUvkar A = φ (0.T75F ) = 0.7520(0..375⋅10× 400) = 90.2mm

3
2
g
t u

cemøIy eRbIEdk threaded rod Ggát;p©it 16mm ¬ A = 201mm ¦

g
2

Edk tie rod EdlP¢ab;édrENgenARBMdMbUl ¬rUbTI 3>30 c¦

14
P = 20.3 = 20.9kN
13.6

muxkat;EdkEdlRtUvkar A = φ (0.T75F ) = 0.7520(0..375⋅10× 400) = 90.2mm

3
2
g
t u

cemøIy eRbIEdk threaded rod Ggát;p©it 16mm ¬ A = 201mm ¦

g
2

sRmab;ragFrNImaRtrbs; truss nigkardak;bnÞúk Ggát;xageRkam (bottom chord) nwgrgkug

RtaMgTaj ehIyGgát;xagelI (top chord) nwgrgkugRtaMgsgát;. Ggát;RTnugxøHrgkugRtaMgTaj nigxøH
eTotrgkugRtaMgsgát;. enAeBleKbBa¢Úl\T§iBlxül;kñúgkarviPaK Tisxül;epSgKñaRtUv)aneKykmk
BicarNa eBlenaHkmøaMgenAkñúgGgát;RTnug (web member) xøHGacnwgERbRbYlcenøaHkugRtaMgsgát;
nigkugRtaMgTaj. kñúgkrNIEbbenH Ggát;EdlrgGMeBIRtUv)anKNnaeday[mannaTICaGgát;rgkarsgát;
pg nigrgkarTajpg.
sRmab; truss Edlcab;b‘ULúg (bolted truss) muxkat;EdkEkgDub (double-angle section)
RtUv)aneRbICajwkjab;sRmab;Ggát;xagelI (top chord) nigGgát;RTnug (web member) . karKNnaenH
sRmYldl;karP¢ab;Ggát;EdlCYbKñaenARtg;dMNedayGnuBaØatnUvkareRbIR)as;bnÞHEdkeTal (single
gusset plate) dUcbgðajenAkñúgrUbTI 3>31. enAeBlGgát;xagelIrbs;eRKOgbgÁúM truss EdlpSareRbI

Edkmuxkat;GkSret EdkRTnugEdlmanmuxkat;EdkEkgGacpSarP¢ab;CamYyeCIg (stem) rbs;Edkmux

kat;GkSret. RbsinebI kmøaMgenAkñúgGgát;RTnug (web member) mantémøtUc eKGaceRbIEdkEkgeTal
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(single angle) ebIeTaHbIkareFVIkarEbbenaH)ankat;bnßybøg;sIuemRTIBI truss ehIybNþal[Ggát;RTnug

rgbnÞúkcakp©itk¾eday. CaTUeTAGgát;xagelI nigGgát;xageRkam (chord member) CaGgát;Cab; ehIy
eKGackat;vaCakMNat;²RbsinebIcaM)ac;.

CakarBitEdlfa chord member CaGgát;Cab; ehIytMNRtUv)ancab;b‘ULúg b¤pSarEdleKmin

Gacsnμt;fa truss CaeRKOgbgÁúMtMN pin-connected )aneT. PaBrwgrbs;tMNBitCanaMmknUvm:Um:g;Bt;enA
kñúgGgát; b:uEnþCaTUeTAvamantémøtUc ehIyRtUv)anBicarNavaCakmøaMgrg (secondary effect) dUcenH
kñúgkarGnuvtþTUeTAeK)anecalva. EtkarBt;EdlbNþaledaysarbnÞúkxageRkAEdlGnuvtþedaypÞal;
eTAelIGgát;cenøaHtMN RtUvEtykmkKitBicarNadac;xat. eyIgKitkrNIenHenAkñúgemeronTI 6.
ExSeFVIkar (working line) énGgát;rbs;eRKOgbgÁúM truss TaMgGs;RtUvkat;KñaRtg;tMNnImYy².
sRmab; truss EdlP¢ab;edayb‘ULúg CYrrbs;b‘ULúg (bolt line) Ca working line ehIysRmab; truss pSar
G½kSTIRbCMuTm¶n;rbs;TwkbnSarCa working line. karsnμt;kñúgdMeNIrkarviPaK truss RbEvgGgát;RtUv)an
vas;BIcMNuceFVIkar (working point) eTA working point.

]TahrN_TI3>14³ eRCIserIsmuxkat;GkSretsRmab;Ggát;xageRkam (bottom chord) rbs;eRKOgbgÁúM

dMbUl Warren truss dUcbgðajenAkñúgrUbTI 3>32 a. Truss RtUv)anpSar nigmanKMlatcmøay 6m .
snμt;fakarP¢ab;rbs;Ggát;xageRkamRtUv)aneFVIeLIgdaykarpSarbuitkaMtambeNþay (longitudinal fillet
weld) enAnwgsøabRbEvg 230mm . edayeRbIEdk A36 CamYynwgTinñn½ybnÞúkxageRkam ¬xül;minRtUv

)anBicarNaenAkñúg]TahrN_enHeT¦.
édrENg (purlin)³ M 200 × 0.097
RBwl³ 0.95kN / m elIbøg;edk
2

eRKOgbgÁúMrgkarTaj 67 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

kRmaldMbUlEdk (metal deck): 0.1kN / m 2

dMbUl³ 0.2kN / m
2

kRmalGIusULg;³ 0.15kN / m2

dMeNaHRsay³
KNnabnÞúk³
RBwl = 0.95 × 6 × 12 = 68.4kN

T.Chhay 68 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

bnÞúkefr kRmaldMbUlEdk 0.1kN / m 2

¬elIkElgédrENg¦ = dMbUl 0.2kN / m 2
kRmalGIusULg; 0.15kN / m 2
srub 0.45kN / m 2

bnÞúkefrsrub = 0.45 × 6 × 12 = 32.4kN

Tm¶n;édrENgsrub = 0.097 × 6 × 12 = 7kN
snμt;faTm¶n; truss esμI 10% énbnÞúkepSg²
0.1(68.4 + 32.4 + 7 ) = 10.78kN
bnÞúkenAelItMNxagkñúgKW
32.4 10.78
D= + + 0.097 × 6 = 6kN
8 8
68.4
S= = 8.55kN
8
enAelItMNxageRkA RkLaépÞrgbnÞúkKWesμInwgBak;kNþalRkLaépÞrgbnÞúkrbs;tMNxagkñúg. bnÞúkenAelI
tMNxageRkAKW
32.4 10.78
D= + + 0.097 × 6 = 3.28kN
2×8 2×8
68.4
S= = 4.3kN
2×8
karbnSMbnÞúk A4-3 nwgTTYl)antémøFMCageK³
Pu = 1.2 D + 1.6S
enAelItMNxagkñúg P = 1.2 × 6 + 1.6 × 8.55 = 20.88kN
u

enAelItMNxageRkA P = 1.2 × 3.28 + 1.6 × 4.3 = 10.82kN

u

Truss EdlrgbnÞúkRtUv)anbgðajenAkñúg rUbTI 3>32 b.

Ggát;xageRkamRtUv)anKNnaedaykMNt;kmøaMgkñúgGgát;nImYy²rbs;Ggát;xageRkam nigeFVIkar
eRCIserIsmuxkat;smrmüedIm,ITb;nwgkmøaMgEdlFMCageK. enAkñúg]TahrN_enH kmøaMgenAkñúgGgát; IJ
mantémøFMCageK. GgÁesrI (free body) enAxageqVgmuxkat; a-a RtUv)anbgðajenAkñúg rUbTI 3>32 c.
eRKOgbgÁúMrgkarTaj 69 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

∑ M E = 83.9(6) − 10.82(6) − 20.88(4.5 + 3.0 + 1.5) − 1.2 FIJ = 0

FIJ = 208.8kN
sRmab;muxkat;eBj (gross section)
.8 ⋅ 10 3
muxkat;EdlRtUvkar A = 0.F9F = 208
g
IJ
0.9 × 250
= 928mm 2
y

sRmab; net section

208.8 ⋅ 10 3
muxkat;EdlRtUvkar A = 0.75
e
F
F
= IJ
0.75 × 400
= 696mm 2
u

sakl,g WT125 × 0.09

Ag = 1140mm 2 > 928mm 2

kartP¢ab;eFVIeLIgedaykarpSartambeNþay ehIyGgát;minEmnCaEdkbnÞH b¤Edksrés dUcenHkartP¢ab;

enHminsßitenAkñúgkrNIBiessNamYysRmab;Ggát;EdlpSarEdlrg shear leg.
⎛x⎞ ⎛ 34.5 ⎞
U =1− ⎜ ⎟ =1− ⎜ ⎟ = 0.85 < 0.9
⎝L⎠ ⎝ 230 ⎠
Ae = UAg = 0.85 × 1140 = 969mm 2 > 696mm 2 (OK)

RbsinebIGgát;xageRkamRtUv)anBRgwgenA panel point

L 1500
= = 75.4 < 300 (OK)
r 19.9
cemøIy eRbIEdk WT125 × 0.09

3>9> Ggát;EdltPa¢b;edayknøas; (Pin-Connection Members)

enAeBlGgát;RtUv)antP¢ab;edayknøas; rn§RbehagRtUv)aneFVIeLIgenAcugTaMgsgçagrbs;Ggát;
nigEpñkEdlvaRtUvP¢ab; ehIyknøas;RtUv)ans‘ktamrn§enaH. kareFVIEbbenHedIm,IkMu[Ggát;rgm:Um:g;Bt;.
Ggát;rgkarTajEdltP©ab;tamTRmg;EbbenHRbQmnwgkar)ak;eRcInRbePT EdlRtUv)anerobrab;enAkñúg
AISC D3 nigRtUv)anBnül;dUcxageRkam.

Eyebar CaRbePTBiessrbs;Ggát;EdlP¢ab;edayknøas; (pin-connected member) EdlenA

xagcugrbs;vamanrn§knøas; dUcbgðajkñúgrUbTI 3>33. ersIusþg;KNnaKWQrelIersIusþg;yalrbs;mux

kat;eBj. k,ÜnlMGitsRmab;KNnaTMhM eyebar manenAkñúg AISC D3 EtminRtUv)anykmkerobrab;enA
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TIenHeT. Eyebar RtUv)aneRbIy:agTUlMTUlayenAeBlmun vaCaGgát;rgkarTajEdleRbIenAkñúg truss

s<an b¤enAkñúgs<anBüÜr. vaminRtUv)aneKeRbIeT naeBlbc©úb,nñ.
Ggát;EdltP¢ab;edayknøas;KYrRtUv)anKNnasRmab;sßanPaBkMNt;dUcxageRkam ¬rUbTI 3>34¦
!> kugRtaMgTajenAelI net effective area ¬rUbTI 3>34 a ¦
φt = 0.75 / Pn = 2tbeff Fu (ASIC Equation D3.1)

@> kugRtaMgkmøaMgkat;enAelI net effective area ¬rUbTI 3>34 b¦

φsf = 0.75 / Pn = 0.6 Asf Fu (ASIC Equation D3.21)

#> kugRtaMg bearing . tRmUvkarenHmanenAkñúg chapter J (“Connections, Joints and

fastener”) ¬rUbTI 3>34 c¦

φ = 0.75 / Pn = 1.8Fy Apb (ASIC Equation J8-1)

$> kugRtaMgTajenAelI gross area

φ = 0.9 / Pn = Fy Ag (ASIC Equation D1-1)

Edl t= kRmas;rbs;EpñkEdltP¢ab;
beff = 2t + 16 ≤ b ¬KitCa mm ¦
b = cmøayBIépÞxagrbs;rn§knøas;eTAépÞxagrbs;Ggát; EdlEkgeTAnwgTisrbs;kmøaMg

Asf = 2t (a + d / 2)

a= cm¶ayBIépÞxagrbs;rn§knøas;eTAépÞxagrbs;Ggát; EdlRsbeTAnwgTisrbs;kmøaMg
d = Ggát;p©itknøas;
A pb = projected bearing area = dt

tRmUvkarbEnßmsRmab;karkMNt;TMhMrbs;knøas; nigGgát;manbkRsayenAkñúg AISC D3.

eRKOgbgÁúMrgkarTaj 71 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

T.Chhay 72 Tension Members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

IV. eRKOgbgÁúMrgkarsgát;
Compression Members
4>1> esckþIepþIm (introduction)
eRKOgbgÁúMrgkarsgát; CaeRKOgbgÁúMsMNg;EdlrgEtkmøaMgsgát;tamG½kS. bnÞúkEdlGnuvtþtam
G½kSbeNþaykat;tamTIRbCMuTm¶n;rbs;muxkat;Ggát; ehIykugRtaMg (stress) GacesμInwg f a = P A Edl
f a RtUv)anKitfamantMélesμIKñaelImuxkat;TaMgmUl. b:uEnþCak;EsþgeKminEdlTTYl)ansßanPaBl¥Ebb

enHeT eKminGaceCosputBIkmøaMgcakp©itxøH)aneLIy. CalT§pleKnwgTTYl)ankarBt; b:uEnþvaGac

RtUv)aneKKitkmøaMgrg (secondary load) nigGacRtUv)anecalRbsinebIlkçxNÐénkardak;bnÞúkesÞIrEt
dUcKñanwgRTwsþI. karBt;minGacRtUvecaleT RbsinebIvaCam:Um:g;Bt;Edl)anBIkarKNna. eyIgnwgKit
sßanPaBenHenAkñúgCMBUkTI6.
CaTUeTA Ggát;rgkarsgát;EdlekItmanenAkñúgGKar nigs<anKW ssr ¬CaGgát;bBaÄrEdlman
tYnaTIcMbgKWRTnUvbnÞúkbBaÄr¦. Ggát;rgkarsgát;k¾RtUv)aneRbIenAkñúgeRKOgbgÁúM truss nigCaeRKOgbgÁúMén
RbBn§½BRgwgpgEdr. Ggát;rgkarsgát;EdlmanRbEvgxøIminRtUv)aneKcat;cMNat;fñak;Ca column eT Etva
RtUv)aneKehAfa strut.
4>2> RTwsþIssr (Column Theory)

edayBicarNaGgát;rgkarsgát;Evg ehIyRsavdUcbgðajenAkñúgrUbTI 4>1 a . RbsinebIbnÞúktam

G½kS P RtUv)andak;yWt² enAeBlmYybnÞúkenaHnwgmantémøRKb;RKan;edIm,IeFVI[Ggát;KμansßirPaBehIy
eRKOgbgÁúMrgkarsgát; 73 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

ragrbs;Ggát;nwgekagdUcbgðajedayExSdac;. bnÞúkEdleFVI[Ggát;ekagRtUv)aneKehAfa critical

buckling load. RbsinebI Ggát;manRbEvgxøI ehIyFat;dUcbgðajenAkñúgrUbTI 4>2 b enaHeKRtUv karbnÞúk

EdlmantémøFMCagmunedIm,IeFVI[Ggát;enaHsßitkñúgsßanPaBKμansißrPaB. RbsinebIGgát;enaH kan;EtxøI

kar)ak;nwgekIteLIgeday compressive yielding Cageday buckling. munnwg)ak; kugRtaMgsgát; P A
nwgrayesμIenAelImuxkat;RKb;cMNucTaMgGs;énbeNþayRbEvgrbs;ssr eTaHCa)ak;eday yielding b¤
k¾)ak;eday buckling. bnÞúkEdleFVI[ buckling ekItman CaGnuKmn_eTAnwg slendernesss ehIy
sRmab;Ggát;EdlRsavxøaMg bnÞúkenHnwgmantémøtUcNas;.
RbsinebIGgát;manlkçN³RsavxøaMg EdlkugRtaMgmunnwg buckling EdltUcCagEdnsmamaRt
(proportional limit) ¬EdlGgát;sßitenAkñúglkçN³eGLasÞic¦ critical buckling load RtUv)an[dUc

xageRkam³
π 2 EI
Pcr = 2
L
¬$>!¦
Edl E Cam:UDuleGLasÞic (modulus of elasticity), I Cam:Um:g;niclPaBénRkLaépÞmuxkat; (moment
of inertia of the cross-sectional are) EdleFobnwgG½kSemEdltUc (minor principal axis), L CaRb

Evgrbs;Ggát;cenøaHTRm. edIm,I[smIkar ¬$>!¦ mann½y luHRtaEtGgát;sßitkñúgsßanPaBeGLasÞic

ehIycugrbs;vaGacviledayesrI EtminRtUvrMkileTAxageT. cugTRmenHbMeBjlkçxNÐedayTRmsnøak;
(hinge) b¤ pinned dUcbgðajkñúgrUbTI 4>2 . TMnak;TMngd¾KYr[cab;GarmμN_enHRtUv)anrkeXIjdMbUgbMput

edayGñkR)aCJKNitviTüaCnCatisVIseQμaH Leonhard Euler Edle)aHBum<enAkñúgqñaM 1759. bnÞúkeRKaH

fñak; (critical load) enH enAeBlxøHRtUv)aneKehAfa Euler load b¤ Euler buckling load . smIkarTI
$>! RtUv)aneKbgðajedIm,IeFVI[eCOedaykarBiesaFy:ageRcIn. karsMraybBa¢ak;rbs;smIkarenH RtUv)an
[edIm,IbgðajBIPaBsMxan;rbs;lkçxNÐcugTRm.

T.Chhay 74 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

edIm,IgayRsYlkñúgkarbkRsay Ggát;RtUv)andak;[edkelIG½kS x dUcEdl[kñúgrUbTI 4>3.

TRm roller Edldak;enATIenHedIm,ITb;Ggát;min[cl½teTAelI b¤cuHeRkam. bnÞúksgát;tamG½kS
RtUv)anGnuvtþ ehIyekIneLIgsnSwm². bnÞúkxagbeNþaHGasnñRtUv)andak;edIm,IeFVI[Ggát;dabdUcrUb
ragEdlbgðajedayExSdac; ehIyGgát;nwgRtLb;eTArkrUbragedImvijenAeBlEdlbnÞúkbeNþaHGsnñ
enaHRtUv)aneKdkecjRbsinebIbnÞúktamG½kSmantémøtUcCag critical buckling load . Critical
buckling load, Pcr RtUv)ankMNt;CabnÞúkEdlmantémøFMRKb;RKan;edIm,IrkSarUbragdabrbs;Ggát;enA

eBlEdlbnÞúkxagbeNþaHGasnñRtUv)aneKdakecj.

smIkarDIepr:g;Esül (differential equation) sRmab;rUbragdabrbs;Ggát;eGLasÞicEdlrgkar

Bt;KW³
d2y
dx 2
=−
M
IE
¬$>@¦
Edl x Cacm¶ayrbs;cMNucEdlsßitenAelIG½kSbeNþayrbs;Ggát;/ y CaPaBdabrbs;Ggát;enARtg;
cMNucenaH/ nig M Cam:Um:g;Bt;enARtg;cMNucenaH. E nig I RtUv)anbgðajBIxagelI b:uEnþm:Um:g;niclPaB
I enATIenHKWeFobnwgG½kSénkarBt;. smIkarenHRtUv)anTajeday Jacob Bernoulli ehIyRtUv)an

bMEbkeday Euler EdleRbIR)as;vasRmab;bBaðaekagrbs;ssr. BI rUbTI 4>3 eyIgeXIjfaenAeBl

EdlGgát;ekagedaysarbnÞúktamG½kS Pcr enAcm¶ay x BITRmxageqVgeyIgmanPaBdab y ehIy
m:Um:g;Bt;enARtg;cMNucenaHKW Pcr y . enaHsmIkar $>@ GacsresrdUcxageRkam³
Pcr
y"+ y=0
EI
Edl RBIm KWCaDIepr:g;Esültam x . smIkarenHCa second order, linear, ordinary differential
equation CamYynwgemKuNefr ehIymandMeNaHRsay

eRKOgbgÁúMrgkarsgát; 75 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

y = A cos(cx) + B sin(cx)

Edl c = PEIcr
ehIy A nig B Catémøefr. témøefrTaMgenH RtUv)ankMNt;edayGnuvtþnUvlkçxNÐRBMEdndUcxageRkam³
Rtg; x = 0 / y = 0 ³ 0 = A cos(0) + B sin(0) enaH A = 0
Rtg; x = L / y = 0 ³ 0 = B sin(cL)
lkçxNÐcugeRkayenHtRmUv[ sin(cL) = 0 RbsinebI B ≠ 0 ¬cemøIyminsMxan; EdlRtUvKñanwg P = 0 ¦.
sRmab; sin(cL) = 0 /
cL = 0, π , 2π , 3π , ... = nπ , n = 0, 1, 2, 3, ...

BI c = Pcr
EI

eyIgTTYl)an cL = ⎛⎜⎜ ⎞
ehIy Pcr = n πL2 EI
2 2
Pcr Pcr 2
⎟ L = nπ , L = n 2π 2
⎟
⎝ EI ⎠ EI

témøCaeRcInrbs; n RtUvKñanwgrUbragekag (buckling mode) epSg². n = 1 bgðajnUvrUbragekagTImYy

(first mode). n = 2 KWrUbragekagTIBIr (second mode).l. témø n = 0 CakrNIKμanbnÞúk EdlCa

krNIminsMxan;. rUbragénkarekagTaMgenHRtUv)anbgðajenAkñúgrUbTI 4>4. témø n minGacFMCagmYy

elIkElgEtGgát;rgkarsgát;RtUv)anTb;BIkardabenARtg;cMNucEdleFVI[kMeNagbt;Ebn.

dUcenHdMeNaHRsayrbs;smIkarDIepr:g;EsülKW
T.Chhay 76 Compression members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

⎛ nπx ⎞
y = B sin ⎜ ⎟
⎝ L ⎠
ehIyemKuN B CatémøminkMNt;. lT§plenHRtUv)aneRbICacemøIy linear kñúgsmIkarDIepr:g;EsültM
Nag)atuPUt nonlinear.
sRmab;krNIFmμtarbs;Ggát;rgkarsgát;EdkKμanTRmenAcenøaHcugsgçagrbs;va n = 1 enaH
smIkar Euler RtUv)ansresrCa
π 2 EI
Pcr = 2
L
¬$>#¦
vamanlkçN³gayRsYlCagkñúgkarsresrsmIkar $># kñúgTRmg;dUcxageRkam
π 2 EI π 2 EAr 2 π 2 EA
Pcr = = =
L2 L2 (L / r )2
Edl A CaRkLaépÞmuxkat; nig r CakaMniclPaB (radius of gyration) EdleFobnwgG½kSEdlekag.
pleFob L / r Ca slenderness ratio. Ggát;EdlmanlkçN³kan;EtRsav témø slenderness ration
kan;EtFM.
RbsinebI critical load RtUv)anEckedayRkLaépÞmuxkat; enaHeKnwgTTYl)an critical
buckling stress dUcxageRkam³
π 2E
P
Fcr = cr = ¬$>$¦
A 2
(L / r )
sRmab;kugRtaMgrgkarsgát; karekagnwgekIteLIgtamG½kSEdlRtUvKñanwg r . karekagnwgekIteLIg
Pøam² enAeBlEdlbnÞúkEdlGnuvtþmkelIGgát;esμInwgbnÞúkEdl[kñúgsmIkar $># ehIyssrnwgKμanesßr
PaBeFobG½kSem (principal axis) EdleFVI[ slenderness ratio mantémøFMCageK. CaTUeTAvaCa
G½kSEdlmanm:Um:g;niclPaBtUcCageK ¬eyIgnwgBinitükrNIenHenAeBleRkay¦. dUcenHm:Um:g;niclPaB
Gb,brma nigkaMniclPaBGb,brmaRtUv)aneRbIenAkñúgsmIkar $># nig $>$.

]TahrN_4>1³ ssrEdlmanmuxkat W 300 × 0.73 RtUv)aneRbIedIm,IRTbnÞúksgát;tamG½kS 645kN .

ssrenHmanRbEvg 6m nigmanTRm pinned enAcugsgçag. edaymikKitBIemKuNbnÞúk nigemKuN
ersIusþg; cUreFVIkarGegátBIesßrPaBrbs;Ggát;enH. ¬eKminRtUvkardwgBIm:akrbs;EdkeT edaysar critical
buckling load CaGnuKmn_énm:UDuleGLasÞic minEmn yield stress b¤ ultimate tensile strength¦.

eRKOgbgÁúMrgkarsgát; 77 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

dMeNaHRsay³ sRmab; W 300 × 0.73

témøGb,brmarbs; r = r = 49.8mm
y

témøGtibrmarbs; Lr = 6000
49.8
= 120.5

π 2 EA π 2 × 200 ⋅ 103 × 9.48 ⋅ 103

Pcr = = ⋅ 10 − 3 = 1288.7kN
(L r )
2
120.5 2

cemøIy³ edaysarbnÞúkGnuvtþKW 645kN tUcCag P enaHssrrkSasßirPaBehIymanemKuNsuvtßiPaB

cr

RbqaMgnwg bucklingesμInwg 1288.7 / 645 = 2.0 .

eRkaymkeK)anrkeXIjfa smIkarrbs; Euler minGaceRbICamYyGgát;rgkarsgát;EdlFat; xøI

nigminRsav. mUlehtuKWfa slenderness ratio tUcrbs;Ggát;bNþal[man buckling stress FM
¬BIsmIkar $>$¦. RbsinebI buckling stress FMCag proportional limit rbs;smÖar³ enaHTMnak;TMng
rvag stress nig strain nwgminmanlkçN³Ca linear eT ehIym:UDuleGLasÞic E nwgminGacyk
mkeRbI)aneT. ¬kñúg]TahrN_ 4>1 buckling stress KW Pcr / A = 1288.7 / 9.48 = 136MPa EdltUc
Cag proportional limit sRmab;RKb;eRKOgbgÁúMEdkTaMgGs;. enAkñúgqñaM 1889 Friedrich
Engesser )anesñIeLIgdMbUgkñúgkareRbIR)as; tangent modulus Et enAkñúgsmIkar $>#. sRmab;smÖar³

EdlmanExSekag stress-strain dUckñúgrUbTI 4>5/ E ElgCatémøefrsRmab;kugRtaMgEdlFMCag

proportional limit Fpl . Tangent modulus Et RtUv)ankMNt;Ca slope énbnÞat;b:HeTAnwgExSekag

stress-strain sRmab;témørbs; f EdlsßitenAcenøaH Fpl nig Fy . RbsinebI buckling stress Pcr / A

sßitenAkñúgtMbn;enH vaRtUv)anbgðajdUcxageRkam³
π 2 Et I
Pcr =
L2
¬$>%¦
smIkar $>% dUcKñanwgsmIkar Euler RKan;EtCMnYs E eday Et .
ExSekag stress-strain EdlbgðajenAkñúgrUbTI 4>5 manlkçN³xusKñaBIrUbEdl)anbgðajBImun
sRmab; ductile steel ¬enAkñúgrUbTI 1>3 nig1>4¦ edaysarEtvamantMbn; nonlinear . ExSekag
enHCaRbePTénkarBiesaFkarsgát;rbs;Edk W-shape RbEvgxøI EdleKehAfa stub column.
Nonlinearity CalT§pldMbUgénvtþmanrbs; residual stress enAkñúg W-shape. enAeBlEdlEdk hot-

rolled shape Tuk[RtCak; muxkat;TaMgmUlrbs;EdkminRtUv)anRtCak;edayGRtadUcKñaeT. ]TahrN_

T.Chhay 78 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

enAcugsøabrbs;EdkRtCak;elOnCagkEnøgCYbKñarvagsøab nigRTnug. karRtCak;minRBmKñaEbbenH

begáIt[
mankugRtaMgenACab;kñúgEdkrhUt. ktþaepSgeTotdUcCakarpSar nigkarBt;RtCak;edIm,IbegáIt Fñwmekag
GacCaktþabNþal[man residual stress b:uEnþdMeNIrkareFVI[RtCak;CaktþacMbg.

cMNaMfa Et mantémøtUcCag E ehIysRmab; L / r EdlmantémødUcKñaRtUvKña eKnwgTTYl)an

critical load Pcr tUc. edaysarEtPaBERbRbYlrbs; Et karkMNt;témø Pcr enAkñúg inelastic range

edayeRbIsmIkarTI $>% BitCamankarBi)ak. CaTUeTA trial-and-error approach RtUv)aneRbICamYynwg

ExSekag stress-strain dUcbgðajkñúgrUbTI 4>5 edIm,IkMNt; Et sRmab;témøsakl,grbs;témø Pcr .
sRmab;mUlehtuenH design specification CaeRcIn rYmTaMg AISC Specification manrUbmnþEdl)an
BIkarBiesaF (empirical formulas) sRmab; inelastic column.
sRmab;RKb;smÖar³TaMgGs; critical buckling stress RtUv)ansg;CadüaRkamCaGnuKmn_eTAnwg
slenderness dUcbgðajenAkñúgrUbTI 4>6 . ExSekag tangent modulus b:HeTAnwgExSekag Euler Rtg;

cMNucEdlRtUvKñanwg proportional limit rbs;smÖar³. bnSMExSekagenH RtUv)aneKehAfa column

strength curve EdlBN’naBIesßrPaBrbs;RKb;ssrTaMgGs;. eRkABI Fy , E nig Et EdlCalkçN³

rbs;smÖar³ ersIusþg;CaGnuKmn_nwg slenderness ratio.

eRKOgbgÁúMrgkarsgát; 79 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

RbEvgRbsiT§PaB (effective Length)

TaMgsmIkar Euler nigsmIkar tangent modulusQrelIkarsnμt;dUcxageRkam³
!> ssrmanlkçN³Rtg;l¥
@> bnÞúkGnuvtþtamG½kS KμancMNakp©it
#> ssrmanTRm pinned enAcugsgçag
lkçxNÐBIrdMbUgmann½yfa Kμanm:Um:g;Bt;enAkñúgGgát;mugeBlekag (buckling). dUc)anerobrab;
BIxagedIm m:Um:g;écdnüxøHnwgekItman b:uEnþvaRtUv)anecalkñúgkrNICaeRcIn. tRmUvkarsRmab;TRm
pinned CakarkMNt;mYyEdlBi)ak Edlkarpþl;[RtUv)aneFVIsRmab;lkçxNÐTRmepSg²eTot. lkçxNÐ

TRm pinned tRmUv[Tb;Ggát;BIkarrMkilxag b:uEnþminTb;nwgkarvilCMuvijTRmeT. CakarBit karbegáIttMN

pinned EdlKμankkitKWminGaceFVIeTA)anl¥enaHeT dUcenHlkçxNÐTRmenHRKan;EtmanlkçN³Rbhak;

RbEhlb:ueNÑaH. Cak;EsþgssrTaMgGs;RtUvEtxUcRTg;RTaytamG½kSedayesrI.
lkçxNÐcugepSgeTotGacRtUv)anBnül;enAkñúgsmIkarTI $>#. CaTUeTA m:Um:g;Bt;GacCaGnuKmn_
én x EdlCalT§plenAkñúg nonhomogeneous differential equation. vamanlkçxNÐRBMEdnxusBI
smIkaredIm EtviFIsaRsþKNnadUcKñaTaMgRsug. smIkarEdlCacemøIysRmab; Pcr manTRmg;dUcKña.
]TahrN_ edayBicarNaGgát;rgkarsgát;EdlmanTRmmYyCa pinned nigmYyeTotCa fixed Tb;nwg
karvil nigkarrMkil dUcbgðajenAkñúgrUbTI 4>7 . smIkar Euler sRmab;krNIenH EdlRtUv)anbkRsay
tamrebobdUcsmIkar $># eKTTYl)an

T.Chhay 80 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

2.05π 2 EI
Pcr =
L2
2.05π 2 EA π 2 EA
b¤ Pcr =
(L / r)2
=
(0.70 L / r ) 2
dUcenHGgát;rgkarsgát;enHmanlT§PaBRTbnÞúkesμInwgGgát;EdlmanTRm pinned sgçagEdr Et
RbEvgrbs;vaRtUv)anKitRtwm 70% bueNÑaH. eKnwgTTYl)ansmIkarkñúgTRmg;RsedogKñaenHsRmab;
ssrEdlmanlkçxNÐTRmepSg².
Column-buckling problem GacRtUv)anbegáItCarUbmnþkñúgTRmgCa forth-order differential

equation CMnYs[smIkar $>@. kareFVIEbbenHedIm,IgayRsYlkñúgkaredaHRsayCamYylkçxNÐRBMEdn

eRkABITRm pinned . edIm,IPaBgayRsYl smIkarsRmab; critical buckling load nwgRtUv)ansresrkñúg

TRmg;dUcxageRkam³
π 2 EA π 2 Et A
Pcr = b¤ P = ¬$>^ a/ $>^ b¦
(KL / r ) (KL / r )
2 cr 2

Edl KL CaRbEvgRbsiT§PaB (effective length) nig K CaemKuNRbEvgRbsiT§PaB (effective length

factor). emKuNRbEvgRbsiT§PaBsRmab;Ggát;rgkarsgát; fixed-pinned KW 0.70 . sRmab;cugsgçag

manTRm fixed Tb;nwgkarvil nigrMkil enaH K = 0.50 . témørbs; K sRmab;krNITaMgenH nigkrNI

epSgeTotmanenAkñúgtarag C_C2.1 enAkúñg Commentary to the AISC Specification. enAkñúg
taragenaH eK[témørbs; K cMnYnBIr³ mYyCatémøtamRTwsþI nigmYyeTotCatémøsRmab;karKNna
eRKOgbgÁúMrgkarsgát; 81 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

(recommended design value) EdlRtUv)anykmkeRbIenAeBlEdleKmanlkçxNÐTRmesÞIrl¥\tex©aH.

dUcenH luHRtaEtTRm fixed KWbgáb;\tex©aHeTIbtémøKNnaEdlmanlkçN³snSMsMécCagRtUv)anykmk
eRbI. EtcMNaMfa témøtamRTwsþI nigtémøsRmab;karKNnamantémødUcKñasRmab;lkçxNÐ (d)nig (f)
enAkñúg Commentary Table C-C2.1. mUlehtuKWfaPaBEdlminGaceFVI)anrbs;TRmsnøak;Kμankkit
Edll¥\tex©aH b¤rbs;TRm pinned )anbegáIt[mankarTb;nwgkarvil nigeFVI[témø K fycuH. dUcenH
kareRbItémøtamRTwsþIkñúg krNITaMgBIrKWmantémøtUc.
kareRbIRbEvgRbsiT§PaB KL CMnYs[RbEvg L min)aneFVI[mankarpøas;bþÚrTMnak;TMng Edl)an
erobrab;knøgmkeT. ExSekagersIusþg;ssr (column strength curve) Edl)anbgðajenAkñúg rUbTI 4>6
minmankarpøas;bþÚreT ebIRKan;EteFVIkarpøas;bþÚreQμaHG½kSGab;sIusmk KL enaH. Critical buckling
stress EdlRtUvKñanwgRbEvgEdl[ eTaHCaRbEvgBitR)akd b¤RbEvgRbsiT§PaBk¾eday k¾eQμaHrbs;vaelI

G½kSGredaenenArkSadEdl.
4>3> tRmUvkarrbs; AISC (AISC Requirements)

tRmUvkarCamUldæansRmab;Ggát;rgkarsgát;RtUv)anerobrab;enAkñúg Chapter E of the AISC

Specification. TMnak;TMngrvagbnÞúk nigersIusþg; ¬smIkar @>#¦ manTRmg;

Pu ≤ φc Pn
Edl Pu = plbUkbnÞúkemKuN
Pn = nominal compressive strength = Ag Fcr
Fcr = critical buckling stress
emKuNersIusþg;sRmab;Ggát;rgkarsgát; = 0.85
φc =
CMnYs[kareRbIsmIkar critical buckling stress Fcr CaGnuKmn_én slenderness ration KL / r

specification eRbInUv slenderness parameter

KL Fy
λc = (AISC Equation E2-4)
rπ E
vaCa)a:ra:Em:RtKμanxñat ebIeTaHCasmIkarmanlkçN³smÖar³cUlrYmk¾eday. sRmab;ssreGLasÞic
(elastic column) smIkar $>$ GacRtUv)ansresrCa
π 2E 1
Fcr = = Fy
(LK / r ) 2
λc2

T.Chhay 82 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

edIm,IKitbBa¢ÚlnUv\T§iBlrbs;PaBminRtg;dMbUg (initial crookedness) smIkarxagelIRtUv)ankat;bnßy

dUcxageRkam
0.877
Fcr = Fy
λ2c
sRmab; inelastic column EdleRbI tangent modulus equation ¬smIkar $>^ b¦ RtUv)anCMnYseday
(
Fcr = 0.658λc Fy
2
)
Edl)anKitpgEdrnUv initial crookedness. dUcenHdMeNaHRsayedaypÞal;GacTTYl)an edayeCos
vagnUv trial-and error approach EdlmanCab;CamYynwgkareRbIR)as; tangent modulus equation.
RbsinebIeKyk λc = 1.5 CaRBMEdnrvagssreGLasÞic nigssrminEmneGLasÞic enaH AISC equation
sRmab; critical buckling stressGacRtUv)ansegçbdUcxageRkam³
sRmab; λc ≤ 1.5
(
Fcr = 0.658λc Fy
2
) (AISC Equation E2-2)

sRmab; λc > 1.5

0.877
Fcr = Fy (AISC Equation E2-3)
λc2
tRmUvkarTaMgenHRtUv)anbgðajCalkçN³RkaPicenAkñúgrUbTI 4>8.

AISC Equation E2-2 nig E2-3 RtUv)ansegçbBIsmIkarcMnYn 5 Edlman λc 5 lMdab;

(Galambos, 1988). smIkarTaMgenHQrelIkarBiesaF nigRTwsþIEdlKitbBa¢ÚlnUv residual stress nig

initial out-of straightness esμInwg L / 1500 / Edl L CaRbEvgGgát;.

eRKOgbgÁúMrgkarsgát; 83 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

esñInUvpleFobPaBrlas;Gtibrma (maximum slenderness ration) KL / r esμInwg

AISC

200 sRmab;Ggát;rgkarsgát;. eTaHbICamankarkMNt;EtmYyk¾eday EtenAkñúgkarGnuvtþn_eKGacyk

pleFobkMNt;FMCagenH edaysarssrEdlmanlkçN³RsavCag nigmanersIusþg;tUc ehIyvanwgmin

manlkçN³esdækic©.

]TahrN_4>2³ kMNt;ersIusþg;sgát;KNnarbs; W 360 ×1.08 EdlmanRbEvg 6m nigmanTRm pinned.

eRbIEdk A36 .
dMeNaHRsay³ Slenderness ratio³
1.0(6000)
témøGtibrmarbs; KLr = KL
r
=
63
= 95.24 < 200 (OK)
y

KL Fy 95.24 250
λc = = = 1.072
rπ E π 200000
sRmab; λ c < 1.5

Fcr = (0.658)λc Fy = (0.658)1.072 (250 ) = 154.5MPa

2 2

Pn = Ag Fcr = 14100 × 154.5 × 10 −3 = 2177kN

φc Pn = 0.85 × 2177 = 1850kN

cemøIy³ ersIusþg;sgát;KNna (design compressive strength) = 1850kN .

enAkñúg]TahrN_ 4>2/ eday ry < rx enaHvanwgmanersIusþg;FMCagtamTis x . EdkTIbRCugmux

kat;kaer: Camuxkat;EdlmanRbsiT§PaBCageKsRmab;Ggát;rgkarsgát; edaysar ry = rx enaHersIusþg;
rbs;vanwgesμIKñaTaMgBIrTis. eBlxøHEdkTIbmUlRbehagk¾RtUv)aneRbICaGgát;egkarsgát;sRmab;mUl
ehtudUcKña.
rUbragénkar)ak;Edl)anBicarNayUrmkehIyKWsMedAeTAelIkarekagedaykarBt; (flexural
buckling) dUcGgát;rgkarBt; enAeBlEdlvaKμanesßrPaB. sRmab;muxkat;xøH Ggát;nwg)ak;edayrmYl

(twisting) KWekagedayrmYl (torsional buckling) b¤edaybnSMén twisting nig bending (flexural-

torsional buckling). eyIgnwgBicarNavaenAkñúgEpñkTI 4>6.

T.Chhay 84 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

sißrPaBedaytMbn; Local Stability

ersIusþg;EdlRtUvKñanwg buckling mode minGacnwgekIteLIg)aneT RbsinebIEpñkrbs;muxkat;
manlkçN³esþIgeBkEdlnwgekItman local buckling. GesßrPaBRbePTenHKWCakarekagedaytMbn; b¤
wrinkle enAtMbn;epSg²Kña. RbsinebIvaekIteLIg muxkat;KμanRbsiT§PaBeBj)anyUr hIyGgát;nwg)ak;.

muxkat;rUbragGkSr I nig H Edlmansøab b¤RTnugesþIgnwggayrg)atuPUtenH ehIyeKKYrEteCogvagkñúg

kareRbIR)as;va. RbsinebImindUecñaHeT ersIusþg;sgát;Edl[eday AISC Equation E2-2 nig E2-3
RtUvEtkat;bnßy. karvas;EvgnUvPaBgayrgnUv)atuPUtenHKWKNnapleFobTTwgelIkRmas; (width-
thickness ratio) rbs;Epñkénmuxkat;nImYy². EpñkBIrRbePTRtUv)anBicarNa ³ unstiffened element

EdlRCugmYytambeNþayTisedAbnÞúkminRtUv)an support, nig stiffened element EdlRCugTaMg

sgçagrbs;vaRtUv)an support.
témøkMNt;rbs; width-thickness ratio RtUv)an[enAkñúg AISC B5, “Local Buckling” Edl
rUbragrbs;muxkat;RtUv)ancat;cMNat;fñak;Ca compact, noncompact b¤ slender GaRs½yeTAtamtémø
rbs;pleFob. sRmab;Epñkrgkarsgát;esμI dUcCaGgát;rgkmøaMgsgát;tamG½kS ersIusþg;RtUv)ankat;bnßy
RbsinebIrUbragman slender element. Width-thickness ratio RtUv)an[eQμaHsMKal;CaTU eTAfa λ .
GaRs½yeTAnwgEpñkrbs;muxkat; λ GacCapleFob b / t b¤ h / tw EdlnwgRtUv)anbgðajenA TIenH.
RbsinebI λ FMCagtémøkMNt; λr rUbragKW slender ehIyeKrkviFIedIm,IkarBar local buckling.
¬sRmab;rUbrag compact nig uncompact nwgRtUvykmkniyaykñúgCMBUkTI5¦ sRmab;rUbragGkSr I nig
H søabrbs;vaRtUv)ancat;TukCa unstiffened element ehIyTTwgrbs;søabGacRtUv)anKitEtBak;

kNþal.
edayeRbI AISC notation eyIg)an³
b bf / 2 bf
λ= = =
t tf 2t f

Edl b f nig t f CaTTwg nigkRmas;rbs;søab. lImItx<s;KW

250
λr =
fy

RTnugrbs;rUbragGkSr I nig H Ca stiffened element ehIy stiffened width KWCacm¶aycenøaH root

rbs;søab. Width-thickness parameter KW
eRKOgbgÁúMrgkarsgát; 85 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

h
λ=
tw
Edl h Cacm¶aycenøaH root rbs;søab ehIy tw CaTTwgsøab. lImItx<s;bMputKW
665
λr =
fy

témørbs;pleFob b f / 2t f nig h / tw RtUv)anerobcMdak;enAkñúg dimension and properties tables in

Part 1 of the manual.

Stiffened element nig unstiffened element rbs;rUbragmuxkat;CaeRcInRtUv)anbgðajenAkñúg

rUbTI 4>9. EdnkMNt; λr Edl)anmkBI AISC B5 RtUv)an[sRmab;krNInImYy².

T.Chhay 86 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

]TahrN_ 4>3³ Gegát;ssrenAkñúg]TahrN_ 4>2 sRmab; local buckling.

dMeNaHRsay³ sRmab; W 360 × 1.08 / b = 256mm / t = 19.9mm / nig
f f
bf 256
= = 6.43
2t f 2 × 19.9

témøén b f / 2t f k¾RtUv)andak;enAkñúg properties table.

250
= 15.8 > 6.43 (OK)
250
h
tw
= 25.3 ¬BI
properties table ¦
665 665
= = 42 > 25.3 (OK)
fy 250

cemøIy³ Local instability minmanbBaða.

eKk¾GnuBaØat[eRbIrUbragmuxkat;EdlminbMeBjtRmUvkar width-thickness ration pgEdr k¾

b:uEnþGgát;EbbenaHminRtUv)anGnuBaØat[RTbnÞúkF¶n;²dUcrUbragmuxkat;EdlbMeBjlkçxNÐeT. müa:gvij
eTot design strength k¾GacRtUv)ankat;bnßyedaysarEt local buckling. dMeNIrkarTUeTAkñúgkar
GegátmandUcxageRkam.

- RbsinebI width-thickness ration λ eyagtam FMCag λr Appendix B of the

Specification nigKNnaemKuNkat;bnßy (reduction factor) Q .

Fy
- KNna λc dUcFmμta³ λc = KL
rπ E
- RbsinebI Qλc ≤ 1.5 / Fcr = Q⎛⎜ 0.658Qλc2 ⎞⎟Fy (AISC Eq. A-B5-15)
⎝ ⎠

- RbsinebI Qλc > 1.5 / Fcr = ⎡⎢ 0.877 ⎤

⎥ Fy (AISC Eq. A-B5-16)
⎢⎣ λc ⎥⎦
2

- Design strength KW φc Pn = 0.85 Ag Fcr

kñúgkrNICaeRcIneKGacrk rolled shape EdlbMeBjtRmUvkar width-thickness ratio dUcenHeK
mincaM)ac;eFVInUvdMeNIrénkarKNnaenHeT. enAkñúgesovePAenH eyIgBicarNaEtGgát;rgkarsgát;Edlman
λ < λr bu:eNÑaH.

eRKOgbgÁúMrgkarsgát; 87 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

taragsRmab;Ggát;rgkarsgát; Tables for Compression Members

Manual mantaragEdlmanRbeyaCn_CaeRcInsRmab;karviPaK nigkarKNna. sRmab;Ggát;rg

karsgát;Edl strength rbs;valubeday flexural buckling ¬RbePTEdl)anBicarNaknøgmk¦/ tarag

3-36, 3-50 nig 4 enAkñúg Numerical Value section rbs; Specification nig column load table

enAkñúg part 3 rbs; Manual, “Column Design,” manRbeyaCn_CageK. tarag 3-36 [nUvtémø
φc Fcr CaGnuKmn_én KL / r sRmab; Fy = 36ksi = 250 MPa . tarag 3-50 sRmab; F = 50ksi y

= 350 MPa nig tarag 4 [ φc Fcr / Fy CaGnuKmn_én λc . ¬RKb; Manual table TaMgGs;sRmab;

Fy = 50ksi = 350 MPa xusBItaragsRmab; Fy = 36ksi = 250 MPa edaykarpat;BN’RbepH¦.

Column load table [ design strength rbs;rUbragEdleRCIserIssRmab;témøRbEvgRbsiT§PaB

(effective length) CaeRcIn. tarag 3-36 nig 3-50 bBa©b;edaylImItx<s;bMput KL / r = 200 ehIy

column load table rYm bBa©Últémø KL EdlRtUvKñanwg KL / r = 200 . kareRbIR)as;nUvtarag

nImYy²RtUv)anbgðajenA kñúg]TahrN_xageRkam.

]TahrN_ 4>4³ KNna design strength rbs;Ggát;rgkarsgát;rbs; W14 × 74 EdlmanRbEvg 20 ft

nigmanTRm pinned renAcugsgçag edayeRbI ¬!¦ Table 3-36 ¬@¦ Table 4 nig ¬#¦ column load
table . eRbIEdk A36 .

dMeNaHRsay³
Slenderness ratio:
1.0(20 × 12 )
témøGtibrma KLr = KL
r
=
2.48
= 96.77 < 200 (OK)
y

KL Fy 96.77 36
λc = = = 1.085
rπ E π 29000
¬!¦ sRmab; Fy = 36ksi / eyIgeRbI Table 3-36 .
témørbs; φc Fcr RtUv)an[sRmab;témø KL / r Kt;/ sRmab;témø KL / r TsSPaK eyIgGaceFVIkarrMkil
ex,óseLIg (rounded up) b¤eFVI linear interpolation. enAkñúgesovePAenHeyIgnwgeRbI linear
interpolation sRmab;RKb;taragTaMgGs;elIkElgEtmankarbgðajR)ab;. sRmab; KL / r = 96.77

φc Fcr = 18.69ksi
φc Pn = φc Ag Fcr = Ag (φc Fcr ) = 21.8(18.69 ) = 407 kips

T.Chhay 88 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

¬@¦ BI Table 4 sRmab; λc = 1.085 eyIg)an

Fcr
φc = 0.519
Fy
⎛ ⎞
φc Pn = Ag ⎜ φc
Fcr ⎟ Fy = 21.8(0.519 )(36 ) = 407 kips
⎜ Fy ⎟
⎝ ⎠
¬#¦ Column load table in Part 3 of the Manual [ design strength sRmab;muxkat;rUbrag W, HP,
pipe, tube, double-angle, WT nig single-angle. témøenAkñúgtaragsRmab;rUbragsIuemRTI (W, HP,

pipe nig tube)RtUv)anKNnaedayeRbI radius of gyrationsRmab;rUbragnImYy². sRmab;]TahrN_

enH k = 1.0 dUcenH

KL = 1.0(20 ) = 20 ft
sRmab; W 14 × 74 / Edk A36 nig KL = 20 ft eyIgTTYl)an
φc Pn = 407 kips .

témøEdl)anBI Table 3-36, 3-50 nig 4 KWQrelI flexural buckling nig AISC Equation E2-
2 nig E2-3. dUcenH local stability RtUv)ansnμt; ehIy width-thickness ratio nwgminFMCagtémø

kMNt;eLIy. Design strength enAkñúg column load table )anKitbBa¢ÚlenAkarkat;bnßycaM)ac;

enAeBlEdl width-thickness ratio FMCagtémøkMNt;.
4>4> karKNnamuxkat; (Design)

kareRCIserIsnUv rolled shape EdlmanlkçN³esdækic© edIm,ITb;nwgbnÞúksgát;Edl[man

lkçN³samBaØCamYynwgkareRbIR)as; column load tables. emIltaragCamYynwg effective length
ehIyrMkiltamTisedk rhUtdl;eyIgrkeXIjnUv design strength EdleyIgcg;)an ¬b¤mantémøFMCag
bnþicbnþÜc¦. kñúgkrNIxøH eyIgRtUvbnþrkrhUtdl;eyIgGacrk)anrUbragEdlmanTm¶n;RsalCageK. CaTU
eTArUbrag (W, WT, etc) RtUv)aneKeFVIkarsMercmuneK. CaerOy² TMhM nigrUbragrbs;muxkat;
RtUv)andwgmun edaytRmUvkarsßabtükmμ nigtRmUvkardéTeTot. dUcEdl)anbgðajBIxagedIm RKb;témø
EdlmanenAkñúgtaragRtUvKñanwg slenderness ratio tUcCagb¤esμInwg 200 . rUbragGt;sIuemRTI
(structural tees and the single and double-angles) RtUvkarnUvkarBicarNaBiessEdlnwgmanbk

eRKOgbgÁúMrgkarsgát; 89 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

RsayenAkñúgEpñk 4>6.
]TahrN_ 4>5³ Ggát;rgkarsgát;RTnUv service dead load 165kips = 734kN nig service live load
535kips = 2380kN . Ggát;enHmanRbEvg 26 ft = 7925mm ehIymanTRm pinned sgçag. eRbIEdk

A36 nigerIsrUbrag W 14 .

dMeNaHRsay³ KNnabnÞúkemKuN (factored load)³

Pu = 1.2 × 165 + 1.6 × 535 = 1054kips b¤ 4689kN

dUcenH required design strength φc Pn = 1054kips

BI column load table sRmab; KL = 26 ft / W 14 × 176 man design strength φc Pn = 1150kips
cemøIy³ eRbI W 14 × 176 .

]TahrN_ 4>6³ eRCIserIsrUbrag W EdlmanTm¶n;RsalCageKbMputEdlGacRTbnÞúksgát;emKuN

Pu = 190kips = 845kN . RbEvgRbsiT§PaBKW 24 ft = 7315m . eRbIEdk ASTM A572 Grade 50.

dMeNaHRsay³ viFId¾smrmüenATIenHKWdMbUgeyIgerIsrUbragEdlRsalCageKenAkñúg nominal size nI

mYy² ehIybnÞab;mkeTIberIsrUbragEdlRsalCageKelIrUbragTaMgGs;. CeRmIsmandUcxageRkam³
W 4 / W 5 nig W 6 ³ KμanrUbragNamYyenAkñúgtaragEdlGacyk)an

W8 ³ W 8 × 58 / φc Pn = 194kips

W 10 ³ W 10 × 49 / φc Pn = 239kips

W 12 ³ W 12 × 53 / φc Pn = 247 kips

W 14 ³ W 14 × 61 / φc Pn = 276kips

cMNaMfa load capacity minsmamaRtnwgTm¶n;eT ¬b¤RkLaépÞmuxkat;eT¦. eTaHbICa W 8 × 58 man

design strength tUcCageKkñúgcMeNamCeRmIsTaMgbYn EtvamanTm¶n;F¶n;CageKbnÞab; W 14 × 61 .

cemøIy³ eRbI W 10 × 49 .
sRmab;rUbragEdlKμanenAkñúg column load table, eKRtUveRbI trial-and-error approach.
dMeNIrkarTUeTAKWsnμt;rUbrag bnÞab;mkKNna design strength rbs;va. RbsinebIersIusþg;tUceBk
¬KμansuvtßiPaB¦ b¤FMeBk ¬KμanlkçN³esd©kic©¦ eKRtUveFVIkarsakl,gepSgeTot. viFIsaRsþkñúgkareFVI
trial selection mandUcxageRkam³

T.Chhay 90 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

!> snμt;témøsRmab; critical buckling stress Fcr . karBinitü AISC equation E2-2 nig E2-
3 bgðajfatémø Fcr GtibrmatamRTwsþICa yield stress Fy .

@> BItRmUvkarKW φc Pn ≥ Pu / yk
φc Ag Fcr ≥ Pu enaH Ag ≥ φ PFu
c cr

#> eRCIserIsrUbragEdlRtUvKñanwgRkLaépÞcaM)ac;.
$> KNna Fcr nig φc Pn sRmab;rUbragsakl,g.
%> eFVIkarEktRmUveLIgvijRbsinebIcaM)ac;. RbsinebI design strength mantémøEk,rtémøRtUvkar
TMhMEdlmanenAkñúgtaragbnÞab;GacRtUv)ansakl,g. RbsinebImindUecñaHeT eFVIkarKNna
eLIgvijTaMgRsug. eRbItémø Fcr EdlrkeXIjsRmab;témøsakl,gCatémøsRmab;CMhan
TI !>.
^> RtYtBinitü local stability ¬RtYtBinitü width-thickness ration). EktRmUveLIgvijRbsin
ebIcaM)ac;.
]TahrN_ 4>7³ eRCIserIsrUbrag W 460 rbs;Edk A36 EdlGacRTbnÞúkemKuN (factored load)

4688kN . RbEvgRbsiT§PaBKW 7925mm .

dMeNaHRsay³ sakl,g Fcr = 165.5kN ¬BIrPaKbIén Fy ¦³

Pu 4688 ⋅103
Required Ag = = = 33.325 ⋅10 − 3 m 2
φc Fcr 0.85 ×165.5
sakl,g W 460 × 2.8

Ag = 36.39 ⋅ 10 −3 m 2 > 33.325 ⋅ 10 −3 m 2

KL 7925
= = 111.8 < 200 (OK)
rmin 70.9
KL Fy 111.8 250
λc = = = 1.258 < 1.5
rπ E π 200000
eRbI AISC Equation E2-2
⎛ 2⎞
Fcr = ⎜ 0.658λc ⎟ Fy = (0.658)(1.258) (250) = 128.9 MPa
2

⎝ ⎠
φc Pn = 0.85 Ag Fcr = 0.85 × 36.39 ⋅10 −3 ×128.9 ⋅103 = 3987 kN < 4688kN (N.G)

eRKOgbgÁúMrgkarsgát; 91 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

sakl,g Fcr = 128.9MPa ¬témøEdleTIbnwg)anBIkarKNnasRmab; W 460 × 2.8 ¦

Pu 4688 ⋅10 3
Required Ag = = = 42.787 ⋅10 − 3 m 2
φc Fcr 0.85 ×128.9
sakl,g W 460 × 3.41

Ag = 44.39 ⋅10 −3 m 2 > 42.787 ⋅10 −3 m 2

KL 7925
= = 109.5 < 200 (OK)
rmin 72.4
KL Fy 109.5 250
λc = = = 1.232 < 1.5
rπ E π 200000
eRbI AISC Equation E2-2
⎛ 2⎞
Fcr = ⎜ 0.658λc ⎟ Fy = (0.658)(1.232 ) (250 ) = 132.45MPa
2

⎝ ⎠
φc Pn = 0.85 Ag Fcr = 0.85 × 44.39 ⋅10 −3 ×132.45 ⋅103 = 4997.5kN > 4688kN (O.K)

edaysarrUbragenHminmanenAkñúg column load table dUcenHeKRtUvkarRtYtBinitü width-thickness

ration
bf 250
= 2 .8 < = 15.8 (O.K)
2t f 250
h 665
= 13.8 < = 42.2 (O.K)
tw 250
cemøIy³ eRbIEdk W 460 × 3.41

RbsinebIeKeRbI table 3-36 b¤ table 3-50 témøsakl,grbs; φc Fcr manlkçN³gayRsYlkñúg

kareRbIenAkñúgsmIkar
Pu
Required Ag =
φc Fcr

4>5> esckþIbEnßmsRmab;RbEvgRbsiT§PaB (More on Effective Length)

enAkñúgEpñk 4>2 “column theory” )anENnaMBIRbEvgRbsiT§PaB. RKb;gGát;rgkarsgát;TaMg
RtUv)anKitCaTRm pinned edayminKitBIlkçxNÐcugTRmBitR)akd EdlnegeFVI[RbEvgRbsiT§PaB KL
mantémøxusBIRbEvgBitR)akd. CamYynwgkarEkERbenH load capacity rbs;Ggát;rgkarsgát;Ca
GnuKmn_Etnwg slenderness parameter λc . enAeBlEdleKsÁal;lkçN³rbs;smÖar³ vaCaGnuKmn_eTA
T.Chhay 92 Compression members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

nwg slenderness ration KL .

RbsinebIGgát;rgkarsgát;manTRmepSgKñaenAelIG½kSemrbs;va enaHvanwgmanRbEvgRbsiT§PaB
epSgKñaenAelIG½kSTaMgBIr. enAkñúgrUbTI 4>10 W -shape RtUv)aneRbICassr ehIyenAEpñkxagelIva
RtUv)anBRgwgedayGgát;edkenAelITisTaMgBIrEdlEkgKña. Ggát;TaMgenHkarBarkarrMkilrbs;ssrRKb;
TisedA EtkarlMGitrbs;ssrminRtUv)anbgðajEdlGnuBaØat[karviltictYcekItman. eRkamlkç-
xNÐenH Ggát;GacnwgRtUv)anKitCaTRm pinned enAEpñkxagelI. sRmab;mUlehtudUcKña tMNedIm,I
RTTRmenAxageRkamk¾GacKitCatMN pinned Edr. CaTUeTA eKBi)aknwgTTYl lkçxNÐ rigid b¤ fixed
Nas; luHRtaEteKdak;lkçxNÐBiess. tMNFmμta CaTUeTAxiteTArktMN hinge b¤ pinned . enARtg;
Bak;kNþalkm<s;ssrRtUv)anBRgwgEttamTismYy. tMNkarBarEtkarrMkil EtvaminTb;karvileT. kar
BRgwgenHkarBarkarrMkiltamG½kSexSayrbs;muxkat; b:uEnþmin)anTb;karrMkilTisxøaMgeT. dUc)anbgðaj
enAkñúgrUbTI 4>10 RbsinebIGgát;ekagtamG½kSxøaMg RbEvgRbsiT§PaBrbs;vaKW 7.9m b:uEnþkarekagtam
TisexSayGacekagkñúgrUbrag second buckling mode RtUvKñanwgRbEvgRbsiT§PaB 3.95m . eday
eRKOgbgÁúMrgkarsgát; 93 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

sarersIusþg;rbs;vaRcassmamaRteTAnwgkaerén slenderness ratio ssrnwgekagkñúgTisedA Edlman

slenderness ration FMCageK dUcenHeKRtUveRbobeFob K x L / rx CamYynwg K y L / ry . enAkñúgrUbTI

4>10 pleFob 7900 / rx RtUv)aneRbobeFobCamYynwg 3950 / ry ¬Edl rx nig ry KitCa mm ¦ ehIy

pleFobEdlmantémøFMCageKRtUv)aneRbIsRmab;kMNt; nominal axial compressive strength Pn .

]TahrN_4>8³ Edk W 300 × 0.95 manRbEvg 7.2m RtUv)anRTedayTRm pinned sgçag

ehIyTb;tamTis exSayRtg;cMNucmYyPaKbI dUcbgðajkñúgrUbTI 4>11. eRbIEdk A36 kMNt; design
compressive strength .

dMeNaHRsay³
K x L 7200
= = 53.7
rx 134.1
K y L 2400
= = 31.3
ry 76.7

K x L / rx mantémøFMCag dUcenHvamanlkçN³lub. BI table 3-36 CamYynwg KL / r = 53.7

φc Fcr = 26.29ksi = 26.29 × 6.895 = 181.3MPa

φc Pn = Ag (φc Fcr ) = 12.32 ⋅ 103 × 181.3 ⋅ 10 −3 = 2233.6kN

cemøIy³ Design strength = 2233.6kN

T.Chhay 94 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Design strengthEdl[enAkñúg column load table KWQrelIRbEvgRbsiT§PaBtamG½kS y .

dMeNIrkarsRmab;eRbIR)as;taragenHCamYynwg K x L GaceFVIeTA)anedaydwgBIedImehtuEdleKTTYl)an
témøenAkñúgtaragenH. edaycab;epþImCamYynwgtémø KL eKnwgTTYl)an φc Pn edaydMeNIrkarRsedog
KñanwgdMeNIrkarxageRkam³
- KL RtUv)anEckeday ry edIm,ITTYl)an KL / ry .
- KNna slenderness parameter λc = rKLπ FEy
y

- KNna Fcr
- KNna design strength φc Pn = 0.85 Ag Fcr
dUcenHersIusþg;Edl)anerobCataragKWQrelItémørbs; KL EdlesμInwg K yL . RbsinebIlT§PaBRT
RTg;eFobnwgTisedA x eKGaceRbItaragedayCMnYs
KxL
KL =
rx / ry

enaHbnÞúkEdlenAkñúgtaragnwgQrelI
KL K x L /( rx / ry ) K x L
= =
ry ry rx

pleFob rrx RtUv)an[enAkñúg column load table sRmab;rUbragnImYy².

y

]TahrN_ 4>9³ Ggát;rgkarsgát;dUcbgðajenAkñúgrUbTI 4>12 manTRm pinned sgçagehIyenA

RtUv)anTb;tamTisenABak;kNþalkm<s;ssr. Service load KW 400Kips EdlbnÞúkefr nigbnÞúkGefr
mantémøesμIKña. eRCIserIs W-Shape EdlmanTm¶n;RsalCageK.
dMeNaHRsay³ Factored load = Pu = 1.2 × 200 + 1.6 × 200 = 560kips
edaysnμt;faTisedAexSaylub ehIyBinitüemIlkñúg column load table CamYynwg KL = 9 feet .
cab;epþImCamYynwgrUbragtUcCageK dMbUgeyIgrk)anrUbrag W 10 × 77 CamYynwg design strength
632kips .

RtYtBinitüG½kSxøaMg
KxL 18
= = 10.40 ft > 9 ft
rx / ry 1.73

eRKOgbgÁúMrgkarsgát; 95 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

KxLmanlkçN³lubsRmab;rUbragenH
emIltaragCamYy KL = 10.4 feet . W 10 × 77 enAEtCarUbragRsalCageKsRmab; W 10 CamYynwg
design strength 612kips ¬eRkayeBleFVI interpolation¦.

bnþGegátelI W 12 × 72 ³
KxL 18
= = 10.3 ft > 9 ft
rx / ry 1.75

KxL enAEtlub ehIyman design strength 592kips .

kMNt;rUbragEdkRsalCageKsRmab; W 14 . rUbragEdlRsalCageKKW W 14 × 74 EtvaF¶n;CagrUbrag
Edl)anrkBIelIkmun.
cemøIy³ eRbIEdk W 12 × 72
RKb;eBlTaMgGs;EdlGaceFVIeTA)an GñkKNnaKYrEtbEnßmTRmsRmab;TisedAexSayrbs;ssr.
RbsinebImindUcenaHeT Ggát;nwgKμanRbsiT§PaB³ vamanersIusþg;FMEtmYyTis. enAeBl K x L mantémø
xusKñaBI K y L enaH K y L nwglub elIkElgEt rx / ry tUcCag K x L / K y L . enAeBlpleFobTaMgBIr
esμIKña ssrnwgmanersIusþg;esμIKñakñúgTisedATaMgBIr. sRmab; W-shape enAkñúg column load table
rx / ry sßitenAcenøaH 1.6 nig 1.8 elIkElgsRmab;rUbragEdlRsalCagxøH.

]TahrN_ 4>10³ ssrEdlbgðajenAkñúgrUbTI 4>13 RTnUv factored axial load 840 Kips . eRbIEdk
A36 ehIyeRCIserIs W-Shape.

T.Chhay 96 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dMeNaHRsay³ K x L = 20 ft nigtémøGtibrmarbs; K y L = 8 ft
RbEvgRbsiT§PaB K x L manlkçN³lubenAeBlEdl
KxL
> K yL
rx / ry

b¤k¾enAeBlEdl
⎛r ⎞
KxL
rx / ry
> K yL KxL > ⎜ x
⎜ ry
(
⎟ K yL
⎟
)
⎝ ⎠
kñúgkrNIenH
K x L 20
kyL
=
8
= 2.5 b¤ k x L = 2.5K y L
edaysar K x L mantémøFMCag K y L q¶ay enaH K x L RbEhlCanwglub. mUlehtuKWfatémø
rx / ry EdlmanenAkñúgtaragPaKeRcInmantémøtUcCag 2.5 dUcenH k x L = 2.5 K y L TMngCanwgFMCag

(rx / ry )K y L . sakl,g rx / ry = 1.7 ³

K x L 20
= = 11.76 > K y L
rx / ry 1.7

rMkillT§pl[eTACa KL = 12 ft ehIyBinitüemIlenAkñúg column load table. sakl,g W 10 ×112

¬ φc Pn = 865kips ¦³
témøBitR)akd rK/xrL = 120.74 = 11.5 ft < 12 ft
x y

φc Pn > 840kips EdlRtUvkar

¬edayeFVI interpolation φc Pn = 876kips RtYtBinitü W 12 ×106
KxL 20
= = 11.4 ft
rx / ry 1.76

sRmab; KL = 12 ft
φc Pn = 853kips > 840 ft (OK)
GegátrUbrag W 14 . sRmab; rx / ry = 1.7 ¬pleFobRbEhlsRmab;RKb;krNIEdlGacekItman¦
K x L 20
= = 11.76 ft > K y L = 8 ft
rx / ry 1.7

sRmab; KL = 12 ft / W 14 ×109 EdlmanlT§PaBRTRTg; 905kips CarUbragEdlRsalCagsRmab;

eRKOgbgÁúMrgkarsgát; 97 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

W 14 . RbEvg 12 ft CatémøEdlmanlkçN³snSMsMécénRbEvgRbsiT§PaBBitR)akd rUbragenHKWRKb;

RKan;.
cemøIy³ eRbI W 12 ×106 ¬RsalCageKkñúgcMeNambIrUbragEdl)ansikSa¦

T.Chhay 98 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

sRmab;ssrdac;edayELk (isolated column) EdlminEmnCaEpñkrbs;eRKagCab;

(continuous frame), Table C-C2.1 enAkñúg Commentary to the specification manlkçN³RKb;

RKan;CaTUeTA. EtsRmab;eRKagrwg (rigid frame) enAkñúgrUbTI 4>14. ssrenAkñúgeRKagenHminman

lkçN³ÉkraCü EtvaCaEpñkrbs;rcnasm<n§½Cab;. elIkElgsRmab;ssrEdlenACan;eRkamssrRtUv)an
Tb;enAcugsgçagrbs;va edayFñwmnwgssrdéTeTot. eRKagenHk¾Ca unbraced frame mann½yfaeRKag
GacmanbMlas;TItamTisedk ehIyssrTaMgGs;rgnUv sidesway. RbsinebIeKeRbI Table C-C2.1
sRmab;eRKagenH ssrCan;eRkameKmanlkçxNÐRbhak;RbEhlnwglkçxNÐ (f) ehIytémørbs; K = 0
GacRtUv)aneRbI. sRmab;ssrEdldUcssr AB témørbs; K = 1.2 EdlRtUvKñanwglkçxNÐ (c) Gac
RtUv)aneRCIserIs. EtdMeNIrkarEdlsmRsbCaghñwg KWKitGMBIkRmiténkarTb;Edlpþl;[edaytMN
rbs;Ggát;.
karTb;nwgkarvilEdlpþl;[edayFñwm b¤rtenAxagcugssrCaGnuKmn_eTAnwg rotational
stiffness rbs;Ggát;EdlRbsBVKñaenARtg;cMNucenaH. Rotational stiffness rbs;Ggát;CasmamaRteTA

nwg EI / L / Edl I Ca moment of inertia rbs;muxkat;eFobnwgG½kSénkarBt;. Gaylord nig

Stallmeyer (1992) )anbgðajfaemKuNRbEvgRbsiT§PaB K GaRs½ynwgpleFobrbs; column

stiffness elI girder stiffness enAxagcugrbs;Ggát;nImYy² EdlGacsMEdgCa

G=
∑ Ec I c / Lc = ∑ I c / Lc ¬$>&¦
∑E I /L g g ∑I /L
g g g

Edl ∑ Ec I c / Lc = plbUk stiffness rbs;ssrTaMgGs;EdlenAcugrbs;ssrEdlBicarNa

∑ E g I g / Lg = plbUk stiffness rbs;rtTaMgGs;EdlenAcugrbs;ssrEdlBicarNa
Ec = E g = E =m:UDuleGLasÞicrbs;eRKOgbgÁúMEdk
RbsinebIssrEdlRsavxøaMg (very slender column) RtUv)anP¢ab;eTAnwgrtEdlmanmuxkat;FM
enaHrtnwgkarBarkarvilrbs;ssry:agmanRbsiT§PaB. cugrbs;ssrmanlkçN³ approximately
fixed enaH K nwgmantémøtUc. lkçxNÐenHRtUvKñanwgtémøtUcbMputrbs; G Edl[edaysmikar $>&.

b:uEnþ cugrbs;ssrmaM (stiff column) EdlP¢ab;eTAnwg flexible beam Gacnwgpþl;karvileday

esrIdl;ssr EdlRtUvKñanwglkçxNÐTRm pinned Edl[témø G nig K FM.
TMnak;TMngrvag G nig K RtUv)andak;enAkñúg Jackson-Mooreland Alignment Chart
(Johnston, 1976) EdlRtUv)anpliteLIgvijenAkñúg Figure C-C2.2 enAkñúg Commentary . edIm,I

eRKOgbgÁúMrgkarsgát; 99 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

TTYl)antémø K BIr nomogram mYykñúgcMeNamTaMgBIr dMbUgKNnatémø G enAcugnImYy²rbs;ssr

eday[mYyCa G A nigmYyeTotCa GB . P¢ab; G A nig GB edaybnÞat;Rtg; ehIyGantémø K
enAelIbnÞat;kNþal. emKuNRbsiT§PaBEdlTTYl)anCatémøEdleFobTAnwgG½kSénkarBt; EdlCaG½kS
EkgeTAnwgbøg;rbs;eRKag. karviPaKdac;edayELkGaceFVIeLIgsRmab;karekagEdleFobnwgG½kSmYy
eTot. CaFmμta beam-to-column connection enAkñúgTisedAenHnwgminbBa¢Únm:Um:g; ¬ sidesway
RtUv)ankarBareday bracing ¦ ehIy K GacnwgykesμI 1.0 .

]TahrN_ 4>11³ eRKagrwgEdlbgðajenAkñúgrUbTI 4>15 CaeRKag unbraced frame . Ggát;nImYy²

RtUv)andak;eday[RTnugrbs;vasßitenAkñúgbøg;rbs;eRKag. kMNt;emKuNRbEvgRbsiT§PaB K x
sRmab;ssr AB nig BC .

dMeNaHRsay³ ssr AB ³
sRmab;tMN A
G=
∑ I c / Lc = 347 / 3.6 + 445 / 3.6 = 220 = 0.95
∑ I g / Lg 560 / 6 + 762 / 5.5 231.9
sRmab;tMN B
G=
∑ I c / Lc = 445 / 3.6 + 445 / 4.6 = 220.3 = 0.95
∑ I g / Lg 560 / 6 + 762 / 5.5 231.9
BI alignment chart sRmab; sidesway uninhibited CamYynwg G A = 0.95 nig GB = 0.95 / K = 1.3
T.Chhay 100 Compression members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

sRmab;ssr AB .
ssr BC
sRmab;tMN B KNnadUcmun
G = 0.95
sRmab;tMN C Rtg;TRm pinned . sßanPaBrbs;vamanlkçN³dUceTAnwgssrEdlmaMxøaMgP¢ab;eTAnwg
infinity flexible girder Edlrtman stiffness esμIsUnü. dUcenHpleFobPaBrwgRkajrbs;ssr

(column stiffness) elIPaBrwgRkajrbs;rt (girder stiffness) mantémøesμIGnnþsRmab;snøak;Kμan

kkiteBjelj (perfectly frictionless hinge).

lkçxNÐcugenHGaceFVIeTA)ansRmab;karsμanenAkñúgkarGnuvtþ dUcenH eyIgGacyk G = 10 sRmab;
tMNenH.
BI alignment chart CamYynwg G A = 0.95 nig GB = 10 / K = 1.85 sRmab;ssr BC .
dUcEdl)anKUsbgðajenAkñúg]TahrN_4>11 sRmab;TRm pinned G KYrRtUv)anykesμInwg
10.0 sRmab; TRm fixed G KYrRtUv)anykesμInwg 1.0 . lkçxNÐTRm fixed RtUvKñanwgrtEdlrwgmaMxøaMg

(infinitely stiff girder) nig flexible column EdlRtUvKñanwgtémøtamRTwsþI G = 0 . kñúgkareRbIR)as;

alignment chart enAkñúg Commentary )anENnaM[eRbI G = 1.0 edaysarEteKBi)annwgTTYl)anTRm

fixed eBjelj.

Unbraced frame manlT§PaBTb;nUvkmøaMgxagedaysartMNEdlTb;nwgm:Um:g;rbs;va. Ca

erOy²eRKagbEnßmedayRbB½n§BRgwgtamrUbragepSg² eRKagEbbenHRtUv)aneKehAfa braced frame.

karTb;kmøaMgxagbEnßmGaceFVIeLIgkñúgTRmg;Ca diagonal bracing dUcbgðajenAkñúgrUbTI 4>16 b¤ rigid
shear wall. kñúgkrNIepSgeTot ssrRtUv)anTb;eday panel b¤ bay sRmab;km<s;TaMgmUlrbs;eRKag.

TRmenHbegáItCa cantilever structure EdlTb;nwgbMlas;TItamTisedk ehIyk¾pþl;nUvTRmtamTisedk

sRmab;ElVgdéTeTot. GaRs½yeTAnwgTMhMrbs;eRKOgbgÁúM ElVgeRcInCagmYyGacRtUv)anBRgwg. ssr
EdlCaGgát;rbs; braced frame RtUv)ankarBarBI sidesway nigmankarTb;karvilenAxagcugrbs;vaxøH.
dUcenH vaCaRbePTGgát;sßitenAkúñgcenøaHkrNI (a) nig (d) enAkñúg Table C-C2.1 rbs; Commentary
ehIy K sßitenAcenøaH 0.5 nig 1.0 . dUcenH 1.0 CatémøEdltUcsRmab;Ggát; én braced frame
ehIyCatémøEdl AISC C2.1 ENnaM[eRbI elIkElgEtmankarviPaKNamYyeFVIeLIg. karviPaKGaceFVI
eRKOgbgÁúMrgkarsgát; 101 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

eTA)anedayeRbI alignment chart sRmab; braced frame . kareRbI nomogram nwgpþl;lT§-

plCa effective length factor EdltUcCag 1.0 bnþicbnþÜc ehIyeKnwgTTYl)ankarsnSMsMécxøH . *

CamYynwg design aid xøH eKeRbI alignment chart kñúglkçxNÐEdleKbegáItvaeLIg. lkçxNÐ

TaMgenHmanenAkñúg Section C2 of the Commentary to the Specification ehIyminRtUv)anerobrab;
enATIenHeT. RKb;lkçxNÐTaMgGs;nwgRtUv)anbMeBjesÞIrEtTaMgGs;CaTUeTA RbsinebIdUcenaHeT PaBxus
KñaenaHCaEpñkmYyKYr[RbugRbytñ½. lkçxNÐmYyEdlminRtUv)anbMeBjCaTUeTAenaH KWtRmUvkarEdlfa
RKb;karRbRBwtþeTArbs;Ggát;sßitkñúglkçN³eGLasÞic. RbsinebI slenderness parameter λc tUcCag
1.5 ssrnwgekageday inelastic ehIyemKuNRbEvgRbsiT§PaBEdlTTYl)anBI alignment chart nwg

mantémøtUcEmnETn. ssrPaKeRcInsßitenAkñúgRkumenH. dMeNIrkargayRsYlkñúgkarkMNt; K sRmab;

inelastic column GnuBaØat[eRbI alignment chart (Yura, 1971 and Dique, 1973). edIm,IbkRsay

*
RbsinebIeRKagRtUv)anBRgwgTb;nwg sidesway tMN beam-to-column minRtUvkar moment resisting ehIyRbBn§½BRgwgGac
RtUv)anKNnaedIm,ITb;nUvRKb; sidesway tendency . b:uEnþRbsinebItMNminEmnCa moment resisting vanwgminmanPaBCab;
rvagssr nigrt ehIyeKminGaceRbI alignment chart . sRmab; braced frame RbePTenH K x KYrRtUvykesμInwg 1.0 .
T.Chhay 102 Compression members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dMeNIrkarenH eyIgcab;epþImCamYynwg critical buckling load sRmab; inelastic column Edl[eday

smIkar $>^ b. edayEckvanwgRkLaépÞmuxkat;eKTTYl)an buckling stress³
π 2 Et
Fcr =
(KL / r )2
rbs;ssrenAkñúgkrNIenHCasmamaRtnwg Et I c / Lc ehIytémøEdlsmRsb
Rotational stiffness

rbs; G sRmab;eRbIenAkñúg alignment chart KW

Ginelastic =
∑ Et I c / Lc = Et G
elastic
∑ EI g / Lg E
eday Et tUcCag E enaH Ginelastic nwgtUcCag Gelastic ehIy effective length factor K nwgRtUv)an
kat;bnßy CalT§pleKTTYl)ankarKNnamYyEdlmanlkçN³esdækic©Cag. edIm,IkMNt; Et / E Edl
eK[eQμaHfa emKuNkat;bnßyPaBrwgRkaj (stiffness reduction factor SRF)/ BicarNaTMnak;TMng
xageRkamsRmab;ssrEdlmanTRmcug pinned ³
Fcr (inelastic) π 2 Et / (L / r )2 Et
= = ¬$>*¦
F cr ( elastic)
2
π E / (L / r )
2 E

AISC eRbItémøRbhak;RbEhlsRmab;Epñk inelastic én column strength curve dUcenHsmIkar $>*

CatémøRbhak;RbEhlenAeBlEdl AISC Equation E2-2 nig E2-3 RtUv)aneRbIsRmab; Fcr . Rbsin
ebI eyIg[
P P /φ
Fcr = cr ≈ u c
A A
enAeBlEdl Fcr (inelastic) / Fcr (elastic) CaGnuKmn_én Pu /(φc A) . ]TahrN_ sRmab;
Pu / (φc A) = 180 MPa nig F y = 250 MPa

Fcr (inelastic) ≈ 180 MPa = 0.658λc F y = 0.658λc (250 )

2 2

λ2c = 0.785
0.877 0.877
Fcr (elastic) = Fy = 250 = 279.3MPa
λ2c 0.785

dUcenHemKuNkat;bnßyPaBrwgRkajKW
Fcr (inelastic) 180
SRF = = = 0.644
Fcr (elastic) 279.3

eRKOgbgÁúMrgkarsgát; 103 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

edaysar φc efr enaH SRF k¾CaGnuKmn_én Pu / A . témørbs; SRF EdlCaGnuKmn_én Pu / A

RtUv)an[enAkúñg Table 3-1 in Part 3 of the Manual.

]TahrN_ 4>12³ rUb 4>17 bgðajBI rigid unbraced frame. Ggát;TaMgGs;RtUv)andak;edayeFVIy:ag

Na[karBt; eFobnwgG½kSxøaMg. TRmxagRtUv)andak;enAtMNnImYy²edaytMNFmμtaEdlBRgwgkñúgTis
edAEkgeTAnwg eRKag. kMNt;emKuNRbEvgRbsiT§PaBedayeFobnwgG½kSnImYy²sRmab;Ggát; AB .
bnÞúktamG½kSemKuNenAelIGgát;enHKW 180kips ehIyeKeRbIEdk A36 .

dMeNaHRsay³ KNnaemKuNeGLasÞicrbs; G
sRmab;tMN A /
∑ (I c / Lc ) = 170 / 12
=
14.17
= 1.52
∑ (I g / Lg ) 88.6 / 20 + 88.6 / 18 9.35
sRmab;tMN B
∑ (I c / Lc ) = 2(170 / 12) = 28.3 = 1.35
∑ (I g / Lg ) 190 / 20 + 190 / 18 21.0
BI alignment chart sRmab; unbraced frames, K x = 1.43 / edayQrelI elastic behavior dUcenH
KxL Fy 1.43(12 )(12 ) 36
λc = = = 0.5512
rxπ E 4.19 ⋅ π 29000
edaysar λc tUcCag 1.5 enaHeKRtUveRbIemKuN K inelastic Edl[
Pu 180
= = 18.5ksi
A 9.71
BI Table 3-1in Part 3 of the Manual emKuNkat;bnßyPaBrwgRkaj SRF = 0.83
sRmab;tMN A
Ginelastic = SRF × Gelastic = 0.83 × 1.52 = 1.26
sRmab;tMN B
Ginelastic = SRF × Gelastic = 0.83 × 1.35 = 1.12
cemøIy³ BI alignment chart K x = 1.37 . edaysarlkçxNÐTRmFmμtasRmab;eRKag enaH K y esμInwg
1.

T.Chhay 104 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RbsinebIcugssrCaTRm fixed (G=1.0) b¤ pinned (G=10.0) témørbs; G minRtUv)anKuNnwg SRF

eT.

4>6>karekagedayrmYl nigedayBt;-rmYl (Torsional and Flexural-Torsional Buckling)

enAeBlEdlGgát;rgkarsgát;edaybnÞúkcMG½kS køayCaKμansßirPaB¬minEmn locally unstable¦
vaGacekagkñúgrUbragmYykñúgcMeNamrUbragbI dUcbgðajenAkñúgrUbTI 4>18.
!> karekagedaykarBt; (flexural buckling) eyIg)anBicarNakarekagRbePTenHtaMgBImunrhUtmk
dl;eBlenH. vaCaPaBdabEdlekIteLIgedaykarBt; (bending or flexure) CMuvijG½kSEdlRtUv
nwgpleFobPaBrwgRkaj (slenderness ratio) FMCageK ¬rUbTI 4>18 a¦. CaTUeTAvaCa minor
principle axis EdlmankaMniclPaB (radius of gyration) tUcCageK. Ggát;rgkarsgát;Edlman

muxkat;RKb;rUbragGac)ak;tamTRmg;enH.
@> karekagedayrmYl (torsional buckling) kar)ak; (failure) edayRbePTenHKWbNþaledaykarmYl
(twisting) tamG½kSbeNþayrbs;Ggát;. vaGacekIteLIgEtCamYynwgGgát;EdlmanlkçN³Rsav

xøaMg ehIymanmuxkat;sIuemRTIDub (double symmetrical cross section) ¬rUbTI 4>18 b¦.

Standard hot-rolled shapes mingaynwgrgnUvkarekagedayrmYlenHNas; b:uEnþGgát; built-up BI

eRKOgbgÁúMrgkarsgát; 105 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

bnÞHesþIggayeRKaH nigKYreFVIkarGegát. rUbragExVgbgðajnUvPaBgayrgeRKaHBiesssRmab;RbePT

énkarekagenH. rUbragenHGac)anmkBIkarpÁúMBIbnÞHdUcbgðajenAkñúgrUb b¤ built-up BImMubYnTl;xñgKña.

#> karekagedaykarBt;-rmYl (flexural-torsional buckling) kar)ak;RbePTenHbegáIteLIgedaybnSM

énkarekagedaykarBt; nigkarekagedayrmYl. Ggát;ekag nigrmYlkñúgeBlEtmYy¬rUbTI4>18 c¦.
karekagRbePTenHGacekIteLIgEtCamYymuxkat;EdlmanrUbragminsIuemRTI TaMgrUbragEdlman
G½kSsIuemRTImYyTis dUcCa channel, structural tee, double-angle shape nig equal-leg sigle
angles nigrUbragEdlKμanG½kSsIuemRTI dUcCa unequal-leg single angle.

AISC Specification tRmUvnUvkarviPaKBI torsional b¤ flexural-torsional buckling enAeBl

smrmü. Section E3 of the Specification erobrab;BIGgát; double angle nig tee-shaped ehIy
Appendix E3 pþl;nUvviFITUeTAEdlGaceRbIsRmab;RKb;rUbragminsIuemRTI.

dMbUgeyIgerobrab;BIviFIEdlmanenAkñúg Appendix E3. vaQrenAelIkareRbIR)as; slenderness

parameter λe CMnYs[ λc . eyIgTTYl λe dUcxageRkam. BI Euler buckling stress/

T.Chhay 106 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

π 2E
Fe =
(KL / r )2
Slenderness ratio GacsresrCa
KL π 2E
=
r Fe

RbsinebI Fe RtUv)ankMNt;Ca elastic buckling stress EdlRtUvnwgrUbragénkar)ak;Edllub eTaHeday

flexural, torsional b¤ flexural-torsional enaH slenderness ratio EdlRtUvKñaKW

⎛ KL ⎞ π 2E
⎜ ⎟ =
⎝ r ⎠e Fe

ehIy slenderness parameter EdlRtUvKñaKW

(KL / r )e Fy Fy ( KL / r ) e2 Fy
λe = = =
π E π 2E Fe

dMeNIrkarKNnamandUcxageRkam³
!> kNt; Fe sRmab; torsional elastic buckling b¤ flexural-torsional elastic buckling BIsmIkar
Edl[enAkñúg Appendix E3.
@> KNna effective slenderness parameter, λe .
#> KNna critical stress Fcr BIsmIkarFmμta (AISC Equations E2-2 and E2-3) b:uEnþeRbI λe CMnYs
[ λc . bnÞab;mk design strength KW
φc Pn = φc Ag Fcr

Edl φc = 0.85 dUcKñasRmab; flexural buckling.

smIkarsRmab; Fe Edl[enAkñúg AISC Appendix E3KWQrelI well-established theory
Edlmankñúg Theory of Elastic Stabality (Timoshenko and Gere, 1961). elIkElgsRmab;kar
pøas;bþÚrxøHenAkñúg notation vamansmIkardUcKñaenAkñúgesovePAenaH edayKμankarsRmYl. sRmab;
doubly symmetrical shapes (torsional buckling)/
⎡ π 2 EC w ⎤ 1
Fe = ⎢ + GJ ⎥ (AISC Equation A-E3-5)
⎢⎣ (K z L )2 ⎥⎦ I x + I y
sRmab; singly symmetrical shape (flexural-torsional buckling)/

eRKOgbgÁúMrgkarsgát; 107 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Fey + Fez ⎛ ⎞
⎜ 4 Fey Fez H ⎟
Fe = − −
( )
⎜⎜ 1 1 ⎟⎟ (AISC Equation A-E3-6)
2H Fey + Fez 2
⎝ ⎠
sRmab;rUbragEdlKμanG½kSsIuemRTI (flexural-torsional buckling)/
(Fe − Fex )(Fe − Fey )(Fe − Fez ) − Fe2 ( Fe − Fey )(xo / r o )2
(AISC Equation A-E3-7)
− Fe2 (Fe (
− Fex ) yo / r o )
2
=0
smIkarcugeRkayCasmIkardWeRkTI3 dUcenHrbs; Fe KWtUcNas;. CasMNagl¥ PaBcaM)ac;kñúgkaredaH
RsaysmIkarenHKWticbMput edaysareKkMreRbIrUbragminsIuemRTICaGgát;rgkarsgát;Nas;. GgÁEdl
min)ankMNt;BImunEdleRbIenAkñúgsmIkarTaMgbIenHRtUv)ankMNt;dUcteTA³
C w = warping constant
Kz = emKuNRbEvgRbsiT§PaBsRmab;karekagedayrmYl EdlQrelIbrimaNénkarTb;cug
RbqaMgnwgkarrmYltamG½kSbeNþay.
G = shear modulus
J = torsional constant ¬esμIeTAnwg polar moment of inertia sRmab;Etmuxkat;mUl¦
π 2E
Fex = (AISC Equation A-E3-10)
(K x L / rx )2
π 2E
Fey =
(K y L / ry )2
(AISC Equation A-E3-11)

Edl y CaG½kSsIuemRTIsRmab; singly symmetric shapes.

⎡ π 2 EC w ⎤ 1
Fez = ⎢ + GJ ⎥ (AISC Equation A-E3-12)
⎢⎣ (K z L )2 ⎥⎦ Ar o2
⎛ x2 + y2 ⎞
H = 1− ⎜ o o ⎟ (AISC Equation A-E3-9)
⎜ 2 ⎟
⎝ ro ⎠
Edl xo nig yo CakUGredaenén shear center rbs;muxkat;edayeFobnwgTIRbCMuTm¶n;. Shear
center CacMNucenAelImuxkat;EdlbnÞúkeFVI[Ggát;ekagedayminrmYl. Shear center RtUv)anniyay

lMGitenAkñúgCMBUk 5.
2 Ix + I y
r o = xo2 + yo2 + (AISC Equation A-E3-8)
A
eKGacrktémøefrEdleRbIenAkñúgsmIkarTaMgbIsRmab; Fe enAkñúgtarag torsion properties nig
flexural-torsional properties enAkñúg part 1 of the Manual . sRmab; W, M, S nig HP shapes,

T.Chhay 108 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

J nig Cw RtUv)an[. eK[témø J / Cw / r o nig H RtUv)an[sRmab; channel, single angle nig

structural tee. taragsRmab; double angle [témø r o nig H ¬ J nig C w esμInwgBIrdgén

témøEdl[sRmab; single angle¦.

dUc)anbgðajBIxagelI eKkRmnwgviPaKkarekagedayrmYlsRmab;muxkat;sIuemRTIDub. dUcKña
eKkRm eRbIrUbragKμanG½kSsIuemRTICaGgát;rgkarsgát; ehIyeKkMrnwgviPaK flexural-tensional buckling
én Ggát;RbePTenHEdr RbsinebIman eKcaM)ac;RtUvEtviPaKva. sRmab;ehtuplTaMgenH eyIgkMNt;kar
BicarNaelIrUbrag flexural-torsional buckling CamYynwgG½kSsIuemRTImYy. elIsBIenH double angle
EdlCa built-up shape CaRbePTrUbragEdleKniymeRbIeRcIn.
sRmab; singly symmetrical shape, flexural-torsional buckling stress Fe TTYl)anBI
AISC Equation A-E3-6. enAkñúgsmIkarenH y RtUv)ankMNt;CaG½kSsIuemRTI ¬edayminKitBITisedA

rbs;Ggát;¦ehIy flexural-torsional buckling RtUv)anKitEttamG½kSmYyenH ¬flexural buckling

tamTisenHnwgminekItman¦. G½kS x RbQmEtnwg flexural buckling. dUcenH sRmab; singly
symmetrical shape eKGacmanersIusþg;BIrKW flexural-torsional buckling tamG½kS y ¬G½kSsIuemRTI¦

b¤ flexural buckling eFobG½kS x . edIm,IkMNt;mYyNamanlkçN³lub KNnaersIusþg;EdlRtUvnwg

G½kSnImYy² ehIyeRbItémøNaEdltUcCag.

]TahrN_ 4>13³ KNna design compressive strength rbs; WT13.5 × 80.5 . RbEvgRbsiT§PaB
tamG½kS x KW 25 feet 6inches RbEvgRbsiT§PaBtamG½kS y KW 20 feet ehIyRbEvgRbsiT§PaBtam
G½kS z KW 20 feet . eRbIEdk A36 .
dMeNaHRsay³ KNna design compressive strength sRmab;G½kS x ³
K x L 25.5(12)
= = 77.27
rx 3.96
KL Fy 77.27 36
λc = = = 0.8666 < 1.5
rπ E π 29000
eRbI AISC Equation E2-2
Fcr = (0.658)λc F y = (0.658)0.8666 (36) = 26.29ksi
2 2

φc Pn = φc Ag Fcr = 0.85(23.7 )(26.29 ) = 530kips

eRKOgbgÁúMrgkarsgát; 109 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

KNna flexural-torsional buckling strength CMuvijG½kS y

π 2E π 2 (29000 )
Fey = = = 52.17 ksi
(K y L / ry )2 (74.07) 2
⎡ π 2 EC w ⎤ 1
Fez = ⎢ + GJ ⎥
⎣⎢ (K z L )
2 2
⎦⎥ Ar o
⎡ π 2 (29000 )(42.7 ) ⎤
+ 11200(7.31)⎥
1
=⎢ = 107.7 ksi
⎣⎢ (20 × 12 ) ⎦⎥ 23.7(5.67 )
2 2

Fey + Fez = 52.17 + 107.7 = 159.9ksi

Fey + Fez ⎡ 4 Fey Fez H ⎤

Fe = ⎢1 − 1 − ⎥
2H ⎢
⎣
(
Fey + Fex 2 ⎥
⎦
)
159.9 ⎡ 4(52.17 )(107.7 )(0.813) ⎤
= ⎢1 − 1 − ⎥ = 45.81ksi
2(0.813) ⎢⎣ (159.9)2 ⎥⎦
Fy 36
λe = = = 0.8865
Fe 45.81

edaysartémøenHtUcCag 1.5 eRbI AISC Equation E2-2 CamYynwg λe CMnYs[ λc ³

⎛ 2 ⎞
Fcr = ⎜ 0.658λe ⎟ F y = (0.658)(0.8865) (36) = 25.91ksi
2

⎝ ⎠
φc Pn = φc Ag Fcr = 0.85(23.7 )(25.91) = 522kips (controls)

cemøIy³ Design strength = 522kips

cMNaMfa enAeBlEdl Fcr nig Fe RtUv)anKNna karKNnasRmab; flexural buckling CMuvij

G½kS x nig flexural-torsional buckling CMuvijG½kS y manlkçN³dUcKña. dUcenHbnÞab;BI Fcr nig Fe
RtUv)anKNna TaMg λc nig λe GacRtUv)anKNna ehIytémøEdltUcCagRtUv)aneRbIedIm,IKNna
strength . kareFVIEbbenHedIm,Ikat;bnßykarcaM)ac;kñúgkarKNna strength sRmab;G½kSTaMgBIr.

dMeNIrkarviPaK flexural-torsional buckling elI double-angle nig tee Edl[enAkñúg AISC

Section E3 CakarEksRmYldMeNIrkarviPaKEdl[enAkñúg AISC Appendix E3. vak¾mankarEkERb

kMNt;cMNaMxøHdUcCa³ BI Fe eTACa Fcrft / Fey eTACa Fcry nig Fez eTACa Fcrz . kugRtaMg Fcry
RtUv)anrkBI AISC E2 nigQrelI flexural buckling eFobG½kS y .
edIm,ITTYl)an Fcrz eyIgGacecalG½kSTImYyrbs; AISC Equation A-E3-12 enaH
T.Chhay 110 Compression members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

GJ
Fcrz =
2
Ar o
karlubecalenHGacGnuBaØat)an BIeRBaHsRmab; double-angle nig tee GgÁTImYymantémøtUc
Gacecal)anebIeFobnwgGgÁTIBIr.
Flexural buckling stress Fcry RtUv)anKNnaCamYynwgsmIkarFmμtarbs; AISC Chapter E

edayeRbI KL / r EdlRtUvKñanwgG½kS y ¬G½kSsIuemRTI¦.

bnÞab;mkeTot nominal strength GacRtUv)anKNnadUcxageRkam
Pn = Ag Fcrft

⎛ Fcry + Fcrz ⎞⎡ 4 Fcry Fcrz H ⎤

Edl Fcrft = ⎜⎜ ⎟ ⎢1 − 1 − ⎥
( )
⎟⎢ (AISC Equation E3-1)
⎝ 2H ⎠⎣ Fcry + Fcrz 2 ⎥
⎦
RKb;GgÁTaMgGs;Edl)anmkBI Appendix E3 rkSadEdl. dMeNIrkarenH RtUv)aneRbIsRmab;Et
double-angle nig tee eRBaHvapþl;nUvcemøIysuRkitCagkareRbIdMeNIrkarEdl[enAkñúg Appendix E3.

]TahrN_ 4>14³ KNna design strength rbs;rUbragenAkñúg]TahrN_TI 4>13 edayeRbIsmIkarrbs;

AISC Equation E3.

dMeNaHRsay³ BI]TahrN_ 4>13 flexural buckling strength sRmab;G½kS x KW 530kips ehIy

K y L / ry = 74.07 . BI AISC E2-4, slenderness parameter KW

KL Fy 74.07 36
λc = = = 0.8307 < 1.5
rπ E π 29000
BI AISC Equation E2-2,
⎛ 2 ⎞ (0.8307 )2 (36) = 26.97ksi
Fcr = Fcry = ⎜ 0.658λc ⎟ F y = (0.658)
⎝ ⎠
BI AISC E3,
GJ 11200(7.31)
Fcrz = = = 107.5ksi
Ar o
2
23.7(5.67 )2
Fcry + Fcrz = 26.97 + 107.5 = 134.5ksi

⎛ Fcry + Fcrz ⎞⎡ 4 Fcry Fcrz H ⎤

Fcrft = ⎜⎜ ⎟ ⎢1 − 1 − ⎥
⎝ 2H ⎟⎢
⎠⎣ (
Fcry + Fcrz 2 ) ⎥
⎦

eRKOgbgÁúMrgkarsgát; 111 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

134.5 ⎡ 4(26.97 )(107.5)(0.813) ⎤

= ⎢1 − 1 − ⎥ = 25.48ksi
2(0.813) ⎢ ( )2
⎥⎦
⎣ 134 . 5
φc Pn = φc Ag Fcrft = 0.85(23.7 )(25.48) = 513 (Control)

cemøIy³ Design strength = 513kips

lT§plenAkñúg]TahrN_ 4>13 nig 4>14 bgðajBIkMhuskñúgkareRbIR)as; Appendix E3

sRmab; rUbragenHmanlkçN³minsnSMsMéc. viFIsaRsþEdleRbIenAkñúg]TahrN_ 4>14 EdlQrelI
AISC Specification E3 EtgEtRtUv)aneRbIsRmab; double angle nig tee. b:uEnþkñúgkarGnuvtþ ersIusþg;

rbs; double angle nig tee PaKeRcInGacrk)anenAkñúg column load table. taragTaMgenaH KWQrelI
viFIsaRsþEdlesñIeLIgeday AISC E3 ehIyk¾GaceRbIedIm,IepÞógpÞal;lT§plrbs;]TahrN_ 4>14.
taragpþl;nUvtémø design strength BI EdlmYyCa flexural buckling eFobG½kS x nigmYyeTotCa
flexural-torsional buckling eFobG½kS y .

taragTaMgenaHk¾pþl;pgEdrsRmab;Ggát;rgkarsgát; single-angle. Design strength Edl

[edayminQrelIRTwsþI flexural-torsional buckling RtUv)an[enAkñúg specification dac;edayELk
sRmab; single-angle member enAkñúg Part 6 of the Manual, Specification and Codes.
4>7> Built-up Member

RbsinebIeKsÁal;lkçN³muxkat; (cross-sectional properties)rbs;Ggát;rgkarsgát; built-up

karviPaKrbs;vamanlkçN³RsedogKñasRmab;Ggát;rgkarsgát;epSgeTot RbsinebIEpñkpÁúMrbs;muxkat;t
P¢ab;)anl¥. AISC E4 mankarlMGitCaeRcInEdlTak;TgeTAnwgkartP¢ab;enH CamYynwgtRmUvkardac;
edayELksRmab;Ggát;EdlpÁúMeday rolled shape mYy b¤eRcIn nigGgát;EdlpÁúMeday plate b¤bnSMén
plate nig Edkrag (shape). munnwgBicarNaBIbBaðatP¢ab; eyIgnwgrMlwkBIkarKNnalkçN³muxkat;rbs;

rUbrag built-up.
Design strength rbs;Ggát;rgkarsgát; built-up CaGnuKmn_eTAnwg slenderness parameter

λc . dUcenHeKRtUvkMNt;G½kSem nigkaMniclPaBEdlRtUvKñanwgG½kSTaMgenaH. sRmab;muxkat;

homogenous G½kSemRtYtsIunwgG½kSTIRbCMuTm¶n;. viFIsaRsþkñúgkarKNnaRtUv)anbgðajenAkñúg]TahrN_

4>15. EpñkpÁúMrbs;muxkat;RtUv)ansnμt;fatP¢ab;)anl¥.
T.Chhay 112 Compression members
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

]TahrN_ 4>15³ ssrEdlbgðajenAkñúgrUbTI 4>19 RtUv)anplitedaykarpSarEdkbnÞH 4"× 38 " BIelI

søabrbs;Edk W 18× 35 . EdkpÁúMTaMgBIrCaEdk A36 . RbEvgRbsiT§PaBeFobG½kSTaMgBIrKW 15 feet .
edaysnμt;EdkpÁúMTaMgBIrRtUv)antP¢ab;edayeFVIy:agNa[Ggát;manRbsiT§PaBeBj ehIyKNna design
strength edayQrelI flexural buckling.

dMeNaHRsay³ CamYynwgkarbEnßmEdkBIelI rUbragmanlkçN³minsIuemRTIbnþic b:uEnþ\T§iBl flexural-

torsionalRtUv)anecal.

G½kSsIuemRTIbBaÄrCaG½kSemmYyEdleKminRtUvkarKNna. eKnwgrkG½kSemedkedayeRbI
principle of moment³ plbUkm:Um:g;RkLaépÞrbs;FatupSMnImYy²eFobnwgG½kSNamYy ¬enAkñúg]Ta-

hrN_enH G½kSedksßitenAEpñkxagelIrbs; plateRtUv)aneRbI¦ RtUvEtesμInwgm:Um:g;RkLaépÞsrub.

eyIgeRbItarag 4>1 edIm,IsRmYldl;karKNna.
tarag 4>1
Component A y Ay
Plate 1.500 0.1875 0.2812
W 10.3 9.225 95.02
∑ 11.8 95.30
y=∑
Ay 95.30
= = 8.076in
∑ A 11.8
CamYynwgTItaMgrbs;G½kSTIRbCMuTm¶n;edkEdl)anKNnaxagelI eyIgGacKNnam:Um:g;niclPaB
eFobnwgG½kSenHedayeRbI parallel-axis theorem³
I = I + Ad 2
Edl I= m:Um:g;niclPaBeFobG½kSTIRbCMuTm¶n;rbs;RkLaépÞpSM
A = RkLaépÞrbs;EpñkpSM

I = m:Um:g;niclPaBeFobG½kSRsbeTAnwgG½kSTIRbCMuTm¶n;rbs;RkLaépÞpSM

eRKOgbgÁúMrgkarsgát; 113 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

cm¶ayEkgrvagG½kSBIr
d=

karcUlrYmBIRkLaépÞpSMnImYy²RtUv)anKNna nigRtUv)anbUkedIm,ITTYl)anm:Um:g;niclaPaBrbs;
composite area. tarag 4>2 CataragEdlbEnßmBIelItarag 4>1 edayrYmbBa©ÚlkarKNnaenH.

sRmab;G½kSQr
y = (3 8)(4)3 + 15.3 = 17.30in 4
1
12
¬ controle¦
Iy 17.30
ry = = = 1.211in
A 11.8
tarag 4>2
Component A y Ay I d I + Ad 2
Plate 1.500 0.1875 0.2812 0.01758 7.889 93.37`
W 10.3 9.225 95.02 510 1.149 523.6
∑ 11.8 95.30 617.0= I x
KL Fy 15(12) 36
λc = = = 1.667 > 1.5
rπ E 1.211π 29000
⎡ 0.877 ⎤ ⎡ 0.877 ⎤
Fcr = ⎢ ⎥ Fy = ⎢ ⎥ (36) = 11.36ksi
⎢⎣ λ2c ⎥⎦ ⎢⎣ (1.667 )2 ⎥⎦
φc Pn = φc Ag Fcr = 0.85(11.8)(11.36 ) = 114kips

cemøIy³ Design strength = 114kips .

tRmUvkarkartP¢ab;sRmab; Built-up Members EdlpSMeLIgeday Rolled Shapes

rUbrag built-up EdleKniymCageKKWrUbragEdlpÁúMeLIgeday rolled shap EdleK[eQμaH fa
double-angle shape. Ggát;RbePTenHnwgRtUv)aneRbIedIm,IbgðajBItRmUvkarsRmab;Ggát; built-up Rb

ePTenH. rUbTI 4>20 bgðajGgát;rgkarsgát;rbs; truss EdlP¢ab;eTAnwg gusset plate enAxagcugnImYy

²rbs;va. edIm,IrkSa back-to-back seperation rbs; angle tambeNþayRbEvg fillers nig spacers
EdlmankRmas;esμInwg gusset plate RtUv)andak;enA angles edayKMlatesμI²Kña. KMlatRtUvEtmantémø
tUcRKb;RKan;edIm,IeFVI[ built-up member enHeFVIkarCalkçN³EtmYy. RbsinebIGgát;ekageFobG½kS x
¬flexural buckling¦ eRKOgP¢ab; (connector) minrgnUvbnÞúkKNnaNamYyeT ehIybBaðaénkartP¢ab;
KWsamBaØedayrkSaTItaMgrbs;Ggát;TaMgBIr. edImI,Fanafa built-up member eFVIkarCalkçN³EtmYy

T.Chhay 114 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

AISCtRmUvfa stiffness rbs;FatupSMnImYy²minRtUvFMCagbIPaKbYnén stiffness rbs; built-up

member eT.
a 3 KL
≤
ri 4 r
Edl a= KMlatrbs;eRKOgP¢ab;
ri = kaMniclPaBGb,brmarbs;FatupÁúM

KL / r = maximum slenderness ratio rbs; built-up member

RbsinebIGgátekageFobG½kSsIuemeRTI ¬EdlvargnUv flexural-torsional buckling eFobG½kS

y ¦ eRKOgP¢ab;rgnUvkmøaMgkat;. lkçxNÐenHGacRtUv)anemIleXIjedayBicarNa planks BIrEdleRbICa

Fñwm RtUv)anbgðajenAkñúgrUbTI 4>21. RbsinebI plank minRtUv)anP¢ab; vanwgrGiltamépÞb:H enAeBl

EdlvargbnÞúk ehIyvanwgeFVIkarCaFñwmBIrdac;edayELkBIKña. enAeBlEdlvaRtUv)anP¢ab;edayb‘ULúg
¬b¤eRKOgP¢ab;epSgeTotdUcCa EdkeKal¦ plank TaMgBIrnwgeFVIkarEtmYy ehIyersIusþg;Tb;nwgkarrGil
nwgbegáItCakmøaMgkat;enAkñúgb‘ULúg. kareFVIkarEbbenHekItmanenAkñúg double-angle shape enAeBl
karekageFobnwgG½kS y . RbsinebIFñwm plank RtUv)andak;eday[karekagekItmaneFobnwgG½kSepSg
eTot ¬G½kS b ¦ enaH plank TaMgBIrnwgekagkñúglkçN³dUcKña ehIyKμankarrGil nigKμankmøaMgkat;.
kareFVIkarenHmanlkçN³RsedogKñanwgkarekageFobG½kS x rbs; double-angle shape . enAeBlEdl
eRKOgP¢ab;rgnUvkmøaMgkat; eKRtUvkar modified slenderness ratio EdlmantémøFMCagtémøBitR)akd.
eRKOgbgÁúMrgkarsgát; 115 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

BicarNaeRKOgP¢ab;BIrRbePT³ ¬!¦ snug-tight bolt nig ¬@¦ pSar b¤ fully tightned

ASIC E4

bolt . karbriyaylMGitBIkartP¢ab;manenAkñúgCMBUkTI7. Column load table sRmab; double-angle

KWQrelIkarpSar b¤ fully tightened bolt. sRmab;krNIenH³

2 2
⎛ KL ⎞ ⎛ KL ⎞ α2 ⎛ a ⎞
( )
⎜ ⎟ = ⎜ ⎟ + 0.82 ⎜⎜ ⎟⎟ (AISC Equation E4-2)
⎝ r ⎠m ⎝ r ⎠o 1 + α 2 ⎝ rib ⎠
Edl (KL / r )o = original unmodified slenderness ratio
(KL / r )m = modified slenderness ratio
rib = kaMniclPaBrbs;FatupSMeFobG½kSRsbeTAG½kSénkarekagrbs;Ggát;
h
α = separation ratio =
2rib
h= cm¶ayrvagTIRbCMuTm¶n;rbs;FatupSM ¬EkgeTAnwgG½kSénkarekagrbs;Ggát;¦
enAeBlEdleRKOgP¢ab;Ca snug-tight bolts
2 2
⎛ KL ⎞ ⎛ KL ⎞ ⎛⎜ a ⎞⎟
⎜ ⎟ = ⎜ ⎟ +⎜ ⎟ (AISC Equation E4-1)
⎝ r ⎠m ⎝ r ⎠ o ⎝ rib ⎠
Column load tablesRmab; double-angle shape bgðajBIcMnYneRKOgP¢ab;caM)ac;sRmab;
flexural-torsional buckling strength Edl[tamG½kS y . cMnYneRKOgP¢ab;sRmab; flexural buckling

strength tamG½kS x RtUv)ankMNt;tamPaBcaM)ac;Edlfa slenderness rbs; angle mYyminRtUvFMCagbI

PaKbYnén slenderness rbs; double-angle shape TaMgmUleT.

]TahrN_ 4>16³ KNna design strengthrbs;Ggát;rgkarsgát;EdlbgðajenAkñúgrUbTI 4>22. Edl

rag angle BI 5 × 3 × 12 RtUv)andak;eday[eCIgEvgTl;xñgKña ehIyXøatBIKña 38 inch . RbEvg
RbsiT§PaB KL = 16 feet nigman fully tightened intermediate connectors cMnYn 3 . eRbIEdk A36 .

T.Chhay 116 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dMeNaHRsay³
KNna flexural buckling strength sRmab;G½kS x
KL 16(12)
= = 120.8
rx 1.59
KL Fy 120.8 36
λc = = = 1.355 < 1.5
rπ E π 29000
eRbI AISC Equation E2-2
Fcr = (0.658)λc Fy = (0.658)(1.355) (36) = 16.69ksi
2 2

φc Pn = φc Ag Fcr = 0.85(7.5)(16.69) = 106kips

sRmab;G½kS y
KL 16(12
= = 153.6
ry 1.25

edIm,IkMNt; flexuaral-torsional buckling strength sRmab;G½kS y eRbI modified slenderness ratio

edayQrelIKMlatrbs;eRKOgP¢ab;. KMlatrbs;eRKOgP¢ab;KW
16(12)
a= = 48in
4
bnÞab;mk a a
= =
48
ri rz 0.648
= 74.07 < 0.75(153.6 ) = 115.2 (OK)

rib = ry = 0.829in

h = 2(0.75) + = 1.875in
3
8
h 1.875
α= = = 1.131
2rib 2(0.829)
BI AISC Equation E4-2, modified slenderness ration KW
2 2
⎛ KL ⎞ ⎛ KL ⎞ α2 ⎛ a ⎞
⎜ ⎟ = ⎜
⎝ r ⎠m
⎟ + 0.82
⎝ r ⎠o
⎜⎜ ⎟⎟
(
1 + α 2 ⎝ rib ⎠ )
(153.6)2 + 0.82 (1.131) 2 ⎛⎜ 48 ⎞⎟
2 2
=
[1 + (1.313) ]⎝ 0.829 ⎠ = 158.5

témøenHRtUv)aneRbICMnYs[ KL / ry sRmab;KNna Fcry

KL Fy 158.5 36
λc = = = 1.778 > 1.5
rπ E π 29000

eRKOgbgÁúMrgkarsgát; 117 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

eRbI AISC Equation E2-3

⎡ 0.877 ⎤ ⎡ 0.877 ⎤
Fcry = ⎢ ⎥ Fy = ⎢ ⎥ (36 ) = 9.987ksi
⎣⎢ λc ⎦⎥ ⎣⎢ (1.778) ⎦⎥
2 2

GJ 11200(2 × 0.322)
Fcrz = = = 151.4ksi
2
Ar o 7 .5( 2 .52 )2

Fcry + Fcrz = 9.987 + 151.4 = 161.4ksi

⎛ Fcry + Fcrz ⎞⎡ 4 Fcry Fcrz H ⎤

Fcrft = ⎜⎜ ⎟ ⎢1 − 1 − ⎥
⎝ 2H ⎟⎢
⎠⎣ (Fcry + Fcrz 2) ⎥
⎦
161.4 ⎡ 4(9.987 )(151.4 )(0.645) ⎤
= ⎢1 − 1 − ⎥ = 9.748ksi
2(0.645) ⎢ ( )2
⎥⎦
⎣ 161 . 4
φc Pn = φc Ag Fcrft = 0.85(7.50 )(9.748) = 62.1kips (control)

cMNaMfa lT§plenAkñúg]TahrN_enHmantémøRsedogKñanwgtémøEdl[enAkñúg column load table

cemøIy³ Design strength KW 62kips

]TahrN_ 4>17³ KNnaGgát;rgkarsgát;EbEvg 14 feet edIm,IRTbnÞúkemKuN 50kips . eRbIEdkrUbrag

double angle EdlmaneCIgxøITl;xñgKña nigmanKMlatBIKña 3 8 inch . Ggát;RtUv)anTl;BRgwgenARtg;

Bak;kNþalRbEvgedIm,ITb;nwgkarekageFobG½kS x ¬G½kSEdlRsbeTAnwgeCIgEvg¦. kMNt;cMnYneRKOg

P¢ab;enAkNþalEdlRtUvkar ¬EdkEdlBRgwgenABak;kNþalRbEvgRtUv)anpþl;eRKOgP¢ab;mYy¦. eRbIEdk
A36 .

dMeNaHRsay³ BI column load table eRCiserIs 2L3 12 × 3 × 14 EdlmanTm¶n; 10.8lb / ft .

smtßPaBrbs;muxkat;enHKW 51kips edayQrelIkarekageFobG½kS y CamYynwgRbEvgRbsiT§PaB
14 feet . ¬ersIusþg;EdlRtUvKñanwg flexural buckling eFobG½kS x KW 60kips EdlQrelIRbEvg

RbsiT§PaB 7 feet ¦.
karekageFobG½kS y eFVI[eRKOgP¢ab;rgkmøaMgkat; dUcenHcMnYneRKOgP¢ab;RKb;RKan; RtUv)andak;
edIm,ITb;Tl;nwgkmøaMgenH. taragbgðajfa vaRtUvkareRKOgP¢ab;cMnYn 3 .
cemøIy³ eRbI 2L3 12 × 3 × 14 CamYynwgeRKOgP¢ab;cMnYn 3 sRmab;RbEvg 14 feet .

T.Chhay 118 Compression members

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

tRmUvkarcaM)ac;énkartP¢ab;sRmab; built-up member EdlpSMeLIgeday plate b¤ both plate

CamYynwg shapes
enAeBlEdl built-up member EdlpSMeLIgeday rolled shapes BIr b¤eRcInedaymanKMlat
dac;BIKña plate RtUv)aneRbIedIm,ItP¢ab; shape. AISC E4 mankarlMGitCaeRcInGMBItRmUvkarcaM)ac;
sRmab;kartP¢ab; nigTMhMrbs; plate . tRmUvkarcaM)ac;énkartP¢ab;RtUv)an[bEnßmsRmab; built-up
compression member d¾éTeTotEdlpSMeLIgeday plate b¤ plate CamYynwg shape .

eRKOgbgÁúMrgkarsgát; 119 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

V. Fñwm
Beams
5>1> esckþIepþIm (Introduction)
FñwmCaGgát;rbs;eRKOgbgÁúMEdlRTbnÞúkTTwg dUcenHehIy)aneFVI[vargnUvkarBt; (flexural or
bending). RbsinebImanvtþmanbnÞúktamG½kSkñúgbrimaNmYyFMKYrsm vanwgRtUv)aneKehAvafa beam-

column ¬EdlnwgRtUvbkRsayenAkñúgCMBUkTI6¦. enAkñúgGgát;eRKOgbgÁúMxøHEdlmanvtþman axial load

kñúgtémøtictYc Et\T§iBld¾sþÜcesþIgenHRtUv)aneKecalenAkñúgkarGnuvtþCaeRcIn ehIyeK)ancat;TukvaCa

beam. CaTUeTAFñwmRtUv)aneKdak;kñúgTisedk nigrgnUvbnÞúkbBaÄr EtvamincaM)ac;EtkñúgkrNIEbbenHeT.

Ggát;eRKOgbgÁúMEdlRtUv)aneKcat;TukCa beam RbsinebIvargnUvbnÞúky:agNaEdleFVI[vaekag(bending).

rUbragmuxkat; (cross-sectional shape)EdlRtUv)aneKeRbICaTUeTArYmman W-, S- nig M-shapes.
eBlxøH chanel shape k¾RtUv)aneRbIdUcCaFñwmEdlpSMeLIgBIEdkbnÞH kñúgTRmg; I-, H- b¤ box shape.
Doubly symmetric shape dUcCa standard rolled W-, M- nig S-shape CarUbragEdlman

RbsiT§PaBCaeK.

CaTUeTA rUbragEdl)anBIkarpSMrbs;EdkbnÞHRtUv)aneKKitCa plate girder b:uEnþ AISC Speci-

fication EbgEck beam BI plate girder edayQrelIpleFobTTwgelIkRmas; (width-thickness ratio)

rbs;RTnug. rUbTI 5>1 bgðajTaMg hot-rolled shape nig built-up shapeCamYynwgTMhMEdlRtUv

eRbIsRmab; width-thickness ratios. Rbsin
t
h 2555
≤
F
¬xñat IS¦
t
h
≤
970
F
¬xñat US¦
w y w y

Ggát;eRKOgbgÁúMRtUv)aneKcat;TukCa beam edayminKitfavaCa rolled shape b¤Ca built-up. EpñkenH

RtUv)anerobrab;enAkñúg chapter F of the Specification, “Beams and Other Flexural Members”
ehIyvak¾CaRbFanbTEdlRtUvykmkniyayenAkñúgCMBUkenH. RbsinebI

T.Chhay 120 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

h 2555
tw
>
Fy
¬xñat IS¦ h
tw
≤
970
Fy
¬xñat US¦
enaHGgát;eRKOgbgÁúMRtUv)aneKcat;TukCa plate girder nwgRtUv)anerobrab;enAkñúg Chapter G of the
specification, “Plate Girders”. enAkñúgesovePAenHeyIgnwgniyayBI plate girder kñúgCMBUkTI 10.

edaysarEt slenderness rbs;RTnug plate girder RtUvkarBicarNaBiessenABIelI nigBIeRkamEdl

caM)ac;sRmab;Fñwm.
RKb; standard hot-rolled shape EdlGacrk)anenAkñúg Manual KWsßitenAkñúgRbePT beams.
Built-up shape PaKeRcInRtUv)ancat;cMNat;fñak;Ca plate girder b:uEnþ built-up shape xøHRtUv)ancat;

TukCaFñwmedaykarkMNt;rbs; AISC.
sRmab; beams/ TMnak;TMngeKalrvag\T§iBlbnÞúk (load effects) nig strength KW
M u ≤ φb M n
Edl Mu = bnSMénm:Um:g;emKuNEdlFMCageK
φb = emKuNersIusþg;sRmab;Fñwm = 0.9
M n = nominal moment strength
Design strength, φb M n enAeBlxøHRtUv)aneKehAfa design moment.

5>2> kugRtaMgBt; nigm:Um:g;)øasÞic (Bending Stress and the Plastic Moment)

edIm,IGackMNt; nominal design strength M n dMbUgeyIgRtUvBinitüemIlkarRbRBwtþeTA

(behavior) rbs;Fñwmtamry³énkardak;bnÞúkRKb;lkçxNÐ taMgBIbnÞúktUcrhUtdl;bnÞúkEdlGaceFVIeday

Fñwm)ak;. BicarNaFñwmEdlbgðajenAkñúgrUbTI 5>2 a EdlRtUv)andak;edayeFVIy:agNa[vaekageFobnwg

G½kSem ¬G½kS x − x sRmab; I- nig H-shape¦. sRmab; linear elastic material nigkMhUcRTg;RTaytUc
karBRgaykugRtaMgBt;RtUv)anbgðajenAkñúg rUbTI 5>2 b CamYynwgkugRtaMgEdlRtUv)ansnμt;faBRgay
esμItamTTwgrbs;Fñwm. ¬kmøaMgkat;RtUv)anBicarNaedayELkenAkñúgEpñkTI 5>7¦. BI elementary
mechanics of materials/ kugRtaMgRtg;cMNucNamYyGackMNt;)anBI flexural formula³

fb =
My
Ix
¬%>!¦
Edl M CamU:m:g;Bt;enAelImuxkat;EdlBicarNa/ y Cacm¶ayEkgBIbøg;NWt ¬neutral plane) eTAcMNuc
Edlcg;dwg nig I x Cam:Um:g;niclPaBénmuxkat;EdleFobnwgG½kSNWt. sRmab; homogeneous
Fñwm 121 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

material G½kSNWtRtYtsIuKñanwgG½kSTIRbCMuTm¶n;. smIkar %>! KWQrenAelIkarsnμt;fa karBRgay strain

manlkçN³CabnÞat;BIelIdl;eRkam Edlmüa:geToteyIgGacsnμt;fa muxkat;Edlrab (plane) munrgkar
Bt;enArkSarabdEdleRkaykarBt;. el;IsBIenH muxkat;FñwmRtUvEtmanG½kSsIuemRTIbBaÄr ehIybnÞúkRtUv
EtsßitenAkñúgbøg;EdlmanG½kSsIemRTIenaH. FñwmEdlminbMeBjtamklçxNÐTaMgenH RtUv)anBicarNaenA
kñúgEpñkTI 5>13. kugRtaMgGtibrmanwgekItenAsrésEpñkxageRkAbMput Edl y mantémøGtibrma.
dUcenH vamantémøGtibrmaBIrKW kugRtaMgsgát;GtibrmarnAsrésEpñkxagelIbMput nigkugRtaMgTaj
GtibrmaenAsrésEpñkxageRkambMput. RbsinebIG½kSNWtCaG½kSsIuemRTIkugRtaMgTaMg BIrenHnwgmantémø
esμIKña.
sRmab;kugRtaMgGtibrma smIkar %>! GacsresrkñúgTRmg;
f max =
Mc
=
M
Ix Ix / c Sx
=
M
¬%>@¦
Edl c CacMNayEdkBIG½kSNWteTAsrésrEpñkxageRkAbMput ehIy S x Cam:UDulmuxkat;eGLasÞicénmux
kat; (elastic section modulus) . sRmab;RKb;rUbragmuxkat; section modulus mantémøefr. sRmab;
mux kat;minsIuemRTI S x nwgmantémøBIr³ mYysRmab;srésEpñkxagelIbMput nigmYyeTotsRmab;srés
EpñkxageRkambMput. témørbs; S x sRmab; standard rolled shape RtUv)andak;kñúg dimension and
properties table enAkñúg Manual.

T.Chhay 122 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

smIkar %>! nig %>@ mantémøeTA)ankñúgkrNIbnÞúktUclμmEdlsmÖar³enAEtsßitenAkñúg linear

elastic range. sRmab;eRKOgbgÁúMEdk vamann½yfakugRtaMg f max minRtUvFMCag f y ehIymann½yfa

m:Um:g;minRtUvFMCag
M y = Fy S x

Edl M y Cam:Um:g;Bt;EdleFVI[FñwmeTAdl;cMNuc yielding.

enAkñúgrUbTI 5>3 FñwmTRmsamBaØCamYynwgbnÞúkcMcMNcu enAkNþalElVgRtUv)anbgðajnUvkardak;

bnÞúktamdMNak;kalCabnþbnÞab;. enAeBl yielding cab;epþIm karBRgaykugRtaMgenAelImuxkat;Elg
Fñwm 123 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

manlkçN³CabnÞat; ehIy yielding nwgrIkralBIsrésEpñkxageRkAeTAG½kSNWt. kñúgeBlCamYyKña

tMbn;Edlrg yield nwglatsn§wgtambeNþayFñwmBIG½kSkNþalrbs;FñwmEdlm:Um:g;Bt;mantémøesμInwg
M y enATItaMgCaeRcIn. tMbn;Edlrg yield enHRtUv)angðajedayépÞBN’exμAenAkñúgrUbTI 5>3 c nig d.

enAkñúgrUbTI 5>2 b yielding eTIbnwgcab;epþIm. enAkñúgrUbTI 5>2 c yielding )anrIkralcUleTAkñúgRTnug

ehIyenAkñúgrUbTI 5>2 b muxkat;TaMgmUl)an yield. eKRtUvkarm:Um:g;bEnßmkñúgtémøCamFüm vaesμIRb
Ehl 12% én yield moment edIm,InaMFñwmBIdMNak;kal (b) eTAdMNak;kal (d) sRmab; W-shape .
enAeBleKeTAdl;dMNak;kal (d) RbsinebIenAEtbEnßmbnÞúkeTotFñwmnwg)ak; enAeBlEdlFatuTaMgGs;
rbs;muxkat;)aneTAdl; yield plateau rbs; stress-strain curve ehIy unrestrict plastic flow nwg
ekIteLIg. Plastic hing RtUv)aneLIgRtg;G½kSrbs;Fñwm ehIysnøak;enHCamYynwgsnøak;BitR)akdenA
xagcugrbs;FñwmbegáIt)anCa unstable machanism . kñúgeBl plastic collapse, mechanism motion
RtUv)anbgðajenAkñúgrUbTI 5>4. Structural analysis EdlQrelIkarBicarNa collapse mechanism
RtUv)aneKehAfa plastic analysis. karENnaMBI plastic analysis nig design RtUv)anerobrab;enAkñúg
Appendix A kñugesovePAenH.

lT§PaBm:Um:g;)aøsÞic EdlCam:Um:g;EdlRtUvkaredIm,IbegáItsnøak;)aøsÞic GacRtUv)anKNnay:ag

gayRsYlBIkarBicarNakarBRgaykugRtaMgRtUvKña. enAkñúgrUbTI 5>5 ers‘ultg;kugRtaMgsgát; nigkug
RtaMgTajRtUv)anbgðaj Edl Ac CaRkLaépÞmuxkat;Edlrgkarsgát; nig At CaRkLaépÞmuxkat;Edl
rgkarTaj. RkLaépÞTaMgenHCaRkLaépÞEdlenABIxagelI nigBIxageRkamG½kSNWt)aøsÞic (plastic
neutral axis) EdlmincaM)ac;dUcKñanwgG½kSNWteGLasÞc i . BIsßanPaBlMnwgrbs;kmøaMg eyIg)an
C =T
Ac F y = At F y

Ac = At

T.Chhay 124 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dUcenHG½kSNWt)aøsÞicEckmuxkat;CaBIcMENkesμIKña. sRmab;rUbragEdlsIemRTIeFobnwgG½kSénkarBt;
G½kSNWteGLasÞic nigG½kSNWt)aøsÞicKWdUcKña. m:Um:g;)aøsÞic M p Ca resisting couple EdlbegáIteLIg
edaykmøaMgBIresμIKña nigmanTisedApÞúyKña b¤
⎛ A⎞
M p = Fy ( Ac )a = Fy ( At )a = Fy ⎜ ⎟a = Fy Z
⎝2⎠
Edl A= RkLaépÞmuxkat;srub
a = cm¶ayrvagG½kSNWtrbs;RkLaépÞBak;kNþalTaMgBIr
⎛ A⎞
Z = ⎜ ⎟a = m:UDulmuxkat;)aøsÞic (plastic section modulus)
⎝2⎠

]TahrN_ 5>1³ CamYynwg built-up shape EdlbgðajenAkñúgrUbTI 5>6 cUrkMNt; ¬k¦ elastic section
modulus S nig yielding moment M y nig ¬x¦ plastic section modulus Z nig plastic moment

M p . karekageFobnwgG½kS x ehIyEdkEdleRbIKW A572 Grade 50 .

dMeNaHRsay³
¬k¦ edaysarvamanlkçN³sIuemRTI enaH elastic neutral axis ¬G½kS x ¦ sßitenABak;kNþalmuxkat;
¬TItaMgrbs;TIRbCMuTm¶n;¦. m:Um:g;niclPaBrbs;muxkat;GacRtUvkMNt;)anedayeRbIRTwsþIbTG½kS
Rsb (parallel axis theorem) ehIylT§plénkarKNnaRtUv)ansegçbenAkñúgtarag 5>1.
tarag 5>1
Fñwm 125 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Component I A d I + Ad 2
Flange 260417 5000 162.5 132291667
Flange 260417 5000 162.5 132291667
Web 28125000 - - 28125000
Sum 292.71×106

Elastic section modulus KW

I 292.71 ⋅10 6 292.71 ⋅10 6
S= = = = 1.67 ⋅10 6 mm 3
c 25 + (300 / 2 ) 175
Yield moment KW
M y = Fy S = 345 × 1.67 = 576.15kN .m

cemøIy³ S = 1.67 ⋅106 mm3 nig M y = 576.15kN .m

¬x¦ edaysarrUbragenHmanlkçN³sIuemRTIeFobnwgG½kS x / enaHG½kSenHEckmuxkat;CaBIrcMEnkesμIKña
ehIyG½kSenHk¾Ca plastic neutral axis Edr. TIRbCMuTm¶n;rbs;épÞBak;kNþalxagelIRtUv)an
kMNt;edayeRbI principle of moment. Kitm:Um:;g;eFobG½kSNWténmuxkat;TaMgmUl ¬rUbTI 5>6¦
ehIykarKNnaRtUv)anerobCatarag 5>2.
tarag 5>2
Component A y Ay
Flange 5000 162.5 812500
Web 1875 75 140625
Sum 6875 953125

y=
∑ Ay = 953125 = 138.64mm
∑A 6875

rUbTI 5>7 bgðajfaédXñas;m:Um:g;rbs;m:Umg: ;KUrEdlekItmanenAxagkñúgKW

a = 2 y = 2(138.64) = 277.28mm

T.Chhay 126 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

ehIy plastic section modulus KW

⎛ A⎞
Z = ⎜ ⎟a = 6875 × 277.28 = 1.906 ⋅10 6 mm 3
⎝2⎠
Plastic moment KW
M p = F y Z = 345 × 1.906 = 657.6kN .m

cemøIy³ Z = 1.906 ⋅106 mm3 nig M p = 657.6kN .m

]TahrN_ 5>2³ KNna plastic moment, M p sRmab; W 10 × 60 rbs;Edk A36 .

dMeNaHRsay³ BI dimensions and properties tables enAkñúg Part1 of the Manual
A = 17.6in 2
A 17.6
= = 8.8in
2 2
TIRbCMuTm¶n;sRmab;RkLaépÞBak;kNþalGacrk)anBIkñúgtaragsRmab; WT-shapes EdlRtUv)an
kat;ecjBI W-shapes. rUbragEdlRtUvKñarbs;vaKW WT 5 × 30 ehIycm¶ayBIépÞxageRkAbMputrbs;søab
eTATIRbCMuTm¶n;KW 0.884in dUcbgðajenAkñúgrUbTI 5>8.
a = d − 2(0.884 ) = 10.22 − 2(0.884 ) = 8.452in
⎛ A⎞
Z = ⎜ ⎟a = 8.8(8.452) = 74.38in 3
⎝2⎠
lT§plEdlTTYl)anenHmantémøRbhak;RbEhlnwgtémøEdl[enAkñúg dimensions and properties

tables ¬PaBxusKñabNþalmkBIkarKitcMnYnxÞg;eRkayex,ós¦

cemøIy³ M p = Fy Z = 36(74.38) = 2678in. − kips = 223 ft − kips

5>3> lMnwg (Stability)

Fñwm 127 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

RbsinebIFñwmGacrkSalMnwgrbs;va)anrhUtdl;vasßitkñúglkçxNÐ)aøsÞiceBjelj enaH nominal

moment strength RtUv)aneKKitfamantémøesμInwg plastic moment capacity Edl

Mn = M p

pÞúymkvij M n < M p .
dUckrNIssrEdr PaBKμanlMnwgGacmann½yCalkçN³srub b¤Gacmann½yCalkçN³edaytMbn;.
karekagrbs;Ggát;RtUv)anbgðajenAkñúgrUbTI 5>9 a. enAeBlFñwmekag tMbn;rgkarsgát; ¬EpñkxagelI
G½kSNWt¦ manlkçN³ nigkareFVIkarRsedognwgssr ehIyvanwg buckle RbsinebIEpñkrbs;muxkat;man
lkçN³RsavRKb;RKan;. EtvamindUcssr edaysartMbn;rgkarsgát;rb;muxkat;RtUv)anTb;edayEpñkEdl
rgkarTaj ehIyPaBdabmkxageRkA (flexural buckling) RtUv)anbegáIteLIgeday twisting (torsion).
karbegáItnUvPaBKμanlMnwgenHRtUv)aneKehAfa lateral-torsional buckling (LTB). eKGacbgáar
Lateral-torsional buckling )aneday lateral bracing tMbn;rgkarsgát; CaBiesssøabEdlrgkar

sgát;CamYynwgcenøaHRKb;RKan;. karBRgwgenHRtUv)anbgðajlkçN³nimitþsBaØaenAkñúgrUbTI 5>9 b. dUcGVI

EdleyIg)aneXIj moment strength GaRs½yeTAnwgRbEvgEpñkEdlmin)anBRgwgEdlCacm¶ayrvag
cMNucénTRmxag (lateral support) .
eTaHbICaFñwmGacTTYlm:Um:g;RKb;RKan;edIm,IeFVI[vaeTAdl;lkçxNÐ)aøsÞiceBjelj vak¾RtUv
GaRs½yfaetIva)anrkSa cross-sectional integrity b¤Gt;. vanwg)at;bg; integrity RbsinebIEpñkrgkar
sgát;NamYyrbs;muxkat; buckle. RbePT buckling GacCa compression flange buckling Edl
eKehAfa flange local buckling (FLB) b¤ buckling énEpñkrgkarsgát;rbs;RTnug EdleKehAfa web
local buckle (WLB). dUcEdl)anerobrab;enAkñúgCMBUk 4 RbePT local buckling epSgeTotekIteLIg

edayGaRs½ynwg width-thickness ratio rbs;Epñkrgkarsgát;rbs;muxkat;.

T.Chhay 128 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

rUbTI 5>10 bgðajBI\T§iBlrbs; local and lateral-torsional buckling. FñwmR)aMdac;eday

ELkRtUv)anbgðajenAkñúgRkaPicénbnÞúk-PaBdab. ExSekagTI ! CaExSekagbnÞúk-PaBdabrbs;FñwmEdl
KμanlMnwg ¬edayviFINak¾eday¦ ehIy)at;bg;lT§PaBRTbnÞúkrbs;vamuneBlvaeTAdl; first yield ¬rUbTI
5>3 b¦. ExSekag @ nig # RtUvKñanwgFñwmEdlGacRTbnÞúkedayqøgkat; first yield bu:Enþmin)anyUrRKb;
RKan;edIm,IbegáItsnøak;)aøsÞic nigTTYl)an plastic collapse. RbsinebIvaGaceTAdl; plastic collapse
enaHExSekagbnÞúk-PaBdabnwgmanlkçN³dUcExSekag $ b¤ %. ExSekag $ sRmab;krNIm:Um:g;esμIenA
eBjRbEvgFñwmTaMgmUl ehIyExSekag % sRmab;FñwmEdlrgm:Um:g;ERbRbYl (moment gradient) .
eKGacTTYl)ankarKNnaRbkbedaysuvtßiPaBCamYynwgFñwmEdlRtUvKñanwgExSekagNamYyénExSekag
TaMgenH b:uEnþExSekag ! nig @ bgðajBIkareRbIsmÖar³edayKμanlkμN³RbsiT§PaB.

5>4> cMNat;fñak;rbs;rUbrag (Classification of Shapes)

AISC cat;cMNat;fñak;rUbragmuxkat;Ca compact, noncompact b¤ slender GaRs½ynwgtémø

rbs; width-thickness ratios. sRmab; I- nig H-shapes pleFobsRmab;søab (unstiffened element)

KW b f / 2t f ehIypleFobsRmab;RTnug (stiffened element) KW h / t w . eKGacrk)an karcat;cMNat;
fñak;rbs;muxkat;enAkñúg Section B5 of the specification, “Local Buckling” in Table B5.1. vanwg
RtUv)ansegçbdUcxageRkam. edayyk
λ = width-thickness ratio
λ p = upper limit for compact category
λr = upper limit for noncompact category
enaH RbsinebI λ ≤ λp ehIysøabP¢ab;eTAnwgRTnugCab;Kμandac; enaHrUbragmanlkçN³ compact.

Fñwm 129 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

RbsinebI λ p < λ ≤ λr enaHrUbragmanlkçN³ uncompact.

RbsinebI λ > λr enaHrUbragmanlkçN³ slender.
cMNat;fñak;RtUvQrelI width-thickness ratio rbs;muxkat;EdlmantémøFMCag. ]TahrN_ RbsinebI
RTnugCa compact ehIysøabCa noncompact enaHrUbragRtUv)ancat;cMNat;fñak;Ca noncompact .
tarag 5>3 RtUv)andkRsg;ecjBI AISC Table B5.1 nigman width-thickness ratio sRmab;muxkat;
hot-rolled I- nig H-shape.

tarag 5>3 Width-thickness parameters*

λp λr
Element λ
IS US IS US
bf 170 65 370 141
Flange
2t f Fy Fy Fy − 69 F y − 10
h 1680 640 2550 970
Web
tw Fy Fy Fy Fy
* sRmab; hot-rolled I- nig H-shape rgkarBt;

5>5> Bending Strength of Compact Shapes

FñwmGac)ak;edayvaTTYlm:Um:g; M p ehIyvakøayCa)aøsÞiceBjelj b¤k¾vaGac)ak;eday

!> lateral-torsional buckling (LTB), eday elastically b¤ inelastically
@> flange local buckling (FLB), eday elastically b¤ inelastically
#> web local buckling (WLB), eday elastically b¤ inelastically
RbsinebIkugRtaMgBt;Gtibrma (maximum bending stress) tUcCagEdnsmamaRt
(proportional limit) enAeBlEdl buckling ekIteLIg failure enHRtUv)aneKehAfa elastic. RbsinebI

minGBa©wgenH vaCa inelastic. ¬sUmemIlkarbkRsayEdlTak;TgenAkñúgEpñk 4>2 rbs;emeronTI 4 .¦

edIm,IgayRsYl CadMbUgeyIgcat;cMNat;fñak;FñwmCa compact, noncompact b¤ slender. kar
erobrab;enAkñúgEpñkenHGnuvtþcMeBaHFñwmBIrRbePT³ ¬!¦ hot-rolled I-nig H-shape ekageFobG½kSxøaMg
ehIyEdlbnÞúkenAkñúgbøg;énG½kSexSay ehIy ¬2¦ channels ekageFobG½kSxøaMg ehIybnÞúkdak;tam
shear center b¤k¾RtUv)anTb;RbqaMgnwgkarrmYl. ¬ Shear center CacMNucenAelImuxkat; EdltamcMNuc

enHbnÞúkTTwgRtUv)ankat;tam RbsinebIFñwmekagedayKμankarrmYl.¦ vanwgekItmancMeBaH I-nig H-

T.Chhay 130 Beams
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Shapes . eKminBicarNaGMBI Hybrid beam ¬Edlsøab nigRTnugrbs;vamanersIusþg;epSgKña¦eT ehIy

smIkar AISC xøHnwgRtUv)anEkERbbnþicbnþÜcedIm,IeqøIytbeTAnwgkarkMNt;enH edayeKCMnYs Fyf nig
F yw EdlCa yield strength rbs;søab nigRTnugeday F y .

eyIgcab;epþImCamYynwg compact shape EdlRtUv)ankMNt;CarUbragEdlRTnugrbs;vaRtUv)an

P¢ab;eTAsøabCab;\tdac; ehIyEdlbMeBjnUvtRmUvkar width-thickness ratio xageRkamsRmab;søab nig
RTnug³
bf bf
2t
≤
170
F
nig t
h 1680
≤
F
¬xñatCa IS ¦
2t
≤
65
F
nig t
h
≤
640
F
¬xñatCa IS ¦
f y w y f y w y

sRmab;RKb; standard hot-rolled shape Edl)anrayeQμaHenAkñúg Manual )aneKarBlkçxNÐxag

elI dUcenHeKRtUvkarBinitüEtpleFobsøabb:ueNÑaH. rUbragPaKeRcInk¾bMeBjtRmUvkarrbs;søabEdr
dUcenH vaRtUv)ancat;cMNat;fñak;Ca compact. RbsinebIFñwmCa compact ehIymanTRmxagCab; b¤
unbraced length xøI enaH nominal moment strength, M n Ca plastic moment capacity eBjrbs;

rUbrag M p . sRmab;Ggát;EdlminmanTRmxagRKb;RKan; moment resistance RtUv)ankMNt;eday

lateral-torsional buckling strength EdlmanlkçN³Ca elastic b¤ inelastic .

RbePTTImYy (laterally supported compact beam) CakrNIEdlFmμta nigsamBaØCageK.

AISC F1.1 [ nominal strength Ca
Mn = M p (AISC Equation F1.1)

Edl M p = F y Z ≤ 1 .5 M y

témøkMNt;eday 1.5M y sRmab; M p KWedIm,IkarBarbnÞúkEdleFVIkarelIslb;

nigRtUv)anbMeBj enAeBlEdl
Fy Z ≤ 1.5Fy S b¤ ZS ≤ 1.5
sRmab; I- nig H-shape ekageFobG½kSxøaMg enaH Z / S EtgEttUcCag 1.5 Canic©. ¬b:uEnþsRmab; I- nig
H-shape ekageFobG½kSexSay enaH Z / S nwgminEdltUcCag 1.5 eT.¦

]TahrN_ 5>3³ FñwmEdlbgðajenAkñúgrUbTI 5>11 CaEdl A36 EdlmanrUbrag W16 × 31 . vaRTkM

ralxNÐebtugGarem:Edlpþl;nUv continuous lateral support dl;søabrgkarsgát;. Service dead
Fñwm 131 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

load KW 450lb / ft . bnÞúkenHRtUv)andak;BIelIFñwm vaminRtUv)anKItbBa©ÚlbnÞúkpÞal;rbs;FñwmeT. Service

live load KW 550lb / ft . etIFñwmenHman moment strength RKb;RKan;b¤eT?

dMeNaHRsay³ Service dead load srub edayrYmbBa©ÚlTaMgTm¶n;rbs;FñwmKW

wD = 450 + 31 = 481lb / ft
sRmab;FñwmTRmsamBaØrgbnÞúkBRgayesμI m:Um:g;Bt;GtibrmaekItmanenAkNþalElVgesμInwg
1
M max = wL2
8
Edl w CabnÞúkEdlmanxñatkmøaMgelIÉktþaRbEvg ehIy L CaRbEvgElVg. enaH
1 0.481× 30 2
M D = wL2 = = 54.11 ft − kips
8 8
0.55 × 30 2
ML = = 61.88 ft − kips
8
edaysar dead load tUcCag live load min)an 8 dg enaHbnSMbnÞúk A4-2 nwgmantémøFMCageK³
M u = 1.2 M D + 1.6 M L = 1.2 × 54.11 + 1.6 × 61.88 = 164 ft − kips
müa:gvijeTot bnÞúkGacRtUv)anKitemKuNmun
wu = 1.2 wD + 1.6 wL = 1.2 × 0.431 + 1.6 × 0.550 = 1.457kips / ft
1 1.457 × 30 2
M u = wu L2 = = 164 ft − kips
8 8
RtYtBinitü compactness ³
bf
2t
= 6.3 ¬BI Part 1 of the Manual ¦
f
65
Fy
=
65
36
= 10.8 > 6.3 dUcenH søabCa compact .
h
tw
<
640
Fy
¬sRmab;RKb;rUbragenAkñúg Manual ¦
dUcenH W 16 × 31 Ca compact sRmab;Edk A36 .
edaysarFñwmCa compact ehIymanTRmxag
M n = M p = Fy Z x = 36(54.0 ) = 1944in − kips = 162 ft − kips
T.Chhay 132 Beams
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RtYtBinitüsRmab; M p ≤ 1.5M y ³
Zx 54
= = 1.15 < 1.5 (OK)
S x 47.2
φb M n = 0.90(162 ) = 146 ft − kips < 164 ft − kips (NG)
cemøIy³ Design moment tUcCagm:Um:g;emKuN dUcenH W 16 × 31 minRKb;RKan;.
eTaHbICakarRtYtBinitüsRmab; M p ≤ 1.5M y RtUv)aneFVIenAkñúg]TahrN_xagelI b:uEnþvamin
caM)ac;sRmab; I- nig H-shape ekageFobG½kSxøaMg ehIyvaminRtUv)aneFVIdEdl²enAkñúgesobePAenHeT.

Strength momentrbs; compact shape CaGnuKmn_nwg unbraced length, Lb EdlRtUv)ankM

Nt;Cacm¶ayrvagcMNucénTRmxag b¤karBRgwg. enAkñúgesovePAenH bgðajcMNucénTRmxageday “X”
dUcbgðajenAkñúgrUbTI 5>12. TMnak;TMngrvag nominal strength M n nig unbraced length RtUv)an
bgðajenAkñúgrUbTI 5>13 . RbsinebI unbraced length minFMCag L p FñwmRtUv)anBicarNamanTRm
xageBj ehIy M n = M p . RbsinebI Lb FMCag L p b:uEnþtUcCag b¤esμI)a:ra:Em:Rt Lr enaHersIusþg;nwg
QrelI inelastic LTB . RbsinebI Lb FMCag Lr enaHersIusþg;nwgQrelI elastic LTB .

Fñwm 133 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

eKGacrksmIkarsRmab; theorical elastic lateral-torsional buckling strength enAkñúg

Theory of Elastic Stability (Timoshenko and Gere, 1961) nigCamYykarpøas;bþÚrnimitþsBaØaxøH

smIkarenHmanragdUcxageRkam³
2
π ⎛ πE ⎞
Mn = EI y GJ + ⎜⎜ ⎟⎟ I y C w ¬%>#¦
Lb ⎝ Lb ⎠
Edl Lb = unbraced length

G = shear modulus = 77225 MPa b¤ = 11200ksi sRmab;eRKOgbgÁúMEdk

J = torsional constant
C w = warping constant ( mm 6 )
RbsinebIm:Um:g;enAeBlEdl lateral-torsional buckling ekIteLIgFMCagm:Um:g;EdlRtUvKñanwg first yield
enaH strength QrenAelI inelastic behavior. m:Um:g;EdlRtUvKñanwg first yield KW
M r = FL S x (AISC Equation F1-7)
Edl FL CatémøEdltUcCageKkñúgcMeNam ( Fyf − Fr ) nig Fyw . enAkñúgsmIkarenH yield stress enA
kñúgsøabRtUv)ankat;bnßyeday Fr kugRtaMgEdlenAsl; (residual stress) . sRmab; nonhybrid
member, F yf = F ym = Fy ehIy FL EtgEtesμInwg F y − Fr . teTAmuxeTotenAkñúgCMBUkenH eyIg

CMnYs FL eday Fy − Fr . Ca]TahrN_ eyIgsresr AISC Equation E1-7 Ca

(
M r = F y − Fr S x) (AISC Equation F1-7)

T.Chhay 134 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

EdlkugRtaMgEdlenAsl; Fr = 10ksi = 69MPa sRmab; rolled-shapes nig Fr = 16.5ksi = 114MPa

sRmab; welded built-up shapes. dUcbgðajenAkñúgrUbTI 5>13 RBMEdnrvag elastic behavior nig
inelastic behavior KW unbraced length Lr Edltémørbs; Lr RtUv)anTTYlBIsmIkar %># enAeBl

Edl M n RtUv)andak;[esμI M r . eKTTYl)ansmIkarxageRkam³

Lr =
ry X 1
(Fy − Fr ) (
1 + 1 + X 2 F y − Fr 2 ) (AISC Equation F1-6)

Edl
π EGJA
X1 =
Sx 2
2
(AISC Equation F1-8 and F1-9)
4C w ⎛ S x ⎞
X2 = ⎜ ⎟
I y ⎝ GJ ⎠

dUckrNIssrEdr inelastic behavior rbs;FñwmmanlkçN³sμúKsμajCag elastic behavior CaTUeTAeK

eRcIneRbIrUbmnþEdl)anmkBIkarBiesaF (empirical formulas). CamYynwgkarEktRmUvd¾tictYc AISC
)an[eRbIsmIkarxageRkam³
⎛ Lb − L p ⎞
M n = M p − (M p − M r )⎜ ⎟ ¬%>$¦
⎜L −L ⎟
⎝ r p⎠
790ry 300ry
Edl Lp =
Fy
¬xñat IS¦ Lp =
Fy
¬xñat US¦ (AISC Equation F1-4)

Nominal bending strength rbs; compact beam RtUv)anbgðajedaysmIkar %># nig %>$ rgnUv
upper limit M p sRmab; inelastic beam RbsinebIm:Um;g;EdlGnuvtþBRgayesμIelI unbraced length

Lb . RbsinebIdUcenaHeT vaman moment gradient ehIysmIkar %># nig %>$ RtUv)anEksRmYl

edayemKuN Cb . emKuNenHRtUv)an[eday AISC F1.2 kñúgTRmg;

12.5M max
Cb = (AISC Equation F1-3)
2.5M max + 3M A + 4 M B + 3M C
Edl M max =témødac;xatrbs;m:Um:g;GtibrmaenAkñúg unbraced length (including the end points)
M A = témødac;xatrbs;m:Um:g;enAcMNucmYyPaKbYnén unbraced length

M B = témødac;xatrbs;m:Um:g;enAcMNucBak;kNþalén unbraced length

M C = témødac;xatrbs;m:Um:g;enAcMNucbIPaKbYnén unbraced length

enAeBlm:Um:g;Bt;BRgayesμI témø Cb esμInwg

Fñwm 135 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

12.5M
Cb = = 1.0
2.5M + 3M + 4 M + 3M

]TahrN_ 5>4³ kMNt; Cb sRmab;FñwmTRmsamBaØRTbnÞúkBRgayesμICamYyEtnwgkarTb;xagenAxagcug

b:ueNÑaH.
dMeNaHRsay³ edaysarlkçN³suIemRTI m:Um:g;GtibrmasßitenAkNþalElVg dUcenH
1
M max = M B = wL2
8
dUcKña edaysarlkçN³sIuemRTI m:Um:g;enAcMNucmYyPaKbIesμIm:Um:g;enAcMNucbIPaKbYn. BIrUbTI 5>14
wL ⎛ L ⎞ wL ⎛ L ⎞ wL 2 wL2 3
M A = MC = ⎜ ⎟− ⎜ ⎟= − = wL2
2 ⎝4⎠ 4 ⎝8⎠ 8 32 32
12.5M max 12.5(1 / 8)
Cb = = = 1.14
2.5M max + 3M A + 4 M B + 3M C 2.5(1 / 8) + 3(3 / 32) + 4(1 / 8) + 3(3 / 32)
cemøIy³ Cb = 1.14

rUbTI 5>15 bgðajBItémørbs; Cb sRmab;krNIFmμtaCaeRcInénkardak;bnÞúk nigTRmxag.

sRmab; unbraced cantilever beams, AISC kMNt;témø Cb = 1.0 . témø 1.0 CatémøtUc
¬edayminKitBIrrUbragrbs;Fñwm nigkardak;bnÞúk¦ b:uEnþkñúgkrNIxøHvaCatémøEdltUcEmnETn. karkMNt;
TaMgGs;én nominal moment strength sRmab; compact shapes GacRtUv)ansegçbdUcxageRkam³
sRmab; Lb ≤ L p /
M n = M p ≤ 1 .5 M y (AISC Equation F1-1)

T.Chhay 136 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

sRmab; L p < Lb ≤ Lr /
⎡ ⎛ ⎞⎤
(
M n = Cb ⎢ M p − M p − M r )⎜⎜ LLb −− LL p ⎟⎟⎥ ≤ M p (AISC Equation F1-2)
⎢⎣ ⎝ r p ⎠⎥⎦

sRmab; L p > Lr /
M n = M cr ≤ M p (AISC Equation F1-12)
2
π ⎛ πE ⎞
Edl M cr = Cb EI y GJ + ⎜⎜ ⎟⎟ I y C w (AISC Equation F1-13)
Lb ⎝ Lb ⎠
C S X 2 X 12 X 2
= b x 1 1+
Lb / ry 2 Lb / ry 2 ( )
témøefr X1 nig X 2 RtUv)ankMNt;BImun ehIyRtUv)anrayCataragenAkñúg dimensions and
properties tables in the Manual.

Fñwm 137 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

\T§iBlrbs; Cb eTAelI nominal strength RtUv)anbgðajenAkñúgrUbTI5>16. eTaHbICa strength

smamaRtedaypÞal;eTAnwg Cb k¾eday EtRkaPicenH)anbgðajy:agc,as;BIsar³sMxan;rbs; upper limit
M p edayminKitBIsar³sMxan;rbs;smIkarEdlRtUveRbIsRmab; M n .

]TahrN_ 5>4³ kMNt; design strength φb M n sRmab; W14 × 68 rbs;Edk A242 Edl³
k> TRmxagCab;
x> unbraced length = 20 ft / Cb = 1.0
K> unbraced length = 20 ft / Cb = 1.75

dMeNaHRsay³
k> BI Part 1 of the Manual /W 14 × 68 KWsßitenAkñúg shape group 2 /dUcenHvaGacman yield stress
F y = 50ksi / kMNt;faetIrUbragenHCa compact, noncompact b¤ slender.
bf 65
= 7.0 <
2t f 50

rUbragenHKW compact dUcenH

M n = M p = Fy Z x = 50(115) = 5750in. − kips = 479.2 ft − kips

cemøIy³ φb M n = 0.9(479.2) = 431 ft − kips

x> Lb = 20 ft nig Cb = 1.0 . KNna L p nig Lr ³

T.Chhay 138 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

300ry 300 × 2.46

Lp = = = 104.4in. = 8.7 ft
Fy 50

BI torsion properties tables in Part 1 of the Manual,

J = 3.02in 4 nig C w = 5380in 6

eTaHbICa X1 nig X 2 RtUv)anerobCataragenAkñúg dimensions and properties table in part 1 of

the Manual eyIgnwgKNnavaenATIenHsRmab;bgðaj
π EGJA π 29000(11200)(3.02)(20)
X1 = = = 3021ksi
Sx 2 103 2
2 2
C ⎛S ⎞ ⎛ 5380 ⎞⎛ 103 ⎞ −2
X 2 = 4 w ⎜ x ⎟ = 4⎜ ⎟⎜ ⎟ = 0.001649ksi
I y ⎝ GJ ⎠ ⎝ 121 ⎠⎝ 11200 × 3.02 ⎠
ry X 1
Lr = 1 + 1 + X 2 ( F y − Fr ) 2
( F y − Fr )
2.46(3021)
= 1 + 1 + 0.001649(50 − 10 )2 = 316.8in = 26.40 ft
(50 − 10)
edaysar L p < Lb < Lr strength QrelI inelastic LTB nig
(
M r = F y − Fr S x = ) (50 − 10)(103) = 343.3 ft − kips
12
⎡ ⎛ Lb − L p ⎞⎤
(
M n = Cb ⎢ M p − M p − M r ⎜ )⎟⎥
⎜ Lr − L p ⎟⎥
⎢⎣ ⎝ ⎠⎦
⎡ ⎛ 20 − 8.7 ⎞⎤
= 1.0 ⎢479.2 − (479.2 − 343.3)⎜ ⎟⎥
⎣ ⎝ 26.4 − 8.7 ⎠⎦
cemøIy³ φb M n = 0.90(392.4) = 353 ft − kips
K> Lb = 20 ft nig Cb = 1.75 . Design strength sRmab; Cb = 1.75 KWesμInwg 1.75 dgén Design
strength sRmab; Cb = 1.0 . dUcenH

M n = 1.75(392.4 ) = 686.7 ft − kips > M p = 479.2 ft − kips

Nominal strength minGacFMCag M p / dUcenHeRbI nominal strength M n = 479.2 ft − kips

cemøIy³ φb M n = 0.90(479.2) = 431 ft − kips

mantaragmanRbeyaCn_
Part 4 of the Manual of Steel Construction, “Beam and Girder Design,”

CaeRcInsRmab;viPaK nigKNnaFñwm. Ca]TahrN_ Load Factor Design Selection Table raynUvrUbrag

Fñwm 139 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

EdleRbICaTUeTAsRmab;Fñwm EdlRtUv)anerobCalMdab;én Z x . edaysar M p = Fy Z x rUbragk¾RtUv)an

erobCalMdab;én design moment φb M p . témøefrdéTeTotEdlmanRbeyaCn_k¾RtUv)anerobCatarag
EdlrYmman L p nig Lr ¬EdlCaEpñkmYyEdlKYr[FujRTan;kñúgkarKNna¦.

Plastic Analysis
enAkñúgkrNICaeRcIn m:Um:g;emKuNGtibrma M u nwgRtUv)anTTYlBI elastic structural analysis
edayeRbIbnÞúkemKuN. eRkamlkçxNÐc,as;las; ersIusþg;EdlcaM)ac; (required strength) sRmab;rcna
sm½<n§EdlminGackMNt;edaysþaTic (statically inderteminate structure) RtUv)anrkedayeRbI plastic
analysis. AISC GnuBaØat[eRbI plastic analysis RbsinebIrUbrag compact nigRbsinebI

Lb ≤ L pd
24800 + 15200(M 1 / M 2 )
Edl L pd =
Fy
ry ¬xñat SI ¦ (AISC Equation F1-17)

M1 =m:Um:g;EdltUcCageKkñúgcMeNamm:Um:g;cugTaMgBIrsRmab; unbraced segment

M 2 = m:Um:g;EdlFMCageKkñúgcMeNamm:Um:g;cugTaMgBIrsRmab; unbraced segment

pleFob M1 / M 2 viC¢manenAeBlEdlm:Um:g;begáIt reverse curvature enAkñúg unbraced

segment. enAeBlenH Lb Ca unbraced length EdlenACab;nwgsnøak;)aøsÞicEdlCaEpñkmYyén failure

mechanism. b:uEnþRbsinebIeKeRbI plastic analysis, nominal moment strength M n EdlenACab;nwg

snøak;cugeRkayEdlminenAEk,rsnøak;)aøsÞicRtUv)anKNnatamviFIdUcKñasRmab;FñwmEdlviPaKedayviFIeG
LasÞic ehIyvaRtUvEttUcCag M p .

5>6> Bending Strength of Noncompact Shapes

dUckarkt;cMNaMBImun standard W-, M-, nig S-shapes PaKeRcInCa compact sRmab; F = y

250 MPa nig F y = 350 MPa . cMnYntictYcb:ueNÑaHCa noncompact edaysar width-thickness ratio

rbs;søab b:uEnþKμanrUbragmYyNaCa slender eT. edaysarmUlehtuTaMgenH AISC Specification edaH

Rsay noncompact nig slender flexural member enAkñúg]bsm<n§½ (Appendix F). enAkñúgesovePA
enH eyIgnwgBicarNa slender flexural member enAkñúgCMBUkTI10.

T.Chhay 140 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

CaTUeTA FñwmGac)ak;eday lateral-torsional buckling, flange local buckling b¤ web local

buckling. RKb;RbePTénkar)ak;GacsßitenAkñúgEdneGLasÞic b¤ inelastic range. RTnugrbs;RKb;

rolled shapes enAkñúg Manual Ca compact dUcenH noncompact shapes CaRbFanbTsRmab;Etsßan

PaBkMNt; (limit states) én lateral-torsional buckling nig flange local buckling. ersIusþg;EdlRtUv
nwgsßanPaBkMNt;TaMgBIrRtUv)anKNna ehIyeKyktémøEdltUcCageK. BI AISC Appendix F CamYy
bf
λ=
2t f

RbsinebI λ p < λ ≤ λr / enaHsøabCa noncompact ehIy buckling Ca inelastic eyIgnwgTTYl)an

⎛ λ − λp ⎞
(
Mn = M p − M p − Mr ⎜ )⎟
⎜ λr − λ p ⎟
(AISC Equation A-F1-3)
⎝ ⎠
Edl λp =
170
Fy
IS ¬sRmab; ¦
λp =
65
Fy
¬sRmab; US ¦
λr =
370
F y − Fr
¬sRmab; IS ¦ λr =
141
F y − Fr
¬sRmab; US ¦
(
M r = Fy − Fr S x )
kugRtaMgEdlenAesssl; = 69MPa = 10ksi sRmab; rolled shapes ¬GgÁenHRtUv)an
Fr =

kMNt;sRmab; nonhybrid beam¦

]TahrN_ 5>6³ FñwmTRmsamBaØmYymanRbEvg 40 feet RtUv)anTb;xagenAxagcugrbs;va ehIyvargnUv

service load dUcxageRkam³

Dead load = 400lb / ft ¬edayrYmbBa©ÚlTaMgTm¶n;Fñwm¦

Live load = 1000lb / ft
RbsinebIeKeRbI AISC A572 Grade 50 etI W14 × 90 RKb;RKan;b¤Gt;?
dMeNaHRsay³ bnÞúkemKuN nigm:Um:g;emKuNKW
wu = 1.2 wD + 1.6 wL = 1.2(0.40) + 1.6(1.00) = 2.08kips / ft
1 2.08(40 )2
M u = wu L2 = = 416.0 ft − kips
8 8
kMNt;lkçN³rUbragmuxkat; ¬faetICa compact, noncompact b¤ slender¦³

Fñwm 141 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

bf
λ= = 10.2
2t f
65 65
λp = = = 9.19
Fy 50
141 141
λr = = = 22.3
Fy − Fr 50 − 10

eday λ p < λ < λr dUcenHrUbragenHKW noncompact. RtYtBinitülT§PaBRTRTg;edayQrelIsßanPaB

kMNt;rbs; flange local buckling³
50(157 )
M p = Fy Z x = = 654.2 ft − kips
12
Mr ( )
= Fy − Fr S x = (50 − 10 )
143
12
= 476.7 ft − kips

⎛ λ − λp ⎞
Mn (
= M p − M p − Mr ⎜ )
⎜ λr − λ p ⎟
⎟ = 652.4 − (654.2 − 476.7 )⎛⎜ 10.2 − 9.19 ⎞⎟ = 640.5 ft − kips
⎝ ⎠ ⎝ 22.3 − 9.19 ⎠

Design strength EdlQrenAelI FLBdUcenH

φb M n = 0.9(640.5) = 576 ft − kips
RtYtBinitülT§PaBRTRTg;EdlQrelIsßanPaBkMNt;rbs; lateral-torsional buckling. BI Load
Factor Design Selection Table³

L p = 15 ft nig Lr = 38.4 ft

Lb = 40 ft > Lr
dUcenHvanwg)ak;edayeGLasÞic LTB.
BI Part 1 of the Manual/
I y = 362in 4

J = 4.06in 4
C w = 16000in 6
sRmab;FñwmTRmsamBaØRTbnÞúkBRgayesμICamYynwgTRmxagenAxagcugsgçag
Cb = 1.14
AISC Equation F1-13 [
2
π ⎛ πE ⎞
M n = Cb EI y GJ + ⎜⎜ ⎟⎟ I y C w ≤ M p
Lb ⎝ Lb ⎠
T.Chhay 142 Beams
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⎡ 2 ⎤
π ⎛ π × 29000 ⎞
= 1.14 ⎢ 29000(362 )(11200 )(4.06 ) + ⎜ ⎟ (362 )(16000 )⎥
⎢ 40(12) ⎝ 40 × 12 ⎠ ⎥
⎣ ⎦
= 1.14(5412 ) = 6180in. − kips = 515.0 ft − kips
M p = 654.2 ft − kips > 515.0 ft − kips

edaysar 515.0 < 640.5 dUcenH LTB lub ehIy

φb M n = (0.90)515.0 = 464 ft − kips > M u = 416 ft − kips (OK) /
cemøIy³ eday M u < φb M n enaHFñwmman moment strength RKb;RKan;.

lkçN³kMNt;rbs; noncompact shapes RtUv)ansRmYleday Load Factor Design Selection

Table. Noncompact shapes RtUv)ankMNt;sMKal;eday footnote farUbragCa noncompact sRmab;

F y = 250 MPa = 36ksi b¤ F y = 350 MPa = 50ksi . Noncompact shapes k¾RtUv)anerobcMenAkñúg

taragedaylkçN³xusEbøkKñadUcxageRkam³
!> sRmab; noncompact shapes témøEdlmanenAkñúgtaragrbs; φb M p CatémøBitR)akd
rbs; design strength EdlQrelI flange local buckling. enAkñúg]TahrN_TI 5>6
eyIg)an KNnatémøenHesμInwg 576 ft − kips b:uEnþtémøRtwmRtUvenAkñúgtarag φb M p KW
0.90(654.2 ) = 589 ft − kips
@> témø L p enAkñúgtaragCatémørbs; unbraced length Edl nominal strength EdlQr elI
inelastic lateral torsional buckling esμInwg nominal strength EdlQrelI flange local

buckling dUcenH nominal strength sRmab; unbraced length GtibrmaGacRtUv)an

KitCaersIusþg;EdlQrelI web local buckling. ¬rMlwkfa L p sRmab; compact shapes

Ca unbraced length GtibrmaEdl nominal strength GacRtUv)anKitesμInwg plastic
moment¦. sRmab;rUbragenAkñúg]TahrN_5>6 karKNna nominal strength EdlQrelI

FLB eTAersIusþg;EdlQrelI inelastic LTB (AISC Equation F1-2) CamYynwg

Cb = 1.0 ³
⎛ Lb − L p ⎞
M n = M p − (M p − M r )⎜ ⎟ ¬%>%¦
⎜L −L ⎟
⎝ r p ⎠

Fñwm 143 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

témørbs; M r nig Lr RtUv)anTTYlBI]TahrN_ 5>6 ehIynwgminRtUv)anpøas;bþÚr. b:uEnþ

témørbs; L p RtUvEt)anKNnaBI AISC Equation F1-4³
300ry 300(3.70)
Lp = = = 157.0in. = 13.08 ft.
Fy 50

CMnYstémøxagelIkñúgsmIkar %>% eyIgTTYl)an

⎛ L − 13.08 ⎞
640.5 = 654.2 − (654.2 − 476.7 )⎜ b ⎟
⎝ 38.4 − 13.08 ⎠
Lb = 15.0 ft.
enHCatémøbBa©ÚlkñúgtaragCa L p sRmab; W = 14 × 90 CamYynwg Fy = 50ksi . cMNaMfa
300ry
Lp =
Fy

GaceRbIsRmab; noncompact shapes. RbsinebIeFVIEbbenH lT§plEdlTTYl)anenAkñúg

smIkarsRmab; inelastic LTB EdlRtUv)aneRbIenAeBl Lb minmantémøFMRKb;RKan; enaH
ersIusþg;EdlQrelI FLB nwglub.

5>7> Summary of Moment Strength

viFIsaRsþkñúgkarKNna nominal moment strength sRmab; I- nig H-shaped sections Edl

ekageFobnwgG½kS x nwgRtUv)ansegçbenATIenH. GgÁTaMgGs;EdlmanenAkñúgsmIkarxageRkamRtUv)an
kMNt;rYcehIyBImun ehIyelxsmIkarrbs; AISC minRtUv)anbgðajenATIenHeT.
karsegçbenHsRmab;Et compact shapes nig noncompact shapes Etb:ueNÑaH ¬minmansRmab;
slender shapes eT¦.

!> kMNt;faetIrUbrag compact b¤Gt;

@> RbsinebIrUbrag compact, RtYtBinitüsRmab; lateral-torsional buckling dUcxageRkam³
RbsinebI Lb ≤ L p vaminEmn LTB ehIy M n = M p
RbsinebI L p < Lb ≤ Lr / vaman inelastic LTB ehIy
⎡ ⎛ ⎞⎤
(
M n = Cb ⎢ M p M p − M r )⎜⎜ LLb −− LL p ⎟⎟⎥ ≤ M p
⎣⎢ ⎝ r p ⎠⎦⎥
RbsinebI Lb > br / vaman elastic LTB ehIy
T.Chhay 144 Beams
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

2
π ⎛ πE ⎞
M n = Cb EI y GJ + ⎜⎜ ⎟⎟ I y C w ≤ M p
Lb ⎝ Lb ⎠
#> RbsinebIrUbrag noncompact edaysarsøab/ RTnug b¤TaMgBIr enaH nominal strength nwgCa
témøtUcCageKénersIusþg;EdlRtUvKñanwg flange local buckling, web local buckling nig
lateral-torsional buckling.

k> Flange local buckling³

RbsinebI λ ≤ λ p vaminman FLB.
RbsinebI λ p < λ ≤ λr søabCa noncompact, ehIy
⎛ λ − λp ⎞
(
Mn = M p − M p − Mr ⎜
⎜ λr − λ p
) ⎟≤Mp
⎟
⎝ ⎠
x> Web local buckling³
RbsinebI λ ≤ λ p vaminman WLB.
RbsinebI λ p < λ ≤ λr RTnugCa noncompact, ehIy
⎛ λ − λp ⎞
(
Mn = M p − M p − Mr ⎜
⎜ λr − λ p
) ⎟≤Mp
⎟
⎝ ⎠
K> Lateral-torsional buckling³
RbsinebI Lb ≤ L p vaminman LTB.
RbsinebI L p < Lb ≤ Lr / vaman inelastic LTB ehIy
⎡ ⎛ ⎞⎤
(
M n = Cb ⎢ M p M p − M r )⎜⎜ LLb −− LL p ⎟⎟⎥ ≤ M p
⎢⎣ ⎝ r p ⎠⎥⎦
RbsinebI Lb > br / vaman elastic LTB ehIy
2
π ⎛ πE ⎞
M n = Cb EI y GJ + ⎜⎜ ⎟⎟ I y C w ≤ M p
Lb ⎝ Lb ⎠

5>8> ersIusþg;kmøaMgkat;TTwg (Shear Strength)

ersIusþg;kmøaMgkat;rbs;FñwmRtUvEtRKb;RKan;edIm,IbMeBjTMnak;TMng
Vu ≤ φvVn

Fñwm 145 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Edl Vu =kmøaMgkat;TTwgGtibrmaEdll)anBIkarbnSMbnÞúkemKuNFMCageK
φv = emKuNersIusþg;sRmab;kmøaMgkat;TTwg = 0.9
Vn = nominal shear strength/

BicarNaFñwmsamBaØenAkñúgrUbTI 5>17. enAcm¶ay x BITRmxageqVgnigsßitenAelIG½kSNWtrbs;

muxkat; sßanPaBrbs;kugRtaMgRtUv)anbgðajenAkñúgrUbTI 5>17 d . edaysarFatuenHsßitenAelIG½kS
NWt vaminrgnUvkugRtaMgBt;eT. BI elementary mechanics of materials/ kugRtaMgkmøaMgkat;TTwg
(shearing stess) KW

fv =
VQ
Ib
¬%>^¦

Edl fv = kugRtaMgkmøaMgkat;TTwgbBaÄr nigedkenARtg;cMNucEdleyIgBicarNa

V = kmøaMgkat;TTwgbBaÄrenARtg;muxkat;EdlBicarNa

Q = m:Um:g;RkLaépÞTImYyeFobG½kSNWt rvagcMNucEdlBicarNanwgEpñkxagelIb¤EpñkxageRkam

rbs;muxkat;
T.Chhay 146 Beams
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

m:Um:g;niclPaBeFobnwgG½kSNWt
I=

b = TTwgrbs;muxkat;enAcMNucEdlBicarNa

smIkar %>^ KWQrelIkarsnμt;fakugRtaMgmantémøefreBjelITTwg b dUcenHvapþl;témøsuRkit

sRmab;Et b mantémøtUc. sRmab;muxkat;ctuekaNEkgEdlmankm<s; d nigTTwg b témølMeGog
sRmab; d / b = 2 KWRbEhl 3% . sRmab; d / b = 1 témølMeGogKW 12% nigsRmab; d / b = 1/ 4
témølMeGogKW 100% (Higdon, Ohlsen, and Stiles, 1960). sRmab;mUlehtuenH smIkar %>^ min
GacGnuvtþ)ansRmab;søabrbs; W-shape dUcKñasRmab;RTnugrbs;va.

rUbTI 5>18 bgðajBIkarBRgaykugRtaMgkmøaMgkat;sRmab; W-shape. ExSdac;CakugRtaMgmFüm

V / Aw EdlBRgayenAkñúgRTnug ehIytémøenHminxusKñaBIkugRtaMgGtibrmaenAkñúgRTnugeRcIneT. eyIg
eXIjc,as;ehIyfa RTnugnwg yield y:agyUrmunnwgsøabcab;epþIm yield. edaysarbBaðaenH yielding
rbs;RTnugsMEdgnUvsßanPaBlImItkMNt;mYy. edayyk shear yield stress esμInwg 60% én tensile
yield stress eyIgGacsresrsmIkarsRmab;kugRtaMgenAkñúgRTnugenAeBl)ak;Ca
V
f v = n = 0.60 Fy
Aw
Edl Aw = RkLaépÞmuxkat;rbs;RTnug. dUcenH nominal strength EdlRtUvKñanwgsßanPaBkMNt;enHKW
Vn = 0.6 Fy Aw

ehIyvaGacCa nominal strength in shear RbsinebIRTnugminman shear buckling. RbsinebIvaekIt

eLIgvanwgGaRs½ynwgpleFob width-thickness ratio h / t w rbs;RTnug. pleFob h / t w rbs;RTnug
EdlRsavxøaMgmantémøFMNas; enaHRTnugGacnwg buckle in shear eday inelastic b¤ elastic. TMnak;TM
ngrvag shear strength nig width-thickness ration manlkçN³RsedogKñanwgTMnak;TMngrvag flexural
Fñwm 147 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

strength nig width-thickness ratio ¬sRmab; FLB b¤ WLB¦ nigrvag flexural strength nig
unbraced length ¬sRmab; LTB¦. TMnak;TMngRtUvbgðajenAkñúgrUbTI 5>19 nigRtUv)an[enAkñúg AISC

F2.2 dUcxageRkam³

sRmab; h / t w < 418 / Fy ¬sRmab; US¦/ h / t w < 1100 / Fy ¬sRmab; IS¦

RTnugmanesßrPaB
Vn = 0.6 Fy Aw (AISC Equation F2-1)

sRmab; 418 / Fy < h / t w ≤ 523 / Fy ¬sRmab; US¦/ 1100 / Fy ≤ h / t w < 1375 / Fy

¬sRmab; IS¦ enaH inelastic web buckling GacnwgekIteLIg

418 / Fy 1100 / Fy
Vn = 0.6 Fy Aw
h/t
¬sRmab; US¦ Vn = 0.6 F y Aw
h/t
¬sRmab; IS¦
w w
(AISC Equation F2-1)
sRmab; 523 / Fy < h / t w ≤ 260 ¬sRmab; US¦/ 1375 / Fy ≤ h / t w < 260 ¬sRmab; IS¦
enaH sßanPaBkMNt;KW elastic web buckling
Vn =
132000 Aw
¬sRmab; US¦ Vn =
910 Aw
¬sRmab; IS¦ (AISC Equation
(h / t w )
2
(h / t w )
2

F2-1)
Edl Aw =RkLaépÞmuxkat;rbs;RTnug = dt w KitCa ¬ mm 2 ¦
d = km<s;srubrbs;Fñwm

Vn = nominal strength ¬KitCa KN ¦

RbsinebI h / t w > 260 enaHeKRtUvkar web stiffener ehIyvaRtUv)anbriyayenAkñúg Appendix

F2 ¬b¤ Appendix G sRmab; plate girder ¦.

AISC Equation F2-3 KWQrelI elastic stability theory, ehIy Equation F2-2 CasmIkar

Edl)anBIkarBiesaFsRmab;tMbn; inelastic Edlpþl;nUvkarpøas;bþÚrrvagsßanPaBkMNt; web yielding

nig elastic web buckling.
kmøaMgkat;CabBaðaEdlkRmekItmansRmab; rolled steel beams karGnuvtþTUeTAKWbnÞab;BIKNna
FñwmsRmab; flexural ehIyeyIgnwgRtYtBinitümuxkat;EdlTTYl)ansRmab;kmøaMgkat;TTwg.

T.Chhay 148 Beams

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]TahrN_ 5>7³ RtYtBinitüFñwmenAkñúg]TahrN_ 5>6 sRmab;kmøaMgkat;TTwg.

dMeNaHRsay³ BI]TahrN_ 5>6/ wu = 2.080kips / ft nig L = 40 ft . Edk W 14 × 90 CamYynwg
F y = 50ksi RtUv)aneRbI. sRmab;FñwmTRmsamBaØRTbnÞúkBRgayesμI kmøaMgkat;GtibrmaekItmanenA

elITRm ehIyesμInwgkmøaMgRbtikmμ
w L 2.080(40)
Vu = u = = 41.6kips
2 2
BI dimensions and properties tables in Part 1 of the Manual, web width-thickness ratio rbs;
W 14 × 90 KW
h
= 25.9
tw
418 418
= = 59.11
Fy 50

edaysar h / t w < 418 / Fy enaHersIusþg;RtUv)anRKb;RKgeday shear yielding rbs;RTnug

Vn = 0.6 F y Aw = 0.6 F y (dt w ) = 0.6(50 )(14.02 )(0.44 ) = 185.1kips
φvVn = 0.90(185.1) = 167kips > 41.6kips (OK)
cemøIy³ Shear design strength FMCagkmøaMgkat;emKuN dUcenHFñwmmanlkçN³RKb;RKan;.

Fñwm 149 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

témø φvVn EdlRtUv)anerobCataragenAkñúg factored uniform load table enAkñúg part 4 of

the Manual dUcnHkarKNnarbs;vaminmanRbeyaCn_sRmab; standard hot-rolled shapes.
,
Block Shear
Block shear Edl)anBicarNasRmab;tMNenAkñúgGgát;rgkarTaj k¾GacekItmanenAkñúgRbePT
xøH rbs;tMNenAkñúgFñwmEdr. edIm,IsRmYlkñúgkartP¢ab;BIFñwmmYyeTAFñwmmYyeTot eday[nIv:UsøabxagelI
esμIKña enaHRbEvgd¾xøIrbs;søabxagelIrbs;FñwmmYyRtUvEtkat;ecj b¤ coped. RbsinebI coped beam
RtUv)antP¢ab;edayb‘ULúgdUckñúgrUbTI 5>20 kMNt; ABC cg;rEhkecj. bnÞúkEdlGnuvtþenAkñúgkrNI
enHnwgCaRbtikmμbBaÄrrbs;Fñwm dUcenHkmøaMgkat;nwgekItenAtamExS AB ehIynwgekItmankmøaMgTaj
tam BC . dUcenH block shear strength nwgCatémøEdlkMNt;rbs;Rbtikmμ.
eyIg)anerobrab;BIkarKNna block shear strength enAkñúgCMBUkTI3rYcehIy b:uEnþeyIgnwgrMlwk
vaeLIgvijenATIenH. kar)ak;GacekIteLIgedaybnSMén shear yielding nig tendion fracture b¤eday
shear fracture nig tension yielding. AISC J4.3, “Block Shear Rupture Strength,” [smIkar

BIrsRmab; block shear design strength³

φRn = φ [0.6 Fy Agv + Fu Ant ] (AISC Equation J4.3a)
[
φRn = φ 0.6 Fu Anv + Fy Agt ] (AISC Equation J4.3b)

Edl φ = 0.75
Agv = gross area rgkmøaMgkat; ¬enAkñúgrUbTI 5>20 RbEvg AB KuNnwgkRmas;RTnug¦
Anv = net area rgkmøaMgkat;

Agt = gross area rgkmøaMgTaj ¬enAkñúgrUbTI 5>20 RbEvg BC KuNnwgkRmas;RTnug¦

Ant = net area rgkmøaMgTaj

smIkarEdlmanlT§plFMCagKWCasmIkarEdlmantY fracture FMCag.

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]TahrN_ 5>8³ kMNt;RbtikmμemKuNGtibrma EdlQrelI block shearEdlGacRTFñwmdUcbgðajkñúg

rUbTI 5>21.
dMeNaHRsay³ Ggát;p©itRbehagRbsiT§PaBKW 3 / 4 + 1/ 8 = 7 / 8in. .
gross nig net shear areas KW

Agv = (2 + 3 + 3 + 3)t w = 11(0.300) = 3.300in.2

⎛ 7⎞
Anv = ⎜11 − 3.5 × ⎟(0.300) = 2.381in.2
⎝ 8⎠
gross nig net tension areas KW
Agt = 1.25t w = 1.25(0.300) = 0.375in.2
⎛ 7⎞
Ant = ⎜1.25 − 0.5 × ⎟(0.300) = 0.2438in.2
⎝ 8⎠
AISC Equation J4.3a [
[ ]
φRn = φ 0.6 Fy Agv + Fu Ant = 0.75[0.6(36 )(3.3) + 58(0.2438)] = 64.1kips

AISC Equation J4.3b [

[ ]
φRn = φ 0.6 Fu Anv + Fy Agt = 0.75[0.6(58)(2.381) + 36(0.3750 )] = 72.3kips

tY fracture enAkñúg AISC Equation J4.3b mantémøFMCag ¬Edl 82.86>14.14¦ dUcenHsmIkarenH

mantémøFMCag.
cemøIy³ RbtikmμemKuNGtibrmaEdlQrelI block shear=72.3kips.

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mhaviTüal½ysMNg;sIuvil NPIC

5>9> PaBdab (Deflection)

bEnßmBIelIsuvtßiPaB eRKOgbgÁúMRtUvEt serviceable . eRKOgbgÁúMEdlman serviceable CaeRKOg
bgÁúMEdleFVIkar)anl¥ minbNþal[GñkEdleRbIR)as;vamanGarmμN_favaKμansuvtßiPaB. sRmab;Fñwm edIm,I
TTYl)an serviceable eKRtUvkMNt;bMlas;TIbBaÄr b¤PaBdab. PaBdabFMCaTUeTAekItmancMeBaH flexible
beam EdlGacmanbBaðaCamYynwgrMjr½. PaBdabGacbgábBaðaeTAdl;Ggát;déTeTotEdlP¢ab; eTAnwgva

edaybNþal[mankMhUcRTg;RTaytUc. elIsBIenH GñkeRbIR)as;sMNg;nwgeXIjPaB GviC¢manedaysar

PaBdabFM ehIyeFVIkarsnidæanxusfasMNg;KμansuvtßiPaB.
sRmab;krNITUeTArbs;FñwmTRmsamBaØEdlRTbnÞúkBRgayesμIdUckúrñ UbTI 5>22 PaBdabbBaÄr
GtibrmaKW³
5 wL4
Δ=
384 EI
eKGacrk)anrUbmnþPaBdabsRmab;FñwmeRcInRbePT niglkçxNÐdak;bnÞúkenAkñúg Part 4, “Beam
and Girder Design,”of the Manual. sRmab;sßanPaBminFmμtaeKGaceRbI standard analytical

method dUcCa method of virtual work CaedIm. PaBdabCa serviceability limit state minEmnCa

sßanPaBkMNt;sRmab;ersIusþg;eT dUcenHCaTUeTAPaBdabRtUv)ankMNt;CamYy service loads.

karkMNt;d¾smrmüsRmab;PaBdabGtibrmaGaRs½yeTAnwgtYnaTIrbs;Fñwm nwgkarRbmaNBIPaB
xUcxatEdlekItBIPaBdab. AISC Specification pþl;nUvkarENnaMtictYcEdlmanEcgenAkñúg Chapter
L, “Serviceability Design Consideration,” faeKRtUvEtRtYtBinitüPaBdab. eKGacrk)ankarkMNt;

d¾smrmüsRmab;PaBdabBI governing building code. témøxageRkamCaPaBdabGnuBaØatGtibrma

srub ¬service dead load bUknwg service live load¦.
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L
Plastered construction:
360
L
Unplastered floor construction:
240
L
Unplastered roof construction:
180
Edl L CaRbEvgElVg.

eBlxøHeKcaM)ac;eRbIkarkMNt;PaBdabCatémøelx CagkareRbIPaBdabCatémøRbPaK. eBlxøH

karkMNt;RtUv)anKitcMeBaHPaBdabEdlbNþalEtBI live load, edaysarCaerOy² dead load
deflection RtUv)ankarBarkñúgeBlsagsg;.

]TahrN_ 5>9³ RtYtBinitüPaBdab;rbs;FñwmEdlbgðajenAkñúg rUbTI 5>23. PaBdabGtibrmasrub

GnuBaØatKW 240
L
.
dMeNaHRsay³ PaBdabGtibrmasrubGnuBaØat = 240
L
=
9100
240
= 38mm
Total service load = 7.3 + 8 = 15.3kN / m
5 wL4 5 × 15.3 × 9100 4
Maximum total deflection = = = 32.2mm < 38mm (OK)
384 EI 384 × 2 ⋅105 × 212 ⋅10 6
cemøIy³ FñwmbMeBjlkçxNÐPaBdab

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Ponding CaPaBdabmYyEdlb:HBal;dl;suvtßiPaBrbs;eRKOgbgÁúM. vaeRKaHfñak;bMputsRmab;

RbB½n§kRmalxNÐrabesμIGaceFVI[TwkePøógdk;. RbsinebIRbB½n§bgðÚrTwksÞHkñúgGMLúgeBlePøógTm¶n;rbs;
Twk Edldk;elIkRmaleFVI[kRmaldab EdlvabegáIt)anCaGagsRmab;sþúkTwkkan;EteRcIn.
RbsinebIkrNI enHekIteLIg\tQb;Qr enaHeRKOgbgÁúMGacnwg)ak;. AISC specificationtRmUvfaRbB½n§
dMbUlRtUvEtmanPaBrwgRkajRKb;RKan;edIm,IkarBar ponding, elIsBIenH vaerobrab;BIkarkMNt;m:Um:g;
niclPaB nig)a:ra:Em:RtdéTeTotenAkñúg Section K2, “Ponding”.

5>10> karKNnamuxkat; (Design)

karKNnamuxkat;FñwmtRmUvkareRCIserIsrUbragmuxkat;EdlmanersIusþg;RKb;RKan; nigbMeBj
tRmUvkar serviceability. enAeBleyIgKitBIersIusþg; flexure EtgEtmaneRKaHfñak;CagkmøaMgkat; dUc
enHkarGnuvtþTUeTAKWeKKNnamuxkat;sRmab; flexure rYcehIyRtYtBinitükmøaMgkat;tameRkay. viFI
saRsþkñúg karKNnamuxkat;RtUv)anerobrab;xageRkam³
!> kMNt;m:Um:g;emKuN/ M u . vadUcKñanwg required design strength, φb M n . Tm¶n;rbs;Fñwm
CaEpñkrbs; desd load b:uEnþvaminRtUv)andwgenARtg;cMNucenH. eKGacsnμt;témøenH b¤k¾eK
ecalvasin bnÞab;mkeKnwgRtYtBinitüvaeLIgvijeRkayeBleKeRCIseIsrUbragehIy.
@> eRCIserIsrUbragEdlbMeBjnUvtRmUvkarersIusþg;enH. eKGacGnuvtþtamviFImYykñúgcMeNamviFI
BIrxageRkam³
k> eRkayeBlsnμt;rUbragEdk KNna design strength rYcehIyeRbobeFobvaCamYy
nwgm:Um:g;emKuN. epÞogpÞat;eLIgvijRbsinebIcaM)ac;. eKGaceRCIserIsrUbragsnμt;
y:aggayRsYlEtenAkñúgsßanPaBkMNt;mYycMnYn ¬]TahrN_ 5>10¦.
x> eRbI beam design charts in Part 4 of the Manual. eKcUlcitþviFIenH ehIyva
RtUv)anBnül;enAkñúg]TahrN_ 5>10 xageRkam.
#> RtYtBinitü shear strength.
$> RtYtBinitüPaBdab.

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]TahrN_ 5>10³ eRCIserIs standardhot-rolled shape of A36 sRmab;FñwmEdlbgðajenAkñúg rUbTI

5>24. FñwmenHmanTRmxagCab; ehIyRtUv)anRT uniform service live load 5kips / ft . PaBdab
GtibrmaGnuBaØatsRmab;bnÞúkGefrKW L / 360 .

dMeNaHRsay³ snμt;Tm¶n;FñwmesμI 100lb / ft .

wu = 1.2 wD + 1.6 wL = 1.2(0.10 ) + 1.6(5.00 ) = 8.120kips / ft
1 8.12(30)2
M u = wu L2 = = 913.5 ft − kips = requiredφb M n
8 8
snμt;farUbrag compact. sRmab;rUbrag compact ehIymanTRmxagCab;
M n = M p = Z x Fy

BI φb M n ≥ M u /
φb F y Z x ≥ M u
Mu 913.5(12)
Zx ≥ = = 338.3in.3
φb Fy 0.90(36)
CaFmμta Load Factor Design Selection Table erob rolled shapes EdlRtUv)aneRbICaFñwmeday
témø plastic section modulus fycuH. elIsBIenH RtUv)andak;CaRkumedayrUbragenAxagelIeKenAkñúg
Rkum ¬GkSrRkas;¦ rUbragEdlRsalCageKEdlman section modulus RKb;RKan;edIm,IbMeBj section
modulus EdlfycuHenAkñúgRkum. kñúg]TahrN_enH rUbragEdlmantémøEk,rnwg section modulus

requirement KW W 27 × 114 CamYynwg Z x = 343in.3 b:uEnþrUbragEdlRsalCageKKW W 30 × 108 Ca

mYynwg Z x = 343in.3 . edaysar section modulusminsmamaRtedaypÞal;nwgRkLaépÞ karEdlman

section modulus FMCamYynwgRkLaépÞtUc dUcenHTm¶n;k¾GacRsaleTAtamRkLaépÞ.

sakl,g W 30 ×108 . rUbrag compact dUcEdl)ansnμt; ¬noncompact shapesRtUv)ankM

Nt;cMNaMenAkñúgtarag¦ dUcenH M n = M p dUcEdl)ansnμt;.

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mhaviTüal½ysMNg;sIuvil NPIC

Tm¶n;rbs;vaF¶n;Cagkarsnμt;bnþic dUcenHeKRtUvKNna required strength eLIgvij eTaHbICa

W 30 × 108 manlT§PaBRTRTg;FMCaglT§PaBRTRTg;tRmUvkaredayrUbragsnμt;k¾eday EtvaPaKeRcIn

EtgEtmanlT§PaBRTRTg;FMCaglT§PaBRTRTg;tRmUvkaredayrUbragsnμt;.
wu = 1.2(1.08) + 1.6(5.00 ) = 8.130kips / ft
8.130(30 )2
Mu = = 914.6 ft − kips
8
BI Load Factor Design Selection Table,
φb M p = φb M n = 934 ft − kips > 914.6 ft − kips (OK)

CMnYs[kareRCIserIsrUbragEdlQrelI required section modulus, eKGaceRbI design strength

φb M p edaysarvasmamaRtedaypÞal;nwg Z x ehIyvak¾RtUv)anrayenAkñúgtarag. bnÞab;mkeTot

epÞógpÞat;kmøaMgkat;
w L 8.13(30 )
Vu = u = = 122kips
2 2
BI factored uniform load tables /
φvVn = 316kips > 122kips (OK)
cugeRkaybMput epÞógpÞat;PaBdab. PaBdabGtibrmaGnuBaØatsRmab;bnÞúkGefrKW L / 360
L 30 × 12
= = 1in.
360 360
5 wL L4 5 (5.00 / 12 )(30 × 12 )4
Δ= = = 0.703in. < 1in. (OK)
384 EI x 384 29000(4470 )
cemøIy³ eRbI W 30 × 108 .
dff
Beam Design Charts
eKmanRkaPic nigtaragCaeRcInsRmab;visVkrEdlGnuvtþ ehIyRkaPic nigtaragCMnYyTaMgenHCYy
sRmYly:ageRcIndl;dMeNIrkarKNnamuxkat;. vaRtUv)aneKeRbIy:agTUlMTUlayenAkñúg design office
b:uEnþvisVkrRtUvEteRbIvaedayRbytñ½. enAkñúgesovePAenHmin)anENnaMnUvRkaPic nigtaragTaMgGs;enaH
lMGitGs;eT b:uEnþRkaPic nigtaragxøHmansar³sMxan;kñúgkarENnaM CaBiessKW ExSekag design moment
versus unbraced length Edl[enAkñúg Part 4 of the Manual.

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ExSekagenHRtUv)anbgðajenAkñúgrUbTI 5>25 EdlbgðajBIRkaPic design moment φb M n Ca

GnuKmn_én unbraced length Lb sRmab; particular compact shape. eKGacsg;RkaPicEbbenH
sRmab;muxkat;epSg²CamYynwgtémøCak;lak;én Fy nig Cb edayeRbIsmIkarsmRsbsRmab;
moment strength.

Manual chartrYmmanRKYsarénExSekagsRmab; rolled shapes CaeRcIn. ExSekagTaMgenHRtUv

)anbegáIteLIgCamYy Cb = 1.0 . sRmab;ExSekagepSgeTotrbs; Cb KuN design moment Edl)an
BItarageday Cb . RtUvcaMfa φb M n minGacFMCag φb M p ¬b¤ sRmab; noncompact shapes φb M n
QrelI local buckling¦. beRmIbRmas;rbs;RkaPicRtUv)anbgðajbgðajenAkñúgrUbTI 5>26 Edl ExS
ekagEbbenHBIrRtUv)anbgðaj. cMNucNak¾edayenAelIRkaPicenH dUcCacMNucCYbKñaénExSdac;BIrbgðaj
BI design moment nig unbraced length. RbsinebIm:Um:g;Ca required moment capacity enaH ExS
ekagEdlenABI elIcMNucenaHRtUvKñanwgFñwmEdlman moment capacity FMCag. ExSekagEdlenAxag
sþaMKW sRmab;FñwmEdl man required moment capacity Cak;lak; eTaHbIsRmab; unbraced length
FMCag k¾eday. dUcenH enA kñúgkarKNnamuxkat; RbsinebIeyIgdak; unbraced length nig required
design strength cUleTAkñúgRkaPic ExSekagenABIelI nigenABIsþaMcMNucenaH RtUvKñanwgFñwmEdlGacTTYl

yk)an. RbsinebIeKKitTaMg ExSekagdac;² enaHExSekagsRmab;rUbragRsalCagsßitenABIelI nigBIxag

sþaMExS ekagdac;². cMNucenAelI ExSekagEdlRtUvnwg L p RtUv)anbgðajeday solid circle ehIy Lr

Fñwm 157 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

RtUv)anbgðajeday open circle. eKmanExSekagBIrRbePT mYysRmab; Fy = 36ksi = 250MPa nig

mYyeTotsRmab; Fy = 50ksi = 350 MPa .
kñúg]TahrN_ 5>10 required design strength ¬EdlrYmbBa©ÚlTaMgTm¶n;Fñwmsnμt;¦ KW 913.5
ft − kips ehIyvaman continuous lateral support. sRmab;TRmxagCab; eKGacyk Lb = 0 .

BIRkaPic Fy = 36ksi ExSekagRkas;TImYyenABIelI 913.5 ft − kips KW W 30 ×108 EdldUcKña

nwgkareRCIserIs enAkñúg]TahrN_ 5>10. eTaHbICa Lb = 0 minRtUv)anbgðajenAkñúgRkaPicBiessk¾
eday k¾témøtUcbMputrbs; Lb EdlbgðajKWtUcCag L p sRmab;RKb;rUbragenAelITMB½renaH.

ExSekagFñwmEdlbgðajenAkñúgrUbTI 5>25 KWsRmab; compact shape dUcenHtémørbs; φb M n

sRmab;témøtUcEdlRKb;RKan;rbs; Lb KW φb M p . dUcEdl)anerobrab;enAkñúgEpñk 5>6 RbsinebIrUb
ragCa noncompact témøGtibrma φb M n nwgQrelI flange local buckling. vaCakarBitEdl
maximum unbraced length sRmab; φb M n xagelInwgxusKñaBItémø L p EdlTTYlCamYynwg AISC

Equation F1-4. The moment strength rbs; noncompact shape RtUv)anbgðajCalkçN³RkaPic

enAkñúgrUbTI 5>27 Edl maximum design strength RtUv)ankMNt;sMKal;eday φb M 'n ehIy

maximum unbraced length EdlRtUvnwg φb M ' n xagelIRtUv)ansMKal;eday L' p .

eTaHbICaRkaPicsRmab; compact nig noncompact shapes manlkçN³RsedogKñak¾eday k¾

φb M n nig Lb RtUv)aneRbIsRmab; compact shapes Et φb M 'n nig L' p RtUv)aneRbIsRmab;

noncompact shapes.

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]TahrN_ 5>11³ FñwmEdlbgðajenAkñúg rUbTI 5>28 RtUvRTbnÞúkcMcMNucGefrBIrEdlmYy²mantémø

20kips Rtg;cMNucmYyPaKbYn. PaBdabGtibrmaminRtUvFMCag L / 240 . Lateral support RtUv)an

pþl;[enAcugrbs;Fñwm. eRbIEdk A572 Grade50 nigeRCIserIs rolled shape.

Fñwm 159 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

dMeNaHRsay³ RbsinebIeKecalTm¶n;rbs;Fñwm enaHkMNat;FñwmcenøaHbnÞúkcMcMNucrgnUvm:Um:g;efr.

M A = M B = M C = M max
ehIy Cb = 1.0
eTaHRbsinCaeKKitTm¶n;pÞal;rbs;Fñwmk¾eday k¾vaGacRtUv)anecaledayeFobnwgbnÞúkcMcMNuc
ehIy Cb k¾enAEtmantémøesμI 1.0 EdlGnuBaØat[eKGaceRbIRkaPicedayKμankarEkERb.
edayminKitBITm¶n;FñwmbeNþaHGasnñ eyIgTTYl)an
M u = 6(1.6 × 20 ) = 192 ft − kips
BIRkaPic CamYynwg Lb = 24 ft sakl,g W 15× 53 ³
φb M n = 219 ft − kips > 192 ft − kips (OK)
\LÚveyIgKitBITm¶n;Fñwm
M u = 192 +
1
(1.2 × 0.053)(24)2 = 197 ft − kips < 219 ft − kips (OK)
8
kmøaMgkat;TTwgKW
1.2(0.053)(24 )
Vu = 1.6(20 ) + = 32.8kips
2
BI factored uniform load tables/
φvVn = 112kips > 32.8kips (OK)
PaBdabGtibrmaGnuBaØatKW
L 24(12 )
= = 1.2in.
240 240
BI Beam Diagrams nig Formulas section in Part 4 of the Manual/ PaBdabGtibrma
¬enAkNþalElVg¦ sRmab;bnÞúkBIresμIKñaEdlRtUv)andak;sIuemRTIKñaKW
Δ=
Pa
24 EI
(
3L2 − 4a 2 . )
Edl P= GaMgtg;sIuetbnÞúkcMcMNuc
a. =cm¶ayBITRmeTAbnÞúk

L = RbEvgElVg

Δ=
20(6 × 12 )
24 EI
[ ]
3(24 × 12 )2 − 4(6 × 12 )2 =
13.69 × 10 6
EI
sRmab;Tm¶n;pÞal;rbs;Fñwm PaBdabGtibrmak¾sßitenAkNþalElVgEdr dUcenH

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5 wL4 5 (0.053 / 12 )(24 × 12 )4 0.04 × 10 6

Δ= = =
384 EI 384 EI EI
PaBdabsrub
13.69 × 10 6 0.04 × 10 6 13.73 × 10 6
Δ= + = = 1.114in. < 1.2in. (OK)
EI EI 29000(425)
cemøIy³ eRbI W 12 × 53 .

eTaHbICaRkaPicQrelI Cb = 1.0 k¾eday b:uEnþeKk¾GaceRbIvay:agRsYledIm,IKNnamuxkat;enA

eBlEdl Cb minesIμnwg 1.0 edayEck required design strength eday Cb munnwgdak;vaeTAkñúgRka
Pic. ]TahrN_ 5>12 nwgbgðajBIbec©keTsenH.

]TahrN_ 5>12³ eRbIEdk A36 ehIyeRCIserIs rolled shapes sRmab;FñwmenAkñúg rUbTI 5>29. bnÞúkcM
cMNucCa service live load ehIybnÞúkBRgayesμIKW 30% CabnÞúkefr nig 70% CabnÞúkGefr.
Lateral bracing RtUv)anpþl;[enAcug nigkNþalElVg. vaminmankarkMNt;sRmab;PaBdabeT.

dMeNaHRsay³ edaysnμt;Tm¶n;FñwmesμI 100lb / ft. enaH

wD = 0.30(3) + 0.10 = 1kips / ft.

wL = 1.2(1.0 ) + 1.6(0.7 × 3) = 4.560kips / ft.

Pu = 1.6(9 ) = 14.4kips
bnÞúkemKuN nigRbtikmμRtUv)anbgðajenAkñúgrUbTI 5>30.
m:Um:g;EdlcaM)ac;sRmab;KNna Cb ³ m:Um:g;Bt;enAcm¶ay x BIcugxageqVgKW
⎛ x⎞
M = 61.92 x − 4.590 x⎜ ⎟ = 61.92 x − 2.280 x 2
⎝2⎠
¬sRmab; x ≤ 12 ft ¦

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sRmab; x = 3 ft / M A = 61.92(3) − 2.280(3)2 = 165.2 ft − kips

sRmab; x = 6 ft / M B = 61.92(6) − 2.280(6)2 = 289.4 ft − kips
sRmab; x = 9 ft / M C = 61.92(9) − 2.280(9)2 = 372.6 ft − kips
sRmab; x = 12 ft / M max = M u = 61.92(12) − 2.280(12)2 = 414.7 ft − kips
12.5M max
Cb =
2.5M max + 3M A + 4 M B + 3M C
12.5(414.7 )
= = 1.36
2.5 414.7 + 3 165.2 ) + 4(289.4 ) + 3(372.6 )
( ) (
bBa©ÚleTAkñúgRkaPicCamYynwg unbraced length Lb = 12 ft nigm:m:gU ;Bt;KW
M u 414.7
= = 305 ft − kips
Cb 1.36
sakl,g W 21× 62 ³
φb M n = 343 ft − kips ¬sRmab; Cb = 1 ¦
edaysar Cb = 1.36 design strength BitR)akdKW
φb M n = 1.36(343) = 466 ft − kips
b:uEnþ design strength minRtUvelIs φb M p EdlesμIRtwmEt 389 ft − kips ¬TTYl)anBIRka
Pic¦ dUcenH design strength BitR)akdRtUvEtesμInwg
φb M n = 389 ft − kips < M u = 414.7 ft − kips (N.G.)
sRmab;rUbragsakl,gbnÞab; eyIgRtUvrMkileLIgelIeTArkExSekagCab;Rkas;bnÞab;enAelIRkaPic
eyIgTTYl)an W 21× 68 . sRmab; Lb = 12 ft design strength Edl)anBIRkaPicKW
385 ft − kips sRmab; Cb = 1.0 . ersIusþg;sRmab; Cb = 1.36 KW

φb M n = 1.36(385) = 524 ft − kips > φb M p = 432 ft − kips

dUcenH φb M n = φb M p = 432 ft − kips > M u = 414.7 ft − kips (OK)

Tm¶n;FñwmKW 68lb / ft EdltUcCagTm¶n;snμt; 100lb / ft . (OK)

kmøaMgkat;TTwgKW
Vu = 61.92kips
¬lT§plBitR)akdnwgtUcCagenHbnþic edaysarTm¶n;pÞal;rbs;FñwmtUcCagbnÞúksnμt;¦
BI factored uniform load table
φvVn = 177kips > 61.92kips (OK)

T.Chhay 162 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

cemøIy³ eRbI W 21× 68

RbsinebItRmUvkarPaBdabRKb;RKgelIkarKNnamuxkat; eKRtUvkMNt;m:Um:g;niclPaBcaM)ac;Gb,-
brma ehIyeKRtUvrkrUbragRsalCageKEdlRtUvnwgtémøenH. kargarenHRtUv)ansRmYly:ageRcIneday
sar moment of inertia selection table in part 4 of the Manual. ]TahrN_ 5>13 nwgbgðajBIkar
eRbIR)as;taragenH ehIynwgBnül;pgEdrBIviFIsaRsþkñúgkarKNnamuxkat;FñwmenAkñúgRbB½n§kRmalxNÐ.

]TahrN_ 5>13³ EpñkénRbB½n§eRKagkRmalRtUv)anbgðajenAkñúg rUbTI 5>31. kRmalebtugBRgwg

edayEdkmankRmas; 4in. RtUv)anRTeday floor beams EdlmanKMlatBIKña 7 ft. . Floor beams
RtUv)anRT eday girders EdlRtUv)anbnþedayssr. ¬eBlxøH floor beamsRtUv)aneKehAfa filler
beams¦. bEnßmBIelITm¶n;rbs;rcnasm½<n§ bnÁÞúkrYmmanbnÞúkGefrBRgayesμI 80 psf nig movable

partitions EdlRtUv)anKitCabnÞúkBRgayesμI 20 psf elIépÞkRmal . PaBdabsrubGtibrmaminRtUv

elIsBI 1/ 360 énRbEvgElVg. eRbIEdk A36 nigKNnamuxkat;rbs; floor beams. snμt;fa kRmal
pþl;nUv continuous lateral support rbs; floor beams.

Fñwm 163 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

dMeNaHRsay³
eRbIebtugGarem:Tm¶n;FmμtaEdlmanTm¶n; 150lb / ft 3 sRmab;KNnabnÞúkefr. Tm¶n;GacRtUv)anKitCa
bnÞúk kñúgmYyÉktþaépÞedayKuNTm¶n;maDnwgkRmas;kRmalxNÐ.
Tm¶n;kRmalxNÐ = 150⎛⎜⎝ 124 ⎞⎟⎠ = 50 psf
snμt;faFñwmnImYy²RTnUvTTwgrgbnÞúk (tributary width) 7 ft. rbs;kRmalxNÐ.
kRmalxNг 50(7) = 350lb / ft
Partition³ 20(7 ) = 140lb / ft

Tm¶n;Fñwm³ = 40lb / ft ¬)a:n;sμan¦

srub³ = 530lb / ft ¬ service dead load¦

eTaHbI partition Gaccl½t)an b:uEnþ national model building codes KitvaCabnÞúkefr (BOCA,
1996; ICBO, 1997;nig SBCC, 1997). eyIgk¾KitvaCabnÞúkGefrEdrenATIenH.

bnÞúkGefr³ 80(7) = 560lb / ft

ehIybnÞúkemKuNsrubKW
wu = 1.2wD + 1.6wL = 1.2(0.53) + 1.6(0.56) = 1.532kips / ft
kartP¢ab;kRmal-Fñwmpþl;nUv no moment restraint ehIyFñwmRtUv)anKitCaFñwmEdlRTedayTRmsamBaØ.
1 1.532(30 )2
M u = wu L2 = = 172.4 ft − kips
8 8
T.Chhay 164 Beams
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

BI beam design chart CamYynwg Lb = 0 sakl,g W 18 × 35 ³

φb M u = 179.5 ft − kips > 172.4 ft − kips (OK)
kmøaMgkat;TTwgKW
1532(30 )
Vu ≈ = 22.98kips
2
BI factored uniform load tables
φvVn = 103kips > 22.98kips (OK)
PaBdabGtibrmaGnuBaØatKW
L 30(12 )
= = 1in.
360 360
5 wL4 5 (0.35 + 0.14 + 0.035 + 0.56)(30)4 (12 )3
Δ= = = 1.3in. > 1in. (N.G.)
384 EI 384 29000(510 )
edayedaHRsaysmIkarPaBdabsRmab; required moment of inertia TTYl)an
5wL4 384 5(1.085)(30 )4 (12 )3
I required = = = 682in.4
384 EΔ required 384(29000)(1)

Moment of Inertia Selection Table RtUv)anerobcMeLIgkñúgviFIdUcKñanwg Load Factor Design

Selection Table dUcenHkareRCIserIsrUbragEdlRsalCageKCamYynwgm:Um:g;niclPaBRKb;RKan;man

lkçN³samBaØ. BI I x Table sakl,g W 21× 44 ³

I x = 843in.4 > 682in.4 (OK)
φb M n = 257.5 ft − kips > 172.4 ft − kips (OK)
Tm¶n;rbs;rUbragenHFMCagkarsnμt;dMbUgbnþic b:uEnþTm¶n;EdlbEnßmenHminGaceRbobeFobnwg moment
capacity d¾FMenaH)aneT.
φvVn = 141kips > 22.98kips (OK)
cemøIy³ eRbI W 21× 44 .

5>11> rn§RbehagenAkñúgFñwm (Holes in Beam)

RbsinebIkartP¢ab;FñwmRtUv)aneFVIeLIgCamYyb‘ULúg søab b¤RTnugrbs;FñwmRtUv)anecaHRbehag
b¤xYg. elIsBIenH eBlxøHRTnugFñwmRtUv)anecaHrn§F²M edIm,Irt;eRKOgbrikçaepSg²dUcCa bMBugExSePøIg
GKÁisnI bMBugxül;CaedIm. eKcUlcitþecaHrn§enAelIRTnugFñwmRtg;kEnøgNaEdlmankmøaMgkat;TTwgtUc

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ehIyrn§RbehagRtUv)anecaHenAelIsøabRtg;kEnøgNaEdlmanm:Um:g;tUc. b:uEnþeKminGaceFVIEbbenH)an
rhUteT dUcenHeKRtUvKitBI\T§iBlrbs;rn§Rbehag.
sRmab;rn§RbehagtUc dUcsRmab;b‘ULúg \T§iBlrbs;vanwgtUc CaBiesssRmab; flexure eday
mUlehtuBIr. TI1KW karkat;bnßymuxkat;tUc. TI2KW muxkat;EdlenAEk,rmin)ankat;bnßy ehIykar
pøas;bþÚrmuxkat;énPaBminCab;tUcFMCag “weak link”.
dUcenH AISC B10 GnuBaØat[ecalnUv\T§iBlrbslrn§RbehagenAeBlEdl
0.75 Fu A fn ≥ 0.9 Fy A fg (AISC Equation B10-1)

Edl A fg = gross flange are

A fn = net flange are

RbsinebIeKminCYbnUvlkçxNÐenHeT flexural properties RtUvEtQrelIRkLaépÞsøabrgkarTajRbsiT§

PaB
5 Fu
A fe = A fn (AISC Equation B10-3)
6 Fy

]TahrN_ 5>14³ KNna elastic section modulus EdlRtUv)ankat;bnßy S x sRmab;muxkat;Edl

bgðajenAkñúgrUbTI 5>32. eKeRbIEdk A36 nigRbehagsRmab;b‘ULúgGgát;p©it 1in. .

dMeNaHRsay³ A fg = b f t f = 7.635(0.81) = 6.184in 2

Ggát;p©itRbehagRbsiT§PaBKW
1 1
dh =1+ =1 in.
8 8
net flange area KW
A fn = A fg − ∑ d h t f = 6.184 − 2(1.125)(0.810 ) = 4.362in.2

T.Chhay 166 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

BI AISC Equation B10-1

0.75Fu A fn = 0.75(58)(4.362 ) = 189.7kips

nig 0.9Fy A fg = 0.9(36)(6.184) = 200.4kips

edaysar 0.75Fu A fn < 0.9Fy A fg eyIgRtUvEtKitrn§Rbehag. edayeRbI AISC Equation B10-3
[RkLaépÞsøabRbsiT§PaB
5 Fu 5 ⎛ 58 ⎞
A fg = A fn = ⎜ ⎟4.362 = 5.856in.2
6 Fy 6 ⎝ 36 ⎠

RkLaépÞsøabenHRtUvKñanwgkarkat;bnßyeday 6.184 − 5.856 = 0.328in.2 . G½kSNWteGLasÞicsßitenA

cm¶ay y BIkMBUlrbs;muxkat;
20.8(18.47 / 2 ) − 0.328(18.47 − 0.405)
y= = 9.094in.
20.8 − 0.328
m:Um:g;niclPaBEdlRtUv)ankat;bnßyKW
I x . = 1170 + 20.8(9.094 − 9.235)2 − 0.328(9.094 − 18.06 )2 = 1144in.4
Sx sRmab;søabxagelIKW
I 1144
Sx = x = = 126in.3
y 9.094
Sx sRmab;søabxageRkamKW
Ix 1144
Sx = = = 122in.3
d − y 18.47 − 9.094
cemøIy³ The reduced elastic section modulus sRmab;EpñkxagelIKW 126in.3 nigsRmab;Epñkxag
eRkamKW 122in.3 .

FñwmEdlmanrn§RbehagFMenAelIRTnug RtUvkarkarKNnaBiessEdlminmanerobrab;enAkñúgesov
ePAenHeT. Design of Steel and Composite Beam with Web Openings KWCakarENnaMd¾manRb
eyaCn_sRmab;RbFanbTenH (Darwin, 1990).

5>12> Open-Web Steel Joists

CaRbePT truss EdlplitrYcCaeRscdUcbgðajenAkñúgrUbTI 5>33.

Open-web steel joists

Open-web steel joists xøHEdlmanTMhMtUc eRbIr)arEdkmUlCab;sRmab;eFVICaGgát;RTnug (web

Fñwm 167 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

member) ehIyvaRtUv)aneKehA bar joists. vaRtUv)aneKeRbIenAkñúgkRmal nigRbB½n§dMbUlsRmab;

eRKOgbgÁúMCaeRcIn. sRmab;RbEvgElVgEdl[dUcKña open-web steel joists manTm¶n;RsalCag rolled
shapes ehIyGvtþmanrbs;RTnugtan;GnuBaØat[eKrt;RbB½n§brikçary:agRsYl. GaRs½yeTAnwgRbEvg

ElVg open-web steel joist manlkçN³esdækic©Cag rolled shapes eTaHbICavaKñaeKalkarN_ENnaM

sRmab;karkMNt;vak¾eday.
eKGacrk open-web steel joists CamYynwgkm<s;sþg;dar niglT§PaBRTbnÞúkBIeragcRkCaeRcIn.
Open-web steel joist xøHRtUv)anKNnaedIm,IeFVIkarCa floor b¤ roof joists ehIy open-web steel

joists xøHeTotRtUv)anKNnaedIm,IeFVIkarCa girder EdlRTRbtikmμEdlRbmUlpþúMBI joists. AISC

Specification min)anerobrab;BI open-web steel joists eT Etsßabn½mYyepSgeTotEdleKehAfa Steel

Joist Institute (SJI) manBiBN’naBIva. ral;kareRbIR)as; steel joists rYmTaMgkarKNna nigkarplit

RtUv)ane)aHBum<pSayenAkñúg Standard Specifications, Load Tables, nig Weight Table for Steel
Joists and Joist Girders (SJI, 1994).

eKGaceRCIserIs open-web steel joists CamYynwg the aid of the standard load tables (SJI,
1994) ehIytaragmYyenAkñúgcMeNamenaHRtUv)anbgðajenAkñúgrUbTI 5>34 . CamYynwgkarpSMKñarvag

ElVg nig joist eKnwgTTYl)antémøbnÞúkmYyKUr. elxxagelICa total service load capacity KitCa
pounds kñúgmYy foot ehIyelxenAxageRkamCa service live load kñúgmYy foot EdlnwgbegáItPaBdab

esμInwg 1/ 360 énRbEvgElVg. ¬eTaHbICabnÞúkenAkñúgtaragCa service load capacities k¾eday k¾eK

GaceRbItaragenHy:aggayRsYlCamYynwgviFI LRFD EdleyIgnwgbgðajenATIenH¦. elxdMbUgénelx
sMKal;Cakm<s;rbs; open-web steel joist EdlKitCa in. . taragk¾[pgEdr nUvTm¶n;Rbhak;RbEhl
EdlKitCa pound kñúgmYy foot énRbEvg.
eKGacrk open-web steel joists EdlRtUv)anKNnaedIm,ImannaTICa floor or roof joist ¬Edl
pÞúyBImannaTICa girder¦ Ca open-web steel joist (K-series, both standard and KCS), longspan
steel joists (LH-series), nig deep longspan steel joist (DLH-series). enAeBleyIgrMkilesrIeLIg

kan;Etx<s; eyIgnwgTTYl)anRbEvgElVg niglT§PaBRTbnÞúkkan;EtFM. Ca]TahrN_ 8K1 manRbEvg

ElVg 8 ft. niglT§PaBRTbnÞúk 550lb / ft. b:uEnþ 72DLH19 GacRTbnÞúk)an 497lb / ft. elIRbEvg 144 ft. .

T.Chhay 168 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

edayelIkElg KCS joists, open-web steel joists TaMgGs;RtUv)anKNnaCa trusses EdlRT

edayTRmsamBaØ CamYynwgbnÞúkBRgayesμIenAelI top chord. kardak;bnÞúkenHeFVI[ top chord rgnUv
bending k¾dUc axial compression dUcenH top chord RtUv)anKNnaCa beam-column ¬emIlCMBUk 6¦.

edIm,IFananUvsißrPaBrbs; top chord eKRtUvP¢ab; the floor or roof deck kñúgviFIEbbNaedIm,IeFVI[ man
continuous lateral support.

Fñwm 169 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

TaMg top nig bottom chord members rbs; K-series joists RtUv)anplitedayEdkEdlman
yield stress 50ksi . lT§PaBRTbnÞúkrbs; K-series joists RtUv)anepÞógpÞat;edaykarBiesaF ehIy

emKuNsuvtßiPaBGb,brmaRtUv)anbgðaj[eXIjesμInwg 1.65 .
viFIsaRsþd¾samBaØsRmab;eRbIR)as; standard load tables CamYynwg LRFD RtUv)anENnaMeday
SJI (1994) ehIyRtUv)anbgðajenATIenH kñúgTRmg;EkERbbnþicbnþÜc. BicarNa TMnak;TMngeKal LRFD

smIkar @>#³
∑ γ i Qi ≤ φRn
vaRtUv)ansresrsRmab;bnÞúkBRgayesμIkñúgTRmg;Ca
wu ≤ φwn ¬%>&¦
Edl wu CabnÞúkBRgayesμIemKuN nig wn Ca nominal uniform load strength of the joist. Rbsin
ebIeyIgeRbIpleFobmFümén nominal strength elI allowable strength esμInwg 1.65 eyIgGac *

sresr nominal strength eday

wn = 1.65wsji

Edl wsji Ca allowable strength (allowable load) Edl[enAkñúg standard load tables.
Design strength KW

( )
φwn = 0.9 1.65wsji = 1.485wsji ≈ 3 2 wsji

\LÚveyIgGacsresrsmIkar %>& Ca
wu ≤ 3 2 wsji

sRmab;eKalbMNgénkarKNna eyIgGacsresrTMnak;TMngenHCa
required wsji = 2 3 wu

]TahrN_ 5>15³ eRbI load table Edl[enAkñúg rUbTI 5>34 eRCIserIs open-web steel joist sRmab;
RbB½n§kRmal nigbnÞúkxageRkam.
Joist spacing = 3 ft
Span length = 20 ft
bnÞúkKW³ kRmalxNÐkRmas; 3in.
*
cMNaMfaemKuNsuvtßiPaBsRmab; K-series joists RtUv)ankMNt;edaykarBesaFEdleFVIeLIgedayplitkr.
T.Chhay 170 Beams
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

bnÞúkefrepSgeTot = 20 psf
bnÞúkGefr = 50 psf
dMeNaHRsay³ sRmab;bnÞúkefr
kRmalxNг 50⎛⎜⎝ 123 ⎞⎟⎠ = 37.5 psf
bnÞúkefrepSgeTot = 20 psf
Tm¶n;rbs; joist = 3 psf ¬]bma¦
srub = 60.5 psf

wD = 60.5(3) = 181.5lb / ft
sRmab;bnÞúkGefr 50 psf
wL = 50(3) = 150lb / ft
bnÞúkemKuNKW
wu = 1.2 wD + 1.6 wL = 1.2(181.5) + 1.6(150 ) = 457.8lb' ft
bMElgbnÞúkenHeTACa required service load³
wu = (457.8) = 305lb / ft
2 2
required wsji =
3 3
rUbTI 5>34 bgðajfa joist xageRkambMeBjnUvtRmUvkarénbnÞúkxagelI³ 12K 5 Tm¶n;RbEhl
7.1lb / ft / 14 K 3 Tm¶n;RbEhl 6lb / ft nig 16 K 2 Tm¶n;RbEhl 5.5lb / ft . edayminman

karkMNt;sRmab;km<s; dUcenHeyIgerIsnUv joist NaEdlRsalCageK.

cemøIy³ eRbI 16K 2 .

5>13> bnÞHRTFñwm nigbnÞH)atssr (Beam Bearing Plates and Column Base Plate)
viFIKNnabnÞHRTssrmanlkçN³RsedogKñanwgviFIKNnabnÞHRTFñwm ehIyedaysarmUlehtu
enH eyIgnwgBicarNavaCamYyKña. elIsBI karkMNt;kRmas;rbs;bnÞH)atssrtRmUv[mankarBicarNa
BI flexure dUcenHvaRtUv)anelIkykmkerobrab;enATIenH EdlminEmnenAkñúgCMBUk 4. kñúgkrNITaMgBIr
tYnaTIrbs;bnÞHEdkKWEbgEckbnÞúkEdlRbmUlpþúM (concentrated load) eTAsmÖar³EdlRTva.
bnÞHRTFñwmmanBIrRbePTKW³ mYysRmab;bBa¢ÚnRbtikmμrbs;FñwmeTATRm dUcCaCBa¢aMgebtug nig
mYyeTotsRmab;bBa¢ÚnbnÞúkeTAsøabxagelIrbs;Fñwm. dMbUg BicarNaTRmFñwmEdlbgðajenAkñúgrUbTI
Fñwm 171 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

5>35 . eTaHbICaFñwmCaeRcInRtUv)antP¢ab;eTAssrb¤eTAFñwmepSgeTotk¾eday EtRbePTénTRmEdl

bgðajenATIenH RtUv)aneRbICaerOy² CaBiessenARtg; bridge abutments. karKNnaBIbnÞHRTrYmman
bICMhan³
!> kMNt;TMhM N EdleKGackarBar web yielding nig web crippling.
@> kMNt;TMhM B EdlRkLaépÞ B × N manTMhMRKb;RKan;edIm,IkarBarsmÖar³EdlRT ¬CaTUeTAKW
ebtug¦ BIkarEbk.
#> kMNt;kRmas; t EdlbnÞHRTman bending strength RKb;RKan;.
karBN’naBI Web yielding and web crippling manenAkñúg Chapter K of AISC Specifica-
tion, “Strength Design Consideration”. ÉcMENk bearing strength rbs;ebtugRtUv)anniyayenA

kñúg Chapter J, “Connections, Joints, and Fasteners”.

Web Yielding
Web yielding KWCakarpÞúHEbkedaykarsgát; (compressive crushing) rbs;RTnugFñwmEdl
bNþalBIkarGnuvtþn_kmøaMgsgát;edaypÞal;eTAsøabEdlenABIxagelI b¤BIxageRkamRTnug. kmøaMgenH
GacCakmøaMgRbtikmμBITRménRbePTdUcbgðajkñúg rUbTI 5>35 b¤vaGacCabnÞúkEdlbBa¢ÚneTAsøabeday
ssr b¤FñwmepSgeTot. Yielding ekIteLIgenAeBlEdlkugRtaMgsgát;enAelImuxkat;edktamry³RTnug
xiteTArkcMNuc yield. enAeBlbnÞúkRtUv)anbBa¢Úntamry³bnÞHEdk web yielding RtUv)ansnμt;faekIt
manenAEk,rmuxkat;EdlmanTTwg t w . enAkñúg rolled shape muxkat;enARtg;cugénBitekag (toe of the
fillet) Edlmancm¶ay k BIépÞxageRkArbs;søab ¬TMhMenHRtUv)anerobCatarag enAkñúg dimensions and

properties tables in the Manual). RbsinebIbnÞúkRtUv)ansnμt;faEbgEckxøÜnvaeday slope 1 : 2.5

T.Chhay 172 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dUcbgðajenAkñúg rUbTI 5>36 RkLaépÞenARtg;TRmrgnUv yielding KW (2.5k + N )t w . edayKuN

RkLaépÞenHnwg yield stress [ nominal strength sRmab; web yielding enARtg;TRm³
Rn = (2.5k + N )F y t w (AISC Equation K1-3)

The bearing length N enARtg;TRmmikKYrtUcCag k . enARtg;bnÞúkxagkñúg beNþayrbs;muxkat;rgnUv

yielding KW
2(2.5k ) + N = 5k + N
The nominal strength KW
Rn = (5k + N )F y t w (AISC Equation K1-2)

The design strength KW φRn , Edl φ = 1.0

Web Cripplimg
Ca buckling rbs;RTnugEdlbNþalBIkmøaMgsgát;EdlbBa¢Úntamry³søab.
Web crippling

sRmab;bnÞúkxagkñúg nominal strength sRmab; web crippling KW³

⎡ 1.5 ⎤
⎛N ⎞⎛⎜ t w ⎞⎟ ⎥ Fy t f
Rn = 135t w2 ⎢1 + 3⎜ ⎟ (AISC Equation K1-4)
⎢ ⎝ d ⎠⎜⎝ t f ⎟⎠ ⎥ tw
⎣⎢ ⎦⎥
sRmab;bnÞúkenARtg; b¤Ek,rTRm ¬minFMCagBak;kNþalkm<s;FñwmBIcug¦ nominal strength KW³
⎡ 1.5 ⎤
⎛N ⎞⎛⎜ t w ⎞⎟ ⎥ Fy t f
Rn = 68t w2 ⎢1 + 3⎜
⎢
⎟
⎝ d ⎠⎜⎝ t f ⎟⎠ ⎥ tw
sRmab; N
d
≤ 2 (AISC Equation K1-5a)
⎣⎢ ⎦⎥
⎡ 1.5 ⎤
2⎢ ⎛ N ⎞⎛⎜ t w ⎞⎟ ⎥ F y t f
b¤ Rn = 68t w 1 + ⎜ 4 − 0.2 ⎟
⎢ ⎝ d ⎠⎜⎝ t f ⎟⎠ ⎥ t w
sRmab; N
d
> 2 (AISC Equation K1-5b)
⎢⎣ ⎥⎦
emKuNersIusþg;sRmab;sßanPaBkMNt;enHKW φ = 0.75
Fñwm 173 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Concrete Bearing Strength

smÖar³EdleRbIsRmab;RTFñwmGacCa ebtug \dæ b¤smÖar³epSg²eTot b:uEnþCaTUeTAvaCaebtug.
smÖar³enHRtUvEtTb;nwg bearing load EdlGnuvtþedaybnÞHEdk. The nominal bearing strength
EdlbBa¢ak;enAkñúg AISC J9 dUcKñaenAkñúg American Concrete Institute’s Building Code (ACI,
1995). RbsinebI plate RKbeBjelIépÞrbs;TRm enaH nominal strength KW
Pp = 0.85 f 'c A1 (AISC Equation J9-1)

RbsinebI plate minRKbeBjelIépÞrbs;TRmeT enaH nominal strength KW

Pp = 0.85 f 'c A1 A2 / A1 (AISC Equation J9-2)

Edl ersIusþg;rgkarsgát; 28éf¶rbs;ebtug

f 'c =

A1 = bearing area R

A2 = full area rbs;TRm

RbsinebI A2 mincMCamYy A1 enaH A2 KYrmantémøFMCag A1 EdlvamanragFrNImaRtRsedog

Kñanwg A1 dUcbgðajenAkñúgrUbTI 5>37. AISC tRmUv[
A2 / A1 ≤ 2
The design bearing strength KW φc Pp Edl φc = 0.60 .
m
T.Chhay 174 Beams
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Plate Thickness
enAeBlEdlbeNþay nigTTwgrbs;bnÞHTRmRtUv)ankMNt;ehIy bearing pressure mFüm
RtUv)anKitCabnÞúkBRgayesμIeTAelI)atén plate EdlRtUv)ansnμt;RTedayTTwg 2k EdlenAkNþalFñwm
nigbeNþay N dUcbgðajenAkñúgrUbTI 5>38. bnÞab;mkeTotbnÞHRtUv)anBicarNafaekageFobG½kSRsb
eTAnwgElVgFñwm. dUcenH bnÞHRtUv)anKitCa cantilever EdlmanRbEvgElVg n = (B − 2k )/ 2 nigTTwg
N . edIm,IgayRsYl TTwg 1in. RtUv)anBicarNa CamYynwgbnÞúkBRgayesμIKitCa lb / in. EdlesμInwg

bearing pressure EdlKitCa lb / in.2 .

BIrUbTI 5>38 m:Um:g;GtibrmaenAkñúgbnÞHKW

Ru n R n2
Mu = × n× = u
BN 2 2 BN
Edl Ru / BN Ca bearing pressure mFümrvagbnÞH nigebtug. sRmab;muxkat;ctuekaNEkg
EdlekageFobG½kSexSay (minor axis) enaH nominal moment strength M u esμInwg plastic moment
capacity M p . dUcbgðajenAkñúgrUbTI 5>39 plastic moment sRmab;muxkat;ctuekaNEkg

EdlmanTMhMTTwgmYyÉktþa nigkRmas; t KW
⎛ t ⎞⎛ t ⎞ t2
M p = Fy ⎜1× ⎟⎜ ⎟ = Fy
⎝ 2 ⎠⎝ 2 ⎠ 4

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edaysar φb M n RtUvEttUcCag M u
φb M n ≥ M u
t 2 Ru n 2
0 .9 F y ≥
4 2 BN
2 Ru n 2 2.222 Ru n 2
t≥
0.9 BNF y
b¤ t≥
BNF y
¬%>* / %>(¦

]TahrN_ 5>16³ KNna bearing plate edIm,IEbgEckRbtikmμrbs; W 21× 68 CamYynwgRbEvgElVg

15 ft. 10in. KitBIG½kSeTAG½kSrbs;TRm. Service load srub EdlKitbBa©ÚlTaMgTm¶n;FñwmKW 9kips / ft

EdlmanbnÞúkefr nigbnÞúkGefresμIKña. FñwmRtUv)anRTenABIelICBa¢aMgebtugGarem:Edlman

f 'c = 3500 psi . TaMgbnÞHEdk nigFñwmCaEdk A36 .

dMeNaHRsay³ bnÞúkemKuNKW
wu = 1.2 wD + 1.6 wL = 1.2(4.5) + 1.6(4.5) = 12.6kips / ft.
ehIyRbtikmμKW
w L 12.6(15.83)
Ru = u = = 99.73kips
2 2
kMNt;RbEvgrbs; bearing N EdlcaM)ac;edIm,IkarBar web yielding. BI AISC Equation K1-3,
design strength sRmab;sßanPaBkMNt;enHKW

Rn = (2.5k + N )Fy t w

sRmab; φRn ≥ Ru /
1[2.5(1.438) + N ](36 )(0.430 ) ≥ 99.73

N ≥ 2.85in.
eRbI AISC Equation K1-5edIm,IkMNt;témørbs; N EdlcaM)ac;edIm,IkarBar web crippling. snμt;
N / d ≥ 0.2 nigsakl,gTRmg;TIBIrrbs;smIkar. sRmab; φRn ≥ Ru /
⎡ 1.5 ⎤
2⎢ ⎛ N ⎞⎛⎜ t w ⎞⎟ ⎥ Fy t f
φ 68t w 1 + ⎜ 4 − 0.2 ⎟ ≥ Ru
⎢ ⎝ d ⎠⎜⎝ t f ⎟⎠ ⎥ tw
⎣⎢ ⎦⎥
⎡ ⎛ 4N ⎞⎛ 0.43 ⎞ ⎤ 36(0.685)
1.5
0.75(68)(0.43)2 ⎢1 + ⎜ − 0.2 ⎟⎜ ⎟ ⎥ ≥ 99.73
⎢⎣ ⎝ 21.13 ⎠⎝ 0.685 ⎠ ⎥⎦ 0.43
N ≥ 5.27in. (controls)
T.Chhay 176 Beams
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RtYtBinitükarsnμt;
N 5.268
= = 0.25 > 0.2 (OK)
d 21.13
sakl,g N = 6in. . kMNt;TMhM B BI bearing strength. karsnμt;EdlmansuvtßiPaBKWRkLaépÞeBj
TaMgGs;rbs;TRmRtUv)aneRbI.
φc (0.85) f 'c A1 ≥ Ru

0.6(0.85)(3.5)A1 ≥ 99.73

A1 ≥ 55.87in 2
témøGb,brmarbs;TMhM B KW
A 55.87
B= 1 = = 9.31in.
N 6
TTwgsøabrbs; W 21× 68 KW 8.270in. EdleFVI[bnÞHEdkFMCagsøabbnþic EdleKcg;)an. sakl,g
B = 10in. .

kMNt;kRmas;bnÞHEdkEdlcaM)ac;
B − 2k 10 − 2(1.438)
n= = = 3.562in.
2 2
BIsmIkar ¬%>(¦
2.222 Ru n 2 2.222(99.73)(3.562)2
t= = = 1.14in.
BNF y 10(6)(36 )

cemøIy³ eRbI PL1 14 × 6 ×10 .

RbsinebIFñwmminRtUv)anBRgwgxagenARtg;cMNucrgbnÞúk ¬kñúgviFIEbbNaedIm,IkarBarbMlas;TIxag
rvagsøabrgkmøaMgsgát; nigsøabrgkmøaMgTaj¦ eTenaH Specification tRmUv[Gegát sidesway web
buckling (AISC K1.5). enAeBlbnÞúkGnuvtþeTAelIsøabTaMgBIr eKRtUvRtYtBinitü compression

buckling (AISC K1.6).

Fñwm 177 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Column Base Plate

dUcKñanwgkarKNna beam bearing plateEdr karKNna column base plate tRmUv[mankar
BicarNaBI bearing pressure eTAelIsmÖar³EdlRT nig bending rbs;bnÞHEdk. PaBxusKñad¾FMbMputKW
bending enAkñúg beam bearing plate KWmYyTis b:uEnþ column base plate rgnUv bending BIrTis.

elIsBIenHeTot web crippling nig web yielding minEmnCabBaðaenAkñúgkarKNna column base plate
eT.

Column base plateGacRtUv)ancat;cMNat;fñak;CabnÞHFM b¤bnÞHtUc EdlbnÞHtUcmanTMhMRbhak;

RbEhlTMhMssr. elIsBIenH bnÞHtUceFVIkarxusKña enAeBlvargbnÞúkRsal nigeBlvargbnÞúkF¶n;.
kRmas;rbs;bnÞHFMRtUv)ankMNt;BIkarBicarNaén bending rbs;EpñkénbnÞHEdllyecjBI
ssr. Bending RtUv)ansnμt;faekItmaneFobnwgG½kSenAkm<s;Bak;kNþalrbs;bnÞHEk,rRCugrbs;søab
ssr. G½kSBIrRsbeTAnwgRTnugmancm¶ayBIKña 0.80b f nigG½kSBIreTotRsbeTAnwgsøabmanKMlatBIKña
0.95d . kñúgcMeNamceRmok cantilever 1in. BIrEdlsMKal;eday m nig n dUcenAkñúgrUbTI 5>40 témø

EdlFMCag eKRtUv)aneRbICMnYs[ n enAkñúgsmIikar %>* edIm,IKNnakRmas;bnÞH b¤

t ≥l
2 Pu
0.9 BNF
¬%>!0¦
y

T.Chhay 178 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Edl l CatémøFMCageKkñúgcMeNam m nig n . viFIenHsMedAdUceTAnwg cantilever method.

bnÞH)attUcEdlRTTm¶n;RsalRtUv)anKNnaedayeRbI Murray-Stockwell method (Murray,
1983). enAkñúgviFIenH EpñkénbnÞúkssrEdlGnuvtþenAkñúgRBMEdnrbs;muxkat;ssr ¬BIelIRkLaépÞ

b f d ¦ RtUv)ansnμt;faEbgEckesμIenAelIRkLaépÞ H-shaped dUcbgðajkñúg rUbTI 5>41. dUcenH

bearing pressure KWRbmUlpþúMenAEk,rExSRBMrbs;ssr. kRmas;bnÞHRtUv)ankMNt;BI flexural analysis

rbs;ceRmok cantilever énTTwgÉktþa nigénRbEvg c . viFIenHpþl;lT§plCasmIkar

t≥c
2 Po
0.9 A F
¬%>!!¦
H y

Edl P
Po = u × b f d
BN
= bnÞúkenAkñúgRkLaépÞ b f d
= bnÞúkenAelIRklaépÞ H-shape

AH = RklaépÞ H-shape

c = TMhMEdlcaM)ac;edIm,I[kugRtaMg o esμIeTAnwg design bearing stress rbs;smÖar³EdlRT.

P
A
H

cMNaMfasmIkar %>!! manTRmg;RsedogKñanwgsmIkar %>!0 edayeRbIkugRtaMg Pu / BN

EdlCMnYseday Po / AH .
sRmab;bnÞHEdlRTTm¶n;F¶n; ¬RBMEdnrvagbnÞHRTTm¶n;Rsal nigbnÞHRTTm¶n;F¶n;minRtUv)ankMNt;
Cak;lak;¦/ Thornton (1990a) EdlesñIrnUvkarviPaKedayQrelIkarBt;BIrTisrbs;EpñkénbnÞHrvagRT

Fñwm 179 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

nug nigsøab. dUcEdl)anbgðajenAkñúg rUbTI 5>42 kMNat;énbnÞHenHRtUv)ancat;Tukfa fixed enAnwgRT

nug/ TRmsamBaØenAnwgsøab nigTMenrenARCugmYyeTot. kRmas;EdltRmUvkarKW
2 Pu
t ≥ n'
0.9 BNF y

Edl n'=
1
4
db f ¬%>!@¦

viFITaMgbIenHRtUv)anbBa©ÚlKñaeday Thornton (1990b) ehIykarsegçbmandUcxageRkam. kM

ras;bnÞHEdlcaM)ac;KW
t ≥l
2 Pu
0.9 BNF
¬%>!#¦
y

Edl l = max(m, n, λn' )

2 X
λ= ≤1
1− 1− X
⎛ 4db ⎞ P
X =⎜ ⎟ u
f

⎝ (
⎜ d + b 2 ⎟φ P
f ⎠ c p)
1
n'= db f
4
φc = 0.60
Pp = nominal bearing strength BI AISC Equation J9-1 b¤ J9-2.

T.Chhay 180 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

CamYynwgsmIkarxagelIenH eKmincaM)ac;kMNt;fabnÞHFM b¤tUc rgbnÞúkRsal b¤F¶n;. λ Gacyk

esμInwg 1.0 (Thornton, 1990b).
viFIenHRsedogKñaeTAnwgGVIEdl[enAkñúg Part 11 of the Manual (Volume II), “Connections
for Tension and Compression”.

]TahrN_ 5>17³ eKeRbI W10× 49 CassrnwgRtUv)anRTeday concrete pierdUcbgðajkñúgrUbTI 5>43.

épÞxagelIrbs; piermanTMhM 18in. ×18in. . KNnabnÞH A36 sRmab;bnÞúkefr 98kips nig bnÞúkGefr
145kips . ersIusþg;ebtugKW f 'c = 3000 psi .

dMeNaHRsay³ bnÞúkemKuNKW
Pu = 1.2 D + 1.6 L = 1.2(98) + 1.6(145) = 349.6kips
KNna required bearing area
φc Pp ≥ Pu

φc (0.85) f 'c A1 A2 / A1 ≥ Pu
0.6(0.85)(3)A1 18(18) / A1 ≥ 349.6

A1 ≥ 161.1in.2
RtYtBinitü
A2 / A1 = 18(18) / 161.1 = 1.41 < 2 (OK)
mü:ageTot bnÞHRtUvEtmanTMhMFMCagTMhMssr dUcenH
b f d = 10.00(9.98) = 99.8in.2 < 161.1in.2 (OK)

Fñwm 181 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

sRmab; B = N = 13in. . A1 = 13(13) = 169in.2

TMhMrbs;ceRmok cantilever m nig n GacRtUv)ankMNt;BI rUbTI 5>43 b¤
N − 0.95d 13 − 9.48
m= = = 1.76in
2 2
N − 0.8b f 13 − 8
n= = = 2.5in.
2 2
BIsmIkar %>!@
9.98(10) = 2.497in.
1 1
n' = db f =
4 4
edayyk λ = 1.0 eKTTYl)an
l = max(m, n, n') = max(176,2.5,2.497 ) = 2.5in.
BIsmIkar %>!#/ required plate thickness KW
2 Pu 2(349.6)
t =l = 2.5 = 0.893in.
0.9 BNFy 0.9(13)(13)(36)

cemøIy³ eRbI PL1×13 ×13 .

5>14> Biaxial Bending

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viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Biaxial bending ekItmanenAeBlEdlFñwmrgnUvlkçxNÐbnÞúkEdlbegáIt bending tamTaMgG½kS

xøaMg (major or strong axis) nigG½kSexSay (minor or weak axis). dUckrNIbgðajenAkñúgrUbTI 5>44
EdlbnÞúkcMcMNuceTaleFVIGMeBIeTAelIG½kSbeNþayrbs;Fñwm b:uEnþeRTteFobeTAnwgG½kSeKalnImYy²rbs;
muxkat;. eTaHbICakardak;bnÞúkenHmanlkçN³TUeTACagkardak;bnÞúkBIelIkmunk¾eday k¾vaenAEtCakrNI
Biess edaysarbnÞúkkat;tam shear center rbs;muxkat;. The shear center KWCacMNucEdlbnÞúkeFVIGM
eBIelIFñwmedaymin[FñwmrgrmYl (no twisting nor torsion). TItaMgrbs; shear center GacRtUv)an
kMNt;BI elementary mechanics of materials edayKNna internal resisting torsional moment
EdlbMEbkBIrMhUrkmøaMgkat;enAkñúgmuxkat;eTA external torque.

TItaMgrbs; shear center sRmab;muxkat;TUeTACaeRcInRtUv)anbgðajenAkñúg rUbTI5>45 a Edl

shear center RtUv)ansMKal;eday “o”. témørbs; eo EdlkMNt;TItaMgrbs; shear center sRmab;

channel shapes RtUv)anerobcMCataragenAkñúg Manual. CaTUeTA shear center EtgEtsßitenAelIG½kS

sIuemRTI dUcenH shear center nwgsßitenAelITIRbCMuTm¶n;rbs;muxkat;EdlG½kSsIuemRTITaMgBIrkat;Kña. rUbTI

Fñwm 183 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

5>45 b bgðajTItaMgdabrbs;FñwmBIrepSgKña enAeBlbnÞúkGnuvtþkat;tam shear center nigminkat;tam

shear center .

krNITI1³ bnÞúkEdlGnuvtþkat;tam shear center

RbsinebIbnÞúkeFVIGMeBIkat;tam shear center bBaðaFñwmrgnUvm:Um:g;Bt;FmμtakñúgTisedAEkgBIr.
dUcbgðajkñúg rUbTI 5>46 bnÞúkGacRtUv)anbMEbkCakMub:Usg;ctuekaNEkgkñúgTisedA x nigTisedA y
EdlkMub:Usg;bnÞúknImYy²begáIt bending eFobG½kSepSgKña.

edIm,IedaHRsayCamYybnÞúkpÁÜb mundMbUgeyIgsakl,gemIl chapter H of the Specification,

“Manuals Under Combined Forces and Torsion” ¬ehIyemIleTACMBUkTI6 kñúgesovePAenH¦ sin.

The Specification edaHRsaybnÞúkpÁÜbCadMbUgtamry³kareRbI interaction formulas EdlKitBIsar³sM

xan;én\T§iBlbnÞúknImYy²EdlmanTMnak;TMngeTAnwgersIusþg;EdlRtUvKñanwg\T§iBlénbnÞúkenaH. ]Tahr-
N_ RbsinebIman bending eFobEtnwgG½kS x /
M ux ≤ φb M nx b¤ φ MMux ≤ 1.0
b nx

Edl M ux = m:Um:g;Bt;emKuNeFobG½kS x
M nx = nominal moment strength eFobG½kS x

dUcKña RbsinmanEt bending eFobG½kS y enaH

M uy ≤ φb M ny b¤ φ MMuy ≤ 1.0
b ny

Edl M uy = m:Um:g;Bt;emKuNeFobG½kS y
T.Chhay 184 Beams
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

M ny = nominal moment strength eFobG½kS y

enAeBlmanRbePT bending TaMgBIr viFI interaction formula tRmUv[plbUkpleFobTaMgBIrtUcCag
b¤esμInwg 1.0 Edl
M uy
M ux
φ M
+
φ M
≤ 1.0 ¬%>!$¦
b nx b ny

tamkarBit tRmUvkarenHGnuBaØat[ designer dak;bnÞúkkñúgTisedAmYyEdlminmandak;enAelITisedA

mYyeTot. AISC Section H1 bBa©ÚlpleFobsRmab;bnÞúktamG½kS nig[ interaction formulas BIr
EdlmYysRmab;bnÞúktamG½kStUc nigmYyeTotsRmab;bnÞúktamG½kSFM ¬eyIgnwgsikSamUlehtusRmab;
krNIenHenAkñúgCMBUk 6¦. CamYynwgm:Um:g;Bt;BIrTis ehIyKμanbnÞúktamG½kS rUbmnþsRmab;bnÞúktam
G½kStUcKW
Pu M ux M uy
+ + ≤ 1.0 (AISC Equation H1-1b)
2φPn φb M nx φb M ny

RbsinebIbnÞúktamG½kS Pu = 0 enaHsmIkarenHRtUvKñanwgsmIkar %>!$.

mkdl;cMNucenH eKminBicarNaersIusþg;rbs;muxkat; I- nig H-shaped EdlekageFobG½kS
exSayeT. RbsinebIeFVIEbbenH vanwgmanlkçN³smBaØ. RKb;rUbragEdlekageFobnwgG½kSexSayrbs;
vaminGac buckle kñúgTisedAepSgeToteT dUcenH lateral-torsional buckling minEmnCasßanPaBkM
Nt;eT. RbsinebIrUbragmanlkçN³ compact enaH
M ny = K py = F y Z y ≤ 1.5M yy

Edl M yy = Fy S y = yield moment sRmab;G½kS y . sRmab;muxkat; I- nig H-shaped Edlekag

eFobG½kSexSay Ednx<s;bMput 1.5M yy nwglubCanic© ¬ Z y / S y nwgFMCag 1.5 Canic©¦. RbsinebIrUbrag
Ca noncompact ersIusþg;Edl[eday AISC Equation A-F1-3 sRmab; flange local buckling b¤
web local buckling. ¬RKb; standard shapes EdlRtUv)anerobCataragenAkñúg Manual manRTnug

compact dUcenHvaGacekItmanEt flange local buckling Etb:ueNÑaH.¦

]TahrN_ 5>18³ W 21× 68 RtUv)aneRbICaFñwmTRmsamBaØEdlmanRbEvg 12 feet . søabrgkarsgát;

RtUv)andak;TRmxagEtenAxagcug. bnÞúkeFVIGMeBItamry³ shear center CamYym:Um:g;emKuN

Fñwm 185 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

M ux = 200 ft − kipsehIy M uy = 25 ft − kips . RbsinebIeKeRbI A36 etIFñwmenHbMeBjlkçxNÐ

rbs; AISC Specification? snμt;fam:Um:g;TaMgBIrEbgEckesμIenAelIRbEvgrbs;Fñwm.
dMeNaHRsay³ eKTTYl)anTinñn½yxageRkamsRmab; A36 BI Load Factor Design Selection Table.
rUbragCa compact ehIy
L p = 7.5 ft , Lr = 22.8 ft

φb M p = 432 ft − kips, φb M r = 273 ft − kips

The unbraced length Lb = 12 ft , dUcenH L p < Lb < Lr ehIysßanPaBkMNt;EdllubKWsßitenAkñúg

elastic lateral-torsion buckling enaH
⎡ ⎛ ⎞⎤
(
φb M nx = φb Cb ⎢ M p − M p − M r ⎜ )⎜ LLb −− LL p ⎟⎟⎥
⎢⎣ ⎝ r p ⎠ ⎥⎦

⎡ ⎛ ⎞⎤
(
= Cb ⎢φb M p − φb M p − φb M r )⎜⎜ LLb −− LL p ⎟⎟⎥ ≤ φb M P
⎢⎣ ⎝ r p ⎠⎥⎦

edaysarm:Um:g;Bt;BRgayesμI/ Cb = 1.0 ehIy

⎡ ⎛ 12 − 7.5 ⎞⎤
φb M nx = 1.0⎢432 − (432 − 273)⎜ ⎟⎥ = 385.2 ft − kips
⎣ ⎝ 22.8 − 7.5 ⎠⎦
müa:gvijeTot eKGacTTYl φb M nx BI beam design charts
edaysarrUbrag compact dUcenHvaKμan flange local bucklingehIy
φb M ny = φb M py = φb Z y Fy = 0.90(24.4 )(36 ) = 790.6in. − kips = 65.88 ft − kips

RtYtBinitü Zy
Sy
=
24.4
15.7
= 1.55 > 1.5

dUcenHeRbI M ny = 1.5M yy = 1.5 F y S y = 1.5(36 )(15.7 ) = 847.8in. − kips = 70.75 ft − kips

φb M ny = 0.9(70.75) = 63.59 ft − kips

BIsmIkar %>!!
M ux M uy 200 25
+ = + = 0.912 < 1.0 (OK)
φb M nx φb M ny 385.2 63.59
cemøIy³ W 21× 68 RKb;RKan;

T.Chhay 186 Beams

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

krNITI2³ bnÞúkEdlGnuvtþminkat;tam shear center

enAeBlEdlbnÞúkGnuvtþminkat;tam shear center rbs;muxkat; lT§plKWFñwmnwgrg flexure bUk
nwg torsion. RbsinebIGaceFVIeTA)an rUbragFrNImaRtrbs;eRKOgbgÁúM nigtMNrKYrRtUvEkERbedIm,IbM)at;cM
Nakp©it. bBaðarbs; torsion enAkñúg rolled shapes KWsμúKsμaj ehIyeyIgnwgedaHRsayvaCamYyviFIRb
hak;RbEhl. eKGacrkkarerobrab;EdllkçN³lMGitsRmab;RbFanbT nig design aid RKb;RKan; enA
kñúg Torsional Analysis of Structural Steel Members (AISC, 1997). lkçxNÐénkardak;bnÞúkEdl
eFVI[ekItman torsion RtUv)anbgðajenAkñúg rUbTI 5>47 a. bnÞúkpÁÜbRtUv)andak;enAelIG½kSrbs;søab
xagelI b:uEnþExSskmμrbs;vaminkat;tam shear center rbs;muxkat;eT. RbsinebIeyIgKitBIsßanPaBlM
nwg eyIgGacrMkilkmøaMgeTA shear center edaybEnßm couple. dUcenHeKTTYl)anRbB½n§lMnwgEdlpSM
eLIgedaykmøaMgEdl[eFVIGMeBIkat;tam shear center bUknwg twisting moment dUcEdl)anbgðaj.
enAkñúg rUbTI 5>47 b eKmankMub:Usg;bnÞúkEtmYyEdlRtUvedaHRsay EtKMnitKWEtdUcKña.

rUbTI 5>48 bgðajBIviFIEdlsRmYlkñúgkaredaHRsaykrNITaMgBIrenH. enAkñúgrUbTI5>48 a eK

snμt;søabxagelIpþl;nUversIusþg;srubeTAnwgkMub:Usg;bnÞúkedk. enAkñúg rUbTI5>48 b m:Um:g;rmYl (twisting
moment) RtUv)anTb;eday couple EdlpSMeLIgedaybnÞúkBIresμIKñaeFVIGMeBIelIsøabnImYy². tamviFIRb
hak;RbEhl eKGacsnμt;fasøabnImYy²Tb;nwgkmøaMgdac;edayELkBIKña. dUcenH bBaðaRtUv)ankat;bnßy
Fñwm 187 T.Chhay
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eTACakrNIén bending rbs;rUbragBIr EdlrUbragnImYy²TTYlbnÞúktamry³ shear center. kñúgsßan

PaBnImYy²Edl)anBiBN’naenAkñúg rUbTI 5>48 muxkat;EtRbEhlBak;kNþalb:ueNÑaH RtUv)anBicarNa
famanRbsiT§PaBtamG½kS y dUcenH enAeBlBicarNaersIusþg;rbs;rbs;søabeTal eRbItémøEtBak;
kNþalrbs; Z y sRmab;muxkat;EdlmanenAkñúgtarag.

Design of Roof Perlins

édrENgdMbUl (roof purlin) CaEpñkénRbB½n§dMbUlCRmal (sloping roof system) EdlrgnUvm:U
m:g;Bt;BIrTis (biaxial bending) énRbePTEdleTIbnwgBN’na. sRmab; roof purlin EdlbgðajenAkñúg
rUbTI 5>49 bnÞúkmanTisedAbBaÄr EtG½kSénkarBt;KWeRTt. lkçxNÐénkardak;bnÞúkenHRtUvnwgrUbTI
5>48 a. kMub:Usg;EkgeTAnwgdMbUlnwgbegáIt bending eFobG½kS x ehIykMub:Usg;RsbBt;FñwmeFobG½kS
y rbs;va. RbsinebI purlin RtUv)anRTedayTRmsamBaØenAnwg trusses ( b¤ rigid frame rafter) m:Um:g;

Bt;GtibrmaeFobG½kSnImYy²KW wL2 / 8 Edl w CakMub:Usg;rbs;bnÞúk. RbsinebIeKeRbI sag rods vanwg

pþl;nUv lateral support tamG½kS x ehIynwgCaTRmsRmab;G½kS y EdltRmUv[Kit purlin CaFñwmCab;.
sRmab; sag rods EdlmanKMlatesμI eKGaceRbIrUbmnþsRmab;FñwmCab;enAkñúg Part 4 of the Manual.

]TahrN_ 5>19³ RbB½n§dMbUl trusses EdlbgðajenAkñúg rUbTI 5>50 EdlmanKMlatBIKña 15 ft. . éd

rENgRtUv)andak;enAelItMN nigenAelIcMNuckNþalrbs;Ggát;xagelI. eKdak; sag rods enAkNþal
purlin nImYy². bnÞúk gravity srub EdlrYmbBa©ÚlTaMgTm¶n;édrENgsnμt;KW 30 psf énépÞdMbUl CamYy

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nwgpleFobbnÞúkGefrelIbnÞúkefresμInwg 1.0 . edaysnμt;favaCalkçxNÐdak;bnÞúkeRKaHfñak; cUreRbIEdk

A36 nigeRCIserIs W-shape Edlmankm<s; 6in. sRmab;édrENg.

dMeNaHRsay³ sRmab;lkçxNÐbnÞúkenH bnÞúkefr bUknwg roof live load edayKμanxül; nigRBil

bnSMbnÞúk (A4-3) nwgmantémøFMCageK³
wu 1.2wD + 1.6 Lr = 1.2(15) + 1.6(15) = 42 psf
TTwgénépÞrgsMBaFEdlmanGMeBIelIédrENgKW
15 10
= 7.906 ft.
2 3
enaH bnÞúkelIédrENg = 42(7.906) = 332.1lb / ft
kMub:Usg;Ekg = 10
3
(332.1) = 315.1lb / ft

kMub:Usg;Rsb = 110 (332.1) = 105.0lb / ft

nig M ux = 18 (0.3151)(15)2 = 8.862 ft − kips
CamYynwg sag rods Edldak;enAcMNuckNþalédrENgnImYy² enaHédrENgCaFñwmCab;BIrElVgtamTis
exSay. BI “Beam Diagrams and Formulas” section in Part 4 of the Manual, m:Um:g;Bt;enAelI
TRmxagkñúgCamYynwgkarrgbnÞúkEtmYyElVgKW
1
M= wL2
16
Edl w=bnÞúkBRgayesμI
L = RbEvgElVg ¬ElVgBIresμIKña¦

CamYynwgbnÞúkenAelIElVgTaMgBIr m:Um:g;GacTTYleday superposition³

wL2 (2 ) = wL2
1 1
M = M max =
16 8
dUcenH M uy =
1
8
(0.105)(15 / 2)2 = 0.7382 ft − kips

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edIm,IeRCIserIsrUbragsakl,g eRbI beam design charts nigeRCIserIsrUbragCamYynwgersIusþg;tam

G½kSxøaMgFM. sRmab; unbraced length 15 / 2 = 7.5 ft / sakl,g W 6 × 9 .
sRmab; Cb = 1.0 / φb M nx = 14.0 ft − kips . BI rUbTI 5>15 b Cb = 1.3 sRmab;lkçxNÐbbnÞúk nig
lkçxNÐTRmxagénFñwmenH. dUcenH
φb M nx = 1.30(14.0) = 18.20 ft − kips
b:uEnþ φb M px = 16.8 ft − kips < 18.20 ft − kips
dUcenHeRbI φb M nx = 16.8 ft − kips
rUbragenH compact dUcenH
φb M ny = φb M py = φb Z y Fy = 0.9(1.72 )36 = 55.73in. − kips = 4.644 ft − kips
Zy
b:uEnþ Sy
=
1.72
1.11
= 1.55 > 1.5

dUcenH
( ) ( )
φb M ny = φb 1.5M yy = φb 1.5F y S y = 0.9(1.5)(36)(1.11) = 53.95in. − kips = 4.496 ft − kips

edaysarbnÞúkRtUv)anGnuvtþenAelIsøabxagelI eRbIlT§PaBenHEtBak;kNþaledIm,ITb;Tl;nwg\T§iBl
rmYl. BIsmIkar %>!$
M ux M uy 8.862 0.7382
+ = + = 0.856 < 1.0 (OK)
φb M nx φb M ny 16.8 4.496 / 2
kmøaMgkat;TTwgKW
0.3151(15)
Vu = = 2.363kips
2
BI factored uniform load table³
φvVn = 19.5kips > 2.363kips (OK)
cemøIy³ eRbI W 6 × 9 .

5>15> ersIusþg;m:Um:g;Bt;rbs;rUbragepSg² (Bending Strength of Various Shape)

W-, S- nig M-shapes Ca hot-rolled shapes EdleKeRbICaTUeTAsRmab;Fñwm ehIy bending

strength rbs;vaRtUv)anerobrab;BIxagedIm. b:uEnþeBlxøHeKk¾eRbIrUbragepSg²eTotCa flexural mem-

bers Edr ehIykñúgEpñkenHnwgniyaysegçbBIkarpþl;[rbs; AISC. smIkarTaMgGs;)anBI Chapter F

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b¤ Appendix F of the Specification. eK[ Nominal strength sRmab; compact nig noncompact
hot-rolled shapes b:uEnþminEmnsRmab; slender shapes b¤rUbragEdlpSMeLIgBIEdkbnÞHeT. kñúgEpñkenH

min)anpþl;nUv]TahrN_CatémøelxeT Et]TahrN_ 6>11 bBa©ÚlnUvkarKNnaBI flexural strength

rbs; structural tee-shape.
dUcEdl)anerobrab;BIxagedIm smIkarKWsRmab; nonhybrid section ( Fyw = Fyf = Fy ) nig
sRmab;krNIBt;Etb:ueNÑaH ¬minmanbnÞúktamG½kSeT¦.
I. Channels
A. Width-thickness parameters for flexure
1. søab
bf
λ=
tf
/ λp =
65
Fy
nig λr =
141
F y − 10
¬sRmab; US¦
bf
λ=
tf
/ λp =
170
Fy
nig λr =
370
F y − 69
¬sRmab; IS¦
2. RTnug
λ=
h
tw
/ λp =
640
Fy
nig λr =
970
F y − 10
¬sRmab; US¦
λ=
h
tw
/ λp =
1680
Fy
nig λr =
2550
Fy
¬sRmab; IS¦
B. Bending eFobG½kSxøaMg [CamYy ¬!¦ bnÞúkGnuvtþkat;tam shear center ehIysßitenA
kñúgbøg;RsbnwgRTnug b¤ ¬@¦ karTb;RbqaMgnwgkarrmYlenAcMNucbnÞúkGnuvtþ nigenARtg;
TRm] ³ M n dUcKñasRmab; I-shapes ¬emIlEpñk 5>5 nig 5>6¦.
C. Bending eFobG½kSexSay³ M n dUcKñasRmab; I-shapes ¬emIlEpñk 5>14¦.
II. Rectangular Structural Tubes
A. Width-thickness parameters ¬emIlrUb 5>51¦
1. søab
λ=
b
t
/ λp =
190
Fy
nig λr =
238
Fy
¬sRmab; US¦
λ=
b
t
/ λp =
500
Fy
nig λr =
625
Fy
¬sRmab; IS¦
2. RTnug
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λ=
h
t
/ λp =
640
Fy
nig λr =
970
Fy
¬sRmab; US¦
λ=
h
t
/ λp =
1680
Fy
nig λr =
2550
Fy
¬sRmab; IS¦
RbsinebIeKmindwgTMhMBitR)akd b nig h EdlbgðajenAkñúg rUbTI 5>51 eKGac)a:n;
sμanedayykTTwgsrub b¤km<s;srubdknwgbIdgkRmas; ¬lkçN³rbs;EdkTIb
RCugEdlmanenAkñúg Manual KWQrelIkaMxageRkAEdlesμInwg 2t ¦.

B. Bending eFobG½kSxøaMg ¬bnÞúkenAkñúgbøg;sIuemRTI¦

1. rUbrag compact
sRmab;rUbrag compact ersIusþg;nwgQrelIsßanPaBkMNt;én lateral-torsional
buckling (LTB).

sRmab; Lb ≤ L p
M n = M p ≤ 1.5M y (AISC Equation F1-1)

sRmab; L p < Lb ≤ Lr
⎡ ⎛ ⎞⎤
(
M n = Cb ⎢ M p − M p − M r )⎜⎜ LLb −− LL p ⎟⎟⎥ ≤ M p (AISC Equation F1-2)
⎢⎣ ⎝ r p ⎠⎥⎦
sRmab; Lb > Lr
M n = M cr ≤ M p (AISC Equation F1-12)

Edl M cr =
57000Cb JA
Lb / ry
xñat US (AISC Equation F1-14)

M cr =
393000Cb JA
Lb / ry
xñat IS
3750ry JA
Lp =
Mp
xñat US (AISC Equation F1-5)

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25855ry JA
Lp =
Mp
xñat IS
57000ry JA
Lr =
Mp
xñat US (AISC Equation F1-10)

393000ry JA
Lr =
Mp
xñat IS
M r = Fy S x (AISC Equation F1-11)

2. rUbrag noncompact ³ The nominal strength esμInwgtémøEdltUcCageKéntémø

Edl)anKNnasRmab;sßanPaBkMNt; lateral torsional buckling (LTB), flange
local buckling (FLB) b¤ web local buckling (WLB). sRmab;sßanPaB

nImYy² én local buckling TaMgBIr ersIusþg;RtUv)ankMNt;BIsmIkarxageRkam³

⎛ λ − λp ⎞
(
Mn = M p − M p − Mr ⎜ )
⎜ λr − λ p
⎟ (AISC Equation A-F1-3)
⎟
⎝ ⎠
C. Bending eFobG½kSexSay³ vaminmansßanPaBkMNt; LTB sRmab;RKb;rUbragEdlrg
karBt;eFobG½kSexSayrbs;va.
1. rUbrag compact
M n = M p ≤ 1 .5 M y (AISC Equation F1-1)

2. rUbrag nonompact³ RtYtBinitü FLB nig WLB CamYynwg AISC Equation A-F-
1-3.
III. Square Structural Tubes
A. Width-thickness parameters
λ=
b
t
/
λp =
190
Fy
nig λr =
238
Fy
¬sRmab; US¦
λ=
b
t
/ λp =
500
Fy
nig λr =
625
Fy
¬sRmab; IS¦
B. Nominal bending strength
vaminmansßanPaBkMNt; LTB sRmab;rUbragkaer ¬b¤ctuekaNEkgeT¦.
1. rUbrag compact
M n = M p ≤ 1 .5 M y (AISC Equation F1-1)

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2. rUbrag nonompact³ ersIusþg;RtUv)ankMNt;eday local buckling eday WLB b¤

FLB edayykmYyNaEdl M n tUcCageK.
⎛ λ − λp ⎞
(
Mn = M p − M p − Mr ⎜
⎜ λr − λ p
) ⎟
⎟
(AISC Equation A-F1-3)
⎝ ⎠
IV. Solid Rectangular Bars
sRmab; rectangular bars sßanPaBkMNt;EdlGacGnuvtþ)anKW LTB sRmab;G½kSBt;
xøaMg local buckling minEmnCasßanPaBkMNt;sRmab;G½kSBt;xøaMg b¤k¾exSay.
A. Bending eFobG½kSxøaMg

sRmab; Lb ≤ L p
M n = M p ≤ 1 .5 M y (AISC Equation F1-1)

sRmab; L p < Lb ≤ Lr
⎡ ⎛ ⎞⎤
(
M n = Cb ⎢ M p − M p − M r )⎜⎜ LLb −− LL p ⎟⎟⎥ ≤ M p (AISC Equation F1-2)
⎢⎣ ⎝ r p ⎠⎥⎦

sRmab; Lb > Lr
M n = M cr ≤ M p (AISC Equation F1-12)

Edl M cr =
57000Cb JA
Lb / ry
xñat US (AISC Equation F1-14)

M cr =
393000Cb JA
Lb / ry
xñat IS
3750ry JA
Lp =
Mp
xñat US (AISC Equation F1-5)

25855ry JA
Lp =
Mp
xñat IS
57000ry JA
Lr =
Mp
xñat US (AISC Equation F1-10)

393000ry JA
Lr =
Mp
xñat IS
M r = Fy S x (AISC Equation F1-11)

B. Bending eFobG½kSexSay³
M n = M p ≤ 1 .5 M y (AISC Equation F1-1)
V. Tees and double-anfle Shapes

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A. Width-thickness parameters
1. Tees
a. søab
bf
λ=
2t f
nig λr =
95
Fy
eKmineRbI λ p ¬sRmab; US¦
bf
λ=
2t f
nig λr =
250
Fy
eKmineRbI λ p ¬sRmab; IS¦
b. RTnug
λ=
d
tw
nig λr =
127
Fy
eKmineRbI λ p ¬sRmab; US¦
λ=
d
tw
nig λr =
333
Fy
eKmineRbI λ p ¬sRmab; IS¦
2. Double angles with separators, either leg
λ=
b
t
λr = nig
76
Fy
eKmineRbI λ p ¬sRmab; US¦
λ=
b
t
nig λr =
200
Fy
eKmineRbI λ p ¬sRmab; IS¦

3. Double angles in continuous contact, outstanding leg

λ=
b
t
λr = / 95
Fy
λp eKmineRbI
US ¬sRmab; ¦
λ=
b
t
/ λr =
250
Fy
eKmineRbI λ p ¬sRmab; IS¦
B. CamYybnÞúkenAkñúgbøg;sIuemRTI
π EI y GJ ⎡
M n = M cr = B + 1+ B2 ⎤ (AISC Equation F1-15)
Lb ⎢ ⎣ ⎥ ⎦
Edl M n ≤ 1 .5 M ysRmab; stem rgkarTaj
M n ≤ 1.0 M y sRmab; stem rgkarsgát;
⎛ d ⎞ Iy
B = ±2.3⎜⎜ ⎟⎟ (AISC Equation F1-16)
⎝ Lb ⎠ j
M y = Fy S x

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eKeRbIsBaØabUksRmab; B enAeBlEdl stem rgkarTaj ehIysBaØadkenAeBlEdl

stem rgkarsgát;enARKb;kEnøgTaMgGs;tambeNþay unbraced length.

C. Bending eFobG½kSexSay³

sRmab; nonslender shapes (λ ≤ λr )

M n = M p ≤ 1 .5 M y
VI. Solid circular and square shapes
M n = M p ≤ 1 .5 M y
VII. Hollow circular shapes
A. Width-thickness parameters
λ=
D
t
/
λp =
2070
Fy
nig λr =
8970
Fy
¬sRmab; US¦
λ=
D
t
/ λp =
14270
Fy
nig λr =
61850
Fy
¬sRmab; IS¦
Edl D CaGgát;p©itxageRkA
B. Norminal bending strength:
vaminmansßanPaBkMNt; LTB sRmab;rUbragmUl ¬b¤kaer¦. ersIusþg;RtUv)ankNt;
eday local buckling.
sRmab; λ ≤ λ p
M n = M p ≤ 1 .5 M y

sRmab; λ p < λ ≤ λr
⎛ 600 ⎞
Mn = ⎜ + Fy ⎟ S (AISC Appendix F, Table A-F1.1)
⎝ D/t ⎠

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VI. Fñwm-ssr
Beam-Columns

6>1> esckþIepþIm (Introduction)

enAeBlEdlGgát;eRKOgbgÁúMCaeRcInRtUv)anKitCassrrgkmøaMgtamG½kS b¤CaFñwmEdlrgEtkmøaMg
Bt; (flexural loading) Fñwm nigssrCaeRcInrgnUvkmøaMgTaMgBIrKw kmøaMgBt; nigkmøaMgtamG½kS. vaCakar
Bit CaBiesssRmab;eRKOgbgÁúMsþaTicminkMNt;. sUm,IEtTRm roller rbs;FñwmsamBaØGacpþl;nUvkmøaMg
kkitEdlGacTb;Fñwmcl½ttambeNþay enAeBlEdlbnÞúkGnuvtþEkgnwgG½kSbeNþayrbs;Fñwm. b:uEnþkñúg
krNIBiessenH CaTUeTA\T§iBlrg ¬TIBIr¦mantémøtUc ehIyGacecal)an. ssrCaeRcInRtUv)anCa
Ggát;rgkmøaMgsgát;suT§CamYynwgkMrwtlMeGogEdlGacecal)an. RbsinebIssrCaGgát;sRmab;eRKOg
bgÁúMmYyCan; ehIyTRmrbs;vaTaMgBIrRtUv)anKitCaTRm pinned FñwmnwgrgEt bending EdlCalT§plBI
bnÞúkcMNakp©itEdleRKaHfñak;tictYc.
b:uEnþ sRmab;Ggát;eRKOgbgÁúMCaeRcIn \T§iBlTaMgBIrnwgmantémøFM EdlGgát;TaMgenaHRtUv)aneK
ehAfa beam-columns. BicarNa rigid frame enAkñúgrUbTI 6>1. sRmab;lkçxNÐbnÞúkEdl[Ggát;
edk AB minRtwmEtRTbnÞúkbBaÄrBRgayesμIeT EfmTaMgCYyGgát;bBaÄredIm,ITb;nwgbnÞúkxagcMcMNuc P .
Ggát; CD CakrNIEdleRKaHfñak;Cag eRBaHvaTb;;nwgbnÞúk P1 + P2 edayminmanCMnYyBIGgát;bBaÄr
NaeT. mUlehtuKWfa x-bracing EdlbgðajedayExSdac; karBar sidesway enACan;xageRkam.
sRmab;karbgðajTisedArbs; P2 Ggát; ED nwgrgkmøaMgTaj ehIyGgát; CF nwgFUrRbsinebI bracing
element RtUv)anKNnaedIm,ITb;EtkmøaMgTaj. b:uEnþsRmab;krNIenH Ggát; CD RtUvbBa¢ÚnbnÞúk

P1 + P2 BI C eTA D .

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Ggát;bBaÄrrbs;eRKagenHk¾RtUv)anKitCa beam-columns. enACan;xagelI Ggát; AC nig BD

nigekageRkam\T§iBlrbs; P1 . elIsBIenH enARtg; A nig B m:Um:g;Bt;RtUv)anbBa¢ÚnBIGgát;edktamry³
tMNrwg. karbBa¢Únm:Um:g;enHk¾ekIteLIgenARtg; C nig D ehIyvaBitsRmab;RKb; rigid frame eTaHbI
m:Um:g;TaMgenHtUcCagm:Um:g;Edl)anBIbnÞúkxagk¾eday. ssrCaeRcInenAkñúg rigid frames Ca beam-
columns ehIy\T§iBlrbs;m:Um:g;Bt;minRtUv)anecal. b:uEnþ ssrrbs;GaKarmYyCan;EdlenAdac;BIeK

GacRtUv)anKitCaGgát;rgkmøaMgsgát;cMG½kS.
eBlxøH]TahrN_epSgeTotrbs; beam-columns GacCYbenAkñúg roof trusses. eTaHbICaFmμta
top chord RtUv)anKitCaGgát;rgkmøaMgsgát;tamG½kSk¾eday RbsinebI purlins RtUv)andak;enAcenøaH

tMN kmøaMgRbtikmμrbs;vanwgbegáItCa bending Edldac;xatRtUv)anKitkñúgkarKNna. krNIenHnwg

RtUv)anerobrab;enAkñúgCMBUkenH.

6>2> smIkarGnþrkmμ (Interaction Formulas)

vismPaBrbs;smIkar @># GacRtUv)ansresrkñúgTRmg;xageRkam³
∑ γ i Qi ≤ 1.0 ¬^>!¦
φRn
b¤ ∑ resistance
load effects
≤ 1.0

RbsinebIman resistance eRcInRbePTBak;B½n§ smIkar ^>! GacRtUv)ansresrkñúgTRmg;eKal

rbs; interaction formulas. dUcEdl)anerobrab;enAkñúgCMBUk 5 Rtg;Epñkm:Um:g;Bt;BIrTis plbUkén
pleFob load-to-resistance RtUv)ankMNt;RtwmmYyÉktþa. ]TahrN_ RbsinebIeKGnuvtþTaMgm:Um:g;Bt;
nigkmøaMgtamG½kS interaction formulas GacsresrCa
Pu
+
Mu
φc Pn φb M n
≤ 1 .0 ¬^>@¦
Edl Pu = bnÞúksgát;tamG½kSemKuN
φc Pn = compressive design strength
Mu = m:Um:g;Bt;emKuN
φb M n = design moment
sRmab;m:Um:g;Bt;BIrTis vanwgmanpleFobm:Um:g;Bt;BIr

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⎛ M ux M uy ⎞
Pu
+⎜ +
φc Pn ⎜⎝ φb M nx φb M ny
⎟ ≤ 1.0
⎟
¬^>#¦
⎠
Edl x nig y sMedAelIkarBt;eFobG½kS x nigG½kS y .
smIkar ^># CasmIkareKalrbs; AISC sRmab;Ggát;rgkarBt; nigrgkmøaMgtamG½kS. eK[
smIkarBIrenAkñúg Specification: mYysRmab;bnÞúkcMG½kSEdlmantémøtUc nigmYyeTotsRmab;bnÞúkcM
G½kSEdlmantémøFM. RbsinebIbnÞúktamG½kSmantémøtUc tYbnÞúktamG½kSRtUv)ankat;bnßy. sRmab;
bnÞúktamG½kSEdlmantémøFM tYkmøaMgBt;RtUv)ankat;bnßybnþic. tRmUvkarrbs; AISC RtUv)an[enAkñúg
Chapter H, “Members Under Combined Forces and Torsion,” ehIyRtUv)ansegçbdUcxageRkam³

sRmab; φPPu ≥ 0.2

c n
Pu 8 ⎛ M ux M uy ⎞
+ ⎜ + ⎟ ≤ 1.0 (AISC Equation H1-1a)
φc Pn 9 ⎜⎝ φb M nx φb M ny ⎟
⎠
sRmab; Pu
φc Pn
< 0 .2

Pu ⎛ M ux M uy ⎞
+⎜ + ⎟ ≤ 1.0 (AISC Equation H1-1b)
2φc Pn ⎜⎝ φb M nx φb M ny ⎟
⎠
]TahrN_6>1 bgðajBIkarGnuvtþn_smIkarTaMgenH.

]TahrN_6>1³ Fñwm-ssrEdlbgðajenAkñúg rUbTI6>@ manTRm pinned enAcugsgçag ehIyrgbnÞúkem

KuNdUcbgðaj. karBt;KWeFobnwgG½kSxøaMg. kMNt;faetIGgát;enHbMeBjsmIkarGnþrkmμrbs; AISC
Specification b¤eT.

dMeNaHRsay³ dUcEdl)anbkRsayenAkñúgEpñk 6>3 m:Um:g;EdlGnuvtþenAkñúg AISC Equations H1-1a

nig b eBlxøHnwgRtUv)anbegáInedaym:Um:g;bEnßm (moment amplification). eKalbMNgén]TahrN_
enHKWbgðajBIrebobeRbIsmIkarGnþrkmμ.
BI column load table ersIusþg;KNnakmøaMgsgát;tamG½kS (axial compression design
strength) rbs; W 8× 58 CamYynwg F y = 50ksi nigRbEvgRbsiT§PaB K y L = 1.0 × 17 = 17 ft KW

φc Pn = 365kips
edaysarkarBt;eFobG½kSxøaMg m:Um:g;KNna (design moment) φb M n sRmab; Cb = 1.0 GacTTYl
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)anBI beam design chart in Part 4 of the Manual.

sRmab; unbraced length Lb = 17 ft /
φb M n = 202 ft − kips
sRmab;lkçxNÐbnÞúk niglkçxNÐcugsRmab;bBaðaenH Cb = 1.32 ¬emIlrUbTI 5>15 c¦.
sRmab; Cb = 1.32 /
φb M n = 1.32(202) = 267 ft − kips
b:uEnþm:Um:g;enHFMCag φb M p = 224 ft − kips ¬EdlTTYl)andUcKñaBI beam design charts ¦/ dUcenH
design moment RtUv)ankMNt;Rtwm φb M p . dUcenH

φb M n = 224 ft − kips
m:Um:g;Bt;GtibrmaenAkNþalElVgKW
22(17 )
Mu = = 93.5 ft − kips
4
kMNt;faetIsmIkarGnþrkmμmYyNalub
Pu
=
200
φc Pn 365
= 0.547 > 0.2 dUcenHeRbI AISC Eq.H1-1a.
Pu 8 ⎛ M ux M uy ⎞
⎟ = 0.5479 + 8 ⎛⎜ 93.5 + 0 ⎞⎟ = 0.919 ≤ 1.0
+ ⎜ + (OK)
φc Pn 9 ⎜⎝ φb M nx φb M ny ⎟
⎠ 9 ⎝ 224 ⎠

cemøIy³ Ggát;enHbMeBj AISC Specification.

T.Chhay 200 Beam-Column

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6>3> m:Um:g;bEnßm (Moment Amplification)

viFIBImunsRmab;karKNnaGgát;rgkarBt; nigkmøaMgtamG½kSGaceRbI)ansRmab;EtkmøaMgtamG½kS
mantémøminFMeBk. vtþmanrbs;bnÞúktamG½kS ¬elIkElgenAeBlvamantémøtUc¦ begáItm:Um:g;TIBIrEdl
RtUv)anKitbBa©ÚlkñúgkarKNna. rUb TI 6>3 bgðajBIFñwm-ssrCamYybnÞúktamG½kS nigbnÞúkTTwgG½kS
BRgayesμI. Rtg;cMNuc O NamYyEdlmanmanm:Um:g;Bt;EdlbegáIteLIgedaybnÞúkBRgayesμInwgm:Um:g;
bEnßm Py EdlbegáIteLIgedaybnÞúktamG½kSeFVIGMeBIcMNakp©itBIG½kSbeNþayrbs;Ggát;. m:Um:g;TIBIr
enaH mantémøkan;EtFMenAkEnøgNaEdlmanPaBdabkan;EtFM. kñúgkrNIenH Rtg;km<s;Bak;kNþalm:Um:g;
srubesμInwg wL2 / 8 + Pδ . vaCakarBitEdl m:Um:g;bEnßmbegáItPaBdabbEnßmBIelIPaBdabEdl)anBI
bnÞúkTTwgG½kS. edaysareKminGacrkPaBdabsrubedaypÞal; ¬bBaðaenHCa nonlinear¦ ehIyeday
sarEteKminsÁal;PaBdab eKk¾minGacKNnam:Um:g;)anEdr.

viFIviPaKeRKOgbgÁúMFmμta (ordinary structural analysis methode) Edlminykragpøas;TImk

KitRtUv)aneKKitCa viFIdWeRkTImYy (first-order method). eKeRbI Iterative numerical technique
¬EdleKehAfa viFIdWeRkTIBIr (second-order method)¦ edIm,IrkPaBdab nigm:Um:g;TIBIr b:uEnþviFIenHmin
GaceRbIsRmab;karKNnaedayéd EdlvaRtUv)aneRbICaTUeTACamYynwgkmμviFIkMuBüÚT½r. Design codes
nig specifications bc©úb,nñPaKeRcIn rYmbBa©ÚlTaMg AISC Specification GnuBaØatkareRbIR)as; second-

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order analysis b¤ moment amplification method. viFIenHtRmUvkarKNnam:Um:g;Bt;GtibrmaEdl)an

BIlT§plBI flexural loading ¬bnÞúkTTwgG½kS b¤m:Um:g;cugGgát;¦ eday first-order analysis bnÞab;mk
KuNnwgemKuNm:Um:g;bEnßm (moment amplification factor) edIm,IKitm:Um:g;TIBIr.
rUbTI 6>4 bgðajGgát;TRmsamBaØCamYynwgbnÞúkcMG½kS nigPaBminRtg;dMbUg (initial out-of-
straightness). PaBdabdMbUg (initial crookedness) enHGacsMEdgeday³
πx
yo = e sin
L
Edl e CabMlas;TIGtibrmadMbUg EdlekIteLIgenAkNþalElVg.

sRmab;RbB½n§kUGredaendUcEdl)anbgðaj eKGacsresrTMnak;TMngExSkMeNag-m:Um:g;
(moment-curvature relationship) dUcxageRkam³
d2y M
=−
2 EI
dx
m:Um:g;Bt; M ekIteLIgedaysarcMNakp©iténkmøaMgtamG½kS Pu eFobG½kSrbs;Ggát;. cMNak
p©itenHpSMeLIgeday initial crookedness yo bUknwgPaBdabbEnßm y EdlekItBIkarBt;. enARtg;TI
taMgNamYy m:Um:g;KW
M = Pu ( yo + y )
edayCMnYssmIkarenHeTAkñúgsmIkarDIepr:g;Esül eyIgTTYl)an
d2y P ⎛ πx ⎞
= − u ⎜ e sin + y ⎟
dx 2 EI ⎝ L ⎠
d2y P Pe πx
+ u y = − u sin
dx 2 EI EI L

T.Chhay 202 Beam-Column

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EdlCa ordinary, nonhomogenous differential equation. edaysarvaCasmIkardWeRkTIBIr

dUcenHvamanlkçxNÐRBMEdnBIr. sRmab;lkçxNÐTRmEdlbgðaj lkçxNÐRBMEdnKW
enARtg; x = 0 / y = 0 nigenARtg; x = L / y = 0
enHmann½yfa PaBdabesμIsUnüenAcugsgçag. GnuKmn_EdlbMeBjTaMgsmIkarDIepr:g;Esül nig
lkçxNÐRBMEdnKW
πx
y = B sin
L
Edl B Catémøefr. CMnYsvaeTAkñúgsmIkarDIepr:g;Esül eyIgTTYl)an
π2 πxP πx Pe πx
− B sin + u B sin = − u sin
L2 L EI L EI L
eKTTYl)antémøefr
Pe
− u
EI = −e e
B= =
Pu π 2 π 2 EI Pe − 1
− 1− Pu
EI L2 Pu L2

Edl Pe = π
2
EI
= Euler buckling load
2
L

dUcenH y = B sin πLx = ⎡⎢ (P / Pe ) − 1⎤⎥ sin πLx

⎣ e u ⎦
M = Pu ( yo + y )
⎪⎧ πx ⎡ e ⎤ πx ⎫⎪
= Pu ⎨e sin + ⎢ ⎥ sin ⎬
⎪⎩ L ⎣ (Pe / Pu ) − 1⎦ L ⎪⎭

m:Um:g;GtibrmaekItenARtg; x = L / 2 ³
⎡ e ⎤
M max = Pu ⎢e + ⎥
⎣ (Pe / Pu ) − 1⎦
⎡ (P / P ) − 1 + 1 ⎤
= Pu e ⎢ e u ⎥
⎣ (Pe / Pu ) − 1 ⎦
⎡ 1 ⎤
= Mo ⎢ ⎥
⎣1 − (Pu / Pe )⎦
Edl M o minEmnCam:Um:g;bEnßmGtibrma (unampliflied maximum moment). kñúgkrNIenH
vaTTYl)anBI initial crookedness b:uEnþCaTUeTAvaGacCalTßplénbnÞúkTTwgG½kS b¤m:Um:g;cug. dUcenHem

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KuNm:Um:g;bEnßm (moment amplification factor) KW

1
1 − (Pu / Pe )
¬^>$¦
dUcEdl)anerobrab;mkehIy TRmg;emKuNm:Um:g;bEnßmrbs; AISC GacxusEbøkBIsmIkar ^>$
bnþic.

]TahrN_6>2³ eRbIsmIkar ^>$ edIm,IKNnaemKuNm:Um:g;bEnßmsRmab;Fñwm-ssrén]TahrN_ 6>1.

dMeNaHRsay³ edaysar Euler load Pe CaEpñkrbs;emKuNm:Um:g;bEnßm eKRtUvKNnavasRmab;G½kSén
karBt; EdlkñúgkrNIenHKWG½kS x . eKGacsresr Euler load Pe edayeRbI effective length nig
slenderness ratio dUcxageRkam³
π 2 EAg
Pe =
(KL / r )2
¬emIlCMBUk 4 smIkar $>^ a¦. sRmab;G½kSénkarBt;
KL K x L 1.0(17 )(12)
= = = 55.89
r rx 3.65
π 2 EAg π 2 (29000)(17.1)
Pe = = = 1567kips
(KL / r )2 (55.89)2
BIsmIkar ^>$
1 1
= = 1.15
1 − (Pu / Pe ) 1 − (200 / 1567 )
EdlbgðajkarekIneLIg 15% BIelIm:Um:g;Bt;. m:Um:g;bEnßmKW
1.15 × M u = 1.15(93.5) = 107.5 ft − kips
cemøIy³ emKuNm:Um:g;bEnßm 1.15

6>4> Web Local Buckling in Beam-Columns

karkMNt;rbs; design moment tRmUv[RtYtBinitümuxkat;sRmab; compactness . enAeBl
EdlKμanbnÞúktamG½kS RTnugrbs;RKb;rUbragEdlmanenAkñúgtaragsuT§Et compact. RbsinebImanvtþ
manbnÞúktamG½kS RTnugTaMgenaHGacnwgmin compact. enAeBlEdleyIg[ λ = h / t w /
RbsinebI λ ≤ λ p rUbragKW compact.
T.Chhay 204 Beam-Column
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RbsinebI λ p < λ ≤ λr rUbragKW noncompact.

RbsinebI λ > λr rUbragKW slender.
ASIC B5 enAkñúg Table B5.1 erobrab;nUvkarkMNt;xageRkam³
⎛ 2.75Pu ⎞
sRmab; φ PPu ≤ 0.125 / λ p = 640F ⎜
⎜1 −
φ P ⎟
⎟ ¬xñat US¦
b y y ⎝ b y ⎠
1680 ⎛⎜ 2.75Pu ⎞
λp =
Fy ⎜⎝
1−
φb Py
⎟
⎟
¬xñat IS¦
⎠
⎛ ⎞
sRmab; φ PPu /
> 0.125 λ p = ⎜ 2.33 − Pu ⎟ ≥ 253
191
⎜
Fy φb Py ⎟⎠ Fy
¬xñat US¦
b y ⎝
500 ⎛⎜ P ⎞ 665
λp =
Fy ⎜⎝
2.33 − u ⎟ ≥
φb Py ⎟⎠ Fy
¬xñat IS¦
970 ⎛⎜ P ⎞
sRmab;témøepSg²rbs; Pu
φb Py
/λr =
F y ⎜⎝
1 − 0.74 u ⎟
φb Py ⎟⎠
¬xñat US¦
2550 ⎛⎜ P ⎞
λr =
Fy ⎜⎝
1 − 0.74 u ⎟
φb Py ⎟⎠
¬xñat IS¦
Edl Py = Ag Fy / bnÞúktamG½kScaM)ac;edIm,IeTAdl;sßanPaBkMNt; yielding.
edaysar Pu CaGBaØti eKminGacRtYtBinitü compactness rbs;RTnug nigminGacerobcMCata
ragTukCamun)aneT. b:uEnþ rolled shape xøHbMeBjnUvkrNId¾GaRkk;bMput 665 / Fy Edlmann½yfarUb
ragenaHmanRTnug compact edayminTak;TgnwgbnÞúktamG½kS. rUbragEdlmanenAkñúg column load
table in Part 3 of the Manual EdlminbMeBjlkçxNÐRtUv)ankMNt;bgðaj enaHeKRtUvRtYtBinitü

compactness rbs;RTnugrbs;va. rUbragEdlmansøabmin compact k¾RtUv)ankMNt;bgðaj dUcenHRKb;

rUbragTaMgGs;Edlmin)anbgðaj enaHmann½yfarUbragTaMgenaHKW compact.

]TahrN_6>3³ Edk A36 EdlmanrUbrag W 12 × 65 RtUv)andak;[rgm:Um:g;Bt; nigbnÞúktamG½kSem

KuN 300kips . RtYtBinitü compactness rbs;RTnug.
dMeNaHRsay³ rUbragenHKW compact sRmab;RKb;témøbnÞúktamG½kS BIeRBaHminmankarkMNt;cMNaMNa
mYyenAkñúg column load table. b:uEnþ edIm,Ibgðaj eyIgRtYtBinitü width-thickness ratio rbs;RTnug

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Pu Pu 300
= = = 0.4848 > 0.125
( )
φb Py φb Ag Fy 0.9(19.1)(36)
⎛ ⎞
dUcenH λp = ⎜ 2.33 − Pu ⎟ = 191 (2.33 − 0.4848) = 58.74
191
⎜
Fy φb Py ⎟⎠ 36
⎝
253 253
= = 42.17 < 58.74
Fy 36

dUcenH λ p = 58.74
BI dimensions and properties tables/
h
λ= = 24.9 < 58.74
tw

dUcenH RTnugKW compact. cMNaMfa sRmab;RKb;témørbs; Fy enaH th nwgmantémøtUcCag

w

253 / Fy EdlCatémøEdltUcbMputrbs; λ p dUcenHRTnugrbs; W 12 × 65 nwgenAEtCa compact.

6>5> eRKagBRgwg nigeRKagGt;BRgwg (Braced versus Unbraced Frame)

AISC Specification erobrab;BI moment amplification in Chapter C, Frames and other

Structures”. eKmanemKuNbEnßmBIrEdleRbIenAkñúg LRFD: mYyedIm,IKitBIm:Um:g;bEnßmEdlCalT§plBI

PaBdabrbs;Ggát; nigmYyeTotsRmab;KitBI\T§iBl sway enAeBlEdlGgát;CaEpñkrbs; unbraced

frame. viFIenHmanlkçN³RsedogKñaeTAnwgviFIEdleRbIenAkñúg ACI Building Code sRmab;ebtug

BRgwgedayEdk (ACI, 1995). rUbTI 6>5 nwgbgðajBIGgát;TaMgBIr. enAkñúg rUbTI 6>5 a Ggát;RtUv)anTb;
RbqaMgnwg sidesway ehIym:Um:g;TIBIrGtibrmaKW Pδ EdlRtUvbEnßmeTAelIm:Um:g;GtibrmaenAkñúgGgát;
enaH. RbsinebIeRKagminRtUv)anBRgwg vanwgelceLIgnUvm:Um:g;TIBIr EdlbgðajenAkñúg rUbTI 6>5 b Edl
begáIteday sidesway. m:Um:g;TIBIrenHmantémøGtibrma PΔ EdlbgðajBIkarbEnßménm:Um:g;cug.
edIm,IKItBI\T§iBlTaMgBIrenH emKuNm:Um:g;bEnßm B1 nig B2 RtUv)aneRbIsRmab;m:Um:g;BIrRbePT.
m:Um:g;bEnßmEdleRbIsRmab;KNnaRtUv)anKNnaBIbnÞúkemKuN nigm:Um:g;emKuNdUcxageRkam³
M u = B1M nt + B2 M lt (AISC Equation C1-1)

Edl M nt = m:Um:g;GtibrmaEdlsnμt;faminman sidesway ekIteLIg eTaHbICaeRKagBRgwgb¤minBRgwg

k¾eday ¬ nt mann½yfa no translation¦
T.Chhay 206 Beam-Column
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m:Um:g;GtibrmaEdlekIteLIgeday sidesway ekIteLIg ¬ lt mann½yfa lateral transla-

M lt =

tion¦. m:Um:g;enHGacekItBI lateral load b¤edaysar unbalanced gravity loads .

bnÞúkTMnajGacbegáIt sidesway RbsinebIeRKagGt;sIuemRTI b¤k¾bnÞúkTMnaj enaHRtUv)an

dak;edayminmanlkçN³sIuemRTI. M lt nwgmantémøesμIsUnüRbsinebIeRKagRtUv)anBRgwg.
B1 = emKuNm:Um:g;bEnßmsRmab;m:Um:g;EdlekIteLIgenAkñúgGgát;EdlRtUv)anBRgwgTb;nwg sidesway.

B2 = emKuNm:Um:g;bEnßmsRmab;m:Um:g;Edl)anBI sidesway.

eyIgnwgerobrab;BIkarkMNt;emKuNTaMgBIr B1 nig B2 enAkñúgEpñkxageRkam.

6>6> Ggát;enAkñúgeRKagEdlBRgwg (Members in Braced Frames)

emKuNm:Um:g;bEnßmEdl[edaysmIkar ^>$ RtUv)anbMEbksRmab;Ggát;EdlBRgwgRbqaMgnwg
sidesway. rUbTI 6>6 bgðajBIGgát;RbePTenHEdlrgm:Um:g;enAxagcugesμIKñaEdlbegáIt single-

curvature bending ¬kMeNagEdlbegáItkarTaj nigkarsgát;enAEtEpñkmçagrbs;Ggát;¦. m:Um:g;bEnßm

GtibrmaekItenARtg;Bak;kNþalkm<s; EdlPaBdabmantémøFMbMput. dUcenHm:Um:g;TIBIrGtibrma nigm:U

m:g;emGtibrmaRtUv)anbUkbBa©ÚlKña. eTaHRbsinebIm:Um:g;enAxagcugminesIμKñak¾eday RbsinebIm:Um:g;mYy
vilRsbTisRTnicnaLika nigmYyeTotvilRcasRTnicnaLika vanwgbegáIt single-curvature bending
ehIym:Um:g;emGtibrma nigm:Um:g;TIBIrGtibrmanwgekIteLIgenAEk,Kña.

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vanwgminEmnCakrNIeT enAeBlEdlm:Um:g;enAcugEdlGnuvtþbegáIt reverse-curvature bending

dUcbgðajenAkñúg rUbTI 6>7 . enAeBlenH m:Um:g;emGtibrmaKWenAcugmçag ehIym:Um:g;TIBIrGtibrmaekIt
eLIgenAcenøaHcugTaMgBIr. m:Um:g;bEnßmGacFMCag b¤tUcCagm:Um:g;cugGaRs½ynwgbnÞúktamG½kS.
dUcenHm:Um:g;GtibrmaenAkñúg beam-column GaRs½ynwgkarEbgEckm:Um:g;Bt;enAkñúgGgát;. kar
EbgEckenHRtUv)anKitedayemKuN Cm EdlGnuvtþenAkñúgemKuNm:Um:g;bEnßm B1 . emKuNm:Um:g;bEnßm
Edl[edaysmIkar ^>$ RtUv)anbMEbksRmab;krNIGaRkk;bMput dUcenH Cm nwgminRtUvFMCag 1.0 .
TRmg;cugeRkayrbs;emKuNm:Um:g;bEnßmKW³
Cm
B1 = ≥1 (AISC Equation C1-2)
1 − (Pu / Pe1 )

Edl Pe1 = Ag 2Fy = π

2
EAg
λc (KL / r )2
enAeBlKNna Pe1 eRbI KL / r sRmab;G½kSénkarBt; ehIyemKuNRbEvgRbsiT§PaB K ≤ 1 .0 ¬Edl
RtUvKñanwglkçxNÐEdlBRgwg¦.

karKNnaemKuN Cm
emKuN Cm GnuvtþEtelIlkçxNÐEdlBRgwgEtb:ueNÑaH. eKmanGgát;BIrRbePT EdlmYyman
bnÞúkTTwgG½kSGnuvtþenAcenøaHcug nigmYyeTotminmanbnÞúkTTwgG½kS.
rUbTI 6>8 b nig c bgðajBIkrNITaMgBIrxagelIenH ¬Ggát; AB Ca beam-column EdlRtUvKit¦.
T.Chhay 208 Beam-Column
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!> RbsinebIminmanbnÞúkTTwgG½kSeFVIGMeBIenAelIGgát;
⎛M ⎞
C m = 0.6 − 0.4⎜⎜ 1 ⎟⎟ (AISC Equation C1-3)
⎝ M2 ⎠
CapleFobénm:Um:g;Bt;enAcugrbs;Ggát;. M1 Catémødac;xaténm:Um:g;cugEdltUcCag
M1 / M 2

eK ehIy M 2 CatémøFMCag enaHpleFobnwgviC¢mansRmab;Ggát;EdlekagkñúgTRmg; reversecurvature

nigGviC¢mansRmab; single-curvature bending ¬rUbTI 6>9 ¦. Reverse curvature ¬pleFobviC¢man¦
ekIteLIgenAeBlEdl M1 nig M 2 vilRsbRTnicnaLikaTaMgBIr b¤RcasRTnicnaLikaTaMgBIr.
@> sRmab;Ggát;rgbnÞúkTTwgG½kS eKGacyk Cm = 0.85 RbsinebIcugrbs;vaRtUv)anTb;RbqaMg
nwgkarvil nigesμInwg 1.0 RbsinebIcugrbs;vaminRtUv)anTb;nwgkarvil ¬pinned¦. CaTUeTAkarTb;cug
(end restraint) ekItBIPaBrwgRkaj (stiffness) rbs;Ggát;EdlP¢ab;eTAnwg beam-column. lkçxNÐ

TRm pinned CalkçxNÐmYyEdlRtUv)aneRbIsRmab;TajrkemKuNm:Um:g;bEnßm dUcenHvaminmankarkat;

bnßytémøemKuNm:Um:g;bEnßmsRmab;krNIenHeT EdlvaRtUvKñanwg Cm = 1.0 . eTaHbICalkçxNÐcugBit
Fñwm-ssr 209 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

R)akdsßit enAcenøaHkarbgáb;eBj (fully fixity) nigknøas;Kμankkit (frictionless pin) k¾eday eKGac

eRbItémøNa mYyk¾)anEdr eRBaHvanwgpþl;lT§plCaTIeBjcitþ.

viFIsaRsþEdl)aneFVI[RbesIreLIgsRmab;Ggát;rgbnÞúkxagTTwgG½kS ¬krNITIBIr¦ RtUv)anpþl;

[enAkñúg section C1 of the commentary to the Specification. emKuNkat;bnßyKW
P
Cm = 1 +ψ u
Pe1
sRmab;Ggát;TRmsamBaØ
T.Chhay 210 Beam-Column
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

π 2δ o EI
ψ= −1
M o L2
Edl δ o CaPaBdabGtibrmaEdlekItBIbnÞúkxagTTwgG½kS ehIy M o Cam:Um:g;GtibrmaenA
cenøaHTRmEdl)anBIbnÞúkxagTTwgG½kS. emKuN ψ RtUv)anKNnaBIsßanPaBFmμtaCaeRcInehIyRtUv)an
pþl;[enAkñúg commentary Table C-C1.1.

]TahrN_6>4³ Ggát;EdlbgðajenAkñúg rUbTI 6>10 CaEpñkrbs; braced frame. bnÞúk nigm:Um:g;RtUv)an

KNnaCamYybnÞúkemKuN ehIykarBt;KWwFobnwgG½kSxøaMg. RbsinebIeKeRbI A572 Grade 50 etIGgát;
enHRKb;RKan;b¤eT? KL = KL y = 14 ft .

dMeNaHRsay³ kMNt;faetIRtUveRbIrUbmnþGnþrkmμmYyNa
KL K y L 14(12)
maximum = = = 55.63
r ry 3.02

BI AISC Table 3-50, φc Fcr = 33.89ksi dUcenH

φc Pn = Ag (φc Fcr ) = 19.1(33.89 ) = 647.4kips
Pu 420
= = 0.6487 > 0.2
φc Pn 647.4
dUcenHeRbI AISC Equation H1-1a.
enAkñúgbøg;énkarBt;

Fñwm-ssr 211 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

KL K x L 14(12 )
= = = 31.82
r rx 5.28
Ag F y π 2 EAg π 2 (29000 )(19.1)
Pe1 = = = = 5399kips
λ2c (K x L / rx )2 (31.82)2
⎛M ⎞ ⎛ 70 ⎞
C m = 0.6 − 0.4⎜⎜ 1 ⎟⎟ = 0.6 − 0.4⎜ − ⎟ = 0.9415
⎝ M2 ⎠ ⎝ 82 ⎠
Cm 0.9415
B1 = = = 1.021
1 − (Pu / Pe1 ) 1 − (420 / 5399)
BI Beam design charts,CamYynwg Cb = 1.0 nig Lb = 14 ft. moment strength KW
φb M n = 347 ft − kips
sRmab;témø Cb BitR)akd edayeyagtamdüaRkam:Um:g;enAkñúg rUbTI 6>10³
12.5M max 1.25(82 )
Cb = = = 1.06
2.5M max + 3M A + 4 M B + 3M C 2.5(82 ) + 3(73) + 4(76 ) + 3(79 )
dUcenH φb M n = Cb (347) = 1.06(347) = 368 ft − kips
b:uEnþ φb M p = 358 ft − kips ¬BItarag¦ < 368 ft − kips
dUcenHeRbI φb M n = 358 ft − kips
m:Um:g;emKuNKW M nt = 85 ft − kips M lt = 0
BI AISC Equation C1-1,
M u = B1M nt + B2 M lt = 1.021(82 ) + 0 = 83.72 ft − kips = M ux
BI AISC Equation H1-1a,
Pu 8 ⎛ M ux M uy ⎞
⎟ = 0.6487 + 8 ⎛⎜ 83.72 ⎞⎟ = 0.857 < 1.0
+ ⎜ + (OK)
φc Pn 9 ⎜⎝ φb M nx φb M ny ⎟
⎠ 9 ⎝ 358 ⎠

cemøIy³ Ggát;enHKWRKb;RKan;.

]TahrN_ 6>5³ Fñwm-ssredkEdlbgðajenAkñúgrUbTI 6>11 rgnUv service live loads dUcEdlbgðaj

kñúgrUb. Ggát;enHRtUv)anBRgwgxagenAxagcugrbs;vaTaMgBIr ehIykarBt;KWeFobnwgG½kS x . RtYtBinitü
faetIGgát;enHRKb;RKan;tam AISC Specification.

T.Chhay 212 Beam-Column

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dMeNaHRsay³ bnÞúkemKuNKW
Pu = 1.6(20 ) = 32.0kips
ehIym:Um:g;GtibrmaKW
M nt =
(1.6 × 20)(10) + (1.2 × 0.035)(10)2 = 80.52 ft − kips
4 8
Ggát;enHRtUv)anBRgwgTb;nwgkarbMlas;TIxagcug dUcenH M lt = 0 .
KNnaemKuNm:Um:g;bEnßm
sRmab;Ggát;rgbnÞúkxagEdlRtUv)anBRgwgTb;nwg sidesway ehIy unrestrained end enaH Cm = 1.0 .
témøEdlsuRkitCagEdl)anBI AISC Commentary Table C-C1.1 KW
P
C m = 1 − 0 .2 u
Pe1
sRmab;G½kSénkarBt;
KL K x L 1.0(10 )(12 )
= = = 34.19
r rx 3.51
π 2 EAg π 2 (29000)(10.3)
Pe1 = = = 2522kips
(KL / r )2 (34.19)2
⎛ 32.0 ⎞
Cm = 1 − 0.2⎜ ⎟ = 0.9975
⎝ 2522 ⎠
emKuNm:Um:g;bEnßm
Cm 0.9975
B1 = = = 1.010 > 1.0
1 − (Pu / Pe1 ) 1 − (32.0 / 2522 )
sRmab;G½kSénkarBt;
M u = B1M nt + B2 M lt = 1.010(80.52 ) + 0 = 81.33 ft − kips

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edIm,ITTYl design strengths dMbUgemIleTA column load tables in Part 3 of the Manual Edl [
φc Pn = 262kips
BI beam design charts in Part 4 of the Manual sRmab; Lb = 10 ft nig Cb = 1.0
φb M n = 91.8 ft − kips
edaysarTm¶n;FñwmtUcNas;ebIeRbobeFobnwgbnÞúkGefrcMcMNuc enaH Cb = 1.32 BI rUbTI 5>13 c.
φb M n = 1.32(91.8) = 121 ft − kips
m:Um:g;enHFMCag φb M p = 93.6 ft − kips EdlTTYl)anBI beam design chart dUcKña dUcenH design
strength RtUv)ankMNt;RtwmtémøenH. dUcenH

φb M n = 93.6 ft − kips
RtYtBinitürUbmnþGnþrkmμ³
Pu 32.0
= = 0.1221 < 0.2
φc Pn 262
dUcenHeRbI AISC Equation H1-1b³
Pu ⎛ M ux M uy ⎞ 0.1221 ⎛ 81.33 ⎞
+⎜ + ⎟= +⎜ + 0 ⎟ = 0.930 < 1.0 (OK)
2φc Pn ⎜⎝ φb M nx φb M ny ⎟
⎠ 2 ⎝ 93.6 ⎠

cemøIy³ W 8× 35 KWRKb;RKan;

]TahrN_ 6>6³ Ggát;EdlbgðajenAkñúg rUbTI6>12 eFVIBIEdk A242 EdlmanrUbrag W 12 × 65 ehIy

RtUvRTnUvbnÞúksgát;tamG½kSemKuN 300kips . enAcugTMenrmçagCa pinned nigcugmçageTotrgnUvm:Um:g;
emKuN 135 ft − kips eFobG½kSxøaMg nig 30 ft − kips eFobG½kSexSay. eRbII K x = K y = 1.0 cUreFVIkar
GegátBIGgát;enH.
dMeNaHRsay³ dMbUg kMNt; yield stress Fy . BI Table 1-2, Part 1 of the Manual, W12 × 65
CarUbragRkumTIBIr. BI Table 1-1, Edk A242 manersIusþg;EtmYyKW Fy = 50ksi .
bnÞab;mkeTot rk compressive strength. sRmab; KL = 1.0(15) = 15 ft axial compressive design
strength BI column load table KW³

φc Pn = 626kips
cMNaMfa taragbgðajfasøabrbs; W12 × 65 KW noncompact sRmab; Fy = 50ksi .
T.Chhay 214 Beam-Column
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

KNnam:Um:g;Bt;eFobG½kSxøaMg (strong axis bending moment).

= 0.6 − 0.4(0 ) = 0.6
M1
Cmx = 0.6 − 0.4
M2
K x L 15(12 )
= = 34.09
rx 5.28
π 2 EAg π 2 (29000 )(19.1)
Pe1x = = = 4704kips
(K x L / rx )2 (34.09)2
C mx 0.6
B1x = = = 0.641 < 1.0
1 − (Pu / Pe1x ) 1 − (300 / 4704)
dUcenH eRbI B1x = 1.0
M ux = B1x M ntx + B2 x M ltx = 1.0(135) + 0 = 135 ft − kips
BI beam design charts CamYy Lb = 15 ft / φb M nx = 342 ft − kips sRmab; Cb = 1.0 ehIy
φb M px = 357.8 ft − kips . BI rUbTI 5>15 g, Cb = 1.67 ehIy

Cb × (φb M nx for Cb = 1.0 ) = 1.67(342) = 571 ft − kips

lT§plenHFMCag φb M px dUcenHeRbI φb M nx = φb M px = 357.8 ft − kips
KNna m:Um:g;Bt;eFobG½kSexSay (weak axis bending moment).
= 0.6 − 0.4(0) = 0.6
M1
Cmy = 0.6 − 0.4
M2
K yL 15(12)
= = 59.60
ry 3.02

Fñwm-ssr 215 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

π 2 EAg π 2 (29000)(19.1)
Pe1 y = = = 1539kips
(K y L / ry )2 (59.60)2
C mx 0.6
B1 y = = = 0.745 < 1.0
( )
1 − Pu / Pe1 y 1 − (300 / 1539)

dUcenH eRbI B1y = 1.0

M uy = B1 y M nty + B2 y M lty = 1.0(30 ) + 0 = 30 ft − kips

edaysarsøabrbs;rUbragenH noncompact enaHersIusþg;m:Um:g;Bt;eFobG½kSexSayRtUv)ankMNt;eday

FLB.
bf
λ= = 9.9
2t f
65 65
λp = = = 9.192
Fy 50
141 141
λr = = = 22.29
Fy − 10 50 − 10

edaysar λ p < λ < λr

⎛ λ − λp ⎞
(
Mn = M p − M p − Mr ⎜ ⎟
⎜ λr − λ p ⎟
) (AISC Equation A-F1-3)
⎝ ⎠
50(44.1)
M p = M py = F y Z y = = 183.8 ft − kips
12
( )
M r = M ry = F y − Fr S y = (50 − 10)(29.1) = 1164in. − kips = 97.0 ft − kips

edayCMnYscUleTAkñúgsmIkar AISC Equation A-F1-3 eyIgTTYl)an

⎛ 9.9 − 9.192 ⎞
M n = M ny = 183.8 − (183.8 − 97.0 )⎜ ⎟ = 179.1 ft − kips
⎝ 22.29 − 9.192 ⎠
φb M ny = 0.90(179.1) = 161.2 ft − kips

rUbmnþGnþrkmμ[
Pu 300
= = 0.4792 > 0.2
φc Pn 626
dUcenHeRbI AISC Equation H1-1a³
Pu 8 ⎛ M ux M uy ⎞
⎟ = 0.4792 + 8 ⎛⎜ 135 + 30 ⎞⎟ = 0.980 < 1.0 (OK)
+ ⎜ +
φc Pn 9 ⎜⎝ φb M nx φb M ny ⎟
⎠ 9 ⎝ 357.8 161.2 ⎠

cemøIy³ W 12 × 65 RKb;RKan;
T.Chhay 216 Beam-Column
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

6>7> Ggát;enAkñúgeRKagEdlminBRgwg (Members in Unbraced Frames)

Fñwm-ssrEdlcugrbs;vaGacrMkil)an m:Um:g;dMbUgGtibrmaEdl)anBI sidesway CaTUeTAeRcIn
sßitenAelIEtcugmçag. dUcEdl)anbgðajenAkñúgrUbTI 6>5 m:Um:g;TIBIrGtibrmaEdl)anBI sidesway Etg
EtsßitenAelIcugmçag. dUcenHsRmab;krNIenH m:Um:g;TImYy nigm:Um:g;TIBIrGtibrmaCaTUeTARtUv)anbUk
bBa©ÚlKña ehIyminRtUvkaremKuN Cm eT ¬karBit Cm = 1.0 ¦. eTaHbICaenAeBlEdlmankarkat;bnßy
k¾va mantémøtictYc nigGacecal)an. cUrBicarNaFñwm-ssrEdlbgðajenAkñúgrUbTI 6>13. m:Um:g;esμIKña
enAxagcug)anmkBI sidesway ¬BIbnÞúkedk¦. bnÞúktamG½kS ¬EdlCaEpñkmYyénbnÞúkEdlmanGMeBIelI
Fñwm-ssrminbNþal[man sidesway¦RtUv)anKitbBa©ÚleTAkñúgm:Um:g;cugEdr.

emKuNm:Um:g;bEnßmsRmab; sidesway moments B2 RtUv)an[smIkarBIr. eKGaceRbIsmIkar

NamYyk¾)anEdr GaRs½ynwgPaBgayRsYlsRmab;GñkKNna³
1
B2 = (AISC Equation C1-4)
1 − ∑ Pu (Δ oh / ∑ HL )

b¤ B2 =
1
1 − (∑ Pu / ∑ Pe 2 )
(AISC Equation C1-5)

Edl ∑ Pu = plbUkbnÞúkemKuNenAelIRKb;ssrenAelICan;EdlBicarNa
Fñwm-ssr 217 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Δ oh = drift (sidesway displacement) rbs;Can;EdlBIcarNa

∑ H = plbUkénbnÞúkedkTaMgGs;EdlbegáIt Δ oh

L = km<s;Can;

∑ Pe 2 = plbUkén Euler loads rbs;ssrTaMgGs;enAelICan;EdlBicarNa ¬enAeBlEdl

KNna Pe2 eKRtUveRbI KL / r sRmab;G½kSénkarBt; ehIy K CatémøEdlRtUvKñanwg

unbraced condition.

plbUkén Pu nigplbUkén Pe2 GnuvtþeTARKb;ssrEdlsßitenAkñúgCan;EdlBicarNaCamYyKña.

eKeRbIplEckrvagplbUkbnÞúkTaMgBIrsRmab;smIkarxagelIedaysar B2 GnuvtþsRmab; unbraced
frames ehIyRbsinebI sidesway nwgekItman enaHssrTaMggs;enAkñúgCan;EdlBicarNanwg sway kñúg

eBlCamYyKña. enAkñúgkrNICaeRcIn eRKOgbgÁúMRtUv)anKNnaenAkñúgbøg; dUcenH ∑ Pu nig ∑ Pe2 KWsRmab;

ssrenACan;rbs;eRKag ehIybnÞúkxag H CabnÞúkxagEdleFVIGMeBIenAelIeRKag nigBIelICan;Edl
BicarNa. CamYynwg Δ oh EdlekIteLIgeday ∑ H pleFob Δ oh / ∑ H GacQrelIbnÞúkemKuN b¤
bnÞúkKμanemKuN. TRmg;epSgeTotrbs; B2 RtUv)an[eday AISC Equation C1-5 manlkçN³Rs
edognwgsmIkarsRmab; B1 elIkElgsRmab;plbUk.
AISC Equations C1-4 nig C1-5 RtUv)anbMEbkedayviFIBIrepSgKña b:uEnþenAkñúgkrNICaeRcInva

nwgpþl;nUvlT§pldUcKña (Yura, 1988). enAkñúgkrNICaeRcInEdltémø B2 TaMgBIrxusKñaxøaMg tYénbnÞúk

cMG½kSrbs;rUbmnþGnþrkmμnwglub ehIylT§plcugeRkaynwgminxusKñaeRcIneT. dUcEdl)anerobrab;BI
xagedIm kareRCIserIsKWsßitenAelIPaBgayRsYl vaGaRs½ynwgtYenAkñúgsmIkar.
kñúgkrNIEdl M nt nig M lt eFVIGMeBIenAcMNucBIrepSgKñaenAelIGgát; dUcbgðajenAkñúgrUbTI 6>14
AISC Equation C1-1 nwgpþl;nUvlT§plEdlsnSMsMéc.

rUbTI 6>14 bgðajbEnßmeTotBI superposition concept. rUbTI 6>14 a bgðajBI braced frame
rgnUvTaMgbnÞúkTMnaj (gravity load) nigbnÞúkxag (lateral load). m:Um:g;enA M nt enAkñúgGgát; AB
RtUv)anKNnaedayeRbIEt gravity load. edayPaBsIuemRTI eKminRtUvkar bracing edIm,IkarBar
sidesway BIbnÞúkenH. m:Um:g;enHRtUv)anbEnßmCamYyCamYynwgemKuN B1 edIm,IkarBar\T§iBl Pδ .

M lt m:Um:g;EdlRtUvKñanwg sway ¬EdlbegáIteLIgedaybnÞúkedk H ¦ nwgRtUv)anbEnßmeday B2 edIm,I

karBarnwg\T§iBl PΔ .
T.Chhay 218 Beam-Column
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

enAkñúg rUbTI 6>14 b unbraced frame RTEtbnÞúkbBaÄr. edaysarkardak;bnÞúkenHminsIuemRTI

vanwgman sidesway bnþic. m:Um:g; M nt RtUv)anKNnaedayBicarNafaeRKagRtUv)anBRgwg ¬kñúgkrNI
enH edaysarTRmedkkkit nigkmøaMgRbtikmμRtUvKμaEdleKehAfa tMNTb;nimitþ (artificial joint
restraint AJR). edIm,IKNnam:Um:g; sidesway eKRtUvykTRmkkitecj ehIyCMnYsedaykmøaMgEdlman

témøesμInwg artificial joint restraint b:uEnþmanTisedApÞúyKña. kñúgkrNIenH m:Um:g;TIBIr PΔ nwgmantémø

tUcNas; ehIyeKGacecal M lt )an.
RbsinebITaMgbnÞúkxag nigbnÞúkTMnajminsIuemRTI eKGacbEnßmkmøaMg AJR eTAelIbnÞúkxagBit
R)akd enAeBlEdl M lt RtUv)ankMNt;.

]TahrN_ 6>7³ Edk W 12 × 65 RbePT A572 grade 50 RbEvg 15 ft sRmab;eRbICassrenAkñúg

unbraced frame. bnÞúkcMG½kS nigm:Um:g;cugTTYl)anBI first-order analysis énbnÞúkTMnaj ¬bnÞúkefr

Fñwm-ssr 219 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

nigbnÞúkGefr¦ RtUv)anbgðajenAkñúg rUbTI 6>15 a . eRKagmanlkçN³sIuemRTI ehIybnÞúkTMnajk¾

RtUv)andak;sIuemRTIEdr. rUbTI 6>15 b bgðajBIm:Um:g;énbnÞúkxül;Edl)anBI first-order analysis. m:U
m:g;Bt;TaMgGs;KWeFobnwgG½kSxøaMg. emKuNRbEvgRbsiT§PaB K x = 1.2 sRmab;krNI sway nig
K x = 1.0 sRmab;krNI nonsway ehIy K y = 1.0 . kMNt;faetIGgát;enHeKarBtam AISC

Specification b¤eT?

dMeNaHRsay³ karbnSMbnÞúkTaMgGs;Edl[enAkñúg AISC A4.1 suT§EtmanbnÞúkGefr ehIyelIk

ElgEtkarbnSMbnÞúkTImYyecj EdlkarbnSMbnÞúkTaMgGs;manbnÞúkxül; b¤bnÞúkGefr b¤TaMgBIr. Rbsin
ebIRbePTbnÞúk ¬ E, Lr , S , nig R ¦ enAkñúg]TahrN_enHminRtUv)anbgðaj lkçxNÐénkarbnSMbnÞúk
RtUv)ansegçbdUcxageRkam³
1 .4 D (A4-1)
1 .2 D + 1 .6 L (A4-2)
1.2 D + (0.5 L or 0.8W ) (A4-3)
1.2 D + 1.3W + 0.5L (A4-4)
1 .2 D + 0 .5 L (A4-5)
0.9 D ± 1.3W (A4-5)

enAeBlEdlbnÞúkefrtUcCagbnÞúkGefrR)aMbIdg enaHbnSMbnÞúk (A4-1) GacminRtUvKit. bnSM

bnÞúk (A4-4) nwgmantémøFMCag (A4-3) dUcenH (A4-3) Gacdkecj)an. bnSMbnÞúk (A4-5) k¾Gac
ecal)anedaysarvanwgpþl;eRKaHfñak;tUcCag (A4-2). cugeRkay karbnSMbnÞúk (A4-6) nwgmineRKaH

T.Chhay 220 Beam-Column

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

fñak;dUc (A4-4) ehIyk¾Gacdkecj)anBIkarBicarNa EdlenAsl;EtbnSMbnÞúkBIrEdlRtUveFVIkarGegátKW

(A4-2)nig (A4-4) ³

1.2 D + 1.6 L nig 1.2 D + 1.3W + 0.5L

rUbTI 6>16 bgðajBIbnÞúktamG½kS nigm:Um:g;Bt;EdlKNnaecjBIbnSMbnÞúkTaMgBIrenH

kMNt;G½kSeRKaHfñak;sRmab;ersIusþg;kmøaMgsgát;tamG½kS
K y L = 15 ft
K x L 1.2(15)
= = 10.29 ft < 15 ft
rx / ry 1.75

dUcenHeRbI KL = 15 ft
BI column load tables CamYynwg KL = 15 ft / φc Pn = 626kips
sRmab;lkçxNÐbnÞúk (A4-2)/ Pu = 454kips / M nt = 104.8 ft − kips nig M lt = 0 ¬eday
sarEtsIuemRTI vaminmanm:Um:g; sidesway¦. emKuNm:Um:g;Bt;KW
⎛M ⎞ ⎛ 90 ⎞
Cm = 0.6 − 0.4⎜⎜ 1 ⎟⎟ = 0.6 − 0.4⎜ ⎟ = 0.2565
⎝ M2 ⎠ ⎝ 104.8 ⎠
sRmab;G½kSénkarBt;
KL K x L 1.0(15)(12 )
= = = 34.09
r rx 5.28
¬krNIenHKμan sidesway dUcenHeKeRbI K x sRmab; braced condition¦. enaH
π 2 EAg π 2 (29000)(19.1)
Pe1 = = = 4704kips
(KL / r )2 (34.09)2
emKuNm:Um:g;bEnßmsRmab;m:Um:g; nonsway KW
Cm 0.2565
B1 = = = 0.284 < 1.0
1 − (Pu / Pe1 ) 1 − (454 / 4704 )
dUcenHeRbI B1 = 1.0
M u = B1M nt + B2 M lt = 1.0(104.8) + 0 = 104.8 ft − kips
BI beam design charts CamYynwg Lb = 15 ft
φb M n = 343 ft − kips ¬sRmab; Cb = 1.0 ¦

Fñwm-ssr 221 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

φb M p = 358 ft − kips

rUbTI 6>17 bgðajBIdüaRkamm:Um:g;Bt;sRmab;m:Um:g;énbnÞúkTMnaj. ¬karKNna

Cb KWQrelItémø dac;xat dUcsBaØaenAkñúgdüaRkamenHminmansar³sMxan;eT¦. dUcenH
12.5M max
Cb =
2.5M max + 3M A + 4M B + 3M C
12.5 × (104.8)
= = 2.24
2.5(104.8) + 3(41.3) + 4(74) + 3(56.1)
sRmab; Cb = 2.24
φb M n = 2.24(343) > φb M p = 358 ft − kips

dUcenHeRbI φb M n = 358 ft − kips

T.Chhay 222 Beam-Column

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

kMNt;smIkarGnþrkmμEdlsmRsb
Pu 454
= = 0.7252 > 0.2
φc Pn 626
eRbIsmIkar AISC Equation H1-1a.
Pu 8 ⎛ M ux M uy ⎞
⎟ = 0.7252 + 8 ⎛⎜ 104.8 + 0 ⎞⎟ = 0.985 < 1.0
+ ⎜ + (OK)
φc Pn 9 ⎜⎝ φb M nx φb M ny ⎟
⎠ 9 ⎝ 358 ⎠

sRmab;lkçxNÐbnÞúk (A4-4), Pu = 212kips / M nt = 47.6 ft − kips ehIy

M lt = 171.6 ft − kips . sRmab; unbraced condition/
⎛M ⎞ ⎛ 40.5 ⎞
Cm = 0.6 − 0.4⎜⎜ 1 ⎟⎟ = 0.6 − 0.4⎜ ⎟ = 0.2597
⎝ M2 ⎠ ⎝ 47.6 ⎠
Pe1 = 4704kips ¬ Pe1 minGaRs½ynwglkçxNÐbnÞúk¦
Cm 0.2597
B1 = = = 0.272 < 1.0
1 − (Pu / Pe1 ) 1 − (212 / 4704 )
dUcenH B1 = 1.0
eyIgminmanTinñy½nRKb;RKan;edIm,IKNnaemKuNm:Um:g;bEnßm[)ansuRkitsRmab; sway
moment B2 BI AISC Equation C1-4 b¤ C1-5. RbsinebIeyIgsnμt;fapleFobrvagbnÞúktamG½kS

EdlGnuvtþmkelIGgát; nig Euler load capacity mantémødUcKñasRmab;RKb;ssrenAkñúgCan; nigsRmab;

ssrEdleyIgBicarNa enaHeyIgGacsresr Equation C1-5³
1 1
B2 = ≈
1 − (∑ Pu / ∑ Pe2 ) 1 − (Pu / Pe 2 )
sRmab; Pe2 eRbI K x EdlRtUvnwg unbraced condition³
KL K x L 1.2(15)(12 )
= = = 40.91
r rx 5.28

Fñwm-ssr 223 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

π 2 EAg π 2 (29000)(19.1)
Pe 2 = = = 3266kips
(KL / r )2 (40.91)2
BI AISC Equation C1-5/
1 1
B2 ≈ = = 1.069
1 − (Pu / Pe 2 ) 1 − (212 / 3266)
m:Um:g;bEnßmsrubKW
M u = B1M nt + B2 M lt = 1.0(47.6) + 1.069(171.6) = 231.0 ft − kips
eTaHbICam:Um:g; M nt nig M lt mantémøxusKñak¾eday k¾BYkvaRtUv)anEbgEckdUcKña ehIy Cb
nwgenAdEdl . enARKb;GRtaTaMgGs; BYkvamantémøFRKb;RKan;Edl φb M p = 358 ft − kips Ca design
strength edayminKitBIm:Um:g;NamYyeLIy.
Pu 212
= = 0.3387 > 0.2
φc Pn 626
dUcenHeRbI AISC Epuation H1-1a³
Pu 8 ⎛ M ux M uy ⎞
⎟ = 0.3387 + 8 ⎛⎜ 231.0 + 0 ⎞⎟ = 0.912 < 1.0
+ ⎜ + (OK)
φc Pn 9 ⎜⎝ φb M nx φb M ny ⎟
⎠ 9 ⎝ 358 ⎠

cemøIy³ Ggát;enHbMeBjtRmUvkarrbs; AISC Specification.

6>8 KNnamuxkat;Fñwm-ssr (Design of Beam-Column)

edaysarenAkñúgrUbmnþGnþrkmμmanGBaØtiCaeRcIn enaHkarKNnamuxkat;Fñwm-ssrCadMeNIrkar
KNnaEdlRtUvkarCacaM)ac;nUv trial-and-error process. sRmab;kareRCIserIscugeRkay KWeKeRCIserIs
rUbragNakan;EtEk,r kan;Etl¥. muxkat;sakl,gRtUv)aneRCIserIs nigRtUv)anepÞógpÞat;eLIgvijeday
eRbIrUbmnþGnþrkmμ. dMeNIrkard¾manRbsiT§PaBbMputkñúgkareRCIserIsmuxkat;sakl,gRtUv)anbegáIteLIg
CadMbUgsRmab; allowable stress design (Burgett, 1973), ehIyRtUv)anTTYl ykmkeRbIsRmab;
LRFD Edlmanerobrab;enAkñúg part 3 of the Manual, “Column Design”. lkçN³sMxan;sRmab;viFI

enHKWCa karbMElgBIm:Um:g;Bt;eTACabnÞúktamG½kSsmmUl. bnÞúkEdl)anBIkarbMElgRtUv)anykeTA

bEnßmelIbnÞúkCak;Esþg ehIyrUbragEdlRtUvRTbnÞúksrubRtUv)aneRCIserIsBI column load tables.
bnÞab;mkeKRtUvBinitürUbragsakl,genHCamYy Equation H1-1a b¤ H1-1b. bnÞúktamG½kSRbsiT§PaB
srubRtUv)an[eday
T.Chhay 224 Beam-Column
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Pu eq = Pu + M ux m + M uy mu

Edl Pu = bnÞújktamG½kSemKuNCak;Esþg
M ux = m:Um:g;emKuNeFobG½kS x

M uy = m:Um:g;emKuNeFobG½kS y

m = témøefrEdlmanenAkúñgtarag

n = témøefrEdlmanenAkúñgtarag

eKalkarN_énkarviFIenHGacRtUv)anRtYtBinitüedaysresrsmIkar ^># eLIgvijdUcxageRkam.

dMbUgKuNGgÁTaMgBIreday φc Pn ³
φ PM φc Pn M uy
Pu + c n ux + ≤ φc Pn
φb M nx φb M ny
b¤ Pu + (M ux × a constant ) + (M uy × a constant ) ≤ φc Pn
GgÁxagsþaMénvismIkarCa design strength rbs;Ggát;EdlBicarNa ehIyGgÁxageqVgGacCa
bnÞúkemKuNxageRkAEdlRtUvTb;Tl;. tYnImYy²énGgÁxageqVgmanxñatkmøaMg dUcenHtémøefrCaGñkbM
Elgm:Um:g;Bt; M ux nig M uy eTACakMub:Usg;bnÞúktamG½kS.
témøefrmFüm m RtUv)anKNnasRmab;RkumepSgKñarbs; W-shape ehIyRtUv)an[enAkñúg
Table 3-2 in Part 3 of the Manual. témø u RtUv)an[enAkñúg column load table sRmab;rUbrag

nImYy²EdlmanenAkñúgtarag. edIm,IeRCIserIsrUbragsakl,gsRmab;Ggát;CamYynwgbnÞúktamG½kS nigm:U

m:g;Bt;eFobG½kSTaMgBIr eKRtUvGnuvtþdUcxageRkam.
!> eRCIserIstémøsakl,g m edayQrelIRbEvgRbsiT§PaB KL . yk u = 2.0
@> KNnabnÞúksgát;tamG½kSRbsiT§PaB³
Pu eq = Pu + M ux m + M uy mu

eRbIbnÞúkenHedIm,IeRCIserIsrUbragBI column load tables.

#> eRbItémø u Edl[enAkñúg column load tables nigtémøfμIrbs; m BI Table 3-2 edIm,I
KNnatémøfμIrbs; Pu eq . eRCIserIsrUbragepSgeTot.
$> eFVIeLIgvijrhUtdl;témø Pu eq ElgERbRbYl.

Fñwm-ssr 225 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

]TahrN_ 6>8³ Ggát;eRKOgbgÁúMxøHenAkñúg braced frame RtUvRTbnÞúksgát;tamG½kSemKuN 150kips nig

m:Um:g;cugemKuN 75 ft − kips eFobnwgG½kSxøaMg ehIy 30 ft − kips eFobnwgG½kSexSay. m:Um:g;TaMgBIr
enHeFVIGMeBIenAelIcugmçag ÉcugmçageTotCaTRm pinned. RbEvgRbsiT§PaBeFobnwgG½kSnImYy²KW 15 ft .
minmanbnÞúkxageFVIGMeBIelIGgát;enHeT, eRbIEdk A36 nigeRCIserIs W-shape EdlRsalCageK.
dMeNaHRsay³ emKuNm:Um:g;bEnßm B1 Gacsnμt;esμInwg 1.0 edIm,IeFVIkareRCIserIsmuxkat;sakl,g.
sRmab;G½kSnImYy²
M ux = B1M ntx ≈ 1.0(75) = 75 ft − kips
M uy = B1M nty ≈ 1.0(30 ) = 30 ft − kips

BI Table 3-2, part 3 of the Manual, m = 1.75 edayeFVI interpolation

eRbItémøedIm u = 2.0
Pu eq = Pu + M ux m + M uy mu = 150 + 75(1.75) + 30(1.75)(2.0 ) = 386kips

cab;epþImCamYynwgrUbragtUcCageKenAkñúg column load tables, sakl,g W 8 × 67 ¬ φc Pn = 412kips /

u = 2.03 ¦³

m = 2.1
Pu eq = 150 + 75(2.1) + 30(2.1)(2.03) = 435kips

témøenHFMCag design strength= 412 ft − kips dUcenHeKRtUvsakl,gmuxkat;epSgeTot.

sakl,g W10 × 60 ¬ φc Pn = 416kips / u = 2.0 ¦³
m = 1.85
Pu eq = 150 + 75(1.85) + 30(1.85)(2.00 ) = 400kips < 416kips (OK)

dUcenH W 10 × 60 CarUbragsakl,gEdlGaceRbIkar)an. RtYtBinitü W 12s nig W 14s . sakl,g

W 12 × 58 ¬ φc Pn = 397kips / u = 2.41 ¦³

m = 1.55
Pu eq = 150 + 75(1.55) + 30(1.55)(2.41) = 378kips < 397 kips (OK)

dUcenH W 12 × 58 CarUbragsakl,gEdlGaceRbIkar)an. W14 EdlRsalCageKsRmab;eFVIkarCamYy

nwgbnÞúkxageRkAKW W 14 × 61 EtvaF¶n;Cag W 12 × 58 . dUcenHeRbI W 12 × 58 CarUbragsakl,g³
Pu 150
= 0.3778 > 0.2
φc Pn 397

T.Chhay 226 Beam-Column

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dUcenHeRbI AISC Equatiom H-1-1a

KNnam:Um:g;Bt;eFobG½kS x
K x L 15(12 )
= = 34.09
rx 5.28
π 2 EAg π 2 (29000)(17.0)
Pe1 = = = 4187kips
(KL / r )2 (34.09)2
C m = 0.6 − 0.4(M 1 / M 2 ) = 0.6 − 0.4(0 / M 2 ) = 0.6 ¬sRmab;G½kSTaMgBIr¦
Cm 0 .6
B1 = = = 0.622 < 1.0
1 − (Pu / Pe1 ) 1 − (150 / 4187 )
dUcenHeRbI B1 = 1.0
M ux = B1M ntx = 1.0(75) = 75 ft − kips
bnÞab;mk kMNt; design strength. BI beam designth curves, sRmab; Cb = 1 nig Lb = 15 ft /
φb M n = 220 ft − kips . BIrUbTI 5>15g, Cb = 1.67 . sRmab; Cb = 1.67 design strength KW

Cb × 220 = 1.67(220) = 367 ft − kips

m:Um:g;enHFMCag φb M p = 233 ft − kips
dUcenHeRbI φb M n = 233 ft − kips
KNnam:Um:g;Bt;eFobG½kS y
K yL 15(12 )
= = 71.71
ry 2.51
π 2 EAg π 2 (29000)(17.0)
Pe1 = = = 946.2kips
(KL / r )2 (71.71)2
Cm 0.6
B1 = = = 0.713 < 1.0
1 − (Pu / Pe1 ) 1 − (150 / 946.2 )
dUcenHeRbI B1 = 1.0
M uy = B1M nty = 1.0(30 ) = 30 ft − kips

W 12 × 58CarUbrag compact sRmab;RKb;témørbs; Pu dUcenH nomical strength KW M py ≤ 1.5M yy .

Design strength KW

φb M ny = φb M py = φb Z y F y = 0.90(32.5)(36 ) = 1053in. − kips

= 87.75 ft − kips

Fñwm-ssr 227 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

b:uEnþ Z y / S y = 32.5 / 21.4 = 1.52 > 1.5 Edlmann½yfa φb M ny KYrEtykesμInwg

φb (1.5M yy ) = φb (1.5 F y S y ) = 0.90(1.5)(36 )(21.4 ) = 1040in. − kips = 86.67 ft − kips

BI AISC Equation H1-1a,

Pu 8 ⎛ M ux M uy ⎞
⎟ = 0.3778 + 8 ⎛⎜ 75 + 30 ⎞⎟
+ ⎜ +
φc Pn 9 ⎜⎝ φb M nx φb M ny ⎟
⎠ 9 ⎝ 233 86.67 ⎠
= 0.972 < 1.0 (OK)
cemøIy³ eRbI W 12 × 58 .

ebIeTaHbICaviFIEdleTIbnwgbgðajsRmab;eRCIserIsrUbragsakl,gqab;rkeXIjk¾eday k¾viFIEdl
manlkçN³smBaØCagenHRtUv)anesñIeLIgeday Yura (1988). bnÞúktamG½kSEdlsmmUlEdlRtUv)an
eRbIKW
2 M x 7.5M y
Pequiv = P +
d
+
b
¬^>%¦
Edl P = bnÞúktamG½kSemKuN
M x = m:Um:g;emKuNeFobG½kS x

M y = m:Um:g;emKuNeFobG½kS y

d = km<s;Fñwm

b = TTwgFñwm

tYTaMgGs;enAkñúgsmIkar ^>@ RtUvEtmanxñatRtUvKña.

]TahrN_ 6>9³ eRbI Yura’s method edIm,IeRCIserIsrUbragsakl,g W12 sRmab;Fñwm-

ssrén]TahrN_ 6>8.
dMeNaHRsay³ BIsmIkar 6>5 bnÞúktamG½kSsmmUlKW
2 M x 7.5M y 2(75 × 12 ) 7.5(30 × 12 )
Pequiv = P + + = 150 + + = 525kips
d b 12 12
EdlTTwg b RtUv)ansnμt;esμInwg 12inches . BI column load tables, sakl,g W 12 × 72
¬ φc Pn = 537kips ¦.
CamYynwg Yura’s method eKTTYl)anrUbragsakl,gFMCag Manual method Etvaminy:agdUcenH
T.Chhay 228 Beam-Column
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

rhUteT.

enAeBlEdltYm:Um:g;Bt;lub ¬]TahrN_ Ggát;manlkçN³CaFñwmCagssr¦ Yura ENnaMfa bnÞúk

tamG½kSRtUvbMElgeTACam:Um:g;Bt;smmUleFobG½kSG½kS x . bnÞab;mkrUbragsakl,gRtUv)aneRCIserIs
BI beam design charts in part 3 of the Manual. m:Um:g;smmUlKW³
d
M equiv = M x + P
2

karKNnamuxkat;Fñwm-ssrEdlminBRgwg Design of Unbraced Beam-Column

karKNnamuxkat;dMbUgrbs;Fñwm-ssrenAkñúg braced frame RtUv)anbgðajrYcehIy. emKuNm:U

m:g;bEnßm B1 RtUv)ansnμt;esμI 1.0 edIm,IeRCIserIsmuxkat;sakl,g bnÞab;mk B1 RtUv)ankMNt;sRmab;
rUbragenaH. sRmab;Fñwm-ssrRbQmnwg sidesway emKuNm:Um:g;bEnßm B2 EdlQrelIGBaØtiCaeRcIn
EdlminsÁal;rhUtdl;ssrTaMgGs;enAkñgú eRKagRtUv)aneRCIserIs. RbsinebI AISC Equation C1-4
RtUv)aneRbIsRmab; B2 enaHeKminman sidesway deflection Δ oh sRmab;karKNnamuxkat;dMbUgeT.
Rb sinebIeKeRbI AISC Equation C1-5 enaHeKGacminsÁal; ∑ Pe2 . viFIxageRkamRtUv)anesñIeLIg
edIm,Irk B2 .
viFITI1> snμt; B2 = 1.0 . bnÞab;BIeRCiserIsrUbragsakl,g KNna B2 BI AISC Equation C1-5 eday
snμt;fa ∑ Pu / ∑ Pe2 KWdUcKñanwg Pu / Pe2 sRmab;Ggát;EdlBicarNa
¬dUcenAkñúg]TahrN_6>7¦.
viFITI2> eRbIkarkMNt;dMbUg (predetermined limit) sRmab; drift index Δ oh / L EdlCapleeFob
story drift elIkm<s;Can;. kareRbInUv drift index GnuBaØatGtibrmasRmab; serviceability

requirement RsedogKñanwgkarkMNt;PaBdabrbs;Fñwm. eKENnaM[eRbI drift index cenøaHBI

1 / 500 eTA 1 / 200 . cMNaMfa Δ oh Ca drift EdlekItBI ∑ H dUcenHRbsinebI drift index

QrenAelI service load enaHbnÞúkxag H RtUvEtCa service load Edr.

]TahrN_ 6>10³ rUbTI 6>18 bgðajBI single-story unbraced frame EdlrgnUvbÞúkefr bnÞúkGefrelI
dMbUl nigxül;. rUbTI 6>18 a bgðajBI service gravity load nig rUbTI6>18 b bgðajBI service wind
Fñwm-ssr 229 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

load ¬EdlrYmbBa©ÚlTaMg uplift b¤ suction enAelIdMbUl¦. eRbIEdk A572 grade 50 nigeRCIserIs

rUbrag W 12 sRmab;ssr ¬Ggát;bBaÄr¦. KNnamuxkat;sRmab; drift index 1/ 400 edayQrelI
service wind load. m:Um:g;Bt;eFobnwgG½kSxøaMg ehIyssrnImYy²BRgwgxagenAxagcug nigKl;.

dMeNaHRsay³ eRKagenHCaeRKagsþaTicminkMNt;mYydWeRk. karviPaKrcnasm<½n§minkMNt;minRtUv)aneFVI

enATIenHeT. lT§plénkarviPaKeRKagRtUv)anbgðajenAkñúgrUbTI 6>19edaysegçb. bnÞúktamG½kS nig
m:Um:g;cugRtUv)an[dac;edayELkBIKñasRmab;bnÞúkefr bnÞúkGefr bnÞúkxül;EdlmanGMeBIelIdMbUl nig
bnÞúkxül;xag. bnÞúkbBaÄrTaMgGs;RtUv)andak;sIuemRTIKña ehIycUlrYmEtCamYynwgm:Um:g; M nt b:ueNÑaH.
bnÞúkxagbegáItm:Um:g; M lt .
bnSMbnÞúkEdlBak;B½n§CamYynwgbnÞúkefr D / bnÞúkGefrelIdMbUl Lr nigbnÞúkxül; W KWdUcxageRkam³
A4-2: 1.2 D + 0.5 Lr
Pu = 1.2(14 ) + 0.5(26) = 29.8kips

M nt = 1.2(50 ) + 0.5(94 ) = 107 ft − kips

M lt = 0
A4-3: 1.2 D + 1.6 Lr + 0.8W
Pu = 1.2(14 ) + 1.6(26 ) + 08(− 9 + 1) = 52.0kips

M nt = 1.2(50 ) + 1.6(94 ) + 0.8(− 32 ) = 184.8 ft − kips

M lt = 0.8(20 ) = 16.0 ft − kips

A4-4: 1.2 D + 0.5 Lr + 1.3W
Pu = 1.2(14 ) + 0.5(26 ) + 1.3(26 ) = 19.4kips

T.Chhay 230 Beam-Column

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

M nt = 1.2(50 ) + 0.5(94 ) + 1.3(− 32 ) = 65.4 ft − kips

M lt = 1.3(20 ) = 26 ft − kips
bnSMbnÞúk A4-3 pþl;nUvtémøFMCageK.

sRmab;eKalbMNgénkareRCIserIsrUbragsakl,g snμt;fa B1 = 1.0 . témørbs; B2 Gac

RtUv)anKNnaBI AISC Equation C1-4 nig design drift index³
1 1 1
B2 = = = = 1.107
1 − ∑ Pu (Δ oh / ∑ HL ) 1 − (∑ Pu / ∑ H )(Δ oh / L ) 1 − [2(52.0 ) / 2.7](1 / 400)
bnÞúkedkKμanemKuN ∑ H RtUv)aneRbIBIeRBaH drift index KWQrelI drift GtibrmaEdlbNþalmkBI
service load. dUcenH

M u = B1M nt + B2 M lt = 1.0(184.8) + 1.107(16 ) = 202.5 ft − kips

edayminsÁal;TMhMrbs;Ggát; eKminGaceRbI alignment chart sRmab;emKuNRbEvgRbsiT§PaB)aneT.
Table C-C2.1 enAkñúg Commentary to the Specification bgðajfakrNI (f) RtUvKñay:agxøaMgeTAnwg

lkçxNÐcugsRmab;krNI sidesway én]TahrN_enH ehIyEdl K x = 2.0 .

sRmab; braced condition, eKeRbI K x = 1.0 . edaysarEtGgát;TaMgGs;RtUv)anBRgwgTisedA
mYyeTotEdr enaHeKyk K y = 1.0 . bnÞab;mk eKGaceRCIserIsmuxkat;sakl,gEdlman[enAkñúg
Fñwm-ssr 231 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Part 3 of the Manual . BI Table 3-2 emKuNm:Um:g;Bt; m = 1.5 sRmab; W12 CamYynwg KL = 15 ft .
Pu eq = Pu + M ux m + M uy mu = 52.0 + 202.5(1.5) + 0 = 356kips

sRmab; KL = K y L = 15 ft / W 12 × 53 man design strength φc Pn = 451kips . sRmab;G½kS x

K x L 2.0(15)
= = 14.2 ft < 15 ft
rx / ry 2.11

dUcenH KL = 15 ft lub
sakl,g W 12 × 53 . sRmab; braced condtition
K x L 1.0(15)(15)
= = 34.42
rx 5.23
π 2 EAg π 2 (29000 )(15.6)
Pe1x = = = 3769
(K x L / rx )2 (34.42)2
⎛M ⎞ ⎛ 0 ⎞
C m = 0.6 − 0.4⎜⎜ 1 ⎟⎟ = 0.6 − 0.4⎜⎜ ⎟⎟ = 0.6
⎝ M2 ⎠ ⎝ M2 ⎠
BI AISC Equation C1-2
Cm 0 .6
B1 = = = 0.608 < 1.0
1 − (Pu / Pe1 ) 1 − (52.0 / 3769 )
dUcenHeRbI B1 = 1.0
cMNaMfa B1 = 1.0 Catémøsnμt;dMbUg ehIyedaysarEt B2 minRtUv)anpøas;bþÚr enaHtémø
M u = 202.5 ft − kips Edl)anKNnaBIdMbUgk¾minRtUv)anpøas;bþÚrEdr. BI beam design chart in Part

4 of the manual CamYynwg Lb = 15 ft design moment sRmab; W 12 × 53 CamYynwg Cb = 1.0 KW

φb M n = 262 ft − kips
sRmab;m:Um:g;Bt;EdlERbRbYlsmamaRtBIsUnüenAcugmçag eTAGtibrmaenAcugmçageTot
témørbs; Cb = 1.67 ¬emIlrUbTI 5>15 g¦. dUcenHtémøEdlEktRmUvén design moment KW
φb M n = 1.67(262) = 438 ft − kips
b:uEnþ m:Um:g;enHFMCag plastic moment capasity φb M p = 292 ft − kips / EdleKGacek)anenA
kñúg charts. dUcenH design strength RtUv)ankMNt;Rtwm
φb M n = φb M p = 292 ft − kips

kMNt;rUbmnþGnþrkmμEdlsmRsb

T.Chhay 232 Beam-Column

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Pu 52
= = 0.1153 < 0.2
φc Pn 451
dUcenHeRbI AISC Equation H1-1b:
Pu ⎛ M ux M uy ⎞ 0.1153 ⎛ 202.5 ⎞
+⎜ + ⎟= +⎜ + 0 ⎟ = 0.751 < 1.0 (OK)
2φc Pn ⎜⎝ φb M nx φb M ny ⎟
⎠ 2 ⎝ 292 ⎠

edaysarlT§plenHtUcCag 1.0 xøaMg dUcenHsakl,grUbragEdltUcCagenHBIrTMhM.

sakl,g W12 × 45 . sRmab; KL = K y L = 15 ft, φc Pn = 299kips . sRmab;G½kS x
K x L 2.0(15)
= = 11.3 ft < 15 ft
rx / ry 2.65

dUcenH KL = 15 ft lub
sRmab; braced condtition
K x L 1.0(15)(15)
= = 34.95
rx 5.15
π 2 EAg π 2 (29000 )(13.2 )
Pe1x = = = 3093
(K x L / rx )2 (34.95)2
BI AISC Equation C1-2,
Cm 0 .6
B1 = = = 0.610 < 1.0
1 − (Pu / Pe1 ) 1 − (52.0 / 3093)
dUcenHeRbI B1 = 1.0
BI beam design charts CamYynwg Lb = 15 ft m:Um:g;KNnasRmab; W12 × 45 CamYynwg
Cb = 1.0 KW

φb M n = 201 ft − kips
sRmab; Cb = 1.67
φb M n = 1.67(201) = 336 ft − kips > φb M p = 242.5 ft − kips

dUcenH design strength KW

φb M n = φb M p = 242.5 ft − kips

kMNt;rUbmnþGnþrkmμEdlsmRsb³
Pu 52.0
= = 0.1739 < 0.2
φc Pn 299

Fñwm-ssr 233 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

dUcenHeRbI AISC Equation H1-1b:

Pu ⎛ M ux M uy ⎞ 0.1739 ⎛ 202.5 ⎞
+⎜ + ⎟= +⎜ + 0 ⎟ = 0.922 < 1.0 (OK)
2φc Pn ⎜⎝ φb M nx φb M ny ⎟
⎠ 2 ⎝ 242.5 ⎠

cemøIy³ eRbI W12 × 45 .

enA]TahrN_6>10 karkMNt; drift index CaviFIkñúgkarKNna ehIyeKminmanviFINaedIm,I

KNnaemKuNm:Um:g;bEnßm B2 . RbsinebIeKminR)ab; drift index témørbs; B2 GacRtUv)ankMNt;ecj
BI AISC Equation C1-5 dUcxageRkam ¬edayeRbIlkçN³rbs; W 12 × 45 ¦³
K x L 2.0(15)(12 )
= = 69.90
rx 5.15
π 2 EAg π 2 (29000)(13.2)
Pe 2 x = = = 773.2kips
(K x L / rx )2 (69.90)2
1 1
B2 = = = 1.072
1 − (∑ Pu / ∑ Pe 2 ) 1 − [2(52.0) / 2(773.2 )]

6>9> Trusses With Top Chord Loads Between Joints

RbssinebIGgát;rgkarsgát;rbs; truss RtUvRTbnÞúkEdlmanGMeBIenAcenøaHcugsgçagrbs;va enaH
vanwgRtUvrgnUvm:Um:g;Bt; k¾dUcCabnÞúksgát;tamG½kS dUcenHGgát;enHCa beam-colum. krNIenHGacekIt
manenAelI top chord of the roof truss edayédrEngsßitenAcenøaHtMN. eKk¾RtUvKNna top chord of
an open-web steel joist Ca beam-column Edr BIeRBaH open-web steel joist RtUvRTbnÞúkTMnajEdl

BRgayesμIenAelI top chord rbs;va. edIm,IkarBarbnÞúkenH eKRtUveFVIm:UEdl truss CakarpSMeLIgeday

man continuous chord member nig pin-connected web members. bnÞab;mkeKGacedaHRsayrk
bnÞúktamG½kS nigm:Um:g;Bt;edayeRbIkarviPaKeRKOgbgÁúMdUcCag stiffness method. eK)anesñIeLIgnUvviFI
saRsþdUcxageRkam³
!> KitGgát;nImYy²rbs; top chord CaFñwmbgáb;cug. eRbIm:Um:g;bgáb;cugCam:Um:g;GtibrmaenAkñúg
Ggát;. Cak;Esþg top chord CaGgát;Cab; CagCaesrIénGgát;tMNsnøak; dUcenHkarcat;TukenH
manlkçN³suRkitCagkarEdlcat;TukGgát;nImYy²CaFñwmsmBaØ.
@> bEnßmkmøaMgRbtikmμBIFñwmbgáb;cugenHeTAbnÞúkenARtg;tMNedIm,ITTYl)anbnÞúkelItMNsrub.
T.Chhay 234 Beam-Column
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

#> viPaK truss CamYynwgbnÞúkRtg;tMNTaMgenH. bnÞúktamG½kSEdlCalT§plenAkñúg top chord

member CabnÞúksgát;tamG½kSEdlRtUvykeTAeRbIkñúgkarKNna.

viFIenHRtUv)anbgðajCalkçN³düaRkamenAkñúg rUbTI 6>20. müa:gvijeTot eKGacrkm:Um:g;Bt;

nigRbtikmμrbs;Fñwmedaycat;Tuk top chord CaFñwmCab;EdlmanTRmenARtg;tMNnImYy².

]TahrN_ 6>11³ rUbTI 6>21 bgðajBI parallel-chord roof trussEdl top chord RTédrENgenA
Rtg;tMN nigenARtg;cenøaHtMN. bnÞúkemKuNEdlbBa¢ÚnedayédrENgRtUv)anbgðaj. KNnamuxkat;
top chord. eRbIEdk A36 nigeRCIserIs structural tee Edlkat;ecjBI W-shape.

dMeNaHRsay³ m:Um:g;Bt; nigkmøaMgelItMNEdlbNþalmkBIbnÞúkEdlmanGMeBIenAcenøaHtMNRtUv)anrk

edaycat;Tuk top chord nImYy²CaFñwmbgáb;cug. BI Part 4 of the Manual, “Beam and girder
Design,”m:Um:g;bgáb;cugsRmab;Ggát; top chord nImYy²KW
PL 2.4(10 )
M = M nt = = = 3.0 ft − kips
8 8

Fñwm-ssr 235 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

m:Um:g;cug nigkmøaMgRbtikmμTaMgenHRtUv)anbgðajenAkñúg rUbTI 6>22 a. enAeBlEdleKbEnßmkmøaMg

RbtikmμeTAelIbnÞúkelItMN enaHeKTTYl)ankardak;bnÞúkdUcbgðajenAkñúgrUbTI 6>22 b. kmøaMgsgát;
GtibrmatamG½kSnwgekItmanenAkñúgGgát; DE ¬nwgenAkñúgGgát;EdlenAEk,r EdlenAxagsþaMG½kSrbs;
ElVg¦ nigGacRtUv)anrkedayBicarNalMnwgrbs;GgÁesrIrbs;Epñkrbs; truss EdlenAxageqVgmuxkat;
a-a³

∑ M I = (19.2 − 2.4 )(30 ) − 4.8(10 + 20 ) + FDE (4 ) = 0

FDE = −90kips ¬rgkarsgát;¦
KNnamuxkat;sRmab;bnÞúktamG½kS 90kips nigm:Um:g;Bt; 3.0 ft − kips
Table 3-2 in Part 3 of the Manual min)anpþl;[sRmab; structural tee. eKGaceRbI Yura’s

method (Yura, 1988) Edl)anbegáIteLIgsRmab;Ggát; I- nig H-shape. eKRtUvkarrUbragtUc BIeRBaH

bnÞúktamG½kStUc ehIym:Um:g;k¾tUcebIeFobnwgbnÞúktamG½kS. RbsinebIeKeRbI tee Edlmankm<s; 6in.

2 M x 7.5M y 2(3)(12)
Pequiv = P + + = 90 + + 0 = 102kips
d b 6
BI column load table CamYynwg K x L = 10 ft nig K y L = 5 ft / sakl,g WT 6 ×17.5
¬ φc Pn = 124kips ¦. m:Um:g;Bt;KWeFobnwgG½kS x ehIyGgát;RtUv)anBRgwgRbqaMgnwg sidesway³
/
M nt = 3.0 ft − kips M lt = 0

edaysarmankmøaMgxagmanGMeBIelIGgát; ehIycugRtUv)anTb;enaH Cm = 0.85 ¬Commentary

approach minRtUv)aneRbIenATIenHeT¦. KNna B1 ³
KL K x L 10(12 )
= = = 68.18
r rx 1.76

T.Chhay 236 Beam-Column

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

π 2 EAg π 2 (29000)(5.17 )
Pe1 = = = 318.3kips
(KL / r )2 (68.18)2
Cm 0.85
B1 = = = 1.185
1 − P1 / Pe1 1 − 90 / 318.3)
( ) (
m:Um:g;bEnßmKW
M u = B1M nt + B2 M lt = 1.185(3.0 ) + 0 = 3.555 ft − kips
RbsinebImuxkat;RtUv)ancat;fñak;Ca slender enaH nominal moment strength rbs; structural tee
nwgQrelI local buckling EtRbsinebImindUecñaHeT vanwgQrelI lateral-torsional buckling ¬emIl
AISC Equation F1.2c nig Epñk 5>14 kñúgesovePAenH¦. sRmab;søab
bf 6.560
λ= = = 6.308
2t f 2(0.520)
95 95
λr = = = 15.83 > λ
Fy 36

Fñwm-ssr 237 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

sRmab;RTnug
d 6.25
λ= = = 20.83
t w 0.300
127 127
λr = = = 21.17 > λ
Fy 26

edaysar λ < λr sRmab;TaMgsøab nigRTnug rUbragminEmnCa slender eT ehIy lateral-torsional

buckling lub. BI AISC Equation F1-15/
π EI y GJ ⎛ 2⎞
M n = M cr = ⎜ B + 1+ B ⎟ (AISC Equation F1-15)
Lb ⎝ ⎠
≤ 1 .5 M ysRmab;eCIg b¤tYxøÜnrgkarTaj
≤ 1.0 M y sRmab;eCIg b¤tYxøÜnrgkarsgát;

BI AISC Eqution F1-16,

⎡ 6.25 ⎤ 12.2
B = ±2.3(d / Lb ) I y / J = ±2.3⎢ ⎥ = ±1.378
⎣ 5(12 ) ⎦ 0.369
ehIy nominal strength BI AISC Equation F1-15 KW`
π 29000(12.2)(11200)(0.369) ⎛ 2⎞
Mn = ⎜ ± 1.378 + 1 + (1.378) ⎟
5(12 ) ⎝ ⎠
= 2002(± 1.378 + 1.703) = 6168in. − kips b¤ 650.5in. − kips

témøviC¢manrbs; B RtUvKñanwgkmøaMgTajenAkñúgtYxøÜnrbs; tee ehIysBaØaGviC¢manRtUv)aneRbIedIm,ITTYl

ersIusþg;enAeBltYxøÜnrgkmøaMgsgát;. sRmab;kardak;bnÞúkenAkñúg]TahrN_enH m:Um:g;GtibrmaekItman
enATaMgcugbgáb; nigkNþalElVg dUcenHersIusþg;RtUv)anRKb;RKgedaykmøaMgsgát;enAkñúgtYxøÜn ehIy
M n = 650.5in. − kips = 54.12 ft − kips
RbQmnwgtémøGtibrmaén
1.0(36 )(3.23)
1.0 M y = 1.0 Fy S x = = 9.690 ft − kips < 54.21 ft − kips
12
dUcenHeRbI M n = 9.690 ft − kips
φb M n = 0.90(9.690) = 8.721 ft − kips
kMNt;rkrUbmnþGnþrkmμEdlRtUveRbI
Pu 90
= = 0.7258 > 0.2
φc Pn 124

T.Chhay 238 Beam-Column

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dUcenHeRbI AISC Equation H1-1a:

Pu 8 ⎛ M ux M uy ⎞
⎟ = 0.7258 + 8 ⎛⎜ 3.555 + 0 ⎞⎟
+ ⎜ +
φc Pn 9 ⎜⎝ φb M nx φb M ny ⎟
⎠ 9 ⎝ 8.721 ⎠
= 1.09 > 1.0 (N.G)
enAkñúg]TahrN_enH m:Um:g;Bt;mantémøtUc ehIydUcKñasRmab; bending strength dUcenHehIyeFVI[tY
m:Um:g;Bt;rbs;rUbmnþGnþrkmμmantémøFM. kñúgkareRCIserIsmuxkat;EdlsmRsb GñkKNnaRtUvdwgc,as;
fa bending strength nig axial compressive strength mantémøFM. rUbragbnÞab;enAkñúg column load
tables KW WT 6 × 20 CamYynwg axial compressive strength 133kips . tamkarGegátenAelI

dimensions and peoperties tables bgðajfaeyIgkMBugbBa©ÚlRkumrUbragEdlmanG½kS x CaG½kS

exSay. dUcenHkarBt;rbs;eyIg\LÚvenHKWeFobnwgG½kSexSay ehIyvaKμansßanPaBkMNt; lateral-

torsional buckling. elIsBIenH RbsinebIrUbrag slender enaH nominal strength nwgQrelI yielding

ehIyesμInwg plastic moment capacity EdlRtUvnwgEdlx<s;bMputRtwm 1.5M y .

dUcenHsakl,g WT 6 × 20 ¬ φc Pn = 133kips ¦. dMbUg KNna B1 ³
KL K x L 10(12 )
= = = 76.43
r rx 1.57
π 2 EAg π 2 (29000)(5.89)
Pe1 = = = 288.6kips
(KL / r )2 (76.43)2
Cm 0.85
B1 = = = 1.235
1 − (P1 / Pe1 ) 1 − (90 / 288.6 )
m:Um:g;bEnßmKW
M u = B1M nt = 1.235(3.0) = 3.705 ft − kips
RtYtBinitü slenderness parameters. sRmab;søab
bf 8.005
λ= = = 7.772 < λr = 15.83
2t f 2(0.515)

sRmab;RTnug λ = td = 50..970
295
= 20.2 < λr = 21.17
w

edaysarkarBt;eFobnwgG½kSexSay
5.30(36 )
M n = M p = Z x Fy = = 15.9 ft − kips
12
RbQmnwgtémøGtibrmaén
Fñwm-ssr 239 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

1.5(36 )(2.95)
1.5M y = 1.5 Fy S x = = 13.28 ft − kips
12
edaysarEt M p > 1.5M y
φb M n = φb (1.5M y ) = 0.90(13.28) = 11.95 ft − kips

kMNt;rkrUbmnþGnþrkmμEdlRtUveRbI
Pu 90
= = 0.6767 > 0.2
φc Pn 133
dUcenHeRbI AISC Equation H1-1a:
Pu 8 ⎛ M ux M uy ⎞
⎟ = 0.6767 + 8 ⎛⎜ 3.705 + 0 ⎞⎟ = 0.952 < 1.0
+ ⎜ + (OK)
φc Pn 9 ⎜⎝ φb M nx φb M ny ⎟
⎠ 9 ⎝ 11.95 ⎠

cemøIy³ eRbI WT 6 × 20 .

T.Chhay 240 Beam-Column

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

VII. tMNsamBaØ
Simple Connections
7>1> esckþIepþIm (Introduction)

kartP¢ab;rbs;eRKOgbgÁúMEdkCaEpñkmYyEdlmansar³sMxan;bMput. kartP¢ab;Edlminman
lkçN³minRKb;RKan; EdleKGac[eQμaHfa “weak link” enAkñúgeRKOgbgÁúM GacbegáItnUvkar)ak;Ca
eRcInkrNI. kar)ak;rbs;Ggát;eRKOgbgÁúMKWkRmnwgekIteLIgNas; kar)ak;rbs;rcnasm<½n§PaKeRcInKW
bNþalmkBIkar KNnakartP¢ab; nigkarlMGitkartP¢ab;. bBaðaenHbNþalmkBIkarTTYlxusRtUvkñúg
karKNnakartP¢ab;. kñúgkrNIxøH kartP¢ab;minRtUv)anKNnaedayvisVkrEdlKNnaGgát;rbs;eRKOg
bgÁúMeT EtvaRtUv)anpþl;[edayplitkrEdlpÁt;pÁg;smÖar³sRmab;KMerageTAvij. b:uEnþvisVkreRKOgbgÁúM
Edlplitbøg;KNna CaGñkTTYlxusRtUvkñúgkarKNnaTaMgGs;rYmTaMgkartP¢ab;. kñúgkrNIEdltMN
RtUv)anKNnaedayvisVkrepSgeTot epSgBIvisVkrEdlKNnaGgát;eRKOgbgÁúM dUcenHeKRtUvkarvisVkr
EdlmanCMnajc,as;las;kñúgkarKNnakartP¢ab;.

eRKOgbgÁúMEdkTMenIbRtUv)antP¢ab;edaykarpSar nigedayb‘ULúg ¬ersIusþg;x<s; b¤Fmμta¦ b¤eday

bnSMénkartP¢ab;TaMgBIr. BIeBlmun kartP©ab;eFVIeLIgedaykarpSar b¤edayrIev. enAkñúgqñaM 1947
Research Council of Riveted and Bolted Structural Joints RtUv)anbegáIteLIg ehIy Specifi-

cation dMbUgrbs;vaRtUv)anecjpSayenAkñúgqñaM 1951. ÉksarenH)anGnuBaØat[CMnYs edayb‘ULúg

ersIusþg;x<s;sRmab;rIev. taMgBIeBlenaHmk b‘ULúgersIusþg;x<s;TTYl)anRbCaRbiyPaBy:agelOn ehIy

eKk¾gakmkeRbIb‘ULúgersIsþg;x<s;enAkñúgsMNg;sIuvilvij. eKmanmUlehtuCaeRcInkñúgkarpøas;bþÚrenH.
kmμkrBInak;EdlKμanCMnajGacdMeLIgb‘ULúgersIusþg;x<s;)an cMENkkardMeLIgrIevvij eKRtUvkarkmμkr
tMNsamBaØ 241 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

EdlmanCMnajdl;eTAbYnnak;. elIsBIenHeTot vapþl;nUvsemøg nigeRKaHfñak;tictYckñúgRbtibtþkarN_

tP¢ab;rIev edaysarkarpþl;kMedAkñúgkardMeLIgrIev. b:uEnþkartP¢ab;edayrIevk¾enAEtmanerobrab;enAkñúg
AISC Specfication nig Manual of steel construction edaysarEtsMNg;cas;²eRbItMNrIev dUcenH

karyl;dwgBIkarRbRBwtþeTArbs;vamansar³sMxan;Nas;sRmab;karvaytémøersIusþg; nigkarCYsCulnUv
sMNg;TaMgenaH. karKNna nigkarviPaKtMNrIevmanlkçN³RsedogKñanwgtMNb‘ULúgFmμtaEdr Etvaxus
KñaRtg;lkçN³smÖar³Etb:ueNÑaH.
tMNpSarmanGtßRbeyaCn_eRcInCagtMNb‘ULúg. kartP¢ab;edaykarpSarmanlkçN³samBaØ nig
RtUvkarrn§ticCagtMNb‘ULúg. kartP¢ab;EdlmanlkçN³sμúKsμajCamYynwgeRKOgP¢ab;GacmanlkçN³
gayRsYlCamYynwgkarpSar dUckrNIkñúgrUbTI 7>1. muneBlEdlkarpSarmanlkçN³eBjniym kar
dMeLIgrUbrag built-up RbePTenHRtUv)anplitedayrIev. edIm,IP¢ab;bnÞHEdksøabeTAnwgbnÞHEdkRTnug
EdkEkg (angle shape) RtUv)aneRbIedIm,IbMElgbnÞúkcenøaHFatuTaMgBIr. RbsinebIeKbEnßmbnÞHEdkBIelI
mYyeTot enaHplitplsMercnwgmanlkçN³kan;EtsμúKsμaj. b:uEnþkartP¢ab;edaykarpSarmanlkçN³
gayRsYlCag. b:uEnþsRmab;tMNpSar eKRtUvkarkmμkrCMnajxagpSar ehIyvaBi)akkñúgkarGegát nig
cMNayR)ak;eRcIn. EtKuNvibtþienHeKGacedaHRsay)anedaykarpSarenAkñúgeragCagCMnYs[kar
pSarenAkardæanenARKb;eBlEdlGaceFVIeTA)an. enAeBlEdlkartP¢ab;eFVIeLIgedaybnSMénkarpSar nig
b‘ULúg enaHeKeRcInpSarenAeragCag ehIycab;b‘ULúgenAkardæan. sRmab; single-plate beam-to-
column connectioction EdlbgðajenAkñúgrUbTI 7>2 bnÞHEdkRtUv)anpSarP¢ab;eTAnwgsøabrbs;ssrenA

eragCag ehIycab;b‘ULúgCamYynwgRTnugrbs;FñwmenAkardæan.

edIm,IBicarNaBIkarRbRBwtþeTAénRbePTepSg²rbs;tMN eKRtUvEbgEckvaeTAtamRbePTénkar
dak;bnÞúk. rUbTI 7>3 a bgðajBI tension member lap splice EdlmaneRKOgP¢ab;rgnUvkmøaMgkat;. dUc
Kña tMNpSarenAkñúgrUbTI 7>3 b RtUvTb;Tl;nwgkmøaMgkat;TTwg. tMNrbs; bracket eTAnwgsøabssr
T.Chhay 242 Simple Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dUckñúgrUbTI 7>3 c edaykarpSar b¤edayb‘ULúg eFIV[eRKOgP¢ab; b¤TwkbnSarrgnUvkmøaMgkat;enAeBl

EdlbnÞúkGnuvtþmkelIva. tMNBÜürEdlbgðajenAkñúgrUbTI 7>3 d dak;[eRKOgP¢ab;rgkmøaMgTaj.
kartP¢ab;EdlbgðajenAkñúgrUbTI 7>3 e begáItTaMgkmøaMgkat;TTwg nigkmøaMgTajenAkñúgeRKOgP¢ab;CYr
xagelI. ersIusþg;rbs;eRKOgP¢ab;KWGaRs½yelIfaetIvargnUvkmøaMgkat; b¤kmøaMgTaj b¤k¾kmøaMgTaMgBIr.
karpSarmankmøaMgexSaysRmab;kugRtaMgkmøaMgkat; ehIyCaTUeTAvaRtUv)ansnμt;fadac;edaykmøaMgkat;
edayminKitBITisedAénkardak;bnÞúk.

enAeBlEdlkmøaMgkñúgeRKOgP¢ab;mYy b¤kmøaMgkñúgmYyÉktþaRbEvgrbs;TwkbnSarRtUv)ankMNt;
vaCaerOgmYyEdlgayRsYlkñúgkarkMNt;PaBRKb;RKan;rbs;tMN. karkMNt;enHQrelIeKalkarN_én
tMNsamBaØ 243 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

kartP¢ab;cMbgBIr. RbsinebIExSskmμrbs;kmøaMgpÁÜbEdlRtUvTb;Tl;kat;tamTIRbCMuTm¶n;rbs;tMN enaH

EpñknImYy²rbs;tMNRtUv)ansnμt;faTb;Tl;nwgbnÞúkEdlEbgEckesμI ehIytMNEbbenHRtUv)aneK[
eQμaHfa tMNsamBaØ. enAkñúgtMNEbbenH ¬EdlbgðajenAkñúgrUbTI 7>3 a nig b¦ eRKOgP¢ab;nImYy²
nigRbEvgÉktþrbs;TwkbnSarnwgTb;Tl;nUvkmøaMgesμIKña*. bnÞab;mkeKGacrklT§PaBTb;Tl;bnÞúkrbs;
tMNedayKuNlT§PaBTb;Tl;kmøaMgrbs;eRKOgP¢ab;nImYy² b¤RbEvgÉktþarbs;TWkbnSar CamYynwgcMnYn
eRKOgP¢ab;srub b¤RbEvgsrubrbs;TwkbnSar. kartP¢ab;énkmøaMgcakp©it RtUv)anerobrab;enAkñúgCMBUkTI 8
EdlExSskmμrbs;bnÞúkmineFVIGMeBIkat;tamTIRbCMuTm¶n;rbs;tMN. kartP¢ab;enAkñúgrUbTI 7>3 d nig e Ca
RbePTéntMNenH. kñúgkrNIenHbnÞúkRtUv)anTb;Tl;esμIKñaedayeRKOgP¢ab;nImYy² b¤RbEvgÉktþarbs;Twk
bnSareT ehIykarkMNt;énkarEbgEckbnÞúkKWCaktþad¾sμúKsμajkñúgkarKNnaénRbePTtMNenH.
AISC Specification erobrab;BIkartP¢ab;EdlrYmman b‘ULúg rIev nig karpSarenAkñúg Chapter

J, ”Connections, Joints and Fasteners”. EtenAkñúgesovePAenH eyIgmin)anBicarNaBItMNrIeveT.

7>2> Bolted Shear Connections: Failure Mode

munnwgBicarNaBIersIusþg;Cak;lak;rbs;b‘ULúg eyIgRtUvBicarNaBIrebobénkardac;EdlGacekIt
manenAelItMNEdlmaneRKOgP¢ab;rgkmøaMgkat;TTwg. eKmanrebobénkardac;FMBIr³ kardac;rbs;eRKOg
P¢ab; nigkardac;rbs;EpñkEdlRtUvP¢ab;. BicarNa lap joint EdlbgðajenAkñúgrUbTI 7>4 a. kardac;rbs;
eRKOgP¢ab;GacRtUv)ansnμt;fanwgekIteLIgdUcEdl)anbgðaj. kmøaMgkat;TTwgmFümenAkñúgkrNIenHKW

*
Cak;EsþgvamancMNakp©ittUcenAkñúgtMNTaMgBIrenH EtvaRtUv)anecal
T.Chhay 244 Simple Connections
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P P
fv = =
A πd 2 / 4
Edl P CabnÞúkEdlmanGMeBIelIeRKOgP¢ab;nImYy² A CaRkLaépÞmuxkat;rbs;eRKOgP¢ab; nig d CaGgát;
p©itrbs;va. enaHbnÞúkenHGacsresrCa
P = fv A
eTaHbICakardak;bnÞúkkñúgkrNIenHmincMcMNucl¥k¾eday k¾cMNakp©itmantémøtUcEdlGacecal)an. kar
tenAkñúgrUbTI 7>4 b manlkçN³RsedogKña EtkarviPaKdüaRkamGgÁesrIrbs;eRKOgP¢ab;bgðajfamuxkat;
nImYy²rgEtBak;kNþalbnÞúksrub b¤eKGacniyayfamuxkat;TaMgBIrTb;Tl;nUvkmøaMgsrub. kñúgkrNIenH
kmøaMg P = 2 f v A ehIybnÞúkenHRtUv)aneKehAfa double shear. karbEnßmbnÞHenAkñúgkartnwgbegáIn
cMnYnbøg;kat; ehIyvanwgkat;bnßykmøaMgenAkúñgbøg;nmI Yy². b:uEnþ vanwgbegáInRbEvgrbs;eRKOgP¢ab; ehIy
vanwgrgkugRtaMgBt;.
rebobénkadac;mYyeTotsRmab; shear connection Bak;B½n§nwgkardac;rbs;EpñkEdlRtUv)an
P¢ab; ehIyCaTUeTAvaRtUv)anEbgEckCaBIrEpñk³
!> kardac;EdlbNþalBI karTaj kmøaMgkat; b¤m:Um:g;Bt;FMenAkñúgEpñkEdlRtUvtP¢ab;. RbsinebI
Ggát;rgkarTajRtUv)antP¢ab; kmøaMgTajelI gross area nig effective net area RtUv)anGegát.
GaRs½ynwgrUbragénkartP¢ab; block shear k¾RtUv)anBicarNa. eKk¾RtUvRtYtBinitü block shear enA
kñúgkartP¢ab; beam-to-column ¬Edlmanerobrab;enAkñúgCMBUkTI 3 nigTI5 ehIyvak¾RtUv)anerobrab;enA
kñúg AISC J4.3¦. GaRs½ynwgRbePTénkartP¢ab; nigkardak;bnÞúk ral;kartP¢ab;eTAnwg gusset plate
nig framing angle TamTarnUvkarviPaKsRmab; kugRtaMgkat; kugRtaMgTaj kugRtaMgBt; nig block shear.
karKNnakartP¢ab;rbs;Ggát;rgkarTajRtUv)aneFVIeLIgRsbKñaCamYynwgkarKNnaGgát;rgkarTajBI
eRBaHdMeNIrkarTaMgBIrenHTak;TgKñaeTAvijeTAmk.
@> kardac;rbs;EpñkEdlRtUvP¢ab;edaysar bearing EdlbegáIteLIgedayeRKOgP¢ab;. RbsinebI
RbehagmanTMhMFMCageRKOgP¢ab;bnþicbnþÜc ehIyeRKOgP¢ab;RtUv)ansnμt;faRtUv)andak;y:agENnenAkñúg
Rbehag épÞb:HrvageRKOgP¢ab; nigEpñkEdlRtUvP¢ab;nwgekItmaneRcInCagBak;kNþalénbrimaRtrbs;
eRKOgP¢ab;enAeBlEdlbnÞúkGnuvtþ. krNIenHRtUv)anbgðajenAkñúgrUbTI 7>5. kugRtaMgnwgERbRbYlBI
GtibrmaenARtg; A eTAsUnüenARtg; B . edIm,IgayRsYl eKeRbIkugRtaMgmFümEdlRtUv)anKNna
edayEckkmøaMgnwgépÞRbeyalb:H.
tMNsamBaØ 245 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

dUcenH bearing stees RtUv)anKNnaeday f p = P /(dt ) Edl P CakmøaMgEdlGnuvtþ

mkelIeRKOgP¢ab;/ d CaGgát;p©iteRKOgP¢ab; nig t CakRmas;rbs;EpñkEdlrgnUv bearing. dUcenH
bearing load KW

P = f p dt

karKNna bearing GacmanlkçN³sμúKsμajedaysarvtþmanrbs;b‘ULúgEdlenAEk,r b¤eday

sarcm¶ayBIrn§eTARCugEKmkñúgTisedArbs;bnÞúkmancm¶ayxøI dUcbgðajenAkñúgrUbTI 7>6. KMlatrvagb‘U
Lúg nigcm¶ayBIrn§eTARCugEKmman\T§iBlelI bearing strength.

7>3> Bearing Strength, Spacing and Edge-distance Requirements

Bearing strengthminTak;TgnwgRbePTrbs;eRKOgP¢ab;eT BIeRBaHkugRtaMgEdlRtUvBicarNasßit
enAelIEpñkEdlRtUvP¢ab; minEmnenAelIeRKOgP¢ab;eT. sRmab;mUlehtuenH bearing strength k¾dUcCag
T.Chhay 246 Simple Connections
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tRmUvkarKMlat nig edge-distance k¾minTak;TgnwgRbePTeRKOgP¢ab;Edr ehIyvaRtUv)anBicarNamunkug

RtaMgkat;kñúgb‘ULúg nigersIusþg;Taj.
karpþl;[rbs; AISC Specification sRmab; bearing strength k¾dUcCatRmUvkarepSg²sRmab;
b‘ULúgersIusþg;x<s; KWQrelIkarpþl;[rbs; specification of the Research Council on Structural
Connections of the Engineering Foundation (RCSC, 1994). kare)aHBum<pSayfμI²rbs;ÉksarenH

minTan;CaEpñkrbs; AISC Specification (AISC, 199a) EtvaRtUv)aneRbIenAkñúgesovePAenH drabNa

manlkçN³minRtUvKña eKnwgeRbIkarpþl;[eday AISC. enAeBlsmIkarenAkñúg RSCS Specification
RtUv)anbgðajelxsmIkarmkBIÉksarenaHnwgRtUv)aneRbI ¬]TahrN_/ RCSC Equation LRFD 4.3¦.
karerobrab;xageRkam EdlQrelI Commentary EdlENnaMeday RCSC Specification nwgBnül;BI
eKalkrN_rbs;smIkar RCSC sRmab; bearing strength.
rebobdac;EdlGacekItmanEdl)anBI bearing FM KWkmøaMgkat;rEhk (shear tear-out) enAxag
cugrbs;FatuEdlRtUvtP¢ab; dUcbgðajenAkñúgrUbTI 7>7 a. RbsinebIépÞdac;manlkçN³l¥dUcrUbTI 7>7 b,
failure load enAelIépÞmYyénépÞTaMgBIresμInwg shear fracture stress KuNnwgRkLaépÞkat; b¤
Rn
= 0.6 Fu Lc t
2
Edl rbs;EpñkEdlRtUvP¢ab;
0.6 Fu = shear fracture strees

Lc = cm¶ayBIRCugEKRmbs;RbehageTAcugrbs;EpñkEdlRtUvP¢ab;

t = kRmas;rbs;EpñkEdlRtUvP¢ab;

ersIusþg;srubKW
Rn = 2(0.6 Fu Lc t ) = 1.2 Fu Lc t ¬&>!¦
kmøaMgkat; tear-out enHekItmanenAxagcugrbs;EpñkEdlRtUvtP¢ab; dUcEdlbgðaj b¤enAcenøaH
rn§BIrkñúgTisedAén bearing load. edIm,IkarBarsac;lUtFMrbs;Rbehag eKRtUvkMNt;EdnkMNt;x<s;bMput
rbs; bearing load Edl[edaysmIkar &>!. EdkkMNt;enHsmamaRteTAnwg fracture stress KuNnwg
bearing area b¤

Rn = C × Fu × bearing area = CFu dt ¬&>@¦

Edl C = témøefr
d = Ggát;p©itb‘ULúg

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mhaviTüal½ysMNg;sIuvil NPIC

t= Ggát;rbs;EpñkEdlRtUvtP¢ab;

RCSC Specification eRbIsmIkar &>! sRmab; bearing strength RbQmnwgEdnkMNt;Edl[eday

smIkar &>@. RbsinebIeKminKitkMhUcRTg;RTay témøefr C GacykesμInwg 3.0 . RbsinebIkMhUcRTg;
RTayFMRtUv)anKit C GacykesμInwg 2.4 ehIyCaTUeTAvaCatémøEdleKykmkeRbI. témøenHRtUvKñanwg
sac;lUtrbs;RbehagRbEhl 1 / 4in. = 6mm ¬RCSC, 1994¦. enAkñúgesovePAenH eyIgBicarNa
kMhUcRTg;RTaysRmab;karKNna. RCSC bearing strength sRmab;b‘ULúgeTalGacRtUv)ansMEdgCa
φRn Edl

φ = 0.75
nig Rn = 1.2 Lc tFu ≤ 2.4dtFu ¬RCSC Equation LRFD 4.3¦
Edl Lc = clear distance enAkñúgTisRsbnwgbnÞúkEdlGnuvtþ BIcg u énrn§b‘ULúgeTARCugEKmrbs;rn§Edl
enAEk,r b¤eTARCugEKmrbs;smÖar³.
t = kRmas;rbs;eRKOgP¢ab;

d = Ggát;p©itb‘ULúg ¬minEmnGgát;p©itrbs;RbehageT¦

Fu = ultimate tensile stress rbs;EpñkEdlRtUvP¢ab; ¬minEmnrbs;b‘ULúg¦

rUbTI 7>8 bgðajbEnßmeTotBIcm¶ay Lc . enAeBlEdlKNna bearing strength sRmab;b‘ULúg eKRtUv

BicarNacm¶ayBIb‘ULúgenaHeTAb‘ULúgEdlenAEk,r b¤eTARCugEKmkñúgTisedArbs; bearing load elIEpñk
T.Chhay 248 Simple Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

EdlRtUvP¢ab;. sRmab;krNIEdl)anbgðaj bearing load sßitenAEpñkxageqVgrbs;rn§nImYy². dUcenH

ersIusþg;sRmab;b‘ULúg ! RtUv)anKNnaCamYy Lc Edlvas;eTAb‘ULúg @ ehIyersIusþg;sRmab;b‘ULúg @
RtUv)anKNnaCamYy Lc Edlvas;eTARCugEKmrbs;EpñkEdlRtUvP¢ab;.

RCSC Equation LRFD 4.3 mantémøsRmab; standard, oversized, short-slotted and long
slotted holes CamYynwg slot EdlRsbeTAnwgbnÞúk. eyIgeRbIEt standard holes enAkñúgesovePAenH

¬RbehagEdlmanGgát;p©itFMCagGgát;p©itb‘ULúg 1/16in. = 2mm ¦.

enAeBlEdlKNnacm¶ay Lc eRbIGgát;p©itRbehagCak;Esþg nigmincaM)ac;bUkbEnßm 2mm dUc
EdlRtUvkarenAkñúg AISC B.2 sRmab;KNna net area rbs;Ggát;rgkarTaj. müa:gvijeTot eRbIGgát;
p©it d + 1 / 16in. = d + 2mm minEmn d + 1 / 8in. = d + 4mm . RbsinebI h bgðajBIGgát;p©itRbehag
enaH
h = d + 1 / 16in.
karKNnarbs; bearing strength BI RCSC Equation LRFD 4.3 GacRtUv)ansRmYlxøHdUcxageRkam.
EdnkMNt;nwgmanRbsiT§PaBenAeBl
1.2 Lc tFu = 2.4dtFu
b¤ eRkayeBlEdlsRmYlehIy
Lc = 2d
TMnak;TMngenHGacRtUv)aneRbIedIm,IKNnaenAeBlEdlEdnkMNt; 2.4dtFu lub³
RbsinebI Lc ≤ 2d eRbI Rn = 1.2Fu Lct
RbsinebI Lc > 2d eRbI Rn = 1.2Fu dt

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mhaviTüal½ysMNg;sIuvil NPIC

Spacing and Edge-Distance Requirments

edIm,IrkSacenøaHTMenrrvagex©Ab‘ULúg nigedIm,Ipþl;nUvTIFøaRKb;RKan;sRmab; wrench socket AISC
J3.3 tRmUvfaKMlatBIG½kSeTAG½kS (center-to-center spacing) rbs;eRKOgP¢ab; ¬enARKb;Tis¦ minRtUv

tUcCag 2 2 3 d ehIyCakarniymKWminRtUvtUcCag 3d Edl d CaGgát;p©iteRKOgP¢ab;. cm¶ayBIRCugEKm

smÖar³ ¬RKb;Tis¦ Edlvas;BIG½kSrbs;Rbehag RtUv)an[enAkñúg AISC Table3.4 CaGnuKmn_eTA
nwgTMhMrbs;b‘ULúg nigRbePTrbs;RCug ¬sheared, rolled or gas cut¦. KMlat nigcm¶ayeTARCugEKm
EdlsMKal;eday s nig Le RtUv)anbgðajenAkñúgrUbTI 7>9.

Summary fo Bearing Strength, Spacing and Edge-Distance Requirements

(standard hole)
a. Bearing strength:
φRn = 0.75(1.2 Lc tFu ) ≤ 0.75(2.4dtFu ) (RCSC Equation LRFD 4.3)
b¤ eyIgGacsresrmüa:geTot
RbsinebI Lc ≤ 2d / φRn = 0.75(1.2 Lc tFu )

RbsinebI Lc > 2d / φRn = 0.75(2.4dtFu )

b. KMlat nigsMgayeTARCugEKmGb,brma³ sRmab;RKb;Tis TaMgRsbnwgExSskmμ nigEkgnwgExS

skmμ
s ≥ 2 23 d ¬CakareBjniym 3d ¦
Le ≥ témøBI AISC J3.4

sRmab; single- nig double-angle shapes CaTUeTA gage distances RtUv)an[enAkñúg Part 9 of
the Manual, Volume II (emIlEpñk 3>6)EdlGaceRbICMnYs[témøGb,brma.

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]TahrN_ 7>1³ RtYtBinitü KMlatb‘ULúg nigcm¶ayeTARCugEKmsRmab;kartP¢ab;EdlbgðajenAkñúgrUbTI

7>10.

dMeNaHRsay³ BI AISC J3.3, KMlatGb,brmasRmab;RKb;TisTaMgGs;KW

⎛3⎞
2 2 3 d = 2.667⎜ ⎟ = 2in.
⎝4⎠
KMlatCak;Esþg = 2.5in. > 2in. (OK)
cm¶ayeTARCugEKmGb,brmasRmab;RKb;TisTaMgGs;EdlTTYlBI AISC Table J3.4. RbsinebI
eyIgsnμt; sheared edges ¬krNIEdlGaRkk;CageK¦ enaHcm¶ayeTARCugEKmGb,brmaKW 1 1 4 in.
dUcenH
cm¶ayeTARCugEKmCak;Esþg = 1 14 in. (OK)
edIm,IKNna bearing strength eRbIGgát;p©itrn§
1 3 1 13
h=d+ = + = in.
16 4 16 16
RtYtBinitü bearing TaMgelIGgát;rgkarTaj nig gusset plate. sRmab;Ggát;rgkarTaj nigEdl
enAEk,rRCugEKmrbs;Ggát;CageK
h 13 / 16
Lc = Le − = 1.25 − = 0.8438in.
2 2
φRn = φ (1.2 Lc tFu ) ≥ φ (2.4dtFu )
⎛1⎞
φ (1.2 Lc tFu )0.75(1.2)(0.8438)⎜ ⎟(58) = 22.02kips
⎝2⎠
⎛ 3 ⎞⎛ 1 ⎞
φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟⎜ ⎟(58) = 39.15kips > 22.02kips
⎝ 4 ⎠⎝ 2 ⎠
dUcenHyk φRn = 22.02kips / bolt
sRmab;rn§epSgeTot
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mhaviTüal½ysMNg;sIuvil NPIC

13
Lc = s − h = 2.5 − = 1.688in.
16
φRn = φ (1.2 Lc tFu ) ≤ φ (2.4dtFu )
⎛1⎞
φ (1.2 Lc tFu ) = 0.75(1.2)(1.688)⎜ ⎟(58) = 44.06kips
⎝2⎠
φ (2.4dtFu ) = 39.15kips < 44.06kips
dUcenHyk φRn = 39.15kips / bolt
sRmab;Ggát;rgkarTaj bearing strength KW
φRn = 2(22.02) + 2(39.15) = 122kips > 65kips (OK)
sRmab; gusset plat nigrn§EdlenAEk,rRCugEKmrbs;bnÞHCageK
h 13 / 16
Lc = Le − = 1.25 − = 0.8438in.
2 2
φRn = φ (1.2 Lc tFu ) ≤ φ (2.4dtFu )
⎛3⎞
φ (1.2 Lc tFu ) = 0.75(1.2)(0.8438)⎜ ⎟(58) = 16.52kips
⎝8⎠
⎛ 3 ⎞⎛ 3 ⎞
φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟⎜ ⎟(58)
⎝ 4 ⎠⎝ 8 ⎠
= 29.36kips > 16.52kips
dUcenHyk φRn = 16.52kips / bolt
sRmab;rn§déTeTot
13
Lc = s − h = 2.5 − = 1.688in.
16
φRn = φ (1.2 Lc tFu ) ≤ φ (2.4dtFu )
⎛3⎞
φ (1.2 Lc tFu ) = 0.75(1.2)(1.688)⎜ ⎟(58) = 33.04kips
⎝8⎠
⎛ 3 ⎞⎛ 3 ⎞
φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟⎜ ⎟(58) = 29.36kips < 33.04kips
⎝ 4 ⎠⎝ 8 ⎠
dUcenHyk φRn = 33.04kips
bearing strength sRmab; gusset plate KW

φRn = 2(16.52) + 2(29.36) = 91.8kips

gusset plate man bearing strength tUcCag bearing strength rbs;Ggát; dUcenH gusset plate lub
φRn = 91.8kips > 65kips (OK)

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cemøIy³ tRmUvkar bearing strength, KMlat nig cm¶ayeTARCugEKmmanlkçN³RKb;RKan;.

KMlatb‘ULúg nigcm¶ayeTARCugEKmenAkñúg]TahrN_ 7>1 mantémødUcKñasRmab;Ggát;rgkarTaj

nig gusset plate. vaxusKñaEtkRmas; dUcenH gusset plate lub. sRmab;krNIdUc]TahrN_enH eKRtYt
BinitüEteRKOgbgÁúMNaEdlmankRmas;esþIgCag. b:uEnþRbsinebIcm¶ayeTAcugEKmmantémøxusKña dac;xat
eKRtUvEtRtYtBinitüTaMgGgát;rgkarTaj nig gusset plate.

7>4> b‘ULúgFmμta (Common Bolts)

eyIgcab;epþImkarerobrab;BIersIusþg;rbs;eRKOgP¢ab;CamYynwg b‘ULúgFmμta EdlxusKñaBIb‘ULúger-
sIusþg;x<s;minRtwmEtlkçN³smÖar³b:ueNÑaHeT EfmTaMgkmøaMgrwtbNþwgb‘ULúgeTotpg. b‘ULúgFmμta Edl
eKsÁal;Ca unfinished bols RtUv)ansMKal;Ca ASTM A307.
Design shear strength rbs; A307 KW φRn / EdlemKuNersIusþg; φ = 0.75 ehIy nominal

shear strength KW

Rn = Fv Ab
Edl Fv = ultimate shearing stress

Ab = RkLaépÞmuxkat;rbs;EpñkEdlKμaneFμjrbs;b‘ULúg ¬EdleKsÁal;Ca nominal bolt area

b¤ nominal body area¦
Ultimate shearing stress RtUv)an[enAkñúg AISC Table J3.2 KW 24ksi = 165MPa Edl

[ nominal strength
Rn = Fv Ab = 24 Ab

]TahrN_ 7>2³ kMNt; design strength rbs;kartP¢ab;EdlbgðajenAkñúgrUbTI 7>11 edayQrelI

kmøaMgkat;TTwg nig bearing.
dMeNaHRsay³ kartP¢ab;GacRtUv)ancat;cMNat;fñak;CatMNsamBaØ ehIyeRKOgP¢ab;mYy²RtUv)anBicar-
NaedIm,ITb;Tl;karEbgEckkmøaMgesμIKña. kñúgkrNICaeRcInvamanlkçN³gayRsYlkñúgkarkMNt;ersIusþg;
rbs;eRKOgP¢ab;mYy rYcbnÞab;mkKuNnwgcMnYneRKOgP¢ab;srub.
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Shear strength: vaCakrNI single shear ehIy design shear strength rbs;b‘ULúgmYyKW
φRn = φFv Ab = 0.75(24 Ab )
Nominal bolt area KW
πd 2 π (3 / 4)2
Ab = = = 0.4418in 2
4 4
dUcenH design shear strength sRmab;b‘ULúgmYyKW
φRn = 0.75(24 )(0.4418) = 7.952kips
sRmab;b‘ULúgBIrKW
φRn = 2(7.952) = 15.9kips
Bearing strength: edaysarcm¶ayeTARCugEKRmbs;Ggát;rgkarTaj nigrbs; gusset plate dUcKña enaH
beaing strength rbs; gusset plate nwglub BIeRBaHkRmas;rbs;vaesþIgCagkRmas;rbs;Ggát;rgkarTaj.

sRmab;karKNna bearing strength eRbIGgát;p©itRbehag

1 3 1 13
h=d+ = + = in.
16 4 16 16
sRmab;rn§EdlenAEk,rRCugEKRmbs; gusset plate CageK
h 13 / 16
Lc = Le − = 1.5 − = 1.094in.
2 2
⎛3⎞
2d = 2⎜ ⎟ = 1.5in.
⎝4⎠
edaysar Lc < 2d
⎛3⎞
φRn = φ (1.2 Lc tFu ) = 0.75(1.2)(1.094)⎜ ⎟(58) = 21.42kips
⎝8⎠
sRmab;rn§déTeTot
13
Lc = s − h = 3 − = 2.188in. > 2in.
16

T.Chhay 254 Simple Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dUcenH φRn = φ (2.4dtFu ) = 0.75(2.4)⎛⎜⎝ 34 ⎞⎟⎠⎛⎜⎝ 83 ⎞⎟⎠(58) = 29.36kips

Bearing strength sRmab;tMNKW

φRn = 21.42 + 29.36 = 50.8kips

Bearing strength enHFMCag shearing strength dUcenH shear strength lub ehIyersIusþg;rbs;tMNKW
φRn = 15.9kips
cMNaMfaRKb;tRmUvkarKMlat nigcm¶ayeTARCugEKmTaMgGs;RtUvEtRKb;RKan;. sRmab; sheared edge
cm¶ayeTARCugEKmEdlTamTareday AISC Table J3.4 KW 1 1 4 in. = 30mm ehIykarTamTarenHKW
RKb;RKan;sRmab;TaMgTisbeNþay nigTisTTwg. KMlatb‘ULúgKW 3in = 75mm EdlFMCag 2 d = 2
3

2.667( 3
4 ) = 2in. .
cemøIy³ edayQrelI shear nig bearing, design strength rbs;tMNKW 15.9kips . ¬cMNaMfa sßanPaB
kMNat;déTepSgeTotEdlminTan;)anRtYtBinitüdUcCa kugRtaMgTajenAelI net area rbs;Ggát;Gacnwg
CaGñkkMNt; design strength¦.

]TahrN_ 7>3³ r)arEdk 4 × 3 / 8in. RtUv)aneRbICaGgát;rgkarTajedIm,ITb;Tl;nwg service dead load

8kips nig service live load 22kips . Ggát;enHRtUv)anKNnaeRkamkarsnμt;fa b‘ULúg A307 Ggát;
p©it 3 / 4in. mYyCYrRtUv)aneRbIedIm,IP¢ab;Ggát;enHeTA gusset plate EdlmankRmas; 3 / 8in. . TaMgGgát;
rgkarTaj nig gusset plate CaEdk A36 . etIeKRtUvkarb‘ULúgb:unμanRKab;?
dMeNaHRsay³ bnÞúkemKuNKW
Pu = 1.2 D + 1.6 L = 1.2(8) + 1.6(22) = 44.80kips
KNnalT§PaBrbs;b‘ULúgmYy. BI]TahrN_ 7>2 shear strength KW
φRn = 7.952kips / bolt
sRmab; eKminsÁal;KMlat nigcm¶ayeTARCugEKm dUcenHeyIgsnμt;fa EdnkMNt;
bearing strength,

φ 2.4dtFu nwglub enaHeyIgTTYl)an

⎛ 3 ⎞⎛ 3 ⎞
φRn = 0.75(2.4)⎜ ⎟⎜ ⎟(58) = 29.36kips / bolt
⎝ 4 ⎠⎝ 8 ⎠

tMNsamBaØ 255 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Bearing strength Cak;EsþgsRmab;tMNenHnwgGaRs½yelItémørbs; Lc sRmab;b‘ULúgnImYy². enA

eBl EdltémøenHRtUv)ankMNt;enAkñúgkarKNnacugeRkay enaH bearing strength RtUv)anRtYtBinitü
eLIgvijb:uEnþ shear enAEtTMngCalub.
cMnYnb‘ULúgEdlRtUvkarKW
44.80kips
= 5.63bolts
7.952kips / bolt
cemøIy³ eRbIb‘ULúg A307 Ggát;p©it 3 / 4in. cMnYnR)aMmYyRKab;.

7>5> b‘ULúgersIusþg;x<s; (High-Strength Bolts)

b‘ULúgersIusþg;x<s;sRmab;tMNrbs;eRKOgbgÁúMmanBIry:agKW ASTM A325 nig ASTM A490 .
karpþl;[rbs; AISC sRmab;ersIusþg;x<s;KWCaEpñkxøHrbs;karpþl;[rbs; specification of the
Research Council on Structural Connections of the Engineering Foundation (RCSC, 1994).

b‘ULúg A490 man ultimate tensile strength FMCagb‘ULúg A325 ehIyRtUv)ankMNt;faman

nominal strength FMCag. b‘ULúg A490 RtUv)andak;[eRbIR)as;ry³eBly:agyUrbnÞab;BIb‘ULúg

A325 RtUv)aneRbICaTUeTA sRmab;eRbICamYyEdkEdlmanersIusþg;x<s; ¬Bethlehem, 1969¦. b‘ULúg

A490 mantémøéføCag A325 b:uEnþCaTUeTAeKRtUvkarvacMnYnticCag.

kñúgkrNIxøH b‘ULúg A490 nig A325 RtUv)andMeLIgCamYynwgkRmittwgEdleFVI[BYkvargnUv

kmøaMgTajFMEmnETn. ]TahrN_ kmøaMgTajdMbUgenAkñúgb‘ULúg A325 Ggát;p©it 5 / 8in. GacFMesμInwg
19kips = 85KN . bBa¢IénkmøaMgTajGb,brmasRmab;tN M TaMgenaHRtUvkarRtUv)an[enAkñúg AISC
Table J3.1, Minimum Bolt Tension. témønImYy²esμInwg 70% énersIusþg;TajGb,brmarbs;b‘ULúg.

eKalbMNgEdleKRtUvkarkmøaMgTajFMEbbenHKWedIm,ITTYl)ankmøaMgrwtEdlbgðajenAkñúgrUbTI 7>12.
b‘ULúgEbbenHRtUv)aneKehAfa fully tensioned.
enAeBlEdlex©ARtUv)anmYlP¢ab;eTAnwgb‘ULúg EpñkEdlRtUvP¢ab;rgnUvkmøaMgsgát; ehIyb‘ULúglUt.
düaRkaGgÁesrI (free body diagram) enAkñúgrUbTI 7>12 a bgðajfakmøaMgsgát;srubEdlmanGMeBIelI
EpñkEdlRtUvP¢ab;esμInwgkmøaMgTajenAkñúgb‘ULúg. RbsinebIeKGnuvtþkmøaMgxageRkA P kmøaMgkkitnwg
ekItmanenAcenøaHEpñkP¢ab;. kmøaMgGtibrmaEdlGacekItmanKW
F = μN

T.Chhay 256 Simple Connections

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Edl μ CaemKuNkkitsþaTicrvagEpñkEdlRtUvP¢ab; ehIy N CakmøaMgsgát;EdlmanGMeBIenAelIépÞxag

kñúg. témørbs; μ GaRs½ynwglkçxNÐépÞrbs;Edk ]TahrN_dUcCa épÞrbs;vamanlabfñaM b¤manERcHsIu.
dUcenHb‘ULúgnImYy²enAkñúgkartP¢ab;RtUvmanlT§PBedIm,ITb;Tl;nwgbnÞúk P = F . RbsinebIkmøaMgkkit
minFM vanwgminman bearing b¤ shear. RbsinebI P FMCag F slip ekIteLIg enaH shear nig bearing nwg
CH\T§iBldl;lT§PaBrbs;tMN.

kardMeLIg (Installation)
etIeKTTYl)ankmøaMgTajFMEdlmanPaBsuRkitedayrebobNa? bc©úb,nñeKmanviFIsaRsþEdl
GnuBaØat[cMnYnbYnsRmab;kardMeLIgb‘ULúgersIusþg;x<s; (RCSC, 1994).
!> Turn-of-the-nut method. viFIenHQrelIlkçN³bnÞúk-kMhUcRTg;RTay (load-deforma-
tion characteristic) rbs;eRKOgP¢ab; nigEpñkEdlRtUvP¢ab;. ex©AEdlmYlP¢ab;eTAnwgb‘ULúgGaceFVI[

b‘ULúg lUtsac;. TMnak;TMng stress-strain sRmab;smÖar³b‘ULúgGacRtUv)aneRbIedIm,IKNnakmøaMgTaj

tMNsamBaØ 257 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

enAkñúgb‘ULúg. dUcenHsRmab;RKb;TMhM nigRbePTrbs;b‘ULúg cMnYnCMumYlex©AEdlRtUvkaredIm,IbegáItkmøaMg

TajGacRtUv)anKNna. Table 5 enAkñúg high-strength bolt specification (RCSC, 1994) [nUvcMnYn
CMurbs;ex©AEdlRtUvkarsRmab;TMhMepSg²rbs;b‘ULúgkñúgTMrg;pleFobRbEvgelIGgát;p©it. viFIsaRsþenHeK
eRbI ordinary spud wrench.
@> Calibrated wrench tightening. kñúgviFIsa®sþenHeKRtUveRbI torque wrench. kmøaMgrmYl
EdlRtUvkaredIm,ITTYlkmøaMgTajkMNt;enAkñúgb‘ULúgRtUv)ankMNt;edaykarrwtbNþwgb‘ULúgenHCamYy]b
krN_EdlbgðajkmøaMgTaj.
#> Alternated wrench bolts. eKRtUvkar wrench BiessedIm,IdMeLIgb‘ULúg. karRtYtBinitükar
gardMeLIgenHmanlkçN³gayRsYlCaBiess.
$> Direct tension indicators. smÖar³EdleKniymeRbIenAkñúgviFIsaRsþenHKW washer Edlman
protrusion enAelIépÞrbs;va. enAeBlEdleKrwtb‘ULúg protrusion rgnUvkmøaMgsgát;EdlsmamaRteTA

nwgkmøaMgTajenAkñúgb‘ULúg.

7>6> Shear Strength of High-Strength Bolts

Design shear strength rbs;b‘ULúg A325 nig A490 KW φRn EdlemKuNersIusþg; φ = 0.75 . dUc
Kñanwgb‘ULúgFmμtaEdr nominal shear strength rbs;b‘ULúgersIusþg;x<s;RtUv)an[eday ultimate
shearing stress KuNnwg nominal bolt area. Etb‘ULúg A307 mindUcb‘ULúg A325 nig A490 Rtg; shear

strength rbs;b‘ULúgersIusþg;x<s;GaRs½ynwgeFμjrbs;b‘ULúgsßitenAkñúgbøg;kat;b¤ minsßitenAkñúgbøg;kat;.

edIm,IsRmYlkñúgkareRbI reduced cross-sectional area enAeBlEdlEpñkEdlmaneFμjrgnUvkmøaMgkat;

TTwg enaH ultimate shearing stress rbs;vaRtUvKuNnwg 0.75 EdlCapleFobRbhak;RbEhlénRkLa
épÞEdlmaneFμj elIRkLaépÞEdlKμaneFμj. ersIusþg;RtUv)an[enAkñúg AISC Table J3.2 ehIyRtUv)an
segçbenAkñúgtarag 7>1 . AISC Table J3.2 sMedAeFμjenAkñúgbøg;kat;Ca “not excluded from shear
planes” ehIysMedAeFμjEdlminenAkñúgbøg;kat;Ca “excluded from shear planes”. RbePTTImYy

eFμjsßitenAkñúgbøg;kat; eKsMedACaRbePTtMN “N” ehIyb‘ULúg A325 énRbePTenHGacsmÁal; eday

A325 − N . karsMKal; “X” GacRtUv)aneRbIedIm,IbgðajfaeFμjminsßitenAkñúgbøg;kat;eT ]TahrN_

A325 − X .

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tarag 7>1
Nominal shear strength
eRKOgP©ab; Rn = Fv Ab
US IS
A325 / eFμjenAkñúgbøg;kat; 48 Ab 330 Ab

A325 / eFμjminenAkñúgbøg;kat; 60 Ab 415 Ab

A490 / eFμjenAkñúgbøg;kat; 60 Ab 415 Ab

A490 / eFμjminenAkñúgbøg;kat; 75 Ab 520 Ab

]TahrN_7>4³ kMNt; design strength rbs;tMNEdlbgðajenAkñúgrUbTI 7>13. GegÁt bolt shear,

bearing nig tensile strength rbs;Ggát;. b‘ULúgEdleRbICaRbePT A325 Ggát;p©it 7 / 8in. ehIyeFμj
rbs;vaminsßitenAkñúgbøg;kat;. Ggát;CaRbePTEdk A572 Grade 50 .

dMeNaHRsay³ shear strength sRmab;b‘ULúgmYy

π (7 / 8)2
Ab = = 0.6013in.2
4
φRn = φFv Ab = 0.75(60)(0.6013) = 27.06kips
sRmab;b‘ULúgbI
φRn = 3(27.06) = 81.2kips
Bearing strength ³ sRmab;karKNna bearing strength eRbIGgát;p©itrn§

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mhaviTüal½ysMNg;sIuvil NPIC

1 7 1 15
h=d+ = + = in.
16 8 16 16
RtYtBinitü bearing EdlekItmanTaMgelI Ggát;rgkarTaj nig gusset plate. sRmab;Ggát;rgkarTaj
nigb‘ULúgEdlenAEk,rRCugEKmCageKrbs;Ggát;
h 15 / 16
Lc = Le − = 1.25 − = 0.7812in.
2 2
2d = 2(7 / 8) = 1.75in.
edaysar Lc < 2d
⎛1⎞
φRn = φ (1.2 Lc tFu ) = 0.75(1.2)(0.7812)⎜ ⎟(65) = 22.85kips
⎝2⎠
sRmab;RbehagepSgeTot
15
Lc = s − h = 2.75 − = 1.812in. > 2d
16
⎛ 7 ⎞⎛ 1 ⎞
dUcenH φRn = φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟⎜ ⎟(65) = 51.19kips
⎝ 8 ⎠⎝ 2 ⎠
Bearing strength sRmab;Ggát;rgkarTajKW
φRn = 22.85 + 2(51.19) = 125kips
KNna bearing strength rbs; gusset plate. sRmab;rn§EdlenAEk,rRCugEKRmbs; gusset CageK
h 15 / 16
Lc = Le − = 1.5 − = 1.031in. < 2d
2 2
⎛3⎞
dUcenH φRn = φ (1.2 Lc tFu ) = 0.75(1.2)(1.031)⎜ ⎟(65) = 22.62kips
⎝8⎠
sRmab;RbehagdéTeTot
15
Lc = s − h = 2.75 − = 1.812in. > 2d
16
⎛ 7 ⎞⎛ 3 ⎞
dUcenH φRn = φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟⎜ ⎟(65) = 38.39kips
⎝ 8 ⎠⎝ 8 ⎠
Bearing strength rbs; gusset plate KW
φRn = 22.62 + 2(38.92) = 99.4kips
Gusset plate man strength tUcCag dUcenH bearing strength sRmab;tMNKW
φRn = 99.4kips
RtYtBinitü tensile strength rbs;Ggát;rgkarTaj.
Tension on the gross atea:

T.Chhay 260 Simple Connections

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⎛ 1⎞
φt Pn = φt Fy Ag = 0.90(50)⎜ 3 × ⎟ = 67.5kips
⎝ 2⎠
Tension on the net area: muxkat;TaMgGs;rbs;Ggát;RtUv)antP¢ab; dUcenHvaminman shear lag eT
dUcenHeyIg)an Ae = An . eRbIGgát;Rbehag
1 7 1
h = d + = + = 1.0in.
8 8 8
Design strength KW
φt Pn = φt Fu Ae = φt Fu t (wg − ∑ h ) = 0.75(65)⎜ ⎟[3 − 1(1.0)] = 48.8kips
⎛1⎞
⎝2⎠
karTajenAelI net section mantémøtUcCageK
cemøIy³ Design strength rbs;tMNKW 48.8kips

7>7> Slip-Critical Connections

eKcat;cMNat;fñak;kartP¢ab;EdleRbIb‘ULúgersIusþg;x<s;Ca slip-critical connection b¤ bearing-
type connection. Slip-critical connection CakartP¢ab;EdleKminGnuBaØat[man slip EdlminRtUv

FMCagkmøaMgkkit. sRmab; bearing-type connection eKGnuBØat[man slip ehIy shear nig bearing
ekIteLIgFmμta. enAkñúgRbePTeRKOgbgÁúMxøH CaBiesss<an kmøaMgEdlmanGMeBIelItMNGacekIteLIgCa
lkçN³xYb. kñúgkrNIEbbenH fatigue rbs;eRKOgP¢ab;GackøayCaeRKaHfñak;RbsinebIeKGnuBaØat[man
slip rYmCamYynwgkarekIteLIgsarcuHsareLIg enaHeKRtUvRtYtBinitü slip-critical connec-tion. enAkñúg

eRKOgbgÁúMCaeRcIn eKGnuBaØat[man slip ehIy bearing-type connection RtUvEt RKb;RKan;. ¬b‘ULúg

A307 RtUv)aneRbIsRmab;Et bearing-type connection¦. sRmab; slip-critical connection eKcaM)ac;

RtUvEteFVIkardMeLIg[)anl¥ edIm,ITTYlnUvkmøaMgTajdMbUgRKb;RKan;dUcEdl)anerobrab;. AISC J1.11

erobrab;BIsßanPaBkMNt;Edlb‘ULúgersIusþg;x<s;RtUvEtmankmøaMgTajeBj. enAkñúg bearing-type
connection tRmUvkarcaM)ac;EtmYyKt;kñúgkardMeLIgb‘ULúgKWeKRtUvpþl;nUvkmøaMgTajRKb;RKan;edIm,I[épÞ

b:HKñaGacTb;Tl;Kña)aneTAvijeTAmk. kardMeLIgenHbegáItnUv snug-tight condition Edl)anerobrab;

enAkñúg turn-of-the-nut method.
eTaHbICatamRTwsþI slip-critical connection minRbQmnwg shear nig bearing k¾eday k¾eKRtUv

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mhaviTüal½ysMNg;sIuvil NPIC

Etman shear strength nig bearing strength RKb;RKan;sRmab;krNI overload EdlGaceFVI[ekItman

slip.

edIm,IkarBar slip eKRtUvmanEdnkMNt;sRmab; service load b¤ factored load. eTaHbICakar

karBar slip mansar³sMxan;sRmab; serviceability requiremnent k¾eday k¾ AISC Specification
GnuBaØat[ slip-critical strength GacQrelI service load b¤ factored load.
dUcEdl)anerobrab;BIxagelI lT§PaBTb;nwg slip CaGnuKmn_énplKuNrvagemKuNkkitsþaTic
nig normal force cenøaHEpñkP¢ab;. TMnak;TMngenHRtUv)anbgðajenAkñúg RCSC Specification Edl
eyIgeRbIenATIenHsRmab; slip-critical connection (RCSC, 1994). Slip-critical strength rbs;tMN
KW φRstr Edl φ = 1.0 sRmab; standard hole ehIy
Rstr = 1.13μTm N b N s (RCSC Equation LRFD 5.3)
Edl μ = mean slip coefficient ¬emKuNkkitsþaTic¦ = 0.33 sRmab;épÞ Class A
Tm = kmøaMgTajrbs;eRKOgP¢ab;Gb,brmaEdl)anBI AISC Table J3.1 b¤ RCSC Table 4

N b = cMnYnb‘ULúgenAkñúgtMN

N s = cMnYn slip plan ¬bøg;kat;¦

épÞ Class A CaépÞEdlmanEdkG‘uksIutenAépÞrbs;va. enAkñúg Specification manENnaMnUvRbePTépÞ

CaeRcIneTot EtenAkñúgesovePAenH eyIgeRbIEtépÞ Class A Edlpþl;nUv slip coefficient tUcCageKbMput.
Slip-critical design strength sRmab;b‘ULúgmYyén single shear KW

φRstr = φ (1.13μTm N b N s ) = 1.0(1.13)(0.33)Tm (1)(1)

= 0.373Tm kips

]TahrN_ 7>5³ kartP¢ab;EdlbgðajenAkñúgrUbTI 7>14 eRbIb‘ULúg A325 Ggát;p©it 3 / 4in. EdleFμj

rbs;vasßitenAkñúgbøg;kat;. eKminGnuBaØat[man slip. TaMgGgát;rgkarTaj nig gusset plate CaRbePT
Edk A36 . kMNt; design strength.
dMeNaHRsay³ Shear strength: sRmab;b‘ULúgmYy
π (3 / 4 )2
Ab = = 0.4418in.2
4
φRn = φFv Ab = 0.75(48)(0.4418) = 15.90kips

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sRmab;b‘ULúgbYnRKab;
φRn = 4(15.90) = 63.60kips
Slip-critical strength: edaysareKminGnuBaØat[man slip enaHkartP¢ab;enHRtUv)ancat;Ca slip-

critical. BI AISC Table J3.1 kmøaMgTajkñúgb‘ULúgGb,brmaKW Tm = 28kips . BIsmIkar &>#/

φRstr = 0.373Tm = 0.373(28) = 10.4kips / bplt

sRmab;b‘ULúgbYn
φRstr = 4(10.4) = 41.6kips
Bearing strength: edaysarcm¶ayeTARCugEKmmanRbEvgdUcKña ehIy gusset palte esþIgCagr)ar enaH
eyIgenwgeRbI gusset plate EdlmankRmas; 3 / 8in. edIm,IKNna bearing strength.
Ggát;p©itRbehag
1 3 1 13
h=d+ = + = in.
16 4 16 16
sRmab;RbehagEdlenACitRCugEKRmbs; gusset plate CageK
h 13 / 16
Lc = Le − = 1.5 − = 1.094in.
2 2
⎛3⎞
2d = 2⎜ ⎟ = 1.5in.
⎝4⎠
edaysar Lc < 2d
⎛ 3⎞
φRn = φ (1.2 Lc tFu ) = 0.75(1.2)(1.094)⎜ ⎟(58) = 21.42kips / bolt
⎝8⎠
sRmab;déTeTot
tMNsamBaØ 263 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

13
Lc = s − h = 3 − = 2.188in. > 2d
16
dUcenH φRn = φ (2.4dtFu ) = 29.36kips / bolt
Bearing strength sRmab;kartMNKW

φRn = 2(21.42) + 2(29.36) = 102kips

RtYtBinitü tensile strength rbs;Ggát;rgkarTaj
karTajenAelI gross area:
⎛ 1⎞
φt Pn = φt Fy Ag = 0.90(36)⎜ 6 × ⎟ = 97.2kips
⎝ 2⎠
karTajenAelI net area: muxkat;TaMgmUlrbs;Ggát;RtUv)antP¢ab; dUcenHvaKμan shear lag eT enaHeyIg
TTYl)an Ae = An .
Ggát;p©itRbehag
1 3 1 7
h=d+ = + = in.
8 4 8 8
Design strength KW
( ) ⎛ 1 ⎞⎡ ⎛ 7 ⎞⎤
φt Pn = φt Fu Ae = φt Fu t wg − ∑ h = 0.75(58)⎜ ⎟ ⎢6 − 2⎜ ⎟⎥ = 92.4kips
⎝ 2 ⎠⎣ ⎝ 8 ⎠⎦
Block shear stredngth: failure block sRmab; gusset plate manTMhMdUcTMhMsRmab;Ggát;rgkarTaj
Edr EtxusKñaRtg;kRmas; ¬rUbTI 7>14 b¦. Gusset plate EdlmankRmas;esþIgCagnwgmanersIusþg;tUc
Cag. vaman shear-failure plane cMnYnBIr³
Agv = 2 ×
3
(3 + 1.5) = 3.375in.2
8
edaysarvaman 1.5 Ggát;p©itRbehagkñúgmYyCYredkrbs;b‘ULúg
3⎡ ⎛ 7 ⎞⎤
Anv = 2 × ⎢(3 + 1.5) − (1.5)⎜ ⎟⎥ = 2.391in.2
8⎣ ⎝ 8 ⎠⎦
sRmab;RkLaépÞrgkarTaj
Agt =
3
(3) = 1.125in.2
8
3⎛ 7⎞
Ant = ⎜ 3 − ⎟ = 0.7969in.2
8⎝ 8⎠
AISC Equation J4-3a [
[ ]
φRn = φ 0.6 Fy Agv + Fu Ant = 0.75[0.6(36 )(3.375) + 58(0.7969 )]

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= 0.75[72.90 + 46.22] = 89.3kips

AISC Equation J4-3b [
[ ]
φRn = φ 0.6 Fy Anv + Fy Agt = 0.75[0.6(58)(2.391) + 36(1.125)]

= 0.75[83.21 + 40.50] = 92.8kips

tY fracture ¬EdlBak;B½n§nwg Fu ¦ enAkñúgsmIkarTIBIrmantémøFMCagenAkñúgsmIkarTImYy dUcenH AISC
Equation 4.3b lub.

design strength sRmab; block shear = 92.8kips

kñúgcMeNamsßanPaBkMNt;TaMgGs;Edl)aneFVIkarGegát eyIgeXIjfaersIusþg;EdlRtUvKñanwg slip man

témøtUcCageK.
cemøIy³ Design strength rbs;tMNKW 41.6kips

]TahrN_ 7>6³ Ggát;rgkarTajkRmas; 5 / 8in. RtUv)antP¢ab;eTAnwg splice plate kRmas; 1 / 4in.

cMnYnBIr dUcEdl)anbgðajenAkñúgrUbTI 7>15. bnÞúkEdl)anbgðajCabnÞúk service load. eKeRbIEdk
A36 nig b‘ULúg A325 Ggát;p©it 5 / 8in. . RbsinebIeKGnuBaØat[man slip etIeKRtUvkarb‘ULúg

b:unμanRKab;? G½kSrbs;b‘ULúgnImYy²EdlbgðajKWCaCYrrbs;b‘ULúgkñúgTisTTwgrbs;bnÞHEdk.

dMeNaHRsay³ Shear: sRmab; shear, norminal bolt area KW

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π (5 / 8)2
Ab = = 0.3068in.2
4
snμt;fa eFμjb‘ULúgsßitenAkúñgbøg;kat;. enaH design strength sRmab;b‘ULúgmYyKW
φRn = φFv Ab × 2planes of shear = 0.75(48)(0.3068)(2) = 22.09kips
Bearing: Beating force enAelIGgát;rgkarTajkRmas; 5 / 8in. nwgFMCag bearing force enAelI splice
plate kRmas; 1 / 4in. nImYy² BIrdg. edaysarbnÞúksrubenAelI splice plates esμInwgbnÞúkenAelIGgát;

rgkarTaj enaH splice plate nwgmaneRKaHfñak;enAeBlEdlkRmas;srubrbs; splice plate esþIgCag

kRmas;rbs;Ggát;rgkarTaj. eRbIGgát;p©itRbehag
1 5 1 11
h=d+ = + = in.
16 8 16 16
sRmab;RbehagEdlenAEk,rRCugEKmCageK
h 11 / 16
Lc = Le − = 1.5 − = 1.156in.
2 2
⎛5⎞
2d = 2⎜ ⎟ = 1.25in.
⎝8⎠
edaysar Lc < 2d / bearing strength KW
⎛1 1⎞
φRn = φ (1.2 Lc tFu ) = 0.75(1.2)(1.156)⎜ + ⎟(58) = 30.17kips / bolt
⎝4 4⎠
sRmab;rn§déTeTot
11
Lc = s − h = 3 − = 2.312in. > 2d
16
⎛ 5 ⎞⎛ 1 1 ⎞
dUcenH φRn = φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟⎜ + ⎟(58) = 32.62kips / bolt
⎝ 8 ⎠⎝ 4 4 ⎠
Shearing strength kñúgb‘ULúgmYyKWtUcCagtémø bearing TaMgBIr dUcenHersIusþg;rbs;tMNKW 22.09kips .
bnÞúkemKuNKW
Pu = 1.2 D + 1.6 L = 1.2(25) + 1.6(25) = 70kips

cMnYnb‘ULúgEdlRtUvkar =
total load
load per bolt
70
= = 3.17bolts
22.09
cemøIy³ eRbIb‘ULúgbYn EdlkñúgmYyCYrmanBIrRKab; enAelIRCugnImYy²rbs; splice. b‘ULúgcMnYn R)aMbI
RKab;GacRtUvkarsRmab;kartP¢ab;enH.

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]TahrN_ 7>7³ C 6 ×13 EdlbgðajenAkñúgrUbTI 7>16 RtUv)aneRCIserIsedIm,ITb;Tl;nwgbnÞúkTajem

KuN 108kips . Ggát;enHRtUv)anP¢ab;eTAnwg gusset plate kRmas; 3 / 8in. CamYynwgb‘ULúg A325 Edl
manGgát;p©it 7 / 8in. . ]bmafaeFμjrbs;b‘ULúgsßitenAkñúgbøg;énkmøaMgkat;TTwg ehIyeKGnuBaØat[man
slip sRmab;kartP¢ab;enH. kMNt;cMnYn nigeFVIkarteRmobb‘ULúgy:agNaedIm,ITTYl)anRbEvgtP¢ab; h

Gb,brma. eKeRbIEdk A36 .

dMeNaHRsay³ kMNt;lT§PaBrbs;b‘ULúgeTal
kmøaMgkat;TTwg³
π (7 / 8)2
Ab = = 0.6013in.2
4
φRn = φFv Ab = 0.75(48)(0.6013) = 21.65kips
bearing ³ edaysarkRmas;rbs; gusset plate esþIgCaRTnugrbs;Edk channel dUcenH bearing
strength rbs; gusset plate nwgtUcCagEdk channel. snμt;faRbEvg Lc EdlRsbnwgkmøaMgEdl

GnuvtþmantémøFMCag 2d sRmab;b‘ULúgTaMgGs;. enaH

⎛ 7 ⎞⎛ 3 ⎞
φRn = φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟⎜ ⎟(58) = 34.26kips
⎝ 8 ⎠⎝ 8 ⎠
enaH kmøaMgkat;TTwglub. dUcenH
cMnYnb‘ULúgEdlRtUvkar = 21108.65 = 4.99
eTaHbICab‘ULúg 5 pþl;nUversIusþg;RKb;RKan;k¾eday k¾eKsakl,gb‘ULúg 6RKab;EdlGacerobCalkçN³
sIuemRTI edaymanb‘ULúg 3RKab;BIrCYr dUcbgðajenAkñúgrUbTI 7>17. ¬b‘ULúgBIrCYrRtUv)aneRbIedIm,I
TTYl)anRbEvgtP¢ab;Gb,brma¦. eyIgmin)andwgfaetIkarKNnamuxkat;Ggát;rgkarTajenHQrelI
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karsnμt;eRKOgP¢ab;b:unμanCYr dUcenHlT§PaBTb;karTajrbs;Edk channel CamYynwgb‘ULúgBIrCYrRtUv)an

RtYtBinitümunnwgdMeNIrkarKNnakartP¢ab;bnþ.

karTajenAelI gross area:

φt Pn = 0.90 Fy Ag = 0.90(36 )(3.83) = 124kips
net area
An = 3.83 − 2(1.0)(0.437 ) = 2.96in.2
edaysareyIgminTan;sÁal;RbEvgtP¢ab;BitR)akd dUcenHeyIgRtUveRbItémømFümrbs; U BI
Commentary.

Ae = UAn = 0.85(2.96) = 2.51in.2

kmøaMgTajenAelI net area
φt Pn = 0.75Fu Ae = 0.75(58)(2.51) = 109kips ¬lub¦
dUcenH lT§PaBrbs;Ggát;rgkarTajKWQrelIb‘ULúgBIrCYr.
RtYtBinitüKMlat nigRbEvgeTARCugEKmtamTisEkgnwgkmøaMg. BI AISC J3.3
KMlatGb,brma = 2.667⎛⎜⎝ 78 ⎞⎟⎠ = 2.33in.
BI AISC Table J3.4
RbEvgeTARCugEKmGb,brma = 1 18 in.
KMlat 3in. nigRbEvgeTARCugEKm1 1 2 in. nwgRtUv)aneRbIkñúgTisEkgnwgkmøaMg.
eKGackMNt;RbEvgtP¢ab;Gb,brmarbs;kartP¢ab;edayeRbIKMlat nigRbEvgeTARCugEKmGnuBaØat
Gb,brmakñúgTisbeNþay ¬RsbnwgkmøaMg¦. KMlatGb,brmakñúgTisnImYy²KW 2 2 3 d = 2.33in. .
sakl,g 2 1 2 in. . RbEvgeTARCugEKmGb,brmaKW 1 18 in. . cm¶ayGb,brmaTaMgenHnwgRtUv)aneRbI

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sRmab;epÞógpÞat; bearing strength rbs;kartP¢ab;. sRmab;karKNna bearing strength

eKeRbIGgát;p©it rn§
1 7 1 15
h=d+ = + = in.
16 8 16 16
sRmab;RbehagEdlenAEk,rRCugEKmrbs; gusset plate CageK
h 15 / 16
Lc = Le − = 1.125 − = 0.6562in.
2 2
2d = 2(7 / 8) = 1.75in.
edaysar Lc < 2d bearing strength KW
⎛3⎞
φRn = φ (1.2 Lc tFu ) = 0.75(1.2)(0.6562)⎜ ⎟(58) = 12.85kips / bolt
⎝8⎠
sRmab;RbehagdéTeTot
15
Lc = s − h = 2.5 − = 1.562in. < 2d
16
dUcenH φRn = φ (1.2LctFu ) = 0.75(1.2)(1.562)⎛⎜⎝ 83 ⎞⎟⎠(58) = 30.58kips / bolt
Bearing strength srubsRmab;kartP¢ab;KW
φRn = 2(12.85) + 4(30.58) = 148kips > Pu = 108kips (OK)
rUbTI 7>18 bgðajBIkartP¢ab;sakl,gsRmab;RtYtBinitüemIl block shear enAkñúg gusset
plate ¬sRmab;ragGrNImaRtén failure block enAkñúgEdl channel KWdUcKña b:uEnþ gusset plate man

kRmas;esþIgCag¦.

Shear areas:
Agv = (2.5 + 2.5 + 1.125)(2) = 4.594in.2
3
8

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ehIyedaysarEtvamanRbehag 2.5 enAtamépÞkat;nImYy²

Anv =
3
[6.125 − 2.5(1.0)](2) = 2.719in.2
8
Tension area
Agt = (3) = 1.125in.2
3
8
ehIy Ant = (3 − 1.0) = 0.75in.2
3
8
RtYtBinitüsRmab; tension yield nig shear fracture CamYynwg AISC Equation J4-3a:
φRn = φ [0.6 Fy Agv + Fu Ant ]

= 0.75[0.6(36 )(4.594 ) + 58(0.75)] = 0.75[99.23 + 43.50] = 107.0kips

RtYtBinitüsRmab; tension fracture nig shear yield CamYynwg AISC Equation J4-3b:
φRn = φ [0.6 Fu Anv + Fy Agt ]

= 0.75[0.6(58)(2.719 ) + 36(1.125)] = 0.75[94.62 + 40.50] = 101.3kips

tY fracture ¬tYEdlBak;B½n§nwg Fu ¦ enAkñúgsmIkarTIBIrmantémøFMCagtY fracture enAkñúgsmIkarTImYy
dUcenH smIkarTIBIrlub.
Design strength sRmab; block shear = 101.3kips < 108kips (N.G.)

viFIEdlsamBaØbMputkñúgkarbegáIn block shear strength sRmab;kartP¢ab;enHKWbegáIn shear area eday

begáInKMlatb‘ULúg. RbsinebIeKbegáInKMlat AISC Equation J4-3b enAEtlubdEdl. ebIeTaHbICaKM
latEdlRtUvkarGackMNt;eday trial and error k¾eday k¾eKGacedaHRsayedaypÞal;dUcEdleyIg
nwgeFVIenATIenH. BI AISC Equation J4-3b, eK[
0.75[0.6(58)Anv + 40.50] = 108kips
dUcenHeKRtUvkar Anv = 2.974in.2
Anv =
3
(2s + 1.125 − 2.5)(2) = 2.974in.2
8
dUcenH s = 2.67in.
yk s = 3in.
CamYynwgKMlat 3in. net shear area KW
Anv =
3
(3 + 3 + 1.125 − 2.5)(2) = 3.469in.2
8
ehIy block shear strength BI AISC Equation J4-3b KW
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[
φRn = φ 0.6 Fu Anv + Fy Agt ]
= 0.75[0.6(58)(3.469 ) + 36(1.125)] = 0.75[120.7 + 40.50] = 120.9kips
edayeRbIKMlat nigRbEvgeTARCugEKmEdl)ankMNt; dUcenHRbEvgGb,brmaKW
h = 1.125 + 2 × 3 + 1.125 = 8.5in
cemøIy³ eRbIkartP¢ab;lMGitEdlbgðajenAkñúgrUbTI 7>19.

karteRmobb‘ULúgenAkñúg]TahrN_ 7>7 manlkçN³sIuemRTIeFobnwgG½kSRsbnwgG½kSTIRbCMu

Tm¶n;. dUcenHkmøaMgpÁÜbEdlTb;Tl;kmøaMgEdlpþl;[edayeRKOgP¢ab;k¾eFVIGMeBItamG½kSenH ehIyrag
FrNImaRt enHRtUvKñanwgkartP¢ab;samBaØ. RbsinebIeKRtUvkarcMnYnb‘ULúgess ehIyeKeRbIBIrCYr vanwg
minmanPaBsIuemRTIeT ehIykartP¢ab;nwgmanlkçN³cakp©it. kñúgkrNIEbbenH GñkKNnamuxkat;nwg
manCeRmIseRcIn³ ¬!¦ minKitcMNakp©it edaysnμt;fa\T§BlenHGacecal)an/ ¬@¦ KitcMNakp©it/ ¬#¦
eRbIkartM erobqøas; (staggered pattern) EdlGacrkSanUvPaBsIuemRTI/ b¤ ¬$¦ bEnßmcMnYnb‘ULúgedIm,I
TTYl)ankarteRmobEdlmanlkçN³sIuemRTI. visVkrPaKeRcInRbEhlCanwgeRCIserIsCeRmIscugeRkay.

]TahrN_ 7>8³ Ggát;rgkarTajRbEvg 13 ft nigkartP¢ab;rbs;vaRtUv)anKNnasRmab; service dead

load 8kips nig service live load 22kips . eKminGnuBaØat[man slip sRmab;kartP¢ab;enHeT.
Ggát;enHRtUv)antP¢ab;eTAnwg gusset plate kRmas; 3 / 8in. dUcbgðajenAkñúgrUbTI 7>20. eRbIEdkEkg
eTal (single angle) sRmab;Ggát;rgkarTaj. eRbIb‘ULúg A325 nigEdk A572 grade
50 sRmab;Ggát;rgkarTaj nig gusset plate.

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dMeNaHRsay³ bnÞúkemKuNEdlRtUvTb;Tl;KW
Pu = 1.2 D + 1.6 L = 1.2(8) + 1.6(22 ) = 44.8kips
edaysarTMhMb‘ULúg nigkarteRmobb‘ULúgCH\T§iBldl; net area rbs;Ggát;rgkarTaj eyIgnwgcab;epþIm
CamYynwgkareRCIserIsb‘ULúg. yuT§saRsþKWkareRCIserIssRmab;karsakl,g/ kMNt;cMnYnb‘ULúgEdlRtUv
kar/ rYcbnÞab;mksakl,gTMhMepSgeTotRbsinebITMhMEdl)ansakl,gFMeBk b¤tUceBk. Ggát;p©itb‘U
LúgsßitenAcenøaHBI 1/ 2in. ≈ 13mm eTA 1 12 in. ≈ 38mm edayekIneLIgmþg 1 / 8in. ≈ 3mm
sakl,gb‘ULúg 5 / 8in. . Nominal bolt area KW
π (5 / 8)2
Ab = = 0.3068in.2
4
Shear strength KW
φRn = φFv Ab = 0.75(48)Ab = 0.75(48)(0.3068)
= 11.04kips / bolt¬edaysnμt;faeFμjsßitenAkñúgbøg;kat;¦
edayeKminGnuBaØat[man slip dUcenHkartP¢ab;enHCa slip-critical. eyIgsnμt;épÞ Class A ehIy
sRmab;b‘ULúgGgát;p©it 5 / 8in. kmøaMgTajGb,brmaKW Tm = 19kips ¬BI AISC Table J3.1). BI RCSC
Equation LRFD 5.3, slip critical strength sRmab;b‘ULúgeTalKW

φRstr = φ (1.13μTm N b N s ) = 1.0(1.13)(0.33)(19)(1)(1) = 7.085kips / bolt

eday slip-critical strength tUcCag shear strength dUcenH slip-critical strength lub. eyIgnwgkM
Nt;cMnYnb‘ULúgedayQrelI slip-critical strength ehIyRtYtBinitü bearing bnÞab;BIeRCIserIsGgát;
¬edaysar bearing strength minGackMNt;)an Tal;EteKsÁal;kRmas;Ggát;sin¦. dUcenH
cMnYnb‘ULúg = load
total load
=
44.8
per bolt 7.085
= 6.3bolts

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dUcenHeKRtUvkarb‘ULúgy:agtic 7 RKab;. RbsinebIeKeRbIBIrCYr eKRtUvbEnßmb‘ULúgmYyRKab;edIm,IrkSaPaB

sIuemRTI. rUbTI 7>21 bgðajBIkarteRmobb‘ULúgEdlmanCaeRcInTRmg;.
karteRmobb‘ULúgTaMgenHeKGaceRbI)anTaMgGs; EtRbEvgénkartP¢ab;GacRtUv)ankat;bnßyedayeRbITMhM
b‘ULúgFM nigcMnYntic.
sakl,gb‘ULúgEdlmanGgát;p©it 7 / 8in. . Nominal bolt area KW
π (7 / 8)2
Ab = = 0.6013in.2
4
Shear strength KW
φRn = 0.75(48)Ab = 0.75(48)(0.6013)
¬edaysnμt;faeFμjsßitenAkñúgbøg;kat;¦
= 21.65kips / bolt

kmøaMgTajGb,brmasRmab;b‘ULúg A325 Ggát;p©it 7 / 8in. KW Tm = 39kips dUcenH slip-critical

strength KW

φRstr = φ (1.13μTm N b N s ) = 1.0(1.13)(0.33)(39)(1)(1) = 14.54kips / bolt ¬lub¦

eKRtUvkarb‘ULúgEdlmanGgát;p©it 7 / 8in. cMnYn
44.8
= 3.1bolts
14.54

dUcenHeyIgeRbIb‘ULúg A325 EdlmanGgát;p©it 7 / 8in. cMnYn 4 RKab;. BI AISC J3.3, KMlatGb,brmaKW

⎛7⎞ ⎛7⎞
s = 2.667d = 2.667⎜ ⎟ = 2.33in. ¬b¤sRmab;karniym/ 3d = 3⎜ ⎟ = 2.62in. ¦
⎝8⎠ ⎝8⎠
BI AISC Table J3.4, cm¶ayeTARCugEKmKW
Le = 1.5in. ¬edaysnμt; sheared edges¦
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edaysakl,gkarteRmobdUcbgðajenAkñúgrUbTI 7>22 eRCIserIsGgát;rgkarTaj. Gross area Edl

RtUvkarKW
Pu 44.8
Ag ≥ = = 0.996in.2
0.9 Fy 0.9(50 )

Effective net area EdlRtUvkarKW

Pu 44.8
Ae ≥ = = 0.9190in.2
0.75Fy 0.75(36 )

edaysar effective net area KW A = UA / net area EdlRtUvkarKW

e n

requiredAe
An =
U
BIkarteRmobb‘ULúgEdlbgðajenAkñúgrUbTI 7>22/ CamYynwgb‘ULúgeRcInCagBIrkñúgTisénkmøaMgEdlGnuvtþ
témømFümrbs; U BI Commentary to the AISC Specification KW 0.85 . ¬enAeBlEdleKeRCIserIs
Ggát;rYcehIy eKGackMNt;témø U CamYynwg AISC Equation B3-2¦. dUcenH
0.9190
An ≥ = 1.08in.2
0.85

cMNaMfa net area EdlRtUvkarKWFMCag gross area EdlRtUvkar. kaMniclPaBGb,brmaEdlRtUvkarKW

L 13(12 )
rmin = = = 0.52in.
300 300
sakl,g L3 1 2 × 2 12 × 14
Ag = 1.44in.2 > 0.996in.2 (OK)
rmin = rz = 0.544in. > 0.52in. (OK)
sRmab;karKNna net area, eRbIGgát;p©itrn§ 7 8 + 18 = 1.0in.
⎛1⎞
An = Ag − Ahole = 1.44 − 1.0⎜ ⎟ = 1.190in.2 > 1.08in.2 (OK)
⎝4⎠
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KNna U CamYynwg AISC Equation B3-2:

x
U =1− ≤ 0.9
L
0.785
= 1− = 0.913
9
edaysartémøenHFMCag 0.9 / dUcenHeRbI U = 0.9 . Effective net area KW
Ae = UAn = 0.9(1.190) = 1.071in.2 > 0.9190in.2 (OK)
RtYtBinitü bearing strength. cm¶ayeTARCugEKmsRmab;EdkEkgesμInwgcm¶ayeTARCugEKmsRmab;
gusset plate ehIyedaysarEdkEkgmankRmas;esþIgCag gusset plate dUcenHeyIgeRbIEdkEkgEdl

mankRmas; 1 / 4in. sRmab;KNna bearing strength. sRmab;karKNna bearing strength,

eyIgeRbIGgát;p©itRbehag
1 7 1 15
h=d+ = + = in.
16 8 16 16
sRmab;RbehagEdlenAEk,RCugEKmGgát;CageK
h 15 / 16
Lc = Lc − = 1.5 − = 1.031in.
2 2
2d = 2(7 / 8) = 1.75in.
edaysar Lc < 2d / bearing strength KW
⎛1⎞
φRc = φ (1.2 Lc tFu ) = 0.75(1.2)(1.031)⎜ ⎟(65) = 15.08kips / bolt
⎝4⎠
sRmab;RbehagdéTeTot
15
Lc = s − h = 3 − = 2.062in. > 2d
16
⎛ 7 ⎞⎛ 1 ⎞
dUcenH φRn = φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟⎜ ⎟(65) = 25.59kips / bolt
⎝ 8 ⎠⎝ 4 ⎠
Bearing strength srubsRmab;kartP¢ab;KW
φRn = 15.08 + 3(25.59) = 91.9kips > Pu = 44.8kips (OK)
RtYtBinitü block shear. CamYynwgb‘ULúgEdlP¢ab;enAelIeCIgEvgCamYynwgcm¶ayKMlat ¬emIlCMBUk
III/ rUbTI 3>22¦ failure block RtUv)anbgðajenAkñúgrUbTI 7>23. Shear area KW

Agv =
1
(1.5 + 9) = 2.625in.2
4
Anv = [1.5 + 9 − 3.5(1.0 )] = 1.750in.2
1
4
¬Ggát;p©itRbehagmancMnYn 3.5 ¦
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Tension area KW
Agt =
1
(1.5) = 0.3750in.2
4
Ant = [1.5 − 0.5(1.0 )] = 0.25in.2
1
4
¬Ggát;p©itRbehagmancMnYn 0.5 ¦
AISC Equation J4-3a [
[
φRn = φ 0.6 Fy Agv + Fu Ant ]
= 0.75[0.6(50 )(2.625) + 65(0.25)] = 0.75(78.75 + 16.25) = 71.2kips
AISC Equation J4-3b [
[
φRn = φ 0.6 Fu Anv + Fy Agt ]
= 0.75[0.6(65)(1.75) + 50(0.375)] = 0.75(68.25 + 18.75) = 65.2kips
smIkar J4-3bmantY fracture FMCag dUcenHsmIkarenHlub. dUcenH block shear strength KW
φRn = 65.2kips > Pu = 44.8kips (OK)

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cemøIy³ eRbI L3 12 × 2 12 × 14 CamYynwgkartP¢ab;enAelIeCIgEvg. eRbIb‘ULúg A325 Ggát;p©it 7 8 in.

dUcbgðajenAkñúgrUbTI 7>24.

7>8> b‘ULúgersIusþg;x<s;rgkarTaj High-Strength Bolts in Tension

enAeBlEdlkmøaMgTajEdlGnuvtþelIb‘ULúgedayKμankmøaMgTajedIm (initial tension) kmøaMg
TajenAkñúgb‘ULúgesμInwgkmøaMgEdlGnuvtþ. b:uEnþ RbsinebIb‘ULúgrgeRbkugRtaMg Epñkd¾FMrbs;kmøaMgEdl
GnuvtþRtUv)aneRbIedIm,Ibn§ÚrkmøaMgsgát; b¤kmøaMgrwt (clamping force) enAelIEpñkEdlRtUvtP¢ab; dUcEdl
kMNt;eday Kulak, Fisher, nig Struik (1987) ehIyRtUv)anbkRsayenATIenH. rUbTI 7>25 bgðajBI
tMNBüÜr (hanger connection) EdlpSMeLIgeday structural tee shape EdlRtUv)ancab;b‘ULúgeTAnwg
søabxageRkamrbs; W-shape nigrgnUvkmøaMgTaj. b‘ULúgeTal nwgcMENkénEpñkEdlRtUvtP¢ab; RtUv
)ansikSamun nigeRkayeBldak;bnÞúk.

düaRkamGgÁesrIrbs;kartP¢ab;muneBldak;bnÞúkRtUv)anbgðajenAkñúgrUbTI 7>26 a. ral;kmøaMg

TaMgGs;CakmøaMgkñúg. edIm,IPaBgayRsYl kmøaMgTaMgGs;RtUv)ansnμt;sIuemRTIeFobG½kSrbs;b‘ULúg
ehIycMNakp©itminRtUv)anKit. RbsinebIeKBicarNaEpñkEdlRtUvtP¢ab;dac;edayELk kmøaMgrYmman
kmøaMgTajrbs;b‘ULúg To nigkmøaMgrwt Ekg (normal clamping force) N o EdlbgðajenATIenHRtUv)an
BRgayesμI. edIm,I[manlMnwg eKRtUvkar To = N o . enAeBlEdleKGnuvtþkmøaMgxageRkA kmøaMgenAelI
kartP¢ab;RtUv)anbgðajenAkñúgrUbTI 7>26 b Edl F tMNag[kmøaMgTajsrubEdlGnuvtþmkelIb‘ULúg
mYy. rUbTI 7>26 c bgðajkmøaMgEdlmanGMeBIelIdüaRkamGgÁesrIrbs;Epñkénsøabrbs; structural tee
nigEpñkEdlRtUvKñarbs;b‘ULúg. bUkkmøaMgtamTisG½kSb‘ULúg eyIgTTYl)an
T =F+N

tMNsamBaØ 277 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

kmøaMg F nwgbegáInkmøaMgTajrbs;b‘ULúg ehIyeFVI[valUt)an δ b . kmøaMgsgát;enAkñúgsøab

rbs; structurel atee nwgRtUv)ankat;bnßy CalT§plvamanbMlas;TI δ fl EdlmanTisdUc δ b . TMnak;
TMngrvagkmøaMgGnuvtþn_ nigbERmbRmYlkmøaMgTajrbs;b‘ULúgGacRtUv)ankMNt;dUcxageRkam³

BI elementary mechanics of materials, kMhUcRTg;RTaytamG½kSrbs;bnÞúktamG½kSEdl

GnuvtþelIGgát;KW³
δ=
PL
AE
¬&>$¦
Edl P = kmøaMgtamG½kS
L = RbEvgedIm

A = RkLaépÞmuxkat;

E = m:UDuleGLasÞic

BIsmIkar &>$ eyIgGacTajrkkmøaMg

AEδ
P=
L
¬&>%¦
T.Chhay 278 Simple Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dUcenHbERmbRmYlkmøaMgenAkñúgb‘ULúgEdlRtUvKñaeTAnwgkMhUcRTg;RTay δ b KW
A E δ
ΔT = b b b
Lb
¬&>^¦
BIsmIkar &>% eKTTYl)anbERmbRmYlkmøaMg N
A fl E fl δ fl
ΔN =
L fl
¬&>&¦
Edl L fl CakRmas;rbs;søab. RbsinEpñkEdlRtUvP¢ab; ¬søabTaMgBIr¦ enAb:HKña kMhUcRTg;RTayrbs;
b‘ULúg δ b nigkMhUcRTg;RTaysøab δ fl nwgesμIKña. edaysar E fl esÞIresμInwg Eb (Bickford, 1981),
ehIy A fl FMCag Ab
A fl E fl δ fl A E δ
>> b b b
L fl Lb

dUcenH ΔN >> ΔT
pleFob ΔN elI ΔT sßitenAcenøaHBI 0.05 eTA 0.1 (Kulak, Fisher, nig Struik, 1987). dUcenH ΔT
minRtUvFMCag 0.1ΔN EdlbgðajfakmøaMgEdlGnuvtþPaKeRcInKWbn§ÚrkmøaMgsgát;rbs;EpñkEdlRtUvtP¢ab;.
KNnakmøaMgEdlRtUvkaredIm,IeFVI[EpñkEdlRtUvP¢ab;XøatecjBIKña emIlrUbTI 7>27. enAeBlEdlEpñk
TaMgBIrXøatecjBIKña
T =F
b¤ To + ΔT = F ¬&>*¦
enAeBlEdlCitdl;cMNucEdlRtUvXøatKña sac;lUtrbs;b‘ULúg nigKMlatrbs;søabKWesμIKña
A E A E
ΔT = b b δ b = b b δ fl
Lb Lb
¬&>(¦
Edl δ fl CakMhUcRTg;RTayEdlRtUvKñanwgkmøaMgsgát;edIm N o . BIsmIkar &>$
N o L fl
δ fl =
A fl E fl

CMnYsvaeTAkñúgsmIkar &>( eyIg)an

⎛ A E ⎞⎛ N o L fl ⎞ ⎛ Ab Eb / Lb ⎞ ⎛
⎟ N o = ⎜ Ab Eb / Lb
⎞
ΔT = ⎜⎜ b b ⎟⎟⎜ ⎟=⎜ ⎟To ≈ 0.1To
⎝ Lb ⎠⎜⎝ A fl E fl ⎟ ⎜ A fl E fl / L fl
⎠ ⎝
⎟
⎠
⎜ A fl E fl / L fl
⎝
⎟
⎠
BIsmIkar &>*
To + 0.1To = F b¤ F = 1.1To

tMNsamBaØ 279 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

dUcenH enAxN³eBlEdlcab;epþImXøat kmøaMgTajenAkñúgb‘ULúgFMCagkmøaMgTajedImEdlmanenAeBl

dMeLIgb‘ULúgRbEhl 10% . b:uEnþ enAeBlEdlEpñkEdlRtUvP¢ab;Xøatecj kmøaMgxageRkAEdlekIneLIg
nwgRtUv)anTb;edaykmøaMgEdlekIneLIgRtUvKñaenAkñúgb‘ULúg. RbsinebIeKsnμt;fakmøaMgTajenAkñúgb‘ULúg
RtUv)andak;[esμIkmøaMgxageRkA ¬RbsinebIKμankmøaMgTajedIm¦ ehIykartP¢ab;rgnUvbnÞúkrhUtdl;Epñk
EdltP¢ab;XøatecjBIKña enaHkmøaMgTajenAkñúgb‘ULúgRtUv)anKNnaticCag 10% . sRmab;krNIenH
b‘ULúgersIusþg;x<s;RtUvrgnUveRbkugRtaMgtamtémøEdlmanenAkñúg AISC Table J3.1 eTaHCakartP¢ab; enH
Ca slip-critical b¤minEmnk¾eday. CarYm eKRtUvKNnakmøaMgTajenAkñúgb‘UøLúgedayKitbBa©ÚlTaMgkmøaMg
TajedIm.

Prying Action
sRmab;kartP¢ab;PaKeRcInEdleRKOgP¢ab;rgkmøaMgTaj kMhUcRTg;RTayrbs;EpñkEdlRtUvP¢ab;
GacbegáInkmøaMgTajEdlGnuvtþeTAelIeRKOgP¢ab;. RbePT hanger connection Edl)anerobrab;xag
elICaRbePTkartP¢ab;EdlmanlkçN³eFVIkardUcEdl)anerobrab;. kmøaMgTajbEnßmRtUv)aneKehAfa
prying force ehIyRtUv)anbgðajenAkñúgrUbTI 7>28 EdlrUbenHbgðajBIkmøaMgenAelIGgÁesrIrbs;
hanger. muneBlEdlbnÞúkxageRkAGnuvtþ kmøaMgsgát;Ekg (normal compressive force) N o RbmUl

pþúMenAelIGgS½rbs;b‘ULúg. enAeBlEdlbnÞúkGnuvtþ RbsinebIsøab flexible RKb;RKan; enaHvanwgxUcRTg;

RTaydUcEdlbgðaj ehIykmøaMgsgát;nwgrMkileTAxagcugrbs;søab. karBRgaykmøaMgeLIgvijenH nwg
EkERbTMnak;TMngrvagbnÞúkTaMgGs; ehIykmøaMgTajrbs;b‘ULúgnwgekIneLIg. b:uEnþ RbsinebIEpñkEdl
RtUvP¢ab;manlkçN³rwgRKb;RKan; vanwgminmankarpøas;bþÚrkmøaMgeT ehIyk¾minman prying action Edr.
eKTTYl)antémøGtibrmarbs; prying force enAeBlEdlkac;RCugrbs;søabenAEtb:HCamYynwgEpñk
EdlRtUvP¢ab;déTeTot.
T.Chhay 280 Simple Connections
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enAkñúgkartP¢ab;RbePTenH bending EdlekIteLIgeday prying force EtgEtmanlkçN³lub

kñúgkarKNnaEpñkEdlRtUvP¢ab;. AISC J3.6 tRmUv[KitbBa©Úl prying force eTAkñúgkarKNnakmøaMg
TajEdlGnuvtþelIeRKOgP¢ab;.

viFIsaRsþsRmab;karKNna prying force EdlQrelI Guide to design Criteria for Bolted

and Riveted Joints (Kulak, Fisher, nig Strick, 1987) manenAkñúg Manual in Part 11, “Connec-

tions for Tension and Compression” (Volume II). krNICak;lak;EdlRtUv)anRtYtBinitüCakart

P¢ab; structural tee shape ehIyEdkEkgKUrEdlxñgTl;xñg ( a pair of back-to-back angle) nwg

RtUv)anKitkñúgpøÚvdUcKñaEdr. viFIEdlbgðajenATIenHmanTMrg;xusKñabnþicEtpþl;nUvlT§pldUcKña.
viFIEdleRbIKWQrelIKRmUEdlbgðajenAkñúgrUbTI 7>29. RKb;kmøaMgTaMgGs;KWsRmab;EteRKOg
P¢ab;mYy. dUcenH T CakmøaMgTajemKuNxageRkAEdlGnuvtþeTAelIEtb‘ULúgmYy/ Q Ca prying force
EdlRtUvKñanwgb‘ULúgmYy nig Bc CakmøaMgb‘ULúgsrub. Prying force )anrMkileTAcugrbs;søab ehIy
vamantémøGtibrma.
smIkarxageRkamRtUv)anbMEbkBIsmIkarlMnwgrbs;GgÁesrIkñúgrUbTI 7>29. BIplbUkm:Um:g;Rtg;
muxkat; B-B enAkñúgrUbTI 7>29 b
Tb − M a − a = Qa ¬&>!0¦
tMNsamBaØ 281 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

BIrUbTI 7>29 c
M b − b = Qa ¬&>!!¦
cugeRkay/ kmøaMglMnwgRtUvkarKW
Bc = T + Q ¬&>!@¦
smIkarlMnwgTaMgbIenHGacbBa©ÚlKñaedIm,ITTYl)ansmIkareTalsRmab;kmøaMgb‘ULúgsrub EdlrYmbBa©Úl
TaMg\T§iBl prying force. dMbUgeyIgkMNt;Gefr α CapleFobrvagm:Um:g;kñúgmYyÉktþaRbEvgtam
beNþayG½kSb‘ULúgelIm:Um:g;kñúgmYyÉktþaRbEvgenARtg;épÞKl;. sRmab;G½kSb‘ULúg/ RbEvgCa net length,
dUcenH
/ ( p − d ') M b − b ⎛ ⎞ M b −b
M
α = b −b
M a−a / p
= ⎜⎜
1
⎟=
M a − a ⎝ 1 − d ' / p ⎟⎠ δM a − a
¬&>!#¦
Edl p = RbEvgrgsMBaFrbs;søabsRmab;b‘ULúgmYy ¬emIlrUbTI 7>29 a¦
d ' = Ggát;p©itrbs;Rbehagb‘ULúg
d' net area at bolt line
δ = 1− =
p gross area at web face
(
M a − a = design strength at a − a = φb M p = φb pt 2f F y / 4 )
T.Chhay 282 Simple Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

eyIgGacbBa©ÚlsmIkarlMnwgbI &>!0-&>!@ edIm,ITTYl)ankmøaMgb‘ULúgsrub/ Bc :

⎡ δα b ⎤
Bc = T ⎢1 + ⎥ ¬&>!$¦
⎣ (1 + δα ) a ⎦
CamYynwg bnÞúkEdlTTYl)anBIsmIkar &>!$ eyIgnwgTTYl)ankMhUcRTg;RTayFMEdleFVI[kugRtaMgTaj
pÁÜbenAkñúgb‘ULúgminRtYtsIuKñaCamYyG½kSrbs;b‘ULúg. dUcenH kmøaMgkñúgb‘ULúgEdl[edaysmIkar &>!$
minRtUvKñaCamYynwglT§plBiesaFn_. edIm,ITTYl)anlT§plEdlcg;)an luHRtaEtkmøaMg Bc rMkileTA
kan;Kl;rbs; tee edaybrimaN d / 2 Edl d CaGgát;p©itb‘ULúg. dUcenHtémø b nig a RtUv)anEkERbCa
b' = b −
d
2
ni g a' = a +
d
2
¬edIm,I[RtUvnwglT§plBiesaFn_kan;Etl¥ témørbs; a minRtUvFMCag 1.25b eT¦
CamYynwgkarpøas;bþÚrenHeyIgGacsresrsmIkar &>!$ Ca
⎡ δα b' ⎤
Bc = T ⎢1 + ⎥ ¬&>!%¦
⎣ (1 + δα ) a ' ⎦
eyIgGackMNt; α BIsmIkar &>!% eday[kmøaMgenAkñúgb‘ULúg Bc esμIeTAnwg design tensil strength
EdleyIgsMKal;Ca B . lT§plEdlTTYl)anKW
α=
[(B / T ) − 1](a' / b') ¬&>!^¦
δ {1 − [(B / T ) − 1](a' / b')}
eKGacmansßanPaBkMNt;BIr³ tensil failure rbs;b‘ULúg nig bending failure rbs; tee. eK
snμt;fa failure rbs; tee ekItmanenAeBlEdlsnøak;)aøsÞic (plastic hinges) ekItmanRtg;muxkat; a-a,
Rtg;Kl;rbs; tee, nigenARtg;muxkat; b-b. edayehtuenHvanwgbegáItCa beam mechanism. m:Um:g;énTI
taMgTaMgenHnwgesμInwg M p EdlCalT§PaBm:Um:g;)aøsÞicénRbEvgrbs;RbEvgrgsMBaFrbs;søabsRmab;b‘U
LúgmYy. RbsinebItémødac;xatrbs; α EdlTTYl)anBIsmIkar &>!^ tUcCag 1.0 enaHm:Um:g;enARtg;
G½kSb‘ULúgtUcCagm:Um:g;enARtg;Kl; tee Edlvabgðajfa beam mechanism minRtUv)anbegáIteT ehIy
sßanPaBkMNt;RtUv)ankMNt;Ca tensile failure rbs;b‘ULúg. kmøaMgb‘ULúg Bc kñúgkrNIenH nwgesμInwg
design strength B . RbsinebItémødac;xatrbs; α ≥ 1.0 enaH plastc hinges nwgekItmanenARtg; a-a

nig b-b ehIysßanPaBkMNt;KW flexural failure rbs;søabrbs; tee. edaysarEtm:Um:g;Rtg;kEnøgTaMg

BIrenHRtUv)ankMNt;Rtwmm:Um:g;)aøsÞic M p enaH α KYrEtUv)ankMNt;esμInwg 1.0 .
smIkarlMnwgbI &>!0-&>!@ k¾GacRtUv)anrYmbBa©ÚlKñakøayCasmIkarEtmYysRmab;kMNt;kRmas;
søab t f . BIsmIkar &>!0 nig &>!! eyIgGacsresr
tMNsamBaØ 283 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Tb'− M a − a = M b − b
Edl b' RtUv)anCMnYs[ b . BIsmIkar &>!#
Tb'− M a − a = δαM a − a ¬&>!&¦
[ M a − a esμInwg design strength eKTTYl)an
pt 2f F y
M a − a = φb M p = φb
4
Edl t f CakRmas;søabEdlRtUvkar. CMnYs M a − a eTAkñúgsmIkar &>!& eyIgTTYl)an
4Tb'
tf =
φb pFy (1 + δα )

Edl φb = 0.90
tf =
4.444Tb'
pF y (1 + δα )
¬&>!*¦
karKNnakartP¢ab;EdlrgnUv prying action CatMeNIrkarKNna trial-and-error. enAeBl
eRCIserIsTMhM nigcMnYnrbs;b‘ULúg eyIgRtUvEtKiteRtomTuksRmab; prying force. kareRCIserIskRmas;
tee mankarlM)akCagedaysarvaTak;TgeTAnwgkareRCIserIsb‘ULúg nigTMhM tee. eKGaceRbI Prelimi-

nary Hanger Connection Selection Table EdlmanenAkñúg Part 11 of the Manual sRmab;CYy

sRmYldl;kareRCIserIsrUbragsakl,g. enAeBlEdleKeRCIserIsmuxkat;sakl,g/ dwgcMnYnb‘ULúg nig

karteRmobb‘ULúgrYcehIy eKGaceRbIsmIkar &>!% nig &>!* edIm,IepÞógpÞat;.
RbsinebIkRmas;søabCak;EsþgxusBItémøEdlRtUvkar témøCak;Esþgrbs; α nig Bc k¾GacxusBIGVI
EdleK)anKNnaknøgmkEdr. RbsinebIeKRtUvkmøaMgb‘ULúgCak;Esþg EdlrYmbBa©ÚlTaMg prying force
Q enaHeKRtUvkMNt; α eLIgvijdUcxageRkam.

M b − b = Tb'− M a − a
BIsmIkar &>!#/
M b −b
α=
δM a − a
Tb'− M a − a Tb' / M a − a − 1
= =
δM a − a δ
eday[ M a − a esμIwTAnwg design moment eK)an

T.Chhay 284 Simple Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

⎛ pt 2 F ⎞
⎜ f y⎟
M a − a = φb M p = 0.90⎜ ⎟
⎜ 4 ⎟
⎝ ⎠
Tb'
−1
0.90 pt 2f F y / 4 ⎛ ⎞
1 ⎜ 4.444Tb' ⎟
enaH α=
δ
= ⎜
δ ⎜ pt 2 Fy
− 1⎟ ¬&>!(¦
⎟
⎝ f ⎠
eKGacrkkmøaMgb‘ULúgsrubBIsmIkar &>!%

]TahrN_ 7>9³ WT10.5 × 66 RbEvg 8in. RtUv)anP¢ab;eTAnwg)atsøabrbs;Fñwm dUcbgðajenAkñúgrUbTI

7>30. Hanger enHrgnUvbnÞúkemKuN 90kips . kMNt;cMnYnb‘ULúg A325 Ggát;p©it 7 / 8in. EdlRtUvkar
nigepÞógpÞat;nUvPaBRKb;RKan;rbs; tee. EdkEdleRbICaRbePTEdk A36 .

dMeNaHRsay³ RkLaépÞb‘ULúgKW
π (7 / 8)2
Ab = = 0.6013in.2
4
ehIy design strength rbs;b‘ULúgmYyKW
B = φRn = φFt Ab = 0.75(90 )(0.6013) = 40.59kips

tMNsamBaØ 285 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

cMnYnb‘ULúgEdlRtUvkarKW 90 / 40.59 = 2.22 . cMnYnb‘ULúgGb,brmaEdlRtUvkarKW 4 edIm,IrkSaPaBsIuem-

RTI. BITMhMEdlbgðajenAkñúgrUbTI 7>30
b=
(5.5 − 0.650) = 2.425in.
2
a=
(12.44 − 5.5) = 3.470in.
2
1.25b = 1.25(2.425) = 3.031in. < 3.470in.
yk a = 3.031in.
d 7/8
b' = b − = 2.425 − = 1.988in.
2 2
d 7/8
a ' = a + = 3.031 + = 3.468in.
2 2
bnÞúkxageRkAemKuNkñúgmYyb‘ULúg edayKitTaMg prying force KW T = 90 / 4 = 22.5kips .
KNna δ ³
1 7 1
d'= d + = + = 1in.
8 8 8
8
p= = 4in.
2
d' 1
δ = 1 − = 1 − = 0.75
p 4
KNna α ³
B 40.59
−1 = − 1 = 0.8040
T 22.5
a ' 3.468
= = 1.744
b' 1.988
BIsmIkar &>!^/
α=
[(B / T ) − 1](a' / b') = 0.8040(1.744) = −4.65
δ {1 − [(B / T ) − 1](a' / b')} 0.75[1 − 0.8040(1.744)]
edaysar α > 1.0 / yk α = 1.0 . BIsmIkar &>!*
4.444Tb' 4.444(22.5)(1.988)
tf = =
pF y (1 + δα ) 4(36 )(1 + 0.75)
= 0.888in. < 1.035in. (OK)
TaMgcMnYnb‘ULúgEdleRCIserIs nwgkRmas;søabKWRKb;RKan; ehIyminRtUvkarkarKNnateTAmuxeToteT.
b:uEnþ edIm,IbgðajBIviFIsaRsþKNna eyIgKNna prying force edayeRbIsmIkar &>!( nig &>!%. BI
smIkar &>!(/
T.Chhay 286 Simple Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

⎛ ⎞
1 ⎜ 4.444Tb' ⎟ 1 ⎡ 4.444(22.5)(1.988) ⎤
α= ⎜ 2 − 1⎟ = ⎢ − 1⎥ = 0.3848
δ ⎜ pt F y ⎟ 0.75 ⎣⎢ 4(1.035)2 (36 ) ⎦⎥
⎝ f ⎠
BIsmIkar &>!%/ kmøaMgb‘ULúgsrub edayKitTaMg prying force KW
⎡ δα b' ⎤
Bc = T ⎢1 + ⎥
⎣ (1 + δα ) a ' ⎦
⎡ 0.75(0.3848) ⎛ 1.988 ⎞⎤
= 22.5⎢1 + ⎜ ⎟⎥ = 25.39kips
⎣ 1 + 0.75(0.3848) ⎝ 3.468 ⎠⎦
Prying force KW
Q = Bc − T = 25.39 − 22.5 = 2.89kips
cemøIy³ WT10.5 × 66 RKb;RKan;. eRbIb‘ULúg A325 Ggát;p©it 7 / 8in.

RbsinebIkRmas;søabminRKb;RKan; eKGacsakl,g tee shape EdlmanTMhMFMCag b¤k¾eRbIcMnYn

b‘ULúgbEnßmedIm,Ikat;bnßy T EdlCakmøaMgxageRkAkñúgmYyb‘ULúg. Prying force enAkñúg]TahrN_
7>9 bEnßmRbEhl 13% eTAelIkmøaMgxageRkA. karecalnUvkmøaMgTajbEnßmenHnwgpþl;nUvplvi)ak
y:agF¶n;F¶r.

7>9> kmøaMgpÁÜbrvagkmøaMgTaj nigkmøaMgTajenAkñúgb‘ULúg (Combined Shear and Tension

in Fasteners)
enAkñúgsßanPaBCaeRcInkartP¢ab;EtgRbQmnwgkmøaMgkat; nigkmøaMgTaj. tMNEdlTTYlbnÞúk
cMNakp©itRtUv)anerobrab;enAkñúgCMBUkTI 8. b:uEnþ sRmab;tMNsamBaØxøH eRKOgP¢ab;sßitkñúgsßanPaB
kmøaMgpÁÜb. rUbTI 7>31 bgðajBIkMNat; structural tee EdlP¢ab;eTAnwgsøabrbs;ssrkñúgeKalbMNg
edIm,IP¢ab;Ggát;BRgwg (bracing member). Ggát;BRgwgenHRtg;)andak;tMrg;y:agNaedIm,I[ExSskmμ
rbs;kmøaMgkat;tamTIRbCMuTm¶n;rbs;kartP¢ab;. bgÁúMkmøaMgbBaÄrnwgeFVI[eRKOgP¢ab;rgkugRtaMgkat; ehIy
bgÁúMkmøaMgedknwgbegáItkmøaMgTaj ¬EdlGacmankarpSMCamYynwg prying force¦. edaysarExSskmμ
rbs;kmøaMgeFVIGMeBIkat;tamTIRbCMuTm¶n;rbs;tMN eRKOgP¢ab;nImYy²RtUv)ansnμt;faTTYlkugRtaMgedaycM
ENkesμI²Kña.

tMNsamBaØ 287 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

kñúgkrNIbgÁúMkmøaMgepSgeTot eKGaceRbIviFIrUbmnþGnþrkmμ (interaction formula approach) .

ersIusþg;kmøaMgkat; nigersIusþg;kmøaMgTajsRmab;b‘ULúgRbePT bearing KWQrelIlT§plénkarBiesaF
nwgRtUv)anykBI elliptical interaction curve EdlbgðajenAkñúgrUbTI 7>32. smIkarrbs;ExSenHKW
2 2
⎡ Pu ⎤ ⎡ Vu ⎤
⎢ ⎥ +⎢ ⎥ = 1.0
⎣⎢ (φRn )t ⎦⎥ ⎢⎣ (φRn )v ⎦⎥
Edl Pu = kmøaMgTajemKuNenAelIb‘ULúg
(φRn )t = design strength rbs;b‘ULúgrgkarTaj
Vu = kmøaMgkat;TTwgemKuNenAelIb‘ULúg

(φRn )v = design strength rbs;b‘ULúgrgkarkat;

bnSMkmøaMgkat; nigkmøaMgTajEdlGacTTYlyk)anKWvaCYbKñaRtg;kEnøgEdlsßitenABIeRkamExS
ekag. enHCatRmUvkarrbs; RCSC Specification Edl
2 2
⎡ Pu ⎤ ⎡ Vu ⎤
⎢ ⎥ +⎢ ⎥ ≤ 1 .0 (RCSC Equation LRFD 4.2)
⎣⎢ (φRn )t ⎦⎥ ⎢⎣ (φRn )v ⎦⎥

T.Chhay 288 Simple Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

sRmab; slip-critical connection Edlb‘ULúgrgnUvkmøaMgkat; nigkmøaMgTaj \T§iBlrbs;kmøaMg

TajKWbn§Úrbnßy clamping force EdleFVI[mankarkat;bnßykmøaMgkkit. AISC Specification kat;
bnßy slip-critical shear strength sRmab;krNIenH. BI AISC Appendix J, slip-critical shear
strength RtUv)anKuNedayemKuN
⎡ Tu ⎤
⎢1 − ⎥ (AISC Equation A-J3-2)
⎣ 1.13Tm N b ⎦
Edl kmøaMgTajemKuNenAelItMN
Tu =

Tm = kmøaMgTajb‘ULúgedImEdl)anBI AISC Table J3.1

N b = cMnYnb‘ULúgenAkñúgtMN

cMNaMfa RCSC Equation LRFD 4.2 Edl)anbgðajenATIenHRtUv)anGnuvtþeTAelIb‘ULúgeTal Et

AISC Equation A-J3-2 Edl)anbgðajenATIenHGnuvtþeTAelItMNTaMgmUl. smIkarnImYy²Gac

RtUv)anEkERbedIm,IGnuvtþsRmab;viFIepSgeTot.

]TahrN_ 7>10³ eKeRbI WT10.5 × 31 Ca bracket edIm,IbBa¢Ún service load 60kips eTAssr
W 14 × 90 dUcEdl)anbgðajenAkñúgrUUbTI 7>31. bnÞúkpSMeLIgedaybnÞúkefr 15kips nigbnÞúkGefr

45kips . eKeRbIb‘ULúg A325 Ggát;p©it 7 / 8in. cMnYn 4 RKab;. TaMgssr nig bracket eFVIBIEdk A36 .

snμt;fatRmUvkarKMlat nigcm¶ayeTARCugEKmTaMgGs;KWRKb;RKan; edayrYmbBa©ÚlTaMgPaBcaM)ac;sRmab;

kareRbIR)as; design strengn GtibrmasRmab; bearing ¬dUcCa φ [2.4dtFu ] ¦ nigkMNt;nUvPaBRKb;RKan;
rbs;b‘ULúgsRmab;kartP¢ab;xageRkam³
¬!¦ bearing –types connection EdlmaneFμjsßitenAkñúgbøg;kat;. ¬@¦ slip-critical connection
EdlmaneFμjsßitenAkñúgbøg;kat;.
dMeNaHRsay³ bnÞúkemKuNKW
1.2 D + 1.6 L = 1.2(15) + 1.6(45) = 90kips
¬!¦ sRmab; bearing-type connection EdlmaneFμjsßitenAkñúgbøg;kat; kmøaMgkat;TTwgsrubKW
3
(90) = 54kips
5
kmøaMgkat;TTwgsRmab;b‘ULúgmYyKW

tMNsamBaØ 289 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

54
Vu = = 13.5kips
4
π (7 / 8) 2
nig Ab =
4
= 0.6013in. 2

(φRn )v = φFv Ab = 0.75(48)(0.6013)

= 21.65kips > 13.5kips
Bearing strength ¬søabrbs; tee lub¦ KW
⎛7⎞
φRn = φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟(0.615)(58)
⎝8⎠
= 56.18kips > 13.5kips (OK)
kmøaMgTajsrubKW
4
(90) = 75kips
5
kmøaMgTajsRmab;b‘ULúgmYyKW
72
Pu = = 18kips
4
BI AISC Table J3.2,
(φRn )t = φFt Ab = 0.75(90 )(0.6013) = 40.59kips > 18kips (OK)

BI RCSC Equation LRFD 4.2,

2 2
⎡ Pu ⎤ ⎡ Vu ⎤ ⎛ 18 ⎞
2
⎛ 13.5 ⎞
2
⎢ ⎥ +⎢ ⎥ =⎜ ⎟ +⎜ ⎟ = 0.585 < 1.0 (OK)
⎣⎢ (φRn )t ⎦⎥ ⎢⎣ (φRn )v ⎦⎥ ⎝ 40.59 ⎠ ⎝ 21.65 ⎠
cemøIy³ kartP¢ab;manlkçN³RKb;RKan;Ca . ¬edIm,IkMu[Bi)akyl;kñúgkar
bearing-type connection

bnSMbnÞúkrbs;]TahrN_enH prying action minRtUv)anrYmbBa©ÚleTAkñúgkarviPaKeT¦.

¬@¦ sRmab; slip-critical connection, EdlmaneFμjsßitenAkñúgbøg;kat; BIEpñk ¬!¦ shear, bearing/
and tension strength KWmanlkçN³RKb;RKan;. BI RCSC Equation LRFD 5.3, slip-critical strenght

KW
φRstr = φ (1.13μTm N b N s )
BI AISC Table J3.1, kmøaMgTajsRmab;b‘ULúg A325 Ggát;p©it 7 / 8in. KW
Tm = 39kips
RbsinebIeyIgsnμt;épÞb:HCa Class A, slip coefficent KW μ = 0.33 nigsRmab;b‘ULúgbYnRKab;
φRstr = φ (1.13μTm N b N s ) = 1.0(1.13)(0.33)(39)(4)(1) = 58.17kips
T.Chhay 290 Simple Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

edaysarvamankmøaMgTajenAelIb‘ULúg/ slip-critcal strength RtUv)ankat;bnßyedayemKuN

⎛ Tu ⎞ ⎡ 72 ⎤
⎜⎜1 − ⎟⎟ = ⎢1 − ⎥ = 0.5916
⎝ 1.13Tm N b ⎠ ⎣ 1.13(39 )(4 ) ⎦
dUcenHresIusþg;Edl)ankat;bnßyehIyKW
φRstr = 0.5916(58.17 ) = 34.4kips < 54kips (N.G.)
cemøIy³ kartP¢ab;minmanlkçN³RKb;RKan;Ca slip-critical connection eT.

kartP¢ab;edayb‘ULúgEdlrgnUvkmøaMgkat;TTwg nigkmøaMgTajGacRtUv)anKNnaedaypÞal;. eK
GaceRbI RCSC Equation 4.2 edIm,IedaHRsayTMhMb‘ULúgdUcxageRkam³
2 2 2 2
⎡ Pu ⎤ ⎡ Vu ⎤ ⎛ Pu ⎞ ⎛ Vu ⎞
⎢ ⎥ +⎢ ⎥ = ⎜⎜ ⎟⎟ + ⎜⎜ ⎟⎟
⎣⎢ (φRn )t ⎦⎥ ⎢⎣ (φRn )v ⎦⎥ ⎝ φFt ∑ Ab ⎠ ⎝ φFv ∑ Ab ⎠
2 2
⎛P ⎞ 1 ⎛V ⎞ 1
= ⎜⎜ u ⎟⎟ + ⎜⎜ u ⎟⎟
⎝ φFt ⎠ (∑ Ab )2 ⎝ φFv ⎠ (∑ Ab )2
Edl Pu =kmøaMgTajsrubenAelItMN
Ft = ultimate tensile stress rbs;b‘ULúg

Vu = kmøaMgkat;TTwgsrubenAelItMN

Fv = ultimate shear stress rbs;b‘ULúg

∑ Ab = RkLaépÞmuxkat;b‘ULúgsrub

CMnYseTAkñúg RCSC Equation LRFD 4.2, eyIg)an

2 2
⎛ Pu ⎞ 1 ⎛V ⎞ 1
⎜⎜ ⎟⎟ +⎜ u ⎟⎟ ≤ 1 .0
2 ⎜ φF
⎝ φFt ⎠ (∑ Ab ) ⎝ v ⎠ (∑ Ab )2
2 2
⎛P ⎞ ⎛V ⎞
b¤ ∑ Ab ≥ ⎜⎜ u ⎟⎟ + ⎜⎜ u ⎟⎟ ¬&>@0¦
⎝ φFt ⎠ ⎝ φFv ⎠
Edl ∑ Ab CaRkLaépÞmuxkat;b‘ULúgsrub

]TahrN_ 7>11³ tMNEdlrgbnÞúkcMp©itrgnUv service load shear force 50kips nig service tensile
force 100kips . bnÞúk
CabnÞúkefr nig 75% CabnÞúkGefr. eRKOgP¢ab;rgnUv single shear
25%

ehIy baring strength nwgRtUv)anKNnaCamYynwgEpñkEdlRtUvP¢ab;EdlmankRmas; 5 / 16in. . snμt;

tMNsamBaØ 291 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

fa KMlat nigcm¶ayeTARCugEKmTaMgGs;manlkçN³RKb;RKan; nigsnμt;faeKGnuBaØat[eRbI bearing

strength Gtibrma φ (2.4dtFu ) . kMNt;cMnYnb‘ULúg A325 Ggát;p©it 3 / 4in. EdlcaM)ac;sRmab;krNIxag

eRkam³
¬!¦ bearing-type connection CamYynwgeFμjsßitenAkñúgbøg;kat;
¬@¦ slip-critical connection CamYynwgeFμjsßitenAkñúgbøg;kat;
épÞb:HTaMgGs;man clean mill scale.
karKNnaenHmin)anBicarNa prying action sMxan;eT.
dMeNaHRsay³ kmøaMgkat;TTwgemKuN = 1.2[0.25(50)] + 1.6[0.75(50)] = 75kips
kmøaMgTajemKuN = 1.2[0.25(100)] + 1.6[0.75(100)] = 150kips
¬!¦ sRmab; bearing-type connection CamYynwgeFμjsßitenAkñúgbøg;kat; smIkar &>@0 [
2 2 2
⎛P ⎞ ⎛V ⎞ ⎡ 150 ⎤ ⎡ 75 ⎤
∑ Ab ≥ ⎜⎜ u ⎟⎟ + ⎜⎜ u ⎟⎟ = ⎢ ⎥ +⎢ ⎥ = 3.046in.2
⎝ φFt ⎠ ⎝ φFv ⎠ ⎣ 0.75(90) ⎦ ⎣ 0.75(48)⎦
RkLaépÞrbs;muxkat;eTalKW
π (3 / 4 )2
Ab = = 0.4418in.2
4
dUcenHcMnYnb‘ULúgEdlRtUvkarKW
∑ Ab 3.046
= = 6.89
Ab 0.4418
sakl,gb‘ULúg 7 RKab; ehIyRtYtBinitü bearing:
φRn = φ (2.4dtFu ) × 7
⎛ 7 ⎞⎛ 5 ⎞
= 0.75(2.4)⎜ ⎟⎜ ⎟(58)(7 ) = 171kips > 75kips
⎝ 8 ⎠⎝ 16 ⎠
¬eKminRtUvkarRtYtBinitüKMlat nigcm¶ayeTARCugEKmsRmab;karKNnacugeRkayeT¦
cemøIy³ eRbIb‘ULúg 7 RKab;. ¬RbsinebIeKerobb‘ULúgCaBIrCYr enaHeRbIb‘ULúg 8 RKab;edIm,IPaBsIuemRTI¦
¬@¦ sRmab; slip-critical connection, slip-critical strength Edl[eday RCSC Equation LRFD
RtUv)anKuNedayemKuNkat;bnßyrbs; AISC Equation A-J3-2:
⎛ ⎞
φRstr = φ (1.13μTm N b N s )⎜⎜1 −
Tu
1.13T N ⎟
⎟ ¬&>@!¦
⎝ m b⎠

T.Chhay 292 Simple Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

BI AISC Table J3.1, sRmab;b‘ULúg A325 Ggát;p©it 3 / 4in. / Tm = 28kips . CMnYs Tm eTAkñúgsmIkar
&>@!/ eyIg)an
⎛ Tu ⎞
φRstr = φ (1.13μTm N b N s )⎜⎜1 − ⎟⎟
⎝ 1.13Tm N b ⎠
⎡ ⎤
= 1.0(1.13)(0.33)(28)(N b )(1)⎢1 −
150
⎥
⎣ 1.13(28)N b ⎦
⎛ 4.741 ⎞
= 10.44⎜⎜1 − ⎟ = 10.44( N b − 4.741)
⎝ N b ⎟⎠

dak;lT§plEdlTTYl)anenH nigkmøaMgkat;TTwgEdlGnuvtþ[esμIKña enaHeyIgGacrkcMnYnb‘ULúgEdl

RtUvkaredIm,IkarBar slip³
10.44(N b − 4.741) = 75kips

N b = 11.9
edaysarb‘ULúg 7 RKab;RKb;RKan;sRmab; shear, bearing nig tension dUcenHeKminRtUvkarRtYt
BinitüsßanPaBkMNt;TaMgenHeT.
cemøIy³ eRbIb‘ULúg A325 Ggát;p©it 3 / 4in.

7>10> tMNpSar (Welded connections)

karpSarCadMeNIrkareFVI[EpñkEdlRtUvP¢ab;Cab;Kña. ]TahrN_ Ggát;rgkarTajEdlman lap
joint dUcbgðajenAkñúgrUbTI 7>33 a GacRtUv)aneFVIeLIgedaykarpSartamcugTaMgsgçagrbs;EpñkEdl

RtUvP¢ab;. kMBs;d¾tUcbMputrbs;smÖar³RtUv)anrlay eRkayBITuk[RtCak; eRKOgbgÁúMEdk nig weld

metal eFVIkardUcEpñkEdlCab;KñaenAkEnøgtMN. EdkbEnßmRtUv)andak;BI special electrode EdlCaEpñk

rbs;crnþGKÁisnIeTAelIEpñkEdlRtUvP¢ab; b¤ base metal.

tMNsamBaØ 293 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

enAkñúgdMeNIrkar shielded metal arc welding (SMAW) EdlbgðajenAkñúgrUbTI 7>34 FñÚ

GKÁisnI (current arc) kat;tamcenøaHrvag electrode nig base metal edayrMlayEpñkEdlRtUvP¢ab;
nigdak;Epñkrbs;eGLicRtUteTAkñúg base metal Edlrlay. Specail coating enAelI electrode begáIt
protective gaseous shield edaykarBar molten weld metal BIGuksIutkmμmunnwgvarwg. eKrMkil

electrode kat;tamtMN ehIy weld bead RtUv)andak; TMhMrbs;vaGaRs½ynwgGRtaéndMeNIrrbs;

electrode. enAeBlEdlTwkbnSaRtCak; impuriries elceLIgenAelIépÞ EdlbegáItCa coating EdleK

ehAfa slag ehIy slag enHRtUv)anykecjmunnwglabfñaMelIGgát; b¤EpñkepSg²EdlRtUv)anbegáIteLIg

eday electrode.

CaTUeTA Shielded metal arc welding EdlRtUv)aneFIVeLIgedayéd ehIyCadMeNIrkareKeRbICa

sklenAelIkardæan. sRmab;karpSarenAeragCag eKniymeRbIdMeNIrkarsV½yRbvtþ b¤Bak;kNþalsV½y
Rbvtþ. karRtYtBinitüKuNPaBsRmab;kartP¢ab;edaykarpSarKWmanlkçN³Bi)ak edaykarTwkbnSarEdl
minl¥sßitenABIeRkamépÞ b¤k¾PaBminl¥d¾tictYcEdlmanenAépÞbnSar GaceKcputBIExSEPñkrbs;eyIg)an.
sRmab;karpSarenARtg;kEnøgEdleRKaHfñak;eKRtUvkarCagpSarEdlmanCMnajRtwmRtUv ehIyeKRtUveRbI
bec©keTsBiessdUcCa radiography b¤ ultresonic testion.
eKniymeRbIkarpSarBIrRbePTKW fillet weld nig groove weld. Lap joint EdlbgðajenAkñúgrUb
TI 7>33 a nig b RtUv)anbegáIteLIgeday fillet weld . Groove weld RtUv)aneRbIsRmab; butt, tee
nig corner dUcbgðajenAkñúgrUbTI 7>35 a nig b. rUbTI 7>36 bgðajBI plug and slot wled Edl
eBlxøHva RtUvkaredIm,IbEnßmBIelIkarpSartamRCug. rn§ragmUl b¤RTEvgRtUv)ankat;ecjBIEpñkmYyedIm,I
T.Chhay 294 Simple Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

GacbMeBjTwkbnSar)an.

kñúgcMeNamkarpSarTaMgBIrRbePTenH eyIgnwgelIkykkar pSar fillet weld mkbkRsaylMGit

enATIenH. karKNnasRmab; complete penetration groove weld minmanlkçN³minsMxan;Edlkar
pSar manersIusþg;dUcKñanwg base metal nigEpñkEdlRtUvP¢ab;. ersIusþg;rbs; partial penetration
groove weld GaRs½yeTAnwgbrimaNén penetration. dMeNIrkarénkarKNna groove weld Rsedog

KñanwgkarKNna fillet weld.

7>11> Fillet Welds

karKNna nigkarviPaKsRmab; fillet weld KWQrelIkarsnμt;famuxkat;rbs;TwkbnSarCa
RtIekaNEkgEdlmanmMu 45o dUcbgðajkñúgrUbTI 7>37. TTwgrbs; fillet weld RtUv)ansMKal;eday w .
tMNsamBaØ 295 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

TMhMTWkbnSarbTdæanKWekIneLIgmþg 1 / 16in. = 2mm . eTaHbICaRbEvgrbs;karpSarGacrgnUvbnÞúk tam

TiskmøaMgkat;/ kmøaMgsgát; nigkmøaMgTajk¾eday k¾fillet weld manersIusþg;exSaysRmab;kmøaMgkat;
ehIyvaEtg EtRtUv)aneKsnμt;fadac;edaysarkmøaMgenH. kardac;RtUv)ansnμt;ekItmantambøg;Edl
kat;tam throat rbs;TwkbnSar. sRmab; fillet weld EdlbegáIteLIgCamYy shielded metal arc
process, throat CaRb EvgEkgBIRCugEKm b¤ root rbs;TwkbnSareTAGIub:Uetnus nigmantémøesμI 0.707

dgénTMhMTwkbnSar. ¬Effective throad thickness sRmab;TwkbnSarEdl)anBI arc welding process

manTMhMFMCag. dUcenH kñúgesovePAenH eyIgsnμt;eRbI shielded metal arc welding process¦.
dUcenHsRmab;RbEvg L Edlrg bnÞúk P / kugRtaMgkmøaMgkat;eRKaHfñak;KW
P
fv =
0.707 × w × L
Edl w CaTTwgTwkbnSar

RbsinebIeKeRbI weld ultimate shearing stress/ FW enAkñúgsmIkarenH eKGacsresr

nominal load capacity rbs;TwkbnSardUcxageRkam³

Rn = 0.707 × w × L × FW
ehIy nominal design strength KW
φRn = 0.707 × w × L × φFW ¬&>@@¦

T.Chhay 296 Simple Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

ersIusþg;rbs; fillet weld GaRs½yeTAnwgkareRbIR)as; weld metal EdlCaGnuKmn_eTAnwg

RbePT electrode. ersIusþg;rbs; electrode RtUv)ankMNt;Ca ultimate tensile strength rbs;vaCamYy
nwgersIusþg; 60, 70, 80, 90, 100, nig 120ksi b¤ 415, 480, 550, 620, 690, nig 830MPa sRmab;
shielded metal arc welding process. nimitþsBaØasRmab;kMNt; electrod KWGkSr E Edlbnþ

edayelxBIrxÞg; b¤bIxÞg;EdlbgðajBIersIusþg;rbs;vaCa ksi . edaysarEtersIusþg;CalkçN³dMbUg Edl

design engineer ykcitþTukdak; CaTUeTAGkSrBIrxÞg;cugeRkayRtUv)anbgðajeday XX ehIykMNt;

smÁal;køayCa E70 XX b¤ E 70 EdlbgðajBI electrode CamYy ultimate tensile strength 70ksi .

eKKYreRCIserIs electrode [RtUvKñaCamYynwg base metal. sRmab; grade rbs;EdkEdleRbIR)as;TUeTA
eKBicarNaEt electrode BIrRbePTb:ueNÑaHKW³
eRbI electrode E70 XX CamYynwgEdkEdlman yield strength tUcCag 60ksi
eRbI electrode E80 XX CamYynwgEdkEdlman yied strength 60ksi b¤ 65ksi
nimitþsBaØasRmab; electrode nigkarpþl;[rbs; AISC Specification EdledaHRsayCamYy
nwgTwkbnSarRtUv)andkRsg;ecjBI Structural Welding Code rbs; American Welding Society
(AWS, 1996). eKGacrk)annUvlkçxNÐEdlminmanEcgenAkñúg AISC Specification enAkñúg AWS

Code.

Design strength rbs;TwkbnSarRtUv)anbgðajenAkñúg AISC Table J2.5. Ultimate shearing

stress FW enAkñúg fillet weld esμInwg 0.6 dgén tensile strength rbs; weld metal EdlRtUv)ansM

Kal;eday FEXX . dUcenH design stress KW φFW Edl φ = 0.75 nig FW = 0.60FEXX . sRmab;
electrode FmμtaTaMgBIr design strengths (stresses) RtUv)anbgðajdUcxageRkam³

E 70 XX : φFW = 0.75[0.60(70)] = 31.5ksi

E 80 XX : φFW = 0.75[0.6(80)] = 36ksi

tRmUvkarbEnßmKWfakmøaMgkat;TTwgemKuNenAelI base metal minKYrbegáIt stress FMCag φFBM Edl
φFBM Ca nominal shear strength rbs;smÖar³EdlRtUvP¢ab;. dUcenHbnÞúkemKuNsRmab;tMNRtUv)an
kMNt;Rtwm
φRn = φFBM × area of base metal subject to shear
AISC J5, “Connecting elements” [ shear yielding strength Ca φRn Edl
tMNsamBaØ 297 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

φ = 0.90
R n = 0 .6 A g F y (AISC Equation J5-3)

nig Ag CaRkLaépÞEdlrgkmøaMgkat;TTwg. dUcenH shear strength rbs; base metal CasresrCa

φFBM = 0.90(0.6) F y = 0.54 F y

dUcenH enAeBlEdlbnÞúksßitenAkñúgTisdUcG½kSrbs;TwkbnSar eKRtUveFVIkarGegát base metal edayeRbI

TMnak;TMngénsmIkar &>@#. eKGacBnül;BItRmUvkarenHedayRtYtBinitükartP¢ab; bracket edaykar
pSar EdlbgðajenAkñúgrUbTI 7>38. edaysnμt;fa bnÞúksßitenAEk,rcugEdlpSaredayeyIgGacecal
cMNakp©it. RbsinebITWkbnSarTaMgBIrmanTMhMdUcKña design strength rbs;TwkbnSarmçag²kñúgRbEvg
ÉktþaGacRtUv)anrkBIsmIkar &>@@ Ca
0.707 × w × φFW
b:uEnþBIsmIkar &>@#/ ersIusþg;rbs; bracket plate Tb;nwgkmøaMgkat;kñúgmYyÉktþaRbEvgKW
t × φFBM
Cak;Esþg TwkbnSaminGacTb;Tl;nwgbnÞúkeRcIndUc base metal ¬kñúgkrNIenHvaCa bracket¦eT. eKdac;
xatRtUvEteFVIkarGegátenHenAeBlEdl base metal rgnUvkmøaMgkat;TTwg.
kñúgkrNIkartP¢ab;edaykarpSarCaeRcIn eTaHbICakarviPaKkþI karKNnakþI vamanPaBgayRsYl
EdleKykersIusþg;kñúgmYyÉktþaRbEvgrbs;karpSar EdlGacCaersIusþg;rbs;TwkbnSar b¤CaersIusþg;rbs;
base metal EdlmYyNatUcCagmksikSa. viFIenHnwgRtUv)anbgðajenAkñúg]TahrN_xageRkam.

]TahrN_ 7>12³ eKeRbIEdkbnÞHCaGgát;rgkarTajedayP¢ab;eTAnwg gusset pate dUcbgðajenAkñúgrUbTI

7>39. karpSarCaRbePT fillet welds 3 / 16in. EdleFVIeLIgCamYynwg electrode E70 XX . EpñkEdl
T.Chhay 298 Simple Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RtUvP¢ab;CaRbePTEdk A36 . snμt;faersIusþg;Tajrbs;Ggát;RKb;RKan; cUrkMNt; design strength rbs;

tMNpSar.

dMeNaHRsay³ edaysarkarpSarmanlkçN³sIuemRTIeFobnwgG½kSrbs;Ggát; EpñknImYy²rbs;TwkbnSar

nwgrgnUvkmøaMgEdlEbgEckesμI. manEtRbEvgsrubrbs;TwkbnSar CamYynwgkmøaMgGnuvtþpÁÜbkat;tamTI
RbCMuTm¶n;rbs;TwkbnSar ¬edayminKitcMNakp©ittictYc¦/ TItaMg nigTisedArbs;TwkbnSarnImYy²minTak;
TgeT.
ersIusþg;rbs; weld metal sRmab; electrode KW E 70
φFW = 31.5ksi
⎛3⎞
0.707 × w × φFW = 0.707⎜ ⎟(31.5) = 4.176kips / in.
⎝ 16 ⎠
RtYtBinitü ersIusþg;rbs; base metal ¬kRmas;tUcCageKlub¦. BIwsmIkar &>@#/
φRn = φFBM × area subject to shear
⎛1⎞
= φFBM × t = 0.54 F y t = 0.54(36)⎜ ⎟ = 4.86kips / in.
⎝4⎠
ersIusþg;rbs;TwkbnSarlub. sRmab;kartP¢ab;
φRn = 4.176kips / in. × (4 + 4)in. = 33.4kips
cemøIy³ ersIusþg;rbs;tMNKW 33.4kips

]TahrN_ 7>13³ RbePTtMNEdleRbIenAkñúg]TahrN_ 7>12 RtUvTb;nwgkmøaMgemKuN 40kips . etI

eKRtUvkarRbEvgTwkbnSarsrub RbePT filet weld 3 / 16in. EdleRbI electrode E70 XX b:unñan?
tMNsamBaØ 299 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

dMeNaHRsay³ ersIusþg;rbs;TwkbnSarkñúgmYyÉktþaRbEvgEdl)anBI]TahrN_TI 7>12 KW

φRn = 4.176kips / in.
RbEvgsrubEdlRtUvkarKW
40
= 9.58in.
4.176
cemøIy³ RbEvgsrubKW 10in. EdlRtUvKñanwg 5in. sRmab;mçag².
karKNnakartP¢ab;edaykarpSarTamTarnUvkarBicarNanUv TMhMTwkbnSarGb,brma nigGtibrma
nigRbEvgTwkbnSar. tRmUvkarTaMgenHsRmab; fillet welds RtUv)anbgðajenAkñúg AISC J2.2b
ehIyRtUv)an segçbdUcxageRkam³
TMhMGb,brma
TMhMGb,brmaEdlGnuBaØatCaGnuKmn_eTAnwgkRmas;rbs;EpñkEdlRtUvP¢ab;Rkas;CageK ehIy
RtUv)an[enAkñúg AISC Tabel J2.4.
TMhMGtibrma
tambeNþayRCugEKRmbs;Ggát;EdlmankRmas;tUcCag 1 / 4in. = 6.5mm TMhM fillet weld
GtibrmaesμInwgkRmas;rbs;Ggát;enaH. sRmab;Ggát;EdlRkas;CagenH TMhMGtibrmaKW t − 1 / 16in b¤
t − 2mm Edl t CaTMhMrbs;Ggát;.

RbEvgGb,brma
RbEvgGb,brmaGnuBaØatsRmab; fillet weld KWbYndgTMhMTwkbnSar. karkMNt;enHmintwgEtgeT
b;uEnþRbsinebIminGacpþl;RbEvgTwkbnSarenH)an eKGaceRbIRbEvgxøICagenH)an RbsinebI effective size
rbs;TwkbnSarRtUv)aneKykesμInwgmYyPaKbYnénRbEvfTwkbnSar. kartP¢ab;RbePTEdl)anbgðajenA
kñúgrUbTI 7>40 EdldUcKñanwg]TahrN_BImun CakrNIBiesssRmab; shear lag sRmab;kartP¢ab;eday
TwkbnSar Edl)anerobrab;enAkñúgCMBUkTI 3. AISC B3 )anbgðajfaRbEvgTwkbnSarenAkñúgkrNIenHmin
RtUvtUcCagcm¶ayrvagTwkbnSareT KW L ≥ W .

T.Chhay 300 Simple Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

End returns
enAeBlEdlTwkbnSarlatsn§wgdl;kac;RCug vaRtUvEtbnþCMuvijRCugenaH dUcbgðajenAkñúgrUbTI
7>41. mUlehtusRmab;karbnþ EdleKehAfa end return KWCakarkarBarkugRtaMgRbmUlpþúM (stress
concentration) nigFanafaTMhMTwkbnSarRtUv)anrkSaelIRbEvgeBjrbs;TwkbnSar. End return KYrEt

manRbEvgy:agticesμIBIrdgTMhMTwkbnSar. RbEvgrbs; end return GacRtUv)anKitbBa©ÚleTAkñúgkar

KNna load capacity b¤k¾eKGacecalva)an.
CaTUeTAkarpSarEdlmanTMhMtUcmantémøefakCagkarpSarEdlmanTMhMFM. TMhMGtibrmaEdl
eFVICamYynwgkarpSarmþgmanTMhMRbEhl 5 / 16in. ehIykarpSareRcIndgnwgbEnßmtémø. elIsBIenH
sRmab; load capacity EdleKsÁal; eTaHbICaTwkbnSartUcbegáItRbEvgEvgCag EtTwkbnSarTMhMFMEdl
begáItRbEvgxøInwgRtUvkarbrimaN weld metal eRcInCag.

]TahrN_TI 7>14³ r)arEdk A36 EdlmanTMhM 4 × 1 / 2in. RtUv)aneRbICaGgát;rgkarTajedIm,ITb;Tl;

nwg service dead load 6kips nig service live load 18kips . eKP¢ab;vaeTAnwg gusset plate Edlman
kRmas; 3 / 8in. dUcEdlbgðajenAkñúgrUbTI 7>42. KNnakartP¢ab;edaypSar.

dMeNaHRsay³ enAkñúgkartP¢ab;enH base metal CaEdk A36 dUcenHeyIgRtUveRbI electrode E70 XX .

edaysarEtRbEvgTwkbnSarminRtUv)ankMNt; dUcenHeyIgeRbITMhMGb,brmaGnuBaØat
TMhMGb,brma = 163 in. (AISC Table J2.4)

tMNsamBaØ 301 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

sakl,g electrode E70 XX fillet weld 3 / 16in. . lT§PaBkñúgmYyÉktþaRbEvgKW

⎛3⎞
0.707 w(φFW ) = 0.707⎜ ⎟(31.5) = 4.176kips / in.
⎝ 16 ⎠
lT§PaBrbs; base metal KW
⎛3⎞
0.54 F y t = 0.54(36)⎜ ⎟ = 7.29kips / in.
⎝8⎠
ersIusþg;rbs;TwkbnSartUcCag dUcenHeRbIvaedIm,IKNna.
bnÞúkemKuN
Pu = 1.2 D + 1.6 L = 1.2(6) + 1.6(18) = 36kips

ehIy RbEvgEdlRtUvkar =
36
4.176
= 8.62in.

RbEvgGtibrma = 4⎛⎜⎝ 163 ⎞⎟⎠ = 0.75in < 8.62in (OK)

sRmab; end return,

RbEvgGb,brma = 2⎛⎜⎝ 163 ⎞⎟⎠ = 0.375in. yk 1in.
sRmab;kartP¢ab;RbePTenH RbEvgrbs;TwkbnSarxagRtUvEtFMCagcm¶ayrvagTwkbnSar EdlkñúgkrNIenH
KW esμInwg 4in. . RbEvgTwkbnSarsrubrYmbBa©ÚlTaMg end return
2(4 + 1) = 10in. > 8.62in. EdlRtUvkar

cemøIy³ eRbI electrode E70 XX fillet weld 3 / 16in. CamYynwgRbEvg 10in. dUcEdlbgðajenAkñúgrUb
TI 7>43.

nimitþsBaØasRmab;karpSar
karpSarRtUv)ankMNt;enAelI design drawing edaynimitþsBaØasþg;dar Edlpþl;nUvviFIgayRsYl
sRmab;BN’naBItRmUvkarrbs;karpSar. PaBlMGitRtUv)an[enAkñúg Part 8 of the Manual, “Bolts,
T.Chhay 302 Simple Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Welds, and Connected Elements”(Volume II), ehIyminRtUv)anbgðajenATIenHGs;eT. enAkñúg

esovePAenH eyIgpþl;EtkarENnaMy:agsegçbBInimitþsBaØabTdæansRmab; fillet welds dUcEdlbgðajenA
kñúgrUbTI 7>44.
nimitþsBaØaeKalKWExSedk (reference line) EdlrYmmanB½t’manBI RbePT/ TMhM nigRbEvgrbs;
TwkbnSar rYmCamYynwgk,alRBYjEdlbgðajBITItaMgEdlRtUvpSar. RtIekaNEkgEdlmanRCugQrenA
xageqVgRtUv)aneRbIedIm,Ibgðaj fillet weld. RbsinebIrUbRtIekaNenHenABIeRkam reference line kar
pSarKWsßitenAxagrbs;k,alRBYj. EtpÞúymkvij ebIrUbRtIekaNenHsßitenAxagelI reference line vij
enaHkarpSarRtUvsßitenAmçageTotrbs;kartP¢ab; EdlGac)aMg b¤min)aMgenAkñúgbøg;. elxenAelI
reference line rab;BIeqVgmksþaM manTMhMTwkbnSar nigRbEvgTwkbnSar. vaKYrRtUv)andak;tamlMdab;Ebb

enH. RbsinebITaMgxagmux nigxageRkayrbs;tMNEdlP¢ab;edaykarpSar B½t’manTaMgGs;RtUvEtbgðaj

enAelI reference line TaMgelI nigeRkam. edIm,IkMNt;viFIsRsþEdlRtUveRbI b¤edIm,Ipþl;B½t’manbEnßm eK
Gacdak;knÞúyRBYjenAxagcugrbs; reference line ehIykarkMNt;bgðajGacdak;enAEk,renaH. Rbsin
ebIminmanB½t’manbEnßmeT knÞúyRBYjenaHRtUv)andkecj. cugeRkayrUbdgTg;CatiGacRtUv)andak;enA
kEnøg Edl reference line kac;edIm,IbgðajfapSarenAkardæan.

tMNsamBaØ 303 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

]TahrNI 7>15³ bnÞHEdk A36 TMhM 3 / 4 × 8in. RtUv)aneRbICaGgát;rgkarTajehIyRtUv)anP¢ab;eTAnwg

gusset plate TMhM 3 / 8in. dUcbgðajenAkñúgrUbTI 7>45. RbEvgrbs;karP¢ab;minRtUvelIsBI 8in. . KNna
karpSaredIm,IbegáItkmøaMgTajeBjdl;Ggát;.

dMeNaHRsay³ design strength rbs;Ggát;QrelI gross area rbs;vaKW

⎛3⎞
φt Pn = 0.90 F y Ag = 0.90(36)⎜ ⎟(8) = 194.4kips
⎝4⎠
bnÞab;mk KNna design strength rbs;Ggát;edayQrelI net area rbs;va. sRmab;kartP¢ab;Ggát;
bnÞH RbsinebIkarpSarsßitenAEttamRCugxag enaH Ae = UAg . EtRbsinebImankarpSartamTisTTwg
enA xagcugGgát; enaH Ae = Ag . snμt;ykkrNITIBIr enaHeyIg)an
⎛3⎞
φt Pu = 0.75Fu Ae = 0.75(58)⎜ ⎟(8) = 261kips
⎝4⎠
KNnasRmab;bnÞúkemKuN 194.4kips nigeRbI electrode E 70
φFW = 31.5ksi
BI AISC Table J2.4 TMhMTwkbnSarGb,brmaKW 1 / 4in. . sakl,g fillet weld E 70 TMhM 1 / 4in. ³
⎛1⎞
Design strength kñúgmYyÉktþaRbEvgrbs;TwkbnSar = 0.707⎜ ⎟(31.5) = 5.568kips / in.
⎝4⎠
ersIusþg;rbs; base metal = 0.54Fy t = 0.54(36)⎛⎜⎝ 83 ⎞⎟⎠ = 7.290kips / in.
RbEvgTwkbnSarEdlRtUvkar = 194 .4
5.568
= 34.9in.

tamsmμtikmμ RbEvgEdlGacpSar)anKW 8 + 8 + 8 = 24in. dUcenHeKminGaceRbITMhMTwkbnSar 1 / 4in. eT.

RbsinebIRbEvgRtUv)ankMNt;Rtwm 24in. enaHBIsmIkar &>@@ TMhMTwkbnSarEdlRtUvkarKW
T.Chhay 304 Simple Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

φRn 194.4
= = 0.364in.
0.707 × L × φFW 0.707(24 )(31.5)
sakl,g 3 / 8in.
TMhMTwkbnSarGtibrma = 34 − 161 = 16 11 3
in. > in.
8
(OK)

RbEvgTwkbnSar = 4⎛⎜⎝ 8 ⎞⎟⎠ = 1.5in. < 24in.

3
(OK)

cemøIy³ eRbIkarpSardUcbgðajkñúgrUbTI 7>46.

tMNsamBaØ 305 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

VIII. tMNcakp©it
Eccentric Connections
8>1> ]TahrN_sRmab;tMNcakp©it (Examples of Eccentric Connections)

tMNcakp©itCatMNmYyEdlkmøaMgpÁÜbminkat;tamTIRbCMuTm¶n;rbs;eRKOgP¢ab; b¤TWkbnSar. Rbsin

ebItMNmanbøg;sIuemRTI eKeRbITIRbCMuTm¶n;rbs;RkLaépÞkmøaMgkat;rbs;eRKOgP¢ab; b¤TwkbnSarCacMNuc
eKal (reference point) ehIycm¶ayEkgBIExSskmμrbs;kmøaMgeTATIRbCMuTm¶n;RtUv)aneKehAfa cMNak
p©it. eTaHbICatMNCaeRcInGacrgnUvkmøaMgcakp©it EtkñúgkrNICaeRcIncMNakp©itTaMgenaHmantémøtUc
EdlGacecal)an.
kartP¢ab; framed beam EdlbgðajenAkñúgrUbTI 8>1 a CaRbePTmYyéntMNcakp©it. kart
P¢ab;enH eTaHCakñúgTRmg;tP¢ab;edayb‘ULúg b¤edaypSark¾eday vaRtUv)aneKeRbICaTUeTAsRmab;tP¢ab;Fñwm
eTAssr. eTaHbICacMNakp©itkñúgtMNRbePTenHGacecal)ank¾eday EtvaRtUv)anykmkbgðajenATI
enH. vamankartP¢ab;BIrepSgKñaKW kartP¢ab;BIEdkEkgeTAEdkFñwm nigkartP¢ab;EdkEkgeTAEdkssr.
kartP¢ab;TaMgenHbgðajBItMNcakp©iteKalBIrRbePT³ tMNcMNakp©itEdlbegáItEtkmøaMgkat;TTwgenAkñúg
eRKOgP¢ab; b¤TwkbnSar nigtMNcMNakp©itEdlbegáItTaMgkmøaMgkat;TTwg nigkmøaMgTaj.

RbsinebIeKBicarNaFñwm nigEdkEkgdac;edayELkBIssr dUcEdlbgðajenAkñúgrUbTI 8>1 b

enaHvabgðajy:agc,as;fa Rbtikmμ R eFVIGMeBIcMNakp©it e BITIRbCMuTm¶n;rbs;RkLaépÞrbs;eRKOgP¢ab;enA
T.Chhay 306 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

kñúgRTnugFñwm. dUcenHeRKOgP¢ab;TaMgenHrgTaMgkmøaMgkat;TTwg nigm:Um:g;KU (couple) EdlsßitenAelI

rbs;tMN ehIybegáItCakugRtaMgkmøaMgkat;rmYl (torsional shearing stress).
RbsinebIssr nigEdkEkgRtUv)anpþac;ecjBIFñwm dUcbgðajenAkñúgrUbTI 8>3 c enaHeyIgeXIj
y:agc,as;fa eRKOgP¢ab;enAkñúgsøabssrrgnRbtikmμ R EdlmanGMeBIenAcMNakp©it e BIbøg;rbs;eRKOg
P¢ab; edaybegáIt couple dUcBImun. b:uEnþ kñúgkrNIenH bnÞúkminsßitenAkñúgbøgr; bs;eRKOgP¢ab; dUcenH
couple eFVI[EpñkxagelIrbs;tMNrgkugRtaMgTaj ehIyEpñkxageRkamrgkugRtaMgsgát;. dUcenH eRKOg

P¢ab;enAEpñkxagelIbMputrbs;tMNrgTaMgkmøaMgkat;TTwg nigkmøaMgTaj.
eTaHbICa eyIgeRbIkartP¢ab;edayb‘ULúgenATIenHedIm,Ibgðajk¾eday k¾kartP¢ab;edaykarpSar
Gacbgðajy:agsmBaØBIkarrgEtkmøaMgkat;TTwg b¤kmøaMgkat;TTwgrYmTaMgkmøaMgTaj.
RbtikmμbnÞúkemKuNGtibrmasRmab;tMN framed beam epSg²RtUv)an[enAkñúg Table 9-2
rhUtdl; 9-12 in Part 9 of the Manual, “Simple Shear and PR Moment Connections” (Volume
II). cMNap©itEdltUcEmnETnsRmab;tMNenHGacecal)an ehIyeKBicarNaEtkmøaMgkat;TTwgEt

b:ueNÑaH.

8>2> tMNcMNakp©itedayb‘ULúg³ EtkmøaMgkat; (Eccentric Bolted Connections: Shear only)

rUbTI 8>2 EdlbgðajBI column bracket connection Ca]TahrN_BItMNedayb‘ULúgEdlrg
kmøaMgkat;TTwgcakp©it. eKmanviFIBIrsRmab;edaHRsaybBaðaenH³ traditional elastic analysis ¬viPaK
eGLasÞicburaN¦ nigviFIEdlmanlkçN³suRkitCag ¬b:uEnþsμúKsμajCag¦ Ca ultimate strength
analysis ¬viPaKersIusþg;cugeRkay¦. viFITaMgBIrenHnwgRtUv)anbgðaj.

tMNcakp©it 307 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Elastic Analysis
enAkñúgrUbTI 8>3 a, RkLaépÞkmøaMgkat;TTwgrbs;eRKOgP¢ab; nigbnÞúkRtUv)anbgðajdac;eday
ELkBIssr nig bracket plate. eKGacdak;bnÞúkcMNakp©it P CamYynwgbnÞúkdUcKñaEdlmanGMeBIRtg;
TIRbCMuTm¶n;rYmCamYynwg couple, M = Pe Edl e CacMNakp©it. RbsinebIeyIgeFVIEbbenH bnÞúknwgman
GMeBIcMp©it ehIyeKsnμt;faeRKOgP¢ab;nImYy²Tb;Tl;nUvcMENkbnÞúkesμI²Kña KW pc = P / n Edl n CacMnYn
eRKOgP¢ab;. kmøaMgeRKOgP¢ab;Edl)anBI couple Gacrk)anedaysnμt;fakugRtaMgkmøaMgkat;TTwgenAkñúg
eRKOgP¢ab;CalT§plrbs; torsion énmuxkat;EdlekItBIRkLaépÞmuxkat;rbs;eRKOgP¢ab;. RbsinebI
eyIgeFVIkarsnμt;EbbenH kugRtaMgkMMlaMgkat;enAkñúgeRKOgP¢ab;nImYy²GacRtUv)anrkBIrUbmnþkmøaMgrmYl
fv =
Md
J
¬*>!¦
Edl d = cm¶ayBITIRbCMuTm¶n;rbs;RkLaépÞeTAcMNucEdlkugRtaMgkMBugRtUv)ankMNt;
J = m:Um:g;niclPaBb:UElrba;RkLaépÞeFobTIRbCMuTm¶n;

ehIykugRtaMg f v EkgeTAnwg d . eTaHbICarUbmnþkmøaMgrmYlGnuvtþn_)anEtcMeBaHragsIuLaMg EteKeRbIva

enATIenHedIm,IsnSMsMéc edaysar yielding stress mantémøFMCagkugRtaMgBitR)akd.

RbsinebIeKeRbIRTwsþIbTG½kSRsb (parallel-axis theorem) ehIyeKecalm:Um:g;niclPaBb:UElr

énRkLaépÞeFobG½kSTIRbCMuTm¶n;rbs;va enaHeKGackMNt; J sRmab;RkLaépÞsrubKW
T.Chhay 308 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

J = ∑ Ad 2 = A ∑ d 2
edayRKb;eRKOgP¢ab;manRkLaépÞ A dUcKña. enaHsmIkar *>! GacRtUv)ansresrCa
Md
fv =
A∑ d 2
ehIykmøaMgkat;enAkñúgeRKOgP¢ab;nImYy²EdlekIteLIgeday couple KW
Md Md
Pm = Af v = A =
2
A∑ d ∑d2
dUcenHbgÁúMkmøaMgkat;TTwgTaMgBIrEdl)ankMNt;RtUv)anbUkbEnßmedaybBaÄredIm,ITTYl)ankmøaMgpÁÜb P
dUcbgðajenAkñúgrUbTI 8>3 b EdleyIgykeRKOgP¢ab;enAxagsþaMEpñkxageRkameKbMputmkbgðaj. enA
eBlEdleKkMNt;)ankmøaMgpÁÜbFMCageKbMput TMhMeRKOgP¢ab;k¾RtUv)aneRCIserIsedIm,ITb;Tl;kmøaMgenaH.
eKminGaceFVIkarGegátedIm,IrkeRKOgP¢ab;EdleRKaHfñak;CaeKeT KWeKRtUveFVIkarKNnaCatémøelx.
CaTUeTA vamanlkçN³gayRsYlCagkñúgkareFVIkarCamYynwgbgÁúMkmøaMgctuekaNEkg. sRmab;
eRKOgP¢ab;nImYy² bgÁúMkmøaMgedk nigbgÁúMkmøaMgQrEdl)anBIkmøaMgkat;TTwgedaypÞal;KW
Py
pcx = x
P
n
ni g pcy =
n
Edl Px nig Py CabgÁúMkmøaMgtamTis x nigTis y rbs;kmøaMgsrub P dUcEdl)anbgðajenAkñúgrUbTI
8>4. eKGacrkbgÁúMkmøaMgedk nigQrEdlekIteLIgedaycMNakp©itdUcxageRkam.

cm¶ayBITIRbCMuTm¶n;rbs;tMNeTAeRKOgP¢ab;nImYy²
(
∑ d 2 = ∑ x2 + y2 )
Edl cMNucrYmrbs;RbB½n§kUGredaenKWCaTIRbCMuTm¶n;énRkLaépÞkmøaMgkat;rYmrbs;eRKOgP¢ab;. kmøaMgpÁÜb
tamTis x rbs; pm KW³
tMNcakp©it 309 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

y y Md y Md My
p mx =
d
pm =
d ∑d 2
=
2
d ∑x +y 2
(=
) (
∑ x + y2
2
)
dUcenH pmy = Mx
(
∑ x2 + y2 )
ehIykmøaMgeRKOgP¢ab;srubKW
p= (∑ p x )2 + (∑ p y )2
Edl ∑ p x = pcx + p mx

∑ p y = pcy + p my

RbsinebI P ¬bnÞúkEdlGnuvtþeTAelItMN¦ CabnÞúkemKuN enaHkmøaMg p enAelIeRKOgP¢ab;Ca bnÞúkem

KuNedIm,ITb;Tl;nwg shear nig bearing EdlCa design strength EdlRtUvkar.

]TahrN_ 8>1³ kMNt;kmøaMgrbs;eRKOgP¢ab;EdleRKaHfñak;enAkñúg bracket connection Edl)anbgðaj

enAkñúgrUbTI 8>5.

dMeNaHRsay³ TIRbCMuTm¶n;rbs;RkumeRKOgP¢ab;GacRtUv)anrkedayeRbIG½kSedkkat;tameRkam nigeday

GnuvtþeKalkarN_m:Um:g;
2(5) + 2(8) + 2(11)
y= = 6in.
8
bgÁúMkmøaMgQr nigkmøaMgedkKW
Px =
1
5
(50) = 22.63kips ← nig Py =
2
5
(50) = 44.72kips ↓
T.Chhay 310 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

edayeyageTAtamrUbTI 8>6 a, eyIgGacKNnam:Um:g;rbs;bnÞúkeFobTIRbCMuTm¶n;³

M = 44.72(12 + 2.75) − 22.36(14 − 6 ) = 480.7in. − kips ¬RsbRTnicnaLika¦

rUbTI 8>6 b bgðajBITisedArbs;bgÁúMkmøaMgb‘ULúg nigTMhMénbgÁúMkmøaMgb‘ULúgEdlRtUvKñaEdlekIteLIg

edaym:Um:g;KUr (couple). edayeRbITisedATaMgenH nigTMhMEdlRtUvKñaCakarnaMpøÚvEdlkmøaMgTaMgenaH
RtUv)anbUktamc,ab;RbelLÚRkam. eyIgGacsnñidæan)anfaeRKOgP¢ab;xagsþaMEpñkxageRkameKbMput
nwgmankmøaMgpÁÜbFMCageKbMput.
bgÁúMkmøaMgedk nigbBaÄrrbs;eRKOgP¢ab;nImYy²Edl)anBIkmøaMgcMp©itKW
= 2.795kips ← nig pcy =
22.36 44.72
pcx = = 5.590kips ↓
8 8
sRmab; couple
( ) [ ]
∑ x 2 + y 2 = 8(2.75)2 + 2 (6 )2 + (1)2 + (2 )2 + (5)2 = 192.5in 2

tMNcakp©it 311 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

My 480.7(6 )
p mx =
(∑x +y 2
) 2
=
192.5
= 14.98kips ←

Mx 480.7(2.75)
∑ (x 2 + y 2 )
p my = = = 6.867kips ↓
192.5

∑ p x = 2.795 + 14.98 = 17.78kips ←

∑ p y = 5.590 + 6.867 = 12.46kips ↓

P= (17.78)2 + (12.46)2 ¬emIlrUbTI 8>6 c¦

= 21.7 kips

cemøIy³ kmøaMgb‘ULúgEdleRKaHfñak;KW 21.7kips . karGegátBITMhM nigTisedArbs;bgÁúMkmøaMgedk

nigbBaÄrbBa¢ak;fakarsnñidæanfaeRKOgP¢ab;Edl)aneRCIserIsBitCamaneRKaHfñak;Emn.

Ultimate Strength Analysis

viFIEdlerobrab;BIxagmuxmanlkçN³gayRsYlkñúgkarGnuvtþ b:uEnþminsuRkit. kñúgkarviPaK KW
)ansnñidæanfaTMnak;TMngbnÞúk-kMhUcRTg;RTayrbs;eRKOgP¢ab;manlkçN³smamaRt ¬CabnÞat;¦ ehIy
fa yield stress minRtUvFM. karBiesaFn_bgðajfavaminEmnCakrNI ehIyfaeRKOgP¢ab;nImYy²minman
shear yield stress BitR)akdeT. viFIsaRsþEdlBN’naenATIenHkMNt; ultimate strength rbs;tMN

edayeRbITMnak;TMngminsmamaRtbnÞúk-kMhUcRTg;RTayEdlkMNt;edaykarBiesaFn_ sRmab;eRKOgP¢ab;
nImYy².
karsikSaedaykarBiesaFEdlraykarN_enAkñúg Crawford and Kulak (1971) edayeRbI
b‘ULúgRbePT bearing A325 Ggát;p©it 3 / 4in. nigEdkbnÞH A36 b:uEnþlT§plGaceRbIsRmab;b‘ULúg
A325 EdlmanTMhMepSg²CamYynwgEdkRbePTepSg²CamYynwglT§pllMeGogtictYc. viFIenHnwgpþl;

nUvlT§pllMeGogenAeBleRbICamYyb‘ULúg slip-critical nigCamYyb‘ULúg A490 (AISC, 1994).

kmøaMgb‘ULúgEdlRtUvnwgkMhUcRTg;RTay Δ KW
(
R = Rult 1 + e − μΔ )λ
(
= 74 1 − e10Δ )0.55 ¬*>@¦
Edl Rult = kmøaMgkat;TTwgrbs;b‘ULúgenAeBldac; = 74kips = 330MPa
e = eKalrbs;elakenEB = 2.718

μ = emKuNkat;bnßy = 10
λ = emKuNkat;bnßy = 0.55

T.Chhay 312 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Ultimate strength rbs;tMNKWQrelIkarsnμt;dUcxageRkam³

!> enAeBldac; RkumeRKOgP¢ab;vilCMuvij instantaneous center (IC).
@> kMhUcRTg;RTayrbs;ERKOgP¢ab;mYy²smamaRteTAnwgcm¶ayBI IC nwgeFVIGMeBIEkgeTAkaMén
rgVil.
#> eKGacTTYl)anlT§PaBrbs;tMNenAeBlEdl ultimate strength rbs;eRKOgP¢ab;enAq¶aybM
putBI IC. ¬rUbTI 7>8 bgðajBIkmøaMgb‘ULúgCakmøaMgTb;Tl;EdleFVIGMeBIRbqaMgnwgkmøaMg
Gnuvtþn_¦.
$> EpñkEdlRtUvP¢ab;RtUvEtrwg.
Cavi)akénkarsnμt;TIBIr kMhUcRTg;RTayrbs;eRKOgP¢ab;nImYy²KW
Δ=
r
Δ max =
r
(0.34)
rmax rmax
Edl cm¶ayBI IC eTAeKOgP¢ab;
r=

rmax = cm¶ayeTAeRKOgP¢ab;EdlenAq¶aybMput

Δ max = kMhUcRTg;RTayrbs;eRKOgP¢ab;q¶aybMputenA ultimate = 0.34in. ¬EdlkMNt;eday

karBiesaFn_¦

CamYynwg elastic analysis, vamanPaBgayRsYlCagkñúgkareFVIkarCamYynwgbgÁúMkmøaMgctuekaNEkg b¤

Ry = R
x
r
b¤ y
Rx = R
r

tMNcakp©it 313 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Edl x nig y Cacm¶ayedk nigcm¶aybBaÄrBI instantaneous center eTAeRKOgP¢ab;. enAxN³eBl

dac; lMnwgRtUv)anrkSa ehIysmIkarlMnwgbIxageRkamRtUv)anGnuvtþeTAelIRkumeRKOgP¢ab; ¬eyageTAelI
rUbTI 8>7¦³
m
∑ Fx = ∑ (R x )n − Px = 0 ¬*>#¦
n =1
m
M IC = P(ro + e ) − ∑ (rn × Rn ) = 0 ¬*>$¦
n =1

ehIy ∑ Fy = ∑(R y )n − Py = 0
m
¬*>%¦
Edl Gnu)at n kMNt;nUveRKOgP¢ab;mYy² nig m CacMnYnsrubrbs;eRKOgP¢ab;. viFIsaRsþTUeTAKWsnμt;TI
taMg instantaneous center bnÞab;mkkMNt;témøRtUvKñarbs; P EdlbMeBjsmIkarlMnwg. RbsinebI
GBa©wgEmn TItaMgenHKWRtwmRtUv ehIy P CalT§PaBrbs;tMN. viFIsaRsþCak;lak;KWdUcxageRkam³
!> snμt;témøsRmab; ro .
@> edaHRsayrk P BIsmIkar *>$.
#> CMnYs ro nig P eTAkñúgsmIkar *># nig *>%.
$> RbsinebIsmIkarTaMgenaHRtUv)anbMeBjCamYynwgkRmitlMeGogEdlGacTTYlyk)an kar
viPaKenHRtUv)anbBa©b;. EtebImindUecñaHeT eKRtUveFVIkareRCIserIstémøsakl,g ro fμI ehIy
eKRtUveFVIkarKNnaeLIgvij.
sRmab;krNITUeTAénbnÞúkbBaÄr smIkar *># nwgRtUv)anbMeBjedays½VyRbvtþ. edIm,IPaBgay
RsYl nigkMu[)at;bg;»PasPaB eyIgBicarNaEtkrNIenH. EteTaHbICamYykarsnμt;enH karKNna
sRmab; trial problem CaeRcInmanlkçN³lM)ak EdlRtUvkarCMnYykMuBüÚT½rCacaM)ac;. Epñk (B) rbs;
]TahrN_ 8>2 RtUv)aneFVIkarCamYynwgCMnYyBI standard spreadsheet program sRmab; personal
computers.

]TahrN_ 8>2³ Bracket connection EdlbgðajenAkñúgrUbTI 8>8 RtUvRTkmøaMgemKuNcakp©it 53kips .

tMNRtUv)anKNnaeday[manb‘ULúgBIrCYrQr EdlkñúgmYyCYr²manb‘ULúg 4 RKab; Etb‘ULúgmYyRKab;
RtUv)andkecaledayKμanectna. RbsinebIeKeRbIb‘ULúg bearing-type A325 EdlmanGgát;p©it 7 / 8in.
etItMNenHmanlkçN³RKb;RKan;b¤Gt;? snμt;faeFμjb‘ULúgsßitenAkñúgbøg;kat;. eRbIEdk A36 nigGnuvtþ
nUvkarviPaKxageRkam³ (a) elastic analysis; (b) ultimate strength analysis.
T.Chhay 314 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dMeNaHRsay³ a. Elastic analysis. sRmab;RbB½n§kUGredaenEdlmanKl;enARtg;p©itrbs;b‘ULúgxag

eRkamEpñkxageqVg ¬rUbTI 8>9¦
2(3) + 2(6 ) + 1(9 )
y= = 3.857in.
7
3(3)
x= = 1.286in.
7
( )
∑ x 2 + y 2 = 4(1.286 )2 + 3(1.714 )2 + 2(3.857 )2 + 2(0.857 )2 + 2(2.143)2 + 1(5.143)2 = 82.29in.2

e = 3 + 5 − 1.286 = 6.714in.
M = Pe = 53(6.714 ) = 355.8in. − kips ¬RsbRTnicnaLika¦
53
pcy = = 7.571kips ↓ pcx = 0
7
BITisedA nigTMhMEdlRtUvKñaEdlbgðajenAkñúgrUbTI 8>9 b‘ULúgeRkameKEpñkxagsþaMRtUv)ancat;TukfaCa
b‘ULúgEdlmaneRKaHfñak;CageK
My 355.8(3.857 )
p mx =
( )
∑ x2 + y2
=
82.29
= 16.68kips ←

Mx 355.8(1.714 )
∑ (x + y )
Pmy = = = 7.411kips ↓
2 2 82.29

∑ p x = 16.68kips
∑ p y = 7.571 + 7.411 = 14.98kips

p= (16.68)2 + (14.98)2 = 22.4kips

tMNcakp©it 315 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

edIm,IkMNt; design strength rbs;b‘ULúgrg bearing eRbIGgát;p©itrn§

1 7 1 15
h=d+ = + = in.
16 8 16 16
sRmab;rn§EdlenAEk,rRCugEKmCageK eRbI Le = 2in. enaH
h 15 / 16
Lc = Le − = 2− = 1.513in.
2 2
⎛7⎞
2d = 2⎜ ⎟ = 1.75in.
⎝8⎠
eday Lc < 2d bearing strength KW
φRn = φ (1.2 Lc tFu ) = 0.75(1.2)(1.531)(0.455)(58) = 36.4kips / bolt
sRmab;rn§epSgeTot eRbI s = 3in. enaH
15
Lc = s − h = 3 − = 2.062in. > 2d
16
⎛7⎞
dUcenH φRn = φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟(0.455)(58) = 41.56kips / bolt
⎝8⎠
témø bearing TaMgBIrFMCagkmøaMgkñúgmYyb‘ULúg dUcenH bearing strength KWRKb;RKan;.
sRmab; shear
π (7 / 8)2
Ab = = 0.6013in.2
4
φRn = φFv Ab = 0.75(48)(0.6013) = 21.6kips < 22.4kips (N.G.)
cemøIy³ tMNminbMeBjlkçxNÐeday elastic analysis.

T.Chhay 316 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

b.eyIgedaHRsaytamviFI ultimate strength analysis CamYynwgCMnYyrbs; standard spreadsheet

software. lT§plrbs;témøsakl,gcugeRkayrbs; ro = 1.57104in. RtUv)an[enAkñúgtarag 8>1.

RbB½n§kUGredaen nigelxerogb‘ULúgRtUv)anbgðajenAkñúgtarag 8>10.

tarag 8>1
eKalenARtg; eKalenARtg;
eRKOg
b‘ULúgelx ! IC
Δ Ry
P¢ab; r R rR

x' y' x y
1 0.000 0.000 0.285 -3.857 3.868 0.255 70.774 273.731 5.221

2 3.000 0.000 3.285 -3.857 5.067 0.334 72.553 367.598 47.045

3 0.000 3.000 0.285 -0.857 0.903 0.060 47.649 43.046 15.050

4 3.000 3.000 3.285 -0.857 3.395 0.224 69.563 236.188 67.310

5 0.000 6.000 0.285 2.143 2.162 0.143 63.631 137.555 8.398

6 3.000 6.000 3.285 2.143 3.922 0.259 70.891 278.061 59.377

7 0.000 9.000 0.285 5.143 5.151 0.340 72.631 374.107 4.023

srub 1710.287 206.424

tMNcakp©it 317 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

BIsmIkar *>$
P(ro + e ) = ∑ rR
∑ rR 1710.29
P= = = 206.424kips
ro + e 1.57104 + 6.71429
Edl e RtUv)anyk 5 xÞg;eRkayex,ósedIm,IsuRkitPaBx<s;.
BIsmIkar *>%
∑ F y = ∑ R y − P = 206.424 − 206.424 = 0.00

bnÞúkEdlGnuvtþminmnabgÁúMkmøaMgedk dUcenHsmIkar *># RtUv)anbMeBjedaysV½yRbvtþ.

bnÞúk 206.424kips EdleTIbnwg)ankMNt;Ca failure load sRmab;kartP¢ab; ehIyRtUv)anQr
enAelIeKalkarN_EdleRKOgP¢ab;EdleRKaHfñak;eTAdl; ultimate load capacity. RbsinebIbnÞúkdac;
rbs;tMNRtUv)anKuNedaypleFob fasterner design strength elI fasterner ultimate strength
74kips (Crawford nig Kulak, 1971), eyIgnwgTTYl)anlT§PaBrbs;tMN.

BI a. design strength rbs;b‘ULúgmYy ¬EdlQrelI shear¦ KW 21.6kips .

bnÞúkemKuNGtibrma = 206(21.6 / 74) = 60.1kips > 53kips (OK)
cemøIy³ kartP¢ab;manlkçN³RKb;RKan;eday ultimate strength analysis.

Table 8-18dl; 8-25 enAkñúg Part 8 of the Manual (Volume II) pþl;[emKuNsRmab;viPaK
b¤KNnaKMrUFmμtaénRkumb‘ULúgEdlrgnUvbnÞúkcakp©it. sRmab;kartMeobb‘ULúgnImYy²Edl)anBicarNa
taragTaMgenaHpþl;nUvtémø C EdlCapleFob connection failure load elI fasterner ultimate
strength. edImI,TTYl)anbnÞúktMNEdlmansuvtßiPaB témøefrenHRtUv)anKuNeday design strength

rbs;eRKOgP¢ab;EdleRbI. sRmab;bnÞúkcakp©itminRtUv)anbBa©ÚleTAkñúgtaragTaMgenHeT dUcenH eKGac

eRbI elastic method EdlCaviFImansuvtßiPaB. BitNas; kmμviFIkMuBüÚT½r b¤ spreadsheet software k¾RtUv
)aneRbIedIm,IKNna ultimate strength anlysis.

]TahrN_ 8>3³ eRbItaragenAkñúg Part 8 of the Manual edIm,IkMNt; factored load capacity Pu Edl
QrelI bolt shear sRmab;tMNEdlbgðajenAkñúgrUbTI 8>11. b‘ULúg bearing-type A325 Ggát;p©it
3 / 4in. edayeFμjsßitenAkñúgbøg;kat;. b‘ULúgrgnUv single shear.

T.Chhay 318 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

design strength rbs;b‘ULúgGgát;p©it 3 / 4in. Edlrg single shear KW

φrn = φ (48)Ab = 0.75(48)(0.4418) = 15.90kips
eday C = Pu / φrn /
Pu = Cφrn = 1.53(15.90 ) = 24.3kips
cemøIy³ lT§PaBbnÞúkemKuNGtibrma (maximum factored load capacity) rbs;tMNKW 24.3kips .

8>3> tMNcMNakp©itedayb‘ULúg³ kmøaMgkat;bUknwgkmøaMgTaj

Eccentric Bolted Connections: Shear Plus Tension
sRmab;kartP¢ab;EdleKeRbI tee stub bracket dUckñúgrUbTI 8>12 bnÞúkcMNakp©itbegáIt couple
EdlGacbegáInkmøaMgTajenAkñúgCYrxagelIrbs;eRKOgP¢ab; ehIykat;bnßykugRtaMgTajenAkñúgCYrxag
eRkam. RbsinebIeRKOgP¢ab;Cab‘ULúgEdlKμankugRtaMgTajedIm b‘ULúgxagelInwgRtUv)andak;[rgkug
RtaMgTaj ehIyb‘ULúgxageRkamnwgminrg\T§iBl. edayminKitBIRbePTrbs;eRKOgP¢ab; b‘ULúgnImYy²
nwgrgnUvcMENkkmøaMgkat;esμI²Kña.

tMNcakp©it 319 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

RbsinebIeRKOgP¢ab;Cab‘ULúgersIusþg;x<s;EdlrgeRbkugRtaMg épÞb:Hrvagsøabssr nigsøab

bracket nwgrgkarsgát;esμI munnwgkmøaMgxageRkAGnuvtþmk. Bearing pressure nwgesμInwgkmøaMgTaj

b‘ULúgsrubEdlEckedayépÞb:H. edaysarbnÞúk P Gnuvtþbnþicmþg² kmøaMgsgát;enAxagelInwgRtUv)an

kat;bnßy ehIykmøaMgsgát;enAxageRkamnwgekIneLIg dUcbgðajenAkñúgrUbTI 8>13 a. enAeBlEdlkM
laMgsgát;enAxagelIRtUv)anrMsayGs;rlIg bgÁúMkmøaMgnwgRtUv)anbMEbk ehIy couple Pe nwgRtUv)an
Tb;Tl;edaykmøaMgb‘ULúgTaj ehIykmøaMgsgát;enAelIépÞb:HEdlenAsl; dUcEdlbgðajenAkñúgrUbTI
8>13 b. enAeBlEdlkmøaMgxiteTArk ultimate load kmøaMgenAkñúgb‘ULúgnwgxiteTACit ultimate
tensile strength rbs;va.

viFIEdlsamBaØ nigmansuvtßiPaBRtUv)aneRbIenATIenH. eKsnμt;G½kSNWtrbs;tMNkat;tamTIRbCMu

Tm¶n;rbs;RkLaépÞb‘ULúg. bU‘LúgEdlsßitenABIxagelIG½kSenHrgkmøaMgTaj ehIyb‘ULúgEdlenABIxag
eRkamG½kSenHRtUv)ansnμt;fargkmøaMgsgát; dUcbgðajenAkñúgrUbTI 8>13 c. b‘ULúgnImYy²RtUv)ansnμt;
faTTYl)antémø ultimate rut . edaysarEtmanb‘ULúgBIrRKab;enARKb;nIv:U ¬rUbTI 8>13 c¦ kmøaMgnI-
mYy²RtUv)anbgðaj 2rut . kmøaMgpÁÜbénkmøaMgTaj nigkmøaMgsgát;Ca couple EdlesμInwgm:Um:g;Tb;rbs;
tMN. m:Um:g; couple GacRtUv)anrkedayeFVIplbUkm:Um:g;énkmøaMgb‘ULúgeFobG½kSNamYyEdlgayRsYl
dUcCaG½kSNWt. enAeBlEdlm:Um:g;Tb;RtUv)andak;[esμIm:Um:g;Gnuvtþn_ eKGacrkkmøaMgTajb‘ULúg rut
EdlminsÁal;BIsmIkarEdlTTYl)an. ¬viFIenHRsedogKñanwg Case II in Part 8 of the Manual,
Volume II).

T.Chhay 320 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

]TahrN_ 8>4³ tMN beam-to-column RtUv)anbegáIteLIgeday structural tee dUcbgðajenAkñúgrUbTI

8>14. eKeRbIb‘ULúg fully tightened bearing-type A325 Ggát;p©it 3 / 4in. cMnYn 8 RKab;edIm,IP¢ab;
søabrbs; tee eTAnwgsøabssr. cUrGegátPaBRKb;RKan;rbs;tMN ¬tee-to-column connecvtion¦ Rb
sinebIvargbnÞúkemKuN 88kips enAcMNakp©it 3in. . snμt;faeFμjb‘ULúgsßitenAkñúgbøg;kat;. EdkTaMg
Gs;Ca A36 .

dMeNaHRsay³ shear/bearing load sRmab;b‘ULúgmYyKW 88 / 8 = 11kips . sRmab; bearing design

strength eRbIGgát;p©itRbehag
1 3 1 13
h=d+ = + = in.
16 4 16 16
sRmab;RCugEdlenAEk,rRCugEKmCageKbMput yk Le = 1.5in. . enaH
h 13 / 16
Lc = Le − = 1.5 − = 1.094in.
2 2
⎛3⎞
2d = 2⎜ ⎟ = 1.5in.
⎝4⎠
edaysar Lc < 2d /
φRn = φ (1.2 Lc tFu ) = 0.75(1.2)(1.094)(0.560)(58) = 31.98kips > 11kips (OK)
sRmab;RbehagepSgeTotyk s = 3in. . enaH
13
Lc = s − h = 3 − = 2.188in. > 2d
16
⎛3⎞
dUcenH φRn = φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟(0.560)(58) = 43.85kips > 11kips
⎝4⎠
(OK)

tMNcakp©it 321 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

tMNmanlkçN³RKb;RKan;sRmab; bearing.
sRmab; shear design strength
π (3 / 4 )2
Ab = = 0.4418in 2
4
φRn = φFv Ab = 0.75(48)(0.4418) = 15.90kips
KNnakmøaMgTajsRmab;b‘ULúgmYy nwgbnÞab;mkRtYtBinitü tension-shear interaction. edaysarPaB
sIuemRTI TIRbCMuTm¶n;sßitenAkm<s;Bak;kNþal. rUbTI 8>15 bgðajRkLaépÞb‘ULúg nigkarEbgEckkmøaMg
Tajb‘ULúg.
m:Um:g;rbs; resisting couple RtUv)anrkedayeFVIplbUkm:Um:g;eFobG½kSNWt³
∑ M NA = 2rut (4.5 + 1.5 + 1.5 + 4.5) = 24rut
m:Um:g;EdlGnuvtþKW
M u = Pu e = 88(3) = 264in. − kips
dak;m:Um:g;Tb; nigm:Um:g;Gnuvtþn_[esμIKña eyIg)an
24rut = 264 b¤ rut = 11kips

Tensile design strength KW

φRn = φFt Ab = 0.75(90)(0.4418) = 29.82kips

RtYtBinitü RCSC Equation LRFD 4.2 BI bolt specification (RCSC, 1994) CamYynwg
Pu = rut = 11kips nig Vu = bolt shear force = 11kips
2 2
⎡ Pu ⎤ ⎡ Vu ⎤ ⎛ 11 ⎞
2
⎛ 11 ⎞
2
⎢ ⎥ +⎢ ⎥ =⎜ ⎟ +⎜ ⎟ = 0.615 < 1.0 (OK)
⎢⎣ (φRn )t ⎥⎦ ⎢⎣ (φRn )v ⎥⎦ ⎝ 29.82 ⎠ ⎝ 15.9 ⎠
cemøIy³ tMNKWRKb;RKan;

T.Chhay 322 Eccentric Connections

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enAeBlEdlb‘ULúgenAkñúgtMN slip-critical rgkarTaj slip-critical strength CaFmμtaRtUv)an

kat;bnßyedayemKuNEdlpþl;[eday AISC Equation A-J3-2 ¬emIl Epñk 7>9¦. mUlehtuKWfa
clamping effect nigkmøaMgkkitRtUv)ankat;bnßy. b:uEnþenAkñúgtMNEdleTIbnwgBicarNa vamankmøaMg

sgát;bEnßmenAkñúgEpñkxageRkamrbs;tMNEdlbegáInkmøaMgkkit EdlvaTUTat;nwgkarkat;bnßyenAkñúg
EpñkxageRkamrbs;tMN. sRmab;mUlehtuenH slip-critical strength minKYrRtUv)ankat;bnßyenAkñúgRb
ePTtMNenHeT.

8>4> tMNcMNakp©itedaypSar³ EtkmøaMgkat;

Eccentric Welded Connections: Shear only
eKviPaKtMNcMNakp©itedaypSartamviFIdUcKñasRmab;tMNedayb‘ULúg elIkElgRtg;kmøaMgkñúg
eRKOgP¢ab;mYy²RtUv)anCMnYsedaykmøaMgkñúgRbEvgTwkbnSarÉktþa. dUckñúgkrNIEdltMNcMNakp©it
edayb‘ULúgrgkmøaMgkat; tMNedaypSarrgkmøaMgkat;GacRtUv)anGegátedayviFI elastic method b¤
ultimate strength method.

Elastic method
bnÞúkenAelI bracket EdlbgðajenAkñúgrUbTI 8>16 a GacnwgRtUv)anBicarNa[eGVIGMeBIenA
kñúgbøg;énTwkbnSar EdlCabøg;rbs; throat. RbsinebIeyIgsnμt;EbbenH bnÞúknwgRtUv)anTb;edayRkLa
épÞTwkbnSarEdlbgðajenAkñúgrUb 8>16 b. b:uEnþ karKNnamanlkçN³samBaØ RbsinebIeKeRbI throat
mYyÉktþa. bnÞab;mkbnÞúkEdlKNna)anRtUvKuNnwg 0.707 CamYynwgTMhMrbs;TwkbnSaedIm,ITTYl)an
bnÞúkBitR)akd.

tMNcakp©it 323 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

bnÞúkcMNakp©itenAkñúgbøg;TwkbnSarEdleFVI[TwkbnSarrgTaMgkmøaMgkat;pÞal; (direct shear)

nigkmøaMgkat;edayrmYl (torsional shear). edaysarFatunImYy²rbs;TwkbnSarTb;Tl;nwgcMENk
esμIrbs; direct shear enaH direct shear stress KW
P
f1 =
L
Edl L CaRbEvgsrubrbs;TwkbnSar ehIyesμInwgRkLaépÞkmøaMgkat;edayKitCaelx edaysareKsnμt;
TMhM throat esμInwgmYyÉktþa. RbsinebIeKeRbIkMub:Usg;Ekg
Py
f1x = x
P
L
ni g f1 y =
L
Edl Px nig Py CabgÁúMkmøaMgtamTis x nig y . kugRtaMgkmøaMgkat;EdlekIteLIgedaysar couple
RtUv)aneKrkCamYynwgrUbmnþkmøaMgrmYl
Md
f2 =
J
Edl d= cm¶ayBITIRbCMuTm¶n;rbs;RkLaépÞkmøaMgkat;eTAcMNucEdlkugRtaMgkMBugRtUv)anKNna
J = m:Um:g;niclPaBb:UElrrbs;RkLaépÞenaH

rUbTI 8>17 bgðajBIkugRtaMgTaMgenHenARtg;kac;RCugxagelIEpñkxageRkamrbs;TwkbnSar. tamkMub:Usg;

Ekg
f 2x =
My
J
ni g f2y =
Mx
J
Edl J = ∫A r 2 dA = ∫A (x 2 + y 2 )dA = ∫A x 2 dA + ∫A y 2 dA = I y + I x

Edl I x nig I y Cam:Um:g;niclPaBrbs;RkLaépÞkmøaMgkat;. enAeBlEdlbgÁúMkmøaMgTaMgGs;RtUv)ankM

Nt; eyIgGacbUkbgÁúMkmøaMgedIm,ITTYl)ankugRtaMgkmøaMgkat;srubenARtg;cMNucEdleyIgcg;dwg b¤
fv = (∑ f x )2 + (∑ f y )2

T.Chhay 324 Eccentric Connections

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dUcKñanwgtMNedayb‘ULúg CaTUeTATItaMgeRKaHfñak;sRmab;kugRtaMgpÁÜbGacRtUv)ankMNt;BIkarsegátelI
témø nigTisedArbs;bgÁúM direct shear nig torsional shearing stress.
edaysareKeRbITwkbnSarkñúgmYyÉktþa karKNnaTIRbCMuTm¶n; nigm:Um:g;niclPaBKWmanlkçN³Ca
ExSbnÞat;. enAkñúgesovePAenH eyIgKitGgát;TwkbnSarCaGgát;ExSEdleyIgsnμt;eTARbEvgdUcKñanwgRCug
EKmrbs;EpñkEdlRtUvP¢ab;EdlenAEk,rva. elIsBIenH eyIgecalm:Um:g;niclPaBrbs;Ggát;ExSeFobeTA
nwgG½kSEdlRtYtKñaCamYynwgExS.

]TahrN_ 8>5³ kMNt;TMhMrbs;TwkbnSarEdlRtUvkarsRmab;tMN bracket enAkñúgrUbTI 8>18. bnÞúk

60kips CabnÞúkemKuN. eKeRbIEdk A36 sRmab;ssr nig bracket.

dMeNaHRsay³ eKGacCMnYsbnÞúkcakp©itedaybnÞúkcMp©it nig couple dUcbgðajenAkñúgrUbTI 8>18.

Direct shearing stress KitCa kips / in. KWdUcKñasRmab;RKb;Ggát;TwkbnSar ehIyesμInwg

tMNcakp©it 325 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

60 60
f1 y = = = 2.143kips / in.
8 + 12 + 8 28
munnwgKNnabgÁúMkmøaMgrmYlrbs; shearing stress, eKRtUvkMNt;TItaMgrbs;TIRbCMuTm¶n;rbs;RkLaépÞ
kmøaMgkat;. BIeKalkarN_m:Um:g;CamYynwgplbUkm:Um:g;eFobG½kS y /
x(28) = 8(4 )(2 ) b¤ x = 2.286in.
cMNakp©it e KW 10 + 8 − 2.286 = 15.71in.
ehIym:Um:g;rmYlKW M = Pe = 60(15.71) = 942.6in. − kips
RbsinebIeKecalm:Um:g;niclPaBrbs;TwkbnSartamTisedknImYy²eFobG½kSTIRbCMuTm¶n;rbs;va enaH
m:Um:g;niclPaBénRkLaépÞsrubeFobnwgG½kSTIRbCMuTm¶n;tamTisedkKW
Ix =
1
(1)(12)3 + 2(8)(6)2 = 720.0in.4
12
⎡1 ⎤
dUcKña I y = 2 ⎢ (1)(8)3 + 8(4 − 2.286 )2 ⎥ + 12(2.286 )2 = 195.0in.4
⎣12 ⎦
ehIy J = I x + I y = 720.0 + 195.0 = 915.0in 4
rUbTI 8>18 bgðajTisedArbs;bgÁúMkugRtaMgTaMgBIrenAkac;RCugrbs;tMNnImYy². tamkarsegát/ kac;
RCugxagelIEpñkxagsþaM b¤kac;RCugxageRkamEpñkxagsþaMGacRtUv)anKitCaTItaMgEdlmaneRKaHfñak;. Rb
sinebIeKeRCIserIskac;RCugxageRkamEpñkxagsþaM enaH
My 942.6(6)
f 2x = = = 6.181kips / in.
J 915.0
M 942.6(8 − 2.286 )
f2y = x = = 5.886kips / in.
J 915.0
fv = (6.181)2 + (2.143 + 5.886)2 = 10.13kips / in.
RtYtBinitüersIusþg;rbs; base metal. BIsmIkar &>@!
φRn = φFBM × area subject to shear
⎛9⎞
= φFBM × t = 0.54 F y t = 0.54(36)⎜ ⎟
⎝ 16 ⎠
= 10.94kips / in. > 10.13kips / in. (OK)
BIsmIkar &>@0 weld strength KW
φRn = 0.707 × w × L × φFW
Electrode EdlRtUvKñasRmab;Edk A36 KW E 70 / CamYynwg φFW = 31.5ksi .
dUcenHTMhMTwkbnSarEdl RtUvkarKW
T.Chhay 326 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

φRn 10.13
w= = = 0.455in.
0.707 LφFW 0.707(1.0)(31.5)
cemøIy³ eRbI fillet weld 1 / 2in. CamYynwg electrode E 70 .

Ultimate Strength Analysis

eKGacKNna Eccentric welded shear connection edayeRbI elastic method y:agsuvtßiPaB
b:uEnþemKuNsuvtßiPaBGacFMCagGVIEdlRtUvkar ehIyGacERbRbYlBItMNmYyeTAtMNmYy (Bultler, Pal,
and Kulak, 1920). karviPaKRbePTenHmanKuNvibtþixøHdUc elastic method sRmab; eccentric bolted

connections, edayrYbbBa©ÚlTaMgkarsnμt;faTMnak;TMngrvag bnÞúk-kMhUcRTg;RTay sRmab;karpSar. Rb

PBepSgeTotrbs;kMhusKWkarsnμt;faersIusþg;rbs;TwkbnSarminGaRs½ynwgTisedArbs;bnÞúkEdlGnuvtþ.
Ultimat strength procedure RtUv)anbgðajenAkñúg Part 8 of the Manual (Volume II) ehIyRtUv)an

segçbenATIenH. vaQrelIkarsikSaRsavRCavrbs; Butler et al. (1972) nig Timler (1984) ehIyviFI

EdlesÞIrEtdUcKñaEdlbegáIteLIgsRmab; eccentric bolted connections eday Crawford and Kulak
(1971).

CMnYs[karBicarNaelIeRKOgP¢ab;mYy² eyIgKitTwkbnSarEdlCab;CaGgát;TwkbnSardac;² Edl

pÁúMP¢ab;Kña. enAeBldac; bnÞúkEdlGnuvtþmkelItMNRtUv)anTb;edaykmøaMgenAkñúgFatunImYy² CamYynwg
kmøaMgEdleFVIGMeBIEkgeTAnwgkaMEdlbegáIteLIgBI instantaneous center of rotation eTATIRbCMuTm¶n;
rbs;Ggát;TwkbnSar dUcbgðajenAkñúgrUbTI 8>19. KMnitkñúgkarKNnaenHKWRsedogKñanwgKMnitEdleRbI
sRmab;eRKOgP¢ab;. b:uEnþ karkMNt;kMhUcRTg;RTayGtibrmarbs;Ggát;TwkbnSar nigkarkMNt;kmøaMgkñúg
énGgát;TwkbnSarnImYy²enAeBlEdldac;KWBi)ak. edIm,IkMNt;FatuEdlmaneRKaHfñak; eKRtUvkMNt;pl
eFob Δ max / r sRmab;FatunImYy²/ Edl
Δ max = 1.087 w(θ + 6)−0.65 ≤ 0.17 w
θ= mMurvagkmøaMgTb; nigG½kSrbs;Ggát;TwkbnSar ¬emIlrUbTI 8>19¦
w = TMhMTwkbnSar

r = cm¶ayBI IC eTATIRbCMuTm¶n;rbs;Ggát;TwkbnSar

tMNcakp©it 327 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

FatuEdlmanpleFobtUcCageKKWCaFatuEdleTAdl; ultimate capacity muneK. bnÞab;mkkMhUcRTg;

RTayrbs;FatudéTeTotRtUv)ankMNt;eday
r
Δ= Δ max
rmax
Edl kaMsRmab;Fatu
r=
Δ max Δ
= sRmab;FatuEdleRKaHfñak;
rmax r
eKGackMNt;kmøaMgTb;sRmab;FatunImYy²BI
( )
R = 0.60 FEXX 1.0 + 0.50 sin1.5 θ [ p(1.9 − 0.9 p )]0.3
Edl FEXX = weld electrode tensil strength
Δ
p=
Δ max
¬mindUckrNItMNedayb‘ULúgEdl R CaGnuKmn_eTAnwg θ ¦. karKNnaBImunKWQrelIkarsnμt;TItaMg
rbs; instantaneous center of rotation. RbsinebIvaCaTItaMgBitR)akd smIkarlMnwgnwgRtUv)anbMeBj.
karKNnabnþeTotKWRsedogKñanwgtMNedayb‘ULúg.
!> KNna load capacity BIsmIkar
∑ M IC = 0
Ed;l IC Ca instantaneous center.
@> RbsinebIsmIkarlMnwgkmøaMgBIrRtUv)anbMeBj enaHTItaMg instantaneous center Edl)an
snμt; nigbnÞúkEdl)anrkenAkñúgCMhanmYyBitCaRtwmRtUv EtebImindUecñaHeT eKRtUvsnμt;TI
taMgfμI ehIyeFVIkarKNnasareLIgvij.

T.Chhay 328 Eccentric Connections

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vabgðajy:agc,as;nUv)aBcaM)ac;kñúgkareRbIR)as;kmμviFIkMuBüÚT½r. dMeNaHRsayedaykMuBüÚT½r
sRmab;;TRmg;FmμtaCaeRcInsRmab; eccentric welded shear connection RtUv)an[enAkñúgtaragEdl
manenAkñúg Part 8 of the Manual. Table 8-38 rhUtdl; 8-45 [lT§PaBbnÞúkemKuN (factored load
capacity) sRmab;karbnSMGgát;TwkbnSartamTisedk nigTisbBaÄrFmμtaCaeRcInedayQrelI ultimate

strength analysis. taragTaMgenHGacRtUv)aneRbIsRmab;karKNna b¤karviPaK nwgerobrab;nUvsßanPaB

CaeRcInEdlvisVkrGacnwgCYbRbTH. sRmab;tMNTaMgLayNaEdlmin)anerobrab;enAkñúgtarageKGac
eRbI elastic methoid.

]TahrN_ 8>6³ kMNt;TMhMTwkbnSarEdlcaM)ac;sRmab;kartP¢ab;enAkñúg]TahrN_ 8>5 edayQrelIkar

BicarNa ultimate strength. cUreRbItaragsRmab; eccentrically load weld group Edl[enAkñúg
Part 8 of the Manual.

dMeNaHRsay³ TwkbnSarrbs;]TahrN_ 8>5 CaRbePTdUcKñaeTAnwgrUbEdlbgðajenAkñúg Tabl;e 8-42

(angle = 0 o )/ ehIykardak;bnÞúkk¾dUcKña. eKRtUvkartémøefrxageRkamsRmab;bBa©ÚleTAkñúgtarag³
al e 15.7
a= = = = 1.3
l l 12
kl 8
k= = = 0.67
l 12
edayeFVI interpolation enAkñúg Table 8-42 sRmab; a = 1.3
C = 1.14 sRmab; k = 0.6 ehIy C = 1.30 sRmab; k = 0 .7

enaHsRmab; k = 0.67 eyIgTTYl)an C = 1.25

sRmab; electrode E70 XX / C1 = 1.0
témø D EdlcaM)ac;KW
Pu 60
D= = = 4 .0
CC1l 1.25(1.0 )(12 )
dUcenHTMhMTwkbnSarEdlcaM)ac;KW
1
16
(4.0) = 0.25 ¬TMhMTwkbnSarEdlRtUvkarenAkñúg]TahrN_ 8>5 KW 0.455
cemøIy³ eRbI electrode E 70 / fillet weld 1 / 4in.

tMNcakp©it 329 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

karpþl;[CaBiesssRmab;Ggát;rgbnÞúktamG½kS Special Provision for Axially

Loaded Members
enAeBlEdlGgát;eRKOgbgÁúMrgbnÞúktamG½kS kugRtaMgRtUv)anBRgayesμIenAelImuxkat; ehIy
kmøaMgpÁÜbRtUv)anBicarNafaeFVIGMeBItamG½kSTIRbCMuTm¶n; EdlvaCaG½kSEvgkat;tamTIRbCMuTm¶n;. sRmab;
Ggát;EdlrgbnÞúkcMp©itenAxagcugrbs;va kmøaMgTb;pÁÜbEdlpþl;[edaytMNk¾RtUveFVIGMeBItamG½kSenHEdr.
RbsinebIGgát;enHmanmuxkat;sIuemRTI lT§plGacRtUv)ansMercedaykarpSar b¤P¢ab;b‘ULúgedaysIuemRTI.
RbsinebIGgát;manmuxkat;minsIuemRTI dUcCamuxkat;EdkEkgDub (double-angle section) enAkñúgrUbTI
8>20 karpSar b¤karP¢ab;b‘ULúgedaysIuemRTIeFVI[tMNenaHCatMNrgbnÞúkcakp©it CamYynwg couple Te
dUcbgðajenAkñúgrUbTI 8>20 b.

AISC J1.8GnuBaØat[ecalcMNakp©itenHsRmab;Ggát;rgkmøaMgsþaTic. enAeBlEdlGgát;rg

fatigue EdlbNþalmkBIPaBRcMdEdlénkardak;bnÞúk b¤PaBmanGt;rbs;kugRtaMg cMNakp©itRtUvEtyk

mkBicarNa b¤k¾minykmkBicarNaedaysarkartP¢ab;edaykarpSar b¤edayb‘ULúgEdlmanlkçN³sm

Rsb . ¬CakarBit eTaHbIdMeNaHRsayGacRtUv)aneKeRbIsRmab;EtGgát;EdlrgEtkmøaMgsþaTick¾eday¦.
eKGackMNt;karP¢ab;enHedayGnuvtþsmIkarlMnwgkmøaMg nigm:Um:g;. sRmab;tMNEdlpSarEdlbgðajenA
kñúgrUbTI 8>21 smIkardMbUgGacRtUv)anTTYledayplbUkm:Um:g;eFobTwkbnSartamTisedkxageRkam³

T.Chhay 330 Eccentric Connections

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L
∑ M L2 = Tc − P3 3 − P1 L3 = 0
2

eKedaHRsaysmIkarenHedIm,Irk P1 EdlCakmøaMgTb;caM)ac;enAkñúgTwkbnSartamTisedkxagelI.
bnÞab;mkeKGacCMnYstémøenHeTAkñúgsmIkarlMnwgkmøaMgxageRkam³
∑ F = T − P1 − P2 − P3 = 0
eKGacedaHRsaysmIkarenHedIm,Irktémø P2 EdlCakmøaMgTb;caM)ac;enAkñúgTwkbnSartamTis
edkxageRkam. sRmab;RKb;TMhMrbs;TwkbnSar eKGacedaHRsayrkRbEvg L1 nig L2 . dMeNIrkaredaH
RsayRtUv)anbgðajenAkñúg]TahrN_ 8>7 EdleKsÁal;Ca balancing the weld.

]TahrN_ 8>7³ Ggát;rgkarTajEdlpSMeLIgeday double-angle section, 2L5 × 3 × 1 / 2 EdleKdak;

eCIgEvgrbs;vaTl;xñgKña. EdkEkgRtUv)anP¢ab;eTAnwg gusset plate kRmas; 3 / 8in. . EdkTaMgGs;Ca
A36 . KNnatMNedaykarpSar edayeFVIkarkat;bnßycMNakp©itedIm,ITb;nwg tensil capacity eBj

rbs;Ggát;.
dMeNaHRsay³ Load capacity rbs;Ggát;edayQrelI gross section KW
φt Pn = 0.90 F y Ag = 0.90(36)(7.5) = 243.0kips

Load capacity EdlQrelI net seactionRtUvkartémørbs; U .

eKminsÁal;RbEvgTwkbnSar dUcenHeKminGacKNna U BI AISC Equation B3-2 )aneT. edayeRbI
témømFüm 0.85 eKTTYl)an³
Ae = UAg = 085(7.5) = 6.375in.2

tMNcakp©it 331 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

φt Pn = 0.75Fu Ae = 0.75(58)(6.375) = 277.3kips > 243.0kips

Yeildingrbs; gross section CasßanPaBkMNt;EdlykmksikSa dUcenH φt Pn = 243.0kips .
sRmab;EdkEkgmYy bnÞúkEdlRtUvTb;KW
243.0
= 121.5kips
2
EdlRtUvKñanwgEdk A36 KW E70 XX / ehIy
Electrode

TMhMTwkbnSarGb,brma = 163 in. (AISC Table J2.4)

TMhMGtibrma = 12 − 161 = 167 in. (AISC J2.2b)
sakl,g electrode E 70 fillet weld 5 / 16in. ³
lT§PaBenAkñúgRbEvg 1in. = 0.707w(φFW )
⎛5⎞
= 0.707⎜ ⎟(31.5)
⎝ 16 ⎠
= 6.960kips / in.
lT§PaBrbs; base metal rgkmøaMgkat; = t (φFBM ) = t (0.54Fy )
⎛3⎞
= ⎜ ⎟(0.54)(36)
⎝8⎠
= 7.29kips / in.
edayersIusþg;rbs;TwkbnSartUcCageK dUcenHeRbIersIusþg;rbs;TwkbnSar 6.960kips / in. .

eyagtamrUbTI 8>22. lT§PaBrbs;TwkbnSarenAxagcugrbs;EdkEkgKW

P3 = 6.960(5) = 34.80kips
⎛5⎞
∑ M L2 = 121.5(3.25) − 34.80⎜ ⎟ − P1 (5) = 0
⎝2⎠

T.Chhay 332 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

P1 = 61.58kips
∑ F = 121.5 − 61.58 − 34.80 − P2 = 0 / P2 = 25.12kips

L1 =
P1
=
61.58
6.960 6.960
= 8.85in. yk 9in.
L2 =
25.12
6.960
= 3.61in.yk 4in.

cemøIy³ eRbIkarpSaredUcbgðajenAkñúgrUbTI 8>23

8>5> tMNcMNakp©itedaypSar³ kmøaMgkat; nigkmøaMgTaj

Eccentric Welded Connections: Shear and Tension
tMNcMNakp©itCaeRcIn CaBiesskartP¢ab; beam-to-column TwkbnSarrgkmøaMgTaj nigkmøaMg
kat;. tMNEbbenHBIrRbePTRtUv)anbgðajenAkñúgrUbTI 8>24.
Seated beam connection pSMeLIgedayEdkEkgEdlmanRbEvgxøIRtUv)aneRbICaeFñIr (shelf) edIm,I

RTFñwm. TwkbnSarEdlP¢ab;EdkEkgenHeTAssrRtUvTb;nwgm:Um:g;EdlekIteLIgedayRbtikmμcakp©it k¾dUc

direct shear Edl)anBIRbtikmμrbs;Fñwm. EdkEkgEdlP¢ab;enAxagelIrbs;søabFñwmpþl;nUv torsional

stability eTA[Fñwm Etvamin)anCYyRTRbtikmμeT. eKGacP¢ab;vaeTAnwgRTnugrbs;FñwmCMnYs[karP¢ab;

eTAnwgsøabrbs;Fñwm)an. beam-to-angle connection GacRtUv)aneFVIeLIgedaykarpSar b¤b‘ULúg ehIy

vaminRTnUvbnÞúkKNnaNaeT.
Framed beam connection ¬manlkçN³FmμtaCageK¦ EdlmanEdkEkgbBaÄrpSarP¢ab;eTAnwg

ssr ehIyrgnUvRbePTbnÞúkdUckrNI seated beam connection. Epñkrbs;kartP¢ab; beam-to-angle

k¾CaRbePTcakp©it b:uEnþbnÞúkenAkñúgbøg;énkmøaMgkat;TTwg dUcenHvaminmankmøaMgTajeT. TaMg seated
connection nig framed connection GacRtUv)anP¢ab;edayb‘ULúg.

tMNcakp©it 333 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

enAkñúgRbePTnImYy²Edl)anerobrab;xagelI TWkbnSarbBaÄrenAelIsøabssrrgbnÞúkdUcbgðajenA
kñúgrUbTI 8>25. dUcKñaCamYynwgtMNedayb‘ULúgenAkñúgrUbTI 8>3 bnÞúkcakp©it P nig couple M = Pe .
kugRtaMgkmøaMgkat;KW
P
fv =
A
Edl A CaRkLaépÞ throat srubrbs;TwkbnSar. eKGacKNnakugRtaMgkmøaMgTajGtibrmaBI
flexure formula
Mc
ft =
I
Edl I Cam:Um:g;niclPaBeFobG½kSTIRbCMuTm¶n;rbs;RkLaépÞEdlpSMeLIgedayRkLaépÞ throat
srubrbs;TwkbnSar nig c Cacm¶ayBIG½kSTIRbCMuTm¶n;eTAcMNucq¶abMputrbs;RCugEdlrgkarTaj. eKGac
rkkugRtaMgkmøaMgpÁÜbGtibrmaedayeFVIplbUkviuTr½kMub:Usg;TaMgBIrenH enaHeK)an
fr = f v2 + f t2

sRmab;xñat kips nig in. / kugRtaMgenHnwgRtUv)anKitCa kips / in 2 . RbsinebIkñúgkarKNnaenH eK

eRbITMhM throat Éktþa enaHeKGacsMEdgtémøenAHCa kips / in. . RbsinebI f r RtUv)ankMNt;BIbnÞúkem
KuN eKGaceRbobeFobvaCamYynwg design strength rbs;TwkbnSarénRbEvgÉktþa. eTAHbICaviFIKNna
RtUv)ansnμt;eFVIkarCalkçN³eGLasÞick¾eday k¾vamanlkçN³suvtßiPaBCamYynwg LRFD context Edr.
T.Chhay 334 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

]TahrN_ 8>8³ eKeRbI L6 × 4 × 1 / 2 enAkñúg seated beam connection dUcbgðajenAkñúgrUbTI 8>26.

vaRtUvRTnUvbnÞúkemKuNRbtikmμ 22kips . EdkTaMgGs;Ca A36 ehIyeKeRbI electrode E70 XX . etI
eKRtUvkarTMhMTwkbnSar fillet weld b:unμansRmab;tP¢ab;eTAnwgsøabssr?

dMeNaHRsay³ dUckñúg]TahrN_KNnaBImun/ eKeRbITMhM throat ÉktþasRmab;KNna. eTaHbICakarpSar

enHRtUvkar end return k¾eday edIm,IsRmYlkñúgkarKNna eKnwgecalvasRmab;karKNnaxageRkam.
enARKb;krNI eKGac)a:n;sμanRbEvgrbs;vaenARtg;cMNucenH edaysareKminTan;)ankMNt;TMhMTwkbnSar.
edaysarmanKMlatBIssr 3 / 4in. FñwmRtUv)anRTeday 3.25in. elIRbEvg 4in. éneCIgrbs;
EdkEkg. RbsinebIeKsnμt;[kmøaMgRbtikmμeFVIGMeBIRtg;cMNuckNþalrbs;RbEvgEdlb:H enaHcMNak
p©iteFobnwgTwkbnSarKW
3.25
e = 0.75 + = 2.375in.
2
tMNcakp©it 335 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

ehIym:Um:g;Kw
M = Pe = 22(2.375) = 52.25in. − kips

sRmab;rUbragénkarpSarEdlsnμt;enAkñúgrUbTI 8>27
2(1)(6 )3
= 36in.4 /
6
I= c = = 3in.
12 2
Mc 52.25(3)
ft = = = 4.354kips / in.
I 36
P 22
fv = = = 1.833kips / in.
A 2(1)(6 )
fr = f t2 + f v2 = (4.354)2 + (1.833)2 = 4.724kips / in.

eKGacrkTMhMTwkbnSarEdlcaM)ac; w eday[ f r esμIeTAnwglT§PaBTwkbnSarkñúgmYyÉktþaRbEvg

f r = 0.707 w(φFW )
4.724 = 0.707 w(31.5) / w = 0.212in.

BI AISC Table J2.4,

TMhMTwkbnSarGb,brma = 14 in. ¬edayQrelITMhMsøabrbs;ssr 5 / 8in.
BI AISC J2.2b,
TMhMGtibrma = 12 − 161 = 167 in.
RtYtBinitülT§PaBkmøaMgkat;TTwgrbs; base metal:
Applied direct shear = f v = 1.833kips / in.

(
Shear capacity of angle leg = t (φFBM ) = t 0.54 F y = ) 1
2
(0.54)(36)

T.Chhay 336 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

= 9.72kips / in. > 1.833kips / in. (OK)

cemøIy³ eRbI electrode E70 XX / fillet weld 1 / 4in. .

eyIgecalnUv end returns enAkñúg]TahrN_ 8>8 b:uEnþeKGacbBa©ÚlvaedaykareFVIkarKNna

elIkTIBIrCamYynwg end return EdlmanRbEvgBIrdgTMhMTwkbnSarEdl)anrkeXIjenAkñúgkarKNna
elIkTImYy. ¬CMhanbENßmenHminRtUv)anGnuvtþenAkñúg]TahrN_enHeTedaysarTMhMTwkbnSarGb,-
brmaRKb;RKan;sRmab;karKNna¦. End return RtUv)anykmkniyayenAkñúg]TahrN_ 8>9.

]TahrN_ 8>9³ rUbTI 8>28 bgðajBI framed beam connection edaypSar. Edk framing angle Ca
ehIyssrCa W12 × 72 . EdkTaMgGs;CaRbePT A36 ehIyeKeRbI electrode
L4 × 3 × 1 / 2

E70 XX edIm,IbegáIt fillet weld 3 / 8in. . kMNt;kmøaMgRbtikmμemKuNrbs;FñwmEdlkMNt;edayTwk

bnSarenAelIsøabssr.

dMeNaHRsay³ eKsnμt;kmøaMgRbtikmμrbs;FñwmeFVIGMeBIkat;tamTIRbCMuTm¶n;rbs;TwkbnSarén framing

. dUcenH cMNakp©itrbs;kmøaMgeFobnwgTwkbnSarenARtg;søabssrCacm¶ayBITIRbCMuTm¶n;eTAsøab
angle

ssr. sRmab;TMhM throat mYyÉktþa nigTwkbnSarEdlbgðajenAkñúgrUbTI 8>29 a

2(2.5)(1.25)
x= = 0.1689in. nig e = 3 − 0.1689 = 2.831in.
32 + 2(2.5)
tMNcakp©it 337 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

m:Um:g;enAelITwkbnSarEdlenAelIsøabssrKW
M = Re = R 2.831in. − kips
Edl R CaRbtikmμrbs;FñwmKitCa kips
BITMhMEdl[enAkñúgrUbTI 8>29 b/ lkçN³rbs;TwkbnSarenAelIsøabssr
32(16)
y= = 15.63in.
32 + 0.75
1(32 )3
I= + 32(16 − 15.63)2 + 0.75(15.63)2 = 2918in.4
12
sRmab;TwkbnSarTaMgBIr
I = 2(2918) = 5836in.4
Mc 2.831R(15.63)
ft = = = 0.007582 Rkips / in.
I 5836
R R
fv = = = 0.01527 Rkips / in.
A 2(32 + 0.75)
fr = (0.007582R )2 + (0.01527 R )2 = 0.01705Rkips / in.

yk 0.01705R = 0.707w(φFW ) ykKNnarktémø R

⎛3⎞
0.0175R = 0.707⎜ ⎟(31.5) / R = 489.8kips
⎝8⎠
RtYtBinitülT§PaBkmøaMgkat;TTwgrbs; base metal ¬kRmas;rbs;EdkEkglub¦
( )
t (φFBM ) = t 0.54 F y = 0.5(0.54 )(36 ) = 9.72kips / in.

Direct shear RtUv)anTb;Kw

T.Chhay 338 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

489.8
= 7.48kips / in. < 9.72kips / in. (OK)
2(32.75)
cemøIy³ kmøaMgRbtikmμFñwmemKuNGtibrma = 490kips

8>6> tMNTb;m:Um:g; (Moment-Resisting Connection)

enARKb; beam-to-column connection nig beam-to-beam connection TaMgGs; vaEtgman
karTb;m:Um:g;xøH eTaHbICakarKNnatMNenaHCatMNsamBaØ b¤k¾tMNEdlKμanm:Um:g;k¾eday. müa:gvijeTot
eKBi)akkñúgkareFVI[man perfectly frictionless pin or hinge ehIytMNCaeRcInEdlRtUv)anKNna
CatMNEdldac;edayKμanm:Um:g;. dUcKña eKk¾Bi)akkñúgkareFVI[man perfectly rigid joint EdlGac
manlT§PaBepÞr moment capacity rbs;Ggát;mYyeTAGgát;mYyeTotEdr. dUcenH eTaHbICa framed nig
seated beam connections EdlbgðajkñúgrUbTI 8>24 k¾GacCatMNrwgxøH EdlvaGacbBa¢Únm:Um:g;tictYc

RbsinebI connecting angle man flexible RKb;RKan;. dUcEdl)ankt;cMNaMBIxagelI bnÞúkcakp©iteFob

eTAnwgb‘ULúg b¤TwkbnSarKWtUcNas; ehIyEdlCaTUeTARtUv)anecal.
AISC Specification kMNt;kartP¢ab;enHCaBIrRbePT enAkñúg Section A2.2, “Types of
Comstruction.”
Type FR – Fully Restrained (Rigid, or Continuous, Framing). eRKOgbgÁúMEdlman
moment-resistingg joint GacepÞrm:Um:g;EdlGgát;GacTb;)an edaymineFVI[Ggát;enaHmanmMurgVil

enARtg;tMNenaH. RbsinebIeRKagRtUv)anKNnaCa rigid frame dUcenHtMNRtUv)anKNnaCa moment

connection.

Type PR – Partially Restrained (semirigid Framing). eRKagRbePTenHCa eRKagEdl

RtUv)anKNnaedayQrelIkarsÁal;brimaNTb; (restraint) cenøaHrvagtMNsamBaØ nigtMNrwg. CaTUeTA

moment restraint sßitenAcenøaH 20% eTA 90% rbs; member moment capacity. bBaðacMbgrbs;

eRKagEdlmantMNRbePTenHKWTamTarnUvkarviPaKeRKagd¾saMjauMedaysarvtþmanrbs; partial joint

restraint. tRmUvkarcaM)ac; sRmab;tMNRbePTenHKWExSekag m:Um:g;-mMurgVil.

RbsinebIeKecal partial restraint eKGaccat;TukFñwmCaFñwmTRmsamBaØEdlminman moment

restraint enARtg;tMN. Framed and seated beam connections sßitenAkñúgRbePTenH. CaTUeTAtMN

EdlepÞr member capacity ticCag 20% RtUv)ancat;TukCatMNsamBaØ.

tMNcakp©it 339 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

TRmFñwmEdlRtUv)anKNnaenA kñúgkrNIenH eBlxøHRtUv)aneKehAfa shear connection EdlmanEt

kmøaMgRbtikmμ b¤kmøaMgkat;enAxag cugEdlRtUv)anbBa¢Ún.
eRKagEdlman shear connection RtUv)anBRgwgenAkñúgbøg;rbs;eRKagedaysarvaKμan “frame
action”edIm,IeFVI[man lateral stability. cRmwg (bracing) TaMgenHmaneRcInTRmg; GacCa diagonal

bracing members, shear wall, or lateral support BIeRKagEdlenACab;. m:Um:g;EdlekItBIbnÞúkxag

¬CaTUeTAKW xül; nigrBa¢ÜydI¦ RtUv)anykmkKitkñúgkarKNnasRmab;kareRCIserIs beam-to-column

connections. sRmab;viFIenH eKsnμt;tMN[eFVIkarCatMNsamBaØedIm,ITb;Tl;nwgbnÞúkefr nigbnÞúk

Gefr ¬bnÞúkTMnaj gravity load¦ nigCa moment connection CamYynwglT§PaBEdlmankMNt;kñúgkar

Tb;Tl;m:Um:g;xül;. RbsinebIeKKNnaFñwmCaRbePTTRmsamBaØ m:Um:g;bnÞúkTMnajGtibrmaGac over-
estimated ehIyFñwmGac overdesigned. b:uEnþkñúgkrNICaeRcIn m:Um:g;xül;GacmantémøtUc. RbsinebI

eKeRbItMNsamBaØ Specification TamTar[eKarBnUvlkçxNÐxageRkam³

!> eTaHbICaFñwm ¬rt¦ minRtUv)anRTedayTRmsamBaØk¾eday k¾vaRtUvEtRTbnÞúkTMnajtamEtva
GaceFVI)an.
@> tMN nigGgát;EdlRtUv)anP¢ab; ¬Fñwm nigssr¦ RtUvmanlT§PaBGacTb;m:Um:g;xül;)an.
#> tMNRtUvman inelastic rotational capacity RKb;RKan;EdleRKOgP¢ab; b¤TwkbnSarnwgmin
RtUv)an overload eRkambnSMénbnÞúkTMnaj nigbnÞúkxül;.
enAkñúgsovePAenH eyIgBicarNaEttMNBIrRbePTKW³ tMNsamBaØ (simple connection) Edl
KNnasRmab;bnÞúkTMnaj ¬CamYynwg lateral frame stability Edlpþl;[eday positive bracing
system¦ nigtMNrwg (rigid connection) EdlKNnasRmab; moment capacity rbs;FñwmFMCag 90% .

eyIg)anBicarNa simple connection enAkñúg framed nig seated beam connections rYcehIy dUcenH
eyIgnwgRtUvkarykcitþTukdak;eTAelI rigid connectionsvijmþg.
]TahrN_FmμtaCaeRcInEdleRbI moment connection RtUv)anbgðajenAkñúgrUbTI 8>30. Ca
TUeTA karepÞrm:Um:g;PaKeRcInRtUv)anbBa¢ÚntamsøabFñwm ehIy moment capacity k¾RtUv)aneLIg. tMN
enAkñúgrUbTI 8>30 a bgðajBIKMnitenH. EdkbnÞHEdlP¢ab;RTnugFñwmeTAssrKWRtUv)anpSarP¢ab;eTAnwg
ssrenAeragCag nigRtUv)ancab;b‘ULúgeTAnwgFñwmenAkardæan. CamYynwgkarerobcMEbbenH FñwmRtUv)an
Gacdak;enAelITItaMgy:agRsYleday[søabGacRtUv)anpSarP¢ab;eTAnwgssrenAkardæan. Plate
connection RtUv)anKNnaedIm,ITb;Tl;EtkmøaMgkat; nigTTYlRbtikmμrbs;Fñwm. Complete penetra-

T.Chhay 340 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

tion groove welds P¢ab;søabFñwmeTAssr nigGacepÞrm:Um:g;esμInwg moment capacity rbs;søabFñwm.

vanwgrYmKñaCamYy moment capacity rbs;FñwmPaKeRcIn b:uEnþbrimaNrbs;karTb;RtUv)anpþl;[ eday
plate connection. ¬edaysar strain harderning full plastic moment capacity rbs;FñwmGac

RtUv)anbegáIteLIgtamry³søab¦. kareFVIkartP¢ab;søabTamTarfaEpñkd¾tUcrbs;RTnugFñwmRtUv)andk
ecjehIy “backing bar” RtUv)aneRbIenAelI søabmYyedIm,IGnuBaØat[karpSarTaMgGs;eFVIeLIgBIelI.
enAeBlEdlkarpSarBIxagelIRtCak; vanwgrYjCaTUeTARbEhl 1 / 8in. . bMlas;TItamTisbeNþayEdl
TTYl)anRtUv)anykmkKitsRmab;eRbIR)as; slotted bolt hole nigedayrwtbNþwgb‘ULúgeRkayeBlTwk
bnSarRtUv)anRtCak;. tMNRbePTenH eRbI column stiffenders EdlminRtUvkarCaTUeTAeT ¬emIlEpñk
8>7¦.
Moment connection rbs;rUbTI 8>30 a k¾RtUv)anbgðaj recommended connection design

practice: RKb;eBlTaMgGs; karpSarKYrEtRtUv)aneFVIenAkñúgeragCag ehIykarcab;b‘ULúgKYreFVIenAkardæan.

karpSarenAeragCagmantémøefakCag niggayRsYlkñúgkarRtYtBinitü.
sRmab; beam-to-column moment connections Ggát;CaEpñkrbs; plane frame ehIyRtUv)an
dak;dUcbgðajenAkñúgrUbTI 8>30 a EdlRTnugenAkñúgbøg;rbs;eRKagEdlkarBt;rbs;Ggát;nimYy²eFobeTA
nwgG½kSemrbs;va. enAeBlEdlFñwmRtUv)anP¢ab;eTAnwgRTnugrbs;ssrCaCagsøabrbs;ssr ¬Ca-
]TahrN_ enAkñúgeRKaglMhr¦ eKeRbItMNdUcEdlbgðajenAkñúgrUbTI 8>30 b. tMNenHRsedogKñaeTA
nwgGVIEdlbgðajenAkñúgrUbTI 8>30 a b:uEnþTamTarnUvkareRbI column stiffener edIm,IeFVIkartP¢ab;eTAnwg
søabFñwm.
eTaHbICatMNEdlbgðajenAkñúgrUbTI 8>30 a CatMNsamBaØk¾eday k¾kartMeLIgrbs;faTamTar
nUvkRmitGt;»ntUcEdr. RbsinebIFñwmtUcCagkarrMBwgTukcenøaHrvagssr nigsøabFñwmGacbgáPaBlM)ak
kñúgkarpSar enAeBlxøHeKeRbI backing bar. Three-plate connection EdlbgðajenAkñúgrUbTI 8>30 c
minman handicap eT ehIyvamanGtßRbeyaCn_bEnßmEdlRtUv)anP¢ab;edayb‘ULúgy:agl¥enAkardæan.
Flange plate nig web plate RtUv)anpSarenAkñúgeragCageTAnwgsøabssr nigcab;b‘ULúgeTAFñwmRtUv)an

eFVIenAkardæan. edIm,Ipþl;[sRmab;karERbRbYlenAkñúgkm<s;Fñwm cm¶ayrvag flange plates RtUv)aneFVI

eLIgFMCagkm<s;Fmμtarbs;Fñwm b:uEnþRbEhl 3 / 8in. . KMlatenHRtUv)anbMeBjenAsøabxagelIkñúgeBl
dMeLIgCamYy shims/ Edl thin strip rbs;EdkedayRtUv)aneRbIsRmab;EktRmUvkarP¢ab;enARtg;tMN.
Shim GacCaRbePTmYykñúgcMeNamBIrRbePTKW conventional shim nig finger shim EdlGacs‘k

tMNcakp©it 341 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

eRkayeBlb‘ULúgRtUv)anP¢ab; dUcbgðajenAkñúgrUbTI 8>30 d. enAkñúgtMbn;EdlmantMbn;rBa¢ÜyFM tMN

EdlbgðajenAkñúgrUbTI 8>30 a RtUvkarkarKNnaBiess (FEMA, 1995).

]TahrN_ 8>10 bgðajBIkarKNnarbs; three-plate moment connect edayrYmbBa©ÚlTaMg

tRmUvkarsRmab;kartP¢ab;Ggát; Edlmanerobrab;eday AISC J5.

]TahrN_ 8>10³ KNna three-plate moment connection rbs;RbePTEdl)anbgðajrUbTI 8>31

sRmab;kartP¢ab;Fñwm W 21× 50 eTAsøabrbs;ssr W 14 × 99 . snμt;Fñwm set-back 1 / 2in. . karviPaK
eRKagbgðajfatMNRtUvEtepÞrm:Um:g;bnÞúkemKuN 210 ft. − kips nigkmøaMgkat;emKuN 33kips . RKb;bnÞH
EdkEdlpSareTAnwgssrCamYynwg electrode E70 XX nigkarP¢ab;b‘ULúgeTAFñwmCamYynwg bearing-
type bolts A325 . EdkTaMgGs;CaRbePTEdk A36 .

dMeNaHRsay³ sRmab; web plate ¬edayecalcMNakp©it¦ sakl,gb‘ULúgGgát;p©it 3 / 4in. . snμt;fa

eFμjsßitenAkñúgbøg;kmøaMgkat;. lT§PaBkmøaMgkat;TTwgrbs;b‘ULúgKW
φFv Ab = 0.75(48)(0.4418) = 15.90kips
cMnYnb‘ULúgEdlRtUvkar = 1533.90 = 2.08

T.Chhay 342 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

sakl,gb‘ULúg 3 RKab; nigkMNt;kRmas;bnÞHEdlTamTarsRmab; bearing. eRbIKMlat nigcm¶ay

eTARCugEKmenAkñúgrUbTI 8>32 a ehIyGgát;p©itrn§KW
1 3 1 13
h=d+ = + = in.
16 4 16 16
sRmab;RbehagEdlenAEk,rRCugEKmbMput
h 13 / 16
Lc = Le − = 1.5 − = 1.094in.
2 2
⎛3⎞
2d = 2⎜ ⎟ = 1.5in.
⎝4⎠
edaysar Lc < 2d / bearing strength KW
φRn = φ (1.2 Lc tFu ) = 0.75(1.2)(1.094)t (58) = 57.11tkips / bolt

sRmab;RbehagdéT
13
Lc = s − h = 3 − = 2.188in. > 2d
16

tMNcakp©it 343 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

dUcenH φRn = φ (2.4dtFu ) = 0.75(2.4)⎛⎜⎝ 34 ⎞⎟⎠t (58) = 78.03tkips / bolt

edIm,IrkkRmas;EdlRtUvkardak; total bearing strength esμInwg applied load:
57.11t + 2(78.30t ) = 33 b¤ t = 0.154in.
sRmab;RTnugFñwm (beam web) t w = 0.380in. > 0.154in.
edIm,IkMNt;kRmas;bnÞHEdkEdlRtUvkarsRmab;kmøaMgkat; cUrBicarNamuxkat;bBaÄrkat;tambnÞHEdk. BI
AISC J5, “Connecting Elements,”
[
φRn = 0.90 0.60 Ag F y ] (AISC Equation J5-3)

33 = 0.90[0.60(9t )(36 )]
t = 0.189in. ¬lub¦
dUcenHyk t = 1 / 4in.
sRmab;kartP¢ab; shear plate eTAnwgsøabssr TMhM fillet weld Gb,brmaKW 1 / 4in. . ¬edayQrelI
EpñkEdlRtUvP¢ab;EdlmankRmas;Rkas;Cag TMhM fillet weld Gb,brmaKW 5 / 16in. b:uEnþvaminRtUvkarFM
CagkRmas;rbs;EpñkEdlRtUvP¢ab;EdlesþIgCageT¦. enaH
lT§PaBkñúgmYyÉktþaRbEvg = 0.707w(φFW ) = 0.707⎛⎜⎝ 14 ⎞⎟⎠(31.5)
= 5.568kips / in.
lT§PaBkmøaMgkat;TTwgrbs; base metal KW
(
tφFBM = t 0.54 F y = ) 1
4
(0.54)(36) = 4.86kips / in. ¬lub¦
dUcenHRbEvgEdlcaM)ac;rbs; fillet weld 1 / 4in. KW
33
= 6.79in.
4.86
karpSarCab;KñaenAelIRCugmçagrbs;bnÞHGacRKb;RKan; b:uEnþCaTUeTAeKRtUvpSarsgxag ehIyRtUv)anGnuvtþ
enATIenH.
TTwgGb,brmarbs;bnÞHEdkGacRtUv)ankMNt;BIkarBicarNacm¶ayeTARCugEKm. bnÞúkEdlRtUv
)anRT ¬RbtikmμFñwm¦ KWmanTisbBaÄr dUcenHcm¶ayeTARCugEKmcaM)ac;eKarBtamtRmUvkarrbs; AISC
Table J3.4. RbsinebIeyIgsnμt;RCugEKmCa sheared edge cm¶ayeTARCugEKmGb,brmaKW 1 1 4 in. .

CamYynwg beam setback 1 / 2in. nigcm¶ayeTARCugEKm 1 1 2 in. dUcEdl)anbgðajenAkñúgrUbTI

8>32 b TTwgrbs;bnÞHEdkKW
T.Chhay 344 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

0.5 + 2(1.5) = 3.5in.ykbnÞHEdkTMhM 3 12 × 1 4

sRmab; flange plates, rkkmøaMgRtg;épÞb:HrvagsøabFñwm nigbnÞHEdk. BIrUbTI 8>33

M = Hd nig H = Md = 210 (12) = 121.0kips

20.83
sakl,gb‘ULúg A325 Ggát;p©it 3 / 4in. . ¬edaysarb‘ULúgGgát;p©it 3 / 4in. RtUv)aneRCIserIssRmab;
shear connection dUcenHeyIgsakl,gTMhMb‘ULúgdUcKña¦. RbsinebIkmøaMgkat;TTwgb‘ULúglub cMnYnb‘U

LúgEdlRtUvkarKW
1 3 1 13
h=d+ = + = in.
16 4 16 16
sRmab;RbehagEdlenAEk,rRCugEKmCageK
h 13 / 16
Lc = Le − = 1.5 − = 1.094in.
2 2
2d = 2(3 / 4 ) = 1.5in.
edaysar Lc < 2d / bearing strength KW
φRn = φ (1.2 Lc tFu ) = 0.75(1.2)(1.094 )t (58) = 57.11tkips / bolt
sRmab;RbehagepSgeTot
13
Lc = s − h = 3 − = 2.188in. > 2d
16
⎛3⎞
dUcenH φRn = φ (2.4dtFu ) = 0.75(2.4)⎜ ⎟t (58) = 78.30tkips / bolt
⎝4⎠
edIm,IrkkRmas;EdlRtUvkar dak; total bearing strength [esμI applied load:
2(57.11t ) + 6(78.30t ) = 121.0 b¤ t = 0.207in.

Flange plate TaMgBIrnwgRtUv)anKNnaCa tension connecting elements.

¬ebIeTaHbICabnÞHEdkmYyrgkmøaMgsgát;k¾eday kartP¢ab;lMGitecalnUvbBaðasißrPaBTaMgGs;¦.
tMNcakp©it 345 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

eKnwgkMNt;muxkat;Gb,brmaEdlRtUvkarsRmab;kugRtaMgTajenAelI gross nig net area. BI AISC

Equation J5-1,
φRn = 0.90(Ag F y )

Ag EdlRtUvkar = 0.φ90RnF =
H
=
121.0
0.90 F y 0.90(36)
= 3.735in.2
y

BI AISC Equation J5-2,

φRn = 0.75 An Fu

EdlRtUvkar = 0.φ75RnF = 0.75HF = 0121

An
.75 (
.0
58 )
= 0.782in.2
u u

sakl,gTTwgrbs;bnÞHEdk wg = 6.5in. ¬esμIeTAnwgTTwgsøabrbs;Fñwm¦. kMNt;kRmas;caM)ac;edIm,I

bMeBjtRmUvkar requirement.
Ag = 6.5t = 3.735in.2 b¤ t = 0.575in.

KNnakRmas;EdlcaM)ac;edIm,IbMeBjtRmUvkar net area

( ⎡
) ⎛ 7 ⎞⎤
An = twn = t wg − ∑ d hole = t ⎢6.5 − 2⎜ ⎟⎥ = 4.750t
⎣ ⎝ 8 ⎠⎦
yk 4.750t = 2.782in.2 b¤ t = 0.586in. ¬lub¦
kRmas;k¾RtUvFMCagGVIEdlTamTarsRmab; bearing dUcenHvaRtUvCakRmas;Gb,brmaEdlGacTTYlyk
)an. sakl,gbnÞH 6 1 2 × 5 8 . bnÞHenHCa tension connecting element dUcenH net area rbs;vamin
GacelIsBI 0.85 Ag enAkñúgkarKNna (AISC J5.2):
5⎡ ⎛ 7 ⎞⎤
An = ⎢6.5 − 2⎜ ⎟⎥ = 2.969in.2
8⎣ ⎝ 8 ⎠⎦
0.85 Ag = 0.85(0.625)(6.5) = 3.453in.2 > 2.969in.2 (OK)

ykbnÞH 6 1 2 × 5 8
Epñkrbs;RkLaépÞsøabrbs;FñwmnwgRtUv)an)at;bg;edaysarRbehagrbs;b‘ULúg nig moment capacity
RtUv)ankat;bnßy. AISC B10 GnuBaØatkarkat;bnßyenHedIm,I[ecalenAeBl
0.75Fu A fn ≥ 0.90 F y A fg (AISC Equation B10-1)

Edl A fg = gross flange area

= b f ⋅ t f = 6.530(0.535) = 3.494in.2
A fn = net flange area

T.Chhay 346 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

( ) ⎡ ⎛ 7 ⎞⎤
= t f b f − ∑ d h = 0.535⎢6.530 − 2⎜ ⎟⎥ = 2.557in.2
⎣ ⎝ 8 ⎠⎦
edayeRbI AISC Equation B10-1 eyIgTTYl)an
0.75Fu A fn = 0.75(58)(2.557 ) = 111.2kips

0.9 F y A fg = 0.9(36)(3.494) = 113.2kips > 111.2kips

edaysar AISC Equation B10-1 minRKb;RKan; flexural KYrRtUvQrelIRkLaépÞsøabRbsiT§PaB

(effective flange area)
5 Fu
A fe = A fn
6 Fy
5 ⎛ 58 ⎞
= ⎜ ⎟(2.557 ) = 3.433in.2 (AISC Equation B10-3)
6 ⎝ 36 ⎠
RkLaépÞenHminxusKñay:agxøaMgBI actual gross flange are 3.494in.2 dUcenH flexural strength eday
minRtUvEkERb.
cemøIy³ eRbItMNEdlbgðajenAkñúgrUbTI 8>34 ¬tRmUvkar column stiffener nwgRtUv)anBicarNaenAkñúg
Epñk 8>7¦*

*
rUbTI 8>34 k¾bgðajBInimitþsBaØasMrab; bevel groove weld, edayeRbIenATIenHsMrab; beam flange plate-to-column connection
tMNcakp©it 347 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

8>7> Column Stiffeners and other Reinforcement

m:Um:g;PaKeRcInEdl)anepÞrBIFñwmeTAssrenAkñúgtMNrwgmanTRmg;Ca couple EdlpSMeLIgeday
kmøaMgTaj nigkmøaMgsgát;EdlmanenAkñúgsøabrbs;Fñwm. karGnuvtþn_kmøaMgcMNucEdlmantémøFMGac
TamTarkarBRgwgssr. sRmab;m:Um:g;GviC¢manEdldUckrNICamYybnÞúkTMnaj kmøaMgTaMgenHmanTisedA
dUcbgðajenAkñúgrUbTI 8>35 CamYynwgsøabxagelIbMputrbs;FñwmEdlbBa¢ÚnkmøaMgTajeTAssr ehIy
søabxageRkamEdlbBa¢ÚnkmøaMgsgát;.
kmøaMgTaMgBIrRtUvbBa¢ÚneTARTnugssrCamYynwgkmøaMgsgát;EdlmaneRKaHfñak;Cagedaysar
stability problem. kmøaMgTajenAxagelIGacrMxansøabssr ¬rUbTI 8>35 c¦ EdlbegáItbnÞúkbEnßm

eTAelIkartP¢ab;edaypSarénsøabssreTAsøabFñwm. RbePTeRKOgBRgwg (stiffener) Edl)anbgðaj

)anBRgwgsøabssr. dUc)aneXIjy:agc,as; stiffener RtUv)anpSarP¢ab;eTAnwgRTnug nigsøab. Rbsin
ebIm:Um:g;EdlGnuvtþminpøas;bþÚrTisedA stiffener EdlTb;Tl;nwgkmøaMgsgát; ¬stiffener xageRkam¦ min
RtUvkarkarpSareT.

AISC Specification Requirements

tRmUvkarrbs; AISC sRmab;karBRgwgRTnugssrRtUv)anerobrab;enAkñúg Chapter K, “strength
Design Considerations.”. sRmab;EpñkCaeRcIn karpþl;[enHQrenAelIkarviPaKedayRTwsþIEdlRtUv

)anEkERbedIm,I[RtUvnwglT§plrbs;karBiesaF. RbsinebIbnÞúkemKuNGnuvtþn_EdlRtUv)anepÞreday
søabFñwm b¤ flange plate FMCag design strength φRn sRmab;RKb;sßanPaBkMNt;Edl)anBicarNaTaMg
Gs; enaHeKRtUvEteRbI stiffener.
edIm,IeCosvag local bending failure rbs;søabssr kmøaMgTajBIsøabFñwmdac;xatminRtUv
FMCag
(
φRn = φ 6.25t 2f Fyf ) (AISC Equation K1-1)

Edl φ = 0.90
tf = kRmas;rbs;søabssr
F yf = yield stress rbs;søabssr

sRmab;sßanPaBkMNt;rbs; local web yielding rgkugRtaMgsgát;

T.Chhay 348 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

[
φRn = φ (5k + N )F ywt w ] (AISC Equaton K1-2)

b¤ enAeBlEdlbnÞúkRtUv)anGnuvtþedaycm¶ayBIcugrbs;Ggát;EdlesμIkm<s;rbs;Ggát;
φRn = φ [(2.5k + N )Fywt w ] (AISC Equation K1-3)

Edl φ = 1.0
k = cm¶ayBIépÞsøabxageRkArbs;ssreTAeCIgrbs; fillet EdlenAelIRTnug

N = RbEvgrbs;bnÞúkGnuvtþn_ = kRmas;rbs;søabFñwm b¤ flange plate

F yw = yield stress rbs;RTnugssr

t w = kRmas;rbs;RTnugssr

eyIgk¾eRbI AISC Eqution K1-2 nig K1-3 in Section 5.13 edIm,IGegát web yielding enAkñúgFñwmEdl
rgbnÞúkcMcMNuc.
edIm,IkarBar web crippling enAeBlEdlbnÞúksgát;RtUv)anbBa¢ÚneTAEtsøabmYy dUckñúgkrNI
ssrxageRkAEdlmanP¢ab;CamYyFñwmEtmçag enaHbnÞúkGnuvtþn_minRtUvFMCag design strength Edl[
daysmIkarmYykñúgcMeNamsmIkarxageRkam. ¬eyIgk¾Føab;)anerobrab;BI web crippling enAkñúg web
crippling enAkñúgEpñkTI 5>13¦ enAeBlEdlbnÞúkRtUv)anGnuvtþenAcm¶ayy:agtic d / 2 BIcugrbs;ssr
⎡ 1.5 ⎤
⎛N ⎞⎛⎜ t w ⎞⎟ ⎥ F ywt f
φRn = φ135t w2 ⎢1 + 3⎜ ⎟ (AISC Equation K1-4)
⎢ ⎝ d ⎠⎜⎝ t f ⎟⎠ ⎥ tw
⎢⎣ ⎥⎦
Edl φ = 0.75
d=km<s;srubrbs;ssr
RbsinebIbnÞúkRtUv)anGnuvtþenAcugrbs;ssr
⎡ 1.5 ⎤
⎛N ⎞⎛⎜ t w ⎞⎟ ⎥ Fywt f
φRn = φ 68t w2 ⎢1 + 3⎜
⎢
⎟
⎝ d ⎠⎜⎝ t f ⎟⎠ ⎥ tw
sRmab; N
d
≤ 0.2
⎣⎢ ⎦⎥
(AISC Equation K1-5b)
⎡ 1.5 ⎤
⎛ N ⎞⎛ t ⎞ ⎥ F ywt f
b¤ φRn = φ 68t w2 ⎢1 + ⎜ 4
⎢ ⎝ d
− 0.2 ⎟⎜ w ⎟
⎠⎜⎝ t f ⎟⎠ ⎥ tw
sRmab; N
d
> 0.2
⎢⎣ ⎥⎦
(AISC Equation K1-5b)

tMNcakp©it 349 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

kmøaMgsgát; backling rbs;RTnugRtUv)anGegátenAeBlEdlbnÞúkRtUv)anbBa¢ÚneTAsøabssr

TaMgBIr. bnÞúkEbbenHnwgekItmanenAssrxagkñμúgCamYynwgFñwmEdlP¢ab;eTAssrTaMgsgxag. Design
strength sRmab;sßanPaBkMNt;enHKW
⎡ 4100t w
3
F yw ⎤
φRn = φ ⎢ ⎥ (AISC Equation K1-8)
⎢ h ⎥
⎣ ⎦
Edl φ = 0.90
h= km<s;RTnugssrBIeCIgrbs; fillet eTAeCIgrbs; fillet ¬rUbTI 8>36¦
RbsinebIkartP¢ab;enAEk,rcugrbs;ssr ¬EdlRbsinebIbnÞúkRtUv)anGnuvtþenAcm¶ay d / 2 BI
cug¦ ersIsþg;Edl[eday AISC Equation K1-8 KYrRtUv)ankat;bnßyBak;kNþal.
niyayedaysegçb edIm,IGegátPaBcaM)ac;sRmab; column stiffener eKRtUvRtYtBinitüsßanPaBkM
Nt;bIdUcxageRkam³
!> Local flang bending (AISC Equation K1-1)
@> Loacl web yielding (AISC Equation K1-2 or K1-3)
#> Web crippling b¤kmøaMgsgát; buckling rbs;RTnug. ¬RbsinebIkmøaMgsgát;RtUv)anGnuvtþ
eTAelIsøabEtmYy eKRtUvRtYtBinitü web crippling [AISC Equation K1-4 b¤ K1-5]. RbsinebIkmøaMg
sgát;RtUv)anGnuvtþeTAelIsøabTaMgBIr eKRtUvRtYtBinitü compressive buckling rbs;RTnug [AISC
Equation K1-8]¦.

T.Chhay 350 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RbsinebI stiffener EdlRtUvkareday AISC Equation K1-2 sRmab; local web yielding,
eKGacrkRkLaépÞmuxkat;EdlRtUvkarsRmab; stiffener dUcxageRkam. snμt;faeKGacTTYl)an design
strength bEnßmBIRkLaépÞrbs; stiffener Ast Edl yield. dUcenHBI AISC Equation K1-2.

φRn = φ [(5k + N )F ywt w + Ast Fyst ]

Edl Fyst Ca yield stress rbs; stiffener. dak;[GgÁxagsþaMrbs;smIkarenHesμInwgbnÞúkGnuvtþn_Edl

smÁal;eday Pbf nigedaHRsaysRmab; Ast eKTTYl)an
Pbf / φ − (5k + N )Fywt w
Ast =
F yst
Pbf − (5k + tb )Fywt w
=
Fyst
¬*>^¦
Edl φ = 1.0 nig tb KWkRmas;rbs;søabssr b¤ flange plate. smIkar 8>6 k¾GacRtUv)aneRbIedIm,IRtYt
Binitü local buckling yielding strength rbs;ssr. edaHRsayrk Ast RbsinebITTYl)anlT§pl
GviC¢man eKnwgminRtUvkar stiffener sRmab;sßanPaBenHeT.
RbsinebIeKRtUvkar stifferner AISC K1-9 [nUvTMhMsmamaRtrbs;vadUcxageRkam³
TTwgrbs; stiffener bUknwgkRmas;Bak;kNþalrbs;RTnugssrRtUvFMCagb¤esμInwgmYyPaKbIén
z

TTwgrbs;søabFñwm b¤ flange plate EdlbBa¢ÚnkmøaMgeTAssr b¤BIrUbTI 8>37

t
b+ w ≥ b
2
b
3
dUcenH b
b≥ b − w
3
t
2
kRmas;rbs; stiffener dac;xatRtUvEtFMCagb¤esμInwgBak;kNþalkRmas;rbs;søabFñwm b¤
z

flange plate b¤
t
t st ≥ b
2
z pleFobTTwgelIkRmas;RtUvEt
t
b
≤
250
F
¬xñat IS¦ t st
b
≤
95
Fy
¬xñat US¦
st y

eKRtUvkar Full-depth stiffener sRmab;krNI compression buckling b:uEnþeKGnuBaØat[eRbI

half-depth stiffener sRmab;sßanPaBkMNt;epSgeTot. dUcenHeKRtUvkar full-depth stiffener EtenA

eBlEdlFñwmRtUv)anP¢ab;eTAnwgssrTaMgsgxag.

tMNcakp©it 351 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

sRmab;RKb;sßanPaBkMNt;TaMgGs; karsMerckñúgkarpSar stiffener P¢ab;eTAsøabKWQr

elIlkçxNÐxageRkam³
z enAelIxagEdlrgkmøaMgTaj eKRtUvpSar stiffener P¢ab;eTAnwgRTnug nigsøab.
z enAelIxagEdlrgkmøaMgsgát; stiffener RKan;EtRtUvkardak;EGbnwgsøabEtb:ueNÑaH EteKk¾Gac
pSarvaP¢ab;eTAnwgsøab.
Part 3 of the Manual, “Column Design,” mantémøefrEdlRtUv)anerobCataragEdlGaceFVI

karkMNt;karcaM)ac;sRmab; stiffener. kareRbIR)as;rbs;vaRtUv)anbgðajenAkñúg]TahrN_EdlmanenA

kñúg “General Notes” EtminRtUv)anbgðajenATIenHeT.

kmøaMgkat;enAkñúgRTnugssr Shear in the Column Web

karepÞrm:Um:g;EdlmantémøFMeTAssrGacbegáItkugRtaMgkmøaMgkat;FMenAkñúgRTnugssrenAkñúgRBM
Ednrbs;tMN. ]TahrN_ tMbn; ABCD enAkñúgrUbTI 8>38. eBlxøH eKehAtMbn;enHCa panel zone.
Net moment RtUv)anKit dUcenHRbsinebIFñwmRtUv)antP¢ab;eTARCugTaMgsgxagrbs;ssr plbUkBiC-

KNiténm:Um:g;begáIt web shear enH.

RbsinebIkmøaMgsøabFñwmRtUv)ansnμt;[eFVIGMeBIenAcm¶ay 0.95db BIKña Edl db Cakm<s;Fñwm enaHkmøaMg
søabnImYy²GacRtUv)anykCa
M1 + M 2
H=
0.95d b
RbsinebIkmøaMgkat;ssrenAEk,r panel Ca Vu ehIymanTisedAdUcbgðaj kmøaMgkat;TTwgsrub
enAkñúg panel KW
M + M2
P = H − Vu = 1
0.95d
− Vu ¬*>&¦
b

T.Chhay 352 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RtUv)an[enAkñúg AISC K1.7 Ca φRv Edl φ = 0.90 ehIy Rv Ca

Web shear strength

GnuKmn_ eTAnwgbnÞúktamG½kSenAkñúgssr. enAeBlEdl Pu ≤ 0.4Py

Rv = 0.60 F y d c t w (AISC Equation K1-9)

enAeBlEdl Pu > 0.4Py /

⎡ ⎛P ⎞⎤
Rv = 0.60 F y d c t w ⎢1.4 − ⎜ u ⎟⎥ (ASIC Equation K1-10)
⎢⎣ ⎜ Py ⎟⎥
⎝ ⎠⎦
Edl Pu = bnÞúktamG½kSenAkñúgssr
Py = axial yield strength rbs;ssr = AF y

A = RkLaépÞmuxkat;rbs;ssr edayrYmbBa©ÚlTaMgeRKOgBRgwg ¬]TahrN_/ doubler plates¦

d c = TMhMssrtamTisFñwmsrub

t w = kRmas;RTnugssr edayrYmbBa©ÚlTaMgbnÞHEdkEdlBRgwg

F y = yield stress rbs;RTnugssr

RbsinebIRTnugssrman shear strength minRKb;RKan; eKRtUvBRgwgva. eKGaceRbI double plate

EdlmankRmas;RKb;RKan;edIm,IpSarP¢ab;eTAnwgRTnug b¤ diagonal stiffener mYyKUr. kñúgkarGnuvtþeK
eRcIneRbI stiffener Cag.
tMNcakp©it 353 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

k¾)anpþl;nUvsmIkaredIm,IenAeBlEdleKBicarNaBI frame stabality EdlrYmbBa©Úl

AISC K1.7

TaMgkMhUcRTg;RTayrbs; panel zone. vaminRtUv)anerobrab;enATIenHeT.

]TahrN_ 8>11³ kMNt;faetItMNén]TahrN_ 8>10 RtUvkar stiffener b¤k¾ column web reinforce-
ment. snμt;fa Vu = 0 nig Pu / Py = 0.4 .
dMeNaHRsay³ BI]TahrN_ 8>10 flange force RtUv)anykesμInwg
Pbf = H = 121.0kips

RtYtBinitü local flange bending CamYynwg AISC Equation K1-1:

(
φRn = φ 6.25t 2f Fyf )
[ ]
= 0.90 6.25(0.780)2 (36) = 123kips > 121kips (OK)
RtYtBinitü local web yielding CamYynwg AISC Equation K1-2:
φRn = φ [(5k + N )F ywt w ]
⎡ 5⎤
= 1.0 ⎢5(1.438) + ⎥ (36)(0.485) = 136kips > 121kips (OK)
⎣ 8⎦
RtYtBinitü web crippling CamYynwg AISC Equation K1-4:
⎡ 1.5 ⎤
⎛N ⎞⎛⎜ t w ⎞⎟ ⎥ F ywt f
φRn = φ135t w2 ⎢1 + 3⎜ ⎟
⎢ ⎝ d ⎠⎜⎝ t f ⎟⎠ ⎥ tw
⎣⎢ ⎦⎥
⎡ ⎛ 5 / 8 ⎞⎛ 0.485 ⎞ ⎤ 36(0.780 )
1.5
= 0.75(135)(0.485) ⎢1 + 3⎜
2
⎟⎜ ⎟ ⎥
⎢⎣ ⎝ 14.16 ⎠⎝ 0.780 ⎠ ⎥⎦ 0.485
= 193kips > 121kips (OK)
cemøIy³ eKminRtUvkar column stiffener eT.
sRmab;kmøaMgkat;TTwgeNAkñúgRTnugssr BIsmIkar *>& nigedayecalkRmas;rbs; shim enA
kñúgkarKNnark db kmøaMgkat;TTwgemKuNenAkñúg column web panel zone KW
P=
(M 1 + M 2 ) − V
u
0.95d b
210(12)
= − 0 = 120kips
0.95[20.83 + 2(5 / 8)]
edaysar Pu = 0.4Py eRbI AISC Equation K1-9:
Rv = 0.60 F y d c t w = 0.60(36 )(14.16 )(0.485) = 148.3kips

T.Chhay 354 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Design strength KW
φRv = 0.90(148.3) = 134kips > 120kips (OK)
cemøIy³ eKminRtUvkar column web reinforcement eT.

]TarhrN_ 8>12³ rUbTI 8>39 bgðajBI beam-to-column connection EdlepÞrm:Um:g;emKuN

142 ft − kips. m:Um:g;enHekIteLIgedaysarbnÞúkTMnagefr nigGefr. eKeRbIEdkRbePT A36 nig
electrode E 70 . cUreFVIkarGegát colum stiffener nigtRmUvkar web panel-zone reinforcement.

snμt;fa Vu = 0 nig Pu < 0.4Py .

dMeNaHRsay³ flange force KW
M 142(12)
Pbf = = = 98.07kips
d b − tb 17.90 − 0.525
edIm,IRtYtBinitü flange bending eKeRbI AISC Equation K1-1:
(
φRn = φ 6.25t 2f F yf )
[ ]
= 0.90 6.25(0.560)2 (36) = 63.50kips < 98.07kips (N.G.)
dUcenH eKRtUvkar stiffener edIm,IkarBar loacla flange bending.
edIm,IRtYtBinitü local web yielding eKeRbIsmIkar 8>6 CMnYs[kareRbI AISC Equation K1-2:
Pbf − (5k + tb )F ywt w
Ast =
F yst
98.07 − [5(1.062) + 0.525](36)(0.36)
= = 0.6236in.2
36
edaysar Ast viC¢man dUcenHeKRtUvkar stiffener mYyKUrEdlman combined cross-sectional area
y:agtic 0.623in.2 .
RtYtBinitü web crippling strength edayeRbI AISC Equation K1-4:
⎡ 1.5 ⎤
⎛N ⎞⎛⎜ t w ⎞⎟ ⎥ Fywt f
φRn = φ135t w2 ⎢1 + 3⎜ ⎟
⎢ ⎝ d ⎠⎜⎝ t f ⎟⎠ ⎥ tw
⎣⎢ ⎦⎥
⎡ ⎛ 0.525 ⎞⎛ 0.360 ⎞ ⎤ 36(0.560)
= 0.75(135)(0.36)2 ⎢1 + 3⎜ ⎟⎜ ⎟1.5⎥
⎣ ⎝ 8.25 ⎠⎝ 0.560 ⎠ ⎦ 0.360
= 107.9kips > 98.07kips (OK)
eKeRCIserIsTMhM stiffener edayQrelIlkçxNÐEdlpþl;[eday AISC Section K1-9,
ehIybnÞab;mkeKRtUvRtYtBinitüRkLaépÞmuxkat;EdlTTYl)an.
tMNcakp©it 355 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

TTwgGb,brmaKW
bf t 6.015 0.360
b≥ − w = − = 1.825in.
3 2 3 2
RbsinebIeKminGnuBaØat[bnøay stiffener eTAhYsRCugrbs;søabssr TTwgGtibrmaKW
8.07 − 0.360
b≤ = 3.855in.
2
kRmas;Gb,brmaKW
tb 0.525
= = 0.2625in.
2 2
sakl,g 3× 5 /16 ³
⎛5⎞
Ast = 3⎜ ⎟ × 2stiffeners = 1.875in.2 > 0.6236in 2 (OK)
⎝ 16 ⎠
RtYtBinitüpleFobTTwgelIkRmas; (width-thickness ratio)
b 3
= = 9.6
t st 5 / 16
95 95
= = 15.8 > 9.6 (OK)
Fy 36

T.Chhay 356 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

edaysarEtkartP¢ab;enHmanEtmçag dUcenHeKminRtUvkar full-depth stiffeners eT. dUcenH

= 4.125in. yk 4 1 2 in.
d 8.25
=
2 2
cemøIy³ eRbIEdkTMhM 3 × 5 /16 × 4 12 cMnYn 2 bnÞH. ¬kat;RcwbRCugEkgxagkñúgrbs;bnÞHEdkedIm,IeCos
vag fillet enARtg;kEnøgEdlsøab nigRTnugrbs;ssrCYbKña. kat;RcwbedaymMu 45o sRmab;TMhM
5 / 8in. ¦.

KNnaTwkbnSarsRmab;P¢ab; stiffener eTARTnugssr

TMhMGb,brma = 163 in. (AISC Table J2.4, edayQrelIkRmas;RTnug)
TMhMcaM)ac;sRmab;ersIusþg;KW
force resisted by stiffener
w=
0.707 L(φFW )
BIsmIkar *>^ kmøaMgEdlRtUvTb;eday stiffener KW
Ast F yst = Pbf − (5k + tb )F ywt w

= 98.07 − [5(1.062) + 0.525](36)(0.360 ) = 22.45kips

RbEvgEdlGacpSarP¢ab; stiffener eTAnwgRTnugssrKW
⎛ 5⎞
L = ⎜ 4.5 − ⎟ × 2sids × 2stiffeners = 15.5in.
⎝ 8⎠
¬emIlrUbTI 8>40¦
w=
22.45
0.707(15.5)(31.5)
3
= 0.0650in. < in.
16
TMhMGb,brma
ersIusþg;kmøaMgkat;rbs; base metal KW
⎛5⎞
φRn = φFBM t = 0.54 Fy t st = 0.54(36)⎜ ⎟ = 6.075kips / in.
⎝ 16 ⎠
nig ersIusþg;TwkbnSarcaM)ac; ¬sRmab; stiffener mYy¦ = 0.0650(0.707)(31.5)(2)
= 2.09kips / in. < 6.075kips / in. (OK)
cemøIy³ yk filler weld 3 /16in. .
KNnaTwkbnSarsMrba;P¢ab; stiffener eTAnwgsøabssr
TMhMGb,brma = 14 in. (AISC Table J2.4, edayQrelIkRmas;søab)
lT§PaBTwkbnSarkñúg 1in. = 0.707⎛⎜⎝ 14 ⎞⎟⎠(31.5) = 5.538kips / in.
< 0.54 Fy t st = 0.6075kips / in. (OK)

tMNcakp©it 357 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

RbEvgEdlmansRmab; = ⎛⎜⎝ 3 − 85 ⎞⎟⎠(2)(2) = 9.5in.

TMhMcaM)ac;sRmab;ersIusþg;KW
force resisted by stiffener 22.45 1
w= = = 0.106in. < in.
0.707 L(φFW ) 0.707(9.5)(31.5) 4

cemøIy³ yk fillet weld 1/ 4in. . ¬m:Um:g;Gnuvtþn_EdlekIteLIgedaybnÞúkTMnaj ehIyEdlminGac

bþÚrTisedAGnuvtþn_)an dUcenHeKGacdak; stiffener Pa¢b;eTAnwgsøabssr Edl stiffener enHTb;søabrg
karsgát;rbs;FñwmedaymincaM)ac;pSar b:uEnþkrNIenHmin)anniyayenATIenHeT¦.
RtYtBinitüRTnugssrsRmab;kmøaMgkat;TTwg. BIsmIkar *>&
P=
(M 1 + M 2 ) − V 142(12)
u = − 0 = 100.2kips
0.95d b 0.95(17.90)
BI AISC Equation K1-9
Rv = 0.60 F y d c t w = 0.60(36 )(8.25)(0.360 ) = 64.15kips

Design strength KW
φRv = 0.90(64.15) = 57.74kips < 100.5kips (N.G.)
eRbI AISC Equation edIm,IrkkRmas;RTnugEdlRtUvakar. edaHRsayrk t w edayKuNPaKyk
nigPaKEbgeday φ
t w = required doubler plate thickness

= 0.625 − 0.360 = 0.265in.

sakl,g td = 5 /16in. . TwkbnSarRtUvmanTMhM[RtUvKñanwgersIusþg;kmøaMgkat;énkRmas;caM)ac;
rbs; doubler plate. yk
T.Chhay 358 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

φFBM t d = 0.707 w(φFW )

φFBM t d 0.54(36 )(0.265)
b¤ w=
0.707(φFW )
=
0.707(31.5)
= 0.231in.

yk w = 1/ 4in.
BI AISC J2.2b, TMhMTwkbnSarGtibrmaKW
1 5 1 1
td − = − = in. (OK)
16 16 6 4
cemøIy³ double plate 5 /16in. nig fillet weld 1/ 4in
eRbI diagonal stiffener
eRbI full-depth horizontal stiffeners dUcbgðajenAkñúgrUbTI 8>41 ¬RKan;EtCaCMerIs¦.

kmøaMgkat;TTwgEdlTb;eday web reinforcement KW 100.2 − 57.74 = 42.46kips . RbsinebIkmøaMg

enHRtUv)anKitCakMub:Usg;kmøaMgtamG½kSedk P enAkñúg stiffener
P cosθ = 42.46kips
⎛ db ⎞
⎟⎟ = tan −1 ⎛⎜
17.90 ⎞
Edl θ = tan −1 ⎜⎜
⎝
⎟ = 65.26
⎠
o
⎝ c⎠
d 8 . 25
42.46
P=
(
tan 65.26 o ) = 101.5kips
yk φRn = φAst Fy = 0.9 Ast (36) = 101.5kips
bnÞab;mk Ast =
101.5
0.9(36)
= 3.13in.2

eRbI stiffener BIr/ 3× 9 /16 enAsgxagRTnug

tMNcakp©it 359 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Edlpþl;[ = 2(3)⎛⎜⎝ 169 ⎞⎟⎠ = 3.38in.2 > 3.13in.2 EdlRtUvkar

Ast (OK)

RtYtBinitüpleFobTTwgelIkRmas; (width-thickness ratrio):

b 3 95
= = 5.3 < = 15.8 (OK)
t st 9 / 16 36
KNnaTwkbnSar. RbEvgrbs; diagonal stiffener nImYy²KW
dc 8.25
=
cosθ cos 65.26 o( )
= 19.7in.

RbsinebIeKpSarenAelIépÞTaMgsgxagrbs; stiffener enaHRbEvgTwkbnSarKW

L = 19.7(4 ) = 78.8in.
TMhMTwkbnSarEdlcaM)ac;sRmab;ersIusþg;KW
P 101.5
w= = = 0.058in.
0.707 L(φFW ) 0.707(78.8)(31.5)
eRbITMhMGb,brma 1/ 4in. (AISC Table J2.4)
edaysarTMhMEdlcaM)ac;sRmab;ersIusþg;mantémøtUc eyIgnwgGegátemIllT§PaBkñúgkareRbITwknSarEdl
minCab;Kña. BI AISC J2.2b
RbEvgGb,brma = 4w = 4⎛⎜⎝ 14 ⎞⎟⎠ = 1.0in. b:uEnþvaminRtUvtUcCag 1.5in. ¬1.5in. lub¦
lT§PaB nigKMlatrbs;RkuménTwkbnSarbYnKW
⎛1⎞
4(0.707 )wL(φFw ) = 4(0.707 )⎜ ⎟(1.5)(31.5) = 33.41kips
⎝4⎠
lT§PaBEdlcaM)ac;kñúg 1in. =
101.5
19.7
= 5.152kips / in.

KMlatEdlcaM)ac;rbs;TwkbnSar =
33.41
5.152
= 6.48in.
shear capacity of base metal = 0.54 Fy t w = 0.54(36 )(0.360 ) = 7.00kips / in.

lT§PaBrbs;TwkbnSar = 0.707w(φFW ) = 0.707⎛⎜⎝ 14 ⎞⎟⎠(31.5)

= 5.57kips / in. < 7.00kips / in. (OK)
cemøIy³ eRbITwkbnSarminCab;Kña 1/ 4in.×1 12 in. EdlmanKMlatBImYyeTAmYy 6in. KitBIG½kS enAelIépÞ
nImYy²rbs; diagonal stiffener.
dUcEdl)anbgðajBImun eKniymeRbIdiagonal stiffener Cag doubler plate b:uEnþsRmab;lkçN³
esdækic©eKKYrEteRbIvaCamYynwgmuxkat;ssrFM. témøBlkmμCamYynwg doubler plate nig stiffener TaMg
T.Chhay 360 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Gs;GacnwgbEnßmtémøeRcIneTAelIsMPar³sRmab;ssrmuxkat;FM.

8>8> End Plate Connection

End plate connection Ca beam-to-column nig beam-to-beam connection Edlmankar
eBjniym ehIyRtUv)aneKeRbIcab;taMgBIBak;kNþalTsvtSr_qñaM 1950 mkemøH. rUbTI 8>42 bgðajBI
end plate connection BIrRbePTKW³ tMNsamBaØ b¤tMNrgEtkmøaMgkat; (Type PR construction) nig

tMNrwg b¤tMNTb;m:Um:g; (Type FR construction). Rigid connection k¾RtUv)anehA mü:ageTotfa

extended end plate connection. eKalkarN_rbs;RbePTTaMgBIrKW bnÞHEdkEdlRtUv)anpSarP¢ab;enA

xagcugrbs;FñwmRtUv)ancab;P¢ab;eTAnwgssr b¤Fñwmedayb‘ULúg. tMNenHRtUvkarb‘ULúgticCagkartP¢ab;

epSgeTotEdlGaceFVI[kardMeLIgelOn.
sRmab;tMNsamBaØ eKRtUvykcitþTukdak;kñúgkareFVI[manlkçN³ flexible RKb;RKan;edIm,IeFVI
[FñwmmanmMurgVilenAxagcug. eKGacTTYl)an flexibility enH RbsinebIbnÞHEdkmanTMhMtUc nigesþIg
ebIeRbobeFobCamYynwg tMNRbePT fully restrained. Manual of Steel Construction, in Part 9,
“Simple Shear Connections,” )anENnaMfa kRmas;RtUvsßitenAcenøaH 1 / 4in. nig 3 / 8in. edIm,I

TTYl)an flexibility. EpñkenHrbs; Manual k¾bgðajBIeKalkarN_ENnaM nig]TaheN_EdlrYmman

reaction capacities sRmab;bnSMCaeRcInénbnÞHEdk nigb‘ULúg.

karKNna moment-resisting end plate connections RtUvkarkarkMNt;kRmas;bnÞH TMhMTwk

bnSar nigkarlMGitBIb‘ULúgCaedIm. karKNnaBITwkbnSar nigb‘ULúgCakarGnuvtþn_nUv traditional
analysis procedures. b:uEnþ karKNna kRmas;bnÞHKWQrelIlT§plrbs;karBiesaF nig statistical

research (Krishnamuthy, 1978). EpñkrgkarTajrbs;tMNKWmaneRKaHfñak; Éb‘ULúgenAEpñkrgkar

sgát;mannaTICaGñkrkSatMN[enARtg;G½kS. RbsinebImanm:Um:g;sgxag eKRtUvKNnaEpñkrgkar

TajTaMgsgxag. viFITUeTAKWxageRkam³
!> kMNt;kmøaMgenAkñúgsøabrgkarTajrbs;Fñwm
@> eRCIserIsb‘ULúgEdlcaM)ac;edIm,ITb;Tl;nwgkmøaMgenH nigteRmobva[manlkçN³sIuemRTI
eFobnwgsøabrgkarTaj. RbsinebIm:Um:g;sßitenAsgxag eKRtUveFVIkartMerobdUcKñaenAelIEpñk
rgkarsgát;Edr. b‘ULúgRtUvEtmancMnYnRKb;RKan;edIm,ITb;Tl;nwgkmøaMgkat;TTwgEdl)anmk
BIRbtikmμFñwm.
tMNcakp©it 361 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

#> cat;TukEpñkrbs;søabFñwm nigbnÞHEdkEdlenAek,reFVIkarCa tee-shape EdlrgbnÞúkTajEdl

GnuvtþeTAelIRTnugrbs;va dUcbgðajenAkñúgrUbTI 8>43.
$> eRCIserIsTTwg nigkRmas;rbs;søab tee enHedIm,IbMeBjtRmUvkar flexural dUcKñanwgviFI
KNna tee hanger ¬emIlEpñk 7>8¦.
%> RtYtBinitükmøaMgkat;enAkñúgbnÞHEdk.
^> KNnaTwkbnSar.
Manual of Steel Construction (Volume II), bgðajbIviFIsaRsþKNnalMGitCamYynwg]Ta-

hrN_enAkñúg Part 10, “Fully Restrained (FR) Moment Connection”. viFIsaRsþkñúgkarKNnarbs;

vaRsedogKñanwgGVIEdl)anerobrab;xagelIedaymankarEksRmYlxøH eBlxøHeKehAvafa Split-tee
method (Krishnamurthy, 1978). GVIEdlxusKña KWCMhanTI $ sRmab;karKNnam:Um:g;Bt;enAkñúgbnÞH

Edk. Traditional analysis KitbBa©ÚlTaMg prying forces EdlmanniyayenAkñúgEpñkTI 7>8. sRmab;

viFIKNnanaeBlbc©úb,nñ kareRCIserIsb‘ULúg nigkRmas;bnÞHEdkminGaRs½ynwgkarBIcarNaBI prying
action eT. karKNnam:Um:g;KWQrelIkarsikSa statistical analysis of finite element Edlmankar

bBa¢ak;edaykareFVIBiesaFn_. CMhandMbUgenAkñúgviFIsaRsþKNnaKW KNnakmøaMgenAkñúgsøab gkarTaj

rbs;Fñwm.
T.Chhay 362 Eccentric Connections
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Mu
Puf =
d −t f

bnÞab;mk eKeRCIserIsb‘ULúgedIm,ITb;nwgkmøaMgTajenH ehIyeKtMerobvaCaBIrCYr[manlkçN³

sIuemRTIeFobnwgsøabrgkarTajrbs;Fñwm. eKRtUvbEnßmb‘ULúgy:agticBIrenARtg;søabrgkarsgát;sRmab;
tRmUvkarrbs;RbtikmμFñwm. cMnYnb‘ULúgEdlRtUvkaredIm,ITb;Tl;nwgRbtikmμFñwmnwgQrelI shear capacity
b¤k¾ slip-critical capacity rbs;b‘ULúg EdlGaRs½ynwgRbePTrbs;tMN. RbsinebItMNCa bearing-
type eKRtUvRtYtBinitüGnþrkmμénkmøaMgkat; nigkmøaMgTajenAkñúgb‘ULúg. eKmincaM)ac;eFVIkarGegátenH

sRmab; clip-critcal connection.

m:Um:g;GtibrmaenAkñúg split –tee nwgekItmanenARtg; “load line”, muxkat; 1-1 EdlbgðajenA
kñúgrUbTI 8>43 KW
tMNcakp©it 363 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

M t = F1s

Edl F1 = kmøaMgkat;TTwg = P2uf

s = cm¶ayBI load line eTAcMNucrbt; = e
p
2
pe = p f − 0.25d b − 0.707 w

BIrUbTI 8>43/ p f Cacm¶ayBIG½kSb‘ULúgeTAsøabFñwm EdlCaTUeTAesμnwgGgát;p©itb‘ULúg db + 1/ 2in.

ehIy w CaTMhMTwkbnSar. eKehA p f Cacm¶ayb‘ULúg (bolt distance) ehIy pe Cacm¶ayb‘ULúg
RbsiT§PaB (effective bolt distance b¤ effective span). m:Um:g; M t EdlRtUv)anbMElgedayemKuN
α m edIm,ITTYl)anm:Um:g;RbsiT§PaB M eu

M eu = α m M t
Edl ( )
α m = C a Cb A f / Aw 1 / 3 ( pe / d b )1 / 4

Ca = cMnYnefrEdlTak;TgeTAnwglkçN³rbs;smÖar³rbs;b‘ULúg nigbnÞHEdk.
Cb = b f / b p

bf = TTwgrbs;søabFñwm
bp = TTwgrbs; end plate [Krishnamurthy (1978) )anENnaMnUvTTwgRbsiT§PaBGtibrma
b f + 2w + t p Edl tp CakRmas;rbs; end plate. Manual ENnaMTTwgCak;Esþg

Gtibrma b f + 1in. ]
A f = RkLaépÞsøabFñwm

Aw = RkLaépÞRTnugFñwmEdlenAcenøaH fillet

cMnYnefr Ca CaGnuKmn_EtnwglkçN³rbs;smÖar³ ehIyRtUv)anerobCataragsRmab;cMNat;fñak;

TUeTArbs; structural steel nig b‘ULúgersIusþg;x<s;. taragenHRtUv)anbgðajenAkñúg Table 10-1 enAkñúg
Part 10 én Manual. Table 10-2 [nUvtémø A f / Aw sRmab;rUbragFñwmEdlRtUv)aneRbICaTUeTA. enA

eBlEdleKKNnam:Um:g; M eu rYcehIy eKGacdak;va[esμInwg design strength enaHeKnwgGacrk

kRmas;bnÞHEdkGtibrma t p pre EdlcaM)ac;. sRmab;muxkat;ctuekaNEkgEdlekageFobnwgG½kStUc
(minor axis) enaH design strength KW

T.Chhay 364 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

⎛ b pt 2 ⎞
⎜ p req ⎟
φb M n = φb M p = φb ZF y = 0.90⎜ ⎟ Fy
⎜ 4 ⎟
⎝ ⎠
eday[smIkarenHesμInwgm:Um:g;emKuN eKTTYl)ankRmas;bnÞHEdk
⎛ b pt 2 ⎞
⎜ p pre ⎟
0.90⎜ ⎟ Fy = M eu
⎜ 4 ⎟
⎝ ⎠

dUcenH t p req =
4 M eu
0.90b p Fy

eKGacP¢ab;søabrgkarTajrbs;FñwmeTAnwgbnÞHEdkeday full penetration groove weld b¤k¾

eday filler weld EdlpSarBT§½CMuvijsøabTaMgGs;. kmøaMgenAkñúgsøabTaMgGs;RtUv)anbegáItenAelIEpñk
rgkarTaj. eKKYrpSarRTnugenAépÞsgçagCamYynwg fillet welds EdlmanlT§PaBTb;Tl;nwgRbtikmμFmwñ .
eKRtUveKarBnUveKalkarN_ENnaMbEnßmxageRkamedIm,IbMeBjkarsnμt;sRmab;GnuvtþnUvviFIKNnaxagelI.
!> TaMgbnÞHEdk nigEdkFñwmRtUvman yield stress dUcKñaKw Fy
@> Ggát;p©itb‘ULúg db minRtUvFMCag 1 1 2 in. = 38mm
#> b‘ULúgRtUvEtrgkarTajEdleKarBtam AISC Table J3.1.
$> cm¶ayRCugEKmbBaÄrKYrmantémøRbEhl 1 3 4 db b:uEnþminKYrtUcCag 1 1 2 db

]TahrN_ 8>13³ KNna end plate connection sRmab;Fñwm W 18× 35 . tMNenHRtUvmanlT§PaBkñúg

karbBa¢Únm:Um:g;emKuN 173 ft − kips nigkmøaMgkat;TTwgemKuN 34kips . eRbIEdk A36 / electrode

E70 XX nig slip-critical bolts A325 .

dMeNaHRsay³ kmøaMgsøabKW
Mu 173(12 )
Puf = = = 120.2kips
d − t f 17.7 − 0.425

sakl,gb‘ULúgBIrCYrEdlkñúgmYyCYrmanBIrRKab;enAsøabxagelI nigb‘ULúgBIrRKab;enAsøabxageRka Edl

b‘ULúgTaMgGs;manR)aMmYyRKab;. Design strength rgkmøaMgTajsRmab;b‘ULúgmYyRKab;KW
φRn = 0.75(90) Ab
ehIyRkLaépÞmuxkat;EdlcaM)ac;sRmab;b‘ULúgmYyKW
Required φRn 120.2 / 4
Ab = = = 0.445in.2
0.75(90 ) 0.75(90 )
tMNcakp©it 365 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

cemøIy³ eRbIb‘ULúg A325 Ggát;p©it 7 / 8in. ¬ Ab = 0.6013in.2 ¦

eKGackMNt;kmøaMgkat;GtibrmaEdlRTedaytMNBIkarBicarNa slip-critical strength rbs;b‘ULúg
¬EdlnwgmantémøtUcCag shear strength¦. sRmab;b‘ULúgR)aMmYyRKab;
φRstr = φ (1.13μTm N b N s ) = 1.0(1.13)(0.33)(39)(6)(1) = 87.3kips > 34kips (OK)
¬eKmindwgkRmas;rbs;søabssr ehIyeKminTan;sÁal;kRmas;rbs; end plate dUcenHeKminGaceFVIkar
Gegát bearing strength enAeBlenH)aneT. b:uEnþ enAeBlEdlRKb;EpñkEdlRtUvtP¢ab;TaMgGs;
RtUv)anKNna enaHeKGacRtYtBinitü bearing strength¦. edaysarvaCa slip-critical connection
enaHeKminRtUvkar RtYtBiniüGnþrkmμénkmøaMgkat; nigkmøaMgTajeT.
cemøIy³ eRbIbU‘LúgR)aMmYy EdlbYnRtUv)antMerobsIuemRTIKñaeFobnwgsøabrgkarTaj nigBIreTotsßitenA
Rtg;søabrgkarsgát;.
sRmab; flange weld RbEvgEdlGacpSar)anKW
L = 2b f + 2t f − t w = 2(6.0 ) + 2(0.425) − 0.30 = 12.55in.

TMhMTwkbnSarEdlRtUvkarKW
Puf 120.2
w= = = 0.4301in.
0.707 L(φFw ) 0.707(12.55)(31.5)
eTaHbICaeKminTan;sÁal;kRmas;rbs; end plate k¾eday k¾TMhMTwkbnSarGb,brmaEdl)anBI AISC
Table J2.4 minEdlFMCag 5 / 16in. dUcenH 0.43in. EdlRtUvkarsRmab;ersIusþg;nwgmantémøFMCag.

cemøIy³ eRbI fillet weld 7 /16in.

sRmab; end plate/ yk
1
p f = db + = 0.875 + 0.500 = 1.375in.
2
pe = p f − 0.25d b − 0.707 w
⎛7⎞
= 1.375 − 0.25(0.875) − 0.707⎜ ⎟ = 0.8470in.
⎝ 16 ⎠
sRmab;TTwgbnÞHEdk/ yk
bq = b f + 1 = 6.00 + 1 = 7.00in.
⎛ Puf ⎞⎛ pe ⎞ ⎛ 120.2 ⎞⎛ 0.8470 ⎞
bnÞab;mk M t = F1s = ⎜⎜ ⎟⎜ ⎟ = ⎜
⎟ ⎟⎜ ⎟ = 25.45in. − kips
⎝ 2 ⎠⎝ 2 ⎠ ⎝ 2 ⎠⎝ 2 ⎠
Ca = 1.36 (Table 10-1, Part 10 of the Manula)

T.Chhay 366 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

bf 6.00
Cb = = = 0.9258
bq 7.00
Af
= 0.504 (Table 10-2, Part 10 of the Manual)
Aw
1/ 3 1/ 4
⎛ Af ⎞ ⎛ pe ⎞
α m = C a Cb ⎜⎜ ⎟
⎟
⎜⎜ ⎟⎟
⎝ Aw ⎠ ⎝ db ⎠

= 1.36(0.9258)(0.504)1 / 3 (0.8470 / 0.875)1 / 4 = 0.9939

M eu = α m M t = 0.9939(25.45) = 25.29in. − kips
4M eu 4(25.29)
t p req = = = 0.668in.
0.90b p Fy 0.90(7.00)(36)

cemøIy³ ykkRmas;bnÞHEdk 3 / 4in.

TTwgbnÞHEdkRbsiT§PaBGtibrmaEdlENnaMeday Krishnamurthy (1978) KW
⎛7⎞ 3
b f + 2 w + t p = 6.00 + 2⎜ ⎟ + = 7.62in. > 7.00 (OK)
⎝ 16 ⎠ 4
RtYtBinitükmøaMgkat;. kmøaMgkat;enAkñúgbnÞHEdkKW
Puf 120.2
F1 = = = 60.1kips
2 2
BI AISC J5, ersIusþg;kmøaMgkat;KW (shear strength) KW
( ) ⎛
φRn = 0.90 0.60 Ag Fy = 0.90(0.60)⎜ 7 × ⎟(36) = 102kips > 60.1kips
3⎞
(OK)
⎝ 4⎠
edIm,ITTYl)an shear strength rbs;RTnugdUcKña ersIusþg;TwkbnSarEdlcaM)ac; ¬TwkbnSarBIrCYrEdlenA
sgçagRTnug¦ KW
φvVn 103
= = 5.819kips / in.
d 17.7
TMhMTwkbnSarEdlRtUvkar
5.819 / 2
w= = 0.131in.
0.707(31.5)
kMNt;TMhMTwkbnSarEdlcaM)ac;edIm,ITb;Tl;nwgkarBt;enAkñúgRTnug. enAeBlEdlm:Um:g;Bt;eFVIkardl;m:U
m:g;)øasÞic kugRtaMgenAkñúgRTnugesμInwg yield stress Fy ehIybnÞúkkñúgmYyÉktþaRbEvgrbs;TwkbnSarKW
( )
φb Fy × t w × 1 = 0.90(36 )(0.300 ) = 9.720kips / in.

bnÞúkkñúgmYyÉktþarbs;TwkbnSarmYyCYrKW 9.72 / 2 = 4.86kips / in. ehIyTMhMTwkbnSarEdlRtUvkarKW

tMNcakp©it 367 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

4.860
w= = 0.2182in. > 0.131in.
0.707(31.5)

TMhMTwkbnSarGb,brmaKW 1/ 4in. (AISC Table J2.4, edayQrelIkRmas;rbs;bnÞHEdk).

cemøIy³ eRbI fillet weld 1/ 4in. ¬karKNnaRtUv)ansegçbenAkñúgrUbTI 8>44¦

Column Web Stiffener Consideration

eKbegáIt AISC Equation K1-2 EdlkarBar web yeilding rbs;ssrenAkñúgtMN beam-to-
column connection enAeBlEdleKeRbI end plates. smIkarenHKWQrelIkarkMNt;kugRtaMgenAelImux

kat;rbs;RTnugEdlbegáIteLIgedaykRmas;rbs;va nigRbEvg tb + 5k dUcbgðajenAkñúgrUbTI 8>45 b.

eKnwgTTYl)anRkLaépÞFMCag enAeBlEdlbnÞúkRtUv)anbBa¢Úntamry³ end plate. RbsinebIeKKitTwk
bnSar beam flange-to-plate nigbnÞúkRtUv)ansnμt;EckedayCRmal 1 :1 tamry³bnÞHEdk RbEvgRTnug
EdlrgbnÞúknwgesμInwg tb + 2w + 2t p + 5k . edayQrelIkarsikSaRsavRCavedaykarBiesaF (Hendrick
and Murray, 1984) tYr 5k GacRtUv)anCMnYseday 6k Edlpþl;lT§plenAkñúgsmIkarxageRkamsRmab;

yielding strength rbs;RTnug³

[(
φRn = φ 6k + tb + 2 w + 2t p F ywt w )]
Edl w= TMhMTwkbnSar

T.Chhay 368 Eccentric Connections

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

elIsBIenH eKRtUveFVIkarGegátBI local flange bending ning web stability (web crippling b¤
compression buckling). Part 10 of the Manual maneKalkarN_ENnaMBIkarKit local flange

bending.

8>9> esckþIsnñidæan (Concluding Remarks)

enAkñúgeyIgsgát;F¶n;elIkarKNna nigkarviPaKBIb‘ULúg nigTwkbnSareRcInCag connection
fitting dUcCa framing angle nig beam seats. kñúgkrNICaeRcIn karpþl;[sRmab; bearing enAkñúg

tMNedayb‘ULúg nig base metal/ nigsRmab;kmøaMgkat;enAkñúgtMNedayTwkbnSar nwgFananUvPaBRKb;

RKan;rbs;ersIusþg;rbs;EpñkTaMgenH. b:uEnþeBlxøH eKRtUvkarGegátkmøaMgkat;bEnßm. enAeBlxøHeTot eK
RtUvEtBicarNaBI direct tensiion nigm:Um:g;Bt;.
Flexibility rbs;tMNCakarBicarNad¾sMxan;mYyeTot. sRmab; shear connection (simple

framing), EpñkEdlP¢ab;RtUvman flexible RKb;RKan;edIm,IGnuBaØat[tMNvileRkamGMeBIrbs;kmøaMg. b:uEnþ

tMNRbePT FR (rigid connections) KYrEtrwgRKb;RKan;EdlmMurgVilrbs;Ggát;EdlRtUv)anP¢ab;GacrkSa

nUvtémøGb,brma.
CMBUkenHRKan;EtENnaMBIkarKNnatMNenAkñúgeRKOgbgÁúMEdkEtb:ueNÑaH edaymin)anniyaylMGit
Gs;esckþIeT. Blodgett (1966) KWCaRbPBB½t’mand¾manRbeyaCn_EdlniyaylMGitBItMNedaypSar.
eTaHbICavaRtUv)ane)aHBum<yUrbnþicEmn Etvapþl;nUvkarENnaMEdlmanRbeyaCn_CaeRcIn. dUcKña
Detailing for Stell Construction (AISC, 1983) CaRbPaBEdlmanB½t’manEdlmanGtßRbeyaCn_

sRmab;GñkKNna nigGñklMGitkartP¢ab;.
tMNcakp©it 369 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

IX. eRKOgbgÁúMsmas
Composite Construction
9>1> esckþIepþIm (Introduction)
eRKOgbgÁúMsmasCaeRKOgbgÁúMsMNg;EdlGgát;rbs;vapÁúMeLIgedaysmÖar³BIrRbePTKW EdkeRKag
nigebtugGarem:. niyay[xøIGgát;eRKOgbgÁúMsmaspSMeLIgedaysmÖar³BIr b¤eRcInRbePT. eRKOgbgÁúM
smasRtUv)anerobrab;enAkñúg AISC Chapter I, “Composite Members.”.
Fñwmsmas (composite beam) GacmaneRcInTRmg;. FñwmsmasBIdMbUgRtUv)ancak;bgáb;kñúgeb
tugdUcbgðajenAkñúgrUbTI 9>1 a. vaCaCeRmIsmYyenAeBlEdleKRtUvkarkarBareRKOgbgÁúMEdkBIePøIg
(fireproofing) ehIymUlehtumYyeTotKWeKGacKitBIkarcUlrYmrbs;ersIusþg;ebtugeTAkúñgersIusþg;rbs;

Fñwm. naeBlbc©úb,nñenH eKmanviFIkarBarePøIgEdlmanlkçN³esdækic© nigTm¶n;Rsal dUcenHeKkRmcak;

bgáb;eRKOgbgÁúMEdkkñúgebtugeToteT. eKGacTTYl)an composite behavior edayP¢ab;FñwmEdkeTAnwg
kRmalebtugEdlvaRTEdleFVI[EpñkTaMgBIreFVIkarCamYyKña. enAkñúgRbB½n§kRmal b¤RbB½n§dMbUl Epñk
rbs;kRmalxNÐeFVIGMeBICamYynwgFñwmEdkedIm,IbegáItCaFñwmsmasEdlman rolled steel shape EdlenA
BIelIsøabxagelICasøabebtug ¬rUbTI 9>1 b¦.
kareFVIkarrYmKñaenHGacRbRBwtþeTA)anRbsinebIeKkarBarkarrGiltamTisedk (horizontal
slippage) rvageRKOgbgÁúMTaMgBIr. eKGaceFVIdUcenH)an RbsinebIkmøaMgkat;tamTisedkenARtg;épÞb:H

RtUv)ankarBaredayeRKOgsRmab;P¢ab;EdleK[eQμaHfa shear connectors. eKOgsRmab;P¢ab;enHGac

Ca headed studs, spiral reinforcing steel b¤CaEdkrag channel shape tUc²RbEvgxøIRtUv)anpSar
P¢ab;eTAnwgsøabxagelIrbs;EdkFñwmeTAtamKMlatkMNt; edIm,Ipþl;nUvkarpSarP¢ab;CalkçN³emkanictam
ry³TMBk;enAkñúgebtugEdlrwgmaM ¬rUbTI 9>1 c¦. Stud CaRbePT shear connector EdleKniymeRbICag
eK eKGaceRbIvaelIsBImYyedImenARtg;TItaMgEtmYy RbsinebIsøabFñwmmanTMhMTUlayRKb;RKan; ¬vaGa
Rs½ynwgKMlatGnuBaØatEdlmanniyayenAkñúgkfaxNÐ 9>4¦. mUlehtumYyénPaBeBjniymrbs;
shear stud KWPaBgayRsYlkñúgkardMeLIgrbs;va.

eKRtUvkarcMnYn shear connector RKb;RKan;edIm,IeFVI[FñwmeTACaFñwmsmaseBjelj (fully

composite beam). cMnYn shear conncter EdlticCagtRmUvkarnwgeFVI[ekItmanPaBrGilxøHrvag

eRKOgbgÁúMEdk nigebtug FñwmEbbenHeK[eQμaHfa FñwmsmasedayEpñk (partially composite).

T.Chhay 370 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Partially composite beam ¬EdlCak;Esþgman\T§iBlCag fully composite beam¦ RtUv)anbkRsay

enAkñúgEpñkTI 9>7.

eRKOgbgÁúMsmasenAkñúgGKarPaKeRcInRtUv)anbegáIteLIgedaykRmalEdk (stell deck) EdleFVI

CaBum<sRmab;ebtugkRmal ehIyRtUv)anminRtUv)anykecjeRkayeBlebtugrwgmaM. kRmalEdkk¾cUl
rYmenAkñúgersIusþg;rbs;kRmal EteyIgmin)anBicarNaBIkarKNnakRmalEdkenATIenHeT. eKGaceRbI
kRmalEdkpñt;EdlrnUtmanTisEkg b¤RsbnwgTisrbs;Fñwm. enAkñúgRbB½n§kRmalFmμta rnUtEtgEtEkg
eTAnwgFñwmkRmal ehIyRsbeTAnwgrtEdlRTva. eKpSar Shear stud P¢ab;eTAnwgFñwmEdktamcenøaHrnUt
dUcenHKMlatrbs; stud tambeNþayFñwmRtUv)ankMNt;edaycMnYnpñt;rbs;rnUt. rUbTI 9>2 bgðajBI
kRmalxNÐEdlbegáIteLIgedaykRmalEdkEdlrnUtEkgeTAnwgFñwm.
s<an highway PaKeRcInEdleRbIFñwmEdkCaFñwmsmas ehIyCaerOy²FñwmsmasCaCeRmIsEdl

eRKOgbgÁúMsmas 371 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

manlkçN³esdækic©sRmab;sMNg;GaKar. eTaHbICaeKGaceRbI rolled steel beam EdlmanrUbragtUc

Cag manTm¶n;RsalCagenAkñúgeRKOgbgÁúMsmask¾eday k¾ GtßRbeyaCn_rbs;vaRtUv)ankat;bnßyeday
sartémøbEnßmén shear connector. eTaHbICay:agdUcenHk¾eday k¾GtßRbeyaCn_epSgeTotrbs;vaGac
eFVI[eRKOgbgÁúMsmasmankarTak;TajEdr. eKGaceRbIFñwmEdlrak;Cag ehIyPaBdabrbs;vanwgtUcCag
eRKOgbgÁúMFmμta (conventional noncomposite construction).

kugRtaMgeGLasÞicenAkñúgFñwmsmas Elastic Stresses in Compostie Beams

eTaHbICa design strength rbs;FñwmsmasCaTUeTAQrelIlkçxNÐenAkar)ak;k¾eday k¾karyl;
dwgBIkareFVIkarCamYynwgbnÞúkeFVIkar (service load) mansar³sMxan;sRmab;mUlehtuCaeRcIn. eKEtgEt
eFVIkarGegátPaBdabrbs;eRKOgbgÁúMeRkamGMeBIrbs; service load ehIyenAkñúgkrNIxøH design strength
KWQrelIsßanPaBkMNt;én yield dMbUg.
eKGacKNnakugRtaMgrgkarBt; (flexural stress) nigkugRtaMgrgkarkat; (shearing stress) enA
kñúgFñwmrbs; homogeneous material BIrUbmnþ
fb =
Mc
I
ni g fv =
VQ
It
b:uEnþ edaysarFñwmsmasminEMmnCa homogeneous material dUcenHrUbmnþTaMgenHKμann½y.
edIm,IGaceRbIrUbmnþTaMgenH)an eKRtUvbMElgmuxkat;rbs;ebtug[eTACamuxkat;Edk. viFisaRsþenH
tRmUv[ strain rbs;EdkEdl)anRbDiteLIgBIebtugmantémødUcKñanwg strain rbs;EdkBitR)akd. rUbTI
9>3 bgðajBIkMNat;rbs;FñwmsmasCamYynwgdüaRkam stress nig strain. RbsinebIkRmalxNÐ
RtUv)anP¢ab;y:agl¥eTAnwg rolled steel shape enaH strain RtUvEtmanragdUcGVIEdl)anbgðaj EdlRsb
eTAnwg small displacement theory Edl)anniyayfa muxkat;EdlmanlkçN³erobesμImuneBlrgkar
Bt;enAEtrkSalkçN³erobesμIeRkayeBlrgkarBt;. b:uEnþ karBRgaykugRtaMgCalkçN³smamaRt
T.Chhay 372 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

(linear stress distribution) Edl)anbgðajmann½yEtcMeBaHFñwmTaMgLayNaEdlRtUv)ansnμt;faCa

homogeneous material. dMbUg eKRtUvtRmUv[ strain enAkñúgebtugRtg;RKb;cMNucTaMgGs;esμInwg strain

enAkñúgEdkCMnYsenARKb;cMNucenaH
εc = εs b¤ Efc = Efs
c s

nig fs =
Es
Ec
f c = nf c ¬(>!¦
Edl m:UDuleGLasÞicrbs;ebtug
Ec =

n = s = pleFobm:UDul
E
Ec
AISC I2.2 [m:UDuleGLasÞicebs;ebtug *

Ec = w1c.5 f 'c (US)

(
Ec = w1c.5 1.3 ⋅10 − 3 ) f 'c (SI)

Edl wc = Tm¶n;maDrbs;ebtug
f 'c = ersIusþg;rgkarsgát;rbs;ebtugenA @*éf¶

Tm¶n; normal-weight concrete mantémøRbEhl 145lb / ft 3 = 2320kg / m3

eKGacbkRsaysmIkar (>! dUcxageRkam³ eKRtUvkarebtug n in.2 edIm,ITb;Tl;nwgkmøaMgdUcKña
EdlEdk 1in.2 GacTb;)an. edIm,IkMNt;RkLaépÞrbs;EdkEdlnwgTb;Tl;nwgkmøaMgdUcKñaEdlebtugGac
eFVI)an eKRtUvEckRkLaépÞebtugeday n . mann½yfaCMnYs Ac eday Ac / n . lT§plEdlTTYl)an
CaRkLaépÞbMElg (transformed area).
BicarNamuxkat;smasEdlbgðajenAkñúgrUbTI 9>4 a ¬karkMNt;TTwgsøabRbsiT§PaB b enA
eBlEdlFñwmCaEpñkrbs;RbB½n§kRmalnwgENnaMenAxagmux¦. edIm,IbMElgRkLaépÞebtug Ac [eTACa
RkLaépÞEdk eyIgRtUvEckvanwg n . viFId¾gayRsYlKWeKRtUvEckTTwgeday n ehIyrkSakRmas;[enA
dEdl. kareFVIdUcenHeKTTYl)an homogeneous steel section dUcbgðajkñúgrUbTI 9>4b. edIm,IKNna
kugRtaMg eyIgRtUvrkTItaMgG½kSNWtrbs;rUbragsmas ehIyKNnam:Um:g;niclPaBEdlRtUvKña. bnÞab;mk
eyIgGacKNna bending stresses CamYynwg flexural formula. enAEpñkxagelIbMputrbs;srésEdk

*
The ACI Building Code (ACI, 1995) [témørbs; E c = w1c.5 (33) f ' c KitCa psi b¤ Ec = w1c.5 (0.043) f 'c KitCa
N / mm 2
eRKOgbgÁúMsmas 373 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Myt
f st =
I tr
enAEpñkxageRkambMputrbs;Edk
Myb
f sb =
I tr
Edl M= m:Um:g;Bt;Gnuvtþn_
I st = m:Um:g;niclPaBeFobG½kSNWt ¬dUcKñanwgG½kSTIRbCMuTm¶n;rbs; homogeneous section¦

yt = cm¶ayBIG½kSNWteTAEpñkxagelIbMputrbs;Edk

yb = cm¶ayBIG½kSNWteTAEpñkxageRkambMputrbs;Edk

eKGackMNt;kugRtaMgenAkñúgebtugtamviFIdUcKña b:uEnþedaysarsmÖar³EdleyIgKitCaEdk enaHlT§pl

tUvEcknwg n ¬emIlsmIkar (>!¦ dUcenHeK)an
témøGtibrmarbs; f c = nIM y
tr

Edl y Cacm¶ayBIG½kSNWteTATItaMgx<s;bMputrbs;ebtug.
dMeNIrkarKNnaenHmann½ysRmab;Etm:Um:g;Bt;viC¢man EdlkmøaMgsgát;enAxagelIeRBaHeKmin
KitersIusþg;rgkarTajrbs;ebtug.
]TahrN_ 9>1³ FñwmsmasmYypSMeLIgedayEdk A36 manrag W16 × 36 CamYynwgkRmalebtug
kRmas; 5in. nigTTwg 87in. enABIxagelIFñwm. ersIusþg;rbs;ebtugKW f 'c = 4000 psi . kMNt;kugRtaMg
GtibrmaenAkñúgEdk nigebtugEdlekItBIm:Um:g;Bt;viC¢man 160 ft − klips .

T.Chhay 374 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dMeNaHRsay³ Ec = w1c.5 f 'c = 1451.5 4 = 3495ksi

n=
E s 29000
Ec
=
3495
= 8 .3 yk n = 8
edaysarEtm:UDuleGLasÞicrbs;ebtugCatémøRbhak;RbEhl dUcenHeyIgGacyktémø n CatémøKt;
ehIyvanwgpþl;nUvPaBsuRkitRKb;RKan;. dUcenH
b 87
= = 10.88in.
n 8
rUbTI 9>5 bgðajBI transformed section.

eKGackMNt;TItaMgrbs;G½kSNWtedayGnuvtþeKalkarN_m:Um:g;CamYynwgG½kSrbs;m:Um:g;enAEpñk
xagelIbMputrbs;kRmal. karKNnaRtUv)ansegçbenAkñúgtarag 9>1 ehIycm¶ayBITItaMgx<s;bMputrbs;
kRmaleTATIRbCMuTm¶n;KW
∑ Ay 273.1
y= = = 4.202in.
∑ A 65.00
edayGnuvtþRTwsþIbTG½kSRsb nigedayerobCataragénkarKNnaenAkñúgtarag 9>2 eyIgTTYl)anm:Um:g;
niclPaBrbs; transformed section KW
eRKOgbgÁúMsmas 375 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

I tr = 1526in.4
kugRtaMgenATItaMgx<s;bMputrbs;EdkKW
yt = y − t = 4.202 − 5.00 = −0.7980in.
Edl t CakRmas;rbs;kRmal
Myt (160 × 12 )(0.7980)
f st =
Ltr
=
1526
= 1.00ksi ¬rgkarTaj¦
tarag 9>1
eRKOgbgÁúM A y Ay
ebtug 54.40 2.50 136.0

W 16 × 36 10.6 12.93 137.1

65.00 273.1

tarag 9>21
eRKOgbgÁúM A y I d I + Ad 2
ebtug 54.40 2.50 113.3 1.702 270.9

10.6 12.93 448 8.728 1255

W 16 × 36
1525.9

¬TItaMgx<s;bMputrbs;EdksßitenABIxageRkamG½kSNWt dUcenH f st CakugRtaMTaj¦

kugRtaMgenATItaMgeRkambMputrbs;Edk³
yb = t + d − y = 5 + 15.86 − 4.202 = 16.66in.
Myb (160 × 12 )(16.66 )
f sb =
I tr
=
1526
= 21.0ksi ¬rgkarTaj¦
kugRtaMgenATItaMgx<s;bMputrbs;rbs;ebtugKW
M y (160 × 12 )(4.202 )
fc = = = 0.661ksi
nI tr 8 × 1526
RbsinebIeKsnμt;ebtugminmanersIusþg;Tb;karTaj enaHebtuEdlsßitenABIeRkamG½kSNWtminRtUv)anyk
mkKiteT. enaHragFrNImaRtrbs; transformed section xusBIragFrNImaRtedImEdl)ansnμt;. edIm,I

T.Chhay 376 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

TTYl)anlT§plsuRkit eKRtUveFVIkarKNnaTItaMgG½kSNWteLIgvijedayQrelIragFrNImaRtfμIenH.
eyagtamrUbTI 9>6 nigtarag 9>3 eyIgGacKNnaTItaMgfμIrbs;G½kSNWtdUcxageRkam³
2
∑ Ay 5.44 y + 137.1
y= =
∑A 10.88 y + 10.6

( ) 2
y 10.88 y + 10.6 = 5.44 y + 137.1

5.44 y + 10.6 y − 137.1 = 0

y = 4.140in.
m:Um:g;niclPaBrbs;RkLaépÞsmasEdleFVIeLIgvijenHKW
I tr =
1
(10.88)(4.140)3 + 448 + 10.6(12.93 − 4.140)2 = 1524in.4
3

tarag 9>3
eRKOgbgÁúM A y Ay
ebtug 10.88 y y/2 5.44 y
2

W 16 × 36 10.6 12.93 137.1

ehIykugRtaMgKW
f st =
(160 × 12)(5 − 4.140) = 1.08ksi ¬rgkarTaj¦
1524
f sb =
(160 × 12)(5 + 15.86 − 4.140)
= 21.1ksi ¬rgkarTaj¦
1524
fc =
(160 ×12)(4.140) = 0.652ksi
8(1524)
PaBxusKñarvagkarviPaKTaMgBIrGacecal)an ehIykarKNnaTItaMgG½kSNWteLIgvijminmanRbeyaCn_eT.
eRKOgbgÁúMsmas 377 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

cemøIy³ kugRtaMgGtibrmaenAkñúgEdkKW kugRtaMgrgkarTaj 21.1ksi ehIykugRtaMgGtibrmaenAkñúgeb

tugKW kugRtaMgrgkarsgát; 0.652ksi .

ersIusþg;Tb;nwgkarBt; Flexural strength

enAkñugkrNICaeRcIn eKnwgTTYl)an nomial flecural strength enAeBlEdlmuxkat;EdkTaMg
mUl yield ehIyebtugEbkedaysarkmøaMgsgát;. karEbgEckkugRtaMgEdlRtUvKñaenAelImuxkat;smas
RtUv)aneKehAfa karEbgEcgkugRtaMg)aøsÞic (plastic stress distribution). AISC Specification [nUv
design strength sRmab;m:Um:g;Bt;viC¢manCa φb M n EdlRtUv)ankMNt;dUcxageRkam³

!> sRmab;rUbragEdlman compact web ( h / t w ≤ 640 / Fy sRmab; US b¤

h / t w ≤ 1680 / F y sRmab; SI) emKuNersIusþg; φb = 0.85 ehIy M n RtUv)anTTYlBI plastic stress

distribution.

@> sRmab;rUbragEdlman noncompact web ( h / t w > 640 / Fy sRmab; US b¤

h / t w > 1680 / F y sRmab; SI) φ b= 0.9 ehIy M n RtUv)anTTYlBI elastic stress distribution Edl

RtUvKñanwg yilding dMbUgrbs;Edk.

rUbragTaMgGs;EdlmanenAkñúgtaragrbs; Manual Ca compact web dUcenHeKRtUveRbIlkçxNÐ
TImYysRmab;karedaHRsayFñwmsmas elIkElgEt built-up steel shapes. enAkñúgCMBUkenHeyIg
niyayEt compact shape b:ueNÑaH.
enAeBlEdlFñwmsmaseTAdl;sßanPaBkMNt;)aøsÞic eKEbgEckkugRtaMgtamviFImYykñúgcMeNam
viFIbIEdlbgðajenAkñúgrUbTI 9>7. kugRtaMgebtugRtUv)anbgðajCakugRtaMgsgát;BRgayesμI 0.85 f 'c
EdlbnøayBITItaMgx<s;bMputrbs;kRmaleTACMerAEdlGactUcCag b¤esμInwgkRmas;kRmalsrub. karEbg
EckenHKW Whitney equivalent stress distribution EdlkugRtaMgpÁÜbRtUvKñanwgkugRtaMgpÁÜbrbs;karEbg
EckkugRtaMgBitR)akd (ACI, 1995). rUbTI 9>7 a bgðajBIkarEbgEckEdlRtUvKñanwg full tensil
yielding rbs;Edk nigkugRtaMgsgát;edayEpñkrbs;ebtug CamYynwgG½kSNWt)aøsÞic (PNA) enAkñúg

kRmalxNÐ. edayersIusþg;Tajrbs;ebtugmantémøtUc ehIyvamintUv)aneKKitkñúgkarKNnaeTenaH

KμankugRtaMgNa RtUv)anbgðajenAkEnøgEdlkugRtaMgTajmanGMeBIelIebtug. lkçxNÐenHeKeRbICaTUeTA
enAeBlEdlva man shear connectors RKb;RKan;edIm,ITb;Tl;nwgkarrGil KWedIm,IFananUvkareFVIkarCa
T.Chhay 378 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

eRKOgbgÁúMsmas. kñúgrUbTI 9>7 b bøúkkugRtaMgebtugRtUv)anbnøayeBj kRmas;rbs;kRmal ehIy

PNA sßitenAkñúgsøabrbs;FñwmEdk. dUcenHEpñkrbs;søabnwgrgkugRtaMgsgát; edIm,IbegáInkmøaMgsgát;

enAkñúgkRmalxNÐ. rUbTI 9>7 c bgðajBIlT§PaBTIbI Edl PNAsßitenAkñúgRTnug. cMNaMfa sRmab;

krNITaMgbIenH eKmincaM)ac;bnøaybøúkkugRtaMgebtugeBjkRmas;kRmaleT.
kñúgkrNInImYy²EdlbgðajenAkñúgrUbTI 9>7 eyIgGacrk nominal moment capacity eday
KNnam:Um:g; couple EdlekIteLIgedaykmøaMgTajpÁÜb nigkmøaMgsgát;pÁÜb. eyIgGacTTYlva)aneday
eFVIplbUkm:Um:g;rbs;kmøaMgpÁÜbeFobnwgcMNucgayRsYlNamYy. edaysarkartP¢ab;rbs;FñwmEdkeTAnwg
kRmalebtug vaminmanbBaðaCamYynwg lateral torsional buckling enAeBlEdlebtugrwgmaM ehIyeK
TTYl)an composite action.
edIm,IkMNt;faetIeKRtUvykkrNINamkeRbI eKRtUvKNnakmøaMgsgát;pÁÜbNaEdltUcCageKkñúgcM eNam
!> As Fy
@> 0.85 f 'c Ac
#> ∑ Qn
Edl As = RkLaépÞmuxkat;rbs;EdkFñwm
Ac = RkLaépÞrbs;ebtug = tb ¬emIlrUbTI 9>7¦

∑ Qn = ersIiusþg;kmøaMgkat;srubrbs; shear connector

lT§PaBnImYy²bgðajBIkmøaMgkat;tamTisedkenARtg;épÞb:HrvagEdk nigebtug. enAeBlEdllT§PaBTI

mYylub eKeRbIEdkTaMgmUl ehIyeKGnuvtþkarEbgEcgkugRtaMgrbs;rUbTI 9>7 a. lT§PaBTIBIrRtUvKñanwg
ebtugEdllub ehIy PNA sßitenAkñúgEdk ¬rUbTI 9>7 b b¤ c¦. krNITIbIlubEtenAeBlEdleKeRbI
shear connector ticCagtRmUvkarsRmab; full composite behavior EdleFVI[ekItman partial

composite behavior. eTaHbICa partial composite action GacekItmanCamYynwgkRmalxNÐtan; b¤kM

ralxNÐEdlekItBI steel deck k¾eday k¾vaRtUv)anykmkniyayenAkñúgkfaxNÐ 9>7/ “Composite

Beams with Formed Steel Deck”.

eRKOgbgÁúMsmas 379 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

]TahrN_ 9>2³ KNna design strength rbs;Fñwmsmasrbs;]TahrN_ 9>1. snμt;faeKman shear

connector RKb;RKan;sRmab; full composite behavior.
dMeNaHRsay³ kMNt;kmøaMgsgát; C enAkñúgebtug ¬kmøaMgkat;tamTisedkenARtg;épÞb:Hrvagebtug
nigEdk¦. edaysarvaCa full composite action kmøaMgEdlmantémøtUcCagKW As Fy nig
0.85 f 'c Ac ³

As F y = 10.6(36 ) = 381.6kips

0.85 f 'c Ac = 0.85(4)(5 × 87 ) = 1479kips

T.Chhay 380 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

kmøaMgsgát;enAkñúgEdklub C = 381.6kips .
enHmann½yfaeKminRtUvkarkRmas;TaMgmUlrbs;ebtugedIm,IbegáItkmøaMgsgát;EdlRtUvkareT.
eKTTYl)an karEbgEckkugRtaMgenAkñúgrUbTI 9>8.

eKk¾GacKNnakmøaMgsgát;rYmdUcxageRkam
C = 0.85 f 'c ab

enaHeyIg)an a = 0.85Cf ' b = 0.85381(4.)(687) = 1.290in.

c

kmøaMg C nwgsßitenAelITIRbCMuTm¶n;rbs;RkLaépÞrgkarsgát;enAkm<s; a / 2 BITItaMgx<s;bMput

rbs;kRmalxNÐ. kmøaMgTajpÁÜb T ¬esμInwg C ¦ nwgsßitenATIRbCMuTm¶n;rbs;RkLaépÞEdk. ékXñas;
rbs; couple RtUv)anbegáIteLIgeday C nig T KW
d a 15.86 1.290
y= +t − = +5− = 12.28in.
2 2 2 2
Nominal strength KWm:Um:g; couple b¤
M n = Cy = Ty = 381.6(12.28) = 4686in.kips = 390.5 ft − kips
ehIy design strength KW
φb M n = 0.85(390.5) = 332 ft − kips
cemøIy³ design strength = 332 ft − kips

eRKOgbgÁúMsmas 381 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

enAeBlEdlvaman full composite behavior ]TahrN_ 9>2 CaKMrUsRmab;lkçxNÐenH. karvi

PaKsRmab;krNI PNA EdlmanTItaMgsßitenAkñúgmuxkat;EdknwgRtUv)anrk enAeBlEdleKdwgfavaCa
partial composite action.

9>2> karsagsg;edaymankarTb; nigedayminmankarTb;

Shored Versus Unshored Construction
Tal;EtebtugrwgmaM nwgvaTTYl)annUv design strength rbs;va ¬y:agtic 75% énersIusþg;sgát;
enA 28 éf¶ f 'c ¦ enaHmanminmankareFVIkarCasmas (composite behavior) eT ehIyTm¶n;rbs;kRmal
dac;xatRtUv)anRTedaymeFüa)ayepSg². enAeBlEdlebtugrwgmaM vaGaceFVIkarCaeRKOgbgÁúMsmas
ehIykmøaMgGnuvtþn_bnþbnÞab;RtUv)anTb;Tl;edayFñwmsmas. RbsinebIFñwmEdkRtUv)anRTedaycnÞl;
RKb;RKan;tambeNþayRbEvgrbs;vamunnwgebtugRtUv)ancak; Tm¶n;rbs;ebtugRss;nwgRtUvRTedaycnÞl;
beNþaHGasnñeRcInCagedayEdkFñwm. enAeBlEdlebtugrwgmaM cnÞl;beNþaHGasnñRtUv)anruHerIecj
ehIyTm¶n;rbs;kRmalxNÐk¾dUcCabnÞúkbEnßmnwgRtUvRTedayFñwmsmas. b:uEnþRbsinebIeKmineRbIcnÞl;
rolled steel shape minRtwmEtRTTm¶n;pÞal;rbs;vab:ueNÑaHeT b:uEnþvaRtUvRTTm¶n;rbs;kRmalxNÐ nigBum<

kñúgeBlebtugeFVIkarrwgmaM. enAeBlEdleKTTYl)an composite behavior bnÞúkbEnßmTaMgbnÞúkefr

nigbnÞúkGefrnwgRtUvRTedayFñwmsmas. eyIgnwgBicarNalkçxNÐxusKñaedaylMGitdUcxageRkam.

KμancnÞl;³ muneBlebtugrwgmaM Unshored: Before Concrete cures

AISC I3.4 TamTarfa enAeBlEdleKmineRbIcnÞl; EdkFñwmEtÉgdac;xatRtUvEtmanersIusþg;
RKb;edIm,I Tb;Tl;nwgbnÞúkGnuvtþn_TaMgGs;munnwgebtugTTYl)an 75% énersIusþg;rbs;va. ersIusþg;Tb;
karBt; (flexural strength) RtUv)anKNnaedayviFIFmμta edayQrelI Charpter F of the Specifica-
tion ¬CMBUk 5 enAkñúgesovePAenH¦. edayGaRs½yeTAelIkarKNnarbs;va Bum<sRmab;kRmalebtug

Gacpþl; b¤minGacpþl; lateral support sRmab;EdkFñwm. RbsinebIvaminpþl;Ca lateral support sRmab;

EdkFñwmeT eKRtUvyk unbraced length Lb mkKit ehIy lateral-torsional buckling GaclubelI
flexural strength. RbsinebIeKmineRbIcnÞl;beNþaHGasnñeT EdkFñwmk¾GacRtUv)aneRbIedIm,ITb;Tl;nwg

bnÞúksagsg;bnÞab;bnSMEdr. edIm,IkarBarbnÞúkTaMgenH eKRtUvbEnßmbnÞúk 20lb / ft 2 = 1kN / m 2

(Hansell et al., 1978).
T.Chhay 382 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

KμancnÞl;³ eRkayeBlebtugrwgmaM Unshored: After Concrete cures

eRkayeBleKTTYl)an composite behavior RKb;bnÞúkEdlGnuvtþCabnþbnÞab;TaMgGs;RtUv)an
RTedayFñwmsmas. b:uEnþ enAeBldac; RKb;bnÞúkTaMgGs;RtUv)anRTeday couple xagkñúg EdlRtUvKñanwg
karEbgEckkugRtaMgenAeBldac;. dUcenHmuxkat;smasRtUvEtmanersIusþg;RKb;RKan;edIm,IRTbnÞúkTaMgenH
EdlrYmbBa©ÚlTaMgbnÞúkEdlGnuvtþeTAelIFñwmEdkmunnwgebtugrwgmaM.
karsagsg;edayTl; Shored Construction
kñúgkarsagsg;edayeRbIcnÞl; eKBicarNaEtFñwmsmas edaysareKminRtUvkar[EdkFñwmRT
GVIepSgBIbnÞúkpÞal;rbs;vaeT.
ersIusþg;kmøaMgkat; Shear Strength
tRmUv[kmøaMgkat;TaMgs;RtUvTb;Tl;edayRTnugrbs;EdkFñwm Edlpþl;[enA kñúg
AISC I3.6

Chapter F of the Specification.

]TahrN_ 9>3³ Edk W 12 × 50 eFVIkarrYmKñaCamYynwgkRmalxNÐebtugkRmas; 4in. . TTwgkRmal

xNÐRbsiT§PaBKW 72in. . eKmineRbIcnÞl; m:Um:g;Bt;EdlGnuvtþmkelIvamandUcteTA³ )anmkBITm¶n;Fñwm
M beam = 13 ft − kips )anmkBITm¶n;kRmalxNÐ M slab = 77 ft − kips nigBIbnÞúkGefr
M L = 38 ft − kips . ¬enAkñúg]TahrN_enH eKminKitbnÞúksagsg;bEnßmeT¦. EdkEdleRbIKW A36

ehIy f 'c = 4000 psi . kMNt;faetI flexural rbs;FñwmenHRKb;RKan;b¤Gt;. snμt;favaCa full

composite action ehIyBum<pþl;Ca lateral suppoet dl;muxkat;EdkmuneBlebtugrwgmaM.

dMeNaHRsay³ muneBlebtugrwgmaM vamanEtbnÞúkGefrb:ueNÑaH ¬minmanbnÞúksagsg;enAkñúg]TahrN_

enHeT¦. dUcenHbnSMbnÞúk A4-1 lub ehIym:Um:g;emKuNKW
M u = 1.4(M D ) = 1.4(13 + 77 ) = 126 ft − kips
BI beam design chart enAkñúg Part 4 of the Manual sRmab;Edk A36
φb M n = 195 ft − kips > 126 ft − kips (OK)
eRkayeBlebtugrwgmaM FñwmsmasRtUvTb;Tl;nUvm:Um:g;emKuN
M u = 1.2 M D + 1.6 M L = 1.2(13 + 77 ) + 1.6(38) = 168.8 ft − kips
kmøaMgsgát; C CatémøtUcCageKén
eRKOgbgÁúMsmas 383 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

As F y = 14.7(36 ) = 529.2kips

b¤ 0.85 f 'c Ac = 0.85(4 )(4 × 72) = 979.2kips

PNA KWsßitenAkñúgebtug ehIy C = 529.2kips . BIrUbTI 9>8 km<s;rbs;bøúgkugRtaMgsgát;KW

C 529.2
a= = = 2.162in.
0.85 f 'c b 0.85(4 )(72 )
édXñas;m:Um:g;KW
d a 12.19 2.162
y= +t − = +4− = 9.014in.
2 2 2 2
design moment KW
φb M n = φb C y = 0.85(529.2 )(9.014 ) = 4055in.kips = 338 ft − kips > 168.8 ft − kips (OK)

cemøIy³ FñwmmanersIusþg;Bt; (flexural strength) RKb;RKan; .

Cak;Esþg karsagsg;edayeRBIcnÞl;manRbsiT§PaBCagkarsagsg;EdlmineRbIcnÞl; edaysar

KmineRbImuxkat;EdkedIm,IRTGVIepSgeRkABIbnÞúkxøÜnva. kñúgsßanPaBxøH kareRbIR)as;cnÞl;Gac[eKRbI
R)as;muxkat;FñwmEdktUcCag. b:uEnþ eRKOgbgÁúMsmasCaeRcInminmaneRbIcnÞl;eT edaysartémøbEnßm
rbs;cnÞl; CaBiesséføBlkmμ cMNayGs;ticCagkarsnSMsMécelITm¶n;Edk.

9>3> TTwgsøabRbsiT§PaB (Effect Flange Width )

Epñkrbs;kRmalxNÐEdleFVIkarCaeRKOgbgÁúMsmasCamYynwgEdkFñwmCaGnuKmn_eTAnwgktþaCa
eRcIn EdlrYmmanRbEvgElVg nigKMlatFñwm. AISC I3.1 tRmUv[TTwgRbsiT§PaBrbs;kRmalxNÐenAelI
EpñknImYy²rbs;G½kSFñwmKWtémøEdltUcCageKkñúgcMeNam³
!> mYyPaKR)aMbIénRbEvgElVg.
@> mYyPaKBIrénKMlatFñwmEdlKitBIG½kSeTAG½kS.
#> cm¶ayBIG½kSFñwmeTARCUgEKRmbs;kRmal.
lkçxNÐTIbIRtUv)anGnuvtþcMeBaHEtFñwmxagb:ueNaÑaH dUcenHsRmab;Fñwmxagkñúg TTwgRbsiT§PaBTaMgmUlRtUv
mantémøtUcCageKénmYyPaKbYnénRbEvgElVg b¤KMlatrbs;FñwmEdlKitBIG½kSeTAG½kS ¬edaysnμt;fa
FñwmmanKMlatesμ¦I .

T.Chhay 384 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

]TahrN_ 9>4³ RbB½n§kRmalEdlpSMeLIgedayEdkFñwm W 12 × 44 EdlmanKMlatBIKña 9 ft nigRT

kRmalebtugGarem:kRmas; 4.5in. . RbEvgElVgKW 30 ft . edaybEnßmBIelITm¶n;rbs;kRmal eKman
bnÞúkCBa¢aMgxNÐ 20 psf nigbnÞúkGefr 125 psf . EdkCaRbePT A36 ehIyersIusþg;rbs;ebtugKW
f 'c = 4000 psi . cUreFVIkarGegátFñwmxagkñúgedayeKarBtam AISC Specificastion RbsinebIeKmineRbI

cnÞl;beNþaHGasnñ. snμt; full lateral support kñúgGMLúgeBlsagsg; ehIybnÞúksagsg;bEnßmKW

20 psf . eKpþl;nUv shear connector RKb;RKan;sRmab; full composite action.

dMeNaHRsay³ bnÞúkEdlGnuvtþmuneBlebtugrwgmaMrYmmanTm¶n;rbs;kRmalxNÐ
(4.5 / 12)(150) = 56.25 psf .¬eTaHbICa normal-weight concrete manTm¶n; 145 psf / EtebtugGarem:
RtUv)ansnμt;famanTm¶n; 150 psf ¦. sRmab;FñwmEdlmanKMlat 9 ft bnÞúkGefrKW
56.25 × 9t = 506lb / ft
+ Tm¶n;Fñwm = 44lb / ftt

550lb / ft
bnÞúksagsg;KW 20(9) = 180lb / ft EdlRtUv)anKitCabnÞúkGefr. bnÞúk nigm:Um:g;emKuNKW
wu = 1.2 wD + 1.6 wL = 1.2(550) + 1.6(180) = 948lb / ft

M u = (0.948)(30 )2 = 106.6 ft − kips

1
8
BI load Factor Design Selection Table
φb M n = φb M p = 258 ft − kips > 106.6 ft − kips (OK)

eRkayeBlebtugrwgmaM bnÞúksagsg;minmaneFVIGMeBIeToteT EtbnÞúlCBa¢aMgxNÐeFVIGMeBIvijmþg ehIyva

RtUv)anKitCabnÞúkefr ¬emIl)TahrN_ 5>13¦³
w part = 20(9 ) = 180lb / ft

wD = 506 + 44 + 180 = 730lb / ft

bnÞúkGefrCa
wL = 125(9 ) = 1125lb / ft
bnÞúkGefr nigm:Um:g;GefrKW
wu = 1.2 wD + 1.6 wL = 1.2(730) + 1.6(1125) = 2676lb / ft

M u = (2.676)(30 )2 = 301 ft − kips

1
8

eRKOgbgÁúMsmas 385 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

TTwgRbsiT§PaBCatémøEdltUcCageKkñúgcMeNam
span 30(12)
= = 90in.
4 4
KMlatFñwm = 9(12) = 108in.
edaysareRKOgbgÁúMEdlRtUvKNnaCaFñwmxagkñúg lkçxNÐTIbIminGacGnuvtþ)an. yk b = 90in. CaTTwg
søabRbsiT§PaB. enaH tamkarbgðajenAkñúgrUbTI 9>9 kmøaMgsgát;RtUvEtCatémøEdltUcCageKkñúg
cMeNam
As Fy = 13(36 ) = 468kips

b¤ 0.85 f 'c Ac = 0.85(4)(4.5)(90) = 1377kips

yk C = 468kips . BIrUbTI 9>9
C 468
a= = = 1.529in.
0.85 f 'c b 0.85(4 )(90)
d a 1.529
y = + t − = 10.33 + 4.5 − = 14.07in.
2 2 2
φb M n = φb Cy = 0.85(468)(14.07 ) = 5595in. − kips = 466 ft − kips > 301 ft − kips (OK)
RtYtBinitükmøaMgkat;
w L 2.676(30 )
Vu = u = = 40.1kips
2 2
BItaragbnÞúkBRgayesμIemKuN (facored uniform load tables)
φvVn = 141kips > 40.1kips
cemøIy³ FñwmBitCaeKarBtam AISC Specification.

T.Chhay 386 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

9>4> Shear Connectors

dUcEdleyIg)aneXIjrYcmkehIy kmøaMgkat;tamTisedkEdlekIteLIgcenøaHebtug nigEdkesμI
nwgkmøaMgsgát;enAkñúgebtug C . eyIgsMKal;kmøaMgkat;tamTisedkenHeday Vh . dUcenH Vh Catémø
EdltUcCageKkúñgcMeNam As Fy / 0.85 f 'c Ac b¤ ∑ Qn . RbsinebI As Fy b¤ 0.85 f 'c Ac lub vanwg
man full composite action ehIyeKRtUvkarcMnYn shear connectors cenøaHm:Um:g;sUnü nigm:Um:g;Gtibrma
KW
V
N1 = h
Qn
¬(>@¦
Edl Qn Ca nominal shear strength rbs; connector mYy². Connectors cMnYn N1 KYrRtUv)andak;
edaymanKMlatesμI²KñaelIRbEvgEdlvatRmUv. AISC Specification [smIkarsRmab;ersIusþg;TaMg
stud connector nig channel shear connector. dUcEdl)anbgðajBIdMbUg stud connector CaRbePT

EdleKniymeRbICageK ehIyeyIgBicarNaEtRbePTenH. sRmab; stud shear connector mYy

Qn = 0.5 Asc f 'c Ec ≤ Asc Fu (AISC Equation I5-1)

Edl Asc = RkLaépÞmuxkat;rbs; stud

f 'c = ersIusþg;rgkarsgát;enA 28 éf¶

Ec = m:UDuleGLasÞicrbs;ebtug

Fu = ersIusþg;rgkarTajrbs; stud

sRmab; stud EdleRbICa shear connector enAkñúgFñwmsmas ersIusþg;rgkarTaj Fu KW 60ksi . témø

Edl[eday AISC Equation I5-1 KWQrelIkarBiesaFn_ (Ollgaard, Stutter, and Fisher, 1971).
eKmineRbIemKuNersIusþg;sRmab; Qn eT flexural resistance factor φb )anKitsRmab;RKb;ersIusþg;Edl
manPaBminRbRktI.
smIkar (>@ [cMnYn shear connector EdlRtUvkarenAcenøaHcMNucm:Um:g;sUnü nigcMNucm:Um:g;
Gtibrma. dUcenH sRmab;FñwmTRmsamBaØEdlRTbnÞb;BRgayesμI eKRtUvkar connector cMnYn 2N1
ehIy BYkvamanKMlatesμI²Kña. enAeBlmanbnÞúkcMcMNuc AISC I5-6 TamTar[dak; connector cMnYn
N1 enA cenøaHbnÞúkcMcMNuc nigcMNucm:Um:g;sUnüEdlenAEk,redIm,IbegáItm:Um:g;EdlTamTarenARtg;bnÞúk.

EpñkenH RtUv)aneKsMKal;eday N 2 ehIytRmUvkarenHRtUv)anbgðajenAkñúgrUbTI 9>10. cMNaMfacMnYn

shear connector srubminTTYl\T§iBlBItRmUvkarenHeT.

eRKOgbgÁúMsmas 387 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

tRmUvkarepSg²sRmab; Headed Struds (AISC I5)

Miscellaneous Requirements for Headed Studs (AISC I5)
z Ggát;p©itGtibrma = 2.5 × kRmas;rbs;EdkFñwm
z RbEvgGb,brma = 4 × Ggát;p©it stud
z KMlattambeNþayGb,brma ¬BIG½kSeTAG½kS¦ = 6 × Ggát;p©it stud
z KMlattambeNþayGtibrma ¬BIG½kSeTAG½kS¦ = 8 × kRmas;kRmalxNÐ
z KMlattamTTwgGb,brma ¬BIG½kSeTAG½kS¦ = 4 × Ggát;p©it stud
z lateral cover Gb,brma = 1in. = 25mm ¬minmankarkMNt;sRmab; vertical cover

Gb,brma¦

AWS Structural Code (AWS 1996) rayCabBa¢InUvGgát;p©it stud sþg;darCa 1/ 2 / 5 / 8 /

3 / 4 / 7 / 8 / nig 1in. . edaypÁÚrpÁgGgát;p©itenHCamYynwgRbEvgGb,brmaEdltRmUveday AISC eyIg

TTYl)anTMhM stud FmμtaKW 1/ 2 × 2 / 5 / 8 × 2 1 2 / 3 / 4 × 3 / 7 / 8 × 3 12 nig 1× 4 ¬b:uEnþ eKk¾GaceRbI

stud EdlEvgCagenHEdr¦.

]TahrN_ 9>5³ KNna shear connectors sRmab;RbB½n§kRmalenAkñúg]TahrN_ 9>4.

dMeNaHRsay³ segçbTinñn½yEdl)anTTYlBI]TahrN_ 9>4³
W 21× 44 / Edk A36
f 'c = 4000 psi

T.Chhay 388 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

kRmas;kRmalxNÐ t = 4.5in.
RbEvgElVg = 30 ft
BI]TahrN_ 9>4 kmøaMgkat;tamTisedk Vh EdlRtUvKñanwg full composite action KW
Vh = C = 468kips
sakl,g stud 1/ 2 × 2 . Ggát;GnuBaØatGtibrmaKW
2.5t f = 2.5(0.450 ) = 1.125in. > 0.5in. (OK)

RkLaépÞmuxkat;rbs; shear connector mYyKW

π (0.5)2
Asc = = 0.1963in.2
4
RbsinebIeyIgsnμt;ebtugCaebtugTm¶n;Fmμta (normal-weight concrete) m:UDuleGLasÞicrbs;ebtugKW
Ec = w1c.5 f 'c = (145)1.5 4 = 3492ksi

BI AISC Equation I5-1 ersIusþg;rgkmøaMgkat;rbs; connector mYyKW

Qn = 0.5 Asc f 'c Ec ≤ Asc Fu

= 0.5(0.1963) 4(3492 ) = 11.60kips

Asc Fu = 0.1963(60 ) = 11.78kips > 11.60kips yk Qn = 11.60kips
ehIy KMlattambeNþayGb,brmaKW 6d = 6(0.5) = 3in.
KMlattamTTwgGb,brmaKW 4d = 4(0.5) = 2in.
KMlattambeNþayGtibrmaKW 8d = 8(4.5) = 36in.
cMnYn stud EdlRtUvkarenAcenøaHcugFñwm nigkNþalFñwmKW
V 468
N1 = h = = 40.3
Qn 11.60
ykcMnYnGb,brma 41 sRmab;Bak;kNþalFñwm b¤cMnYnsrub 82 . RbsinebIenARtg;muxkat;nImYy²eKeRbI
stud cMnYnmYy KMlatEdlcaM)ac;KW
30(12)
s=
82
= 4.4in. yk s = 4in.
sRmab;muxkat;mYyeRbI stud BIrRKab;
30(12)
s=
82 / 2
= 8.8in. yk s = 8.5in.

eRKOgbgÁúMsmas 389 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

kartMerob stud mYyNak¾manlkçN³RKb;RKan; ehIyKMlatmYyNak¾sßitenAcenøaHEdnkMNt;TabbMput

nigEdnkMNt;x<s;bMput. kartMerob stud RtUv)anbgðajenAkñúgrUbTI 9>11. eTaHbICakartMerobenHRtUvkar
shear connector eRcInCagtRmUvkark¾eday EteKgayRsYlkñúgkarTTYl)anKMlattamtRmUvkar.

cemøIy³ eRbI stud cMnYn 86 edImEdlmanTMhM 1/ 2in. × 2in. tMerobdUcbgðajkñúgrUbTI 9>11.

9>5> karKNnamuxkat; (Design)

CMhandMbUgkñúgkarKNnamuxkat;rbs;RbB½n§kRmalxNÐKWCakareRCIserIskRmas;rbs;kRmal
xNÐ eTaHbIvaCakRmaltan; b¤kRmalrnUt ¬Edl)anBI steel deck¦ k¾eday. kRmas;CaGnuKmn_eTAnwg
KMlatFñwm nigbnSMCaeRcInénkRmas;kRmal nigKMlatFñwmEdlRtUvkarkarGegát dUcenHeKnwgGacrk)an
nUvRbB½n§kRmal EdlmanlkçN³esdækic©bMput. karKNnakRmalxNÐminRtUv)anelIkykmkniyay
enAkñúgesovePAenHeT b:uEnþeyIgsnμt;faeyIgsÁal;kRmas;kRmalxNÐ nigKMlatFñwm. edaykareFVIsnμt;
EbbenH eyIgGacGnuvtþnUvCMhanxageRkamedIm,IbMeBjnUvkarKNnaRbB½n§kRmalxNÐ EdlKμancnÞl;.
!> kMNt;m:Um:g;emKuNEdleFVIGMeBImun nigeRkayebtugrwgmaM
@> eRCIserIsmuxkat;EdkFñwmsakl,g
#> KNna design strength rbs;EdkFñwm nwgeRbobeFobvaCamYynwgm:Um:g;emKuNEdleFVIGMeBI
muneBlebtugrwgmaM. eKRtUvyk unbraced length mkKit RbsinebIBum<min)anpþl;Ca lateral
support RKb;RKan;. RbsinebImuxkat;EdkFñwmenHminRKb;RKan; eKRtUvsakl,gmuxkat;

FMCagenH.
$> KNna design strength rbs;muxkat;smas nigeRbobeFobvaeTAnwgm:Um:g;emKuNsrub. Rb
sinebImuxkat;smasminRKb;RKan; eRCIserIsmuxkat;EdkFñwmepSgeTotsRmab;sakl,g.
T.Chhay 390 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

%> RtYtBinitüersIusþg;rgkmøaMgkat; (shear strength) rbs;EdkFñwm.

^> KNna shear connectors³
a. KNna Vh / kmøaMgkat;tamTisedkenARtg;épÞb:Hrvagebtug nigEdk.

b. EckkmøaMgenHeday Qn ¬ersIusþg;rgkmøaMgkat;rbs; connector eTal¦ edIm,I

TTYl)ancMnYn chear connector srubEdlRtUvkar. cMnYn connector enHnwgpþl;nUv

full composite action. RbsinebIeKcg;)an partial composite behavior eKGac

kat;bnßycMnYn connectors enH ¬manbkRsayenAkñúgEpñkTI 9>7¦

&> RtYtBinitüPaBdab ¬RtUv)anbkRsayenAkñúgEpñkTI 9>6¦
kargard¾sMxan;enAkñúgdMeNIrkar trial-and-orror Edl)anerobrab;xagelIenHKWkareRCIserIsmux
kat;EdkFñwmsakl,g. rUbmnþEdlnwg[nUvRkLaépÞcaM)ac; ¬b¤Gacniyaymü:ageTotKWTm¶n;EdlRtUvkar
elIRbEvgÉktþa¦ GacekIteLIg)an RbsinebIeKsnμt;km<s;Fñwm. edaysnμt;vaeFVIkarCaeRKOgbgÁúMsmas
TaMgRsug (full composite action) ehIy PNA sßitenAkñúgkRmalxNÐ ¬Edlmann½yfa EdkFñwmlub
ehIyvaCakrNIEdleKeRcInCYbRbTHCageK¦ eyIgGacsresr design strength ¬edayeyageTAelI
rUbTI 9>12¦ Ca
(
φb M n = φb (Ty ) = φb As Fy y )

edaydak;[ design strength esμInwgm:Um:g;emKuN ehIyedaHRsayrk As eyIgTTYl)an

φb As F y y = M u nig As = φ MFu y
b y

b¤ As =
Mu
φb Fy (d / 2 + t − a / 2)
¬(>#¦

eRKOgbgÁúMsmas 391 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

eKk¾GacsresrsmIkar (># vaCaTm¶n;CagkarsresrCaRkLaépÞ. edaysarRbEvg 1 ft manmaD

As / 144 ft 3 ehIyEdkeRKOgbgÁúMmanTm¶n;maD 490lb / ft 3

w = s (490 ) = 3.4 As lb / ft ¬sRmab; As KitCa in.2 ¦

A
144
BIsmIkar (># dUcenHTm¶n;Edl)a:n;sμankñúgmYy ft KW
w=
3.4 M u
φ F (d / 2 + t − a / 2)
lb / ft ¬(>$¦
b y

Edl M u KitCa in. − kips / Fy KitCa ksi / ehIy d / t nig a KitCa in. . eKGaceRbIsmIkar (># b¤
(>$ edIm,IeRCiserIsmuxkat;sakl,g. smIkarTaMgBIrTamTarnUvkm<s;Edlsnμt; nigkar)a:n;sμan a / 2 .
dUcenH CaTUeTAbøúkkugRtaMgmankm<s;tUcNas; kRmitlMeGogkñúgkarKNna a / 2 nwgman\T§iBltictYc
elItémøEdl)anKNna As . eKsnμt; a / 2 = 1.0 .
RbsinebIeKeRbIsmIkar (>$ ehIyeKsnμt; nominal depth d enaHeKGaceFVIkareRCIserIsrUbrag
sakl,g)any:aggayRsYl. kareRbIsmIkarenHk¾pþl;nUvkarKNnaTm¶n;FñwmedaypÞal;.

]TahrN_ 9>6³ RbEvgElVgrbs;RbB½n§kRmalKW 30 ft ehIyKMlatFñwmKW 10 ft edayKitBIG½kSeTAG½kS.

eRCIserIs rolled steel shape nig shear connector EdlcaM)ac;edIm,ITTYl)ankareFVIkarCaeRKOgsmas
TaMgRsugCamYynwgkRmalxNÐebtugGarem:kRmas; 3.5in. . bnÞúkbEnßmEdlmanGMeBIelIkRmalxNÐrYm
manbnÞúkCBa¢aMgxNÐ 10 psf nigbnÞúkGefr 55 psf . ersIusþg;ebtugKW f 'c = 4000 psi nigEdkEdleRbI
CaRbePT A36 . snμt;faFñwmman full lateral support kñúgGMLúgeBlsagsg; ehIymanbnÞúksagsg;
20 psf .

dMeNaHRsay³ bnÞúkEdlRtUvRTmuneBlebtugrwgmaMKW
kRmalxNг (3.5 /12)(150) = 43.75 psf
Tm¶n;kñúg 1 ft : 43.75(10) = 437.5lb / ft
bnÞúksagsg;³ 20(10) = 200lb / ft
¬Tm¶n;FñwmnwgRtUvKitenAeBleRkay¦
bnÞúkEdlRtUvRTeRkayeBlebtugrwgmaMKW
w part = 10(10 ) = 100lb / ft

wD = wslab + w part = 437.5 + 100 = 537.5lb / ft

T.Chhay 392 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

wL = 55(10 ) = 550lb / ft

wu = 1.2 wD + 1.6 wL = 1.2(0.5375) + 1.6(0.550) = 1.525kips / ft

M u = (1.525)(30)2 = 171.6 ft − kips

1
8
sakl,gkm<s; d = 16in. . BIsmIkar (>$ Tm¶n;FñwmEdl)anKNnaKW
3.4 M u 3.4(171.6 × 12)
w= = = 21.8lb / ft
φb Fy (d / 2 + t − a / 2) 0.85(36)(16 / 2 + 3.5 − 1)
sakl,g W16 × 26 . RtYtBinitüFñwmEdkedayminmancnÞl;sRmab;bnÞúkEdlGnuvtþmuneBlebtugrwgmaM
¬Tm¶n;rbs;kRmalxNÐ Tm¶n;rbs;Fñwm nigbnÞúksagsg;¦
wu = 1.2(0.4375 + 0.026 ) + 1.6(0.200) = 0.8762kips / ft

M u = (0.8762)(30)2 = 98.6 ft − kips

1
8
BI Load Factor Design Selection Table
φb M n = φb M p = 119 ft − kips > 98.6 ft − kips (OK)

eRkayeBlebtugrwgmaM nigeRkayeBlEdleKTTYl)an composite behavior

wD = wslab + w part + wbeam = 0.4375 + 0.100 + 0.016 = 0.5535kips / ft

wu = 1.2 wD + 1.6 wL = 1.2(0.5535) + 1.6(0.550) = 1.544kips / ft

M u = (1.544)(30)2 = 174 ft − kips

1
8
muneBlKNna design strength rbs;muxkat;smas dMbUgeyIgRtUvkMNt;TTwgsøabRbsiT§PaB. sRmab;
Fñwmxagkñúg TTwgRbsiT§PaBCatémøtUcCageKkñúgcMeNam
span 30(12)
4
=
4
= 90in. b¤ KMlatFñwm = 10(12) = 120in.
yk b = 90in. . sRmab; full composite behavior kmøaMgsgát;enAkñúgebtugenA ultimate
¬esμInwgkmøaMg kat;tamTisedkenARtg;épÞb:Hrvagebtug nigEdk¦ CatémøEdltUcCageKkñúgcMeNam
As Fy = 7.68(36) = 276.5kips

b¤ 0.85 f 'c Ac = 0.85(4)(90)(3.5) = 1071kips

yk C = Vh = 276.5kips . km<s;bøúkkugRtaMgsgát;enAkñúgkRmalxNÐKw
C 276.5
a= = = 0.9036in.
0.85 f 'c b 0.85(4)(90)
ehIyédXñas;rbs; internal resisting couple KW
eRKOgbgÁúMsmas 393 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

d a 15.69 0.9036
y= +t − = + 3.5 − = 10.89in.
2 2 2 2
design flexural strength KW
φb M n = φb (Cy ) = 0.85(276.5)(10.89) = 2550in.kips = 213 ft − kips > 174 ft − kips (OK)
RtYtBinitükmøaMgkat;
w L 1544(30)
Vu = u = = 23.2kips
2 2
BI factored uniform load tables
φvVn = 76.3kips > 23.2kips (OK)
cemøIy³ eRbI W 16 × 26
eKRtUvkarm:UDuleGLasÞicrbs;ebtugedIm,IKNna shear connector. BI]TahrN_ 9>5/
Ec = 3492ksi sRmab;ebtugFmμtaCamYynwg f 'c = 4000 psi . sakl,g stud 1 / 2 × 2in.

¬ Asc = 0.1963in.2 ¦
Ggát;p©itGtibrma = 2.5t f = 2.5(0.345) = 0.8625in. > 0.5in. (OK)
BI AISC Equation I5-1/ ersIusþg;rgkmøaMgkat;rbs; connector mYyKW
Qn = 0.5 Asc f 'c Ec ≤ Asc Fu

= 0.5(0.1963) 4(3492 )

= 11.60kips
Asc Fu = 0.1963(60) = 11.78kips > 11.60kips
dUcenHyk Qn = 11.60kips
cMnYn stud EdlRtUvkarenAcenøaHcugFñwm nigkNþalElVgKW
V
N1 = h =
276.5
Qn 11.60
= 23.8 eRbI 24 sRmab;Bak;kNþalFñwm b¤Casrub 48
nig KMlattambeNþayGb,brmaKW 6d = 6(0.5) = 3in.
KMlattamTTwgGb,brmaKW 4d = 4(0.5) = 2in.
KMlattambeNþayGtibrmaKW 8t = 8(3.5) = 28in.
RbsinebIeKeRbI stud mYysRmab;muxkat;nImYy² KMlatRbhak;RbEhlKW
30(12)
s= = 7.5in.
48
KMlatenHsßitenAcenøaHEdnx<s;bMput nigEdnTabbMput dUcenHvabMeBjlkçxNÐ.
T.Chhay 394 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

cemøIy³ ykkarKNnaEdlbgðajenAkñúgrUbTI 9>13.

9>6> PaBdab (Deflections)

edaysarm:Um:g;niclPaBrbs;muxkat;bMElg (transformed section) FM dUcenHPaBdabrbs;Fñwm
smasnwgtUcCagFñwmFmμta. b:uEnþ eKGacTTYl)anm:Um:g;niclPaBFMenHEteRkayeBlebtugrwgmaMEt
b:ueNÑaH. PaBdabEdlekIteLIgedaysarbnÞúkGnuvtþn_muneBlebtugrwgmaMRtUv)anKNnaCamYynwgm:Um:g;
niclPaBrbs;FñwmEdk. PaBdabbEnßmnwgekIteLIgenAeBlEdlFñwmrgnUvbnÞúkefrdUcCa Tm¶n;rbs;CBa¢aMg
xNÐ enAeRkayeBlebtugrwgmaM. tMbn;m:Um:g;viC¢man ebtugnwgrgkmøaMgsgát;Cab;rhUt ehIyrgnUv)atuPUt
EdleKsÁal;faCa creep. Creep CakMhUcRTg;RTayEdlekIteLIgeRkamGMeBIrbs;bnÞúksgát;. eRkay
eBlekItmankMhUcRTg;RTaydMbUg kMhUcRTg;RTaybEnßmnwgekItmaneLIgedayGRtayWtelIry³eBld¾
Evg. \T§iBlenAelIFñwmsmasKWkarekIneLIgnUvkMeNag EdlbNþal[PaBdabtambBaÄrekIneLIgEdr.
eKGackMNt;EtPaBdabry³eBlyUr (long-term deflection) edayeRbIbec©keTsEdleKniymeRbI.
bec©keTsenHKWeRbImuxkat;ebtugEdl)ankat;bnßyenAkñúgmuxkat;bMElg dUcenHeKnwgTTYl)anm:Um:g;
niclPaBtUcCagmun ehIyeKnwgTTYl)anPaBdabFMCagmun. muxkat;Edl)ankat;bnßyRtUv)anKNna
edayeRbI 2n b¤ 3n CMnYs[pleFobm:UDulCak;Esþg n . enAkñúgesovePAenH eyIgeRbI 2n . PaBdab
EdlekIneLIgeday creep minRtUv)anENnaMeday AISC Specification eT.
sRmab;karsagsg;edayKμancnÞl; eKmanm:Um:g;niclPaBbIxusKñasRmab;KNna long-term
deflection.

!> eRbI I s / m:Um:g;niclPaBrbs; rolled steel shape

sRmab;PaBdabEdlekIteLIgedaysarbnÞúkGnuvtþn_muneBlebtugrwgmaM.

eRKOgbgÁúMsmas 395 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

@> eRbI I tr / m:Um:g;niclPaBrbs; transfored section EdlKNnaCamYynwg b / n sRmab;PaB

dab EdlekIteLIgedaybnÞúkGefr nigsRmab;PaBdabdMbUg (initial deflection) EdlekIt
edaybnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaM.
#> eRbI I tr EdlKNnaCamYynwg b / 2n sRmab; long-term deflection EdlekIteLIgedaysar
bnÞúkGefrEdlGnuvtþeRkayeBlebtugrwgmaM.

]TaheN_ 9>7³ KNnaPaBdabPøam² (immediate deflection) nig long-term deflection sRmab;Fñwm

enAkñúg]TahrN_ 9>4.
dMeNaHRsay³ segçbTinñn½yBI]TahrN_ 9>4³
W 21× 44 / Edk A36

kRmas;kRmalxNÐ t = 4.5in. ehIyTTwgRbsiT§PaBKW b = 90in.

f 'c = 4000 psi
bnÞúkGefrEdlGnuvtþmuneBlebtugrwgmaMKW wD = 550lb / ft ¬kRmalxNÐbUknwgFñwm¦
bnÞúksagsg;KW wconst = 180lb / ft
bnÞúkGefrKW wL = 125(9) = 1125lb / ft
bnÞúkCBa¢aMgxNÐKW w part = 20(9) = 180lb / ft
PaBdabPøam²³
sRmab;FñwmbUknwgkRmalxNÐ w = 550lb / ft
5wL4 5(0.55 / 12)(30 × 12)4
Δ1 = = = 0.41in.
384 EI s 384(29000)(843)
sRmab;bnÞúksagsg; w = 180lb / ft
5wL4 5(0.18 / 12)(30 × 12)4
Δ2 = = = 0.1342in.
384 EI s 384(29000)(843)
PaBdabPøam²srubKW Δ1 + Δ 2 = 0.41 + 0.1342 = 0.544in.
sRmab;PaBdabEdlenAsl; eKRtUvkarm:Um:g;niclPaBrbs;muxkat;bMElgBIrKW I tr CamYynwg
TTwgkRmalxNÐbMElg b / n nig I tr CamYynwgTTwgkRmalxNÐbMElg b / 2n . sRmab;ebtugTm¶n;
FmμtaEdlman f 'c = 4000 psi / Ec = 3492ksi nigpleFobm:UDulKW
T.Chhay 396 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

n=
E s 29000
Ec
=
3492
yk n = 8
= 8 .3

sRmab;PaBdabrbs;muxkat;smasEdlminTak;Tgnwg creep TTwgRbsiT§PaBKW

b 90
= = 11.25in.
n 8
rUbTI 9>14 bgðajBImuxkat;bMElgEdlRtUvKña. karKNnasRmab;TItaMgG½kSNWt nigm:Um:g;niclPaB
RtUv)ansegçbenAkñúgtarag 9>4.
PaBdabdMbUgEdlbNþalBITm¶n;CBa¢aMgxNÐKW
5w part L4 5(0.180 / 12)(30 × 12)4
Δ3 = = = 0.0441in.
384 EI tr 384(29000)(2566)
PaBdabEdlbNþalBIbnÞúkGefrKW
5wL L4 5(1.125 / 12)(30 × 12)4
Δ4 = = = 0.2755in.
384 EI tr 384(29000)(2566)

tarag 9>4
eRKOgbgÁúM A y Ay I d I + Ad 2
ebtug 50.62 2.25 113.9 85.43 2.571 420

W 12 × 44 13.00 14.83 192.8 843 10.01 2146

63.62 306.7 2566in.4

∑ Ay 306.7
y= = = 4.821
∑ A 63.62

eRKOgbgÁúMsmas 397 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

PaBdabry³eBlyUrEdlbNþalBI creep. eRbITTwgkRmalxNÐbMElg

b 90
= = 5.625in.
2n 2(8)
muxkat;bMElgRtUv)anbgðajenAkñúgrUbTI 9>15. karKNnaTIRbCMuTm¶n;nwg m:Um:g;niclPaBRtUv)ansegçb
enAkñúgtarag 9>5. edayehAm:Um:g;niclPaBenHCa I 'tr eyIgGacKNnaPaBdabry³eBlyUrEdlekIt
eLIgeday creep KW
5w part L4 5(0.180 / 12)(30 × 12)4
Δ5 = = = 0.0504in.
384 EI 'tr 384(29000)(2245)

tarag 9>5
eRKOgbgÁúM A y Ay I d I + Ad 2
ebtug 25.31 2.25 56.95 42.71 4.269 504

W 12 × 44 13.00 14.83 192.8 843 8.311 1741

38.31 249.8 2245in.4

∑ Ay 249.8
y= = = 6.519
∑ A 38.31

cemøIy³ xageRkamenHCakarsegçbrbs;PaBdab
PaBdabPøam²munTTYl)an composite behavior
Δ1 + Δ 2 = 0.4100 + 0.1342 = 0.544in.
PaBdabry³eBlxøICamYynwgCBa¢aMgxNÐedayKμanbnÞúkGefr
T.Chhay 398 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Δ1 + Δ 3 = 0.4100 + 0.0441 = 0.454in.

PaBdabry³eBlxøIedaybEnßmbnÞúkGefr
Δ1 + Δ 3 + Δ 4 = 0.4100 + 0.0441 + 0.2755 = 0.730in.
PaBdabry³eBlEvgedayKμanbnÞúkGefr
Δ1 + Δ 5 = 0.4100 + 0.0504 = 0.460in.
PaBdabry³eBlEvgedaymanbnÞúkGefr
Δ1 + Δ 4 + Δ 5 = 0.4100 + 0.2755 + 0.0504 = 0.736in.
edaysarbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMmantémøtUc PaBdabEdl)anBI creep
mantémøtUcenAkñúg]TahrN_enH.

9>7> FñwmsmasCamYynwgkRmalBum<Edk (Composite Beams with Formed Steel Deck)

kRmalxNÐenAkñúgsMNg;eRKagEdkRtUv)anpÁúMeLIgkñúgTRmg;kRmalEdkrnUt (ribbed steel
deck) EdlRtUv)anTukenAnwgkEnøgedIm,I[vakøayeTACaEpñkrbs;eRKOgbgÁúM. eTaHbICamankrNIelIk

Elgk¾eday k¾rnUtrbs;bnÞHEdkRtUv)andak;[EkgnwgFñwmkRmal ehIyRsbeTAnwgrtEdlRTFñwmenaH.

rUbTI 9>16 bgðajBIrnUtEdlmanTisEkgnwgFñwm. eKdMeLIg shear stud enAelIFñwmsmasEdlman
kRmalrnUt tamviFIdUcKñanwgkardMeLIg shear srud enAelIFñwmsmasEdlKμankRmalrnUt. eKcat;Tukfa
karP¢ab;Kñarvag deck eTAnwgFñwmEdkpþl;nUvTRmxag (lateral support)

sRmab;FñwmEdkmuneBlebtugrwgmaM. karKNna nigkarviPaKFñwmsmasCamYynwg formed steel deck

mansar³sMxan;dUcKñanwgkrNIFñwm smasCamYynwgkRmalEdlmankRmalesμIEdr
EtxageRkamCakrNIelIkElgmYycMnYn³
!> eKminKitebtugenAkñúgrnUt ¬EdlenABIeRkamEpñkxagelIrbs; deck¦ enAeBlrnUtTaMgenaH
EkgnwgFñwm (AISC I3.5b). enAeBlrnUtRsbnwgFñwm ebtugenAkñúgrnUtenaHRtUv)anKitbBa©Úl
eTAkñúgkarkMNt;lkçN³muxkat; ehIyRtUv)anbBa©ÚleTAkñúgkarKNna Ac .
@> lT§PaBrbs; shear connector GacRtUv)ankat;bnßy
#> CaTUeTA eKminGacTTYl)an full composite behavior eT. mUlehtuKWfa KMlatrbs; shear
connector RtUv)ankMNt;edayKMlatrbs;rnUt ehIyeKminGaceRbIRKb;cMnYn connector Edl

eRKOgbgÁúMsmas 399 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

RtUvkar. eTaHbICaeKGaceRbI partial composite design edayKμan formed steel deck k¾

eday k¾vaRtUv)anelIkykmkniyayenATIenH BIeRBaHPaKeRcInvaRtUvkar formed steel deck.
tamBitvaminEmnCaKuNvibtþieT EtvaCaCeRmIsxagEpñkesdækic©.

FñwmsmasPaKeRcInCamYynwg formed steel deck CakRmalFñwmEdlmanrnUtEkgnwgFñwm ehIy

eyIgnwgniyayEtkñúgkrNIenH. tRmUvkarcaM)ac;EdlGnuvtþenAeBlrnUtmanTisRsbeTAnwgFñwmRtUv)an
bgðajenAkñúg AISC I3.5 c.

lT§PaBEdlkat;bnßyrbs; shear connectors

Reduced Capacity of Shear connector
edayBwgEp¥kelIkarBiesaF AISC I3.5b tRmUv[KuN shear strength rbs; shear connector
Qn eTAnwgemKuNkat;bnßyenAeBlEdlrnUtEkgeTAnwgFñwm³
0.85 ⎛ wr ⎞ ⎡⎛ H s ⎞ ⎤
⎜⎜ ⎟⎟ ⎢⎜⎜ ⎟⎟ − 1.0⎥ ≤ 1.0 (AISC Equation I3-1)
Nr ⎝ hr ⎠ ⎣⎝ hr ⎠ ⎦
Edl Nr = cMnYn stud kñúgmYyrnUtRtg;kEnøgEdlkat;KñaCamYynwgFñwm ¬EdlkMNt;RtwmbIenAkñúgkar
KNna¦
wr = TTwgmFümrbs;rnUt

hr = km<s;rbs;rnUt

H s = RbEvgrbs; stud EdlkñúgkarKNnavaminRtUvFMCag (hr + 3) .

TMhMTaMgenHRtUv)anbgðajenAkñúgrUbTI 9>17.

T.Chhay 400 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Partial Composite Action

kareFVIkarCaeRKOgbgÁúMsmasedayEpñk (partial composite action) ekItmaneLIgenAeBlEdl
vaminman shear connector RKb;RKan;edIm,IkarBarPaBrGilrvagebtug nigEdkFñwm. TaMgebtug nigEdk
minGaceFVIkardl; strength rbs;vaeBjeljeT ehIykmøaMgsgát;RtUv)ankMNt;RtwmkmøaMgGtibrma
¬EdlCaersIusþg;rbs; shear connector ∑ Qn ¦ EdlGacbBa¢ÚnkmøaMgkat;tamépÞb:HrvagEdk nigebtug.
rMlwkfa C CatémøEdltUcCageKkñúgcMeNam As Fy / 0.85 f 'c Ac nig ∑ Qn .
CamYynwg partial composite action CaTUeTAG½kSNWt)aøsÞic (PNA) sßitenAñúgmuxkat;Edk. TI
taMgenHnwgeFVI[karviPaKersIusþg;mankarBi)akCagTItaMgrbs; PNA EdlsßitenAkñúgkRmalxNÐbnþic
EteKalkarN_cMbgKWdUcKña.
enAeBlEdleKeFVI elastic analysis k¾dUcCaenAeBlEdleKKNnaPaBdab eKRtUveFVIkar KNna
m:Um:g;niclPaBrbs; partially composite section. eKGaceRbIExSekag parabolic transition BI I s
¬sRmab;EtEdkFñwm¦ eTA I tr ¬sRmab; fully composite section¦ )an (Hansell et al., 1978).
xageRkam CasmIkarEdlnwgpþl;nUvlT§plRbhak;RbEhlsRmab;m:Um:g;niclPaBRbsiT§PaBEdlbgðaj
eday Commentary to the AISC Specification³
I eff = I s + ∑ Qn / C f (I tr − I s ) (AISC Equation C-I3-6)

Edl C f CakmøaMgsgát;enAkñúgebtugsRmab; fully composite condition ¬témøEdltUcCageKkñúg

cMeNam As Fy nig 0.85 f 'c Ac ¦. edaysarEt ∑ Qn CakmøaMgsgát;Cak;EsþgsRmab;krNI partially

eRKOgbgÁúMsmas 401 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

composite enaHpleFob ∑ Qn / C f CacMENkrbs; compositeness Edlman. RbsinebIpleFobenH

tUcCag 0.25 enaHeKminKYreRbI AISC Equation C-I3-6 (Hansell et al., 1978).
eKminGacTTYl)anersIusþg;EdkeBjenAkñúg partially composite beam eT dUcenHvaTamTar
nUvmuxkat;EdkFñwmFMCag muxkat;EdkFñwmsRmab; fully composite behavior. b:uEnþ vaRtUvkar shear
connector ticCag ehIytémørbs;EdkFñwm nig shear connectors ¬EdlrYbbBa©ÚlTaMgtémødMeLIg¦

RtUv)anKitcUleTAkñúgkarviPaKEpñkesdækic©. enARKb;eBlEdl fully composite beam manlT§PaB

Tb;Tl;FM ¬EdleKEtgEtCYbRbTHkrNIEbbenH¦ eKGaceFVIkarkat;bnßycMnYn shear connector Edl
eFVI[FñwmkøayCa partially composite beam.

tRmUvkarepSg² Miscellaneous Requirements

xageRkamCatRmUvkarEdl)anBI AISC Section I3.5 a nig b. GVIEdlnwgerobrab;xageRkamCa
tRmUvkarbEnßmBIelIGVIEdl)anerobrab;BIcxagedIm³
- km<s;rnUtGtibrma hr = 3in. = 75mm
- TTwgmFümGb,brmarbs;rnUt wr = 2in. = 50mm b:uEnþtémørbs; wr EdleRbIenAkñúgkar
KNnaminKYrFMCag clear width rbs;EpñkxagelIbMputrbs; deck eT.
- kRmas;kRmalGb,brmaenABIelIEpñkx<s;bMputrbs; deck = 2in. = 50mm .
- Ggát;p©it stud Gtibrma = 3 / 4in. . karTamTarsRmab; formed steel deck enHCakarbEnßmBI
elIGgát;p©itGtibrma 2.5t f .
- km<s;Gb,brmarbs; stud BIelIEpñkx<s;bMputKW 1 1 2 in.
- KMlattambeNþayGtibrmarbs; shear stud = 36in. = 915mm
- eKRtUvP¢ab; deck eTAnwgsøabFñwmedayKMlatmin[FMCag 18in = 460mm eday stud b¤ eday
spot weld. kareFVIEbbenHedIm,IkarBar uplift.

Tm¶n; deck nigTm¶n;kRmal Slab and Deck Weight

edIm,IsRmYldl;karKNnaTm¶n;kRmal eyIgeRbIkRmas;rbs;kRmalTaMgmUledayvas;BI)at
rbs; deck eTAépÞxagelIrbs;kRmalxNÐ. eTaHbICaviFIenH)a:n;sμanmaDebtugelIsk¾eday Etvaman
T.Chhay 402 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

suvtßiPaB. sRmab;Tm¶n;maDebtugGarem: eyIgeRbITm¶n;ebtugmaDsuT§bUkbEnßm 5 pcf = 80kg / m3 .

CaTUeTA edaysarkRmalxNÐenAelI formed steel deck CaebtugEdlBRgwgedayEdktic ¬eBlxøHeRbI
welded wire mesh CMnYs[kareRbI reinforcing bar¦ karbEnßm 5 pcf = 80kg / m 3 sRmab;EdkBRgwg

GacmantémøFM b:uEnþ deck manTm¶n;cenøaHBI 2 psf = 9.6kg / m 2 eTA 3 psf = 14.5kg / m 2 .

eKGaceRbIvFImü:ageTot edayKitplbUkrvagkRmas;kRmalEdlenABIelI deck Edlx<s;CageK
CamYynwgBak;kNþalkm<s;rbs;rnUtCakRmas;ebtugkñúgkarKNnaTm¶n;rbs;kRmal. CaTUeTA kñúgkar
Gnuvtþ eKGacrkplbUkrvagTm¶n;kRmal nig deck enAkñúgtaragEdlpþl;[edayeragcRkplit deck.

]TahrN_ 9>8³ kRmalxNÐRTedayFñwmEdleRbI formed steel deck EdlbgðajenAkñúgrUbTI 9>18 Ca

mYynwgkRmalebtugGarem:EdlkRmas;srubKW 4.75in. . rnUt deck EkgnwgFñwm. RbEvgElVgKW 30 ft
ehIyFñwmmanKMlatBIKña 10 ft edayKitBIG½kSeTAG½kS. EdkeRKOgbgÁúMCaRbePTEdk A36 ehIyersIusþg;
rbs;ebtugKW f 'c = 3000 psi . Tm¶n;rbs;kRmal nig deck KW 50 psf . Tm¶n;GefrKW 40 psf nigTm¶n;
CBa¢aMgKW 10 psf . kñúgkarsagsg;enH eKminmaneRbIcnÞl;beNþaHGasnñeT ehIyTm¶n;sagsg;KW 20 psf .
!> eRCIserIs W shape
@> KNna shear connector
#> RtYtBinitüPaBdab. PaBdabry³eBlyUrsrubGnuBaØatGtibrmaKW 1/ 240 énRbEvgElVg.

dMeNaHRsay³ !> KNnaFñwm

eRCIserIsrUbragsakl,gedayQrelI full composite behavior
kRmalxNг 50(10) = 500lb / ft
CBa¢aMgxNг 10(10) = 100lb / ft
bnÞúkGefr³ 40(10) = 400lb / ft
eRKOgbgÁúMsmas 403 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

wu = 1.2wD + 1.6wL = 1.2(0.5 + 0.1) + 1.6(0.4) = 1.360kips / ft

M u = (1.36)(30)2 = 153 ft − kips

1
8
edaysnμt;fa d = 16in. / a / 2 = 1in. nigsnμt;Tm¶n;rbs;FñwmBIsmIkar (>$³
3.4M u 3.4(153 × 12)
w= = = 17.4lb / ft
φb Fy (d / 2 + t − a / 2) 0.85(36)(16 / 2 + 4.75 − 1)
sakl,g W 16 × 26 . RtYtBinitüersIusþg;rgkarBt;muneBlebtugrwgmaM
bnÞúksagsg;³ 20(10) = 200lb / ft
wu = 1.2wD + 1.6wL = 1.2(0.5 + 0.026) + 1.6(0.4) = 0.9512kips / ft

M u = (0.9512)(30)2 = 107 ft − kips

1
8
W 16 × 26 Ca compact section sRmab; A36 nigedaysar steel deck nwgpþl; lateral support
RKb;RKan; dUcenH nominal strength M n esμInwgersIusþg;m:Um:g;)aøsÞic M p .
BI Load Factor Design Selection Table
φb M p = 119 ft − kips > 107 ft − kips (OK)

eRkayeBlebtugrwgmaM bnÞúkemKuNsrubEdlRtUvRTedayFñwmsmas EdlRtUv)anEksRmYledaysar

Tm¶n;rbs;EdkFñwmKW
wu = 1.2(0.5 + 0.026 + 0.1) + 1.6(0.4) = 1.391kips / ft
ehIym:Um:g;emKuNKW
Mu =
1
(1.391)(30)2 = 156 ft − kips
8
TTwgkRmalxNÐRbsiT§PaBrbs;muxkat;smasRtUvEtmantémøtUcCageKkñúgcMeNam
span 30(12)
4
=
4
= 90in. b¤ KMlatFñwm = 10(12) = 120in.
yk b = 90in. . sRmab; fully composite action kmøaMgsgát; C enAkñúgebtugKWCatémøtUcCageKkñúg
cMeNam
As Fy = 7.68(36) = 276.5kips

b¤ 0.85 f 'c Ac = 0.85(3)[90(4.75 − 1.5)] = 745.9kips

T.Chhay 404 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

EdleKKitEtebtugenAelIEpñkx<s;bMputrbs; deck ¬dUcbgðajenAkñúgrUbTI 9>19¦ b:ueNÑaHsRmab;smIkar

TIBIrxagelI. CamYynwg C = 276.5kips km<s;rbs;karBRgaykugRtaMgsgát;enAkñúgebtugKW
C 276.5
a= = = 1.205in.
0.85 f 'c b 0.85(3)(90)
édXñas;m:Um:g;rbs; internal resisting couple KW
d a 15.69 1.209
y= +t − = + 4.75 − = 11.99in.
2 2 2 2
ehIy design strength KW
0.85(276.5)(11.99)
φb M n = = 235 ft − kips > 156 ft − kips (OK)
12
RtYtBinitükmøaMgkat;
w L 1.391(30 )
Vu = u = = 20.9kips
2 2
BI factored uniform load tables
φvVn = 76.3kips > 20.9kips (OK)
cemøIy³ !> eRbI W16 × 26
@> Shear connectors
edaysarFñwmenHmanersIusþg;m:Umg: ;FMKYrsm eKGac[vaeFVIkarCa patial composite behavior. dMbUg
eyIgRtUvrkcMnYn shear connector caM)ac;sRmab; full composite behavior nwgbnÞab;mkkat;bnßycMnYn
conntector. sRmab; fully composite beam/ C = Vh = 276.5kips .

sakl,g stud 3 4 × 3in. ¬ Asc = 0.4418in 2 ¦mYyenARtg;muxkat;mYy³

Ggát;p©itGtibrma = 2.5t f = 2.5(0.345) = 0.8625in.
b¤ 34 in. lub
eRKOgbgÁúMsmas 405 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Ggát;p©itCak;Esþg = 34 in. (OK)

KNnaemKuNkat;bnßyersIusþg;rbs; stud
Nr = 1
km<s;rbs; stud BIelIEpñkx<s;bMputrbs; deck = 3 − 1.5 = 1.5in. = témøGnuBaØat (OK)

BI AISC Equation I3-1,

emKuNkat;bnßy = 0.N85 ⎛⎜⎜ wh r ⎞⎟⎟⎡⎢⎛⎜⎜ Hh s ⎞⎟⎟ − 1.0⎤⎥ ≤ 1.0
r ⎝ r ⎠ ⎣⎝ r ⎠ ⎦
0.85 ⎛ 2.25 ⎞⎛ 3 ⎞
= ⎜ ⎟⎜ − 1.0 ⎟ = 1.275 > 1.0
1.0 ⎝ 1.5 ⎠⎝ 1.5 ⎠
eKminRtUvkarkat;bnßyersIusþg; stud eT. sRmab; f 'c = 3000 psi m:UDuleGLasÞicrbs;ebtugKW
Ec = w1c.5 f 'c = 1451.5 3 = 3024ksi

BI AISC Equation I5-1, ersIusþg;rgkmøaMgkat;rbs; connector mYyKW

Qn = 0.5 Asc f 'c Ec ≤ Asc Fu

= 0.5(0.4418) 3(3024 ) = 21.04kips

Asc Fu = 0.4418(60) = 26.51kips > 21.04kips

dUcenHyk Qn = 21.04kips
cMnYnrbs; stud EdlRtUvkarenAcenøaHcugrbs;Fñwm nigkNþalElVgKW
V 276.5
N1 = h = = 13.1
Qn 21.04
yk 14 sRmab;Bak;kNþalFñwm dUcenHsrub 28 .
CamYy stud mYysRmab;rnUtmYy KMlatKW 6in. ehIycMnYnGtibrmaENnaMKW
30(12)
= 60 > 28 EdlTamTar
6
ebIeKeRbI stud mYysRmab;ral;BIrrnUt dUcenHeKRtUvkarva 30 edIm EdlenAEtCacMnYneRcIn.
Rbsin ebIeKeRbI stud mYysRmab;ral;bIrnUt enaHKMlatnwgkøayCa 3(6) = 18in. ehIycMnYnrbs; stud
nwg 30(12)/18 = 20 EdlvatUcCagtRmUvkarsRmab; full composite action. b:uEnþ vaman flexural
strength FM dUcenH partial composite action GacnwgRKb;RKan;.

sakl,g stud 20 edIm sRmab;FñwmmYy dUcenH N1 Edlpþl;[ = 20 / 2 = 10

∑ Qn = 10(21.04)
T.Chhay 406 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

= 210.4kips < 276.5kips

dUcenH C = Vh = 210.4kips
edaysar C tUcCag As Fy dUcenHEpñkxøHrbs;muxkat;EdkFñwmRtUvrgkmøaMgsgát; ehIyG½kSNWt)aøsÞic
KWsßitenAkñúgmuxkat;Edk.
edIm,IviPaKkrNIenH dMbUgeyIgRtUvkMNt;faetI PNA sßitenAelIsøabxagelI b¤sßitenAelIRTnug.
RbsinebI PNA sßitenA)atrbs;søabxagelI enaHtYsøabTaMgmUlnwgrgkmøaMgsgát; ehIykmøaMgsgát;pÁÜb
EdlbgðajenAkñúgrUbTI 9>20 KW
Pyf = b f t f F y = 5.5(0.345)(36) = 68.31kips

kmøaMgsuT§EdlRtUvepÞrenARtg;épÞb:HrvagEdk nigebtugKW
( )
T − C s = T − Pyf = As Fy − Pyf − Pyf = 276.5 − 2(68.31) = 139.9kips

EdlvatUcCagkmøaMgTajsuT§Cak;Esþg 210.4kips dUcenHsøabxagelIminRtUvkarrgkmøaMgsgát;eBj

kRmas;søabrbs;vaeT. enHmann½yfa PNA sßitenAkñúgsøab. BIrUbTI 9>21 kmøaMgkat;tamTisedkEdl
RtUvepÞrKW
( )
T − C s = As F y − b f t ' Fy − b f t ' F y = Vh

276.5 − 2[5.5t ' (36)] = 210.4

edayKNnarkkm<s;énkmøaMgsgát;enAkñúgsøab eyIgTTYl)an
t ' = 0.1669in.

eRKOgbgÁúMsmas 407 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

kmøaMgTajpÁÜbnwgeFVIGMeBIenAelITIRbCMuTm¶n;rbs;RkLaépÞBIeRkam PNA. muneBleyIgKNna moment

strength eKRtUvkMNt;TItaMgTIRbCMuTm¶n;sin. karKNnacm¶ayBITItaMgx<s;bMputrbs;EdkFñwm y RtUv)an

segçbenAkñúgtarag 9>6.
tarag 9>6
eRKOgbgÁúM A y Ay

W 16 × 36 7.68 15.69 / 2 = 7845 60.25

søab − 0.1669(5.50 ) = − 0.918 0.1669 / 2 = 0.0834 − 0.08

srub 6.762 60.17

∑ Ay 60.17
y= = = 8.898in.
∑ A 6.762
km<s;rbs;bøúkkugRtaMgsgát;enAkñúgebtugKW
C 210.4
a= = = 0.9168in.
0.85 f 'c b 0.85(3)(90)
édXñas;sRmab;kmøaMgsgát;rbs;ebtugKW
a 0.9168
y+t − = 8.819 + 4.75 − = 13.11in.
2 2
édXñas;m:Um:g;sRmab;kmøaMgsgát;enAkñúgEdkKW
t' 0.1669
y− = 8.819 − = 8.736in.
2 2
Kitm:Um:g;eFobkmøaMgTaj nigedayeyagtamrUbTI 9>20 eyIgTTYl)an nominal strength³
T.Chhay 408 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

M n = C (13.11) + C s (8.736)

= 210.4(13.11) + 0.1669(5.50)(36)(8.736) = 3047in. − kips = 253.9 ft − kips

Design strength KW
φb M n = 0.85(253.9) = 216 ft − kips > 156 ft − kips (OK)
eKRtUvP¢ab; deck eTAnwgsøabFñwmedayKMlat 18in. dUcenHeKminRtUvkar spot weld edIm,IkarBar uplift
eT.
cemøIy³ @> eRbI shear connector dUcbgðajenAkñúgrUbTI 922.

#> PaBdab
muneBlebtugrwgmaM
wD = wslab + wbeam = 0.500 + 0.026 = 0.526kips / ft
5wD L4 5(0.526 / 12)(30 × 12 )4
Δ1 = = = 1.098in.
384 EI s 384(29000 )(301)
PaBdabEdlbNþalmkBIbnÞúksagsg;KW
5wconst L4 5(0.200 / 12)(30 × 12 )4
Δ2 = = = 0.418in.
384 EI s 384(29000 )(301)
PaBdabsrubmuneBlebtugrwgmaMKW
Δ1 + Δ 2 = 1.098 + 0.418 = 1.52in.
sRmab;PaBdabEdlekItmaneRkayeBlebtugrwgmaM eKRtUvkarm:Um:g;niclPaBrbs;muxkat;
bMElgBIrKW I tr CamYynwgTTwgkRmalbMElg b / n nig I tr CamYynwgTTwgkRmalbMElg b / 2n .
pleFobm:UDulKW
E
n= s =
E
29000
3024
= 9. 6 yk n = 10
c

eRKOgbgÁúMsmas 409 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

sRmab;PaBdabrbs;muxkat;smasEdlBak;B½n§nwg creep TTwgRbsiT§PaBKW

b 90
= = 9in.
n 10
rUbTI 9>23 bgðajBImuxkat;bMElgEdlRtUvKña. karKNnaTItaMgG½kSNWt nigm:Um:g;niclPaB
RtUv)anbgðajenAkñúgtarag 9>7.

tarag 9>7
eRKOgbgÁúM A y Ay I d I + Ad 2
ebtug 29.25 1.625 47.53 25.75 2.282 178

W 16 × 26 7.68 12.60 96.77 301 8.693 881

srub 36.93 144.30 1059in.4

∑ Ay 144.3
y= = = 3.907in.
∑ A 36.93

edaysareKeRbI partial composite action dUcenHeKRtUvkareRbIm:Um:g;niclPaBbMElgEdlkat;

bnßy. BI AISC Equation C-I3-6 m:Um:g;niclPaBRbsiT§PaBKW
I eff = I s + ∑ Qn / C f (I tr − I s )

= 301 + 210.4 / 276.5 (1059 − 301) = 962.2in.4

PaBdabEdlekIteLIgedaysarbnÞúkGefrKW
5wL L4 5(0.400 / 12)(30 × 12)4
Δ3 = = = 0.2613in.
384 EI eff 384(29000)(962.2)

PaBdabEdlbNþalmkBIbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMKYrQrelIm:Um:g;niclPaBbM
ElgEdlTTYlCamYynwg 2n RbesIrCagCamYynwg n . dUcenH eRbITTwgkRmalbMElg
b 90
= = 4.5in.
2n 2(10 )
BIrUbTI 9>24 nig tarag 9>8 m:Um:g;niclPaBbMElgKW
I 'tr = 920.4in.4

T.Chhay 410 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

tarag 9>8
eRKOgbgÁúM A y Ay I d I + Ad 2
ebtug 14.62 1.625 23.76 12.87 3.780 221.8

W 16 × 26 7.68 12.60 96.77 301 7.195 698.6

srub 22.30 120.53 920.4in.4

∑ Ay 120.5
y= = = 5.405in.
∑ A 22.30

m:Um:g;niclPaBRbsiT§PaBEdleyIgnwgehAfa I 'eff KW
I 'tr = I s + ∑ Qn / C f (I 'tr − I s )

= 301 + 210.4 / 276.5 (920.4 − 301) = 841.3in.4

PaBdabry³eBlyUrEdlbNþalBIbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMKW
5(0.100 / 12)(30 × 12)4
Δ4 = = 0.0747in.
384(29000)(841.3)
PaBdabsrubKW
Δ1 + Δ 3 + Δ 4 = 1.098 + 0.2613 + 0.0747 = 1.43in.
30(12)
nig L
240
=
240
= 1.50in. > 1.43in. (OK)

cemøIy³ #> PaBdabGacTTYlyk)an.

eRKOgbgÁúMsmas 411 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

9>8> taragsRmab;karviPaK nigkarKNnaFñwmsmas

Tables for Composite Beam Analysis and Design
enAeBlG½kSNWt)aøsÞicsßitenAkñúgmuxkat;Edk karKNna flexural strength Gacnwgmankar
lM)ak. eK)anbegáItrUbmnþedIm,IsRmYldl;karKNnaenH (Hansell et al., 1978) b:uEnþtaragEdlbgðaj
enAkñúg Part 5 of the manual manPaBgayRsYlCag. eKmantaragBIrKW³ design strengths rbs;bnSM
énrUbragepSg²CamYynwgkRmalsRmab; Fy = 36ksi ≈ 250MPa nigsRmab; Fy = 50ksi ≈ 350MPa
nig taragénm:Um:g;niclPaB “lower bound” sRmab;bnSMdUcKña.
Design strength table EdlmaneQμaHfa “Composite Beam Selection Table,” GaceRbI)an

sRmab;EtrUbragEdlman compact web nigersIusþg; shear connector srub ∑ Qn ≥ 0.25 As Fy ¬Edn

kMNt;EdlENnaMTabCageKsRmab; partially composite beams¦
eK[ersIusþg;KNna (design strength) φM n sRmab;TItaMgrbs; PNA 7 EnøgdUcbgðajenA
kñúgrUbTI 9>25³ Epñkx<s;bMputrbs;søabxagelI/ EpñkTabbMputrbs;søabxagelI/ bITItaMgEdlmanKMlat
esμI²KñaEdlsßitenAkñúgsøabxagelI/ nigBIrTItaMgenAkñúgRTnug*. TItaMg PNA TabCageK ¬nIv:U &¦ RtUvnwg
EdkkMNt;EdlENnaMTabCageK ∑ Qn = 0.25 As Fy . PNA TItaMg ^ RtUvnwg ∑ Qn EdlsßitenAcenøaH
TItaMg & nigTItaMg %.

edIm,IeRbItaragsRmab;viPaKFñwmsmas dMbUgrkEpñkrbs;taragEdlRtUvnwgrUbragEdk
ehIyGnuvtþ dUcxageRkam³
*
nimitþsBaØa φM RtUv)aneKeRbIenAkñúgtaragsRmab; design strength of composite shapes, nig φ M RtUv)aneRbIsRmab; design
n b p

strength of steel shape alone. emKuNRtUv)ansMKal;edayviFIBIrepSgKñaBIeRBaHvamantémøBIrepSgKña.

T.Chhay 412 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

!> eRCIserIs ∑ Qn . enHCakarkMNt;rbs; Manual sRmab;kmøaMgsgát; C EdlCatémøtUcCag

eKén As Fy / 0.85 f 'c Ac nigersIusþg;rbs; shear connector srub ¬EdleyIgehAfa
∑ Qn ¦.

@> eRCIserIs Y 2 cm¶ayBITItaMgx<s;bMputrbs;EdkFñwmeTAkmøaMgsgát;pÁÜbenAkñúgebtugEdl

KNnaCa
a
Y2 = t −
2
TMhMenHRtUv)anbgðajenAkñúgrUbTI 9>26.
#> Gan φM n RbsinebIcaM)ac;eKRtUveFVI interpolation

sRmab;karKNna eKGacbBa©Úl φM n EdlTamTareTAkñúgtarag ehIyeKGacGaceRCIserIsEdk

Fñwm nig ∑ Qn . eKGacRtUvkartémø Y 2 dUcenHeKRtUvsnμt;km<s;rbs;karBRgaykugRtaMgsgát;rbs;
ebtug ehIyeKGaceFVIkarKNnaeLIgvijeRkayeBlEktRmUv. Manual [nUvsmIkarsRmab;)a:n;sμan
Tm¶n;Fñwm EtRbsinebIeKeRbItarag eKminRtUvkarsmIkarenaHeT.
taragk¾[pgEdrnUvtémø φb M p EdlGacRtUvkarsRmab;RtYtBinitüFñwmEdlKμancnÞl;kñúg GMLúg
eBlebtugrwgmaM ehIy Y1 Cacm¶ayBITItaMgx<s;bMputrbs;EdkFñwmeTA PNA.

]TahrN_ 9>9³ KNna design strength rbs;FñwmsmasenAkñúg]TahrN_ 9>1 nig 9>2 edayeRbI
taragenAkñúg Part 5 of the Manual.
dMeNaHRsay³ BI]TahrN_ 9>1 FñwmsmaspSMeLIgedayEdk W 16 × 36 CamYynwgkRmalxNÐEdlman
kRmas; t = 5in. nigTTwgRbsiT§PaB b = 87in. . ersIusþg;sgát;enA @* éf¶rbs;ebtugKW f 'c = 4000 psi .
kmøaMgsgát;enAkñúgebtugCatémøtUcCageKén
eRKOgbgÁúMsmas 413 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

As Fy = 10.6(36) = 381.6kips

b¤ 0.85 f 'c Ac = 0.85(4 )(5 × 87 ) = 1487kips

yk C = 381.6kips . km<s;rbs;bøúkkugRtaMgsgát;
C 381.6
a= = = 1.290in.
0.85 f 'c b 0.85(4 )(87 )
cm¶ayBITItaMgx<s;bMputrbs;EdkeTAkmøaMgsgát; C KW
a 1.290
Y2 = t − = 5− = 4.36in.
2 2
bBa©ÚleTAkñúgtaragCamYynwg ∑ Qn = 382kips nig Y 2 = 4.36 . edayeFVI interpolation eyIg
TTYl)an
φM n = 332 ft − kips
edayepÞógpÞat;CamYynwglT§plenAkñúg]TahrN_ 9>2 eyIgeXIjfavamantémødUcKña. karKNnatam
rUbmnþ nigedayeRbItaragTTYl)anlT§plRsedogKña enAeBlEdl PNA sßitenAkñúgmuxkat;EdkFñwm.
cemøIy³ Design strength = 332 ft − kips

taragsRmab;m:Um:g;niclPaB lower bound EdlsMKal;eday I LB pþl;nUvkar)a:n;sμanm:Um:g;

nicl PaBrbs;muxkat;bMElgmanlkçN³suvtßiPaBsRmab;FñwmdUcKñaEdlmanenAkñúg design strength
table. karsnμt;d¾cMbgkñúgkareFVItaragenHKWfamanEtRkLaépÞebtugEdlTb;Tl;nwgm:Um:g;eTEdlman

RbsiT§PaBkñúgkarKNnam:Um:g;niclPaB. kmøaMgenAkñúgebtugKW C = ∑ Qn nig RkLaépÞénmuxkat;

bMElgEdlRtUvKñaKW
∑ Qn ∑ Qn
Ac = =
stress in transformed area Fy

edIm,ICakarsRmYlteTAeTotkñúgkarKNna eKecalm:Um:g;niclPaBrbs;ebtugeFobnwgG½kSTIRbCMuTm¶n;.
edIm,IbgðajBIviFIsaRsþenH eKnwgyktémømYyenAkñúgtaragmkbMEbkenAkñúg]TahrN_ 9>10.

]TahrN_ 9>10³ karKNnapþl;nUvlT§plCa W16 × 31 CamYynwg ∑ Q n = 241kips ¬TItaMg PNA

3¦ Y 2 = 4in. nig Fy = 36ksi . KNnam:Um:g;niclPaB lower bound.
dMeNaHRsay³ RkLaépÞebtugEdlRtUv)aneRbIKW
T.Chhay 414 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

∑ Qn 241
Ac = = = 6.694in.2
Fy 36

muxkat;bMElgEdlRtUvKñaRtUv)anbgðajenAkñúgrUbTI 9>27 ehIykarKNnaRtUv)ansegçbenAkñúgtarag

9>9. kMNt;TItaMgTIRbCMuTm¶n; Kitm:Um:g;eFobG½kSenA)atrbs;muxkat;Edk.

tarag 9>9
eRKOgbgÁúM A y Ay I d I + Ad 2
ebtug 6.694 19.88 133.1 - 6.88 316.9

W 16 × 31 9.12 7.94 72.4 375 5.06 608.5

srub 15.81 205.5 925.4in.4
∑ Ay 205.5
y= = = 13.00in.
∑ A 15.81

m:Um:g;niclPaBBItaragm:Um:g;niclPaB lower bound KW I LB = 925in.4 edayepÞógpÞat;CmYynwg

lT§plEdl)anKNna.
cemøIy³ I LB = 925in.4

]TahrN_ 9>11³ eFVIkarKNna]TahrN_ 9>8 eLIgvijCamYynwgCMnYyrbs;taragenAkñúg Part 5 of the

Manual .
dMeNaHRsay³ !> KNnaFñwm
BI]TahrN_ 9>8 M u = 153 ft − kips ¬edayminKitbBa©ÚlTm¶n;Fñwm¦.
edaysnμt;fa a = 2in. eyIgTTYl)an
eRKOgbgÁúMsmas 415 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

a 2
Y2 = t − = 4.75 − = 3.75in.
2 2
BI Composite Beam Selection Table, ral;karbnSMénEdkFñwm/ ∑ Qn nig Y 2 Edlpþl;nUv
design strength FMCag 153 ft − kips KWCaFñwmsakl,gEdlGacTTYlyk)an. lT§PaBBIrnwgRtUv)an

segçbenAkñúgtarag 9>10.

tarag 9>10
φM n (ft-kips)
rUbrag TItaMg PNA ∑ Qn (kips)
¬edayeFVI interpolation¦
W 16 × 26 7 69.1 160

W 14 × 22 3 159 159

Edk W 14 × 22 CarUbragEdlRsalCag b:uEnþedaysar ∑ Qn FMCag vanwgRtUvkar shear

connector eRcInCag ¬GaceRcInCagBIrdg¦. sRmab;mUlehtuenH sakl,g W 16 × 26 . KNna Y 2

eLIgvij³
C ∑ Qn 69.1
a= = = = 0.3011in.
0.85 f 'c b 0.85 f 'c b 0.85(3)(90 )
a 0.3011
Y 2 = t − = 4.75 − = 4.60in.
2 2
¬Edl b = 90in. KW)anmkBI]TarhN_ 9>8¦
φM n = 164.4 ft − kips
BI]TahrN_ 9>8/ M u = 156 ft − kips CamYynwgkarKitbBa©ÚlTm¶n;Fñwm . vanwgtUcCag design
strength 164.4 ft − kips dUcenHkareRCIserIsenHGacTTYlyk)an. dUcKñaBI]TahrN_ 9>8 TaMg

flexural strength kñúgeBlsagsg; nig shear strength KWRKb;RKan;sRmab; W 16 × 26 .

cemøIy³ !> eRbI W16 × 26 .

@> Shear connector
dMbUg sakl,g stud 3 / 4 × 3in. . cMnYnrbs; strud EdlRtUvkarKW
∑ Qn
N1 =
Q
=
69.1
21.04
= 3 .3 yk 4 sRmab;Bak;kNþalFñwm dUcenHsrubKW 8 edIm
n

T.Chhay 416 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Stud 8 edImRtUvnwgKMlat
30(12 )
= 45in.
8
KMlatenHFMCagKMlatGnuBaØatGtibrma 36in. dUcenHeKRtUveRbI stud eRcInCagenH. RbsinebI
eKdak; stud ral; 6 rnUtmþg KMlatnwgesμInwg 36 ehIycMnYn stud srubKW
30(12 )
= 10, N1 = 5
36
kmøaMgkat;EdlRtUvKñaEdlRtUvepÞrKW
∑ Qn = 5(21.04 ) = 105.2kips
edIm,IgayRsYlkñúgkareRbItarag eyIgnwgyktémø ∑ Qn = 104kips enaH
104
a= = 0.4532in.
0.85(3)(90 )
0.4532
Y 2 = 4.75 − = 4.523in.
2
BI Composit Beam Selection Table, design strength KW
φM n = 182 ft − kips > 156 ft − kips (OK)
cemøIy³ @> eRbI stud 3 / 4 × 3in. cMnYn 10 edIm edayKMlatesμI²Kña. edIm,IkarBar uplift eFVI spot weld
ral;KMlat 18in. ¬sßitenAcenøaH stud¦.
#> PaBdab
BI]TahrN_ 9>8 PaBdabrbs;EdkFñwmmuneBlTTYl)an composite behavior KW
Δ1 = 1.098in. ¬edayminKitbnÞúksagsg;¦

sRmab;PaBdabEdlekIteLIgeRkayeBlebtugrwgmaM eKGaceRbIm:Um:g;niclPaB lower bound

Edl)anBItarag. eRbI W 16 × 26 CamYynwg ∑ Qn = 104kips ¬PNA TItaMg ^¦ nig Y 2 = 4.523in.
I LB = 623in.4
vaminmankarEbgEckm:Um:g;niclPaBsRmab;karKNnaPaBdabbEnßmEdlekIteLIgedaysar
creep. b:uEnþ m:Um:g;niclPaB lower bound mantémøtUcCagm:Um:g;niclPaBmuxkat;bMElgCak;Esþg

ehIy\T§iBlTaMgmUlKWnwgpþl;nUvPaBdabFMCagkar)a:n;sμan. RbsinebIbnÞúkefrry³eBlyUrtUc
eKGaceRbIm:Um:g;niclPaB lower bound.
w = wD + wL = 0.100 + 0.400 = 0.500kips / ft

eRKOgbgÁúMsmas 417 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

ehIyPaBdabEdlRtUvKñaKW
5wL4 5(0.500 / 12 )(30 × 12 )4
Δ2 = = = 0.5044in.
384 EI LB 384(29000 )(623)
PaBdabsrubKW
Δ1 + Δ 2 = 1.098 + 0.5044 = 1.602in.
PaBdabGnuBaØatGtibrmaKW
L 30(12 )
= = 1.500in. < 1.602in. (N.G.)
240 240
kñúgkarKNna Rtg;cMNucenH eyIgmanCeRmIsBIr³ ¬!¦
KNnaPaBdabEdlmanPaBsuRkitCageday eRbImuxkat;bMElg b¤¬@¦ eRCIserIskarbnSMrvagEdkFñwm nig
shear connector CamYynwgm:Um:g;niclPaB lower bound. edaysareKalbMNgrbs;]TahrN_enHcg;

bgðajBIkareRbItarag eyIgnwgeRCIserIsCeRmIsTI @.
KNnam:Um:g;niclPaB lower bound EdlRtUvkar. PaNdabEdlekItBIkRmalxNÐ nigTm¶n;Fñwm
nwgminpøas;bþÚr dUcenHPaBdabGnuBaØatGtibrmaEdlekIteLIgedaysarbnÞúkEdlGnuvtþeRkayeBlebtug
rwgmaMKW
Δ 2 Gtibrma = 1.50 − Δ1 = 1.50 − 1.098 = 0.4020in.
4
BI Δ 2 = 3845wLEI
LB

I LB EdlRtUvkarKW
5wL4 5(0.500 / 12 )(30 × 12 )4
I LB ≥ = = 782in.4
384 EΔ 2 384(29000 )(0.4020 )
sRmab; W 16 × 26 CamYynwg PNA # nig Y 2 = 4.5in. / m:Um:g;niclPaB lower bound KW
I LB = 804in.4 . BI Composite Design Selection Table, sRmab; PNA # kmøaMgkat;tamTisedkKW

∑ Qn = 208kips
edIm,ITTYltémøRtwmRtUv Y 2 nig I LB dMbUgKNnaTItaMgrbs;kmøaMgsgát;enAkñúgebtug
∑ Qn 208
a= = = 0.9063in.
0.85 f 'c Ac 0.85(3)(90 )
a 0.9063
Y 2 = t − = 4.75 − = 4.30in.
2 2
BItaragm:Um:g;niclPaB lower bound edayeFVI interpolation
T.Chhay 418 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

I LB = 788in.4 > 782in.4 (OK)

cMnYnrbs; shear connector EdlRtUvkarKW
∑ Qn
N1 =
Qn
=
208
21.04
= 9. 9 yk 10 sRmab;Bak;kNþalFñwm b¤srub 20 edIm
edaysarKMlatrbs;rnUt deck, stud mYysRmab;ral;rnUt 3 sRmab;KMlat 18in. nwgpþl;nUv
stud 20 edIm.

cemøIy³ #> edIm,IbMeBjtRmUvkarPaBdab begáIncMnYn stud BI 10 eTA 20 dak;mYyenAkñúgral;rnUt 3 .

]TahrN_ 9>11 bgðajplRbeyaCn_rbs;tarag. CaBiess composite Beam Selection

Table sRmYlkarKNna partially composite beam Edl PNA sßitenAkñúgmuxkat;EdkFñwm.

9>9> FñwmCab; (Continuous Beams)

sRmab;FñwmTRmsmBaØ cMNucénm:Um:g;sUnüenARtg;TRm. cMnYn connector EdlRtUvkarenAcenøaH

TRm nigcMNucEdlmanm:Um:g;GtibrmaKWcMnYnBak;kNþaléncMnYnsrubRtUvkar. sRmab;FñwmCab; cMNucrbt;
k¾CacMNucénm:Um:g;sUnüEdr nigCaTUeTAeKRtUvkar connector 2N1 sRmab;ElVgnImYy². rUbTI 9>28 a
bgðajBIRbePTFñwmCab; nigtMbn;EdlRtUvkar shear connector. enAtMbn;m:Um:g;GviC¢man kRmalebtug
nwgrgkmøaMgTaj dUcenHvanwgKμanRbsiT§PaB. enAkñúgtMbn;enH vanwgminman composite behavior Edl
eyIgRtUvBicarNaenaHeT. RbePT composite behavior EtmYyKt;EdlGacmanKWenAcenøaHFñwmEdk nig
EdkBRgwgtambeNþayenAkñúgkRmal. muxkat;FñwmsmasEdlRtUvKñaRtUv)anbgðajenAkñúgrUbTI 9>28 b.
RbsinebIeK eRbIKMnitenH eKRtUvpþl;nUvcMnYn shear connector RKb;RKan;edIm,ITTYlnUvdWeRkénPaBCab;
rvagEdkFñwm nigEdkBRgwg.
AISC Specification in Section I3.2 pþl;nUvCeRmIsBIrsRmab;m:Um:g;GviC¢man.

!> edayQrEtelIersIusþg;rbs;EdkFñwmb:ueNÑaH.
@> edayrYmbBa©ÚlTaMgEdkBRgwgenAkñúgmuxkat;smasRtUvRbQmnwglkçxNÐxageRkam³
a. EdkFñwmRtUvEt compact nigman latereal support RKb;RKan;

b. eKRtUvEtdak; shear connector enAtMbn;m:Um:g;GviC¢man ¬cenøaHcMNucm:Um:g;sUnü

nigcMNucm:Um:g;GviC¢manGtibrma¦
eRKOgbgÁúMsmas 419 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

c. EdkBRgwgenAkñúgTTwgRbsiT§PaBRtUvEtmanRbEvgbgáb;RKb;RKan; ¬TMBk;¦
ersIusþg;rbs;muxkat;smasKYrEtQrelIkarBRgaykugRtaMg)aøsÞicCamYynwg φb = 0.85 .
RbsinebIeKKit composite behavior AISC I5.2 tRmUv[ykkmøaMgkat;tamTisedkEdl
RtUv)anepÞrrvagcMNucénm:Um:g;GviC¢manGtibrma nigcMNucm:Um:g;sUnümantémøtUcCageKkñúgcMeNam
Ar Fyr nig ∑ Qn Edl

Ar = RkLaépÞrbs;EdkBRgwgenAkñúgTTwgRbsiT§PaBrbs;kRmal

Fyr = yield stress rbs;EdkBRgwg

ersIusþg;bEnßmEdlTTYlBIkarbBa©ÚlEdkBRgwgmantémøNas; b:uEnþeBlxøHeKeRbI cover plate enAkñúg

tMbn;m:Um:g;GviC¢man.

T.Chhay 420 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

9>10> ssrsmas (Composite Columns)

ssrsmasRtUv)anEbgEckCaBIrTRmg;KW EdkbMBgTIbmUl b¤RCugEdlbMeBjedayebtug b¤

rolled steel shape dak;enAkñúgebtugCamYynwgEdkBRgwgbBaÄr nigEdkkgTTwgdUcenAkñúgssrebtug

BRgwgedayEdk. rUbTI 9>29 bgðajBITRmg;TaMgBIrenH.

karviPaKssrsmasRtUv)aneFVIeLIgkñúgviFIdUcKñasRmab;Ggát;rgkarsgát;eRKOgbgÁúMEdkFmμtaEdr
edayeRbIsmIkardUcKñaBI AISC Charpter E b:uEnþCamYynwgtémø Fy / E nig r EdlRtUv)anEkERbedIm,I
TTYllT§plEdlTTYl)anBIkarBesaF nigkarKNnaRtUvKña. munBicarNasmIkar AISC sRmab;témø
TaMgenH eyIgRtUvRtYtBinitüBIeKalkarN_rbs;smIkarsin. RbsinebIeKFananUvsßanPaBlMnwg eKKitfa
ersIusþg;rbs;Ggát;smasrgkarsgát;CaplbUkénersIsu þg;tamG½kSrbs;EdkFñwm/ EdkBRgwg nigebtug.
vaRtUv)aneKehAfa squash load ehIyRtUv)an[eday
Pn = As Fy + Ar Fyr + 0.85 f 'c Ac ¬(>%¦
Edl As = RkLaépÞmuxkat; rolled steel shape
Ar = RkLaépÞmuxkat;srubrbs;EdkBRgwgbBaÄr

Fyr = yield stress rbs;EdkBRgwg

Ac = RkLaépÞmuxkat;rbs;ebtug

srésEdkBRgwgCaeBlbc©úb,nñCaRbePT deformed EdlépÞrbs;vamansac;lanecjEdlCYy

begáItPaBs¥itrvaEdk nigebtug)anl¥. RkLaépÞmuxkat; Ar EdlRtUv)aneRbIkñúgkarKNnaCa nominal
area EdlKitfaRkLaépÞrbs;EdkrelagEdlmanTm¶n;kñúgmYyÉktþaRbEvgdUcKñanwg deformed bar.

tarag 9>11 bgðajBI nomial diameter nigRkLaépÞsRmab;TMhMEdksþg;darEdlkMNt;eday ASTM

(1996) nig ACI (1995).

edIm,ITTYl)ankugRtaMgsrub EckbnÞúkEdlTTYl)anBIsmIkar 9>5 edayRkLaépÞrbs;EdkFñwm³

eRKOgbgÁúMsmas 421 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Fyr
Pn
As
= Fmy = Fy + Ar
As
A
+ 0.85 f 'c c
As
¬(>^¦
témørbs; Fmy EdlTTYlBIsmIkar (>^ ¬enAeBlEdleRbICMnYs[témø Fy enAkñúgsmIkarGgát;rgkar
sgát;¦ [lT§pll¥sRmab;EdkbMBg;TIbmUl b¤RCugEdlbMeBjedayebtugEdlebtugsßitenAkñúg steel
shape. ¬EdkBRgwgbBaÄrminRtUv)aneRbICamYynwgEdkbMBg;TIbmUl b¤RCug (concrete-filled pipe or

tube) eT dUcenH Ar GacniwgmantémøsUnüsRmab;ssrsmasRbePTenH¦.

tarag 9>11
elxEdk Ggát;Edk RkLaépÞmuxkat;
in. mm in.2 mm2
3 0.375 9.50 0.11 71.00
4 0.500 12.70 0.20 129.00
5 0.625 15.87 0.31 200.00
6 0.750 19.05 0.44 283.87
7 0.875 22.23 0.60 387.10
8 1.000 25.40 0.79 509.70
9 1.128 28.65 1.00 645.16
10 1.270 32.26 1.27 819.35
11 1.410 35.81 1.56 1006.45
14 1.693 43.00 2.25 1451.61
18 2.257 57.33 4.00 2580.64

sRmab;eRKOgbgÁúMEdkEdkbgáb;kñúgebtug vaminmanEdkhMuB½T§vaeT ehIy structural stability

Reseach Council (SSRC, 1979) ENnaMfaemKuNkat;bnßyersIusþg; ACI code (ACI, 1995) Edl

mantémø 0.7 RtUv)anGnuvtþeTAelItYénEdkBRgwg nigebtugénsmIkar (>^ dUcxageRkam³

Fyr
Fmy = Fy + 0.7 Ar
A
A
+ 0.7(0.85) f 'c c
A
¬(>&¦
s s
Fyr Ac
= Fy + 0.7 Ar + 0.595 f 'c
As As
edIm,IkarBar\T§iBl slenderness eKRtUvEktRmUvPaBrwgRkajkñúgkarBt;rbs;Ggát;Edl
smamaRt eTAnwgbrimaN EI / L . karEktRmUvenHRtUv)aneFVIeLIgedayEkERbtémørbs; E
dUcxageRkam³
A
E m = E + constant × Ec c
As
¬(>*¦
Edl E = m:UDuleGLasÞicrbs;EdkeRKOgbgÁúM
T.Chhay 422 Composite Construction
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Ec =m:UDuleGLasÞicrbs;ebtug
eTaHbICaPaBrwgRkaj (stiffeness) smamaRteTAnwgm:Um:g;niclPaB pleFobRkLaépÞsRmab;ssr
smaspþl;lT§pll¥CagpleFobm:Um:g;niclPaB (SSRC, 1979). témøefrenAkñúgsmIkar 9>8 KWesμInwg
0.4 sRmab;EdkTIbmUl b¤RCugEdlbMeBjedayebtugEdlbgðajBIPaBGnuBaØaténPaBrwgRkajrbs;

ebtug 40% nig 0.2 sRmab;EdkeRKOgbgÁúMEdlbgáb;kñúgebtug (encased shape).

kaMniclPaBrbs;muxkat;smasKWFMCagkaMniclPaBrbs;muxkat;EdkeRKagbgÁúM nigrbs;ebtug.
viFIEdlsuvtßiPaBKWRtUveRbIkaMniclPaBEdlmantémøFMénkaMniclPaBrbs;muxkat;EdkeRKOgbgÁúM b¤kaM
niclPaBénmuxkat;ebtug EdleKGacykesμInwg 0.3 dgénvimaRtNamYyrbs;muxkat;enAkñúgbøg;
buckling. edaykMNt;kaMniclPaBrbs;muxkat;smasCa rm enaHeKTTYl)an

rm = r ≥ 0.3b
Edl r= kaMniclPaBrbs;muxkat;EdkeRKOgbgÁúMenAkñúgbøg; buckling
b = vimaRtrbs;muxkat;ebtuenAkñúgbøg; buckling

tRmUvkarrbs; Specification
sRmab;ssrsmasmansar³sMxan;dUcKñaeTAnwgGVIEdlerobrab;xagelI. eK
AISC provisions

eRbI Equation E2-1 nig E2-3 BI Chapter E of the specification edIm,IkMNt; design strength b:uEnþ
témørbs; Fy / E nig r RtUv)anEksRmYl. eKRtUvBwgEp¥kelIsmIkar (>^ nig (>& edIm,IeFVIkarEk
sRmYltémøTaMgenH. BI AISC Section I2.2, témøEksRmYlrbs; Fy KW
Fmy = Fy + c1 Fyr ( Ar / As ) + c2 f 'c ( Ac / As ) (AISC Equation I2-1)

Edltémøefr c1 nig c2 RtUv)anKitsRmab;PaBxusKñarvag encased sectoon nig concrete-filled pipes

and tubes:
nig c2 = 0.85 sRmab; pipes and tubes
c1 = 1.0

c1 = 0.7 nig c2 = 0.6 sRmab; encased shapes

témøEdlEksRmYl AISC E KWdUcKñaeTAnwgGVIEdl[edaysmIkar (>* b¤

E m = E + c3 Ec ( Ac / As ) (AISC Equation I2-2)
Edl c3 = 0.4 sRmab; pipes and tubes
c4 = 0.2 sRmab; encased shapes

eRKOgbgÁúMsmas 423 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

AISC I2.2 kMNt;témø rm [esμIeTAnwgGVIEdl[edaysmIkar (>(

rm = r ≥ 0.3b
edIm,I[ssrsmasmanlkçN³RKb;RKan; eKRtUvBinitüemIlnUvkarkMNt;xageRkamEdl[eday AISC
I2.1³

!> EdkeRKOgbgÁúMRtUvEtmany:agtic 4% énRkLaépÞmuxkat;srub b¤Ggát;rgkarsgát;eFVIkardUc

ssrebtugGarem:CaCageFVIkardUcssrsmas.
@> Encased sections RtUvEteKarBtamlkçxNÐlMGitxageRkam³
a. eKRtUvEteRbITaMgEdlbBaÄr nigEdkkg. KMlatrbs;EdkkgminRtUvFMCagBIrPaKbI én

vimaRttUcCageKrbs;ebtug. RkLaépÞmuxkat;rbs;Edkem nigEdkkgminRtUvtUcCag

0.007in.2 / in. b¤ 0.18mm 2 / mm énKMlatEdk.

b. vaRtUvEtmankRmas;ebtugkarBarEdky:agtic 1.5in. ≈ 38mm sRmab;Edkkg

nigEdkbBaÄr.
c. EdkbBaÄrEdlRTbnÞúk (load-carrying longitudinal reinforcement) RtUvEtCab;enA

framed level. EdkbBaÄrsRmab;Tb;ebtugGacpþac;enARtg; framed level.

#> ersIusþg;rbs;ebtug f 'c RtUvEtsßitenAcenøaH 3ksi ≈ 21MPa nig 8ksi ≈ 55MPa sRmab;eb
tugTm¶n;Fmμta ¬minmanlT§plBiesaFn_sRmab; f 'c FMCag 55MPa eT¦ nigy:agticbMput
4ksi ≈ 28MPa sRmab;ebtugTm¶n;Rsal.

$> kñúgkarKNna Yield stress rbs;EdkeRKOgbgÁúM nigEdkBRgwgbBaÄrminRtUvFMCag 55ksi

≈ 380 MPa eT. karkMNt;RtUv)anTTYlBIkarBicarNa local stability. enAeBlEdlEdk

eRKOgbgÁúMhMuB½T§edayebtug vanwgminman local stability eT. ebtugnwgGachMuB½T§Edk)an

RKb;RKan;ebIvaminmankarpÞúHépÞebtug (spall). RbsinebIeKsnμt;[ebtugman spall enAeBl
ebtugman strain 0.0018 enaHkugRtaMgEdkRtUvKñaenAkñúgEdkKW
Fmax = ε max E = 0.0018(29000 ) = 52.2ksi
EdlRtUv)anKitCatémøkMNt;Rtwm 55ksi .
%> edIm,IkarBar local buckling enAkñúg pipes b¤ tubes EdlbMeBjedayebtug kRmas;rbs;
pipes b¤ tubes minRtUvtUcCag

T.Chhay 424 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

t = b F y / 3E sRmab;muxkat;ctuekaNEdlmanTTwgxageRkA b
b¤ t=D Fy / 8 E sRmab;muxkat;rgVg;EdlmanGgát;p©itxageRkA D

]TahrN_ 9>12³ Ggát;rgkarsgát;smasEdlman W 12 ×136 RtUv)andak;enAkñúgssrebtugEdlman

TMhM 20 × 22in. dUcbgðajenAkñúgrUbTI 9>30. eKeRbIEdk #10 bYnedImCaEdkbBaÄr nigEdk #3 CaEdk
kgEdlmanKMlat 13in. edayKitBIG½kSeTAG½kS. Edkman yield stress Fy = 50MPa ehIyeKeRbI
EdkBRgwgRbePT Grade 60. ersIusþg;rbs;ebtugKW f 'c = 5ksi . KNna design strength
sRmab;RbEvg RbsiT§PaB 16 ft sRmab;G½kSTaMgBIr.

cemøIy³ eKkMNt;témøEksRmYl F nig E Edl)anBI AISC Equation I2-1 nig I2-2. témøEdl
my m

RtUvkarsRmab;smIkarTaMgenHKW³
Fyr = 55ksi témøEdlkMNt;eday AISC I2.1
Ar = 4(1.27 ) = 5.08in.2
Ac = net area rbs;ebtug = 20(22) − As − Ar = 440 − 39.9 − 5.08
= 395.0in.2
sRmab; f 'c = 5ksi

Ec = w1c.5 f 'c = (145)1.5 5 = 3904ksi

BI AISC Equation I2-1, yield stress EdlEksRmYlKW

⎛A ⎞ ⎛A ⎞
Fmy = Fy + c1 Fyr ⎜⎜ r ⎟⎟ + c2 f 'c ⎜⎜ c ⎟⎟
⎝ As ⎠ ⎝ As ⎠
⎛ 5.08 ⎞ ⎛ 395 ⎞
= 50 + 0.7(55)⎜ ⎟ + 0.6(5)⎜ ⎟ = 84.60ksi
⎝ 39.9 ⎠ ⎝ 39.9 ⎠
eRKOgbgÁúMsmas 425 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

BI AISC Equation I2-2, m:UDuleGLasÞicEdlEksRmYlKW

⎛A ⎞
⎟⎟ = 29000 + 0.2(3904 )⎛⎜
395 ⎞
E m = E + c3 Ec ⎜⎜ c ⎟ = 36730ksi
⎝ As ⎠ ⎝ 39.9 ⎠
kaMniclPaBEdlRtUv)aneRbIenAkñúgsmIkarGgát;rgkarsgát;én AISC Cahpter E GacCa r sRmab;Edk
eRKOgbgÁúM b¤ 0.3b edayykmYyNaEdlmantémøFMCag. enAkñúg]TahrN_enH buckling nwgekIteLIg
eFobnwgG½kS y rbs;Ggát; dUcenH r sRmab;muxkat;KW ry = 3.16in . enAkñúgbøg; buckling
0.3b = 0.3(20 ) = 6in. ¬lub¦

dUcenH rm = 6in. . eKGacKNna design strength

dUcKñasRmab;Ggát;rgkarsgát;FmμtaedayeRbI témøEksRmYl Fmy / Em nig rm CMnYs[ Fy / E nig
r
KL Fmy 16(12 ) 84.60
λc = = = 0.4888 < 1.5
rmπ Em 6π 36730

Fcr = (0.658)λc Fmy = (0.658)(0.4888) (84.60) = 76.55ksi

2 2

nominal strength KW
Pn = As Fcr = 39.9(76.55) = 3054kips
ehIy design strength KW
φc Pn = 0.85(3054) = 2600kips
cemøIy³ design compressive strength KW 2600kips

taragsRmab;viPaK nigKNna Tables for Analysis and Design

mantaragEdlsRmYly:agxøaMgdl;karviPaK nigkarKNnassrsmas.
Part 5 of the Manual

taragTaMgenHmanlkçN³RsedogKñanwg column strength table enAkñúg Part 3 of the Manual. eK

[ axial compressive design strength CaGnuKmn_eTAnwgRbEvgRbsiT§PaBsRmab; concrete-filled
pipes and tubes nigsRmab; encased W-shapes. sRmab; encased column Edkem nigEdkkgEdlbM

eBjtRmUvkar AISC RtUv)anrab;bBa©Úl. eK[témø rmx / rmy sRmab;krNITaMgenaHEdl K x L ≠ K y L .

T.Chhay 426 Composite Construction

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

]TahrN_ 9>13³ Ggát;rgkarsgát;EdlmanRbEvg 18 ft RtUvRTnUvbnÞúkeFVIkar (service load) srub

1000kips EdlpSMeLIgedaycMENkesμIKñaénbnÞúkefr nigbnÞúkGefr. Ggát;enHmanTRm pinned enAcug
TaMgsgçag CamYynwgTRmbEnßmenAkm<s;Bak;kNþaltamG½kSexSay. eRbItaragenAkñúg Part 5 of the
Manual edIm,IeRCIserIsEdk W EdlmanrUbragkaerEdlbgáb;kñúgebtug (square encased W-shape)

CamYynwgRkLaépÞebtugEdltUcCageKEdlGaceFVIeTA)an. eRbIEdk A36 Edksrés grade 60 nig

f 'c = 3.5ksi .

dMeNaHRsay³ bnÞúktamG½kSemKuNKW
Pu = 1.2(500) + 1.6(500) = 1400kips
tamkarGegátelItaragbgðajfa sRmab; f 'c = 3.5ksi nigtémøén rmx / rmy ERbRbYlBI 1.0 eTA 1.22
EdltémøPaKeRcInesμInwg 1.0 . edaysar
KxL
= 2 > 1.22
KyL

KxL nwglub. snμt;fa rmx / rmy = 1.0 rYcbBa©ÚleTAkñúgtaragCamYynwg

KxL 18
KL = = = 18 ft
rmx / rmy 1.0

taragxageRkambgðajBICeRmIsEdlGaceFVI)an
TMhMmuxkat;ebtug EdkeRKOgbgÁúM rmx / rmy φc Pn
18×18 W10×112 1.0 1450kips
20×20 W12×87 1.0 14250kips

eTaHbICassr 20×20 RtUvkarEdkeRKOgbgÁúMtUcCagk¾eday EtlkçxNÐtRmUv[ykTMhMebtugGb,brma

dUcenHeyIgeRCIserIs 18×18.
cemøIy³ eRbIssrmuxkat; 18×18 CamYynwg W10×12 Edksrés #8 bYnedIm Edkkg #3 edayKMlat
12in.. KitBIG½kSeTAG½kS.

eRKOgbgÁúMsmas 427 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

X. rtEdkbnÞH
Plate Girder
10>1> esckþIepþIm (Introduction)
CaTUeTA plate girder RtUv)aneKKitCa flexural member Edlmuxkat;rbs;vaRtUv)anpÁúMeLIg
eday plate elements. AISC cat;TukFñwmxusBI plate girder edayQrelI web slenderness. Plate
girder CaFñwmFMTaMgElVg nigmuxkat; Edlmuxkat;FMenHCavi)akmkBIElVgEvg. RbsinebIeKminman hot-

rolled steel shape FMRKb;RKan;sRmab;ElVg nigkardak;bnÞúkEdl[ CaTUeTACeRmIsTImYyKWeKeRbI rolled

shape CamYynwg cover plate bEnßmenAelIsøabmYy b¤enAelIsøabTaMgBIr. RbsinebICeRmIsenHminGac

pþl;ersIusþg;m:Um:g;RKb;RKan; muxkat;EdlmanlkçN³RtUvkarBitR)akdGacRtUv)anplitBI plate elements.

b:uEnþRbsinebIElVgmanRbEvgEvg enaHkm<s; nigTm¶n;rbs; built-up girder GacnwgFM eBlenaHeKGac
eRbICeRmIsepSgeTot dUcCa truss.

T.Chhay 428 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

muxkat;rbs; plate girder GacmaneRcInTRmg;. rUbTI 10>1 bgðajBIlT§PaBrbs;muxkat; plate

girder xøH. TRmg;Fmμtarbs; plate girder KWRTnugeTalCamYYynwgsøabBIresμIKña EdlRKb;EpñkTaMgGs;

P¢ab;KñaedaykarpSar. muxkat;RbGb;EdlmanRTnugBIr nigsøabBIrCa torsionally superior shape nig

GacRtUv)aneRbIenAeBlEdleKRtUvkar unbraced length FM. Hubrid girder CaRbePTrtEdlEdksøab
manersIusþg;FMCagEdkRTnug ehIyeBlxøHk¾RtUv)aneKeRbIR)as;.
muneBlEdlkarpSarRtUv)aneRbITUlMTUlay kartP¢ab;eRKOgpÁúMrbs;muxkat;KWCakarBicarNacMbg
kñúgkarKNna plate girder. RKb;tMNTaMgGs;RtUv)aneFVIeLIgedayeRbIrIev dUcenHeKminmanviFIedIm,IP¢ab;
søabeTARTnugedaypÞal;eT. eKRtUvbBa©Úlmuxkat;bEnßmedIm,IepÞrbnÞúkBIeRKOgbgÁúMmYyeTAeRKOgbgÁúMmYy
eTot. bec©keTsFmμtakñúgkartP¢ab;KWkareRbIEdkEkgmYyKUedaydak;xñgTl;xñgedIm,IP¢ab;søabeTART
nugdUcbgðajenAkñúgrUbTI 10>1 b. RbsinebIeKRtUvkar web stiffener EdkEkgmYyKUk¾RtUv)aneRbI
sRmab;eKalbMNgenH. edIm,IeCosvagkarRbqaMgKñarvag stiffener angle nig flang angle eKRtUvbEnßm
filler plate eTAelIRTnug dUcenH stiffener GacXøatBI lange angle dUcbgðajenAkñúgrUbTI 10>1 c. Rb

sinebIeKRtUvkarmuxkat;ERbRbYl eKGaceRbI cover plate EdlmanRbEvgepSgKñamYy b¤eRcInP¢ab;eTAnwg

søabedarIev. eTaHbICaeKGaceRbI cover plate CamYynwg welded plate girder k¾eday k¾viFId¾samBaØ
CageKKWkareRbInUv flange plate EdlmankRmas;epSgKña EdlpSar end-to-end enATItaMgepSgKñatam
beNþayrbs; girder. eKGacemIleXIjy:agc,as;fa welded plate girder KWl¥Cag riveted pr bolted
girder edayKitelIPaBgayRsYl nigRbsiT§PaB. eyIgBicarNaEt I-shaped welded plate girder

enAkñúgCMBUkenH.
munnwgBicarNaBItRmUvkarCak;lak;rbs; AISC Specification sRmab; plate girder eyIgcaM)ac;
RtYtBinitükñúgviFITUeTAbMputBIPaBxusKñarbs; plate girder nig rolled beam Fmμta. eTaHbICaeyIg)an
sikSaBI flexural member enAkñúgCMBUk 5, “Beams” k¾eday k¾ plate girder mantRmUvkar flexural
strength nig shear strength BiessepSg.

10>2> karBicarNaTUeTA (General Considerations)

bBaðad¾FMkñúgkarKNnaeRKOgbgÁúMEdkKWkarpþl;nUv local stability b¤lMnwgsRmab;eRKOgbgÁúMTaMg

mUl. edaysar standard hot-rolled structural shapes manlkçN³smamaRtdUcenHbBaða local
rtEdkbnÞH 429 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

stability RtUv)ankat;bnßy b¤RtUv)ankat;bnßydl;kMritGb,brma. b:uEnþenAeBlEdleKeRbI plate girder,

designer RtUvEtKitBIktþaCaeRcInEdlPaKeRcIn rolled shape minmanbBaðak¾eday. RTnugesþIg nig

x<s;begáItnUvbBaðaCaeRcInenAeBlEdlcapÁúMCamYynwg plate girder edayrYmbBa©ÚlTaMg local instability.

karyl;dwgBIeKalkarN_rbs; AISC provions sRmab; plate girder TamTarnUvcMeNHdwgBI stability
theory CaBiess plate stability. b:uEnþenAkñúgesovePAenHbgðajEteKalkarN_tRmUvkarrbs; Specifi-

cation nigkarGnuvtþrbs;vaEtb:ueNÑaH. RbsinebImankarcab;GarmμN_ nigcg;EsVgyl;bEnßm Guide to

stability Criteria for Metal Structures (Johnston, 1976) CacMNucsRmab;cab;epþImd¾l¥ ehIy

Buckling Strength of Metal Structures (Bleich, 1952) nig Theory of Elastic stability

(Timoshenko and Gere, 1961) nwgpþl;nUvmUldæanRKwHén stability theory.

Plate girder QrelIersIusþg;EdlmaneRkayeBlRTnug buckle dUcenH flexural strength PaK

eRcInnwgekItBIsøab. sßanPaBkMNt;EdlRtUvBicarNaKWsøabrgkarTaj yield nigsøabrgkarsgát;

buckle. søabrgkarsgát;Edlrg buckle GacmanTRmg; vertical buckling enAkñúgRTnug b¤ flange

local buckling (FLB) b¤vaGacekIteLIgedaysar lateral-torsional buckling (LTB).

enAkñúgRTnug girder TItaMgEdlmankmøaMgkat;FMeRcInEtsßitenAEk,rTRm nigenARtg; b¤enAEk,r

G½kSNWt. bøg;emnwgeRTteFobeTAnwgG½kSbeNþayrbs;Ggát; ehIykugRtaMgemCakmøaMgTaj Ggát;RTUg
b¤kmøaMgsgát;Ggát;RTUg. kmøaMgTajGgát;RTUgminbegáItbBaðaeT EtkmøaMgsgát;Ggát;RTUg bNþal[RTnug
buckle. bBaðaenHGaceCosvag)antambIrebob³ (1) eKGaceFVI[pleFobkm<s;elIkRmas; (depth-to-

thickness ratio) rbs;RTnugmantémøtUclμmEdlGaclubbM)at;bBaðaenH)an (2) eKGaceRbI web

stiffeners edIm,IbegáItCa panel edIm,IbegáIn shear strength b¤ (3) eKGaceRbI web stiffeners edIm,I

begáItCa panel EdlTb;Tl;nwgkmøaMgsgát;Ggát;RTUgtamry³ tension field action. rUbTI 10>2 bgðaj

BIKMnitén tension field action. enAcMNucEdlCitekItman buckling RTnug)at;bg;lT§PaBrbs;vakñúg
karTb;Tl;kmøaMgsgát;Ggát;RTUg ehIykugRtaMgenH)anpøas;bþÚreTA stiffeners xag nigsøab. Stiffener
Tb; Tl;nwgbgÁúMkmøaMgsgát;Ggát;RTUgbBaÄr ehIysøabTb;Tl;nwgbgÁúMkmøaMgedk. eKRtUvkar[RTnug
Tb;Tl;nwgkmøaMgTajGgát;RTUg dUcenHeTIbmanBakü tension-field action. kareFVIkarenHmanlkçN³
dUcKñanwg pratt truss EdlGgát;RTnugbBaÄrRTkmøaMgsgát; Ggát;RTnugGgát;RTUgRTkmøaMgTaj dUcbgðaj
kñúgrUbTI 10>2 b. edaysarCak;Esþg tension field ekItman)anluHRtaEtRTnugcab;epþIm buckling
T.Chhay 430 Plate Girders
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dUcenH vaGaccUlrYmenAkñúgersIusþg;kmøaMgkat;rbs;RTnug)anluHRtaEtRTnug buckling sin. ersIusþg;

srubnwg pSMeLIgedayersIusþg;muneBl buckling nigersIusþg;eRkayeBl buckling EdlTTYlBI tension
field action.

RbsinebI unstiffened web minmanlT§PaBGacTb;Tl;nwgkmøaMgkat;Gnuvtþn_ enaHeKRtUveRbI

stiffener EdlmanKMlatesμI²KñaedIm,IbegáIn tension field action. muxkat;EdlRtUvkar stiffener

RtUv)aneKehAfa intermidate stiffener manTMhMtUcBIeRBaHeKalbMNgdMbUgrbs;vaKWpþl;nUv stiffener

RbesIrCagkarTb;Tl;kmøaMgGnuvtþn_edaypÞal;.
eKGacRtUvkar stiffener bEnßmenARtg;cMNucbnÞúkcMcMNucsRmab;eKalbMNgkarBarRTnugBIbnÞúk
sgát;edaypÞal;. stiffener enHRtUv)aneK[eQμaHfa bearing stiffener ehIyvaRtUvEtsmamaRtedIm,I
Tb;Tl;bnÞúkGnuvtþn_. vak¾GaceFVIkarCa intermidate stiffener kñúgeBlCamYyKñapgEdr. rUbTI 10>3
bgðajBI bearing stiffener EdlpSMeLIgedaybnÞHctuekaNEkgBIrenAsgxagRTnug girder. bnÞHEdk
bEnßmRtUv)ankat;biutenARCugxagkñúgTaMgelI nigeRkamedIm,IeCosvagTwkbnSar flange-to-web. Rbsin

rtEdkbnÞH 431 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

ebIeKsnμt; stiffener [Tb;Tl;bnÞúkGnuvtþn_srub P edaysuvtßiPaB ¬karsnμt;ecalnUvkarcUlrYmrbs;

RTnug¦ enaHeKGacsresr bearing stress Rtg;épÞb:HCa
P
fp =
A pb

Edl Apb = projected bearing area = 2at ¬emIlrUbTI 10>3¦

b¤eKGacsresr bearing load CMnYs[kareRbI bearing stress Ca
P = f p A pb ¬!0>!¦

elIsBIenH stiffener mYyKUCamYynwgRTnugEdlmanRbEvgxøIRtUv)anKitCassrEdlmanRbEvg

RbsiT§PaBtUcCagkm<s;rbs;RTnug ehIyRtUv)anGegátedayeRbI Specification provision dUcGgát;rg
karsgát;déTeTotEdr. muxkat;enHRtUv)anbgðajenAkñúgrUbTI 10>4. CaTUeTA ersIusþg;sgát;KYrQrelIkaM
niclPaBeFobG½kSkñúgbøg;rbs;RTnug EdlPaBKμanlMnwgeFobnwgG½kSemd¾éTRtUv)ankarBaredayRTnug
xøÜnÉg.
sßanPaBkMNt;EdlTTYl)anBIkarGnutþrbs;bnÞúkcMcMNuceTAelIsøabxagelIrbs;RTnug yielding,
RTnug crippling (buckling) ehIy sidesway buckling. Sidesway web buckling ekItmanenAeBl
kmøaMgsgát;enAkñúgRTnugbgá[søabrgkarTaj buckle tamTTwg. )atuPUtenHGacekItmanenAeB Edl
søabminmanlT§PaBRKb;RKan;RbqaMgnwgclnaeTAvijeTAmkrbs; stiffener b¤ lateral bracing.

T.Chhay 432 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

TwkbnSarsRmab;kartP¢ab;eRKOgbgÁúMrbs; plate girder RtUv)anKNnadUcKñanwgkarKNnatMN

pSardéTeTotEdr. TwkbnSar flang-to-web RtUvEtTb;Tl;nwgkmøaMgkat;tamTisedkenARtg;épÞb:Hrvag
eRKOgbgÁúMBIr. kmøaMgkat;Gnuvtþn_enH RtUv)aneKehAfa shear flow EdlCaTUeTARtUv)anKitCakMlMagkñúg
mYyÉktþaRbEvgrbs; girder edIm,IGacTb;Tl;edayTwkbnSar. BICMBUk 5 shear flow EdlQrelI
elastic behavior RtUv)an[eday
VQ
f =
Ix
Edl Q Cam:Um:g;TImYyénRkLaépÞrvagbøg;kmøaMgkat;tamTisedk nigépÞénmuxkat;xageRkAeFobnwgG½kS
NWt. smIkarxagenHCasmIkar %>^ sRmab;kugRtaMgkmøaMgkat;EdlKuNedayTTwgrbs;bøg;kmøaMgkat;.
edaysarEtCaTUeTAkmøaMgkat;Gnuvtþn_ERbRbYl dUcenHRbsinebIeKeRbIkarpSaredayEdlminCab; enaH
KMlatrbs;vanwgERbRbYleTAtamenaHEdr.

10>3> tRmUvkarrbs; AISC (AISC Requirments)

tRmUvkarsRmab; plate girder RtUv)anbriyayenAkñúg Chapter 6 of the AISC Speciffication
ehIy Appendix G manniyayBIeKalbMNgkñúgkarGnuvtþrbs; plate girder.
eTaHCa flexural member RtUv)ancat;cMNat;fñak;Ca beam b¤ plate girder k¾eday k¾vaenAEtCa
GnuKmn_eTAnwg web slendernedd h / t w Edl h Cakm<s;rbs;RTnugcenøaHépÞxagkñúgrbs;søab nig t w
CakRmas;rbs;RTnug. RbsinebI h / t w < 2550 / f yf ¬xñat IS ¦ h / t w < 970 / f yf ¬xñat US¦
rtEdkbnÞH 433 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Ggát;RtUv)ancat;cMNat;fñak;Ca beam ehIyeKRtUvGnuvtþkarpþl;[rbs; AISC Chapter F edaymin

KitfaGgát;enHCa bult-up BI plate b¤Ca hot-rolled shape. RbsinebI h / t w > 2550 / f yf ¬xñat IS¦
Ggát;RtUv)ancat;cMNat;fñak;Ca plate girder ehIyeKRtUvGnuvtþkarpþl;[rbs; AISC Chapter G. dUc
enH flexural member Edlman slender web Edl slenderness RtUv)ankMNt;enAkñúg AISC Chapter
B RtUv)anKitCa plate girder. cMNaMfa enAeBlEdleKeRbI hybrid girder témøkMNt;rbs; h / t w KW

QrelI Fyf yield stress rbs;søab. mUlehtuKWfa lMnwgrbs;RTnugRbqaMgnwg flexural buckling KWGa
Rs½ynwg strain enAkñúgsøab (Zahn, 1987).
edIm,Ibgáa vertical buckling rbs;søabeTAkñúgRTnug AISC Appendix G2 )an[nUvEdnkMNt;
x<s;bMputsRmab;pleFobTTwgelIkRmas; (width-thickness ratio) ht w . témøEdlkMNt;enHCa
GnuKmn_eTAnwg aspect ratio a / h rbs; girder plate EdlCapleFobKMlatrbs; intermediate
stiffener elIkm<s;RTnug ¬emIlrUbTI 10>5¦³

sRmab; a / h ≤ 1.5 /
t
h
≤
2000
F
¬xñat US¦
t
h 5250
≤
F
¬xñat IS¦ (AISC Equation A-G1-1)
w yf w yf

sRmab; a / h > 1.5 /

h
tw
≤
14000
Fyf ( Fyf + 16.5)
¬xñat US¦
h
tw
≤
96530
(
Fyf Fyf + 114 )
¬xñat IS¦ (AISC Equation A-G1-2)

Edl a Ca clear distance rvag stiffeners.

T.Chhay 434 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

10>4> ersIusþg;rgkarBt; (Flexural Strength)

rbs; plate girders KW φb M n / Edl φb = 0.90 . Norminal

Design flexural strength

flexural strength M n KWQrenAelIsøabrgkarTaj yielding b¤k¾søabrgkarsgát; buckling. eKGac

kMNt; Bucling strength rbs;søabrgkarsgát;eday flang local buckling (FLB) b¤k¾ lateral-
torsional buckling (LTB). Vertical buckling rbs;søabrgkarsgát;eTAkñúgRTnugRtUv)andkecjBI

karBicarNaedaysarkarkMNt;Edl[eday AISC Equation A-G1-2 nig A-G1-2 (Cooper,

Galambos, and Ravindra, 1978).

Tension Flange Yielding

BICMBUk 5/ kugRtaMgBt;GtibrmaenAkñúg flexural member EdlekageFobeTAnwgG½kSxøaMgrbs;va
KW
M
fb =
Sx
Edl S x Cam:UDulmuxkat;eGLasÞic (elastic section modulus) eFobG½kSxøaMg. sresrsmIkarm:Um:g;
Bt;CaGnuKmn_eTAnwgm:UDulmuxkat; nigkugRtaMg eKTTYl)an
M = S x fb ¬!0>@¦
AISC Appendix G2 [ nominal flexural strength EdlQrelIsøabrgkarTajEdl yield Ca
M n = S xt Re Fyt (AISC Equation A-G2-1)

Edl S xt = elastic section modulus EdlsMedAelIxagEdlrgkarTaj

emKuN hybrid girder
Re =

Fyt = yield stress rbs;søabrgkarTaj

emKuN hybrid girder Re esμInwg 1.0 sRmab; nonhybrid girder. sRmab; hybrid girder
12 + (Aw / A f )(3m − m 3 )
R = ≤ 1 .0
e
(
12 + 2 Aw / A f )
Edl Aw = RkLaépÞrbs;RTnug ≤ 10 A f
A f = RkLaépÞrbs;søabrgkarsgát;

m = Fyw / Fyf ¬karkMNt;enHKWsRmab;sßanPaBkMNt;rbs;søabrgkarTaj yield.

sRmab;søabrgkarsgát; eKk¾eRbIemKuN hybrid girder Edr Et m RtUv)ankMNt;epSg¦.
rtEdkbnÞH 435 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Compression Flange Buckling

EdlRtUvnwgsøabrgkarsgát; buckling k¾QrelIsmIkar !0>@ Edr.
Nominal flexural strength

BI AISC Appendix G2, ersIusþg;enHRtUv)ansresrCa

M n = S xc RPG Re Fcr (AISC Equation A-G2-2)
Edl S xc = m:UDulmuxkat;eGLasÞicsMedAelIxagEdlrgkarsgát;
RPG = emKuNkat;bnßyersIusþg;edIm,IkarBar elastic web buckling

Fcr = kugRtaMgeRKaHfñak;enAkñúgsøabrgkarsgát;EdlQrelI LTB b¤ FLB

Re = emKuN hybrid girder ¬EdlKitedaysmIkardUcKñasRmab;søabrgkarTaj yield b:uEnþ

m = Fyw / Fcr ¦.

emKuNkat;bnßyersIusþg;rbs; plate girder RPG RtUv)aneday

⎛ h ⎞
RPG = 1 −
ar ⎜ − 970 ⎟ ≤ 1.0 ¬xñat US¦ (AISC Equation A-G2-3)
1200 + 300a ⎜ t
r ⎝ w F ⎟
cr ⎠

⎛ h 2550 ⎞
RPG = 1−
ar ⎜ −
1200 + 300a r ⎜⎝ t w
⎟ ≤ 1.0
Fcr ⎟⎠
¬xñat IS¦ (AISC Equation A-G2-3)

Edl a = Aw / A f ≤ 10

cm¶ayBIrdgBITIRbCMuTm¶n;eTAépÞxagkñúgrbs;søabrgkarsgát; ¬ hc = h sRmab; girder

hc =

Edl mansøabesμIKña¦
kugRtaMgeRKaHfñak; Fcr KWQrelI lateral-torsional buckling b¤ flange local buckling.
AISC Specification eRbInimitþsBaØa λ / λ p nig λr edIm,IedaHRsayCamYynwg slanderness para-

meter sRmab;sßanPaBkMNt;TaMgBIr ehIyeKeRbInUvsMnMuénsmIkarxageRkamsRmab;edaHRsay Fcr .

smIkarRtUv)anbgðajenATIenHkñúgTRmg;BnøatbnþicbnþÜckñúgbMNgbBa¢ak;BIkarpþl;[. sRmab; lateral

torsional buckling eKeRbI slenderness énEpñkrbs;tMbn;sgát;rbs; girder dUcenH
Lb
λ= (AISC Equation A-G2-7)
rT

λp =
300
Fyf
¬xñat US¦ λp =
792
Fyf
¬xñat IS¦ (AISC Equation A-G2-8)

λr =
756
Fyf
¬xñat US¦ λr =
1985
Fyf
¬xñat IS¦ (AISC Equation A-G2-9)

T.Chhay 436 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Edl Lb Ca unbraced length nig rT CakaMniclPaBeFobG½kSexSaysRmab;Epñkénmuxkat;Edlman

søabrgkarsgát; nigmYyPaKbIénRTnugEpñkrgkarsgát;. sRmab; girder sIuemRTIDub TMhMenHesμImYyPaK
R)aMmYyénkm<s;RTnug. ¬emIlrUbTI 10>6¦ enaH³
RbsinebI λ ≤ λ p / kar)ak;KWekIteLIgedaysar yielding
Fcr = Fyf (AISC Equation A-G2-4)

RbsinebI λ p < λ ≤ λr / kar)ak;KWekIteLIgedaysar inelastic LTB nig

⎡ 1 ⎛ λ − λp ⎞⎤
Fcr = Cb Fyf ⎢1 − ⎜ ⎟⎥ ≤ Fyf (AISC Equation A-G2-5)
⎜ ⎟⎥
⎣⎢ 2 ⎝ λr − λ p ⎠⎦
Edl Cb RtUv)an[eday AISC Equation F1-3.
RbsinebI λ > λr / kar)ak;nwgekIteLIgedaysar elastic LTB nig
C PG
Fcr = (AISC Equation A-G2-6)
λ2
Edl C PG = 286000Cb (AISC Equation A-G2-10)

sRmab;søabrgkarsgát; EdlQrelI
buckling flange local buckling pleFobTTwgelI
kRmas; (width-thickness ratio) nigEdnkMNt;rbs;vaKW³
bf
λ= (AISC Equation A-G2-11)
2t f

λp =
65
Fyf
¬xñat US¦ λp =
170
Fyf
¬xñat IS¦ (AISC Equation A-G2-12)

rtEdkbnÞH 437 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

λr =
230
Fyf / k c
¬xñat US¦ λp =
605
Fyf / k c
¬xñat IS¦ (AISC Equation A-G2-13)

Edl kc = 4 / h / t w / 0.35 ≤ k c ≤ 0.763

enaH³ RbsinebI λ ≤ λ p / kar)ak;nwgekIteLIgedaysar yielding nig

Fcr = Fyf (AISC Equation A-G2-4)

RbsinebI λ p < λ ≤ λr / kar)ak;nwgekIteLIgedaysar inelastic FLB nig

⎡ 1 ⎛ λ − λp ⎞⎤
Fcr = Cb Fyf ⎢1 − ⎜ ⎟⎥ ≤ Fyf (AISC Equation A-G2-5)
⎢⎣ 2 ⎜⎝ λr − λ p ⎟⎥
⎠⎦
Edl Cb = 1.0

RbsinebI λ > λr / kar)ak;ekIteLIgedaysar elastic FLB nig

C PG
Fcr = (AISC Equation A-G2-6)
λ2
Edl C PG = 26200kc (AISC Equation A-G2-14)

karKNna flexural strength RtUv)anbgðajenAkñúg]TahrN_ 10>1/ cMNuc (a).

10>5> ersIusþg;kmøaMgkat; (Shear Strength)

rbs; plate girder KW φvVn Edl φv = 0.9 . Shear strength Ca Gnu-

Design shear strength

Kmn_eTAnwgpleFobkm<s;elIkRmas; (depth-to-thickness ratio) rbs;RTnug nigKMlatrbs; interme-

diate stiffener. Shear capacity manbgÁúMersIusþg;BIr³ ersIusþg;muneBl buckling nigersIusþg;eRkay

eBl buckling. ersIusþg;eRkayeBl)ak;sMGageTAelI tension field action EdlGacmanlT§PaB

begáItedaysarvtþmanrbs; intermediate stiffener. RbsinebIminmanvtþman stiffener b¤k¾manKMlat
q¶ayBIKñaeBk vak¾minGacman tension field action ehIy shear capacityGacmanEtersIusþg;muneBl
buckling. Nominal shear strength Edl[eday AISC Appendix G3 mandUcxageRkam³

sRmab; th ≤ 187 Fkv ¬xñat US¦ th ≤ 491 Fkv ¬xñat IS¦

w yf w yf
Vn = 0.6 Aw Fyw (AISC Equation A-G3-1)

sRmab; th > 187 kv

Fyf
¬xñat US¦ h
tw
k
> 491 v
Fyf
¬xñat IS¦
w

T.Chhay 438 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

⎛ 1 − Cv ⎞
Vn = 0.6 Aw Fyw ⎜⎜ Cv + ⎟
⎟⎟ (AISC Equation A-G3-2)
⎜ 1.15 1 + (a / h )2
⎝ ⎠
Edl kv = 5 +
5
(a / h )2
=5 RbsinebIa
h
>3 (AISC Equation A-G3-4)
2
a ⎡ 260 ⎤
=5 RbsinebI >⎢ ⎥
h ⎣ (h / t w )⎦

AISc Equation A-G3-1 [nUv shear strength enAeBlEdlKμanvtþman tension-field action ehIy
kar)ak;rbs;RTnugKWedaysar yielding. AISC A-G3-2 rab;bBa©Úl tension-field action. eKk¾Gac
sresr AISC Equation A-G3-2 Ca
1 − Cv
Vn = 0.6 Aw FywCv + 0.6 Fyw
1.15 1 + (a / h )2
GgÁTImYyenAkñúgsmIkarxagelIenHCa web shear buckling strength ehIyGgÁTIBIrCa post-buckling
strength. emKuN Cv CapleFob critical web buckling stress elI web shear yield stress

ehIyRtUv)ankMNt;dUcxageRkam³
sRmab; 187 Fkv ≤ th ≤ 234 Fkv (US) 491 Fkv ≤ th ≤ 614 Fkv (IS)
yf w yf yf w yf

187 k v / Fyf 491 k v / Fyf

Cv = (US) Cv = (IS) (AISC Equation A-G3-5)
h / tw h / tw

sRmab; th > 234 kv

Fyf
(US)
h
tw
> 614
kv
Fyf
(IS)
w
44000k v 303380k v
Cv = (US) Cv = (IS) (AISC Equation A-G3-6)
(h / t w )
2
Fyw (h / t w )2 Fyw
dMeNaHRsayrbs; AISC Equation A-G3-1 nig A-G3-2 RtUv)ansRmYledaytaragEdl[
enAkñúg Numerical Values section of the Specification. Tables 9-36 nig 10-36 Tak;Tgnwg)a:ra:
Em:RténsmIkarTaMgBIrenHsRmab;Edk A36 ehIy Tables 9-50 nig 10-50 sRmab;EdkEdlman yield
stress 50ksi ≈ 345MPa . eyIgnwgniyaylMGitBIkareRbIR)as;tarag TaMgenHenAkñúg]TahrN_xagmux.

Tension field minGacekItmaneBjenAkñúg panel xagcugeT. eKGacdwgy:agc,as;edaycat;

TukbgÁúM tension field tamTisedkEdlbgðajenAkñúgrUbTI 10>7. bgÁúMtamTisbBaÄrRtUv)anTb;eday

rtEdkbnÞH 439 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

.
stiffener Tension field enAkñúg panel CD RtUv)anrkSalMnwgeday tension field enAkñúg panel BC .
dUcenH panel xagkñúgRtUv)anf<k;Cab;eday panel EdlenAEk,r. b:uEnþ panel AB minmankarf<k;enAxag
eqVgeT. eTaHbICakarf<k;Gacpþl;[eday stiffener xagcugEdlKNnaedIm,ITb;Tl;karBt;EdlekItBI
tension field k¾eday k¾vamineFVIkarCakarf<k;Edr. edaysar tension field minekItmanenAeBjkm<s;

RTnug dUcenH internal stiffener k¾RbQmnwgkarBt;xøHEdlekItBI tension field EdllyecjenAkñúg

panel EdlenAEk,r b:uEnþm:Um:g;Bt;enHminsMxan;eT. dUcenHkarf<k;Cab;sRmab; panel BC RtUv)anpþl;

[enAxageqVgeday beam-shear panel RbesIrCag tension field panel Edl)anbgðaj. dUcenH

nominal shear strength KWdUcKñanwg flexural member EdlKμan tension-fiels panel
Vn = 0.6 Aw FywCv (AISC Equation A-G3-3)

cMNaMfasmIkarxagelIenHCaGgÁTImYyrbs; AISC Equation A-G3-2. Tension-field action

minRtUv)anGnuBaØatsRmab; hybrid girder b¤enAeBl a / h > 3 b¤enAeBl a / h > [260 /(h / t w )]2 ¬Edl
krNIxageRkayTaMgBIrenHRtUvKñanwg kv = 5 ¦. dUcenH AISC Equation A-G3-3 GnuvtþenAkñúgsßanPaB
TaMgenH.
AISC G4 erobrab;faeKminRtUvkar intermediate stiffener enAeBl h / t w ≤ 418 / Fyw

¬xñat US¦ b¤ h / t w ≤ 1097 / Fyw EdlTaMgenHGacbgðajdUcxageRkam. enAeBlEdlKμan interme-

diate stiffener a / h > 3 nig k v = 5 [
187 5 / Fyw 418 / Fyw
Cv = = (US)
h / tw h / tw
187 13 / Fyw 1097 / Fyw
Cv = = (IS)
h / tw h / tw
ehIy nominal shear strength
T.Chhay 440 Plate Girders
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Vn =
[
0.6 Aw Fyw 418 / Fyw ] (US) Vv =
[
0.6 Aw Fyw 1097 / Fyw ] (IS)
h / tw h / tw
dUcenHenAeBlEdl t / hw ≤ 418 / Fyw (US) h / t w ≤ 1097 / Fyw (IS)
Vv ≥ 0.6 Aw Fyw

b:uEnþsmIkarenHRtUvnwgEdnkMNt;x<s;bMput (shear yielding) dUcenHsBaØaFMCagRtUv)andkecj eK)an

Vv = 0.6 Aw Fyw (AISC Equation A-G3-1)

EdlCa nominal strength enAeBlEdl h / t w ≤ 187 kv / Fyw (US) h / t w ≤ 491/ kv / Fyw (IS)

RbsinebIeKminKit tension-filed action eTenaH eKTTYl)an shear strength BI AISC

Appendix F2 dUcxageRkam³

sRmab; th ≤ 187 Fkv (US) th ≤ 491 Fkv (IS)

w yw w yw
Vv = 0.6 Fyw Aw (AISC Equation A-F2-1)

sRmab; 187 kv
<
h
Fyw t w
≤ 234
kv
Fyw
(US) 491
kv
Fyf
≤
h
tw
≤ 614
kv
Fyf
(IS)

187 k v / Fyw
Vv = 0.6 Fyw Aw (US) (AISC Equation A-F2-2)
h / tw
491 k v / Fyw
Vv = 0.6 Fyw Aw (IS)
h / tw

sRmab; th > 234 kv

Fyf
(US)
h
tw
> 614
kv
Fyf
(IS)
w
26400k v
Vv = Aw (US) (AISC Equation A-G3-6)
(h / t w )2
182k v
Vv = Aw (IS)
(h / t w )2
segçbmk nominal shear strength RtUv)ankMNt;dUcxageRkam
!> kMNt; aspect ratio a / h
@> kMNt; kv nig Cv
#> sRmab;RKb; panel rbs; hybrid girder nigsRmab; panel xagcugrbs; nonhybrid girders:
RbsinebI th ≤ 187 Fkv (US) t
h
≤ 491
kv
F
(IS)
w yw w yw
Vv = 0.6 Fyw Aw

rtEdkbnÞH 441 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

RbsinebI th > 187 kv

Fyw
(US)
h
tw
> 491
kv
Fyw
(IS)
w
Vv = 0.6 Fyw AwCv

sRmab; panel d¾éTeTotrbs; nonhybrid girder Edlman tention-field action:

RbsinebI th ≤ 187 Fkv (US) t
h
≤ 491
F
kv
(IS)
w yw w yw
Vv = 0.6 Fyw Aw

RbsinebI th > 187 kv

Fyw
(US)
h
tw
> 491
kv
Fyw
(IS)
w

⎛ 1 − Cv ⎞
Vv = 0.6 Fyw Aw ⎜⎜ Cv + ⎟
⎟⎟
⎜ 1.15 1 + (a / h )2
⎝ ⎠
RbsinebIeKmineRbI tension-field action eKnwgGnuvtþ provisions of Appendix F2:
RbsinebI th ≤ 187 Fkv (US) t
h
≤ 491
F
kv
(IS)
w yw w yw
Vv = 0.6 Fyw Aw

RbsinebI 187 kv
<
h
Fyw t w
≤ 234
kv
Fyw
k
(US) 491 v ≤
Fyf
h
tw
≤ 614
kv
Fyf
(IS)

187 k v / Fyw
Vv = 0.6 Fyw Aw (US)
h / tw
491 k v / Fyw
Vv = 0.6 Fyw Aw (IS)
h / tw

RbsinebI th > 234 kv

Fyf
(US)
h
tw
> 614
kv
Fyf
(IS)
w
26400k v
Vv = Aw (US)
(h / t w )2
182k v
Vv = Aw (IS)
(h / t w )2
karkMNt; shear strength RtUv)anbgðajenAkñúg]TahrN_ 10>1 cMNuc (b).

Intermediate Stiffeners

T.Chhay 442 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RbsinebIeKRtUvkar intermediate stiffener edIm,ITTYl shear strength RKb;RKan;enAeBlEdl

eKeRbI tension-field action RkLaépÞmuxkat;Gb,brmarbs; stiffener eTal b¤KURtUv)an[eday AISC
Appendix G4 KW
Fyw ⎡ ⎤
⎢0.15Dht w (1 − Cv )
Vu
Ast = − 18t w2 ⎥ ≥ 0 (AISC Equation A-G4-1)
Fyst ⎣ φvVn ⎦
Edl Ast = RkLaépÞmuxkat;srubrbs; stiffener EdlRtUvkarenAeBlEdleKeRbI tension-field
action
rbs; stiffener
Fyst = yield stress

D = GnuKmn_énTRmg;rbs; stiffener

= 1.0 sRmab; stiffener KU ¬EdkEkg b¤EdkbnÞH¦

= 1.8 sRmab; stiffener EdkEkgeTal

= 2.4 sRmab; stiffener EdkbnÞHeTal

eKRtUvkarRkLaépÞEdlkMNt;eday AISC Equation A-G4-1 edIm,ITb;Tl;nwgbgÁúMkmøaMgbBaÄrrbs;

kmøaMgsgát;Ggát;RTUgenAkñúg panel. Table 10-36 nig 10-50 enAkñúg Numerical Values section of
the Specification Edl[nUv shear strength EdlQrelI tension-field action ehIyk¾[pg

EdrnUvRkLaépÞ stiffener EdlcaM)ac;edaysMEdgCaPaKryénRkLaépÞRTnugsRmab;témøepSg²rbs;

a / h nig h / t w .

m:Um:g;niclPaBGb,brmarbs; stiffener EdlKiteFobnwgG½kSenAkñúgbøg;rbs;RTnug ¬b¤sRmab;

stiffener eTaleFobnwgépÞrbs; stiffener Edlb:HnwgRTnug¦ RtUv)an[enAkñúg AISC Appendix F2.3

KW
I st = at w3 j

Edl j=
2.5
− 2 ≥ 0.5 (AISC Equation A-F2-4)
(a / h )2
eTaHbICa intermediate stiffener minRtUv)anKNnaCaGgát;rgkarsgát;k¾eday k¾karkMNt;pleFobTTwg
elIkRmas;sRmab;eCosvag local buckling GacRtUv)aneRbIkñúgkarkMNt;smamaRtrbs;muxkat;
stiffener. Table B5.1 nig AISC B5 minmankarENnaMsRmab; plate girder stiffener eT. EdnkMNt;

pleFob TTwgelIkRmas;sRmab; outstanding legs rbs;EdkEkgKUEdlCab;RtUv)aneRbIenATIenH

rtEdkbnÞH 443 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

b 95 b 250
= (US) = (IS)
t Fy t Fy

Tal;EtvaeFVIkarCa bearing stiffener ebImindUecñaHeT intermediate stiffener minRtUv)anTamTar

[RTsøabrgkarTajeT dUcenHRbEvgrbs;vaGaceBlxøHmanRbEvgxøICagkm<s;RTnug h ehIyeKGac
eCosvagnUvbBaðaplitEdlbNþalmkBIkardak;[RtUvKña. eyagtam Appendix F2.3 of the speci-
fication RbEvgrbs; stiffener KYrEtsßitenAkñúgEdnkMNt;Edlcm¶ayrvagTwkbnSarEdltP¢ab; stiffener

eTARTnug nigTwkbnSarEdltP¢ab;RTnugeTAsøabrgkarTaj. cm¶ayenHRtUv)ansMKal;eday c enAkñúgrUb

TI 10>8 KYrEtsßitenAcenøaHbYneTAR)aMmYydgénkRmas;RTnug.
karkMNt;smamaRtmuxkat;rbs; intermediate stiffener edayk,Ünrbs; AISC minTamTarkar
KNnakmøaMgNamYyeT b:uEnþkmøaMgRtUvEtepÞrBI stiffener eTARTnug ehIykartP¢ab;KYrEtRtUv)anKNna
sRmab;kmøaMgenH. Basler (1961) ENnaM[eRbI shear flow
Fy3
f = 0.045h
E
¬!0>#¦
Intemittent fillet weld Gb,brmaTMngCaRKb;RKan; (Salmon and John, 1996). manEtkar

ENnaMBI AISC enAkñúg Appendix F2.3 eTEdlTamTar clear distance cenøaH fillet wled EdlminCab;
min[FMCag 16t w b¤ 10in. ≈ 25cm .

10>6> GnþrGMeBIénkarBt; nigkmøaMgkat; (Interaction of Flexural and Shear)

CaTUeTA kugRtaMgRtg;cMNucmYykñúgRTnugrbs; plate girder KWCabnSMénkmøaMgkat; nigm:Um:g;Bt;Ca

mYynwgkugRtaMgG½kSemFMCagbgÁúMkugRtaMgdéTeTot. CaTUeTA kugRtaMgEdlbnSMenaHminmanbBaðaeT Rb
sinebIminman tension-field action eRBaHGnþrGMeBIénkmøaMgkat; nigm:Um:g;Bt;RtUv)anecalkñúgkrNIenH.
RbsinebIman tension field, kugRtaMgTajGgát;RTUgnwgeTAdl;kMritx<s;bMput ehIykarbnSMkugRtaMg
T.Chhay 444 Plate Girders
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RtUv)anBicarNa. AISC TamTarfaGnþrGMeBIRtUvKitenAeBlman tension field CamYynwgkmøaMgkat; nig

m:Um:g;Bt;
0.6φVn ≤ Vu ≤ φVn nig 0.75φM n ≤ M u ≤ φM n
Edl φ = 0.90 . vaRtUvEtbMeBjsmIkarGnþrGMeBIxageRkam
Mu V
+ 0.625 u ≤ 1.375 (AISC Equation A-G5-1)
φM n φVn
karRtYtBinitüsRmab;GnþrGMeBIrbs;m:Um:g;Bt; nigkmøaMgkat;RtUv)anbgðajenAkñúg]TahrN_ 10>1 cMNuc
(C).

10>7> Bearing Stiffeners

eKRtUvkar bearing stiffener enAeBlRTnugminmanersIusþg;RKb;RKan;sRmab;sßanPaBkMNt;Na

mYyén web yielding, web crippling, b¤ sidesway web buckling. sßanPaBkMNt;TaMgenHRtUv)an
bgðajenAkñúg Charpter K of the Specification (“Concentrated Forces, Ponding, and Fatigue”).
sRmab; web yielding, design strength rbs;RTnugKW φRn Edl φ = 1.0 nigenAeBlEdlbnÞúksßitenA
cm¶ayesμInwgkm<s; girder BIxagcug
Rn = (5k + N )Fywt w (AISC Equation K1-2)

enAeBlEdlbnÞúksßitenAcm¶aytUcCagkm<s; girder BIxagcug

Rn = (2.5k + N )Fywt w (AISC Equation K1-3)

Edl cm¶ayBIépÞxageRkArbs;søabeTAeCIgrbs; fillet enAelIRTnug ¬sRmab; rolled beam¦

k=

b¤eTA eCIgrbs;TwkbnSar ¬sRmab; welded girger¦

N = RbEvgrbs; bearing rbs;bnÞúkcMcMNucEdlvas;tamTisrbs;G½kSbeNþayrbs; girder

¬mintUcCag k sRmab;Rbtikmμcug¦
¬eyIg)anerobrab;BIsßanPaBkMNt;enHenAkñúgCMBUk 5 rYcehIy¦.
sRmab; web crippling emKuNrsIusþg; φ = 0.75 nigenAeBlbnÞúksßitenAy:agticcm¶ayBak;
kNþalkm<s; girder BIcug
⎡ 1.5 ⎤
⎛ N ⎞⎛⎜ t w ⎞⎟ Fywt f
Rn = 135t w2 ⎢1 + 3⎜
⎢
⎟
⎝ d ⎠⎜⎝ t f ⎟⎠
⎥
⎥ tw
sRmab; N
d
≤ 0 (AISC Equation K1-4)
⎣ ⎦

rtEdkbnÞH 445 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

enAeBlbnÞúksßitenAcm¶aytUcCagkm<s;rbs; girder BIcugrbs; girder

⎡ 1.5 ⎤
⎛ ⎞⎛ t ⎞ Fywt f
Rn = 68t w2 ⎢1 + ⎜ 4
⎢
N
⎝ d
− 0.2 ⎟⎜ w ⎟
⎠⎜⎝ t f ⎟⎠
⎥
⎥ tw
sRmab; N
d
> 0 (AISC Equation K1-5b)
⎣ ⎦
Edl d= srubrbs; girder
t f = kRmas;rbs;søab girder

¬eyIgk¾)anerobrab;BIsßanPaBkMNt;enHenAkñúgCMBUk 5¦
eKRtUvkar bearing stiffeness edIm,IbgáarEt sidesway web buckling eRkamsßanPaBkMNt;
mYycMnYnEtb:ueNÑaH. eKRtUvRtYtBinitü sidesway web buckling enAeBlEdlsøabrgkarsgát;minTb;
RbqaMgnwgclnaeTAsøabrgkarTaj. Design strength KW φRn / Edl φ = 0.85 .
RbsinebIsøabRtUv)anTb;min[vil
C r t w3 t f ⎡ ⎛ h / tw ⎞ ⎤
3
Rn = ⎢1 + 0.4⎜ ⎟ ⎥ (AISC Equation K1-6)
h2 ⎢ ⎜ l /bf ⎟ ⎥
⎣ ⎝ ⎠ ⎦

[smIkarxagelIenHminRtUvkarRtYtBinitüeTRbsinebI (h / t w ) / (l / b f ) > 2.3 ]

RbsinebIsøabRtUv)anGnuBaØat[vil
C r t w3 t f ⎡ ⎛ h / t w ⎞ ⎤
3
Rn = ⎢0.4⎜ ⎟ ⎥ (AISC Equation K1-7)
h 2 ⎢ ⎜⎝ l / b f ⎟⎠ ⎥
⎣ ⎦
[smIkarxagelIenHminRtUvkarRtYtBinitüeTRbsinebI (h / t w ) / (l / b f ) > 1.7 ]
Edl Cr = 960000 enAeBlEdl M u < M y Rtg;TItaMgrbs;kmøaMg
= 480000 RbsinebImindUecñaHeT

l = unbraced rbs;søabEdlFMCageK

eTaHbICaeKeFVIsmamaRtRTnugedIm,ITb;Tl;edaypÞal;nUvbnÞúkcMcMNuck¾eday k¾CaTUeTAeKenAEt
dak; bearing stiffener. RbsinebIeKmineRbI stiffener Rtg;kEnøgbnÞúkcMcMNucmanGMeBInImYy²enaH eKmin
caM)ac;RtYtBinitüsßanPaBkMNt; web yielding, web crippling nig sidesway web buckling eT.
Bearing strength rbs; stiffener RtUv)an[enAkñúg AISC J8 Ca φRn Edl φ = 0.75 nig
Rn = 1.8 Fy A pb (AISC Equation J8-1)

smIkarenHKWdUcKñanwgsmIkar !0>! Edlman bearing strength f p = 1.8 Fy .

T.Chhay 446 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

AISC K1.9 TamTar[eRbI full-depth bearing stiffener CaKU ehIyviPaKvaCassrrgbnÞúk

tamG½kSdUckarENnaMxageRkam³
!> muxkat;rbs;Ggát;rgbnÞúktamG½kSpSMeLIgeday stiffener plate nigRtUv)andak;sIuemRTItam
beNþayrbs;RTnug ¬emIlrUbTI 10>4¦. RbEvgenHminGacFMCag 12 dgénkRmas;RTnugeT
sRmab; stiffener xagcug b¤ 25 dgénkRmas;RTnugeT sRmab; stiffener xagkñúg.
@> RbEvgRbsiT§PaBKYrykesμInwg 0.75 dgénRbEvgCak;Esþg Edl KL = 0.75h .
Gnuvtþkarpþl;[EdlmanenAkñúg AISC Chapter E.
AISC K1.9 [pgEdrnUvlkçxNÐbEnßmxageRkamsRmab; bearing stiffeners.

z pleFobTTwgelIkRmas;RtUvbMeBjtRmUvkarxageRkam³
b 95 b 250
≥ (US) ≥ (IS)
t Fy t Fy

z TwkbnSarEdltP¢ab; stiffener eTARTnugKYrmanlT§PaBedIm,IepÞrkmøaMgkat;TTwgEdlmintémø

esμIKña. Cavi)ak eKGacKNnaTwkbnSar[RTbnÞúkcMcMNucTaMgmUl.
karviPaK bearing stiffener RtUv)anbgðajenAkñúg]TahrN_ 10>1 cMNuc (d).

]TahrN_ 10>1³ Plate girder Edl)anbgðajenAkñúgrUbTI 10>9 RtUv)anGegátedayeKarBtam AISC

Speciffication . bnÞúkCabnÞúkeFVIkarEdlmanpleFobbnÞúkGefrelIbnÞúkefresμInwg 3 . bnÞúkBRgayKW
4kips / ft edayrYmbBa©ÚlTaMgTm¶n;rbs; girder. søabrgkarsgát;man lateral support enARtg;cug nig

Rtg;cMNucEdlbnÞúkmanGMeBI. søabrgkarsgát;RtUv)anTb;nwgkarvilenARtg;cMNucxagelI. eK)andak;

bearing stiffener dUcbgðajRtg;cug nigRtg;bnÞúkcMcMNucmanGMeBI. eKRcibEKmrbs; stiffener 1in. Rtg;

EKmxagkñúgTaMgelI nigeRkam edIm,IeCosTwkbnSar flange-to-web. vaminman intermediate stiffener

eT ehIyEdkEdleRbITaMgGs;CaRbePTEdk A36 . edaysnμt;faTwkbnSarKWRKb;RKan; cUrRtYtBinitü
a. flexural strength
b. shear strength
c. flexural-shear interaction
d. bearing stiffener

rtEdkbnÞH 447 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

dMeNaHRsay³ rUbTI 10>10 bgðajdüaRkambnÞúk/ düaRkamkmøaMgkat;TTwg nigdüaRkamm:Um:g;Bt;edayQr

elIbnÞúkemKuN. epÞógpÞat;témøEdl)anbgðajRtUv)anTuk[GñkGanCaGñkKit.
CMhandMbUgenAkñúgkarviPaKKWkMNt;faetIGgát;enHRtUvnwgkarkMNt;rbs; AISC Ca palte girder b¤Gt;
h 63
= = 168
tw 3 / 8
970 970
= = 161.7
Fyf 36

edaysar h / t w > 970 / Fyf dUcenH flexural member enHCa plate girder ehIyeKGacGnuvtþkar
pþl;[rbs; AISC Appendix G.
RTnugRtUvEtbMeBj slenderness limitation rbs; AISC G1. témøkMNt;én h / t w GaRs½yeTA
nwg aspect ratio a / h . sRmab; plate girder enH bearing stiffener mannaTICa intermediate
stiffener ehIy
a 12(12)
≈ = 2.286
h 63
pleFobenHCatémøRbhak;RbEhlBIeRBaH a minR)akdCa 12 ft eT. enAkñúg panel xagkñúg 12 ft
CaKMlat stiffener EdlKitBIG½kSeTG½kSRbesIrCag clear spacing. sRmab; panel xagcug a KWtUcCag
12 ft edaysarEt double stiffener enARtg;TRm.

T.Chhay 448 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

edaysar a / h FMCag 1.5 AISC A-Equation A-G1-2 lub³

14000 14000 h
= = 322 > = 168
( )
(OK)
Fyf Fyf + 16.5 36(36 + 16.5) tw
a. Flexural strength
Flexural strengthnwgRtUv)ankMNt;eday strength rbs;søabrgkarTaj b¤rbs;søabkarsgát;.
kñúgkrNImYyNak¾eday eKRtUvkarm:Dulmuxkat;eGLasÞic (elastic section modulus). eday
sarPaBsIuemRTI
S xt = S xc = S x
karKNnasRmab; I x m:Um:g;niclPaBeFobG½kSxøaMgRtUv)ansegçbenAkñúgtaragTI 10>1. eKmin
Kitm:Um:g;niclPaBrbs;søabnImYy²eFobnwgG½kSTIRbCMuTm¶n;rbs;vaeT BIeRBaHvamantémøtUceFob
nwgGgÁdéT. m:UDulmuxkat;eGLasÞicKW
I x 40570
Sx = = = 1248in.3
c 32.5

rtEdkbnÞH 449 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

tarag 10>1
eRKOgbgÁúM A I d I + Ad 2
RTnug - 7814 - 7814

søab 16 - 32 16380

søab 16 - 32 16380

40574

eKnwgRtUvkar hybrid girder factor Re sRmab; tension flange strength nig compression
flange strength. edaysar girder enHCa nonhybrid dUcenH

Re = 1.0
BI AISC Equation A-G2-1, tension flange strength EdlQrelI yielding KW
M n = S xt Re Fyt = 1248(1.0)(36) = 44930in. − kips = 3744 ft − kips

Compression flange buckling strength Edl[eday AISC Equation A-G2-2:

M n = S xc RPG Re Fcr
Edl critical buckling stress Fcr KWQrelI lateral-torsional buckling b¤ flange local
buckling. edIm,IRtYtBinitü lateral-torsional buckling, eyIgRtUvkarkaMniclPaB rT . BIrUbTI

10>11
Iy =
1
(1)(16)3 + 1 (10.5)(3 / 8)3 = 341.4in.4
12 12
A = 16(1.0) + 10.5(3 / 8) = 19.94in.2
Iy 341.4
rT = = = 4.138in.
A 19.94
Unbraced length rbs;søabrgkarsgát;KW 12 ft ehIy slenderness parameter sRmab;
lateral-torsional buckling KW
Lb 12(12 )
λ= = = 34.80
rT 4.138
300 300
λp = = = 50
Fyf 36

T.Chhay 450 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

edaysar λ < λ p / Fcr = Fyf = 36ksi

RtUv)anKNnarYcehIysRmab; flange local buckling.

Critical buckling stress Fcr

Slenderness parameter EdlTak;TgKW

bf 16
λ= = =8
2t f 2(1.0 )
65 65
λp = = = 10.83
Fyf 36

mþgeTot/ edaysar λ < λ p dUcenH Fcr = Fyf = 36ksi

edIm,IKNnaemKuNkat;bnßyersIusþg;rbs; palte girder RPG eKRtUvkartémørbs; ar
Aw 63(3 / 8) 23.62
ar = = = = 1.477 < 10
Af 16(1.0 ) 16

BI AISC Equation A-G2-3

ar ⎛ hc ⎞
RPG = 1 − ⎜ − 970 ⎟ ≤ 1.0
⎜ tw
1200 + 300ar Fcr ⎟⎠
⎝
1.477 ⎛ 970 ⎞
= 1− ⎜⎜168 − ⎟⎟ = 0.9943
1200 + 300(1.477 ) ⎝ 36 ⎠
témøenHesÞIrEtesμInwg 1.0 edaysar flexural member enHesÞIrEtminGaccat;cMNat;fñak;Ca
plate girder ehIyvaxiteTArkcMNat;fñak;Ca beam. BI AISC Equation A-G2-2, nominal

flexural strength sRmab;søabrgkarsgát;KW

M n = S xc RPG Re Fcr = 1248(0.9943)(1.0 )(36 )

rtEdkbnÞH 451 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

= 44670in. − kips = 3723 ft − kips

lT§plenHtUcCag nominal strength sRmab;søabrgkarTajbnþicbnþÜc dUcenHvalub. Design
strength KW

φb M n = 0.90(3723) = 3350 ft − kips `

BIrUbTI 10>10 m:Um:g;emKuNGtibrmaKW
M u = 3168 ft − kips < 3350 ft − kips (OK)
cemøIy³ a. Flexural strength KWRKb;RKan;.
b. Shear strength
Shear strength CaGnuKmn_eTAnwg web slenderness ratio h / t w nig aspect ratio a / h .
dMbUgeyIgRtUvkMNt;faetIeKGaceRbI tension-field action enAkñúgtMbn;epSgBIenA end panel b¤
Gt;. eKGaceRbIva)anenAeBlEdl a / h tUcCag 3.0 nigtUcCag
2
⎡ 260 ⎤ ⎡ 260 ⎤
2
⎢ ⎥ = ⎢⎣ 168 ⎥⎦ = 2.395
⎣ (h / t w )⎦
témøRbhak;RbEhlrbs; a / h KW 2.286 dUcenHeKGaceRbI tension-field action )an.
kMNt; kv nig Cv . BI AISC Equation A-G3-4
5 5
kv = 5 + = 5+ = 5.957
(a / h )2 (2.286)2
KNna Cv
kv 5.957
187 = 187 = 76.07
Fyw 36
kv 5.957
234 = 234 = 95.19
Fyw 36

edaysar h / t w = 168 > 234 k v / Fyw / enaHeKGackMNt; Cv BI AISC Equation A-G3-6

44000k v 44000(5.957 )
Cv = = = 0.2580
(h / t w )
2
Fyw (168)2 (36)
edaysar h / t w > 187 kv / Fyw / eKnwgeRbI AISC A-G3-2 EdlKit tension-field action
edIm,IKNna nominal strength ¬elIkElg panel xagcug¦
⎛ 1 − Cv ⎞
Vn = 0.6 Aw Fyw ⎜⎜ Cv + ⎟
⎟
⎝ 1.15 1 + (a / h )2 ⎠

T.Chhay 452 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

⎡ 1 − 0.2580 ⎤
= 0.6(23.62 )(36 )⎢0.2580 + ⎥ = 263.6kips
⎢ 1.15 1 + (2.286 )2 ⎥
⎣ ⎦
Design shear strength KW
φvVn = 0.90(263.6) = 237kips
BIrUbTI 10>10 kmøaMgkat;emKuNGtibrmaenAkñúgRtg;cm¶aymYyPaKbYnBITRmrbs; girder KW
102kips dUcenH shear strength KWRKb;RKan;Rtg;kEnøgEdleKGnuBaØat[eRbI tension –field

action.

sRmab; panel xagcug tension-field action minRtUv)anGnuBaØat ehIyeKRtUvkMNt;

shear strength BI AISC Equation A-G3-3:

Vn = 0.6 Aw FywCv = 0.6(23.62 )(36 )(0.2580) = 131.6kips

Design strength KW
φvVn = 0.90(131.6) = 118kips
kmøaMgkat;emKuNGtibrmaenAkñúg panel xagcug KW
Vu = 234kips > 118kips (N.G.)
eKmanCeRmIsBIrsRmab;begáIn shear strength KWedaykat;bnßy web slenderness¬edaybegáIn
kRmas;rbs;va¦ b¤kat;bnßy aspect ratio rbs; panel xagcugnImYy²edaybEnßm intermediate
stiffener. Stiffener RtUv)anbEnßmenAkñúg]TahrN_enH. karkat;bnßy web slenderness

edIm,ITTYl)an shear strength RKb;RKan;GaceFVI[ flexural member enHcUleTAkñúgcMNat;fñak;

Ca beam EdleFVI[karviPaKpøas;bþÚrTaMgRsug.
eKkMNt;TItaMgrbs; intermediate stiffener TImYytamviFIdUcteTA³ dMbUg[ shear
strength BI AISC Equation A-G3-3 esμInwg shear strength EdlRtUvkar ehIyedaHRsayrk

témø Cv EdlRtUvkar. bnÞab;mkkMNt kv BI Equation A-G3-6 nigbnÞab;mkeTotkMNt; a / h

BI Equation A-G3-4. edayeFVIdUckarerobrab;xagelIeyIgTTYl)an
φvVn = φv (0.6 Aw FywCv ) (AISC Equation A-G3-3)
φvVn 234
Cv = = = 0.5096
φv (0.6 Aw Fyw ) 0.9(0.6 )(23.62 )(36 )
44000k v
Cv =
(h / t w )2 Fyw
rtEdkbnÞH 453 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Cv (h / t w )2 Fyw 0.5096(168)2 (36 )

kv = = = 11.77
44000 44000
5
kv = 5 + (AISC Equation A-G3-4)
(a / h )2
a 5 5
= = = 0.8594
h kv − 5 11.77 − 5

KMlat stiffener EdlRtUvkarKW

a = 0.8594h = 0.8594(63) = 54.1in.
eTaHbICa a RtUv)ankMNt;Ca clear spacing k¾eday eyIgnwgKitvaedaysuvtßiPaBCaKMlatBIG½kS
eTAG½kS ehIydak; intermediate stiffener TImYyenAcm¶ay 54in. BIcugrbs; girder. kardak;
enHnwgpþl;[nUv design strength mantémøRbhak;RbEhl kmøaMgkat;emKuNGtibrma 234kips .
eKminRtUvkar stiffener bEnßmeT edaysarkmøaMgkat;emKuNenAxageRkA panel xag cugtUcCag
design strength 237 kips .

eKGacsRmYlkarkMNt;KMlat stiffener edayeRbItaragenAkñúg Numerical Value

section of the Specification. eyIgnwgbgðajbec©keTsenHenAkñúg]TahrN_ 10>2.

cemøIy³ b. Shear strength KWRKb;RKan;. bEnßm intermediate stiffener mYycm¶ay 54in. BIcugrbs;
girder nImYy²
c. Flexural shear interaction
eKRtUvRtYtBinitü flexural-shear interaction enAeBlEdlman tension field ¬EdleRkABI
panel xagcug¦ nigenAeBlEdlbMeBllkçxNÐTaMgBIrxageRkam.

!> kmøaMgkat;TTwgsßitenAcenøaH
0.6φVn ≤ Vu ≤ φVn
sRmab; girder enH kmøaMgkat;TTwgeRkABI panel xagcugKW
0.6(237 ) ≤ Vu ≤ 237

142 ≤ Vu ≤ 237
@> m:Um:g;Bt;emKuNsßitenAcenøaH
0.75φM n ≤ M u ≤ φM n
sRmab; girder enH
0.75(3350) ≤ M u ≤ 3350
T.Chhay 454 Plate Girders
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

2510 ≤ M u ≤ 3350
tamkarGegátelIrUbbgðajfavaminmanbnSMénkmøaMgkat; nigm:Um:g;Bt;EdlbMeBjlkç-
xNÐTaMgenHeT.
cemøIy³ c. eKminRtUvkarRtYtBinitü flexural-shear interaction eT.
d. Bearing stiffener
eKpþl;nUv bearing stiffener enARtg;bnÞúkcMcMNucmanGMeBInImYy² dUcenHeKminRtUvkarRtYtBinitü
karpþl;[rbs; AISC Chapter K sRmab; web yielding, web crippling b¤ sidesway web
buckling eT. sRmab; bearing stiffener enAxagkñúg nigenAelITRm
b 7.5
= = 10.0
t 0.75
95 95
= = 15.8 > 10.0 (OK)
Fy 36

sRmab; bearing stiffener xagkñúg dMbUgKNna bearing strength. BIrUbTI 10>12

A pb = 2at = 2(7.5 − 1)(0.75) = 9.750in.2

BI AISC Equation J8-1,

Rn = 1.8Fy APb = 1.8(36 )(9.750 ) = 631.8kips
φRn = 0.75(631.8) = 474kips > 60kips (OK)

rtEdkbnÞH 455 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

RtYtBinitüersIusþg;rbs; stiffener CaGgát;rgkarsgát;. eyagtamrUbTI 10>12 eyIgGaceRbIRb

EvgRTnug 9.375in. Edl[RkLaépÞmuxkat;sRmab;ssr
A = 2(0.75)(7.5) + (3 / 8)(9.75) = 14.77in.2
m:Um:g;niclPaBrbs;RkLaépÞenHeFobnwgG½kSenAelIRTnugKW
I = ∑(I + Ad 2 )
9.375(3 / 8)3 ⎡ 0.75(7.5)3 ⎛ 7 .5 3 / 8 ⎞ ⎤
2
= + 2⎢ + 7.5(0.75)⎜ + ⎟ ⎥ = 227.2in.
4
12 ⎢⎣ 12 ⎝ 2 2 ⎠ ⎥⎦

ehIykaMniclPaBKW
I 227.2
r= = = 3.922in.
A 14.77
Slenderness ratio KW
KL Kh 0.75(63)
= = = 12.05
r r 3.922
BI AISC Table 3-36 enAkñúg Numerical Values section of the Specification,
φc Fcr = 30.37ksi
nig φc Pn = φc Fcr A = 30.37(14.77) = 449kips > 60kips (OK)
BIrUbTI 10>13/ sRmab; bearing stiffener enARtg;TRm design bearing strength KW
φRn = φ (1.8Fy A pb ) = 0.75(1.8)(36)[4(6.5)(0.75)] = 948kips > 234kips (OK)
RtYtBinitü stiffener-web assembly CaGgát;rgkarsgát;. eyagtamrUbTI 10>13 m:Um:g;nicl
PaBeFobG½kSenAkñúgbøg;rbs;RTnugKW
I = ∑(I + Ad 2 )
4.5(3 / 8)3 ⎡ 0.75(7.5)3 ⎛ 7.5 3 / 8 ⎞ ⎤
2
= + 4⎢ + 7.5(0.75)⎜ + ⎟ ⎥ = 454.3in.
4
12 ⎢⎣ 12 ⎝ 2 2 ⎠ ⎥⎦

ehIyRkLaépÞ nigkaMniclPaBKW
A = 4.5(3 / 8) + 4(0.75)(7.5) = 24.19in 2

nig r=
I
A
=
454.3
24.19
= 4.334in.

T.Chhay 456 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Slenderness ration KW
Kh 0.75(63)
= = 10.90
r 4.334
BI AISC Table 3-36, φc Fcr = 30.41kips . Design strength KW
φc Pn = φc Fcr A = 30.41(24.19) = 736kips > 234kips (OK)
cemøIy³ d. Bearing stiffener KWRKb;RKan;.

10>8> kaKNnamuxkat; (Design)

kic©kardMbUgkñúgkarKNna plate girder KWkarkMNt;TMhMrbs;RTnug nigsøab. RbsinebIeKRtUvkar
GBaØtiCam:Um:g;niclPaB eKRtUveRCIserIsykviFIbMErbMrYlTMhMsøabedayeRbI cover plate b¤kRmas;rbs;
søabmanTMhMxusKñaenATItaMgepSgKñatambeNþayrbs; girder. karsMercedayeRbI intermediate
stiffener BIeRBaHvaCH\T§iBldl;kRmas;RTnug. RbsinebIeKRtUvkar bearing stiffener dac;xateKRtUvEt

KNnava. cugeRkay bgÁúMepSg²RtUv)antP¢ab;edaykarKNnaTWkbnSary:agRtwmRtUv. xageRkamCa

CMhankñúgkarKNna³
!> eRCIserIskm<s;srub

rtEdkbnÞH 457 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Girder EdlmansmamaRtl¥RtUvmankm<s;esμInwg 1/10 eTA 1/12 énRbEvgElVg. karkMNt;

rbs; building code elI depth-to span ration b¤PaBdabGacman\T§iBlelIkkareRCIserIs.
@> eRCIserIsTMhMRTnugsakl,g
eKGacKNnakm<s;RTnugedaydkkRmas;søabTaMgBIrBIkm<s;srubEdl)aneRCIserIs. Cak;
Esþg dMNak;kalénkarKNnaenH eKRtUvEt)a:n;sμankRmas;søab. eKGacrkkRmas;RTnug
t w edayeRbIkarkMNt;xageRkam³
h 2000 h 5250
= (US) = (IS) (AISC Equation A-G1-1)
tw Fyf tw Fyf

sRmab; a / h > 1.5

h 14000
=
( )
(US) (AISC Equation A-G1-2)
tw Fyf Fyf + 16.5
h 96530
=
( )
(IS)
tw Fyf Fyf + 114

#> )a:n;sμanTMhMsøab
eKGac)a:n;sμanRkLaépÞsøabEdlRtUvkarBIrUbmnþFmμtaEdlbMEbkdUcxageRkam. yk
I x = I web + I flanges

t w h 3 + 2 A f y 2 ≈ t w h 3 + 2 A f (h / 2 )2
1 1
≈
12 12
Edl A f = muxkat;RkLaépÞrbs;søabmYy
y = cm¶ayBIG½kSNWteGLasÞiceTATIRbCMuTm¶n;rbs;søab

karcUlrYmrbs;m:Um:g;niclPaBénsøabnImYy²eFobnwgG½kSTIRbCMuTm¶n;rbs;vaRtUv)anecalenA
kñúgsmIkar !0$>. eKGac)a:n;sμanm:UDulmuxkat;
I x t w h 3 / 12 2 A f (h / 2 )
2
t h2
Sx = ≈ + = w + Af h
c h/2 h/2 6
RbsinebIeyIgsnμt;karKNnayktam compression flange buckling eyIgk¾Gacrkm:UDul
muxkat;BI AISC Equation A-G2-2:
M n = S xc RPG Re Fcr
Mn M u / φb
S xc = =
RPG Re Fcr RPG Re Fcr

T.Chhay 458 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Edl M u Cam:Um:g;Bt;emKuNGtibrma. eday[m:UDulmuxkat;EdlRtUvkaresμInwgtémøRb

hak;RbEhl eyIg)an
Μ u / φb t h2
= w + Af h
RPG Re Fcr 6

nig Af =
Mu
φb hRPG Re Fcr
t h
− w
6
RbsinebIeyIgsnμt;fa RPG = 1.0 / Re = 1.0 nig Fcr = Fy muxkat;EdlRtUvkarrbs;søab
mYyKW
Mu A
Af = − w
0.9hFy 6

Edl Aw CaRkLaépÞRTnug. enAeBlEdleKkMNt;RkLaépÞsøamEdlRtUvkarrYcehIy eRCIs

erIsTTwg nigkRmas;. RbsinebIeKeRbIkRmas;kñúgkar)a:n;sμankm<s;RTnug dUcenHeKmincaM)ac;
eFVIkarEktRmUvkm<s;RTnugeT. Rtg;cMNucenH eKGacKNnaTm¶n;)a:n;sμanrbs; girder, ehIy
eKRtUvkMNt; M u nig A f eLIgvij.
$> RtYtBinitü bending strength rbs;muxkat;sakl,g.
%> RtYtBinitükmøaMgkat;
RbsinebIeKBicarNa end panel b¤RbsinebIeKmineRbI intermediate stiffener eTenaH eK
Gacrk shear strength BI AISC Equation A-G3-3 Edl[ersIusþg;edayKμanvtþman rbs;
tension field. eKk¾GaceRbI Table 9-36 b¤ 9-50 enAkñúg Numerical Values section of

the Specification sRmab;karKNnaenHEdr. RbsinebIeKmineRbItarag eKGackMNt;KMlat

Intermediate dUcxageRkam³

a. [ shear strength EdlRtUvkaresμInwg shear strength Edl[eday AISC Equation

A-G3-3 ehIyedaHRsayrktémø Cv EdlRtUvkar.

b. edaHRsayrk k v BI AISC Equation A-G3-5 b¤ A-G3-6

c. edaHRsayrktémø a / h BI AISC Equation A-G3-4. RbsinebIeKeRbI tension-fieal

action eKGaceRbI trial-and-error approach b¤ AISC Table 10-36 b¤ 10-50 edIm,I

TTYl a / h EdlRtUvkar. RkLaépÞmuxkat;EdlRtUvkarrbs; stiffener EdlsMEdgCaPaK

ryénRkLaépÞRTnugk¾RtUv)an[enAkñúgtaragsRmab;témøxøHén h / t w nig a / h .
rtEdkbnÞH 459 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

eRCIserIsTMhM stiffener sakl,gEdlbMeBjRkLaépÞtRmUvkar ehIyRtYtBinitüm:Um:g;ni-

clPaBtRmUvkarrbs; AISC Appendix F.3.
^> RtYtBinitüGnþrGMeBIénkmøaMgkat; nigm:Um:g;Bt;
&> RtYtBinitü web resistance sRmab;bnÞúkcMcMNuc (web yielding, web crippling nig web
sidesway buckling)
RbsinebIeKRtUvkar bearing stiffener eKRtUvGnuvtþviFIsaRsþKNnaxageRkam³
a. sakl,gTTwgEdlRCugEKmrbs; stiffener enAEk,rEKmrbs;søab nigkRmas;EdlbMeBj

tRmUvkar width-thickness ratio

b 95 b 250
≤ (US) ≤ (IS)
t Fy t Fy

b. KNnaRkLaépÞmuxkat;EdlRtUvkarsRmab; bearing strength. eRbobeFobRkLaépÞenH

CamYynwgRkLaépÞsakl,g nigeFVIkarKNnaeLIgvijRbsinebIcaM)ac;.
c. RtYtBinitü stiffener-web assembly CaGgát;rgkarsgát;.

*> KNnaTwkbnSar flange-to-web, TwkbnSar stiffener-to-web nigkartP©ab;epSgeTot

¬flange segment, web splices>>>¦

]TahrN_ 10>2³ KNna plate girder TRmsamBaØEdlmanRbEvg 60 ft nigRTbnÞúkeFVIkardUcEdl)an

bgðajenAkñúgrUbTI 10>14 a. km<s;rbs; plate girder GnuBaØatGtibrmaKW 65in. . eRbIEdk A36 nig
electrode E70 XX ehIysnμt;fa girder enHman lateral support Cab;. cug girder manTRmRbePT

bearing ehIyminRtUv)an frame.

dMeNaHRsay³ bnÞúkemKuNedayminKitTm¶n; girder RtUv)anbgðajenAkñúgrUbTI 10>14b.

kMNt;km<s;srub
Span length 60(12 )
= = 72in.
10 10
Span length 60(12 )
= = 60in.
12 12
eRbIkm<s;GnuBaØatGtibrma 65in.
sakl,gkRmas;søab t f = 1.5in. nigkm<s;RTnug
h = 60 − 2(1.5) = 62in.

T.Chhay 460 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

edIm,IkMNt;kRmas;RTnug dMbUgRtYtBinitütémøkMNt;rbs; h / tw . sRmab; flexural member

EdlmanlkçN³Ca plate girder

h 970 970
≥ = = 161.7
tw Fyf 36
h 62
tw ≤ = = 0.383in.
161.7 161.7
BI AISC Equation A-G1-1 nig A-G1-2:
sRmab; a / h. ≤ 1.5
h 2000 2000
≤ = = 333.3
tw Fyf 36
62
tw ≥ = 0.186in.
333.3
sRmab; a / h > 1.5
h 14000 14000
≤ = = 322.0
tw (
Fyf Fyf + 16.5 )
36(36 + 16.5)
62
tw ≥ = 0.192in.
322.0

rtEdkbnÞH 461 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

sakl,g web plate 14 × 62 . kMNt;TMhMsøabEdlRtUvkar. BIrUbTI 10>14 b m:Um:g;

Bt;emKuNGtibrmaKW
186.4(60 ) 4.04(60 )2
Mu = + = 4614 ft − kips
4 8
BIsmIkar !0>% RkLaépÞsøabEdlRtUvkarKW
Mu A
Af = − w
0.90hFy 6
4614(12 ) 62(1 / 4 )
= − = 24.98in.2
0.90(62 )(36 ) 6
KNnaTm¶n; girder
RkLaépÞRTnug³ 62(1/ 4) = 15.5in.2
RkLaépÞsøab³ 2(24.98) = 49.96in.2
srub 65.46in.2
Tm¶n;³ 65144.46 (490) = 222.7lb / ft yk 250lb / ft
m:Um:g;Bt;EktRmUvKW
M u = 4614 +
(1.2 × 0.250)(60)2 = 4749 ft − kips
8
ehIyRkLaépÞsøabEdlRtUvkarKW
4749(12 ) 62(1 / 4)
Af = − = 25.79in.2
0.90(62)(36) 6
RbsinebIenArkSaTukkRmas;søabsnμt; enaHTTwgRtUvkarrbs;vaKW
Af 25.79
bf = = = 17.2in.
tf 1 .5

sakl,g flange plate 1 12 ×18 . rUbTI 10>15 bgðajBImuxkat;sakl,g ehIyrUbTI 10>16

bgðajBIdüaRkamkmøaMgkat; nigdüaRkamm:Um:g;Bt;sRmab;bnÞúkemKuN EdlrYmbBa©ÚlTaMgTm¶n; girder Rb
hak;RbEhl 250lb / ft .

T.Chhay 462 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

RtYtBinitü flexural strength rbs;muxkat;sakl,g. BIrUbTI 10>15 m:Um:g;niclPaBeFobG½kS

rbs;karBt;KW
rtEdkbnÞH 463 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

Ix =
(1 / 4)(62)3
+ 2(1.5)(18)(31.75)2 = 59400in.4
12
ehIym:UDulmuxkat;eGLasÞicKW
I x 59400
Sx = = = 1828in.3
c 32.5
karRtYtBinitüén AISC Equation A-G2-1 nig A-G2-2 bgðajfasRmab; nonhybrid girder
Edlmanmuxkat;sIuemRTI enaH flexural strength nwgmingaylubeday tension flange
yielding dUcenH eKRtUvEtGegátEt compression flange buckling b:ueNÑaH. elIsBIenH

edaysarEt girder enHman lateral support Cab; eKk¾mincaM)ac;BicarNaBI lateral-torsional

buckling Edr. sRmab;sßanPaBkMNt; én flange local buckling
bf 18
λ= = =6
2t f 2(1.5)
65 65
λp = = = 10.83
Fyf 36

edaysarEt λ < λ p /
Fcr = Fyf = 36ksi

eKRtUvkartémøxageRkamsRmab;kMNt;emKuNkat;bnßyersIusþg; RPG ³
⎛1⎞
Aw = 60⎜ ⎟ = 15.5in.2
⎝4⎠
A f = 18(1.5) = 27in.2
Aw 15.5
ar = = = 0.5741 < 10
Af 27
h 62
= = 248
t w 1/ 4
BI AISC Eqution A-G2-3/
ar ⎛ h ⎞
RPG = 1 − ⎜ − 970 ⎟
⎜ tw
1200 + 300a r Fcr ⎟⎠
⎝
0.5741 ⎛ 970 ⎞
= 1− ⎜⎜ 248 − ⎟⎟ = 0.9639
1200 + 300(0.5741) ⎝ 36 ⎠
BI AISC Equation A-G2-2/ nominal flexural strength KW
M n = S xc RPG Re Fcr

T.Chhay 464 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

= 1828(0.9639)(1.0 )(36 ) = 63430in. − kips = 5386 ft − kips

ehIy design sstrength KW
φb M n = 0.9(5286) = 4757 ft − kips > 4749 ft − kips (OK)
RtYtBinitü shear strength. kmøaMgkat;GtibrmamantémøGtibrmaenARtg;TRm
b:uEnþeKminGaceRbI vaenA end panel. eyIgnwgeRbI Table 9-36 enAkñúg Numerical Values
section of the Spec-sification edIm,ITTYl)anTMhM end panel EdlRtUvkar.

eKRtUvbBa©ÚleTAkñúgtaragCamYynwg h / t w = 248in. nig

φvVn 223.4
= = 14.41ksi
Aw 15.5
témøenHTamTar a / h < 0.5 ehIyvasßitenAeRkAtémørbs;taragEdlbBa¢ak;faeKminRtUvkar
kRmas;RTnugeT. sakl,gRTnug 516 × 62
h 62
= = 198.4
t w 5 / 16
⎛5⎞
Aw = 62⎜ ⎟ = 19.38in.2
⎝ 16 ⎠
φvVn 223.4
= = 11.5ksi
Aw 19.38
BI AISC Table 9-36/ sRmab; h / t w = 198 nig a / h = 0.6 témørbs; φvVn / Aw Edl)aneFVI
interpolation rYcKW 11.5ksi . dUcenH yk a / h = 0.6 nig

a = 0.6h = 0.6(62 ) = 37.2in.

eTaHbICacm¶ay a EdlRtUvkarCa clear spacing k¾eday k¾kareRbIcm¶ayBIG½kSeTAG½kSman
lkçN³samBaØCag nigsuvtßiPaBCagbnþicbnþÜc. ykcm¶ay 36in. BIG½kSrbs; bearing
stiffener xagcugeTAG½kSrbs; intermediate stiffener.

munnwgeFVIkarviPaK shear strength/ kMNt;\T§iBlénkarpøas;bþÚrkRmas;RTnug.

dMbUg kMNt;Tm¶n; girder
RkLaépÞRTnug³ 62(5 /16) = 19.38in.2
RkLaépÞsøab³ 2(1.5)(18) = 54.00in.2
srub 73.38in.2
Tm¶n;³ 73144.38 (490) = 250lb / ft ¬dUcKñanwgkarsnμt;BImun¦
rtEdkbnÞH 465 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

bnÞab;mk Ix =
(5 / 16 )(62 )3
+ 2(1.5)(18)(31.75)2 = 60640in.4
12
I x 60640
Sx = = = 1866in.3
c 32.5
A 19.38
ar = w = = 0.7178 < 10
Af 27

BI AISC Equation A-G2-3/

ar ⎛ hc 970 ⎞
RPG = 1 − ⎜ − ⎟
⎜ tw
1200 + 300ar Fcr ⎟⎠
⎝
0.7178 ⎛ 970 ⎞
= 1− ⎜198.4 − ⎟⎟ = 0.9814
1200 + 300(0.7178) ⎜⎝ 36 ⎠
Nominal flexural strength KW
M n = S xc RPG Re Fcr

= (1866 )(0.9814 )(1.0 )(36 ) = 65930in. − kips = 5494 ft − kips

Design strength KW
φb M n = 0.90(5494) = 4944 ft − kips
eTaHbICaersIusþg;enHFMCagtRmUvkarbnþicbnþÜck¾eday vanwgTUTat;CamYynwgTm¶n;rbs; stiffener
nig eRKOgbgÁúMdéTeTotEdleyIgmin)anKit.
cemøIy³ eRbIRTnug 516 × 62 nigsøab 1 12 ×18 dUcbgðajenAkñúgrUbTI 10>17.
kMNt;KMlat intermediate stiffener EdlRtUvkarsRmab; shear strength BIeRkA end panel.
enA cm¶ay 36in. BIcugxageqVg kmøaMgkat;KW
⎛ 36 ⎞
Vu = 223.4 − 4.34⎜ ⎟ = 210.4kips
⎝ 12 ⎠
φvVn 210.4
= = 10.86ksi
Aw 19.38
eKk¾GaceRbI tension-field action BIeRkA end panel dUcenHeKeRbI AISC Table 10-36.
sRmab; h / t w = 200 nig a / h = 1.6
φvVn
= 11.2ksi > 10.86ksi (OK)
Aw
eRbI a / h = 1.6 enaH
a = 1.6h = 1.6(62 ) = 99.2in.

T.Chhay 466 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

cMNaMfaminmantémøNaRtUv)an[enAkñúgtaragenAeBlEdl h / t w = 200 nig a / h = 1.6 eT.

mUlehtuKWfa tension-field action minRtUv)anGnuBaØatenAeBlEdl
2
a ⎡ 260 ⎤
2
⎛ 260 ⎞
>⎢ ⎥ = ⎜ ⎟ = 1.69
h ⎣ (h / t w )⎦ ⎝ 200 ⎠
sRmab;mUlehtuenH KMlat stiffener Gtibrma 99.2in nigGnuvtþsRmab;EpñkenAsl;rbs;
girder b:uEnþedIm,ITTYl)anKMlatesμIcenøaH end panel eKRtUveRbIKMlatBIG½kSeTAG½kS 81in.

dUcbgðajkñúgrUbTI 10>18. CamYynwgKMlatEdlkat;bnßyenH

a 81
= = 1.306
h 62
edIm,IKNna shear strength EdlRtUvKña eKbBa©Últémø a / h = 1.3 nig h / t w = 200 eTAkñúg
Table 10-36. edayeFVI interpolation eKTTYl)an
φvVn
= 12.6
Aw
nig φvVn = 12.6 Aw = 12.6(19.38) = 244.2kips

rtEdkbnÞH 467 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

muxkat;rbs; intermediate stiffener KWQrelIlkçxNÐbI³ (1) RkLaépÞGb,brma/ (2)

m:Um:g;niclPaBGb,brma nig (3) pleFobTTwgelIkRmas;Gb,brma.

RkLaépÞEdlRtUvkarsRmab; stiffener KUKWCaGnuKmn_én h / t w nig a / h ehIyeKGac

rkva)anBI AISC Table 10-36 edayeFVI interpolatrion.
sRmab; a / h = 1.3 nig h / t w = 200 /
Ast = 2.3% énRkLaépÞrbs;RTnug

= 0.023(19.38) = 0.556in.2
BI AISC Equation A-F2-4/
2 .5
j= − 2 ≥ 0 .5
(a / h )2
2.5
= − 2 = −0.534
(1.306)2
edaytémørbs; j < 0.5 dUcenHeRbI j = 0.5

m:Um:g;niclPaBEdlRtUvkarKW
I st = at w3 j = 81(5 / 16 )3 (0.5) = 1.24in.4
eRbItémøGtibrmarbs; b / t
95 95
= = 15.8
Fy 36

sakl,g plate 14 × 4 cMnYnBIr

b 4
= = 16 ≈ 15.8 (OK)
t 1/ 4
⎛1⎞
Ast Edl[KW2(4)⎜ ⎟ = 2.0in.2 > 0.446in.2
⎝4⎠
(OK)

T.Chhay 468 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

BIrUbTI 10>19 nigRTwsþIbTG½kSRsb eyIg)an

I st = ∑(I × Ad 2 )
⎡ 0.25(4)3 ⎤
=⎢ + 0.25(4)(2 + 5 / 32)2 ⎥ × 2 = 11.97in.4 > 1.24in.4 (OK)
⎢⎣ 12 ⎥⎦

edIm,IkMNt;RbEvgrbs; stiffener dMbUgkMNt;cm¶ayrvag stiffener-to-web weld nig web-to-

flange weld ¬emIlrUbTI 10>8¦

cm¶ayGb,brma = 4t w = 4⎛⎜⎝ 165 ⎞⎟⎠ = 1.25in.

cm¶ayGtibrma = 6t w = 6⎛⎜⎝ 165 ⎞⎟⎠ = 1.875in.
RbsinebIeyIgsnμt;TMhM flange-to-web weld 516 in. nigcm¶ayrvagTwkbnSar 1.25in. RbEvg
Rbhak;RbEhlrbs; stiffener KW
h − TMhMTwkbnSar − 1.25 = 62 − 0.3125 − 1.25 = 60.44in. yk 60in.
cemøIy³ eRbI plate 14 in.× 4in.× 5 ft sRmab; intermesiate stiffener.
RtYtBinitüGnþrGMeBIrbs;m:Um:g;Bt; nigkmøaMgkat; EdlRtUvkarsRmab;EtkEnøgNaEdlRtUvkar
tension field. témørbs;kmøaMgkat;EdlRtUveFVIkarGegátKW

0.6φVn ≤ Vu ≤ φVn b¤ 0.6(244.2) ≤ Vn ≤ 244.2

146.5 ≤ Vn ≤ 244.2
témørbs;m:Um:g;Bt;EdlRtUvRtYtBinitüKW

rtEdkbnÞH 469 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

0.75φM n ≤ M u ≤ φM n b¤ 0.75(4944) ≤ M u ≤ 4944

3708 ≤ M u ≤ 4944
BIrUbTI 10>16/ Vu = 146.5kips enAeBlEdl
223.4 − 4.3x = 146.5kips
Edl x = cm¶ayBIcugxageqVgrbs; girder = 17.72 ft
enARtg;TItaMgdUcKña m:Um:g;Bt;KW
4.34(17.72)2
M u = 223.4(17.72) − = 3277 ft − kips
2
enAkñúgtMbn;EdlkmøaMgkat;FMCag 146.5kips m:Um:gBt;tUcCag 3708 ft − kips dUcenHeKmin
caM)ac;BicarNaGnþrGMeBIénm:Um:g;Bt; nigkmøaMgkat;eT.
eKnwgdak; bearing stiffener Rtg;TRm nigRtg;kNþalElVg. edaysarvaman stiffener
enARtg;kEnøgbnÞúkcMcMNucmanGMeBInImYy² dUcenHeKminRtUvkarGegátPaBFn;rbs;RTnugeTAnwg
bnÞúkTaMgenHeT. RbsinebImindak; stiffener eTenaH eKRtUvkarBarRTnugBI yielding nig
crippling. edIm,IeFVIdUcenH eKRtUvkarRbEvg bearing N RKb;RKan;EdlTamTareday AISC

Equation K1-2 rhUtdl; K1-5. Sidesway web buckling minmanCasßanPaBkMNt;Edl

GacekItmaneT BIeRBaH girder enHman lateral support Cab; ¬EdleFVI[ unbraced length
l = 0 nig (h / t w )(l / b f ) > 2.3 ¦.

sakl,gTTwg stiffener b = 8in. . TTwgsrubnwgesμI 2(8) + 5 /16 = 16.31in. EdltUc

CagTTwgsøab 18in. bnþic. BI AISC K1.9
b Fy 8 36
b
t
≤
95
F
b¤ t≥
95
=
95
= 0.505in.
y

sakl,g stiffener 3 4 × 8 BIr. snμt; web-to-flange weld 516 in. nig cutout enAkñúg
stiffener 1 2 in. . RtYtBinitü stiffener enARtg;TRm. Bearing strength KW

φRn = 0.75(1.8Fy A pb )

= 0.75(1.8)(36 )(0.75)(8 − 0.5) × 2 = 547 kips > 223.4kips

RtYtBinitü stiffener Cassr. RbEvgrbs;RTnugEdleFVIkarCamYynwg stiffener plate edIm,IbegáIt
CaGgát;rgkarsgát;KWesμInwg 12 dgénkRmas;RTnugsRmab; end stiffener (AISC K1.9). dUc
T.Chhay 470 Plate Girders
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Edl)aneXIjenAkñúgrUbTI 10>20 RbEvgenHKW 12(5 /16) = 3.75in. . edaysar stiffener RtUv

manTItaMgenARtg;kNþalénRbEvgenH/ cMNucTRm ¬TItaMgrbs;Rbtikmμrbs; girder¦ RtUvEtman
témøRbhak;RbEhlnwg 3.75 / 2 = 1.875in. BIcugrbs; girder. dUcEdlbgðajenAkñúgrUbTI
10>21 b:uEnþQrelIkarKNnaenAelIRbEvgsrubrbs;RTnug 3.75in eKnwgTTYl)an

⎛3⎞ ⎛ 5 ⎞
A = 2(8)⎜ ⎟ + ⎜ ⎟(3.75) = 13.17in.2
⎝ 4 ⎠ ⎝ 16 ⎠
3.75(5 / 16 )3 ⎡ 0.75(8)3 5 ⎞ ⎤
2
⎛ 3 ⎞⎛
I= + 2⎢ + 8⎜ ⎟⎜ 4 + ⎟ ⎥ = 271.3in.4
12 ⎢⎣ 12 ⎝ 4 ⎠⎝ 32 ⎠ ⎥⎦

I 271.3
r= = = 4.539in.
A 13.17
KL Kh 0.75(62)
= = = 10.24
r r 4.539
BI AISC Table 3-36/ φc Fcr = 30.43ksi . Design strength KW
φc Pn = φc Fcr A = 30.43(13.17 ) = 401kips > 223.4kips (OK)
edaysarbnÞúkenAkNþalElVgtUcCagRbtikmμ eRbI stiffener dUcKñaenAkNþalElVg
cemøIy³ eRbI plate 3 4 × 8 BIrsRmab; bearing stiffener.

rtEdkbnÞH 471 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Rtg;cMNucenH RKb;eRKOgpÁúMrbs; girder TaMgGs;RtUv)ankMNt;TMhM. \LÚveyIgRtUveFVIkarsikSaBI

kartP¢ab;. eKeRbI electroce E70 XX Edlman design strength φFw = 31.5ksi .
sRmab;karpSarsøabeTAnwgRTnug (flange-to-web weld) KNnakmøaMgkat;TTwgenARtg;
kEnøgCYbKñarvagsøab nigRTnug³
témøGtibrmarbs; Vu = 223.4kips
Q = RkLaépÞsøab × 31.75 ¬emIlrUbTI 10>17¦

= 1.5(18)(31.75) = 857.2in.3

I x = 60640in.4
.4(857.2)
témøGtibrmarbs; VIu Q = 22360640 = 3.158kips / in.
x

TMhMTwkbnSarGb,brma w sRmab;kRmas;bnÞHEdkEdlRtUvpSarKW 516 in. .

RbsineKpSarminCab; RbEvgTwkbnSarGb,brmarbs;vaKW³
Lmin = 4 × w ≥ 1.5in.
⎛5⎞
= 4⎜ ⎟ = 1.25in.
⎝ 16 ⎠
dUcenHyk 1.5in
sakl,g fillet weld 516 in. ×1 12 in.
lT§PaBkñúg 1in. = 0.707 × w × φFW × 2
= 0.707(5 / 16)(31.5)(2 ) = 13.92kips / in.
lT§PaBTb;kmøaMgkat;rbs; base metal
T.Chhay 472 Plate Girders
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

[ ( )] ( ⎛5⎞
)
t (φFBM ) = t 0.90 0.60 Fy = t 0.54 Fy = ⎜ ⎟(0.54)(36)
⎝ 16 ⎠
= 6.075kips / in. < 13.92kips / in.
eRbIersIusþg;TwkbnSarsrub 6.075kips / in. . ersIusþg;TwkbnSarmYyKURbEvg 1.5in.
6.075 × 1.5 = 9.112kips
edIm,IkMNt;KMlat/ yk
9.112 Vu Q
=
s Ix
Edl s CaKMlatEdlKitBIG½kSeTAG½kSrbs;TwkbnSarKitCa in. ehIy
9.112 9.112
s= = = 2.89in.
Vu Q / I x 3.158
edayeRbIKMlatBIG½kSeTAG½kS 2.75in. eyIgnwgTTYl)an clear spacing 2.75 − 1.5 = 1.25in. .
AISC Specification [nUvKMlatminCab;GnuBaØatGtibrmarbs; fillet weld sRmab;karGnuvtþ

enAkñúg Section B10, “Proportions of Beams and Girders”. karpþl;[sRmab; built-up

compression members (AISC E4) nig built-up tension members (AISC D2) RtUv)aneK

eRbIsRmab;kartP¢ab;søabrgkarsgát; nigsøabrgkarTaj. sRmab;karsgát;

d≤
127t
F
b:uEnþminRtUvFMCag 12in.
y

sRmab;karTaj
d ≤ 24t b:uEnþminRtUvFMCag 12in.
Edl d = clear spacing KitCa in.
t = kRmas;rbs;bnÞHEdlRtUvpSarEdlesþIgCageKenAkñúg built-up shape

edayGnuvtþkarkMNt;TaMgenH eyIg)an
127t 127(1.5)
= = 31.8in. > 12in.
Fy 36

24t = 24(1.5) = 36in. > 12in.

dUcenH Clear spacing GnuBaØatGtibrmaKW 12in. ehIy clear spacing EdlRtUvkar 1.25in. KW
RKb;RKan;.

rtEdkbnÞH 473 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

eTaHbICaeKeRbIKMlatBIG½kSeTAG½kS 2.75in. sRmab;RbEvgTaMgmUlrbs; girder k¾eday

k¾eKGacbegáInKMlatenHRtg;kEnøgNaEdlkmøaMgkat;tUcCagtémøGtibrma 223.4kips . eyIg
nwg GegátKMlatbIepSgKña
!> KMlattRmUvkarEdlCitCageK 2.75in.
@> KMlatBIG½kSeTAG½kSGnuBaØatGtibrma 12 + 1.5 = 13.5in.
#> Intermediate spacing 5in.
enAeBleyIgeRbIKMlat 5in.
Vu Q 9.112
Ix
=
s
b¤ Vu =
9.112
Qs
Ix =
9.112
857.2(5)
(60640) = 128.9kips

eyagtamrUbTI 10>16 nig[ x Cacm¶ayBITRmxageqVg eKTTYl)an

Vu = 223.4 − 4.34 x = 128.9kips

x = 21.77 ft
enAeBleKeRbIKMlat 13.5in.
9.112 I x 9.112(60640)
Vu = = = 47.75kips
Qs 857.2(13.5)
rUbTI 10>16 bgðajfaminmankmøaMgkat;EdlmantémøtUcEbbenHeT dUcenHeKminGaceRbIKMlat
Gtibrma)aneT.
cemøIy³ eRbI fillert weld 516 in.×1 12 in. sRmab; flange-to-web weblds CamYynwgKMlatdUcbgðaj
enAkñúgrUbTI 10>22.

T.Chhay 474 Plate Girders

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

sRmab; intermediate stiffener welds:

TMhMTwkbnSarGb,brma = 163 in. ¬edayQrelIkRmas; t w = 516 in. nig t = 14 in. ¦
RbEvgGb,brma = 4⎛⎜⎝ 163 ⎞⎟⎠ = 0.75in. < 1.5in. yk 1.5
lT§PaBrbs;TwkbnSarkñúg 1in. sRmab;TwkbnSar 4 ¬ 2 sRmab; stiffener plate mYy¦
⎛3⎞
0.707⎜ ⎟(31.5)(4) = 16.70kips / in.
⎝ 16 ⎠
lT§PaBkmøaMgkat;rbs; base metal KW 6.075kips / in. ¬emIlkarKNnaxagelIsRmab;
t = 516 in. ¦

BIsmIkar !0>3 kmøaMgkat;EdlRtUvKW

f = 0.045h
Fy3
= 0.045(62)
(36)3 = 3.539kips / in.
E 29000
eRbITwkbnSardac;. lT§PaBrbs;TwkbnSar 4 EdlmYy²manRbEvg 1.5in.
1.5(6.075) = 9.112kips
[ersIusþg;kmøaMgkat;kñúg 1in. esμInwgersIusþg;EdlRtUvkar eKTTYl)an
9.112
s
= 3.539kips / in. b¤ s = 2.57in.
BI AISC Appendix F2.3 clear spacing Gtib,rmaesμInwg 16 dgkRmas;RTnug b:uEnþminFMCag
10in. b¤
⎛5⎞
16t w = 16⎜ ⎟ = 5in.
⎝ 16 ⎠
eRbIKMlatBIG½kSeTAG½kS 2.5in. Edl clear spacing EdleKTTYl)anKW
2.5 − 1.5 = 1in. < 5in. (OK)
cemøIy³ eRbI fillet welds 3 sRmab; intermediate stiffeners
16 × 1 2
1

EdlmanKMlatdUcbgðajenAkñúgrUbTI 10>23.
sRmab; bearing stiffener welds³
TMhMGb,brma 165 in. ¬edayQrelIkRmas; t w = 516 in. nig t = 3 4 in. ¦
RbEvgGb,brma = 4⎛⎜⎝ 165 ⎞⎟⎠ = 1.25in. < 1.5in. yk 1.5

rtEdkbnÞH 475 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

eRbITwkbnSarBIrsRmab; stiffener mYy dUcenHsrubmanTwkbnSar 4 . dUcKñanwg intermediate

stiffener ersIusþg;kmøaMgkat;rbs; base metal 6.075kips / in. nwgkMNt;ersIusþg;rbs;TwkbnSar

b¤ 9.112kips sRmab;TwkbnSarRbEvg 1.5in. .

sRmab; end bearing stiffener bnÞúkEdlGnuvtþkñúg 1in. KW
reaction 223.4
= = 3.662kips / in.
length avaible for weld 62 − 2(0.5)
BI 9.112
s
= 3.662 eK)an s = 2.49in.

cemøIy³ eRbI fillet weld 316 ×1 12 sRmab; bearing stiffener TaMgGs; EdlKMlatRtUv)anbgðajenA
kñúgrUb TI 10>24.

Edl)anKNnaenAkñúg]TahrN_enHminmanlkçN³esdækic©eT. lT§PaBepSgeTotKW girder

Girder

EdlmanRTnugesþIgCag ehIyeKeRbI intermediate eRcInCag nigmYyeTotKW girder EdlmanRTnugRkas;

Cag ehIyGt;eRbI intermediate stiffener. ktþaEdlb:HBal;dl;lkçN³esdækic©rYmmanTm¶n; ¬maDrbs;
T.Chhay 476 Plate Girders
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

EdkEdlRtUvkar¦ nigtémøkñúgkartMeLIg. eTaHbICa girder Edlman intermedaite EtgEtRtUvkarEdk

tick¾eday k¾karbnSMenHGacbEnßmedaytémøénkardMeLIgEdr. kRmas;søabk¾eKGacykmkBicarNa
pgEdr. CeRmIsTaMgenHsuT§EtsnSMsMécTm¶n; b:EnþeKk¾RtUvBicarNaBItémøkñúgkartMeLIgEdr. viFIEdleK
GnuvtþedIm,ITTYl)annUvkarKNnaEdlmanlkçN³esdækic©KWkarsikSaCeRmIseRcIn ehIyeFVIkareRbob
eFobtémørbs;va edayeRbIkar)a:n;sμansMPar³ nigtémøénkartMeLIg. Design of Welded Structures
(Blodgett, 1996) pþl;nUvsMNUmBrEdlmanRbeyaCn_CaeRcInsRmab;karKNna welded plate girder

EdlmanlkçN³esdækic©.

rtEdkbnÞH 477 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Appendix A. karKNna nigkarviPaKedaylkçN³)aøsÞic

Plastic Analysis and Design
A >1> esckþIepþIm (Introduction)

eyIg)anENnaMBIKMniténkar)ak;eday)aøsÞic (plastic collapse) enAkñúgkfaxNÐ 5>2/“ kug

taMgBt; nigm:Um:g)aø; sÞic” . kar)ak;rbs;eRKOgbgÁúMnwgekIteLIgenAeBlbnÞúkbegáItsnøak;)aøsÞicRKb;RKan;
edIm,IbegáItCa mechanism EdlnwgeFVI[manPaBdabedayminmankarekIneLIgbnÞúk. enAkñúgFñwmEdl
kMNt;edaysþaTic eKRtUvkarEtsnøak;)aøsÞicmYyEtb:ueNÑaH. dUcbgðajenAkñúgrUbTI A>1 snøak;nwgekIt
manenAkEnøgNaEdlmanm:Um:g;Gtibrma ¬krNIenHKWenAkNþalElVg¦. enAeBlEdlm:Um:g;Bt;mantémø
FMRKb;RKan;edIm,IeFVI[muxkat;TaMgmUl yield/ enaHvaminGacTb;nwgkarekIneLIgrbs;m:Um:g;EfmeTot ehIy
snøak;)aøsÞick¾RtUv)anbegáIteLIg. snøak;)aøsÞicenHRsedogKñanwgsnøak;FmμtaEdr EtxusRtg;fasnøak;
)aøsÞicmanlT§PaBTb;nwgm:Um:g;xøH EdldUcKñay:agxøaMgnwg rusty hinge.
lT§PaBm:Um:g;)aøsÞic (plastic moment capacity) EdlsMKal;eday M p Cam:Um:g;Bt;EdlekIt
manenARtg;snøak;)aøsÞic. vamantémøesμInwgm:Um:g;Tb;xagkñúgEdlekItBIkarEbgEckkugRtaMgEdlbgðaj
enAkñúgrUbTI A>1 c EtmanTisedApÞúyKña. eKGackMNt;m:Um:g;)aøsÞicenAeBlEdleKsÁal; yield stress
nigrUbragmuxkat; dUcbgðajenAkñúgrUbTI A>2. RbsinebIkarEbgEckkugRtaMgenAkñúglkçxNÐ)aøsÞiceBj
RtUv)anCMnYsedaykmøaMgsmmUlsþaTicBIrEdlmantémødUcKña nigTisedApÞúyKña enaHvanwgbegáIt couple.
GaMgtg;sIueténkmøaMgnImYy²esμInwgplKuNrvag yield stress nigBak;kNþalRkLaépÞmuxkat;srub.
m:Um:g;EdlbegáIteday couple xagkñúgenHKW
A
M p = Fy a = Fy Z x
2
Edl A CaRkLaépÞmuxkat;srub/ a CacMgayrvagTIRbCMuTm¶n;énRkLaépÞBak;kNþalBIr nig Z x Cam:U
Dulmuxkat;)aøsÞic. emKuNsuvtßiPaBcenøaHsßanPaB yielding dMbUg nigsßanPaB)aøsÞiceBjRtUv)ansM
EdgenAkñúgm:UDulmuxkat;. BIrUbTI A>1 b eKGacsresrm:Um:g;EdlbegáIt yield dMbUg
M p Fy Z x Z x
M y = Fy S x nig = =
M F S
y S
y x x

pleFobenHCatémøefrsRmab;rUbragmuxkat;EdlsÁal; nigRtUv)aneKehAfa emKuNrUbrag. sRmab;Fñwm

EdlKNnaeday allowable stress theory vaCargVas;én reserve capacity ehIymantémømFüm 1.12
sRmab; W-shapes.

T.Chhay 478 Appendix A

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

]bsm<½n§ A 479 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

enAkñúgFñwm b¤eRKagsþaTicminkMNt; eKRtUvkarsnøak;)aøsÞiceRcInCagmYyedIm,IbegáIt collapse

mechanism. snøak;TaMgenHnwgRtUv)anbegáIttamlMdab;lMeday eTaHbICaeKmincaM)ac;dwgBIlMdab;k¾eday.

eKnwgBicarNakarviPaKrcnasm<½n§sþaTicminkMNt;eRkayBIkarBiPakSatRmUvkarrbs; Specification.

A >2> AISC Requirements

AISC Specification GnuBaØat[eRbI plastic analysis and design enAeBleRKOgbgÁúMenArkSa

PaBlMnwgTaMg local nigTaMgmUlRtg;cMNuc plastic collapse. edaysareKtRmUv[Fñwm b¤eRKagrgnUvPaB
dabFMenAeBlEdlsnøak;)aøsÞicRtUv)anbegáIt eKRtUvkar lateral bracing CaBiess.
edIm,IkarBar local buckling, AISC B5.2 TamTarfaGgát;man compact cross-sectional
shape Edl λ ≤ λ p sRmab;TaMgRTnug nigsøab. sRmab;Ggát; I-shaped shape dUcCa W nig S-shapes

pleFobTTwgelIkRmas;EdlkMNt;BI Table B5.2 KW

bf 65 bf 170
≤ (US) ≤ (IS)
2t f Fy 2t f Fy

nig h
tw
≤
640
Fy
(US)
h 1680
tw
≤
Fy
(IS)

edIm,IkarBar lateral buckling, AISC F1.2d kMNt; unbraced length Gtibrma Lb Rtg;TItaMg
snøak;)aøsÞicCa L pd EdlsRmab; I-shaped member
3600 + 2200(M 1 / M 2 )
L pd = ry (US) (AISC Equation F1-17)
Fy
24820 + 15170(M 1 / M 2 )
L pd = ry (IS)
Fy

enAkñúgsmIkarenH M 1 Cam:Um:g;EdltUcCagenARtg;cugén unbraced length nig M 2 CamU:m:g;EdlFMCag.

pleFob M 1 / M 2 KwviC¢manenAeBlEdl M 1 nig M 2 Bt;Ggát;[mankMeNagDub nigmantémø
GviC¢manenAeBlEdlvabegáItkMeNageTal.
sRmab; compact shape Edlman lateral bracing RKb;RKan; eKGacyk M n esμInwg
M p sRmab; eRbIenAkñúg plastic analysis. b:uEnþ AISC F1.2d kMNt;faenAkñúgtMbn;EdlekItman

snøak;)aøsÞiccug eRkay nigenAkñúgtMbn;EdlminEk,rsnøak;)aøsÞiceKRtUveRbIviFIFmμtaedIm,IkMNt; M n .

AISC Specification provision epSgeTotEdlTak;Tgnwg plastic analysis and design

mandUcxageRkam.
T.Chhay 480 Appendix A
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

A5.1 RtUv)anGnuBaØatsRmab;Et Fy ≤ 65ksi .

Plastic analysis

C2.2 kmøaMgtamG½kSEdlbegáItedaybnÞúkTMnajemKuN nigbnÞúktamTisedkemKuNminRtUvFM

Cag 0.75φc Ag Fy .
E1.2 sRmab;ssr slenderness parameter λc minRtUvFMCag 1.5K Edl K CaemKuNRbEvg
RbsiT§PaB.
A >3> karviPaK (Analysis)

RbsinebIvaGacman collapse mechanism eRcInCamYy dUcCaFñwmCab;EdlbgðajenAkñúgrUbTI

A>3 eKGacrk)annUv collapse mechanism EdlRtwmRtUv ehIyviPaKCamYynwgCMnYyénRTwsþIeKalcMnYn

bIrbs; plastic analysis Edl[enATIenHedayKμankarRsaybBa¢ak;.

!> Lower-bound theorem (static theorem): RbsinebIeKGacrk)annUvkarEbgEckm:Um:g;

d¾mansuvtßiPaB ¬Edlm:Um:g;mYytUcCag b¤esμInwg M p RKb;kEnøg¦ ehIyvaGacTTYlbnÞúk
edaysþaTic ¬lMnwgRtUv)anbMeBj¦ bnÞab;mkbnÞúkEdlRtUvKñaRtUvtUcCag b¤esμI collapse
load.

]bsm<½n§ A 481 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

@> Upper-bound theorem (kinetic theorem): bnÞúkEdlRtUvnwg mechanism snμt;RtUvEtFM

Cag b¤esμInwg collapse load. Cavi)ak RbsinebIeKGegát mechanism EdlGacmanTaMg
Gs; mechanism mYyNaEdlRtUvkarbnÞúktUcCageKCa mechanism EdlRtwmRtUv.
#> Uniqueness theorem: RbsineKmankarEbgEckm:Um:g;EdlGacTTYlyk)anedaysþaTic
nigmansuvtßiPaB EdlenAkñúgenaH snøak;)aøsÞicRKb;RKan;begáIt collapse mechanism enaH
bnÞúkEdlRtUvKñaCa collapse load EdlRbsinebI mechanism bMeBjTaMg upper-boud
theorem nig lower-bound theorem vaCa mechanism EdlRtwmRtUv.

karviPaKEdlQrelI lower-bound theorem RtUv)aneKehAfa equilibrium method ehIyRtUv)an

bgðajenAkñúg]TahrN_ A>1.

]TahrN_ A>1³ rkbnÞúkcugeRkay (ultimate load) sRmab;FñwmEdlbgðajenAkñúgrUbTI A>4a eday

equilibrium method rbs; plastic analysis. snμt;eKeRbI continuous lateral support nig EdlRb
ePT A36 .

dMeNaHRsay³ Edk A36 muxkat; W 30 × 99 Ca comapact shape ehIyCamYynwg continuous lateral

support, tRmUvkar lateral bracing KWRKb;RKan; dUcenHeKGacTTYlyk plastic analysis.

T.Chhay 482 Appendix A

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dMNak;karénkardak;bnÞúkelIFñwmBI working load eTAdl; collapse load RtUv)anKUsbBa¢ak;enA

kñúgrUbTI A>4a-d. enAeBl working load muneBl yielding ekIteLIgRKb;TIkEnøg karEbgEckm:Um:g;Bt;
RtUv)anbgðajenAkñúgrUbTI A>4a CamYynwgm:Um:g;GtibrmaEdlekItmanRtg;TRmbgáb;. enAeBlEdlbnÞúk
ekIneLIgbnþicmþg² yielding cab;epþImekItmanRtg;TRm enAeBlEdlm:Um:g;Bt;eTAdl; M y = Fy S x . enA
eBlEdlbnÞúkekIneLIgkan;EtFM vanwgekItmansnøak;)aøsÞickñúgeBldMNalKñaenARtg;cugnImYy² enAeBl
Edl M p = Fy Z x . enARtg;kRmiténkardak;bnÞúkenH eRKOgbgÁúMenAmansißrPaBenAeLIy FñwmRtUv)an
ERbkøayeTACasþaTickMNt;edaykarekItmansnøak;)aøsÞicBIr. Mechanism nwgekIt)anEtenAeBlEdl
ekItmansnøak;)aøsÞicTIbI. vaGacekItmanenAeBlEdlm:Um:g;viC¢manGtibrmamantémø M p . edayGa
Rs½ynwg uniqueness theorem/ bnÞúkEdlRtUvKñaCa collapse load BIeRBaHkarEbgEck m:Um:g;KWsuvtßiPaB
ehIyGacTTYlyk)anedaysþaTic.
enARKb;dMNak;kalénkardak;bnÞúk plbUkénéldac;xaténm:Um:g;viC¢man nigm:Um:g;GviC¢manGti-
brmaKW wL2 / 8 . enAeBl collapse, plbUkenHkøayeTACa
16M p
M p + M p = wu L2 b¤
1
wu =
8 L2
eKRtUvEteRbobeFobbnÞúkemKuNCamYynwgersIusþg;emKuN dUcenHeKeRcIneRbI φb M p Cag M p enAkñúg
smIkarBIxagedIm. b:uEnþedIm,IrkSanimitþsBaØa[manlkçN³samBaØ eyIgeRbI M p enARKb;]TahrN_
TaMgGs;rhUtdl;CMhancugeRkayeTIbeyIgCMnYs φb M p eTAkñúgsmIkar. lT§plEdlRtwmRtUv sRmab;
]TahrN_enHKW
16φb M p
wu =
L2
sRmab; W 30 × 99
36(312)
M p = Fy Z x = = 936 ft − kips
12
ehIy φb M p = 0.9(936) = 842.4 ft − kips
eKk¾GacTTYltémørbs; φb M p edaypÞal;BI Load Factor Design Selection Table enAkñúg Part 4 of
the Manual.
16(842.4 )
cemøIy³ w u =
(30)2
= 15.0kips / ft

]bsm<½n§ A 483 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

]TahrN_ A>2³RbsinebIFñwmenAkñúg]TahrN_ A>1 minman continuous lateral support cUrkMNt;TItaMg

EdlRtUvBRgwg.
dMeNaHRsay³ snøak;)aøsÞicenAxagcugekIteLIgkñúgeBldMNalKña ehIymuneBlsnøak;enAkNþalElVg
ekIteLIg. dUcenHeKKYrEtRtYtBinitü unbraced length GtibrmaedayeFobeTAnwgcug ¬snøak;cugeRkay
EdlekIteLIgmintRmUvkar bracing sRmab; plastic analysis eT¦.
edayeFobnwgsnøak;enAcugxageqVg snμt;facMNucBRgwgKWenAkNþalElVg. kñúgkrNIenH M 1 =
M 2 = M p dUcenHFñwmmankMeNagDub ¬m:Um:g;TaMgBIrmansBaØadUcKña¦ dUcenH M 1 / M 2 = +1 BI AISC

Equation F1-17, unbraced length GtibrmaKW

3600 + 2200(M 1 / M 2 ) 3600 + 2200(1.0 )
L pd = ry = (2.10) = 338.3in. = 28.2 ft
Fy 36

cMNaMfa FñwmenHesÞIrEtRKb;RKan;edayminRtUvkar lateral bracing.

CamYynwg lateral mYyTl;enAkNþalElVg
L p = 15 ft < 28.2 ft (OK)

Unbraced length EdlRtUvBicarNarYmKWrYbbBa©ÚlTaMgsnøak;enAkNþalElVg. vaminmantMbn;Edlmin

enACab;nwgsnøak;)aøsÞiceT dUcenHvaminRtUvkarkarKNna design strength eT.
cemøIy³ eRbI lateral brace mYyenAkNþalElVg.

Mechanism method KWQrelI upper-bound theorem nigRtUvakrGegátRKb; collapse

mechanism EdlGacekItman. Collapse mechanism NaEdlRtUvkarbnÞúktUcCageKnwglub eyIy

bnÞúkEdlRtUvKñaCa collapse laod. eKRtUvGnuvtþeKalkarN_rbs; virtual work sRmab;viPaK

mechanism nImYy². Mechanism snμt;RtUvrgnUv virtual displacement RsbeTAtamclnaEdlGac

ekItmanrbs; mechanism ehIyeK[kmμnþxageRkA nigkmμnþxagkñúgesμIKña. bnÞab;mkeKGacrkTMnak;

TMngrvagbnÞúk niglT§PaBTb;m:Um:g;)aøsÞic M p . bec©keTsenHRtUv)anbgðajenAkñúg]TahrN_ A>3 nig
A>4.

]TahrN_ A>3³ FñwmCab;EdlRtUv)anbgðajenAkñúgrUbTI A>5 man compact cross section Edlman

design strength φb M p = 1040 ft − kips . eRbI mechanism method edIm,Irk collapse load Pu .
snμt; continuous lateral support.
T.Chhay 484 Appendix A
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dMeNaHRsay³ eKman failure mechanism sRmab;FñwmenHBIry:ag. dUcEdlbgðajenAkñúgrUbTI A>5

vamanlkçN³RsedogKñaEdlkMNat;Ggát;nImYy²rgnUv rigid-body motion. edIm,IGegát mechanism
enAkñúgElVg AB dak; vitual rotation θ Rtg; A. karvilEdlRtUvKñaenARtg;snøak;)aøsÞicRtUv)anbgðaj
enAkñúgrUbTI A>5b ehIybMlas;TItamTisQrébnÞúkKW 10θ . BIeKalkarN_rbs; virtual work
kmμnþxageRkA = kmμnþxagkñúg
P(10θ ) = M p (2θ ) + M pθ

¬vaminmankmμnþxagkñúgenARtg; A eT eRBaHvaminmansnøak;)aøsÞic¦
collapse load KW
3M p
Pu =
10
Mechanism sRmab;ElVg AB manlkçN³xusKñabnþic³ RKb;snøak;TaMgbICasnøak;)aøsÞic. Virtual work
xagkñúg nig virtual work xageRkAkñúgkrNIKW

]bsm<½n§ A 485 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

2 Pu (15θ ) = M pθ + M p (2θ ) + M pθ

enaH Pu = 152 M p
lT§PaBTIBIrenHRtUvkarbnÞúktUcCag dUcenHvaCa mechanism EdlRtwmRtUv. Collapse load Edlnwg
TTYl)anedayeRbI φb M p CMnYs[ M p
cemøIy³ P u =
2
15
φb M p = (1040) = 139kips
2
15

]TahrN_ A>4³ kMNt; collapse load P sRmab; rigid frame EdlbgðajenAkñúgrUbTI A>6. Ggát;
u

nImYy²rbs;eRKagKW W 21×147 Edlman Fy = 50ksi . snμt; lateral support Cab;.

T.Chhay 486 Appendix A

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dMeNaHRsay³ W 21×147 Ca compact shape sRmab; F y = 50ksi nigman lateral support Cab; dUc
enHvabMeBjlkçxNÐkñúgkareRbIR)as; plastic analysis.
dUcbgðajenAkñúgrUbTI A>6 eKman failure mode cMnYnbIsRmab;eRKagenH³ Fñwm mechanism enA
kñúgGgát; BC / sway mechanism nigmYyeTotCabnSMén mechanism BIrdMbUg. eyIgcab;epþImkarviPaK
mechanism nImYy²edaydak; virtual rotation θ enARtg;snøak;mYy ehIysresrsmIkarCaGnuKmn_

eTAnwgmMuenH.
Virtual displacement rbs;Fñwm mechanism RtUv)anbgðajenAkñúgrUbTI A>6 b. BIsmPaBén

kmμnþxageRkA nigkmμnþxagkñúg
⎛5 ⎞ ⎛2 ⎞
Pu (10θ ) = M pθ + M p ⎜ θ ⎟ + M p ⎜ θ ⎟
⎝3 ⎠ ⎝3 ⎠
EdleKeRbI M p CMnYs[ φb M p . edaHRsayrk Pu
Pu = 0.3333M p

RbsinebIeKminKit axial strain enAkñúgGgát; BC / sway mechanism nwgxUcRTg;RTaydUcbgðaj

enAkñúgrUbTI A>6 c CamYynwgbMlas;TItamTisedkdUcKñaRtg; B nig C . Cavi)ak muMrgVilénRKb;snøak;
TaMgGs;KWlkçN³RsedogKña³
Pu (15θ ) = M p (4θ ) b¤ Pu = 0.2667 M p

BIrUbTI A>6d/ eKalkarN_én virtual work sRmab; combined mechanism [

⎛5 ⎞ ⎛2 ⎞
Pu (15θ ) + Pu (10θ ) = M pθ + M p ⎜ θ ⎟ + M p ⎜ θ + θ ⎟ + M pθ
⎝3 ⎠ ⎝3 ⎠
Pu = 0.2133M p ¬lub¦
cemøIy³ Collapse load sRmab;eRKagKW Pu = 0.2133φb M p = 0.2133(1400) = 299kips

cMNaMfa vamancMNucdUcKñaxøHrvagviFIénkarviPaKTaMgBIr. eTaHbICa equilibrium method min

RtUvkarBicarNaRKb; mechanism k¾eday k¾vaRtUvkar[eyIgdwgBI mechanism enAeBlEdlkarEbg
Ecgm:Um:g;snμt;RsbeTAnwg mechanism mYy. viFITaMgBIrRtUvkarkarsnμt; failure mechanism b:uEnþenA
kñúg equilibrium method eKRtUvRtYtBinitükarsnμt;nImYy²sRmab;suvtßiPaB nigkarEbgEck m:Um:g;Edl
GacTTYlyk)anedaysþaTic ehIyvaminRtUvkarkarGegátRKb; mechanism eT.

]bsm<½n§ A 487 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

A >4> karKNnamuxkat; (Design)

dMeNIrkarénkarKNnaKWRsedogKñanwgkarviPaKEdr EtvaxusKñaRtg;faGBaØatEdlRtUvrkCalT§
PaBm:Umg;)aøsÞicEdlRtUvkar M p . eKsÁal; collapse load EdlTTYl)anBIkarKuN service load nwgem
KuNbnÞúk.

]TahrN_ A>4³ FñwmCab;bIElVgdUcbgðajenAkñúgrUbTI A>7 RtUvRTnUv gravity service load. bnÞúknI-

mYy²pSMeLIgedaybnÞúkefr 25% nigbnÞúkGefr 75% . eKeRbI cover plate enAkñúgElVg BC nig CD
edIm,ITTYl)an moment strength dUcEdl)anbgðaj. snμt; continuous lateral support nigeRCIs
erIsrUbragEdksRmab;RbePT A36 .

T.Chhay 488 Appendix A

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

dMeNaHRsay³ Collapse load EdlTTYl)anedaykarKuN service load edayemKuNbnÞúksmRsb.

sRmab; service load 45kips
Pu = 1.2(0.25 × 45) + 1.60(0.75 × 45) = 67.5kips
sRmab; service load 75kips
Pu = 1.2(0.25 × 75) + 1.60(0.75 × 75) = 85.5kips
eKRtUvGegát mechanism bIEdlman mechanism mYyenAelIElVgmYy. rUbTI A>7 c-e bgðajBI
mechanism nImYy²eRkayBIrgnUv virtual displacement. enAeBlEdlsnøak;)aøsÞicekIteLIgenARtg;

TRmEdlGgát;nImYy²minmanersIusþg;esμIKña vanwgekIteLIgenAeBlEdlm:Um:g;Bt;esμInwglT§PaBm:Um:g;)aø-
sÞic rbs;Ggát;EdlexSayCag.
sRmab;ElVg AB
kmμnþxageRkA = kmμnþxagkñúg
67.5(5θ ) = M p (2θ + θ ) b¤ M p = 112.5 ft − kips
sRmab;ElVg BC
85.5(10θ ) = M pθ + 2M p (2θ ) + M pθ
5
3
b¤ M p = 128.2 ft − kips
sRmab;ElVg CD
85.5(10θ ) = M p (θ + 2θ + θ )
5
3
b¤ M p = 128.2 ft − kips
Upper-bound theorem RtUv)anbkRsaydUcxageRkam³ témøénm:Um:g;)aøsÞicEdlRtUvKñanwg mechanism

Edlsnμt;KWtUcCag b¤esμInwgm:Um:g;)aøsÞicsRmab; collapse load. dUcenH mechanism EdlTamTar

lT§PaBm:Um:g;FMCageKCa mechanism EdlRtwmRtUv. Mechanism TaMgBIrcugeRkaymantémø M p
dUcKña ehIyGacnwgekIteLIgkñúgeBldMNalKña. CaTUeTAersIusþg;EdlRtUvkarCa design strength Edl
RtUvkar dUcenH
φb M p = 128.2 ft − kips
BI Load Factor Design Selection Table, rUbragEdlRsalCageKKW W 16 × 31 Edlman design
strength θ b M p = 146 ft − kips

sakl,g W 16 × 31 ehIyRtYtBinitükmøaMgkat; ¬eyagtamrUbTI A>8¦

sRmab;ElVg AB
∑ M B = V A (10 ) − 67.5(5) + 128.2 = 0

]bsm<½n§ A 489 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

V A = 20.93kips

VB = 20.93 − 67.5 = −46.57 kips

sRmab;ElVg BC
⎛5⎞
∑ M B = − M p + 85.5(10 ) + ⎜ ⎟ M p − VC (20) = 0
⎝3⎠
85.5(10) + (2 / 3)M p 855 + (2 / 3)(128.2)
VC = = = 47.02kips
20 20
VB = 85.5 − 47.02 = 38.48kips
sRmab;ElVg CD
∑ M C = − M p + M p + 85.5(10) − VD (20) = 0
5 5
3 3
VD = 42.75kips = VC
dUcenH kmøaMgkat;TTwgGtibrma VC KW)anmkBIElVg BC b¤esμIKña 47.02kips .
BItaragbnÞúkBRgayesμIemKuNenAkñúg Part 4 of the Manual, shear design strength rbs;
W 16 × 31 KW
φvVn = 84.9kips > 47.02kips (OK)
cemøIy³ eRbI W 16 × 31 .

A >5> karsnñidæan (Conclusion Remark)

karviPaKén mechanism EdlrgbnÞúkBRgaybgðajBIPaBsμúKsμajbEnßmeTotEdlmin)anerob

rab;enATIenH. bBaðaCak;EsþgenAkñúg plastic analysis or design rYmbBa©ÚlnUvkardak;bnÞúkEbbenH
y:agCak;Esþg. elIsBIenH eKKYrGegátGnþrGMeBIén\T§iBlrbs;kmøaMgtamG½kS nigm:Um:g;Bt;sRmab;Ggát;
EdlrgTaMgkmøaMgtamG½kS nigm:Um:g;Bt; dUcenA rigid frame enAkñúg]TahrN_ A>4 .
cMeBaHviFIviPaKEdlmanlkçN³TUeTAdUcCa equilibrium method manniyayy:aglMGitenAkñúg
the plastic methods of structural analysis (Neal, 1977). ehIyvamanrUbmnþEdlmanlkçN³

sμúKsμajsRmab; mechanism method eTotpg. CamYynwgviFIenH EdleKsÁal;faCa method of

inequalities eKGackMNt; mechanism EdlRtwmRtUveday linear programming technique eday

pÞal;. eKGaceRbI plastic design FmμtasRmab;KNnaeRKOgbgÁúMPaKeRcIn b:uEnþCaTUeTA mechanism

method EdlbgðajenAkñúg]bsm<½n§enHKWRKb;RKan;ehIy.

T.Chhay 490 Appendix A

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Appendix B. karKNnaeRKOgbgÁúMEdkedayQrelIkugRtaMgGnuBaØat
Structural Steel Design Based on Allowable Stress

B >1> esckþIepþIm (Introduction)

PaBxusKñacMbgrvag allowable stress design nig loads and resistance factor design KW
emKuNsuvtßiPaB. * enAkñúg LRFD eKGnuvtþemKuNbnÞúkeTAelIbnÞúk nigemKuNersIusþg;eTAelIersIusþg;.
elIsBIenH témørbs;emKuNbnÞúkGaRs½ynwgRbePTrbs;bnÞúk nigkarbnSMbnÞúk. enAkñúg allowable
stress design (ASD) eKeRbIEtemKuNsuvtßiPaBmYyKt; ehIyvaRtUv)anGnuvtþeTAelIkugRtaMgEdlman

enAkñúgsßanPaBkMNt;. sßanPaBkMNt;rbs; ASD KWRsedogKñasRmab; LEFD KW yielding, fracture

nig buckling. eKalkarN_rbs; allowable stress analysis and design KWmandUcteTA³
kugRtaMgenAkñúg sßanPaBkMNt;RtUv)anEckCamYynwgemKuNsuvtßiPaBedIm,ITTYl)ankugRtaMgGnuBaØat
ehIykugRtaMg Gb,brmaEdlekIteLIgeday service load dac;xatminRtUvFMCagkugRtaMgGnuBaØatenH
eT. ]TahrN_ sRmab;kmøaMgTajtamG½kS
P
ft = ≤ Ft (B.1)
A
Edl kugRtaMgTajKNna
ft =

P = bnÞúkTajtamG½kSeFVIkar

Ft = kugRtaMgTajGnuBaØat

kugRtaMgTajGnuBaØatGacCaplEckrvag yield stress CamYynwgemKuNsuvtßiPaB b¤CaplEckrvag

ultimate tensile stress CamYynwgemKuNsuvtßiPaBepSgeTot. eyIgnwgerobrab;BIGgát;rgkarTajlMGit

enAkñúgEpñk B>2.
eKeRbI ASD sRmab;eRKOgbgÁúMEdkmuneBlEdlmankarENnaMBI LRFD Specification enAkñúgqñaM
1989. kare)aHBum<elIkcugeRkayrbs; ASD Specification (AISC, 1989b) ehIynig Manual of

steel Construction (AISC, 1989a) RtUv)anpSBVpSayenAkñúgqñaM 1989. karerobcMÉksarrbs;Éksar

TaMgBIrxagelImanlkçN³RsedogKñanwgkarerobcMÉksarrbs; LRFD Edr. eKEbgEck Specification

*
snμt;faeyIgsÁal; nigyl;BI AISC LRFD Specification nig Manual
]bsm<½n§ B 491 T.Chhay
mhaviTüal½ysMNg;sIuvil NPIC

CaCMBUk ¬]TahrN_ “Chapter D, Tension members”¦ ehIy Manual RtUv)anEbgEckCaEpñk ¬dUcCa

“Part 2, Beam and Girder Design”¦. enAkñúg Specification mankarENnaM eday Commentary.

nimitþsBaØaenAkñúgsmIkar B.1 manlkçN³RsedogKñaeTAnwgkareRbIR)as;enAkñúg Specification.

eKeRbIGkSr f sRmab;kugRtaMgEdlKNnaCak;Esþg nigeKeRbIGkSr F sRmab;kugRtaMgGnuBaØat.
snÞsSn_R)ab;BIRbePTkugRtaMg.
edaysar]bsm<½n§enHRKan;EtCaesckþIENnaM dUcenHeyIgminRtUvkareRbIelxEpñkrbs; AISC
Specification b¤elxsmIkareT. smIkarenAkñúg]bsm<½n§enHykecjBI Specification EtelxsmIkar

RtUv)andak;eTAedayxøÜneyIg. elIsBIenH enAeBlEdleyIgeRbIBakü Specification b¤ Manual enA

kñúg]bsm<½n§enH )ann½faeyIgeRbI allowable stress elIkElgEtmankarENnaM.
Ggát;CaeRcInénkarKNnaeRKOgbgÁúMEdkKWRsedogKñasRmab; ASD nig LRFD. ]TahrN_ net
area sRmab;Ggát;rgkarTajKWdUcKña rYmbBa©ÚlTaMg s 2 / 4 g sRmab; staggered holed ¬karteRmob

rn§qøas;¦ nigemKuN U sRmab; shear leg ¬eTaHbICa ASD Specification eRbItémømFümrbs; U

nigdak;smIkarsRmab; U enAkñúg Commentary k¾eday k¾eKeRbIGVIEdlmanenAkñúg LRFD
Specification Edr¦. niymn½yrbs; compact member, noncompact member nig slender member

KWdUcKña b:uEnþ LRFD Specication cugeRkaymankarEklMGeRcIn. CaTUeTA enAeBlmanPaBminRtUvKña

rvag ASD nig LRFD provision eKKYredaHRsayedayQrelI LRFD Specification eRBaHvaTan;
sm½ykal.
eTaHCavaminmanemKuNbnÞúkenAkñúg allowable stress design k¾eday eKenAEtGacKitbnÞúk
sMxan;epSg²enAkñúgkarbnSMbnÞúkEdr. ]TahrN_ CaTUeTAeKeRbIbnSMbnÞúksRmab;eRKOgbgÁúMdMbUldUct
eTA³ D + S / D + W / D + (S / 2) + W nig D + S + (W / 3) . elIsBIenH Specification GnuBaØat
[ allowable stress ekIneLIgmYyPaKbIenAeBleKrab;bBa©ÚlbnÞúkxül; nigbnÞúkrBa¢ÜydI. Building
code CaeRcInk¾mankarpþl;EbbenHEdr.

ASD Manual k¾mantarag nigdüaRkamCaeRcInRsedogKñanwg LRFD Manual Edr. eyIgnwg

elIkykEttarag b¤düaRkamNaEdlsMxan;mkbkRsayenAkñúgkarENnaMd¾segçbenH.

T.Chhay 492 Appendix B

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

B >2> Ggát;rgkarTaj (Tension members)

BIsmIkar B.1 kugRtaMgTajtamG½kSEdlKNnaKW ft = P / A . Allowable stress KWQrelI
sßanPaBkMNt; yielding nig fracture EdleRKaHfñak;CageK. sRmab; yielding rbs; gross section
kugRtaMgGnuvtþn_KW
P
ft = (B.2)
Ag

Edl Ag Ca gross cross-sectional area. The factor of safety sRmab;sßanPaBkMNt;enHKW 5 / 3

ehIykugRtaMgGnuBaØatKW
Fy Fy
Ft = = = 0.6 Fy (B.3)
F .S . 5/3
sRmab; fracture rbs; net section
P
ft = (B.4)
Ae
Edl Ae Ca effective net area. emKuNsuvtßiPaBKW 2.0 EdllT§plrbs;kugRtaMgGnuBaØatKW
Fu F
Ft = = u = 0.5 Fu (B.5)
F .S 2

]TahrN_ B>1³ RtYtBinitükugRtaMgenAkñúgGgát;rgkarTajEdlbgðajenAkñúgrUbTI B>1 EdlekItBIbnÞúk

eFIVkar 50kips . eKeRbIEdkRbePT A36 nigb‘ULúgGgát;p©it 7 8 in. .

dMeNaHRsay³ BIsmIkar B.2 nig B.3 kugRtaMgGnuvtþn_enAelI gross section KW

P 50
ft = = = 20.2ksi
Ag 2.48

]bsm<½n§ B 493 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

ehIykugRtaMgGnuBaØatKW
Ft = 0.5Fy = 0.60(36 ) = 21.6ksi > 20.2ksi (OK)

kugRtaMgenAelI net area KW

An = Ag − (thickness × hole diameter )
3⎛ 7 1⎞
= 2.48 − ⎜ + ⎟ = 2.105in.2
8⎝8 8⎠
RbsinebIeyIgeRbItémømFüm U enaH effective net area KW
Ae = UAn = 0.85 An = 0.85(2.105) = 1.789in.2
sRmab;smIkar B.4 nig B.5
P 50
ft = = = 27.9ksi
Ae 1.789
Ft = 0.50 Fu = 0.50(58) = 29ksi > 27.9ksi (OK)
cemøIy³ Ggát;KWmanlkçN³RKb;RKan;.

B >3> Ggát;rgkarsgát; (Compression members)

kugRtaMgenAkñúgGgát;Edlrgkarsgát;tamG½kSKW
P
fa =
Ag

kugRtaMgGnuBaØat EdlsMKal;eday Fa RtUv)anTTYledayEck critical buckling load CamYy

nwgemKuNsuvtßiPaB. emKuNsuvtßiPaBsRmab;ssreGLasÞic (slender column) mantémøefr ehIyem
KuNsRmab;ssr inelastic mantémøERbRbYl. enAkñúg ASD ersIusþg;rgkarsgát;RtUv)ansresrCa
GnuKmn_én slenderness ratio KL / r b:uEnþenAkñúg LRFD ersIusþg;CaGnuKmn_eTAnwg λc =
(KL / rπ ) Fy / E . enAkñúgtMbn;eGLasÞic kugRtaMgeRKaHfñak;KWplEckrvag Euler buckling load
nwgRkLaépÞ b¤
Pcr π EAg
2
π 2E
Fcr = = ÷ =
Ag ( )
KL / r 2
Ag
(KL / r )2
(B.6)

sRmab;tMbn; elastic EdnsmamaRtRtUv)ansnμt;esμInwg F y /2 eKnwgeRbIsmIkarEdl)anBIkarBiesaFdUc

xageRkamCMnYs[ tangent modulus formula³

T.Chhay 494 Appendix B

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

⎡ (KL / r )2 ⎤
Fcr = Fy ⎢1 − ⎥ (B.7)
⎣⎢ 2Cc2 ⎦⎥

Edl Cc témørbs; KL / r EdlRtUvKñanwgkugRtaMg Fy / 2 . smIkar B.7 bgðajBIExS)a:ra:bUlEdlb:H

nwgExSekag Euler enARtg; KL / r = Cc ehIyb:HeTAnwgbnÞat;edkenARtg; KL / r = 0 . eyIgGacrk
smIkarsRmab; Cc edayEpñkxagsþaMrbs;smIkar B.6 esμInwg Fy / 2 ³
Fy π 2E π 2E
= =
2 (KL / r )2 Cc2
2π 2 E
eyIgTTYl)an Cc =
Fy
(B.8)

munnwgkarGnuvtþemKuNsuvtßiPaB ersIusþg;ssrelItMbn; slenderness eBj RtUv)anbgðajedayRkaPic

enAkñúgrUbTI B>2.

edIm,ITTYlnUvkugRtaMgsgát;GnuBaØat eyIgEcksmIkar B.6 nig B.7 CamYynwgemKuNsuvtßiPaB.

emKuNsuvtßiPaBsRmab;ssreGLasÞicKW 23 /12 . sRmab;ssr inelastic eKeRbIemKuNEdlERbRbYl
dUcxageRkam³
5 3(KL / r ) (KL / r )3
F .S . = + −
3 8Cc 8Cc3

]bsm<½n§ B 495 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

smIkarenHmantémø 5 / 3 enAeBl KL / r = 0 ¬dUcKñasRmab; yielding rbs;Ggát;rgkarTaj¦ ehIy

témø 23 /12 enAeBl KL / r = Cc ¬RbEhl 15% eRcInCag 5 / 3 ¦. edayEcksmIkarersIusþg;CamYy
emKuNsuvtßiPaBEdlsmRsb eyIgTTYl)ankugRtaMgGnuBaØatdUcxageRkam³
sRmab; KL / r < Cc
⎡ (KL / r )2 ⎤
Fy ⎢1 − ⎥
⎢⎣ 2Cc2 ⎥⎦
Fa = (B.9)
5 3(KL / r ) (KL / r )3
+ −
3 8Cc 8Cc3
sRmab; KL / r > Cc
π 2E 23 12π 2 E
Fa = ÷ = (B.10)
(KL / r )2 12 23(KL / r )2

sRmab;Ggát;Edlmanmuxkat; slender eKRtUveFVIkarkat;bnßykugRtaMgGnuBaØatedIm,IKitBIlT§PaBEdl

GacekItman local buckling. eKTTYl emKuNkat;bnßyenHBI appendix EdlmanenAkñúg Specifica-
tion.

]TahrN_ B>2³ kMNt;bnÞúkeFVIkarGnuBaØat P sRmab;Ggát;rgkarsgát;EdlbgðajenAkñúgrUbTI B>3.

dMeNaHRsay³ RtYtBinitüemIlfaetIGgát;CaGgát;Edlmanmuxkat; slender b¤Gt;. pleFobTTwgelI

kRmas;sRmab;Ggát;rgkarsgát;Edl[enAkñúg ASD Specification manlkçN³dUcKñaenAkñúg LRFD
Specification:

T.Chhay 496 Appendix B

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

bf
2t f
= 6 .4 ¬BI properties table EdlmanenAkñúg Manual¦
95 95
= = 15.8 > 6.4 (OK)
Fy 36
h
= 25.3
tw
253 253
= = 42.2 > 25.3 (OK)
Fy 36

kugRtaMgKW f a = P / Ag dUcenHbnÞúkEdlRtUvKñaKW P = f a Ag ehIybnÞúksgát;GnuBaØtKW Fa Ag . BI

smIkar B.8
2π 2 E 2π 2 (29000 )
Cc = = = 126.1
Fy 36

pleFob slenderness GtibrmaKW

KL KL KL 1.0(20 )(12)
= = = = 96.77
r rmin ry 2.48

lT§plEdlTTYl)antUcCag Cc dUcenHeKGacrk Fa BIsmIkar B.9:

⎡ (KL / r )2 ⎤ ⎡ (96.77 )2 ⎤
Fy ⎢1 − ⎥ 36 ⎢1 − 2⎥
Fa = ⎣⎢ 2Cc2 ⎦⎥
= ⎣⎢ 2(126.1) ⎦⎥ = 13.38ksi
5 3(KL / r ) (KL / r )3 5 3(96.77 ) (96.77 )3
+ − + −
3 8Cc 8Cc3 3 8(126.1) 8(126.1)3

cemøIy³ P = F A a g = 13.38(21.8) = 292kips

Design Aids
ASD manual man column design aids EdlmanTRmg;RsedogKñaenAkñúg LRFD Manual.
kñúgcMeNam aids TaMgenHPaKeRcInCataragsRmab;bnÞúktamG½kSGnuBaØat. enAeBleKbBa©ÚlRbEvg
RbsiT§PaB KL niglT§PaBRTbnÞúkeFVIkarEdlTamTareTAkñúgtarag eKGacrk)annUvmuxkat;Edlman
lT§PaBRKb;RKan;)any:agelOn. dUcKñanwg LRFD column load table Edr eKKYeRbIRbEvgRbsiT§PaB
K y L eFobnwgkaMniclPaBGb,brma ry . müa:geToteKGacbBa©Úl K x L / (rx / ry ) .

enAeBlEdleKrkemKuNRbEvgRbsiT§PaB K BI Jackson-Mooreland alignment chart eK

]bsm<½n§ B 497 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Gac GnuvtþemKuNkat;bnßy stiffness RbsinebIssrCa inelastic enAeBl)ak; (KL / r < Cc ) .

Manual k¾pþl;taragsRmab;karcg;)anenHEdr.

B >4> Fñwm (Beams)

kugRtaMgBt;GtibrmaenAkñúg homogeneous beam EdlminmankugRtaMgeRkABIEdnsmamaRt
RtUv)an[eday flexural formula³
Mc M M
fb = = =
I I /c S
Edl M= m:Um:g;Bt;GtibrmaenAkñúgFñwm
c = cMgayBIG½kSNWteTAsréseRkAeKbMput

I = m:Um:g;niclPaBeFobG½kSBt;

S = m:UDulmuxkat;eGLasÞic

karBN’nakñúgEpñkenHRtUv)ankMNt;Rtwm hot-rolled I nig H-shaeped cross section EdlrgkarBt;

eFobG½kSEkgeTAnwgRTnug ¬G½kS x ¦.
kugRtaMgBt;GnuBaØatRtUv)ansMKal;eday Fb nigQrelIsßanPaBkMNt;dUcteTA³ yilding, local
buckling b¤ lateral-torional buckling. enAkñúg ASD eKnwgmanPaBgayRsYlRbsinebI eKbMEbkFñwm

CaBIrKW³ FñwmEdlmanTRmxag (laterally supported beam) nigFñwmEdlminmanTRmxag (laterally

unsupported beam). RbsinebIFñwmman lateral support RKb;RKan; kugRtaMgGnuBaØatnwgQrelI

yielding kñúgkrNImuxkat; compact ehIyvanwgQrelI local buckling kñúgkrNImuxkat; uncompact.

kugRtaMgBt;GnuBaØatsRmab; laterally unsupported beams nwgQrelI lateral-torsional buckling.

Lateral support
eKKitfaFñwmEdlman man lateral support RKb;RKan;edIm,IkarBar
unbraced length Lb lateral-

torsional buckling enAeBlEdl Lb ≤ Lc Edl Lc CatémøtUcCageKkñúgcMeNam

76b f 20000
Lc = ≤
Fy ( )
d / A f Fy
(US) (B.12)

200b f 137900
Lc = ≤
Fy ( )
d / A f Fy
(IS)

T.Chhay 498 Appendix B

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

eyIgeRbIlkçxNÐenHedIm,IkMNt;cMNat;fñak;rbs;FñwmfaCa laterally supported b¤ laterally

unsupported.

Laterally Supported Beams

RbsinebI laterally supported beam GacrgkugRtaMgdl;cMnuc yield edayKμan local buckling enaHem
KuNsuvtßiPaBKW 5 / 3 ehIykugRtaMgGnuBaØatKW
Fy Fy
Fb = = = 0.60 Fy
F .S . 5/3
lkçxNÐenHRtUvnwgrUbragEdlmanpleFobTTwgelIkRmas;sßitenAEdnkMNt;x<s;bMputsRmab; noncom-
pactness Edl b f / 2t f = 95 / Fy (US) b¤ b f / 2t f = 250 / Fy (IS). ¬EdnkMNt;enHxusKña

BIEdnkMNt;rbs; LRFD b:uEnþeKeRbIvaenATIenH edaysarvaminTak;TgenAkñúgsmIkar AISC sRmab;

ASD¦. RbsinebImuxkat;enH compact eKGacTTYllkçxNÐ)aøsÞiceBjedayKμan local buckling

ehIyeKGnuBaØat[bEnßm 10% sRmab;kugRtaMgGnuBaØat. dUcenHkñúgkrNIenH kugRtaMgGnuBaØatKW

(
Fb = 1.10 0.60 Fy = 0.66 Fy)
sRmab; noncompact shape, AISC eRbI linear transition cenøaH 0.6Fy nig 0.66Fy
edayQrelItémø b f / 2t f . RKb; hot-rolled I- and H-shapes TaMgGs;enAkñúg Manual man compact
web. kugRtaMg GnuBaØatsRmab;krNIenH[enAkúñsmIkarxageRkam³
⎛ bf ⎞
Fb = Fy ⎜ 0.79 − 0.002 Fy ⎟
⎜ 2t f ⎟
⎝ ⎠
rUbTI B>4 bgðajBITMnak;TMngrvagpleFoTTwgelIkRmas;CamYynwgkugRtaMgGnuBaØatsRmab; laterally
supported beams. eKedaHRsay slender shape enAkñúg appendix EdlmanenAkñúg Specification

b:uEnþvaminman hot-rolled I- and H-shapes enAkñúg Manual Ca slender eT.

kugRtaMgsRmab; laterally supported beam mandUcxageRkam³
RbsinebIrUbragCa compact
Fb = 0.66 Fy (B.13)

RbsinebIrUbragCa noncompact
⎛ bf ⎞
Fb = Fy ⎜ 0.79 − 0.002 Fy ⎟ (B.14)
⎜ 2t f ⎟
⎝ ⎠

]bsm<½n§ B 499 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Laterally Unsupported Beams

ersIusþg;rbs; lateral unsupported beam KWQrelIsßanPaBkMNt;rbs; lateral-torsional
buckling. enAkñúg ASD, sßanPaBenHmanBIry:agKW³ uniform warping nig nonuniform warping.

Uniform warping KWmanlkçN³eGLasÞic ehIysßanPaBkMNt;KW

0.65 E
fu = (B.15)
Lb d / A f

Edl d= km<s;srubrbs;Fñwm
A f = RkLaépÞrbs;søabrgkarsgát;

cMENk nonuniform warping GacCa inelastic b¤k¾eGLasÞic. sRmab;eGLasÞic warping, failure

stress KW
π 2E
f nu =
(Lb / ry )2
(B.16)

sRmab; inelastic warping, eKeRbIsmIkarEdl)anmkBIkarBiesaFEdlmanlkçN³RsedogKñanwg

smIkarsRmab;Ggát;rgkarsgát;
f nu
10 ⎡
= Fy ⎢1 −
(
Lb / ry )2 ⎤⎥ (B.17)
9 ⎢⎣ 2C 2 ⎥⎦

Edl C= témøGtibrmarbs; Lb sRmab; nonuniform warping Ca inelastic ¬RbsinebI Lb > C /

warping Ca elastic¦
E
= 3π
5 Fy

T.Chhay 500 Appendix B

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Buckling stressEdl[edaysmIkar B.15-B.17 RtUv)ankMNt;RtwmEdnx<s;bMputrbs; Fy . rUbTI B.5

bgðajBI uniform warping stress CaGnuKmn_eTAnwg Lb nigrUbTI B.6 bgðajBI nonuniform warping
stress.

edIm,ITTYl)ansmIkar AISC sRmab;kugRtaMgBt;GnuBaØatEdlQrelI lateral-torsional

buckling, eKRtUveFVIkarEktRmUveTAelIsmIkarEdl)anerobrab;BImundUcteTA³

!> eKRtUvEck failure stress TaMgGs;CamYynwgemKuNsuvtßiPaB 5 / 3

@> eKCMnYskaMniclPaB ry eday rT EdlCakaMniclPaBeFobG½kSexSaysRmab; cMENkrbs;
muxkat;Edlmansøabrgkarsgát; nigmYyPaKbIénEpñksgát;rbs;RTnug. témøenHminCaxusKña
BI ry EdlmanenAkñúgtaragrbs; ASD Manual eT.
#> RKb;smIkarTaMgGs;RtUv)ansresredaymanpleFob Lb / rT

]bsm<½n§ B 501 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

$> emKuN Cb RtUv)anKitbBa©ÚlsRmab;bMErbMrYlrbs;m:Um:g;Bt;elI unbraced length ¬smIkar

warping KWQrelIm:Um:g;BRgayesμI¦

%> eTaHbICa lateral-torsional buckling strength RtUv)anbMEbkecjBIbgÁúM uniform nig

nonuniform warping k¾eday k¾ AISC eRbIbgÁúMNaEdlmantémøFMCag.

eKGacsegçbsmIkar AISC sRmab;kugRtaMgBt;GnuBaØatsRmab; laterally unsupported beam

dUcxageRkam³
sRmab; Lr b < 102000
F
Cb
(US)
Lb
r
<
703300Cb
F
(IS)
T y T y

Fb = 0.60 Fy

sRmab; 102000Cb Lb
Fy
≤
rT
≤
510000Cb
Fy

yktémøEdlFMCageKkñúgcMeNam
⎡ 2 Fy (Lb / rT )2 ⎤
Fb = ⎢ − ⎥ Fy ≤ 0.60 Fy (US) (inelastic nonuniform warping) (B.18)
⎢⎣ 3 1530000Cb ⎥⎦
⎡ 2 Fy (Lb / rT )2 ⎤
Fb = ⎢ − ⎥ Fy ≤ 0.60 Fy (IS)
⎢⎣ 3 10550000Cb ⎥⎦

nig Fb =
12000Cb
Lb d / A f
≤ 0.60 Fy (US) (uniform warping) (B.19)

82750Cb
Fb = ≤ 0.60 Fy (IS)
Lb d / A f

sRmab; Lb
rT
>
510000Cb
Fy
(US)
Lb
rT
>
3516500Cb
Fy
(IS)

yktémøFMCageKkñúgcMeNam
170000Cb
Fb = ≤ 0.60 Fy (US) (elastic nonuniform warping) (B.20)
(Lb / rT )2
1172150Cb
Fb = ≤ 0.60 Fy (IS)
(Lb / rT )2
nig Fb =
12000Cb
Lb d / A f
≤ 0.60 Fy (US) (uniform warping) (B.19)

82750Cb
Fb = ≤ 0.60 Fy (IS)
Lb d / A f

T.Chhay 502 Appendix B

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

ASD [nUvsmIkarsRmab; Cb EdlxusBI Cb Edl[eday LRFD

Specification

Specification b:uEnþeKGaceRbImYyNak¾)an. cMNaMfa eTaHbICa flexural strength Edleyagtam

LRFD KWsmamaRtedaypÞal;eTAnwg Cb k¾eday k¾vaminEmnCakrNIsRmab; allowable stress Edl

[edaysmIkar B.18 - B.20 Edr. vamankarsμúKsμajxøHkñúgkarKNna allowable stress rbs;Fñwm.

Shear
kugRtaMgkmøaMgRtUv)anKNnaedayykbnÞúkkmøaMgkat;eFVIkarGtibrmaEcknwgRkLaépÞRTnug.
V V
fv = ≈
Aw t w d
kugRtaMgkmøaMgkat;KWQrelI shear yielding ehIyRtUv)anykesμInwgBIrPaKbIénkugRtaMgTaj
GnuBaØatelI gross section.
Fv =
2
3
2
( )
Ft = 0.60 Fy = 0.40 Fy
3
(B.21)

]TahrN_ B>3³ eKeRbI W 16 ×100 sRmab;FñwmTRmsamBaØEdlrgbnÞúkBRgayesμIehIyman lateral

bracing EtenAxagcugrbs;va. RbsinebIeKeRbIEdkRbePT A36 kMNt;m:Um:g;Bt;eFVIkarGtibrmaEdlFñwm

enHGacTb;)ansRmab;ElVgEdlmanRbEvg (a) 10 ft (b) 15 ft nig (c) 40 ft .
dMeNaHRsay³ dMbUg kMNt; Lc
BIsmIkar B.12
76b f 76(10.42)
= = 132in = 11 ft
Fy 36
20000 20000
= = 336.0in = 28 ft
( )
d / A f Fy 16.97
(36)
10.42(0.985)
eKyktémøEdltUcCageK dUcenH Lc = 11.0 ft
a) sRmab;ElVgEdlmanRbEvg 10 ft

Lb = 10 ft < Lc
dUcenHFñwmCa laterally supported beam.

]bsm<½n§ B 503 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

eday W 16 ×100 Ca compact shape sRmab;Edk A36 / kugRtaMgGnuBaØatEdl)anBIsmIkar

B.13 KW

Fb = 0.66 Fy = 0.66(36 ) = 23.76ksi

kugRtaMgBt;GtibrmasRmab;m:Um:g; M Edl[edaysmIkar B.11 KW f b = M / S dUcenHm:Um:g;

GtibrmaEdlekIteLIgenAeBlkugRtaMg f a esμInwgkugRtaMgGnuBaØat Fb
M = Fb S = 23.76(175) = 4158in. − kips = 346 ft − kips
cemøIy³ a) m:Um:g;Gtibrma = 346 ft − kips
b) sRmab;ElVgEdlmanRbEvg 15 ft
Lb = 15 ft > Lc = 11.0 ft
dUcenHFñwmCa laterally unsupported beam.
rT = 2.81in. ¬témøenHRtUv)an[enAkñúg properties table enAkñúg ASD Manual¦
Lb 15(12 )
= = 64.06
rT 2.81
sRmab;FñwmTRmsamBaØrgbnÞúgBRgayesμIEdlman lateral bracing enAxagcug/ Cb = 1.14 ¬Edl
KNnaCamYynwg LRFD Specification equation b:uEnþeKk¾GaceRbIvaCamYynwg ASD equation
pgEdr¦. kMNt;EdnkMNt;sRmab; Lb / rT
102000Cb 102000(1.14)
= = 56.8
Fy 36
510000Cb 510000(1.14)
= = 127
Fy 36

edaysar 56.8 < Lb / rT < 127 eKeRbIsmIkar B.18 nig B.19

⎡ 2 Fy (Lb / rT )2 ⎤
Fb = ⎢ − ⎥ Fy ≤ 0.60 Fy
⎢⎣ 3 1530000Cb ⎥⎦
⎡2 36(64.06)2 ⎤
=⎢ − ⎥36 = 20.95ksi
⎢⎣ 3 1530000(1.14)⎥⎦

b¤ Fb =
12000Cb
Lb d / A f
≤ 0.60 Fy

12000(1.14)
= = 45.97ksi
(15 × 12)(16.97 ) / (10.42 × 0.985)
lT§plxagelImantémøFMCag 0.60Fy = 0.60(36) = 21.6ksi . dUcenHyk
T.Chhay 504 Appendix B
viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

Fb = 0.60 Fy = 21.6ksi

m:Um:g;Bt;GtibrmaKW
M = Fb S = 21.6(175) = 3780in.kips = 315 ft − kips
cemøIy³ b) m:Um:g;Gtibrma = 315 ft − kips
c) sRmab;ElVgEdlmanRbEvg 40 ft
Lb 40(12) 510000Cb
= = 170.8 > = 127
rT 2.81 Fy

eRbIsmIkar B.19 nig B.20:

170000Cb 170000(1.14)
Fb = = = 6.643ksi < 0.6 Fy
(Lb / rT )
2
(170.8)2
12000(1.14)
b¤ Fb =
12000Cb
Lb d / A f
=
(40 ×12)(16.97 ) / (10.42 × 0.985)
= 17.24ksi < 0.60 Fy

yk Fb = 17.24ksi . m:Um:g;GtibramKW
M = Fb S = 17.24(175) = 3017in. − kips = 251 ft − kips
cemøIy³ c) m:Um:g;Gtibrma = 251 ft − kips .

Design Aids
sRmab;FñwmPaKeRcInEdlmanenAkñúg LRFD Manual k¾manenAkñúg ASD Manual Edr.
Design aids

varYmmanTaMg design chart Edl[ allowable bending moment CaGnuKmn_én unbraced length
sRmab;rUbragEdleKeRbIsRmab;FñwmCaTUeTA. ExSekagTaMgenHQrelI Cb = 1.0 b:uEnþeKminGaceRbIvaeday
pÞal;sRmab;témøepSgeTotrbs; Cb eT edaysar allowable stress Fb minsmamaRtedaypÞal;eTAnwg
Cb .

B >5> Beam-Columns

eKviPaKGgát;eRKOgbgÁúMEdlrgTaMgkugRtaMgBt; nigkugRtaMgtamG½kSCamYynwgsmIkarGnþrGMeBI
edayKitpleFobkugRtaMgCak;EsþgelIkugRtaMgGnuBaØat. ASD Specification equation KW
f a f bx f by
+ + ≤ 1 .0
Fa Fbx Fby

]bsm<½n§ B 505 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

Edl x nig y sMKal;karBt;tamG½kS. eKeRbIsmIkarBIrenAkñúg Specification³ EdlmYyKNnaCamYy

nwgkugRtaMgBt;EdlQrelIm:Um:g;Gtibrmadac;xatenAkñúgGgát; nigmYyeTotCamYykugRtaMgBt;EdlQrelI
m:Um:g;cugGtibrma. eKeRbI amplification factor EtmYy vaminmanemKuNdac;edayELkkñúgkarKit
sway nig nonsway components. Amplification factor enHmanTRmg;dUcxageRkam³
Cm
1− ( f a / F 'e )
Edl Cm RtUv)ankMNt;esμInwg³
sRmab;Ggát;RbQmnwg sidesway
C m = 0.85
sRmab;Ggát;EdlminRbQmnwg sidesway ehIynigminman transverse load
C m 0.6 − 0.4(M 1 / M 2 ) (B.22)
Edl M 1 nig M 2 Cam:Um:g;enAxagcugrbs;Ggát; ehIyEdltémødac;xatrbs; M 1 tUcCag.
pleFob M 1 / M 2 viC¢manRbsinebIGgát;ekagDub ehIyvamantémøGviC¢mansRmab;kMeNageTal.
sRmab;Ggát;EdlTb;RbqaMgnwg sidesway ehIyman transverse load
C m = 0.85 RbsinebIcugRtUv)anTb;min[vil

C m = 1.0 RbsinebIcugminRtUv)anTb;

emKuN F 'e CaplEckrvag Euler buckling stress CamYynwgemKuNsuvtßiPaB 23 /12 ³

12π 2 E
F 'e = (B.23)
23(KLb / rb )2
GkSr sMedAelIG½kSénkarBt;. RbsinebIeKBicarNakarBt;eFobnwgG½kS x enaH
b F 'e = F 'ex nig
KLb / rb = KL x / rx . dUcKñasRmab; F 'ey eRbI K y L / ry .

eKRtUvRtYtBinitüsmIkarGnþrGMeBIxageRkam³
RbsinebI f a / Fa ≤ 0.15 / eKminRtUvkar moment amplification ehIy
f a f bx f by
+ + ≤ 1.0 (B.24)
Fa Fbx Fby

RbsinebI f a / Fa > 0.15 / eKRtUvRtYtBinitüsmIkarTaMgBIrxageRkam³

fa C mx f bx C my f by
+ + ≤ 1 .0 (B.25)
Fa ⎛ fa ⎞ ⎛ f ⎞
⎜⎜1 − ⎟⎟ Fbx ⎜1 − a ⎟ Fby
⎝ F 'ex ⎠ ⎜ F 'ey ⎟
⎝ ⎠

T.Chhay 506 Appendix B

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

f by
nig fa f
+ bx +
0.6 Fa Fbx Fby
≤ 1. 0 (B.26)

smIkar B.25 CakarRtYtBinitüesßrPaB ehIyeKeRbIm:Um:g;Bt;GtibrmaedIm,IKNna fbx nig fby .

smIkar B.26 EdlmineRbI amplification factor CakarRtYtBinitükugRtaMg ehIyeKeRbIm:Um:g;cugGtibrma
edIm,IKNna fbx nig f by . cMNaMfa eKeRbI 0.60Fy CMnYs[ Fa enAkñúgsmIkar B.26 edaysar
sßanPaBkMNt;Ca yielding CaCag buckling. sRmab;mUlehtudUcKña eKGacBicarNaGgát;Ca laterally
supported member sRmab;karKNna Fbx enAkñúgsmIkar B.26 b:uEnþeKRtUvKitlkçxNÐ lateral

bracing Cak;EsþgenAeyIgeRbIsmIkar B.25 edIm,IRtYtBinitü.

eKalbMNgrbs;emKuN Cmx enAkñúgsmIkar B.25 KWedIm,IKitBI gradient m:Um:g;eFobG½kS x

rbs;Ggát;. enAkñúg laterally supported member eKeRbIemKuN Cb kñúgkarKNna Fbx k¾edIm,IKitBI
gradient Edr. dUcenH Specification yk Cb esμImYyenAeBlEdleKKit Fbx sRmab;eRbIenAkñúgsmIkar

B.25 sRmab;Ggát;EdlBRgwgRbqaMgnwgkarrMkiltMN (members braced againt joint translation).

]TahrN_ B>4³ Beam-column EdlbgðajenAkñúgrUbTI B.7 CaEpñkrbs; braced frame. karBt;KWeFob

nwgG½kS x ehIycugrbs;vaRtUvman lateral bracing. snμt;fa K x = K y = 1.0 cUrviPaKGgát;eday
eKarBtam AISC Specification.

dMeNaHRsay³ kugRtaMgrgkarsgát;tamG½kS
P 100
fa = = = 6.944ksi
Ag 14.4

]bsm<½n§ B 507 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

KNnakugRtaMgsgát;GnuBaØat
Slenderness ration GtibrmaKW
KyL 1.0(15)(12 )
= = 70.87
ry 2.54

BIsmIkar B.8
2π 2 E 2π 2 (29000 )
Cc = = = 126.1
Fy 36

edaysar KL / r ≤ Cc / kMNt;kugRtaMgsgát;GtibrmaCamYysmIkar B.9

⎡ (KL / r )2 ⎤ ⎡ (70.87 )2 ⎤
Fy ⎢1 − ⎥ 36 ⎢1 − 2⎥
⎢⎣ 2Cc2 ⎥⎦ ⎢⎣ 2(126.1) ⎥⎦
Fa = = = 16.34ksi
5 3(KL / r ) (KL / r )3 5 3(70.87 ) (70.87 )3
+ − + −
3 8Cc 8Cc3 3 8(126.1) 8(126.1)3
f a 6.944
= = 0.4250 > 0.15
Fa 16.34
dUcenHRtYtBinitüsmIkar B.25 nig B.26
M x 60(12 )
f bx = = = 13.19ksi
Sx 54.6

f bv = 0
KNnakugRtaMgBt;GnuBaØat
BIsmIkar B.12
76b f 76(10.00 )
= = 126.7in. = 10.6 ft
Fy 36
20000 20000
= = 311.7in. = 26.0 ft
(
d / A f Fy ) 9.98
(36)
0.560(10.00 )
témøEdltUcCaglub dUcenH Lc = 10.6 ft . RbEvgenHKWtUcCag unbraced length Lb = 15 ft dUcenH
Ggát;enHRtUv)aneKKitCa laterally unsupported beam. edaysarGgát;enHRtUv)anTb;nwg sidesway
dUcenHyk Cb = 1.0
102000Cb 102000(1.0 )
= = 53.2
Fy 36

T.Chhay 508 Appendix B

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

510000Cb 510000(1.0 )
= = 119
Fy 36
Lb 15(12 )
rT
=
2.74
¬ rT RtUv)anerobCataragenAkñúg Manual¦
= 65.69

edaysar 53.2 < Lb / rT < 119 yktémøEdlKNnaCamYynwgsmIkar B.18 nig B.19 EdlFMCagEtmin
RtUvFMCagEdnkMNt;x<s;bMputén
0.60 Fy = 0.60(36 ) = 21.6ksi

BIsmIkar B.18
⎡ 2 Fy (Lb / rT )2 ⎤ ⎡ 2 36(65.69 )2 ⎤
⎢ − ⎥ Fy = ⎢ − ⎥ = 20.34ksi
⎢⎣ 3 1530000Cb ⎥⎦ ⎢⎣ 3 1530000(1.0 )⎥⎦

BIsmIkar B.19
12000Cb 12000(1.0 )
= = 37.4ksi
lb d / A f (15 × 12)(9.98) / (0.560 × 10.00)
témøEdl)ansmIkarTaMgBIrxagelIFMCag 0.6Fy dUcenH
Fbx = 0.60 Fy = 21.6ksi

dMbUgRtYtBinitüsmIkar B.26. enAkñúgsmIkarenH GVIEdlRtUvRtYtBinitüKWlkçxNÐkugRtaMgenARtg;TRm

dUcenHeKRtUvKNnakugRtaMgBt;GnuBaØatrbs;Ggát;enH RbsinebIGgát;rgkarsgát;rbs;vaman full lateral
support. W 16 × 49 Ca compact sRmab;Edk A36 dUcenHeKGacykkugRtaMgGnuBaØat 0.66 Fy .

eday karBt;eFobnwgG½kS x dUcenHeKecaltYEdlTak;TgnwgkarBt;eFobG½kS y . dUcenHeK)an

fa f 6.944 13.19
+ bx = + = 0.877 < 1.0 (OK)
0.60 Fy Fbx 0.60(36 ) 0.66(36 )

RtYtBinitüsmIkar B.25
BIsmIkar B.22
M1 ⎛ 35 ⎞
C m = 0 .6 − 0 .4 = 0.6 − 0.4⎜ − ⎟ = 0.8333
M2 ⎝ 60 ⎠
Slenderness ratio EdleRbIkñúgkarKNna F 'ex KW
KLb K x L 1.0(15)(12 )
= = = 41.38
rb rx 4.35
12π 2 E 12π 2 (29000 )
ehIy F 'ex = = = 87.21ksi
23(K x L / rx )2 23(41.38)2

]bsm<½n§ B 509 T.Chhay

mhaviTüal½ysMNg;sIuvil NPIC

fa C mx f bx 0.8333(13.19 )
+ = 0.4250 + = 0.978 < 1.0 (OK)
Fa ⎛ fa ⎞ ⎛ 6.944 ⎞
⎜⎜1 − ⎟⎟ Fbx ⎜1 − ⎟21.6
⎝ F 'ex ⎠ ⎝ 87.21 ⎠

cemøIy³ W 10 × 49 RKb;RKan;

Design Aids
eRkABItarag nigdüaRkamsRmab;KNnassr nigFñwm principal Manual design aid sRmab;
beam-column CataragéntémøefrsRmab;eRbIkñúgkareRCIserIsmuxkat;dMbUg (Burgett, 1973). témøefr

TaMgenH Gac[GñkKNnabMElgm:Um:g;Bt;[eTACabnÞkú tamG½kSsmmUlEdlGacpSMCamYynwgbnÞúkCak;

EsþgedIm,ITTYl)anbnÞúktamG½kSRbsiT§PaBsrub. bnÞab;mkeKGacbBa©ÚlbnÞúktamG½kSRbsiT§PaBenH
eTAkñúg Column allowable load table eKnwgTTYl)anmuxkat;sakl,gEdleKGacykvaeTAsikSa
epÞógpÞat;)an.

B>6> snñidæan (Concluding Remarks)

eTaHbICa ASD RtUv)anCMnYsy:agelOneday LRFD k¾eday k¾vaenAEtRtUv)anGnuBaØat
[eRbIeday AISC dEdl ehIyeBlxøHk¾eKenAEteRbIvaEdr. sRmab;GñksikSaEdlmanbMNgcg;dwg
lMGitBI ASD elIsBIGVIEdl)anerobrab;kñúg]bsm<½n§enHGacrk)anenAkñúg Design of Steel structure
(Gaylord and stallmeyer, 1992) EdlenAkñúgenaHk¾manerobrab;BI AISC Specification provision

pgEdr.

T.Chhay 510 Appendix B