CHAPTER 2 Fp. Smbn OFFLECI ANS THE SAuuNG. FORCE REMAWS VETETICAL SM=0 *) 600 (2.95) - 1.5 B-0 F= 140" B= heSe > S. 2 WAONl /asx10? = 325 rm Mons RIGID. SU bMhY LESS DEFLECTION BA Commer “the cthaaien Ben the vale 26 fast abet Toapen: OF his Lekveon the volve med th seat, anal the plnid 4, here te no premoie Prove ach er onn sme of SO mm, doaemsTis Geoncky: he aprng+ compremed $3 mnd Logg of 207 men, Foca -Defevraaton: Sprig face Fo = (x0 hu/m)x 93/0" a SICAL Force Eguclebviinna: cma the vale prse-bobg i fk Sheoi me Fee PEGI | 57 . 2 pe 263X10" Bfye won? 230 Lt Ba, Su, Se be the defections Spregs ob, Gerace Commbedib tet te Se %,. me Terex Deflation: Fa = Rabe er 19 Alf Foe Rede | Ree 14 Raine - Fer keSe y hez & Anfm- Equattbnnen of Dises Comeedin, the Pace bony : 2-1Solve = S= 0.025 » faa hy =o.35hy Fox od by) pes O87 om bheuthe opestey renceves hax Lect at the bottnn 3 the atiche , The wing in ttended om omennt Sand te momecd ofthe abe poce abe the Pook jot be lamcen thee free inthe reel Gecuschy : Sx a8 fer anal dO, Face Deflemeckin: Fy = RS Eqns brian: Conacden flee-Lelly 5 ee" Moz 0: aFe= Feb or Fs BR, ----- Me nee from Cb thab the meme qb the sprig free: abeat O mau howe o Conslend vlne, bFe, tclependeud of the persion of the thrnig oud oh the cenattant: Row the force te be onedted ty he obecaterr caunct he ony allachon im the shrig oral proctio: Themnty proche! arhchow ebbears te be to crrsmae the Aeugh. athe leer joo that the operator's froth ota quests ictomce pe 0. Woke that this Wilh reguine the chewthy 6 mune hen fest’ heey a quests distance, asic Pin prnmntey freed by the bunch pron eferation « Irate alee thak althogh the mastmunn applied duce is reduead, the lrorkaline by the ohereter om each otishe will Remade the same milk the Qelencled leven arm. His foessthh tak te fue fot / Fe 2-22. INTRODUCTION To MECHARICS OF DEFoRmaBLE BODIES 25 _— — 2M.>0 too CVS) > Foy (2) sp fry 245 kn 2MA=0 = >100 (0:5) = Fey (2 >> Fey= 2skn dm + Se Fe =O > Foc Con 820 Ae 20} Ry Foto Fon > Fon Pin D ee tee? Fon > 03 fex= 0 if Eom = Fen =O gs) => Pips Foy = Fskn= Pep +P 2fy 20 Foy = fap AS EEA nd Fac, Foe 4% e Ton rez Fey (Fema (com of Fe.) | ay Dae = LoD Cm> Agp = Tsim Ape = Doom? => “Ege =O Fos= Fre > 2S KN.5 20s “e1Ps|D edlection ace de = Faodnc = 2Sx1000x! | a SKIS phe wae aU Beton) * 100 x 1g4 XE ae (Tension) AE = 2 TS, dae = Foc Abe en Aac E Sep'= FSExIx1o00 gt 1 oe ey Lo in SPE = 4-tsxioS m 7S * shy Ee Bes K108 “the deformation art Vew small > ¢xo Ao¢Bor2 => Sretd Ge > 2 Ain Ain @ > ZAG LSE b = oO OOS” te -3° pe hasxie—_ Z2Fnao => Fon = Faget © Monit etuidtbrivn» Z Me > 20€4)4 fon (2) 2 - Penw)-Fy 20> (De 4m 4 =" 5 Pin E:- — Fe Fe > Fep = bokn —>0¢_ Fep Z2Me =o =y 20 4d~ BO) Fo = AOkN 2 Mazo => 20 (6) -Fe (35> Fe = bokal Pin £3 Foe eH tn=o 2m ° B EB wy 2o0KN fi © 3 c or tt Foy Fey oF $ 20 fe ¥ fy =7 Fon =o ( trom zd> Sb oO €o— Fey (2) =0 Fe > Fey = Aoknl FOr Fry = boned Pin Di. ) Feo Fep 27 Faprotetonse A a Fi ep = bee My Poe = 40 kn) [som Foo 4 Pings) a ee, Sess Feprten _ 9-203 rom C compression ) ° Tee ED Peo x dpe OSA Nore Cr enside D> Te find Le i by Jeomebyy Arcs trac by ew ard AE Cred. AE) mest at a Point My by ABE Bic ince The Val an Very Small we ca, ApPron mate The Arce to tue tet of ares @ That Pornk Heme faces dep — ee ee = And 0 > 0-02"a7 (DEAL zATION ¢ TRUSS wWiTH Fracihontess Joi7S Agree ReATous EXD WANDS INTO Sepforne7s xe awsea lena _ SMp =o 49 Q 18 + 24270 = 3aR, Re = 246 AN EFY=O > Rp = 210 AN Fan Bees Ww DE,EF, ER: My D Foe Fret Foc Grb0°=o g "Foe Heambo+ Ry =O > Foe =- Re /Smto Foe =~ Foe Geos R GEO" TO Ano Fee TAKE A SECTION AS SHowis < 8 Fey > SMgr0 9 For ok =~ Rp 3 = — 102 Rp 3& theo ze For Fer = atox 3x(%) -180($,)> 450 cotvo' Nour Pin R * Far. F. acy Re Fep = Re ettot > CMouMTe DeREMON oF Pont R Sex (Fe\ 4 ( (s & ( AE), (3 SF AE Jen ~~ Bomam 0-52B Coomalvic Cmmpoteblty Refeming ® thy 28> example 2B, we. ace hat te deffecKnn one verig peal owed thee bare Ad dB crema enewtally ane shaisht dine fe Sa % Sane $08, whew Sap; Soa are elergohara 4 hone 4D and DB,aud Sg nthe movement of powt B. Force Equelcbriem: From example (Hf, Fan [3,300/k, Teriom To oblaim Fos, conacder a fase body of jont RB: = Fi Sty20: dfx = !Si000 y 6- toni! (2) + Fem 26,0001, compression fe ® x soot Thro: Fras fea = 2e,ov0d, tense Force - Deformation: fy. GY, = 13,3008 90267 Ht, Bee 19106 extension F Soe = (5E),g2 £0900%3 ~.o04}t, 4x10 x10e orlension. Sa = 0- 002674 0-004 = 0.00667 ft (Cece Gmprtee SolatTON ) —2:4 Z=0 > Fo = twokn Z2Mp =0 >> Fa= AookW By method of Sections we Section: out qe Park Meares slerReo Fee Sinb —S00 +400 = 0 PBe SSRs BoP BO” 2) Arp ? Vig B Peet lent a: dpe = Fee tye _ eee Cofpron.) + a Age E MedialLp ee AR 2 2 “le Feo fietO gp T Fes, - Fea * Be 2 Ne “ EF,=0 . t ft WO 4 + 3 * re Fag? VEW (0), Fag? (7) Ars aye EF gt0 Fay ~ FB + Os Frew Ce) Fs Efj-O fog - B70, Ayr vO 5 5 » Fos Aro m Foo __Fto £Fy2O Se - Fes 80, Fer = (2 W (c) = Ar Efe tO Fag * Ba Fes Fop = oo C7) z = FeoR . 2Wwh Spo? ee oS CEtangarion) a Fn BQ, PEW IER 2WL (compee ss/on) Sar ae Ae ae ‘ 2 fst 2 WL Cecongeron) Sos AE * aé ¢ 272-10 (contr) Oe. ed Foe rHa webricat SEF LgeTIoN OF Seq +1 8a, 5S, covsioge THe Pokrien OF THe russ SHOWN Q Sod Svq* Spot FF Sor s+) a 43 Bes Sys Sv, + Sos = Us ewe wt G+ re) ea = wh Gree) Se o-/t —_ P= co kN SFY +0 Coven. PLATE { Fo+ SFe ~P4 E+ 8tar0 » Ae = O31 x0,3™ Geomereic Com PAT BiLiTY Arz 2x25 mm x In Se2 Se Be= (760 /m> (Se) = (2 Ep= 200 Eu f/m? El, AE Ie Fe _ Fe B5xXIC me KITEN fm? ———- ERSKIO™ X 200 GN/m? Fez 0:0865 Fe F = 305 bn Fez 34.2 4N Oe = 44 MN)me 7 oe= SATMNIu? , Se=Se= Sel = = 0.328 mmze Sfx = /*| 4 a fh - Gere + Fe gO = =O Are ZA ro -F + hth cose +f3 cos@7O A+2R cos® =F Géo merase Com PAarieieirt “1 Foe Smate oskeecrroms Q wie Semen / Aepeoxs mrrecy CONSTANT §am Tae Sa = Ss cos® fi bse 2 Fx bes® Ao & Ae 6 (4 + Zcos8) A se a Ae 5 (+ 2 & cos’e) 2-7/3 —_— Waew THe Lomo 1s ar ee ha , Feom 2h - d (bar Zbe) = = he, = = a Ta a B28 leone ar me ha, a= P Thiet debt beh) Foe ree Lono AT X=-a, ae. As-/ S = § (Lone 47 mera, Kha) * Se + (8, -8)d In Govenae 5. gy | hase + Mbet bat te) P Ea bg + F ba B+ Boke) Wwe hel 2 Zhe -h (bg #24) 2 §, 8 P Cilg? tha Kt Egh) ‘ 247ALUMINOM cag Fo 058 £0.08, Saz0, Se=8 Gerenttn Se2 8 For 8% 0.089, Sa = &-0:08mm PoRCE DEFLETION Bass B. & se iy = TK 18x 625 xj08 Aa ° Te “% 205 de Ey = 103 CN/m* Fg > Ey = 20 buf? Alurainum Teas 16257054 EQUI EQUI 760. oF Aare P= hth SoluTIow Fae 5 < 0,08 ma 88, 4-0 4 00,F =P P= 0212 Sy tu) (B,mm) a 520.08 Ps 97 Fon S> 008mm Sp 2S) Y= S-008; PRR P= 1378(5- 008) 412)3 § Chu) 4g - Pr AN)AS Hofst B= kesh a = 2nrivo®xl490 x4 200m “Wx Coons = 288 x1 Sein SPeing Grttant ke oy 194 ral, a dL weghts won 61 Bo0Sm = ion ay weight [Length =10__ = 32.79 nlm Daes Teal werght Acking = 22-79 %C1940) = be2c2-In ooo) rFek dz Se rsre) B22 xid4+m—m = 0+ 226mm oR lor der an elongation Gf -p-22bmm bs hod Pible. A hypotretice) Solu. woubl be foreduce tre arocl by bursting Sothat S= om. los bsrs2-Imaqo . b S252] 2 =—ase Ax 162 68xt ol A= 16 024 nS 8m? = 16024% ISS mre 2 md =A os Bbrxistmm: How ever This may be too dltnsy f weductira 4? dita w wet Practically Possible « —— —aaaeale T- Temseon is Ape Compressive oa on wind t 27 Cm & pte! \%)- a saat Hes] deeieon = SF 20 osm™m a50 NI: geo hb NIO © Spang constont | AE iia = os = tots 38 ‘Jorak Lemgtr + nw 215-38 ™ tant of Wart = Be. —_— “ae iss? | Spring Ons O9 Swot Smt i 2D 7 aT Cae x150° _ rrene see 4 ae 4 Vso 10” 1 spe te LOX TO re - _ on i T(r ase xl? ) =e pirxto” ° 7. 10-9¢ aN ad on wooden mast, 21 a fo 14-b5 SRNBUT Cymden npec-beety gfe beams yA Qssume that the neemonh of A,Cane CS Bene: Herean be shew be muty a QS pee ebpresimection tb the ne athrcctions Wen St ia pesscble wih the teery devebed in Chapitrs 78 ts make an acowale analyais determine the memerk. Since we are a-l2allow, notin & privtiont make auch oun analysts, tao make the above arumpien: Abulubaum 3 Mya 20% Exo7s= 120x875; E> bb7-Ay ZR =O" tm =RO Oe Bs 533m Geomenac Companbiily — dg = Elewcarnan oF Ropat A & = “ nn Ae » Tidy . $3322 = 0,032m 4 Aye & GIS X 205 7 0.78 Ses WI U7 . 01703 01532 703 IREOK 2OS Spgs 0.703 ¢ 2% (0:/29)= 0. a ose He (01129) = 0.HOmn Before lence, Offer bwadeng — Sresa- Beek of WB! Free Broly of BC! tra gs Fee A Re R, “te PB bee Sis we + Eguittbrinnn: BCI: Fe =P evce Defleckion « Ap: Fas Fy =P Geemehie Conboclsbs ety + ainblacement abe oy Se) a (Wre$,) (la aa) = (ler) = t8s) = (ktm) Overall apg conabmat =F = pe BI Mdealierhion + (iy rue freckion oot Poet Gi Ream ty weaghitine Gi) Springs To cleflect audenronds - Geenncty of De bein aped heme: baz 80. Spe & Ss Force ~ DePimrchien: Fas RSs Be af Fe> kSs 2 192:19 combined Eqpclebreinin > 2Mazo: oe Pe ERS Pe= Ra+ke2a= Ekads é- be > 5H. ia Se . We med Pos ae, 5 bs 2h, w 220 ke Replace thinly : bE Oesg the aul ke ky Whee Kee fuk : rt ka 4 eq a-t8) rye A B La tf 5 P Senctiy Sprogs aeflat * B Sece= Reformation: yom epual anonct 5, | | ‘ ? P j Fae kg & be orden Mat AB ahenld Re kb eee. | Bs fs torn Exist be by tao Fa+Fe =P, Faas PCa-b) o Fae PG-£), Fee Pe Semi) omen, Fa. Fe ye Cbra) 2b %& ake “Re aks thin gees bl kw Lbs = 4s leith a ks+ke kat hits. q Kika +k3Cki tka) oie Sa PC Kit ke) kikit blkith) BI Geothyic Compatlaliy : Fey (i) 620 Sa = Sa-600 9) 5) os am sf Ios Seo 8a -908 py BD FS hes Ga -12008 Lok Freres — chon: Faz KSa, Faz ky oe chien: Fa *) Fox hide Feg ti fh, Fey ai) Fez RSe a-/4DAN Cnt) “These b&tome Fg = 175g [wl fg= 2/8 -b000) > SLmne] Fe= 17 (S$; -/2008-) Edger 24-0 Tqthgrh = 620K" 55 Sy ~ 33x00 = 620 = Mp2=0 3/4 tha = Fe solve ra 55-59 -- 780 O we le Fed: 8 =-15/9x10P Rad: Sy = DIS rm B= 36N Fe = 23647 Foz 3467 ABR Memlenchon 0 Ballpent'n prockinkss, dee B neat amend moment i) Fhaghete eo raged Sopoinitg + sthe pele ceflech one Dremann tn tha N-S plane: Geeameiny : Assume cleffectens ane amwall | Ae that change im angle Ho moghigc ble’ remeron eo! rope Dod @ : z AB’ % AB+ BB’Ce x 8B'A ~ AGT BBb045" Z We Fendeneg for vope® & tb get Le sot Cove Thais wt posteble CD qe lack. Recowne the pele moves mm the plane f © cud® , the elnythin {@ont® prusgligible Saice the tmcbaltnetme weve Jets, Te preettensione ane foe & O.@ ond ® deco Delrometin for O° T+ nel) = EA@eronets Feonens care ais2:22 corckmned Thaw groves Th = 2306 whe Sur fet, Ter lb. Equalebruden af Beles Zmezo: Ti (fg) x50 = Qo0%45 ae 40 tb She grvco 82308 = N40 $= o-1s9ft = 168" RAD Menkselin: pan ane frchimlin, ted mre integhtlem, arccal- free retmbere: Deformations are remall, ao that angles Fis wey rom the teat in hgh g the briblen, He aprng Cone tat 4 eBe - wuz R= Dan 1]_39 Nom “drnsae Leety of pon ab &: betg pbs a t. Sky=0 + fegcadhs = 400 6 or Fig = 642.5N7 Fores DeRrmakon: Seas Fee. SRS = 36, 95mm Rk” 77,39 Geemebrie Com pablehty -te determine BB'= Sg i trms of Sea, drow an euleryed view of fb joot Botha, cg! vabvot patel teen, ABlis almnt parabtel te AB. Sa- Ses Is “rom pommely , BET Bae OE acd 8 Sg = F%3bmm Slate si? oS node - BB 2-76- Asthe mutis tuned am extaa bot aud shew guriv the corp ALSSAOM ra spitively and Theat” © seeont $8 t$s- txt 4 Thy afTLA = le), tHE os TxI5 \ Tale fh qt) = weed 6 i) x0 Te by x 107 N T = [by EN quarter tum Onnrd * [emsionB25 Bree boty of AC Yrse- boty of CF ed P % A a potent ae i ¢ Z € F Jd. 33 he a E 0.07! <5 fy zo: Fata 20 fe Eryz0: 74% = Forfe --- (I) Siero: 2Fetl f= 3P --- C2) Geometwe Compa bby + Ger CF Rome Rewrodnt, ole ffectins at DLE wuat be eqpad: So= Se. eth RUDe NEEL Tay, se Bg, Be nacht -saino truig fe kfe te Gand (2), get Qz2P 2-/72.26 —" Let Dishanee pebween Ane bars =o rovee Per Unit Length A> Ps Wr loom T ene Tense: fovee T = 4rus Pa % 108 xls Us = Pa+\vo Tn tvese Civ Cumhfercnee iret. AE Sa = Te WCnsd2) Wa wr % Dos Ato® x104 TT D (8 ¢ amet ee Dk Pee = Tro) Tyo TRF Dos wiee KIS KID? T = sp-ossN 102 y es. OSE + Prato? A tiWl10 G28 em Lon Gituolinal Spacing = ly. oeosermaad from 2xaneple 2° 64) SFT thine Te tennion atangle 6 sategeny qe 08? ee cont ot O= ©, Tews ces. Go wert P F(O-). wed Te Weer ate= 0, Te NE a order fo tine he porseble, we a . pe -$7 ejaie a free ruck that $P= Tye =eas 232 sty, <0 #9 aasnim - 37% +037,=0 Fam Feo: 7227 © 7° Ta O- 47-157 300mm. Tr 2 O4 (LET, 227 0. ge s87, T= 13d Ta = SPAN 2-29 as Zs ef = 3” ao er 200 . T=) 3,.76x/I0 A 2-30 = “ sm <0 Ff a [lnt_g= O +e, fs . a mpe[r fe Ceessrig Moment) Ler P BEA UNIFORM PRESSURE ON THE lowe SURFACE de fdF = fpdA= fprdarde J ame Jf tp ct dede = Larn7 é 2 Ff Fro pal tO £* gr fF 2 RESISTING FORCE * 2 a 2h,20tric. Comnporkli lity : Sapmmeby Deqneies that tegen] obixphenat Le both Leops + Shue the will be ne shear chores hehoen fhe tue Leops amd “thers sacternction Cmrecsh ofa rackal previre, then vackal expansion murat be equals revue = (Seiten pA te Connuder the nemin cinealan free-beein ! S lect yoit wedth mermal te the ba ber > BRASS HooP STEEL HOOP Equilibrio gute ore re ors BRASS STEEL = a Ces (P-fdX03 + (Se)g= (Axfs) (03) Eg 210310 Mig? 3x10 34107? x 103 x/07 3 Ee = 20Sx)07 mni/ry? OFg = Lixo? » (Sales fe 101303) bxl0 Gx1073 x 205x 10? (Se)g= (Sr)s fr px 2aixiot= (Sel, RB x osx? = (Se)s fe 2h 10N) ng? OF 5 = S63 MIN]? 5 Fy= 70,270 Fy = 5149N Og = 28L MIN /m?® 5 Fre 2-20BM problen 2e31 wanna (fi, and 69e- Ode, get pes I MN/ yg ® 5 Cede = 0.083 mm From O) of Exombk 2B, ans ot ---+ & £6 aud fem ©), T= Tro @ er? + Omabensig and, die 2 yd Tete . the ef. iy R40 $ R46 R? 2 46 ats Tendo. Flan the nequived aeeth,ts/2 y =z o> LL Constdertr§ one half oj tre Acre fox tne Lt halt 7 se) tp pon 7 ; wie 88 ‘ Ssoon Tomnion iy cath Segment tne Sumap pre? On ae Ay of he segmont => T, = 5500 jp > ove Ti > Seon) che “vertrichlon On dhe Aangts {i ole} Imei ed L — Sek ~ 15 24 es Ze Srak for tes canbe half Length = Se 4 SAS Site Grot = SSE 4 so caret AOS DR honor 60x70 = Ales die os bo Kor Sut > OSE Loe o. sizes —LE =) ze = b - (Ug ,025%"7:38 Assume that the footcotial 4 2 8 wanes, —~——dreoned mare. Let Oo Ret om \ Le Reagh of encheable before lending 269 ‘ . $= chimes thal brit Proves ae R pli \e @ rewult of the Prce appleedt [rer a hte . 375 osladen Gecrnthve Com pocbibility : ea Me 4 Ie ' b cAgien mt ateteh by § jenblez Foor rupoer court. murat beth by ox becowe aback. hus cable cam ectienbe on reduced tern er hae ne Pree atoll. ae, aren Si auall, theangh @themg® Qik the rudder mest tan Ga S$ Eapilebviiewn : Dae raring Pellerp ane frchinlen,tenaten ian onthe iy trantinitted unchanged olny ah Length Foot Cotto Faee-Bely : Siteo bed birch: O95 T ~0.250"700- 375 Tz =O A Wnt =HH467 ---------- Ww 5 Free -Debomechin fib G2 inckal Euain in exkles Coble: f= ae 5 Gabke2: 8. Bebe. = CoN . ~ 4 Rem OtLeruire cable 2 gree ofnele cmd thin eqnathon gree ne tafrinebin. e Tare and equate S from ber cqpshine: Totes B-E or Tah = an =2eht- --- % Rom OW) Ty =1633N; Tez Mon S = 6x (1633-1900) /(to/2s) = OS 925 me P= 0.0058 Rad a . = 033° Tf G=0; Assume Ty 70, we cer T-Te = Hor 52233, 77% =e 72-2330 Th Cannot be five Merce we take Th =O aud get T =KL Fen) Thus, without amikal usin thee udder beuld tun threngh am angle tie or lonyjeno it weuld with cackal teem, 222Cy tg Placed tide a holt. R Sind + N-Weosdo = 0 4 Roose + 4+ —-Wiind0 =0 of? d= MN= Mw ces3o0 Rs oo singn - 072 RlOOCH SO Ce ee ea CoA 1§- 425 ef = By 40kN wod = 13.5 A107 § > FL = B4AS x10 x58 AE + 6lmm 2E x04 KI3-S x107 (iid P+ lider wclown raf W Sin 202 0 Re Bo. be kN) d= 1) S32 mM-:2.54 = = | axing mora at B fo = gn g = fe Ae Fa = Fe lia Aa En = de Me Ee de = O-Mloox pas OS = 3:0bmm => 3 dull ban tate138 det Spe = Sinanne he vewdus ob Copper cuit Seg = thcwace in vodbucs ob ataeh coil: Geonihee Compote « Ses= Sre- eSxID?~---- THE TOTAL ouTWARD FARCE = IT x48K FO AN WE may REFINE THS Boby Farce by Any EQUIVOLEMT UTRUAL ~MSSE — ~= 1x 4.9xT0 - 01 934/192 TR GEK 0.075 2-34ace t Lt me mraenoy bETWER THE Cyn + STE Mite BE A RAD PlaSsuRE fi There Phoceome EXBRT AS pr IF Secs Sef) laa)* 0.075 KRUTKIOF Sars = _f (24)* 0.025 x 200 x10% Suesmpanié. 13 C6) P= 0.0608 15 Jig > Rom & (A), Boece = fof? 48x OO)S = 01313 Sample (G)AB jes de> 007m ee = ON MM Fae AS x pox rob x10" — 2egn“g- 40 feom Examete 2.2 (a) £4 70 Fert hy -w (6) Er? OF 2a Fy - Carddw a te @ Sc= R-# So= #- ‘h © Ke he & fo = be So Foam (fie) fe 78 CRB) oe Anrbeh . kA fo = - - beire (ea ° 4o(R-R) Fo- BoR boko fe-bek . he Zee aer we & ype S40 bh bo b-e ®o ora Fe 7 PVFg = &hR- kA rr aR O-r) Lar @) Fo+ Fo = W Foe LO - BR) 2 &tHEIW remy cere cere 2a () Soouma Foe & é= - Gr) a 2aQ _ fort SAry Ww aor INSERTING THE REFINITION OF I ANG BIVIOING BY 4, €eunriewn (1) Caw BE CB TAINED wiry SAAN SPULATION wo 2 Se? eek 14g oriig)t 4 1-3 O-WU+4) w * 2-262-4) mMeTHoDS OF =Examee 2.9 To CAleularTe vey rime Covsomne. THE wWhyeerer DiAGeAnt, 15 Timo snenne ¥ Using THe JHE DEFLECTION 15 GRAPHICNL =METHOO, AVAILABLE (SEE FOR DIS cUsstON Youve , THEeoky oF- Srevervees , Me Geaw~Hreed, Tile Sotuney OF 7S PROGLEmM /S BEST Su/T ZO 7O Digurac COM POTATION Ano nS Giver 100 Sseerion 2.5. Ences’ *Mérien 5 Aeecy A unir lene ar Fy THEN caALcunrEe THE Lono IN EACH meEmeER Due ro ras unir Lona, THE RESveTS ARE Givin = Betouw, ; *, QFE )f/BE)OF yjo-F 2 | fe | Gaeh| Be [Gelse «° 1| 473.33) 2.4 | % 2/.3 z| +200 2.4 % 32.0 | 3 - 25, AS -So| 31.3 4 -/@.67 Ls -Y%\| 20.8 S| -/6,67 Ss -Yo\ 20.8 & | 716.67 15 -5%e) 20.8 7 ° 15 oO o 8 | -833 3.0 ° ° ¢@ | +50 3.6 ° o « €=/0K/08 1b Z= 2147 we = Sry raySimo R2-PL=0, B=P afy =O -"f80 4 fF -P 20, Fag * (2 CF-P) we 2 Fnxt0 ks 7 4220, Fao= CF- fo? » Fro P) » Chee (EF -Fag # SE +9, Fee = F a A / fs EF =O . Fac Fag ~ Fe #0, Fae *F os ne - fie #0, Fae : = g ER nevervee F saz, 2 of PEt Rt FD CA Pe 2Ae *Cyewr-al wat : Uso * Foot , FL Cerne * Yeo + Gsrevcrvee Swe Fo ts At IW TERNAL FORCE Borer =O D Usrexrvee =z - QVeo OF oF 2m f= eee qare 2-38oe Constd ar Loose at DiB, fC Fueh thet moment ak DiBc We Zero, fobs ar Pin Jonks AB AL —> Steel, (ecm with out alofermation - F Z fy s04 Zfn=0 pends Pe Fee, FRC A ° Yo$ Fap 0260 +Fap WS? 304+Fre Cs? Bo > S00? y xt Fap Sin bo t Fag cosz0 Sin(30y 4 FAC CeSSd Sin3n 20, Tx z= Paw > Pre B c Fan ~ S000 M5 Fra > Pre > Seoonl 7 A x pprAc = pees bo = 732m OS 3an cowstler deformation we fake eens = Se se RE tomo nba rio? his fines dine = Seerele ten — = 0+ 028mM 1 SHI yao Selo? bt A ® yt —Enpcos bot 8ne cos?20 + Src (0s? 30 Ey-obe) 2 -0Obbsmm (-y oa) yx —Sppsinbot $ne Coszosinzo tne Cos Z o-in2d = — 0+} bamm C-x da}Alssomé SmAlk DEFLECTIONS, ~Hev The Foeed Fe 1s vebricac YE 20 at ha- Po = bs @ S,* Co Ser Bde = fw Bo (teh) 0 8 cast) & Bae) + Fe ae Pa 4) & (MB) a e- 7) 2-302-45 2 UF Ril Z LAE 4 fee A BAe wEetonT DEITY OF WF ~ & & Us BL, BwL, wh Ox (B24) RAE? MAE bAE aeae 2At w ge son 2m am e 7 Bown 200 300 2e2rtA td we ole rel Comrider wt, ar ‘ gee IF geree acting by much poole Poe wht Pie LZ Ae¢ 2 Ad Kio ee = Gasn mae ; Siow But Com Prewnive doves, = LP's ho: Ore Nee. Condition cloenilt ¢ prisdy “for any Love dev Fention "Member 3 Aoxe? . 26-Fmn Ime 2 Ho on Im Ts wie teselt Saul dentionmemb\ can be dnt bar bar But ‘hot lr *Comprerrion dosent moalidy,2-47 a Assume rng TeNOow FARS AS THE COvceETE GOES (NTO TENSION Foe PRETENSrON 37’ £ Bry +0 “2R42%, 70, AREF 4 Sréesses ARE Gu Vy 3 t A OR = £ . -# a A oe me 7), Or a fe) 7 AW E28 were 770 Ta | bt 3B 2em =. 2756 7 FoR in Teenat PRESSURIBATION, Assume re ConcRere SS i PESTON ZA+0 A +2R b pe . Fe > fee te Fi 7 4 EA +O “2 + Cp-p) rnb =O : A = (p-pilreb OL = £ = wpe wr) Foe Geomerese comeartmrery 8. * &, ~ pt) Ke rt En ie CAT EE eee ¢ Pp" PE (r+ (444) Sx 100 dfe) (19.5 $4)® See ] = 1.92 . C2780) 35 x0" BJT. SIT ei Fee THE CONCRETE TO Go ywro Tensvew C2 +02) =0, e trelte » Fe. #8 pb fe Cc 7 Fae rue rénoon TO FAIL Set Oe = 7.5xO* fb, + ae = Sees, r ' Ez a = s a 346 PCB + 524) HSK te) TE, pe 7m? A, Peerensne Fece , F 2.487%, 6 = 5.6 x10" /6 Comekere PeESTEESS OL = F = 30x10 ® < exo? & & im ze 2-322-48 Assume THE tavern Bemans covsranr Ano YO << z z = ye 72%, 5 ute 7 (Orad)? _ 7 (ate eR 4d4 AO 2, 4 4 4 4veviv = em (pao), Foe Abs! 2 Foam rue Tim RING SoLurion Sp, Fe Aoz 25,2 24208) ce 4v. 2 24P bt wv D ( ee ) a: ow 2 = 13m 2 10 ae te /2,51mm & € 2-49 Fenrig worn P10 mem Mg = 7 (Sem)* (0 wm Hy) C43 HHO Ly) = 6L26N~ (9-50 (8) Rip THE STBINIESS STERL K1IRE 2570 ahs 2prx h.25 & fr = 14.4 MN fn ety . /) ely Tn me Tbe tap et Se= RL? . 144 UM /22)* -2 LE ig =, 4 99X10 tum (25) (40 xI03) “/ma a—332-50 on'r) —_-_—-oO 6) Feessuertng rue reuse eB rs peak - ane “ef w reems oF rwe sreéss Cen = Fee 2 Gite -pur)/e ze Fi = Fora b& 1%: BG Fort Com PAT B1eiTv Seu 85 Aye Bh & Feu && fPt* 276 po Assume TBE FAILS Oty = Of = 210MM Jg? = (Plo) /t Po = 4,1 | ng> C8 = LOO = 293 My™ & Cag R. = 276 Py = 90.4 JAN Jig > hE Vigew * fatW= ie 4a lly lye JW = Ay (lglg) Lgxlg= la Ay (Ly - Lge * Ugo-la)) + Ws Ay (ly-Layt (Lay le) Bur ba Clyo- l= Ae (Leo - Lee) 1 ha Sp td = Deby Sg2 la-lto; Sie lon bag (= bop) + (La Ley) = o ~ Mlge4 lac= ly = 0 34 + Sg = : “ a > ‘ha, by) MOPRDET ofl f 2-342:52 aa) HA e aso] et le fe (q+ 60%) (A+ AA) Ex =n A +YAax + (ntA On) (A4 4A) =O Expanom6, Neseeering Peoouers of A reems ox 44+ A AdK =VASx Duwiwne By am Ane serrine Sm = Go 4 Con STANT > yw rue Lin JA ano =-XA dn Te S dA fda Fb s by 42 2-Le A : So 2m ee Ee a, Se a d,= % © 2 2-352-53 —_— ft L Lids, + rip {- Zqvrerse lum 2 fo24+h Geomeré/e Cuntmenae 5: * & +e, 2 e+e, ese, ZL Rade eS de +Si ve, +J!& de, “Sh de+fidesfPss-2) “SE -P)de +l de.+/ PSs -/Gth-e)de,+[Pds = [rds WHICH SHows THe re TOTAL “cLK fone BY THE EXTERNAL 2040 P is equa To He rerae. POTENTIAL ENELaY SToksd BY THE i rERNAL MEM BERS. 2-s7 Feocesons As ww 2.53 tl ada: eins feon+Se, S45 =Sese+ fe, vp =/suP 2~ 36,2-55 —_—— Foe Fig. 2.7/8 a ae gfe da = Bl fds = Consmee A Smime mckamenr in osPemcenenT Si Eau ro Agz, THs Gwes RISE TO AN inckémenr +N Ch Egume To AX e+ Age Fy dsy 2 Kw*MU Tes Fp Ase = AU oe f= DU “Bs 2 37