Module 4 '- Working steess Method.
*_Theowy of Reioforced acters . —
iE shucture: te an
s¢|WSM— oldest Method ow trod tHion al Methool
| q+ ia based on elosic theory » ——_ A
apt nalysis
een Wee
a aatio Method « Me
nti ent load, mom oe ”
Vaits: ! ”
Gnve foo mild Steel, >
; Ws ercaking Z
p point
ee ff 4
ahress
= Shress a 2
4 f
s ae 7
} sain A
working chess + Pemmissible ehess. he
ze
| Permissible stress = Shkengtn of moaesial
ROS J
| Fos Sor concrete = 3 4
| The metnod | uneconomical
tin LSM — > FAS is applied +p _
dD estimation oflaad. _
2) ee.
lens—> toad —'s
Comerore.— \'Sh'id
| focetee\ = 48 Se i A cr Reinforced ey stre} 4
|__| mass is lenoun as Reinforced Cement Concrete, _
ae | Advantages of Providing steeland concrete
Concert, i
jals dre fadily avaible at al)
pla.loA: , a €s=2m10% Mm?
or all
4 Sra té ;
Shean Ly. GoodLuck | Page No
a s analysis of
Ss. ane E
i Py
Vseinforced concrete secHons, + is us an €d tn transfor
th€_composite_secHons inte an equivatert con
sections: acomstagi Decisis canice.
madiulor xSH MUM Ene doa tro cnn
: a jo of ‘cea am
Goodluck | Page No.
2 =e =,
(IEE. fon rate Bes
In relinforcect ee constaicHon ft
re oe mis,
25;
Example -- M20
Mixed <1 > Specilied compressive Shrength.
| Properifon, of 1somm size cube teed
Ot ABSdays, Crlron~ -
Minimum Qrade of concrete fox RCC oork !: -
™m20 oe
[rade nt
Mise \ FT
| mao 20 | )
| mos Ae ef
| m3o0 Bo |
6Gcbc Gec ma289
ms Silo 4 Niro | 18:66
M20 TEN |rom2 S Nimm | 13:33
Nas B'S N\ rm & irom? | 10°98
M30 (ONY Ln S Nim? 9-33
€ebc - W415 tre. Permissible stesses Jo
Conatte due to bending Cornpression. [
__| Ste = ae isthe permissible slreries in conavte
: i € to direch compression ,
ae Sechon, %
A= re :
te—~ b —» Lebo or feo
lage a be
Den = tt he se Boe | Ae )
na | / /
mA a " 3
Pi On 8 ce AL :
sr Sh /n ET Ret/ Sin t
Balanwcl Under over i
Rrra Rainrced .
D i ‘i jo0
§
i ie 3.
'
i, Ls =
Henn 00 is Calud balanad o ee
[om
‘
ss )
Cver veinforred section of more stee | tran
Ane _stre\ xequiced far balanucl cechon is
called the section \soverreinforced. the _
steel Ie os Cae pon
Sipe : Ana and design of a singy weinfewce Albeam 5
* beam Zoomm wide hocane feck he BSmMm, Z
Cermissib tre. QO conade and cree re
_SNimm>_and a apn of neal 3
AMS areci 6 tee lana / 0 eel LS:+66
Given i.
| conbe, mh = 1
dle. total iampressiveforce te total tensile.”
Cs Ta '
C= bi paee be +6
Eeba+o )
Compressive. foreea SC = be Scbc “¥
= ~J
Tonle —s Toe ee 5 es
force = St a
DX the = Acstxsst 7
a
Y ot steal:
“6 P+ = WOAst a
ba J
Ss
— Scbt ~~ 2c
Séstim . d-xe
a by thectommula> bx 2 =mnAst(d-2)
a
‘
‘ 4 , i; !
mL xc undereloforce K>LC OVET re\ntosce d.
fox_under reinforceal —> My = TAZ
=\Astieet Edie *73)
Vv i = CXz
Q = bx Cone 775) eae Bee |
ee |
—————
E||Standard cores 07 4
ae
- 3) wl ‘2
TT why. aoe
= ee
ve) v w
oh as a
1 4 7
F
i ‘s
wt ,
Qi | A PCC beam 200 ¥ t0OmM= ovetal! clepth 15
atinforced with Bnos A0mmadia bars bottom tover sdrom
som the, cenhre. of tne. reinforcement - 2
alos yar
_Meacand GoodLuck [Pipette |
ee Date
Ataf Steel Ach = Ky x20 7
$942: 42 mm ~
a Similor bfanglee
CUHCal nuelral axis.
schC =i%o |= + =. oe
sst/m A-2Xe 190//3.33 650-2Xe
%e= 24 -08 mm
Beta) neutral axis.
Pee Nh x = m Ast(d-x )
oe
eis xk
300 x +408 % 24 OR = 12.32 x GA2-44 oS
= * C650 -21468)
R= 195 '|\45mm
HePt Oo < 2¢ .') The beam is underreintarce
hence stee.! wi Il reach jt¢ mam permissible
ivolue Sirst
Dace = 1 XZ |
Ast xsset Cd-%) jas-ige
442.44 X190 C650 - 240%)
lO# se x10 6 NM
104< KN-m,
y
»
Wy du
{mum bending moment BM = wA> — iy Wee
F: A F . GoodLuck | Page No
Date EP
-———
Equating max bending moment to moment of
resistance. —
Mr = 8M —
\04-F = 4:5 W
W = 23-266 KN/m
Self wagnt of the beam = C03 x OF x x
ae
= 5-A5KNIM
net welqht of tebeam =.23-266-F95
1 = \8:01G KNIm Be
| Be
H a
Qa\ An RC beam AsdAsD0 mm — (Overalt depth) _ | zi
reinforced with 4nos a2mm dia ba A
conhre of aaa rt espe ts Sum fod. L Hod
| tne toncenhy nicl param of resistance
=SNimm>? lesratiotm) =18:66
Bt = |4ONImm>
Given :- b = ASD mm
D = SDomM 1d = 500- ae - 445mm
Sho = SWitom>
Sst =190Nn)mim>
M =!13:6e ¥ GoodLuck | Page No
Date
4
Hy
Pra of stool 4 ea
15.2055 eras)
By sinfilan piang tet
SCree ee
|| -6stJ/mp Bie ec. "
—
a
= et 2S
| 190feeg 445-%e
| r i.
R= _\SE-43 mm, 7
4 Bids ,
=Actual Neutval axis. % 7
é dy
bm:% = mAst Cdrx) Li
ae : es
Sb KK X = 1S'EE XISLO'SS® CHAS - 2x) a
ee
te 223-924 mm
Hele M>xee -'. the seetion ie over reinforced
op x
az
=z geche _€idg Xa, )
io 6 a Q24% 8 x 46 — 233924
e 5 Ee eS = £
vig ——__
Goodluck | PageNo. >)
Date eet
ss 3 ~J
—==——
i
Genin.
| Nx = 53:04 x10
resichance “ee om
Mire = BM as
5h0q = wl Ta
a
S604 = WXT
4
W = 46432 KN —_
real ee
| Oasxoerl) x25 = 3-1as eNIM a
fending moment = we BIRS RS _ BES \IKN'm
rT Bs oS ihe
flapi Nal _
| loao) js. My -M =
5805 — Veg = 48-985 KN-m.
Me
UAW be the concentraded_lood fn KN ating at 5
Centre of beam GoodLuck | Page No.
Date
a ——
Given’ b, od ) Ast Mest , Ech
Fliod ‘o, ~> Ee = MAst Col-x)
Fiocl 2 > Zaduiay
Equate Mar-+om 4
Mr = Act Sst =z a
i= filet! fees Z
ol Gino) oesc in concrete.
— a
-. Sebo & i |
< estym (-%
an
c., 4
7a x6SommM eval is th 7
tensile reinforcement of 40. diem die baeee 1)
Given‘- b = 350 mm
= 650MM
p= 65D — 2S = 6aASmm = 6AS5 - APF QF
Biot
[2 a 652-5¢mm |
Mr tom
Det eebz, = As Sst (d= %%)
LSamn3 x set x Coag a 2424) reas} $s
$e
Sebo Time ry |
stir Ogee a 4
A ai
Sebc, 6ebe = Die aoe
bs He at ey (o.02 | coe meee i
j
RC Beam 200% F00mm is rinfoxceal with 3
nD aS mm dia bars placed 20mm sam the
of : am 1s subi J
Lag_on of
a
CHven'- b= 300 D = 400mm yy
A = 760 = 30 = 64Omm. 1)
Bc} = mene ™
Sa !
= 1963-49 mm? a
aluut Laxtss
bx Oy Geemeiet iC d~ 2)
“
200 KR y= 13-33 x1963° 49 aC ee)
irs A
= AES*62 mM,
. Sr = = iglics ;
5
Mar = Ast eetaz
= 19g3aare Set x EIA -
WL mi
: SB 4 ! z=
180 KN-m = 130x10° N-mm
u
l
120x108 = 963: AGX Ss tix S84 ES
lést = 112-26 Nm? a
| ifs Find cha iar
ecb | ae Ps a
(cnt
ee
ecHon ae
E Siobete
Ss yen
mm
PemissibI€. chess in concrete.
fermissible. cpeas in gree),
a _Modulars patio: f
Sst/m Ata
Flncl Mrr in the. terms o
SMing =) (aia z 2
= KX Seb fol — Xe
bxxe al ze) aa
a
he
e Mr to ™M
bx 2c. x Kcbe CA=He\ = ™M
Bee ming b, solve the. eq” for ob “ol
b the +toxmula
ae
bec gebt = Ast et oF M= Txe
2 ax =Asteet xz Sloe = Sep seta em
doudlot an is ém
itn oistne beat A pd shaw asin,
adopt M2
De oe phi BSR
w =4OKEN-M 4
L = 60 E
m20 andiFe HS
Eebe. = N/mm ;
Find ac
n étbc = 2a
Bt/m dee +
a Oem or40g Coxe), Rie
: 252 ol 22.6 oAosd = A405 OC :
aa ‘ e LFA HS oAos” see,
\405~ =
L% ae corny \ !
2) Gad Mr 1 s
= Mara CK 2
[= bx 2d se debe |
i a od
= saa (24)
SHASOKRe KF KX OGO4AA
a +
"
: GoodLuck [race na 4
eee Date
Equatin —_ a
E| Moment Moment of reaistance Benoa 5
Sains
eet xg 2 |
ee os kn
at S =
i a ]
Nor — 6 Nemm
Sees = 207106 7
Aas
= 888: 31mm 2 eeg Sagmn, “a
Ast—= ay 42 b
a
pee sea :
Ast ==
it
ci
for libar ast = 3141S mm
ito aie age
Ast ee bx xX ae , : i
oan ” =
Ast X230 = ASdDX O288xgegxr +e
P~
ASt = 974 :03 mm?
ming dia of bay 20mm,
No 'o+ bows = D403 31 2 4nog
3841S = isp Date
i a
“ mr
ft
T %
cc a
Pe psaorm DP / r
af deraling
E
moment of 45° EN-m? if the Beam 6 250mm
‘wide and permissible Sresse) are. \40N/mm~_
and Simm” fos steel and conciete. Nesiqn a.
chon,
{ f
Given- b='45Dmm > a
M =FsRnNem = EG wars D
Gebo = SN )rom*> Bi
6st =196 perio Mir = Cxz. sal
= bxxe x sebe Canze\
aad + oa
= 250% 698d xe (dA - 64980)
ae ageey
= 18307 N-mm
=QUuAtAg ™ to Mor
122 dz = aoe 3 J
d= 640-18mm = 64Omm 4
op COluudar Ast
bAct Got = tprscec, $b.
Bx (40 = oe oo a S
E eeaocs || 28
ia of has os OMmm.
See.) S pra AN ‘ a
echo 1 ps !
CMDB eas. | Similay A 5 —
- eS a ee
\ SB frry Land pia
coi 6cbe, Cao) oO
. “Oe Bee)
k cs eS At = St nx
ees ) Seberrn a
eal £ =, Fat
beam chee Ee ie
a ; ra
' = fs) oF
” CAM 4
ie = Moment of res’
Mas As
= bxx see ee ey
Seed cob zs Ed) wSoeen Goodluck
Date
A. ~~
yas € as } \
= 1k} Scho ba ®
‘2
[= 6933 _ 6904 Ast = Leoxio : q
2 30x0'904 x88 a
-— Tet = 944 mm™ o
po iz
_ section a
.-
a ) Whenthe dimensions of the secon are —___—. "
_ ae sbeicted Chanda) —
2 When the se 3 5! +
poe | 21 . me io
____ |udterdnuen 1
ii f
2) Th comboous T beans. wobere dhe pasivion
E 0 yer middle 5
doubly relo fee ee
| Gq" for Neuhal Aris. iven se0Hon ” PR Bene On_elty
Side of NA are
Ie Moment Of Orea. on compressionside =
Mamont oftarea
2 > on Pim
Moment oF aren ¢ on » tole Side =
hig 4 Ase Cr-d/) + 5m Asc Cay
H Or simplification
= bee 4 Crem—!) Ase Cx-d!)
7
Moment b+ area pn tensile side = MAct
_ ae ‘% + Csm-1) Astle’) = mast (d-x)
By Bpeasion fer miko side fa
| about Jencile sieel + Mament Of equivalent
| rongtole Ante ad-comprective Citel Abouk
ze tee
Ef = Cygy ft C2Z2 ia
(= hier Gan c oF aaa aah SS SS a
q | cs ; — #
[Qe Asowepe +1'5m Ase Sebe fr
| =()em-!) Aec x @tbe ii
_ = =i(a=a) i
as bre Gebe (a- Me )+ Crsm= es
a Ca-a!)
N =r avepareloioncad eochon.
Texcecl iy tise.
ax nvex rel sectan _clirecsH
value of &cbc
6ebC Ce
, f <— 120N]mm>
oe
| Tatking | Moment about densile. are
—
i
Mor = ye Re obec (a= eV Cs sm ~ ~\Jase
a
CLOG ii tt
= 2R0 X94 x AES 6 Csn0- 194)
- es S
“a
= NEGO SENG En
ZNSIC KN Me 100
LCriven dota’: b= 200mm — _B-M6rs
EN-mM ~
if = ADO wD.
1 = 1966 i
| a 480 2e0 oS Os a
Ast = 9A4r Tp X55 1963:4.9 mm> a
2 = 140-39@mI0 ~
Te
Agtc:| =.8% X22
lao calmate obtical numa oxis (a)
actual:
| Gerbec pw +CiSm=\) ASC Ca ve
a z A ASE geeO.
bi obo CRO Due ARs ii
2B
_ ae eo eer iaks'ag (450-2)
ES FV egal 9-9 itn | A a a
a a
e Ce | Ps Ffed a x) Ase
ae toes cape CA + CSm -\) AS
oe Stbe, C A-d he
aks SVOOXIGA Sia eebe (asp 189-32)
Cex ia-eed) x 1140-298 X 0849 Ecbe
f x CAGO~30) i
ae M = 10OKN-M a ENT e
s @quating Mr =M ia
S ;
: [eabo. = SS N/mm]
ala etad est :
an CGPS we =U ls
eae esi) Anam E
a -_
er Sop. 219032. e
Sstheee AGO ANN Ae
[est = 126-62. N/mm
teers Sa = 6¢p ; ce
Scbe re 4
©) | Pinder hoon a0 add 290 i
Mr = bin. cape (d= 90) -(vSin “\) As
a ae “coe CEE TO
subshtule value of een reno 6
Qlequate Me to and ecbe
- — -~
_@ {Bind ext by Shee
7, Find the Act, forms
My = TX Lever Ac
mae Actio. toa Galera
Asto = M1
€s% Ca-d")
c vi) [Find pep = Aa eats.
wih ae ec
> eee as ee a’)
Fee = We 8- *) ———
“tr Sm-')Cxc-3" Re
lh, Ae PCC a fi pion bho
, Tid 2
est]m
wah SANG Hn y
AQ: AG0-%e te
ae Find Ast
eri \ agate apd
bine - stbe” = “Ast SEL
2a om
= Z Z Ast ih iy Mr = brte - cb A= Xe
* 24
My soomuaags + (460-188) —
’ (ay
me
Tite = 4-022 KN ~
ML= 93:49 - 34-022
= 16599 kN a
' lind Aste fn M1 =
mM, =k Ger Ag
TKR oot x Ca-a)
xe
16-428 = Astz x140 x C460 —40)
Aer = 2B 284-4 ¢9nm?
| total Ast
Asti t ASAD
1390 1284-489 = 1664-489 mm
2 “A
———
ie] : ea one
[Asc = 322-65 mm]
Aof 25mm
Providing Aotremmype porter ra
aot es ae or
—
ae : of
eee
—” = ee alae a= 750mm.
BM = 200kKN™M 7
Ecc = IN] mm™ est 2 190N mm —
re M = 18-33 di’ = soon ;
Veto 2. eng enone g
i
ace Scbe Be Aes
ostim da-2¢ i
ee
ge bel ae
_— ae EE SEs | poh! Oe Sa ee
iin 190/332 FSD—-2~C
mn
pe ae
hee MM ard
ee = 2AF-0
Jia ea a
—-
“to ih oe eal de
So ge
pee 2
eee 19
eS eee
ae _
ae Re) a 639° 13.mro~ )
ae
re
aan
ae hy = CML pe es beyhi
! MM) = Neto x 6st Cad)
2-2 RIGS =) RAIS Slane SO
I = ; e
&-| E indste+al Ast
|
| ASH SAgt + Nelo + x0)
—_ = 163813 693.93
| Ast = 9231-36 mm> Cem Ase ‘Coed’
CSm=\) Cxc~ a)
fo eon Bes: 450 ~ 244-02)
\Cexieaa—-
WW C243-00-55)
oe
A
—— revs bars 0 @ bottom
e i of iam c
J aan
sateen ere
— See
: A of 2smmeh_
; -
=e et
“| a ee Element © Ie gubjected to max: shear shtss +
max-_C fre shear zone) and generase
da large nal cracks or shear
cracks.
,
rr
ea ee ~—<— Tmax
wea tago |
'S Subj eded +o both bending 3
ee
al ~ Shear cracks and
CrClOKS ww} be b “4045?
Tmax
* “Ip longisudinal sechi sn
—_M|VerHcal cracks or Hexural cracks:
QM = mox and $F =0 i
©) Diagonal cracks or shear Cracks: \
@_comer_, SF = max and 8BM=0
@]|| Fiexural — Shear cracks:
ber? cuppost and mick ~span uoith <40" 40 45°
Sd avoid the above. types OF Uacks We ned +e
provide cheat rein with tne longiHuolinal
3 __ | lnfrcement:
