Draft
12.2FlexuralStresses 203
- PeandM 0 +MDL+MLL
f 1 =
Pe
Ac
1
ec 1
r
2
M 0 +MDL+MLL
S 1
f 2 =
Pe
Ac
1 +
ec 2
r
2
M 0 +MDL+MLL
S 2
(12.7)
Theinternalstressdistributionat each oneof thosefourstagesis illustratedby Fig.12.7.
S 2Mo
+S 2
e c 2c 1Pi e cIc2
Stage 1Stage 2Stage 4re c
2 )P i( 1 + 2AcMo
+
S 2 re c
2 )P i( 1 + 2AcP iAcP iAcPi e c 1IcP iAc( 1 -
re c
2(^1) )
r
e c
2 )
P i( 1 + 2
Ac
P i
Ac
( 1 -
r
e c
2
(^1) ) -Mo
S 1
MoS 1( 1 -
re c
2P i (^1) )
Ac
Ac
P e
MoS( 1 -
re c
2(^1) ) - Md + Ml
S
- S 1
MtAcP e
( 1 -
re c
2(^1) )
Md + Ml
S
- Mt
r
e c
2 )
( 1 +^2
Ac
P e
r
e c
2 )
( 1 +^2
Ac
P e Mo
- Mt
S 2 2
1 1
Figure12.7: FlexuralStressDistributionfora BeamwithVariableEccentricity; Maximum
Moment SectionandSupportSection,(Nilson1978)
17 Those(service)
exuralstressesmustbe below thosespeci edby theACIcode(wherethe
subscriptsc,t,iandsreferto compression,tension,initialandservicerespectively):
fci permittedconcretecompressionstressat initialstage : 60 f
0
ci
fti permittedconcretetensilestressat initialstage < 3
q
f
0
ci
fcs permittedconcretecompressive stressat servicestage : 45 f
0
c
fts permittedconcretetensilestressat initialstage 6
p
f
0
cor 12
p
f
0
c
Notethatftscanreach 12
p
f
0
c
onlyif appropriatede
ectionanalysisis done,becausesection
wouldbe cracked.
18 Basedontheabove, we identifytwo types of prestressing: