Serviceability limit state - Eurocodes
Serviceability limit state - Eurocodes
Serviceability limit state - Eurocodes
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Stresses in reinforcement for final crack<br />
formation<br />
G. Hanswille<br />
Univ.-Prof. Dr.-Ing.<br />
Institute for Steel and<br />
Composite Structures<br />
University of Wuppertal-Germany<br />
Δσ p2<br />
σ s2<br />
Δσ p2<br />
Δσ p1<br />
σ s1<br />
σ s<br />
A s , d s<br />
A p , d p<br />
σ c<br />
σ c =f ct,eff<br />
x<br />
Equilibrium at the crack:<br />
N − P<br />
Maximum crack spacing:<br />
f<br />
s<br />
ct<br />
δ<br />
s<br />
A<br />
r,max<br />
σ<br />
c<br />
s2<br />
o<br />
= δ<br />
s<br />
=<br />
d<br />
=<br />
2τ<br />
− σ<br />
=σ<br />
p<br />
r,max<br />
=<br />
2<br />
s1<br />
s2<br />
sm<br />
σ<br />
s<br />
s<br />
=<br />
s2<br />
A<br />
[ τ n d π + τ n d π ]<br />
f<br />
(A<br />
sm<br />
ct,eff<br />
s<br />
r,max<br />
s<br />
A<br />
+ ξ<br />
c<br />
2<br />
U<br />
A<br />
− β( σs2<br />
− σs1)<br />
Δσp,2<br />
− β(<br />
Δσp2<br />
− Δσ<br />
=<br />
E<br />
E<br />
s<br />
s<br />
A<br />
Compatibility at the crack:<br />
s<br />
2<br />
+ Δ σ<br />
s<br />
s<br />
p2<br />
p<br />
τ<br />
)<br />
sm<br />
pm<br />
Equilibrium in longitudinal direction:<br />
A<br />
p<br />
σ<br />
p2<br />
p<br />
p<br />
− σ<br />
p1<br />
s<br />
=<br />
r,max<br />
2<br />
p<br />
U<br />
A<br />
p<br />
p<br />
τ<br />
pm<br />
p1<br />
)<br />
s r,max<br />
mean crack spacing: s r,m ≈2/3 s r,max<br />
39
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