Serviceability limit state - Eurocodes

N s
ε
σ
σ c,1
Cracking of concrete (initial crack formation)
L es
σ c,1
w
ε s
ε c
L es
σ s
σ s,1
L es
L es
σ s,1
σ s,2
L es
ρ
Δσ s
s
A
=
A
s
c
N s
Equilibrium in longitudinal direction:
σ
s
A
A s
ρ s
f ctm
s
=
σ
s,1
A
s
+ σ
c,1
A
c
G. Hanswille
Univ.-Prof. Dr.-Ing.
Institute for Steel and
Composite Structures
University of Wuppertal-Germany
Compatibility at the end of the introduction
length:
σs,1
σc,1
εs,1
=εc,1
⇒ =
E E
σs,1
=
σs
⎡
⎢
⎣
s
c
ρs
no
⎤
1+ ρ
⎥
s no
⎦
s
o
E
n o =
E
Change of stresses in reinforcement
due to cracking:
σ
Δσ
s
s = σs
− σs,1
=
1+
ρ n
N
s,r
= f
ctm
A
c
( 1+
ρ n )
s
o
cross-section area of reinforcement
reinforcement ratio
mean value of tensile strength of concrete
s
c
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