Civil Engineering Reference
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following strip area:
t
L
?
b
L
5
?
h
?
1m
1
4
?
100
5
?
160
?
1000
:
175 mm
2
a
L
=
m
In the rest of this example it is assumed that the strain in the strip is reached without the
concrete compression zone in the cross-section failing. Owing to the continuous
longitudinal reinforcement and the distribution of the bending moment, the analysis
is only carried out at mid-span for the maximum moment.
The admissible tensile force in the CFRP strip is therefore given by the ultimate strain,
the modulus of elasticity and the strip area:
F
Ld
a
L
?
ε
Ld
;
max
?
E
L
4
:
20
?
175
?
170
124
:
86 kN
=
m
The prestrain condition at the level of the strip is given by the prestrain determined in
Section 4.3:
d
L
d
s1
d
s1
160
140
140
:
ε
L
;
0
ε
s1
;
0
?
ε
s1
;
0
ε
c
;
0
0
75
0
:
75
0
:
21
0
:
88 mm
=
m
?
The total strain at the bottom edge of the cross-section is therefore
ε
L
;
0
ε
0
:
88
4
:
20
5
:
08 mm
=
m
Ld
;
max
As a result of this strain, which is twice the yield strain of grade BSt 500 steel, it is
assumed that the reinforcing steel is yielding. The tensile force in the reinforcing steel
is therefore
a
s1
?
f
yk
γ
s
43
?
10
2
4
:
?
500
F
s1d
192
:
61 kN
=
m
1
:
15
Assuming a compressive strain in the concrete
ε
c
>
2mm/m leads to the following
expression for the compressive force in the concrete according to Section 3.2:
2
c
f
ck
γ
c
?
ε
12
ε
c
F
c
b
?
x
?
f
cd
?
α
R
b
?
ξ
?
d
L
?
α
cc
?
2
ε
c
ε
c
ε
L
;
0
ε
Ld
;
max
ε
12
ε
c
c
20
1
:
5
?
1000
?
?
160
?
0
:
85
?
2
Equilibrium of the internal forces results in an equation to calculate the compressive
strain in the concrete:
F
s1d
F
cd
Solving the equation results in
ε
c
=
1.84mm/m. As this value is
>
2mm/m, the above
assumption was justi
ed. The relative depth of the compression zone can now be
determined with the help of the strains:
F
Ld
ε
c
ε
c
ε
L
;
0
ε
Ld
;
max
84
1
:
84
5
:
08
0
:
27
1
:
ξ
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