Civil Engineering Reference
In-Depth Information
d
L
d
s1
160
140
140
ε
L
;
0
ε
s1
;
0
?
ε
s1
;
0
ε
c
;
0
0
:
72
0
:
72
0
:
20
0
:
86 mm
=
m
?
d
s1
The variables
ε
L
=
4.04 and
ε
c
=
1.74 were determined iteratively with the following
two conditions:
m
Rd
m
Ed
F
s1d
F
Ld
F
cd
The internal forces and the resistance of the cross-section are determined below in order
to check these
figures and to demonstrate the method of calculation. The internal
compressive force in the concrete is
F
cd
b
?
x
?
f
cd
?
α
R
b
?
ξ
?
d
L
?
f
ck
?
α
cc
γ
c
?
ε
12
ε
c
c
2
2
c
ε
c
ε
c
ε
L
ε
L
;
0
0
1
:
5
?
ε
:
85
12
ε
c
1000
?
?
160
?
20
?
2
1
:
74
2
12
1
:
74
1
:
74
6
:
27
0
:
86
0
:
85
1
:
5
?
1
:
74
2
1000
?
?
160
?
20
?
288
:
69 kN
=
m
The tensile forces in the strip and the reinforcing steel can be determined via the strains,
modulus of elasticity and cross-sectional areas. When determining the tensile force
acting on the reinforcing steel, however, it should be remembered that the reinforcement
is yielding at the calculated strip strain:
F
Ld
a
L
?
E
L
?
ε
L
140
?
170
?
4
:
04
96
:
08 kN
=
m
a
s1
?
f
yk
γ
s
43
?
10
2
4
:
?
500
F
s1d
192
:
61 kN
=
m
1
:
15
To check the iteration, the sum of the internal forces is calculated. As this equals zero,
the boundary condition for the iteration is satis
ed.
F
s1d
F
Ld
F
cd
192
:
61
96
:
08
288
:
69
0
We can use the relative depth of the compression zone and coefficient
k
a
(for
ε
c
>
2mm/m), which is the result according to Section3.2,todeterminetheinternal
lever arms:
ε
c
ε
c
ε
L
;
0
ε
L
1
:
74
ξ
86
0
:
26
1
:
74
4
:
04
0
:
ε
c
24
4
?
ε
c
8
74
24
4
?
17
:
4
0
:
37
8
1
:
k
a
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