Environmental Engineering Reference
In-Depth Information
where
f
ctm
mean value of concrete tensile strength to DIN 1045-1 [33] Tables 9 or 10.
f
yk
characteristic value of yield point of steel reinforcement
E
s
E
c0
¼ g
C
E
s
E
c0m
a
Ed
¼
where
E
c0m
see DIN 1045-1 [33] Tables 9 or 10
2)
From this we get the minimum reinforcement (see Table 3.2):
f
ctm
f
yk
a
Ed
f
ctm
r
s
>
3.2.3 Non-linear stress-strain curve for prestressing steel
We generally assume an idealised bilinear curve (see Figure 3.4).
According to [36], the maximum strain in the prestressing steel at the ultimate limit
state is
e
pud
¼ e
ð
0
Þ
p
þ
25
%
0
:
9
e
puk
Provided the upper limit (0.9
e
puk
) does not govern, the reinforcing steel can be used
up to the design value of its maximum strain (
e
sud
¼
25
%
) in the case of pretensioning
or post-tensioning (Figure 3.5).
Table 3.2 Minimum percentage of reinforcement for ductile behaviour of structural member
Concrete
f
ck
[MPa]
f
ctm
[MPa]
E
c0m
[GPa]
a
Ed
min
r
s
[%]
C 12/15
12
1.57
25.8
11.63
0.33
C 16/20
16
1.90
27.4
10.95
0.40
C 20/25
20
2.21
28.8
10.42
0.46
C 25/30
25
2.56
30.5
9.84
0.54
C 30/37
30
2.90
31.9
9.40
0.61
C 35/45
35
3.21
33.3
9.01
0.68
C 40/50
40
3.51
34.5
8.70
0.75
C 45/55
45
3.80
35.7
8.40
0.81
C 50/60
50
4.07
36.8
8.15
0.87
2)
According to [36], other values apply for the tangent moduli (see above).
