Nonlinear Material Behavior of the Bridge Components - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 70

where ¼e c / e c1 , where e c1 is the strain at peak stress according to Table 2.9 ,

and k¼ 1.05 E cm | e c1 |/ f cm , where f cm is taken from Table 2.9 . Expres-
sion (2.21) is valid for 0 < | e c |

< e cu1 , where e cu1 is the nominal ultimate

strain.
According to EC2 [ 2.27 , 2.28 ] , the value of the design compressive
strength is defined as follows:

22 Þ
where g C is the partial safety factor for concrete and a cc is the coefficient
taking account of long-term effects on the compressive strength, which is
recommended to be taken as 1.0. The value of the design tensile strength,
f ctd , is defined as follows:

f cd ¼a cc f ck = g C ð 2 :

f ctd ¼a ct f ctk , 0 : 05 = g C ð 2 : 23 Þ

where a ct is a coefficient taking account of long-term effects on the tensile
strength, which is recommended to be taken as 1.0.

2.3.5 Stress-Strain Relations for the Design of Cross Sections
To design concrete cross section, simplified stress-strain curves can be
adopted to ease hand calculations. As an example, for the design of cross sec-
tions using EC2, the following stress-strain relationship is recommended (see
Figure 2.6 ) (compressive strain shown as positive):

n

e c
e c2

s c ¼ f cd 1

1 for 0 e c e c2

ð 2 :

24 Þ

s c ¼ f cd for e c2 e c e cu2 ð 2 : 25 Þ

where n is the exponent according to Table 2.9 , e c2 is the strain at reaching
the maximum strength according to Table 2.9 , and e cu2 is the ultimate strain
according to Table 2.9 . Other simplified stress-strain relationships may be
used if equal to or more conservative than the nonlinear one, for instance,
bilinear according to Figure 2.7 (compressive stress and shortening strain
shown as absolute values) with values of e c3 and e cu3 according to Table 2.9 .
A rectangular stress distribution (as given in Figure 2.8 ) may be assumed.
The factor l , defining the effective height of the compression zone, and the
factor , defining the effective strength, can be taken as follows:

l¼ 0 : 8 for f ck 50 Mpa

ð 2 : 26 Þ

l¼ 0 : 8 f ck 50 ð Þ= 400 for 50 < f ck 90 Mpa