Nonlinear Material Behavior of the Bridge Components - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 69

cross section ¼ 2 A c / u , where A c is the concrete cross-sectional area and u is
the perimeter of that part of the cross section, which is exposed to drying.
The autogenous shrinkage strain can be calculated as follows:
e ca ðÞ¼b as ðÞe ca ðÞ 2 : 18 Þ

where

Þ 10 6 e ca ðÞ¼ 2 : 5 f ck 10 ð ð 2 : 19 Þ

and

2 t 0 : 5 b as ðÞ¼ 1 exp 0 : ð 2 : 20 Þ

2.3.4 Stress-Strain Relation of Concrete for Nonlinear
Structural Analysis
In nonlinear structural analysis and in nonlinear finite element modeling,
concrete material should be carefully treated. In the absence of experimental
data, design rules specified in current codes of practice can be adopted. As an
example, EC2 [ 2.27 ] provides the relation between s c and e c shown in
Figure 2.5 (compressive stress and shortening strain shown as absolute values
and the use of 0.4 f cm for the definition of E cm are approximates) for short-
term uniaxial loading, which is described by the following expression:

2

s c
f cm ¼

k

ð 2 : 21 Þ

1+ k 2 ð Þ

s c

f cm

0.4 f cm

a

e c
Figure 2.5 Schematic representation of the stress-strain relation for structural analysis
specified in EC2 [ 2.27 ] .

e c1 e cu1