Nonlinear Material Behavior of the Bridge Components - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 66

where f cm ( t ) is the mean concrete compressive strength at an age of t days, f cm
is the mean compressive strength at 28 days according to Table 2.9 , b cc (t) is a
coefficient that depends on the age of the concrete t , t is the age of the con-
crete in days, and s is a coefficient that depends on the type of cement. The
value of s is equal to 0.2 for cement of strength classes CEM 42,5 R, CEM
52,5N, and CEM 52,5 R (class R). The value of s is equal to 0.25 for cement
of strength classes CEM 32,5 R and CEM 42,5N (class N). The value of s is
equal to 0.38 for cement of strength class CEM 32.5N (class S). The tensile
strength refers to the highest stress reached under concentric tensile loading.
Where the tensile strength is determined as the splitting tensile strength,
f ct,sp , an approximate value of the axial tensile strength, f ct ,maybetakenas
f ct ¼ 0

9 Þ
The development of tensile strength with time is strongly influenced by
curing and drying conditions and by the dimensions of the structural mem-
bers. As a first approximation, it may be assumed that the tensile strength
f ctm ( t ) can be calculated based on the values of f ctm , given in Table 2.9 , as
follows:

: 9 f ct , sp ð 2 :

a

f ctm ðÞ¼ b cc ðÞ ð Þ f ctm ð 2 : 10 Þ

where

a¼ 1 for t < 28

ð 2 : 11 Þ

a¼ 2 = 3 for t 28

According to EC2 [ 2.27 , 2.28 ] , the elastic deformations of concrete
largely depend on its composition (especially the aggregates). The values
given in EC2 should be regarded as indicative for general applications.
However, they should be specifically assessed if the structure is likely to
be sensitive to deviations from these general values. The modulus of elastic-
ity of a concrete is controlled by the moduli of elasticity of its components.
Approximate values for the modulus of elasticity E cm , secant value between
s c ¼ 0 and 0.4 f cm , for concretes with quartzite aggregates, are given in
Table 2.9 . For limestone and sandstone aggregates, the value should be
reduced by 10% and 30%, respectively. For basalt aggregates, the value
should be increased by 20%. According to EC2, variation of the modulus
of elasticity with time can be estimated as follows:

0 : 3

12 Þ
where E cm ( t ) and f cm ( t ) are the values at an age of t days and E cm and f cm are
the values determined at an age of 28 days. Poisson's ratio ( u c ) may be taken

E cm ðÞ¼ f cm ðÞ= ð f cm Þ E cm ð 2 :