Nonlinear Material Behavior of the Bridge Components - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 68

shrinkage strain develops during hardening of the concrete, with the major
part therefore developing in the early days after casting. Autogenous shrink-
age is a linear function of the concrete strength. It should be considered spe-
cifically when new concrete is cast against hardened concrete. Hence, the
values of the total shrinkage strain e cs can be calculated as follows:

e cs ¼ e cd + e ca ð 2 : 15 Þ

where e cs is the total shrinkage strain, e cd is the drying shrinkage strain, and e ca
is the autogenous shrinkage strain. The final value of the drying shrinkage
strain e cd, 1 is equal to k h e cd,0 . e cd,0 may be taken from Table 2.10 . The devel-
opment of the drying shrinkage strain in time can be calculated as follows:
e cd ðÞ¼b ds t , tð ke cd , 0 ð 2 : 16 Þ

where k h is a coefficient depending on the notional size h 0 according to
Table 2.11 :

ð t t s Þ

e cd ðÞ¼ p

h 0

ð 2 : 17 Þ

ð t t s Þ +0 : 04

where t is the age of the concrete at the moment considered in days and t s is
the age of the concrete (days) at the beginning of drying shrinkage (or swell-
ing). Normally, this is at the end of curing; h 0 is the notional size (mm) of the

Table 2.10 Nominal Unrestrained Drying Shrinkage Values e cd0 (%) for Concrete with
Cement CEM Class N Specified in EC2 [ 2.27 ]

Relative Humidity (%)

20 40 60 80 90 100

f ck /f ck,cube

20/25 0.62 0.58 0.49 0.30 0.17 0.00

40/50 0.48 0.46 0.38 0.24 0.13 0.00

60/75 0.38 0.36 0.30 0.19 0.10 0.00

80/95 0.30 0.28 0.24 0.15 0.08 0.00

90/105 0.27 0.25 0.21 0.13 0.07 0.00

Table 2.11 Values for k h Specified in EC2 [ 2.27 ]
h 0 K h

100 1.00

200 0.85

300 0.75

500 0.70