Creep and shrinkage of concrete and relaxation of steel - Concrete Structures: Stresses and Deformations - page 8

Figure 1.4 Relaxation reduction coefficient r .

and relaxation, and ∆ σ pr is the intrinsic relaxation as would occur in a

constant-length relaxation test.
The value of the total loss is generally not known a priori , because it
depends upon the reduced relaxation. Iteration is here required: the total loss
is calculated using an estimated value of the reduction factor

χ r (for example

0.7) which is later adjusted if necessary (see Example 3.1).
Appendix B gives the derivation of the relaxation reduction coe cient

values in Table 1.1 and the graphs in Fig. 1.4. The values given in the table
and the graphs may be approximated by Equation (B.11).

1.6 Creep superposition
Equation (1.2) implies the assumption that the total strain, instantaneous
plus creep is proportional to the applied stress. This linear relationship, which
is generally true within the range of stresses in service conditions, allows
superposition of the strain due to stress increments or decrements and due to
shrinkage. Thus, when the magnitude of the applied stress changes with time,
the total strain of concrete due to the applied stress and shrinkage is given by
(Fig. 1.5):