Effects of temperature - Concrete Structures: Stresses and Deformations - page 375

Calculation of stresses caused by temperature on cracked structures is com-
plex. Simplifying assumptions are necessary to make the calculations reason-
ably simple. In the following, we shall consider that cracking is produced by
loads other than temperature and assume that the depth of the compression
zone remains unchanged by the e

ect of temperature. With these assump-
tions, the analysis of the self-equilibrating stresses in a statically determinate
structure or the continuity stresses in an indeterminate structure may be
performed in the same way as discussed in Sections 10.7 and 10.8. But the
actual cross-section of the members must be replaced by a transformed
section composed of the area of concrete plus

ff

α times the area of steel; where

α = E s / E c is the ratio of the modulus of elasticity of steel to that of concrete.

For qualitative assessment of the e ect of cracking, we consider the cross-

section in Fig. 10.13(a) of a statically determinate structure and calculate
the self-equilibrating stresses and the strain due to a temperature rise which

ff

Figure 10.13 Distributions of strain and self-equilibrating stresses due to temperature in a
homogeneous elastic cross-section: (a) concrete cross-section; (b)
distribution of temperature rise; (c) strain; (d) stress.