Effects of temperature - Concrete Structures: Stresses and Deformations - page 376

varies over the depth as shown in Fig. 10.13(b). Figures 10.13(c) and (d) show
the distributions of strain and stress if the section is considered of homo-
geneous elastic material. The values shown may be checked by the method
presented in Section 10.7 with the following data:

E c = 30.0 GPa (4350 ksi); α t = 1 × 10 −5 per ° C (0.6 × 10 −5 per ° F).

The same cross-section is considered cracked at the bottom or at the top
and provided with 1 per cent reinforcement (6000 mm 2 (9.30 in 2 ) ) at the
cracked face (Figs 10.14(a) and (d) ). Concrete is ignored over a cracked zone
of depth 0.467 m (18.4 in). The distributions of strain and the self-
equilibrating stresses due to the temperature rise in Fig. 10.13(b) are shown in
Figs 10.14(b) and (c) when the cracking is at the bottom and in Figs 10.14(e)
and (f) when the cracking is at the top. The values shown in these

gures are
obtained by application of Equations (2.21), (2.22), (2.29) and (2.30) and
employing the following properties of the transformed section:

fi

α = E s / E c =

6.67; area, A = 0.223 m 2 (346 in 2 ); moment of inertia about centroidal axis, I =

9.00 × 10 −3 m 4 (21 600 in 4 ).
Comparison of the stress values in Figs 10.13(a), 10.14(c) and 10.14(f)
indicates that the self-equilibrating stresses caused by temperature are gener-
ally smaller in the cracked section. However, the corresponding strain values
and particularly the curvatures,

erent (Figs 10.13(c),
10.14(b) and 10.14(e) ). It follows that the strains and hence the displacements

∆ ψ are not much di ff

Figure 10.14 Distributions of strain and self-equilibrating stresses in a cracked reinforced
concrete section due to a temperature rise shown in Fig. 10.13(b):
(a) cracking at bottom face; (b) strain; (c) stress; (d) cracking at top face;
(e) strain; (f) stress.