Displacements of cracked members - Concrete Structures: Stresses and Deformations - page 290

representing the mean curvature starts to deviate from the curve for
state 1 and quickly becomes closer to the curve for state 2. Thus,
prediction of de

ection in design may start by considering state 2 which
gives the upper bound for de

fl

fl ection and the designer may fi nd this

computation su cient when the upper bound is not excessive.

Solution of this example is done, using no graphs in order to demon-
strate the computation for a general case with any cross-section. How-
ever, with a rectangular section, the graphs in Figs 3.5 and 7.4-7.6 can
be used to determine the section properties involved in the calculation.
Additional graphs are presented in Chapter 9 which further simplify
the prediction of de

fl ection when the cross-section is a rectangle.

Example 8.5 Pre-tensioned simple beam: variation of curvature
over span
Find the mean curvature at a section at mid-span of a partially
prestressed beam shown in Fig. 8.9(a), after application of a live

Figure 8.9 Curvature of a partially prestressed beam (Example 8.5): (a) tendon
profile; (b) curvature after creep and shrinkage and application of live
load. For beam cross-section see Fig. 7.12(a).