Simplified prediction of deflections - Concrete Structures: Stresses and Deformations - page 318

9.6 Simplified procedure for calculation of
curvature at a section subjected to M and N
Favre et al. 3 suggest the following approximation for the mean curvature at a
cracked section subjected to a moment and a normal force.
Consider a reinforced concrete section subjected at time t 0 to a moment M
and a normal force N located at the centroid of the gross concrete section
(Fig. 9.5). The force N in this

gure is assumed to be compressive, but the
discussion applies also when the normal force is tensile. The graph repre-
sents the variation of instantaneous curvature, excluding creep, when N is
kept constant and M increased gradually from zero. The straight line AB
represents the curvature

fi

ψ 1 ( t 0 ) in state 1. In the case when the section has
heavier reinforcement at the bottom than at the top, the centroid of the
transformed uncracked section at time t 0 is slightly lower than the centroid

Figure 9.5 Moment versus curvature in presence of constant normal force: (a) actual graph;
(b) idealized graph.