Inelastic deformations of mild-steel beams under symmetrical and unsymmetrical cyclic bending

The behavior of cantilever beams under the constraint of symmetrical and unsymmetrical cyclic deflections is investigated. An analytical technique developed predicts the behavior from cyclic moment-curvature relations derived from cyclic-strain control tests. Twenty tests were conducted on rectangular structural-steel sections under pure bending to establish these relations which couple the moment range and mean moment to curvature range. Models are proposed which fit the moment range and mean moment; these models are capable of accommodating, in discrete form, the phenomena of hardening and softening of a structural section as well as relaxation of the mean moment. Nine tests were conducted on cantilever beams under completely and partially reversed tip deflections. The load range changed little with changes in mean deflection. The mean load, in general, relaxed with increased cycling. The theory presented modelled the experimental behavior fairly accurately. It also suggested that the behavior may comprise:

1. an elastic case, where mean load is proportional to load range;
2. an intermediate range where the effects of mean deflection cannot be ignored; and
3. large inelastic cyclic deformation where the effects of mean deflection can be completely ignored except for associated changes in structural geometry and its secondary membrane effect.