Physical instability and geometric effects in frames

The interaction between physical instability and geometric (2nd-order) effects in plane frames is investigated herein within a finite element based mathematical programming framework, under the assumptions of quasistatic loading and lumped plasticity. The sources of physical instability consist of inelastic bending hinges characterized by softening nonholonomic (irreversible) moment versus rotation constitutive laws. The complex and insightful response spectrum which can arise is illustrated with the aid of simple, albeit instructive, reference examples. Stability domains are obtained for these examples in the space of the parameters characterizing the level of member axial force and the amount of hinge softening. Such domains highlight various key features, which are briefly commented upon, of the interplay between physical and geometric effects.