The interaction between physical instability and geometric (2nd-order) effe
cts in plane frames is investigated herein within a finite element based ma
thematical programming framework, under the assumptions of quasistatic load
ing and lumped plasticity. The sources of physical instability consist of i
nelastic bending hinges characterized by softening nonholonomic (irreversib
le) moment versus rotation constitutive laws. The complex and insightful re
sponse spectrum which can arise is illustrated with the aid of simple, albe
it instructive, reference examples. Stability domains are obtained for thes
e examples in the space of the parameters characterizing the level of membe
r axial force and the amount of hinge softening. Such domains highlight var
ious key features, which are briefly commented upon, of the interplay betwe
en physical and geometric effects. (C) 1998 Elsevier Science Ltd. All right
s reserved.