Behavior of Elastic-Plastic Trusses with Unstable Bars

Sufficient conditions for uniqueness of incremental response and overall stability are established and discussed for elastic plastic trusses containing unstable members. These criteria consist of the positive definiteness of matrices built up with the elastic influence coefficients of bar-forces for dislocations and with the plastic compliances of the members at the yield point. All conditions are proven to be weaker than the usual demand of local stability, for all redundant structures. Normality of the incremental plastic displacement vector in load-space is shown to hold, irrespective of instability, non-linearity in the elastic range and changes of the elastic behavior due to plastic strains. Convexity of the loading surfaces is also briefly discussed, with special reference to the case of non-linear elastic response of some members.