On the bounding of limit multipliers for combined loading

In the framework of classical plasticity, even when limit multipliers and collapse mechanisms associated with different loads independently acting on a solid or structure are known, not much can be inferred on the limit multiplier of the combined loading. Frame structures under the action of dead loads and seismic forces, soil-foundation interaction problems, tunnels under a variety of loads, deepwater pipelines subject to bending and pressure constitute only a few selected examples for which some sort of superposition rule, as well as bounding techniques, would be extremely useful. The present paper introduces a set of theorems for bounding limit multipliers for combined loads. In particular, ranging from a minimum knowledge about the critical state under a particular loading to a reasonable guess of the kinematics of the problem under combined loads, more and more refined bounds for the overall limit multiplier are derived. The results, to the best of the authors' knowledge, are novel and a few examples showing their practical value are presented and discussed.