A numerical procedure for calculating the limit loads is suggested. These loads operate on discrete gradient mechanical systems. A part of elements of these systems can already work at the softening stage. The method is illustrated using the problem of tension and torsion of a framed structure of nonlinear material. The non-convex potential (that describes the stable material condition - strengthening and unstable - softening) determines the properties of this material. This numerical procedure allows one to avoid solving the nonlinear equilibrium equation with a step-by-step increase of the loading and estimating the stiffness for each of these equilibrium states in determining the load values leading to the collapse of the system.
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