Equilibrium models for lower bound limit analyses of reinforced concrete slabs

The paper addresses lower bound limit analyses of reinforced concrete slabs. The assessment problem is formulated in terms of static variables representing hyperstatic fields of moment, and constraints based on biconic yield criteria. These fields are generated directly within triangular Kirchhoff and Reissner–Mindlin type elements, are highly localised, and lead to very sparse matrices for optimisation programmes. Methods of forming particular equilibrating solutions are presented, which include those recovered from a yield line solution based on the same mesh of elements. Numerical examples are presented with Kirchhoff type elements, including the benchmark problem of a square plate with fixed supports.