Limit analysis of reinforced concrete beams under combined bending and torsion using linear programming - Llorin, Maria Genelin D. (2001)
In this study, a general, systematic and efficient approach to limit analysis of reinforced concrete beams under combined bending and torsion is presented. It entails the replacement of a continuous perfectly plastic structure into a discrete mathematical model. It is then formulated as a mathematical programming problem using the static theorem of plasticity. This theorem states that the load on a perfectly plastic structure, corresponding to any arbitrary stress field that is in equilibrium with the load and nowhere violates the yield condition, is a lower bound to the actual collapse load. The discretization is done by writing the equilibrium equations of the discretized structure, and is combined with piecewise linearization of the non-linear yield curve, thereby converting the formulation into a linear programming problem. The yield curves are obtained by utlizing the plastic space-truss theory. To demonstrate the application of the proposed method, the collapse loads of spandrel and circularly curved reinforced concrete beams are presented. The results of the analysis of these beams show that skew-bending theory and the space-truss theory can both be used to derive the interaction diagrams for combined bending and torsion.