Plastic Analysis of Curved Beams under Point Loads

An interaction equation, with values of bending moment and torsion at full plasticity of the section, based on results in the literature, is used in the analysis. The effect of shear force is neglected and it is assumed that the cross-sectional properties of the beam do not vary along its length. The possible modes of failure for beams with one and two concentrated loads are reviewed in detail; it is shown that certain transition modes, not previously described in the literature, are essential for a complete solution. In addition, modes of failure for beams without bending or torsional restraint at the supports are given for the case of a single point load. Methods of solution described are based on a lower bound approach and where the application of the yield criterion at the plastic hinges does not give sufficient equations, the solution is obtained by means of optimization procedure. Complete results plotted in nondimensional form are given for typical beams.