A method to estimate plastic loads for elbows with non-uniform thicknesses

This paper provides a method to estimate plastic loads [defined by the twice-elastic-slope (TES)]for elbows with non-uniform thicknesses under in-plane bending and under internal pressure, based on systematic FE limit analyses using elastic-perfectly plastic materials. The intrados thickness is assumed to be up to 30% thicker than the straight pipe thickness, whereas the extrados thickness up to 30% thinner. The FE plastic loads are compared with estimated ones using closed-form approximations for elbows with uniform thicknesses, to provide guidance on the choice of a representative thickness to predict plastic loads for elbows with non-uniform thicknesses. Results suggest that the use of the straight pipe thickness gives overall satisfactory predictions. Estimated plastic loads are conservative, and differ from FE results by less than 10% for all cases considered. Despite its simplicity, results look very promising, and thus the use of the straight pipe thickness can be recommended to estimate plastic loads for elbows with non-uniform thicknesses in practice.