Plastic limit loads for pipe bends under combined bending and torsion moment

• Parameter r/t is the main factor influencing the plastic limit loads.
• Plastic limit load is independent on loading path and material constants.
• Estimated equations of limit loads for pipe bends under combined loads are proposed.

In present paper, 3D finite element (FE) method is used to determine plastic limit load solutions for pipe bends under combined bending and torsion moment. With a detailed analysis and comparison, a common awareness for loading effect is showing which will raise researchers concern. By the way, past solutions are not appropriate to estimate FE results. In this respect of finite element analysis, overall yielding considering the spread process of yield region from crown to the straight pipe shows these promising finite element results. A wide range of non-dimensional parameters for pipe bends are considered and plastic limit load solutions are suggested. The results show that r/t is the main factor affecting the limit loads. Plastic limit load is independent on the loading path and material constants by normalizing. Results show that the circular interaction rule is a great approximation for pipe bends under combined bending and torsion moment. A series of approaches are confirmed in order to validate our finite element method on plastic limit analysis. Based on the finite element results, approximate plastic limit load solutions are proposed. Present work will further improve the limit load solution for pipe bends under complex loading conditions.