Elastic-plastic behavior of elbows with various geometric parameters and under various bending modes were investigated by 3-dimensional(3D) non-linear finite element(FE) analysis

assuming material behavior was elastic-perfectly-plastic and taking geometric nonlinearity into account.The influences of geometric parameters and bending mode on plastic carrying capacities were studied systemically

and closed form equations of plastic limit loads for uncracked elbow involving effect of tangent pipes were also obtained.Non-linear finite element(FE) analysis indicates that

the influences of geometric nonlinearity on plastic carrying capacities are significant;elbow exhibits dramatically different behaviors at the elastic-plastic states when subjected to in plane opening bending moment and closing bending moment

and the plastic limit load values are varied obviously under both of the bending modes;the ratio of wall thickness and the cross-section radius is the most significant influence factor on plastic carrying capacities of elbow

followed by the bending mode.