Numerical analysis of piping elbows for in-plane bending and internal pressure

This work presents the development of two different finite piping elbow elements with two nodal tubular sections for mechanical analysis. The formulation is based on thin shell displacement theory, where the displacement is based on high-order polynomial or trigonometric functions for rigid-beam displacement, and uses Fourier series to model warping and ovalization phenomena of cross-tubular section. To model the internal pressure effect an additional formulation is used in the elementary stiffness matrix definition. Elbows attached to nozzle or straight pipes produce a stiffening effect due to the restraint of ovalization provided by the adjacent components. When submitted to any efforts, the excessive oval shape may reduce the structural resistance and can lead to structural collapse. For design tubular systems it is also important to consider the internal-pressure effect, given its effect on the reduction of the pipe flexibility. Some conclusions and examples are compared with results produced by other authors.