The effects of a distributed radial load on an elbow or bend within a piping system, caused by large changes in momentum due to fluid flow, are often represented by a single force. The method presented here will result in more accurate results. In this paper, equations are derived to predict deformations of a pipe bend or curved beam cantilever at its free end due to a uniformly distributed radial force. Assuming isotropic, linearly elastic materials of uniform cross section, uniform bend radius, and small deformations, equations are derived using Castigliano’s theorem. Deformation due to shear and axial stresses is also considered. Derived equations are validated through a case example which compares them to a model consisting of a number of straight beam elements assembled to model a curved beam. The example demonstrates that free end deformations can be integrated into a piping analysis program by using the direct stiffness method in order to obtain the resulting displacements, forces, and moments that result from restraint of the bend due to the stiffness of the attached pipe.

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