3D-curved beam element with varying cross-sectional area under generalized loads

This article deals with the stiffness matrix and the equivalent load vector of a 3D-curved beam element with a variable cross-section under generalized loads. The linear ordinary differential system equation governing its structural behaviour is presented, and the boundary value problem is solved by the application of a recurrence scheme obtained by relating the internal forces and deformation at the two end points of an increase in the centroid line. This solution has a transfer matrix structure. Both the stiffness matrix and the equivalent load vector are obtained arranging the transfer matrix. The calculation method used was compared with other methods in the literature and the exact values demonstrated by means of four examples: a straight cantilever beam with a variable rectangular cross-section, a bi-fixed circular arch, a variable cross-section circular helix and a parabolic arch.