Structural analysis of a curved beam element defined in global coordinates

In this article, a system of twelve differential equations expressed in the global Cartesian coordinate system to simulate the structural behavior of a general curved beam element, is presented. Different shape geometry of the curved centroid line, shearing deformations, varying cross section area, non-symmetric section and generalized loads are taken into account. The lower-triangular form of the system of equations permits the determination of analytical results through successive simple integrations row by row. Exact analytical solutions and expressions of transfer and stiffness matrices for widely spread cases of curved beams such as the circular arch and balcony, are provided. Likewise, numerical accurate results for the case of variable cross-section cantilever and circular helical beam are given in the examples for verification.