Higher-order horizontally-curved beam finite element including warping for steel bridges

The flexural stiffness for a horizontally curved beam element is developed for nodal parameters wi, (∂w/∂s)i, βi, (∂β/∂s)i, (∂2β/∂s2)i, (∂3β/∂s3)i by assuming a cubic displacement function for vertical deflection w, and a seventh order polynomical function for the angle of twist β, along the length of the curved beam. The element gives good accuracy with even coarse mesh for the analysis of horizontally‐curved steel beam with open thin‐walled bisymmetrical cross‐section. Warping restraint is considered in the derivation of the stiffness matrix, which has considerable influence on the behavior and design of steel bridges curved in‐plan. The results obtained from such a new element are compared with those given by a lower order finite element, developed previously by the first author, and with theoretical solutions for the particular problem.