Nonlinear Elastic Behavior of I-Beams Curved in Plan

Abstract

The vertical deflections perpendicular to the plane of a horizontal beam curved in plan are coupled with its twist rotations, and its axial deflections are coupled with its horizontal radial deflections. Because of the first of these couplings, a horizontally curved beam subjected to vertical loading has both primary bending and torsion actions. In the nonlinear range, second-order couplings between the vertical and horizontal deflections and the twist rotations are developed, and the nonlinear behavior of the curved beam becomes more complicated. This paper studies the linear, neutral, and nonlinear equilibrium of elastic horizontally curved I-beams under vertical loading and develops a curved finite-element model for their analysis. It is found that when the included angle of a curved beam is small, the primary coupling is also small and bending is the major action. In this case, the nonlinear behavior is similar to the elastic flexural-torsional buckling of a straight beam. However, if the included angle of the curved beam is not small, the primary coupling becomes significant and both torsion and bending are major actions. In this case, nonlinear behavior develops very early and is quite different from the flexural-torsional buckling behavior of a straight beam.