Evaluation of displacements and stresses in horizontally curved beams

The formulation of large strains and displacement relations and equilibrium equations for evaluating the nonlinear behavior of horizontally curved beams is presented. An examination is conducted to investigate the effects of approximations used in existing studies on curved beams. Justification of simplified approach is reviewed based on results from this study. The solution of equations is obtained by the development and use of a line element which incorporates the characteristics of a displacement field and a shape function of curved beams. The results from analysis are compared with those from three-dimensional finite element models of example beams and from test data. Beams with doubly and singly symmetric I-section, symmetric C-section and general cross sectional shape are examined. It is determined that analyses considering only small displacements and small rotations or large displacements and small rotations underestimate deflections and stresses. The effects of p-delta and cross sectional deformation on the load-displacement behavior and stresses of horizontally curved beams are investigated with the result that nonlinearity due to these effects is significant. An equation for maximum stress in curved beams is developed through a parametric study using the line element incorporating the effects of large displacements, large rotations and cross sectional deformations.