In this study the elastoplastic behavior of cantilever beams under a combined compressive axial load and an imposed lateral bending deflection are analyzed. Eventhough the particular condition of elastoplastic buckling has been studied before, the developed theories are limited to the prediction of the initial failure of the beam. In the current study the elastoplastic behavior of cantilever beams under compressive load at levels below the critical buckling load are studied in order to determine the remaining load bearing capacity of the beam under combined bending and axial loads, including the behavior at progressive levels of plastic deformation.
The elastoplastic bending process is analyzed using the finite element method. In particular, the analysis is focused on the evaluation of the limiting bending force necessary to increase or reduce the curvature of the beam in the plastic zone. The bending force depends on the compressive axial load, the geometrical dimensions of the beam, material coefficients, such as Young’s modulus and yield stress, and the hardening model. The large number of variables involved, is reduced by introducing two dimensionless load parameters.
The results of the analysis are presented and discussed for a wide range of dimensionless loads. Also the influence of work hardening on the obtained bending force is analyzed, comparing between an ideal plastic behavior and a bilinear plasticity model with a linear hardening behavior.