New theoretical models for the bending moment of thin-walled beams under three-point bending

Abstract

Bending collapse of thin-walled beams is one of the most important energy dissipation mechanisms for energy absorbing components to absorb the impact kinetic energy during accidents. However, the theories on the bending collapse of thin-walled beams are still not well developed. Three-point bending and pure bending are two most commonly encountered bending loads, but the differences in the responses of thin-walled beams under the two bending loads are not clearly stated in the literatures. The force-displacement responses of thin-walled beams under three-point bending are always converted to the bending moment-rotation responses on the central section. However, the previous theoretical conversion method is oversimplified and leads to large errors. In this work, several theoretical models are proposed in accordance with deformation modes to derive the bending moment on the central section of a beam under three-point bending. The accuracy of the theoretical models is then validated by using the numerical model verified by three-point bending tests. In addition, it is interesting to find that the central section of thin-walled beams is always not the section with the maximum bending moment.