On the contact behavior of a buckled Timoshenko beam constrained laterally by a plane wall

Abstract

This paper discusses the effect of shear deformation of the cross-section on the contact behavior of a buckled Timoshenko beam in frictionless contact with a rigid plane wall. The deformation is assumed to be small, and only planar deformation is considered. The results are compared with those from the Euler beam model. In the case when a buckled Euler beam is in line contact with a plane wall, the plane wall exerts concentrated forces at the boundary points of the line-contact segment but no distributed force. In the case of a Timoshenko beam, on the other hand, the concentrated forces are replaced by a distributed contact force. The distribution of the contact force approaches the two concentrated forces at the boundary points when the shear effect is negligible. The line-contact deformation may become unstable when the edge thrust reaches a secondary buckling load. It is found that the normalized critical length of the contact segment is always smaller when the shear effect is more significant. On the other hand, the normalized secondary buckling load reaches a maximum when the slenderness ratio (beam length over thickness) is in the order of 45.