On the propensity of shear deformable columns to buckle under a tensile axial load

Abstract

The propensity of shear deformable beam members obeying to the Timoshenko beam theory to buckle under axial tension is contested in the paper. For Timoshenko beams under uniform tension, the existing theories supporting this statement extend the findings of Haringx, derived for the compressive case only, to tensile axial forces by considering that the negative root of the quadratic equation arising from the eigenboundary problem related to the stability analysis for compression is itself a critical load, tensile due to its negative sign. Notwithstanding, a tensioned beam is not the mirror case of a compressed one and the appropriate mathematical procedures are applied consistently, in the present paper, to analyse the stability behaviour of Timoshenko beam members under uniform tension. Bearing in mind that a critical state is a mathematical concept that models the physical behaviour of a structural frame under specific circumstances, it is found that no buckling occurs if the mathematical tools are applied correctly, and the mentioned tensile buckling load is not a buckling load, because it does not render null the determinant of the eigenboundary problem that represents the stability problem of columns, neither for tension nor for compression. Therefore, the application in the engineering practice of all theories stating that Timoshenko beams are prone to tensile buckling, in addition to the compressive one, shall be precluded until new and irrefutable proofs come to light. The paper ends with the analysis of a structural system that really buckles when tensioned. It was developed in the literature that lays behind us and consists of two rigid rods connected by a transverse slider. Within this context, a correspondence is established between this latter system and an alternative one, whose propensity to buckling arises from overlapping bars that are compressed as the frame as a whole is being tensioned. By doing this, a connection is established between tensile buckling due to shear singularities and the tensile buckling of Ziegler, which is due to overlapping.