Tensile and compressive buckling of columns with shear deformation singularities

Shear deformations in beam-like structures as well as devices allowing deflection discontinuities, besides influencing the compressive buckling, can induce instability in presence of tensile axial loads. In this work a novel study to address both the compressive and the tensile buckling in slender beams in presence of multiple internal sliders endowed with translational springs, that induce deflection discontinuities along the beam axis, is presented. The general exact closed-form solutions is derived as a function of four boundary conditions only, as in the case of homogeneous beam, irrespective on the number of concentrated singularities. The range where the tensile buckling load values are comparable to the compressive counterpart is highlighted. Furthermore, sudden switches from symmetric to anti-symmetric buckling shapes are identified. Finally, for an increasing number of deflection discontinuities an interesting comparison with a uniform column with distributed shear deformations, according to the Timoshenko model, is presented. The latter comparison suggests that elastic internal sliders, which allow transversal deflection discontinuities, can be interpreted as concentrated shear deformations and are addressed to as shear deformation singularities.