Buckling instabilities of elastically connected Timoshenko beams on an elastic layer subjected to axial forces

Abstract

We study the buckling instability of a system of three simply supported elastic Timoshenko beams, joined together by Winkler elastic layers, and each subjected to the same compressive axial load. The model of the Timoshenko beam includes the effects of axial loading, shear deformation, and rotary inertia. Explicit analytical expressions are derived for the critical buckling load of single, double, and triplebeam systems. It can be observed from these expressions that the critical buckling load depends on the Winkler elastic layer stiffness modulus K , and that the instability of the system increases with an increase in the numbers of beams and elastic layers. These results are of considerable practical interest and have wide application in engineering practice. Vibration and buckling problems of beams and beam-columns on elastic layers occupy an important place in many fields of structural and layer engineering, occurring often in mechanical and civil engineering applications. Their solution demands modeling of the mechanical behavior of the beam, the mechanical behavior of the soil, and the form of the interaction between the beam and the soil. As far as the beam is concerned, most engineering analyses are based on classical Bernoulli‐Euler beam theory, in which straight lines or planes normal to the neutral beam axis remain straight and normal after deformation. This theory thus neglects the effect of transverse shear deformations, a condition that holds only in the case of slender beams. To confront this problem, the well-known Timoshenko beam model, in which the effect of transverse shear deflections is considered, can be used. Matsunaga [1996] studied the buckling instabilities of a simply supported thick elastic beam subjected to axial stresses. Taking into account the effects of shear deformations and thickness changes, the buckling loads and buckling displacement modes of thick beams were obtained. Based on the power series expansion of displacement components, a set of fundamental equations of a one-dimensional higherorder beam theory was derived through the principle of virtual displacement. Several sets of truncated approximate theories were applied to solve the eigenvalue problems for a thick beam. The convergence properties of the buckling loads of a simply supported thick beam were examined in detail and comparison of the results with previously published ones was made.