Elastic buckling of an individual I-beam with consideration of the shear effect

The subject of the paper is a homogeneous I-beam with an individual shape web.The beam, simply supported at one end and at the other simply supported with elastic limitation of rotation, is subjected to axial compression by a force F .The analytical model of the beam is developed with consideration of the shear effect.The deformation of the beam's plane cross-section after buckling is determined analytically, taking into account the classical expression for shear stresses in a beam (known as Zhuravsky or Jourawski shear stress).Longitudinal displacements, strains, and stresses are then formulated.Based on the principle of stationary total potential energy, a system of two equilibrium differential equations is derived.These equations are solved analytically, taking into account the beam support conditions, and the critical force FCR is determined.Detailed calculations are realized for sample beams.