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in strength of materials, the bending of an originally straight column under the effect of centrally applied axial compressive forces that exceed the column’s bearing power. For a column of uniform cross section exhibiting elastic behavior, the various forms of buckling correspond to critical values of the compressive forces Nc = μ2n2EI/(μl)2, where E is the modulus of elasticity of the material of the column, I is the minimum value of the axial moment of inertia of the column’s cross section, l is the length of the column, μ is the coefficient of reduced length dependent on the conditions of end support of the column, and n is an integer. The minimum value for the critical force is usually of practical interest in that for a column with pinned ends (μ = 1), this force causes bending of the column according to a half-cycle sine curve (n = 1). The magnitude of the force is calculated by the Euler formula Nc = π2EI/l2. The stress σc = Nc/F(F is the cross-sectional area of the column) corresponds to the critical force and is called the critical stress. If the value of the critical stress exceeds the proportional limit of the column material, then buckling occurs in the zone of plastic deformations. In this case, the minimum critical force is determined by the formula Nc = π2n2TI/(μl)2, where T is the modulus, which characterizes the dependence between the deformations and the stresses beyond the limits of the elastic deformations.
In structural design, buckling is taken into account in calculating column loads.
L. V. KASAB’IAN