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# gm12_13notes - M12 Buckling of Simple Columns Reading...

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M12 Buckling of Simple Columns Reading Crandall, Dahl and Lardner: 9.4 Now extend the idea of elastic instabilities to a continuous structural member. Model of a column A column is a slender structural member that carries axial compressive loads. (a) Geometry – identical to a beam, long, straight, slender, symmetric cross-section etc. L >> b, h (b) Loading – axial compressive axial forces (c.) Deformations At low loads - same as a rod, axial (x) stresses, axial deformation only At higher loads - buckling deflection (transverse) governed by bending relations i.e., d 2 w dx 2 = M EI

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deflected shape: Draw free body diagram of deflected column: From equilibrium: H A =P, V A =V B =0 We can now use method of sections, by taking a “cut” at an arbitrary x position (as for a beam) By equilibrium
F x = 0 + P + F = 0 F = - P F y = 0 + S = 0 M A = 0 M - Fw ( x ) = 0 M + Pw ( x ) = 0 Substitute for the moment, M, using the moment-curvature relationship, obtain second order differential equation EI d 2 w dx 2 + Pw = 0

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gm12_13notes - M12 Buckling of Simple Columns Reading...

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