This study is concerned with the influence of axial inertia upon the elastic bending motion of initially slightly curved columns acted on by time-dependent axial forces. The equations of motion include both axial inertia and nonlinear strain terms. Numerical solutions were obtained for a similar problem previously studied by Hoff  but in which axial-inertia effects were neglected; i.e., the problem of a simply supported column initially bent in the shape of a half sine wave and loaded by displacing one end axially at a constant rate. The range of solutions pertains to conventional structural compression members (slenderness ratios less than 150), and to minimum rates of loading compatible with elastic response of common engineering materials. This study suggests that axial-inertia effects are of secondary importance in so far as the gross elastic response of conventional structural columns is concerned.
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On the Elastic Bending of Columns Due to Dynamic Axial Forces Including Effects of Axial Inertia
Division of Mechanical Engineering Research, Armour Research Foundation, Illinois Institute of Technology, Chicago, Ill.
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Sevin, E. (March 1, 1960). "On the Elastic Bending of Columns Due to Dynamic Axial Forces Including Effects of Axial Inertia." ASME. J. Appl. Mech. March 1960; 27(1): 125–131. https://doi.org/10.1115/1.3643886
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