Stability of Columns with Transient Loads

by Siegfried M. Holzer, (A.M.ASCE), Asst. Prof. of Civ. Engrg.; Univ. of Illinois, Urbana, IL,


Serial Information: Journal of the Engineering Mechanics Division, 1970, Vol. 96, Issue 6, Pg. 913-930


Document Type: Journal Paper

Abstract:

The dynamic deflection columns with general end fixity loaded with a transient variable compressive force is formulated by an integro-differential equation, which is reduced to a set of ordinary differential equations. For the special case of a hinged column, a stability criterion is obtained in explicit form via Liapunov's direct method. The stability criterion constitutes a relation between a bound on the amplification of an initial perturbation and the corresponding force pulse. The stability criterion is shown for three sample loadings: a trigonometric pulse; a parabolic pulse, and a set pulse. The amplification bounds are evaluated through comparison with the trajectory of maximum response of the governing differential equations of motion.



Subject Headings: Transient loads | Columns | Load factors | Equations of motion | Differential equations | Displacement (mechanics) | Compression | Case studies

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