Pergamon 0020-7403(94)00102-2 Int. J. Mech. Sci. Vol. 37, No. 8, pp. 831-841, 1995 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0020-7403/95 $9.50 + 0.00 CREEP BUCKLING AND RUPTURE OF COLUMNS WITH ARBITRARY SYMMETRIC CROSS SECTION VICTOR BIRMAN t and MARK G. MAGID ~ ~Universityof Missouri-Rolla, Engineering Education Center, 8001 Natural Bridge Road, St. Louis, MO 63121, U.S.A. and ~MICO, St. Louis, MO 63141, U.S.A. (Received 23 May 1994; and in revisedform 3 November 1994) Abstract--A practical method of analysis of simply supported columns subjected to a steady-state creep is developed. The method can be applied to the columns of an arbitrary symmetric cross section manufactured from materials that follow Norton's law. Two modes of failure are considered, i.e. creep buckling and the failure associated with allowable stresses. Numerical examples presented for actual materials illustrate the effects of various parameters on the creep buckling. al B h ki, kj(n) L n Per Po Pj S t tall tcr tf W WO X Z] NOTATION Aj cross-sectional area of the jth pair of layers a 0 non-dimensional amplitude of an initial deviation of the column from the perfect straight shape non-dimensional amplitude of the total deflection from the perfect straight shape constant in Norton's law depth of the column coefficients column length power in Norton's law Euler's buckling load of a simply supported column axial force applied to the column (positive in compression) fraction of the axial force applied to the jth couple of layers safety factor (for creep critical time) time allowable time of loading (for a column subjected to creep) creep critical time creep critical time with the correction for a safety factor creep failure time (based on allowable stresses) total transverse deflection initial deviation of the column from the straight shape axial coordinate distance from the neutral axis to the eentroid of the jth layer corresponding to undeformed shape (positive number) e strain a stress ac constant in Norton's law INTRODUCTION The problems of creep buckling and failure represent a challenge for designers of structures. In particular, columns designed to carry constant compressive loads are often subject to creep. The significant interest in this subject can be explained by its practical implications. The problems of creep buckling of columns have been considered since the beginning of the fifties. The classical analytical solution was presented by Hoff [1, 2] who idealized a column by two flanges and neglected the area of the web. The closed form solution was obtained by assumption of a steady creep with a particular form of the Norton-type strain rate-stress relationship. The creep buckling was associated with an unbounded transverse 831
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