Engineering Transactions, 8, 3, pp. 511-528, 1960

Wpływ Ciężaru Własnego na Pełzające Wyboczenie Prętów

M. Życzkowski
Instytut Podstawowych Problemów Techniki PAN

The problem of creep buckling of vertical cantilever bars loaded by a concentrated force and the weight of the bar is considered. The principal assumptions are as follows: the deflections are infinitely small; the bar has a certain initial curvature (technical type of buckling) the material is subject to a linear creep law of Maxwellian type. The fundamental equation is that of creep buckling (2.10). It is integrated by separating variables and expanding the eigenfunctions into a power series of a small parameter a, for which the weight of the bar is assumed («particular» solutions of the Eq. (2.10). The logarithmic creep buckling rate is expressed by the series (4.1). Then the small parameter method is modified by assuming the Eq. (4.2) where the «reduced» force m is expanded in a series. In the next part of the paper the equation of the initial deflection curve y(x) corresponding to the first particular solution of the creep buckling equation is established. This curve is determined by the Eqs. (5.5), (5.9) and (5.17); it differs very little from the quarter of a sine-curve. The rate of convergence of the series obtained is investigated by calculating the critical weight on the basis of the criterion (8.1) and comparing it with the known accurate solution- As a final conclusion it is found that for an initial deflection curve differing very little from the quarter of a sine-curve, the distributed load (the weight) may be replaced, in an approximate manner, both for creep buckling and
elastic buckling, by the equivalent concentrated force P = 0,3.
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