Effect of Imperfections on Buckling of Thin Cylinders and Columns Under Axial Compression

Abstract

Von Kármán and Tsien have shown that under elastic conditions the resistance of perfect thin cylinders subjected to axial compression drops precipitously after buckling. It is considered that this indicates that this type of buckling is very sensitive to imperfections or disturbances. In this paper the effects of certain imperfections of shape (assumed to be equivalent to all the actual defects or disturbances combined) are studied by the large-deflection shell theory developed in a previous paper (2). It is found that two types of buckling failure may occur. One is of a purely elastic type which occurs when the peak of the average stress versus average strain curve is reached, while the other type is precipitated by yielding, which for thicker cylinders or lower-yield material may occur before such a peak is reached. Curves are derived giving the dependence of each type of failure upon the dimensions and elastic and yield properties of the specimen and also upon an “unevenness factor” U which determines the magnitude of the initial imperfections and is assumed to depend on the method of fabrication. The relations derived are in line with test results, and similar studies of the buckling of struts indicate that the magnitude of the initial imperfections which have to be assumed to explain test strengths are reasonable.