A New Theory for the Buckling of Thin Cylinders Under Axial Compression and Bending

Abstract

Abstract The results of experiments on axial loading of cylindrical shells (thin enough to buckle below the elastic limit and too short to buckle as Euler columns) are not in good agreement with previous theories, which have been based on the assumptions of perfect initial sbape and infinitesimal deflections. Experimental failure stresses range from 0.6 to 0.15 of the theoretical. The discrepancy is apparently considerably greater for brass and mild-steel specimens than for duralumin and increases with the radius-thickness ratio. There is an equally great discrepancy between observed and predicted shapes of buckling deflections. In this paper an approximate large-deflection theory is developed, which permits initial eccentricities or deviations from cylindrical shape to be considered. True instability is, of course, impossible under such conditions; the stress distribution is no longer uniform, and it is assumed that final failure takes place when the maximum stress reaches the yield point. The effect of initial eccentricities and of large deflections is much greater than for the case of simple struts. Measurements of initial eccentricities in actual cylinders have not been made; however, it is shown that most of these discrepancies can be explained if the initial deviations from cylindrical form are assumed to be resolved into a double harmonic series, and if certain reasonable assumptions are made as to the magnitudes of these components of the deviations. With these assumptions the failing stress is found to be a function of the yield point as well as of the modulus of elasticity and the radius-thickness ratio. On the basis of this a tentative design formula [5] is proposed, which involves relations suggested by the theory but is based on experimental data. It is shown that similar discrepancies between experiments and previous theories on the buckling of thin cylinders in pure bending can be reasonably explained on the same basis, and that the maximum bending stress can be taken as about 1.4 times the values given by Equation [5]. It is also shown that puzzling features in many other buckling problems can probably be explained by similar considerations, and it is hoped that this discussion may help to open a new field in the study of buckling problems. The large-deflection theory developed in the paper should be useful in exploring this field, and may be used in other applications as well. The paper presents the results of about a hundred new tests of thin cylinders in axial compression and bending, which, together with numerous tests by Lundquist form the experimental evidence for the conclusions arrived at.