Stability of Thin-Walled Tubes Under Torsion

In this paper a theoretical solution is developed for the torsion on a round thin-walled tube for which the walls become unstable. The results of this theory are given by a few simple formulas and curves which cover all cases. The differential equations of equilibrium are derived in a simpler form than previously found, it being shown that many items can be neglected. The solution obtained is "exact" for the two extreme cases when the diameter-length ratio is zero and infinite, and is a good approximation for intermediate case. The theory is compared with all available experiment , including about 50 tests made by the author. The experimental failure torque is always smaller than the theoretical-buckling torque, averaging about 75 percent of it, with a minimum of 60 percent. As the form of the deflection checks closely with that predicted by theory and the experiments cover a great range of shapes and materials, this discrepancy can reasonably be ascribed largely to initial eccentricities in actual tubes.