Incipient failure of a circular cylinder under gravity

We consider the incipient failure of a circular cylinder under gravitational loading. Axisymmetric slip-line field theory is used to solve for the stress distribution in the plastic region of the cylinder at incipient failure. This extends similar work on the incipient failure of a rectangular block under gravity (Int. J. Mech. Sci. 43(3) (2000) 793), to the axisymmetric geometry. Our calculations show that the height of incipient failure depends not only on the yield stress and density of the material, but also on the radius of the cylinder and the coefficient of friction at the base. In addition, we find that there exists a critical coefficient of friction above which the height of incipient failure is unaffected. These results suggest a method of measuring the yield stress by observing the height of incipient failure.