Shakedown of Bars in Bending and Tension

The behaviour of an element of a beam or plate when subjected to variable repeated loads of bending moment and tension is examined, and the shakedown limit, beyond which incremental collapse occurs, is established. The shakedown limit moment is always less than the full plastic moment if there is fluctuating tension or compression. Alternating plasticity due to moment reversal in beams is shown to be a particular case of a more general class of alternating plasticity involving axial forces as well. The shakedown limit for frames will be significantly reduced if the axial forces are large. Flexural Fatigue tests of the plastic strain reversal type controlled by load limits rather than strain limits are liable to experience incremental collapse. Pressure vessels with fluctuating temperature gradient in the walls and membranes subjected to curvature and tensile variations are liable to incremental collapse by elongation.