Effect of Shear Force on the Fully Plastic Moment of An I-Beam

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Abstract
Lower bound solutions for the plastic collapse load of an end-loaded cantilever beam of I-section are developed, and compared with existing upper bound solutions. It is shown that the end shear load can only exceed the load corresponding to the yield stress in shear acting over the full web area for extremely short beams, and it is suggested that this load represents the practical limit of shear force. For longer beams a lower bound solution is given which agrees closely with an existing upper bound solution, and an empirical interaction relation between shear load and moment at the clamped end is put forward as a summary of the results. It is also shown that the concept of a local interaction relation which only considers conditions at the clamped end gives very misleading results.
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