A continuous beam is loaded as shown in the figure below. Assuming a plastic moment capacity equal to $${{M_P}}$$, the minimum load at which the beam would collapse is

The plastic collapse load $${{W_P}}$$ for the propped cantilever supporting two point loads as shown in the figure in terms of plastic moment capacity, $${{M_P}}$$ is given by

When the triangular section of a beam as shown below becomes a plastic hinge, the compressive force acting on the section (with $${\sigma _y}$$ denoting the yield stress) becomes

A cantilever beam of length $$l,$$ width $$b$$ and depth $$d$$ is loaded with a concentrated vertical load at the tip. If yielding starts at a load $$P,$$ the collapse load shall be