A propped cantilever made of a prismatic steel beam is subjected to a concentrated load $$P$$ at mid span as shown.

If load $$P=80$$ $$kN,$$ find the reaction ܴ$$R$$ (in $$kN$$) (correct to $$1$$-decimal place)using elastic analysis ___________

The value of $$W$$ that results in the collapses of the beam shown in the adjoining figure and having a plastic moment capacity of $${M_P}$$ is

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