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

If the magnitude of loadܲ is increased till collapse and the plastic moment carrying capacity of steel beam section is $$90$$ $$kN$$-$$m$$, ݇ܰ݉determine reaction ܴ$$R$$(in ݇ܰ$$kN$$)(correct to $$1$$-decimal place) using plastic analysis. ____________

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