For the structure shown below, the vertical deflection at point $$A$$ is given by

A frame $$ABCD$$ is supported by a roller at $$A$$ and is on a hinge at $$C$$ as shown below. The reaction at the roller end $$A$$ is given by

Identify the correct deflection diagram corresponding to the loading in the plane frame shown below :

A cantilever beam of length $$L$$ and a cross section with shape factor $$'f'$$ supports a concentrated load $$P$$ as shown below:

The length $${L_P}$$ of the plastic zone, when the maximum bending moment, equals the plastic moment $${M_P}$$, given by