A cantilever beam of span $$l$$ subjected to a uniformly distributed load $$'w'$$ per unit length resting on a rigid prop at the tip of cantilever. The magnitude of the reaction of at the prop is

A simply supported beam of span length $$L$$ and flexural stiffness $$EI$$ has another spring support at the center span of stiffness $$K$$ as shown in fig. The central deflection of the beam due to a central concentrated load of $$P$$ would be

A cantilever beam of span, $$'L'$$ is subjected to a downward load of $$800$$ $$kN$$ uniformly distributed over its length and a concentrated upward load $$P$$ at its free end. For vertical displacement to be zero at the free end, the value of $$P$$ is:

Two elastic rods $$AB$$ and $$BC$$ are hinged at $$B$$. The joint $$A$$ is a hinged one, joint $$C$$ is over a roller and the joint $$B$$ is supported on a spring having its stiffness as $$K.$$

A load $$P$$ acts at mid-point of the rod $$BC$$. The downward deflection of joint $$B$$ is: