A propped cantilever beam of span $$L,$$ is loaded with uniformly distributed load of intensity $$w/unit$$ length, all through the span. Bending moment at the fixed end is

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: