A cantilever beam of length, $$L,$$ with uniform cross-section and flexural rigidity $$ EI,$$ is loaded uniformly by a vertical load, $$w$$ per unit length. The maximum vertical deflection of the beam is given by

The flexural rigidity $$(EI)$$ of a cantilever beam is assumed to be constant over the length of the beam as shown in figure. If a load $$P$$ and bending moment $$PL/2$$ are applied at the free end of the beam then the value of the slope at the free end is

A force $$P$$ is applied at a distance $$x$$ from the end of the beam as shown in the figure. What would be the value of $$x$$ so that the displacement at $$'A'$$ is equal to zero?

A triangular-shaped cantilever beam of uniform- thickness is shown in the figure. The young's modulus of the material of the beam is $$E$$. $$A$$ concentrated load $$P$$ is applied at the free end of the beam.

The area moment of inertia of inertia about the neutral axis of a cross-section at a distance $$x$$ measured from the free end is