A steel cube, with all faces free to deform, has Young’s modulus, $$E,$$ Poisson’s ratio, $$ν,$$ and coefficient of thermal expansion, $$\alpha .$$ The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, $$\Delta T,$$ is given by

A thin plate of uniform thickness is subject to pressure as shown in the figure below

Under the assumption of plane stress, which one of the following is correct?

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