A machine frame shown in the figure below is subjected to a horizontal force of $$600$$ $$N$$ parallel to $$Z$$-direction.

The normal and shear stresses in $$MP$$a at point $$P$$ are respectively

A stepped steel shaft shown below is subjected to $$10$$ N-m torque. If the modulus of rigidity is $$80$$ GPa, the strain energy in the shaft in N-mm is

A uniformly loaded propped cantilever beam and its free body diagram are shown below. The reactions are

A steel rod of length $$L$$ and diameter $$D$$, fixed at both ends, is uniformly heated to a temperature rise of $$\Delta T.$$ The Young's modulus is $$E$$ and the coefficient of linear expansion is $$'\alpha '\,.$$ The thermal stress in the rod is