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

The two shafts $$AB$$ and $$BC$$, of equal length and diameters $$d$$ and $$2d$$, are made of the same material. They are joined at $$B$$ through a shaft coupling, while the ends $$A$$ and $$C$$ are built-in (cantilevered). A twisting moment $$T$$ is applied to the coupling. If $${T_A}$$ and $${T_C}$$ represent the twisting moments at the ends $$A$$ and $$C,$$ respectively, then

A torque of $$10$$ $$N-m$$ is transmitted through a stepped shaft as shown in figure. The torsional stiffnesses of individual sections of lengths $$MN, NO$$ and $$OP$$ are $$20$$ $$N-m/rad,$$ $$30$$ $$N-m/rad$$ and $$60$$ $$N-m/rad$$ respectively. The angular deflection between the ends $$M$$ and $$P$$ of the shaft is

A solid circular shaft of $$60$$ mm diameter transmits a torque of $$1600$$ N - m. The value of maximum shear developed is