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

A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the figure. Assume modulus of elasticity as 200 GPa.

The beam is subjected to a maximum bending moment of

A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the figure. Assume modulus of elasticity as 200 GPa.

The value of maximum deflection of the beam is