The Mohr's circle of plane stress for a point in a body is shown. The design is to be done on the basis of the maximum shear stress theory for yielding. Then, yielding will just begin if the designer chooses a ductile material whose yield strength is

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