The figure shows the state of stress at a certain point in a stressed body. The magnitudes of normal stresses in the $$x$$ and $$y$$ directions are $$100$$ MPa and $$20$$ MPa respectively. The radius of Mohr's stress circle representing this state of stress is

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