The stepped cantilever is subjected to moments, $$M$$ as shown in the figure below. The vertical deflection at the free end (neglecting the self weight) is

The maximum shear stress in a solid shaft of circular cross-section having diameter subjected to a torque $$T$$ is $$\tau $$ . If the torque is increased by four times and the diameter of the shaft is increased by two times, the maximum shear stress in the shaft will be

A continuous beam is loaded as shown in the figure below. Assuming a plastic moment capacity equal to $${{M_P}}$$, the minimum load at which the beam would collapse is

The shape of the cross-section, which has the largest shape factor, is