Consider a simply supported beam of length $$50$$h, with a rectangular cross-section of depth h, and width $$2$$h. The beam carries a vertical point load P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is

Two solid circular shafts of $${{R_1}}$$ and $${{R_2}}$$ are subjected to same torque. The maximum shear stresses developed in the two shafts are $${\tau _1}$$ and $${\tau _2}.$$ If $${{{R_1}} \over {{R_2}}} = 2,$$ then $${{{\tau _1}} \over {{\tau _2}}}$$ is _______.

A force $$P$$ is applied at a distance $$x$$ from the end of the beam as shown in the figure. What would be the value of $$x$$ so that the displacement at $$'A'$$ is equal to zero?

Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is