A hollow circular shaft has an outer diameter of $$100$$ $$mm$$ and a wall thickness of $$25$$ $$mm.$$ The allowable shear stress in the shaft is $$125$$ $$MPa.$$ The maximum torque the shaft can transmit is

A vertical rod $$PQ$$ of length $$L$$ is fixed at its top end $$P$$ and has a flange fixed to the bottom end $$Q.A$$ weight $$W$$ is dropped vertically from a height $$h\left( { < L} \right)$$ on to the flange. The axial stress in the rod can be reduced by

The degree of static indeterminacy of a rigidly jointed frame in a horizontal plane and subjected to vertical loads only, as shown in figure below is

In the theory of plastic bending of beams, the ratio of plastic moment to yield moment is called