A shaft is subjected to a combined bending load 'M' and torsional load 'T'. If the permissible shear stress is 'τ', the diameter 'd' of the shaft will be calculated by the relation:

Consider a solid and a hollow steel column having the same length, material, and cross-sectional area. For the hollow steel column, the inside diameter is 34 of the outside diameter. What will be the ratio of the buckling strength of the solid steel column to that of the hollow one, assuming both have pinned ends?

A tapered circular bar of diameter varying from 30 mm to 15 mm is connected to another uniform circular bar of diameter 15 mm. The length of the tapered bar is 3 m and that of the uniform bar is 2 m. Both the bars are of the same material with a modulus of elasticity E = 2 × 105 N/mm2 and are subjected to an axial load of 100 kN. The deflection of the bar at the free end (in mm) is: