$4.(30\backslash \%)$

$($a$)$ What are the basic assumptions involved in the Saint$-$Venant formulation of torsional analysis?

$($b$)$ Find the rate of twist of a uniform bar of elliptical cross section subjected to a uniform torsion $\backslash ($ T $\backslash ).$

$($c$)$ According to the Bernoulli$-$Euler formulation of a simple beam, shear stresses all vanish. How can we find the shear stress distribution in case shear forces are present?