Chapter 8.2, Problem 17P

Using the notation of Sec. 8.2 and neglecting the effect of shearing stresses caused by transverse loads, show that the maximum normal stress in a circular shaft can be expressed as follows:

$\sigma \max =\frac{c}{J}{[{\left(M_y^2+M_z^2\right)}^{\frac{1}{2}}+{\left(M_y^2+M_z^2+T^2\right)}^{\frac{1}{2}}]}_{\max }$