고체역학 (Beer) — Principal Stresses Under a Given Loading: Problem 8.17

8.17 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: \[ \sigma_{\max} = \frac{c}{J} \left[ (M_y^2 + M_z^2)^{1/2} + (M_y^2 + M_z^2 + T^2)^{1/2} \right]_{\max} \]