Question

A circular shaft is subjected to a bending moment $M_b$ and a twisting moment $M_t$. What is the ratio of maximum shear stress and the maximum bending stress?

• A. $\frac{2M_t}{M_b}$
• B. $\frac{M_t}{M_b}$
• C. $\frac{M_t}{2M_b}$
• D. $\frac{1.5M_t}{M_b}$

Answer 1

The correct option is C $\frac{M_t}{2M_b}$

The maximum shear stress will be

${\tau }_{max}=\frac{16M_t}{\pi D^3}$

The maximum bending stress will be

${\sigma }_{max}=\frac{32M_b}{\pi D^3}$

$\therefore \frac{{\tau }_{max}}{{\sigma }_{max}}=\frac{32M_t/\pi D^3}{32M_b/\pi D^3}=\frac{M_t}{2M_b}$