Question

A shaft of diameter 'd' is subjected to bending moment M and twisting moment T. The developed principal stress will be

• A. $\pm \frac{16}{\pi d^3}\sqrt{M^2+T^2}$
• B. $\frac{16}{\pi d^3}(M\pm \sqrt{M^2+T^2})$
• C. $\frac{16}{\pi d^3}(T\pm \sqrt{M^2+T^2})$
• D. $\frac{16}{\pi d^3}\sqrt{M^2+T^2}\pm M$

Answer 1

The correct option is B $\frac{16}{\pi d^3}(M\pm \sqrt{M^2+T^2})$

Maximum stress due to bending moment

$\sigma =\frac{32M}{\pi d^3}$

Maximum shear stress due to torsion T

$\tau =\frac{16t}{\pi d^3}$

Maximum normal stress due to combined action of bending moment and torque

${\sigma }_1,{\sigma }_3=\frac{\sigma }{2}\pm \sqrt{{\left(\frac{\sigma }{2}\right)}^2+{\tau }^2}$

$=\frac{16}{\pi d^3}[M\pm \sqrt{M^2+{\tau }^2}]$