Question

A circular shaft is subjected to an axial twisting moment T and a bending moment M. It is given that M=1.2T . Then what is the ratio of the maximum shearing stress to the greatest principal stress ?

• A. 0.566
• B. 0.687
• C. 0.825
• D. 0.982

Answer 1

The correct option is A 0.566

$M=1.2T$

${\tau }_{max}=\frac{16}{\pi D^3}\sqrt{M^2+T^2}$

${\sigma }_{p.max}=\frac{16}{\pi D^3}(M+\sqrt{M^2+T^2})$

$\frac{{\tau }_{max}}{{\sigma }_{p.max}}=\frac{\sqrt{M^2+T^2}}{M+\sqrt{M^2+T^2}}$

Put M = 1.2 T

$\frac{{\tau }_{max}}{{\sigma }_{pmax}}=0.566$