Question

Match List-I with List-II and select the correct answer using the codes given below the lists:

List-I
A. Torque-twist relationship for a circular shaft
B. Strain energy of elastic torsion
C. Circumferential shear stress
D. Maximum shearing stress due to combined torsion and direct stress

List-II

Codes :

$\begin{array}{cccc}A& B& C& D\end{array}$

• A. $\begin{array}{cccc}2& 3& 4& 1\end{array}$
• B. $\begin{array}{cccc}4& 1& 2& 3\end{array}$
• C. $\begin{array}{cccc}2& 1& 4& 3\end{array}$
• D. $\begin{array}{cccc}4& 3& 2& 1\end{array}$

Answer 1

The correct option is D $\begin{array}{cccc}4& 3& 2& 1\end{array}$

• For circular shaft

$\frac{\tau }{r}=\frac{T}{J}=\frac{G\theta }{L}$

$T=\left(\frac{GJ}{L}\right)\theta$

• $Strainenergy=\frac{1}{2}T\theta =\frac{1}{2}\left(\frac{GJ}{L}\right){\theta }^2$
• $Shearstress,\tau =\frac{Gr\theta }{L}$
• $Maxshearstress=\sqrt{{\left(\frac{\sigma }{2}\right)}^2+{\tau }^2}$

$=\frac{1}{2}\sqrt{(\sigma {)}^2+4{\tau }^2}$