Question

The side $AD$ of the square block $ABCD$ as shown in the given figure is fixed at the base and it is under a stage of simple shear causing shear stress $\tau$ and shear strain $\Phi$,
where $\Phi =\frac{\tau }{\text{Modulus of Rigidity (G)}}$
The distorted shape is $A{B}^{\prime }{C}^{\prime }D$. The diagonal strain (linear) will be

• A. $\Phi /2$
• B. $\Phi /\sqrt{2}$
• C. $\sqrt{2}\Phi$
• D. $\Phi$

Answer 1

The correct option is A $\Phi /2$

At ${45}^o$
${\sigma }_1,{\sigma }_2=\pm \tau$
$Strain=\frac{{\sigma }_1}{E}-\frac{\mu {\sigma }_2}{E}$ $[E=2G(1+\mu \left)\right]$
$=\frac{\tau }{F}(1+\mu )=\frac{\Phi }{2}$