Question

The shearing stress in a piece of structural steel is 100 MPa. If the elastic modulus is 200 GPa and the Poisson’s ratio is 0.25, then the shearing strain 'γ'  would be
1. 0.00125 rad 
2. 0.8 rad 
3. 1.25 
4. 800

Answer 1

Correct Answer - Option 1 : 0.00125 rad 

Explanation

Given: -

Shearing stress, τ = 100 MPa

Modulus of elasticity, E = 200 GPa

Poisson’s ratio, μ = 0.25

We know,

Modulus of rigidity (G) is defined as the ratio of shearing stress to the shearing strain.

Also,

\( \Rightarrow G = \frac{{200}}{{2\left( {1 + 0.25} \right)}} = 80\;GPa\)

Then,
\(G = \frac{\tau }{\gamma }\)

\( \Rightarrow \gamma = \frac{{100}}{{80 \times {{10}^3}}} = 0.00125\;rad\)