First slide

Stress and strain

Question

A metallic cube is acted upon by a tensile force F acting normally on each of six faces as shown in figure. If Poisson's ratio of metal is 0.2 and longitudinal strain produced in the cube is 0.01, then percentage change produced in the volume is

Moderate

A

3.4%
B

5.2%
C

2.2%
D

1.8%

Solution

Volume strain $\frac{ΔV}{V} = 3 \in (1 - 2 μ)$
$\begin{array}{l} ∴ \frac{ΔV}{V} = 3 \times 0 .01 (1 - 2 \times 0 .2) = 0 .018 \\ ∴ \frac{ΔV}{V} \times 100 % = 1 .8 % \end{array}$

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