Question

A piece of material (v = 0.3 and E = 5GPa) shaped like a cigarette packet (1cm x 3cm x 5cm) is subjected to a pressure of 200MN/m2. Calculate the new volume?

Answer 1

Answer on Question #52016-Engineering-Other

A piece of material (v = 0.3 and E = 5GPa) shaped like a cigarette packet (1cm x 3cm x 5cm) is subjected to a pressure of $\sigma = 200\frac{MN}{m^2}$. Calculate the new volume?

Solution

Let $\sigma = \sigma_{x} = \sigma_{y} = \sigma_{z}$, because we don't know the direction of the pressure. Then

$$\varepsilon = \varepsilon_ {x} = \varepsilon_ {y} = \varepsilon_ {z} = \frac {1}{E} \big (\sigma (1 + v) - v (\sigma + \sigma + \sigma) \big) = \frac {\sigma (1 - 2 v)}{E} = \frac {2 0 0 \frac {M N}{m ^ {2}} (1 - 2 \cdot 0 . 3)}{5 G P a} = 0. 0 8.$$

Thus, the new volume is

$$V ^ {\prime} = (1 + \varepsilon) ^ {3} V = (1 + 0. 0 8) ^ {3} \cdot 1 \cdot 3 \cdot 5 c m ^ {3} = 1 8. 9 c m ^ {3}.$$

Answer: 18.9 cm³.