First slide

Stress and strain

Question

One face CD of a brass cube ABCD having length of side 10 cm is fixed and a tangential force is applied on the free face A. As a result the angular displacement of the other face is 0.18^o. If shear modulus of brass is $4 \times 10^{10} N / m^{2}$ , the elastic potential energy stored in the cube is $(π^{2} \approx 10)$

Difficult

A

150 J
B

300 J
C

200 J
D

50 J

Solution

Shear strain, $θ = 0 {.18}^{o} = \frac{π}{180} \times 0 .18 rad = \frac{π}{1000} rad$
$∴$ strain energy stored per unit volume
$u = \frac{1}{2} {ηθ}^{2} = \frac{1}{2} \times 4 \times 10^{10} \times {(\frac{π}{1000})}^{2} \frac{J}{m^{3}}$
$= 2 \times 10^{10} \times \frac{10}{10^{6}} \frac{J}{m^{3}} = 2 \times 10^{5} \frac{J}{m^{3}}$
$∴$ Total strain energy stored = volume x energy density
$= {(\frac{10}{100})}^{3} \times 2 \times 10^{5} J = 200 J$

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