A material which obeys Hooke’s law is subjected to direct stress
A. Strain is equal to σ<sub>0</sub>/E
B. Maximum shear stress = σ<sub>0</sub>/2
C. Strain energy = (σ<sub>0</sub><sup>2</sup>/2E) x volume
D. All option are correct
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
For material Hooke's Law:
\(\rm{Modulus\; of\; Elasticity (E) = \frac{stress (\sigma)}{strain(\epsilon)}}\)
\(\rm{strain(\epsilon)=\frac{\sigma_o}{E}}\)
Maximum shear stress ⇒ \(\tau=\frac{\sigma_o}{2}\)
Strain energy per unit volume (u) is the area under the stress-strain curve:
\(u = \frac{1}{2}\times \sigma \times \epsilon=\frac{1}{2}\times \sigma \times \frac{\sigma}{E}=\frac{1}{2}\times \frac{\sigma^2}{E}\)
Total strain energy stored (U) in the body is given by:
\(U = u \times V =\frac{1}{2}\times \frac{\sigma^2}{E}\times \rm{Volume}=\frac{\sigma_o^2}{2E}\times \rm{Volume}\)
∴ All of the options are correct.