Topic: Strength of Materials
The elastic strain energy stored in a rectangular cantilever beam due to a bending moment M applied at the end is given by (sigma_max is Maximum Bending Stress, V is Volume and E is Young's Modulus)
- A. sigma^2_max (V/3E)
- B. sigma^2_max (V/2E)
- C. sigma^2_max (V/6E)
- D. sigma^2_max (V/4E)
Answer: C. sigma^2_max (V/6E)
Explanation: Strain energy U = M² * L / (2EI). Maximum bending stress sigma_max = M * (h/2) / I, so M = sigma_max * I / (h/2). Substituting M into U gives U = (sigma_max^2 * I * L) / (2 * E * (h/2)^2). For a rectangle, I = b * h³ / 12, and Volume V = b * h * L. Simplifying the expression yields U = sigma_max^2 * V / 6E.