Question

Strain energy stored in a prismatic bar suspended from one end due to its own weight (elastic behavior) [x = specific weight of material, A = cross-sectional area, L = length of bar]

• A. $$U =\frac{x^2A^2L^2}{6E}$$
• B. $$U =\frac{xAL^3}{6E}$$
• C. $$U =\frac{x^2AL^3}{3E}$$
• D. $$U =\frac{x^2AL^3}{6E}$$

Answer 1

Answer:

$$U =\frac{x^2AL^3}{6E}$$

The strain energy stored in a prismatic bar clue to its own weight is given by $U =\frac{x^2AL^3}{6E}$. Strain energy is the energy absorbed by the member when work done by the load deforms that member. For a prismatic bar, the axial load due to its own weight is $xAL$.