Question

A uniform symmetric cross-section cantilever beam of length \( L \) is subjected to a transverse force \( P \) at the free end, as shown in the figure. The Young’s modulus of the material is \( E \) and the moment of inertia is \( I \). Ignoring the contributions due to transverse shear, the strain energy stored in the beam is \_\_\_\_\_.
\includegraphics[width=0.5\linewidth]{29.png}

• A. \( \frac{P^2 L^3}{6EI} \)
• B. \( \frac{P L^3}{3EI} \)
• C. \( \frac{P L^3}{6EI} \)
• D. \( \frac{P^2 L^3}{3EI} \)

Hint:

For cantilever beams, the strain energy stored due to bending under a load at the free end can be computed using the formula \( U = \frac{P^2 L^3}{6EI} \).

Answer 1

The Correct Option is C

The strain energy stored in a beam subjected to a transverse force \( P \) at the free end can be calculated using the formula for strain energy in bending: \[ U = \frac{P^2 L^3}{6EI} \] This formula applies to a cantilever beam with a load applied at its free end, where \( P \) is the force, \( L \) is the length of the beam, \( E \) is the Young’s modulus, and \( I \) is the moment of inertia.