Topic: Strength of Materials
A cantilever beam of length L is subjected to a concentrated load P at a distance of L/3 from the free end. The deflection at the free end is
- A. 1/3 (PL³ / EI)
- B. 14/81 (PL³ / EI)
- C. 7/18 (PL³ / EI)
- D. 1/2 (PL³ / EI)
Answer: B. 14/81 (PL³ / EI)
Explanation: The load P is applied at a distance of 2L/3 from the fixed support. The deflection at the load application point is y1 = (P * (2L/3)^3) / (3EI) = 8PL^3 / 81EI. The slope at this point is theta = (P * (2L/3)^2) / (2EI) = 2PL^2 / 9EI. The deflection at the free end is y_total = y1 + theta * (L/3). Adding these gives (8PL^3 / 81EI) + (2PL^3 / 27EI) = (8PL^3 + 6PL^3) / 81EI = 14PL^3 / 81EI.