A cantilever beam of length ‘L’ is subjected to a downward load of 1600 kN uniformly distributed over its length and concentrated upward load P at its free end. For vertical displacement to be zero at the free end, the value of P is:
- A300 kN
- B600 kNCorrect
- C800 kN
- D1600 kN
Solution
Concept
Zero deflection at the tip
Formula
δudl = WL³/8EI; δP = PL³/3EI
Step-by-step solution
1. Downward deflection due to UDL (total W = 1600 kN) = WL³/8EI. 2. Upward deflection due to P = PL³/3EI. 3. Equal: P = 3W/8 = 3 × 1600/8 = 600 kN.
Explanation
Superposition of the two tip deflections.
Why the other options are wrong
Other values do not equal 3W/8.
Shortcut
P = 3W/8.
Correct answer: B) 600 kN