In the case of a cantilever of span L subjected to concentrated load W at the free end, the rotation (θ) and deflection (y) of the free end are
- Aθ = WL/EI, y = WL²/2EI
- Bθ = WL²/2EI, y = WL²/3EICorrect
- Cθ = WL³/EI, y = WL⁴/8EI
- Dθ = WL³/24EI, y = WL³/24EI
Solution
Concept
Slope and deflection of a cantilever
Formula
θ = WL²/2EI; y = WL³/3EI
Step-by-step solution
1. EI y″ = −W(L − x). 2. Integrating with θ = 0 and y = 0 at the fixed end: θmax = WL²/2EI and ymax = WL³/3EI at the free end.
Explanation
Option B has the correct slope; its deflection term is printed as WL²/3EI, a typing error for WL³/3EI.
Why the other options are wrong
The other options have the wrong powers of L and wrong constants.
Shortcut
θ = WL²/2EI, y = WL³/3EI.
Common mistake
Mixing the two results.
Correct answer: B) θ = WL²/2EI, y = WL²/3EI