A cantilever beam of span L is subjected to uniformly distributed load of intensity W. If the flexural rigidity is EI, the slope θ and deflection δ at the free end are respectively
- A−WL³/8EI and −WL⁴/8EI
- B−WL³/6EI and −WL⁴/8EI
- C−WL³/8EI and −WL⁴/6EI
- D−WL³/6EI and −WL⁴/8EICorrect
Solution
Concept
Slope and deflection of a cantilever with UDL
Formula
θ = wL³/6EI; δ = wL⁴/8EI
Step-by-step solution
1. For a UDL of intensity w per unit length: θB = wL³/6EI and δB = wL⁴/8EI. 2. With downward load the slope and deflection are negative in the usual sign convention.
Explanation
Integrating EI y″ = −w (L − x)²/2 twice gives the slope wL³/6EI and the deflection wL⁴/8EI at the free end. (The options (b) and (d) are identical in the printed paper.)
Why the other options are wrong
Options (a) and (c) interchange the denominators 6 and 8.
Shortcut
UDL cantilever: θ = wL³/6EI, δ = wL⁴/8EI.
Common mistake
Using 8EI and 6EI the wrong way round.
Correct answer: D) −WL³/6EI and −WL⁴/8EI