The deflection δ at the free end of a cantilever is (where P is point load at the free end, EI is flexural rigidity and L is length of the cantilever.)
- APL² / 2EI
- BPL³ / 3EICorrect
- CPL³ / 2EI
- DPL² / 3EI
Solution
Concept
Free-end deflection of a cantilever
Formula
δ = P L³ / 3EI
Step-by-step solution
1. Double integration of EI y″ = −P (L − x) gives δmax = P L³ / 3EI at the free end.
Explanation
The deflection of a cantilever with an end load is PL³/3EI, and the slope is PL²/2EI.
Why the other options are wrong
PL²/2EI is the slope. PL³/2EI and PL²/3EI are not standard results.
Shortcut
Slope PL²/2EI; deflection PL³/3EI.
Common mistake
Giving the slope.
Correct answer: B) PL³ / 3EI