What is the maximum deflection for cantilever subjected to udl throughout ? (Where E is the modulus of elasticity of concrete, I is the moment of inertia, L is the length of the span, P is the point load)
- A5ωL³ / 384EI
- BPL³ / 3EI
- CωL⁴ / 8EICorrect
- DPL³ / 84EI
Solution
Concept
Free-end deflection of a cantilever under a UDL
Formula
δ = ω L⁴ / 8EI
Step-by-step solution
1. Integrating EI y″ = −ω (L − x)²/2 twice gives δmax = ωL⁴/8EI at the free end.
Explanation
This is the standard result for a cantilever carrying a UDL over its whole span.
Why the other options are wrong
PL³/3EI is for a point load at the free end. 5ωL⁴/384EI is for a simply supported beam (and the option has L³).
Shortcut
UDL cantilever: wL⁴/8EI.
Common mistake
Choosing the simply supported value.
Correct answer: C) ωL⁴ / 8EI