Point out the correct matching of beam and maximum deflection:
Try it first: pick an option, then read the explanation.
Correct answer: D. Cantilever, UDL w: wL⁴/(8EI)
Asked in SSC JE 2012
Detailed Explanation
Compare each option with the standard table of maximum deflections.
Why “Cantilever, UDL w: wL⁴/(8EI)” Is Correct
The cantilever with a UDL has δmax = wL⁴/(8EI) at the free end — option (d) is the only correct pair.
| Beam and loading | Maximum slope | Maximum deflection | Where |
|---|---|---|---|
| Cantilever, point load W at free end | WL²/2EI | WL³/3EI | Free end |
| Cantilever, UDL w over full length | wL³/6EI | wL⁴/8EI | Free end |
| Cantilever, triangular load (w at fixed end, 0 at free end) | wL³/24EI | wL⁴/30EI | Free end |
| Cantilever, couple M at free end | ML/EI | ML²/2EI | Free end |
| Simply supported, central point load W | WL²/16EI | WL³/48EI | Slope at supports, deflection at centre |
| Simply supported, UDL w over full span | wL³/24EI | 5wL⁴/384EI | Slope at supports, deflection at centre |
| Simply supported, equal end couples M (pure bending) | ML/2EI | ML²/8EI | Slope at supports, deflection at centre |
Standard results (EI constant). In a cantilever the slope and deflection are zero at the fixed end and maximum at the free end.
Why the Other Options Are Wrong
- A. Simply supported beam, central point load W: WL³/(384EI): The simply supported central-load deflection is WL³/48EI.
- B. Simply supported beam, UDL w: 3wL⁴/(384EI): The simply supported UDL deflection is 5wL⁴/384EI.
- C. Cantilever, point load W at tip: WL³/(48EI): The cantilever tip-load deflection is WL³/3EI (48 belongs to the simply supported case).
Key Point
Cantilever UDL: wL⁴/8EI; cantilever tip load: WL³/3EI; SS central load: WL³/48EI; SS UDL: 5wL⁴/384EI.
Key Concepts for Students
- Memorise the four basic deflection formulas — they solve most MCQs.
- Swapped coefficients (3 ↔ 48) are a common trap.
- Superposition combines these for multiple loads.
Practice more: this is question 39 in Slope and Deflection MCQs – Part 3. Try the whole set and check every answer instantly.