A cantilever of span L carries a UDL w over its whole length and an upward concentrated load P at its free end. For the vertical displacement at the free end to be zero, P must be:
Try it first: pick an option, then read the explanation.
Correct answer: B. 3wL/8
Asked in SSC JE 30/10/2020 (Morning)
Detailed Explanation
By superposition, the downward tip deflection from the UDL must be cancelled exactly by the upward tip deflection from P. This is the same as finding the prop reaction of a propped cantilever.
\[ \frac{wL^4}{8EI} = \frac{PL^3}{3EI} \Rightarrow P = \frac{3wL}{8} \]
Why “3wL/8” Is Correct
P = 3wL/8. The fixed end then carries the rest of the load, 5wL/8 — the familiar reactions of a propped cantilever with a UDL.
Why the Other Options Are Wrong
- A. 5wL/8: 5wL/8 is the reaction at the fixed end of the propped cantilever, not the prop force.
- C. 3wL/5: 3wL/5 has no basis here.
- D. 2wL/5: 2wL/5 has no basis here.
Key Point
Propped cantilever with UDL: prop reaction 3wL/8, fixed-end reaction 5wL/8.
Key Concepts for Students
- Fixed-end moment of a propped cantilever with UDL = wL²/8.
- Maximum sagging moment = 9wL²/128 at 3L/8 from the prop.
- Compatibility (zero deflection at the prop) solves one redundant.
Practice more: this is question 18 in Slope and Deflection MCQs – Part 2. Try the whole set and check every answer instantly.