A cantilever ABC, fixed at A, carries downward point loads of 20 kN at B (2 m from A) and 10 kN at the free end C (1 m beyond B). EI is constant. The slope at the fixed end A is:
Try it first: pick an option, then read the explanation.
Correct answer: A. zero
Asked in SSC JE 06/06/2024 (4 pm–6 pm)
Detailed Explanation
A fixed (built-in) support stops both translation and rotation of the beam end. This is a boundary condition, not something that depends on the loads.
Why “zero” Is Correct
At the fixed end the tangent to the elastic curve stays horizontal, so the slope is zero. The numbers in the other options are slopes at other points: for example the free-end slope here is 20(2)²/2EI + 10(3)²/2EI = 40/EI + 45/EI = 85/EI.
Why the Other Options Are Wrong
- B. 105/EI: 105/EI is not the slope at any point of this beam.
- C. 13.33/EI: 13.33/EI does not match the loading.
- D. 85/EI: 85/EI is the slope at the free end C, not at the fixed end.
Key Point
Fixed end: slope = 0 and deflection = 0, always.
Key Concepts for Students
- Free-end slope by superposition: Σ W·a²/2EI.
- Maximum slope and deflection of a cantilever occur at the free end.
- Fixed-end conditions are used to find the integration constants.
Practice more: this is question 3 in Slope and Deflection MCQs – Part 1. Try the whole set and check every answer instantly.