Which of the following methods is NOT used for finding the deflection of a beam?
Try it first: pick an option, then read the explanation.
Correct answer: D. Moment distribution method
Asked in SSC JE 23/03/2021 (Morning)
Detailed Explanation
The moment distribution method, developed by Hardy Cross, balances moments at the joints of continuous beams and frames by repeated distribution and carry-over. Its output is a set of end moments.
Why “Moment distribution method” Is Correct
The moment distribution method is an analysis method for statically indeterminate structures: it gives the support moments, after which the beam can be analysed further. It is not itself a deflection method.
| Method | Used for | Basis |
|---|---|---|
| Double integration | Slope and deflection | Integrate EI y'' = M twice; constants from boundary conditions |
| Macaulay's (singularity function) method | Slope and deflection with discontinuous loads | One BM equation with brackets ⟨x − a⟩ |
| Moment-area (Mohr's theorems) | Slope and deflection | Area and moment of area of the M/EI diagram |
| Conjugate beam | Slope and deflection | M/EI diagram applied as load on a conjugate beam |
| Strain energy / Castigliano / unit load | Deflection at a point | Energy principles |
| Mohr's circle | Stresses on inclined planes — not deflection | Graphical stress transformation |
| Moment distribution / three-moment equation | Support moments in indeterminate beams — not deflection | Stiffness and carry-over / compatibility |
Why the Other Options Are Wrong
- A. Moment area method: The moment area method directly gives slopes and deflections.
- B. Castigliano's method: Castigliano's theorem: deflection = ∂U/∂P.
- C. Strain energy method: Strain energy (and the unit load method) is widely used for deflections.
Key Point
Moment distribution → support moments (indeterminate analysis), not deflection.
Key Concepts for Students
- Moment distribution uses stiffness (4EI/L or 3EI/L) and carry-over factors.
- Deflection methods: double integration, Macaulay, moment area, conjugate beam, energy methods.
- Slope-deflection method also solves indeterminate structures.
Practice more: this is question 13 in Slope and Deflection MCQs – Part 1. Try the whole set and check every answer instantly.