Which of the following is NOT a method for estimating deflections in beams?
Try it first: pick an option, then read the explanation.
Correct answer: C. Mohr's circle method
Asked in SSC JE 15/11/2022 (Shift I)
Detailed Explanation
Beam deflection methods all work with the bending moment (or its derivatives) along the beam. Mohr's circle is a stress-transformation tool for a single point in a stressed body.
Why “Mohr's circle method” Is Correct
Mohr's circle gives principal stresses, maximum shear stress and stresses on any inclined plane. It is not used to compute deflections. Do not confuse it with Mohr's theorems (the moment-area method), which are 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. Integration of the bending moment equation: Double integration of EI y'' = M is the basic deflection method.
- B. Integration of the shear force and load equations: EI y'''' = w and EI y''' = V can be integrated four or three times to find deflection.
- D. Moment area method: The moment area method (Mohr's theorems) is a standard deflection method.
Key Point
Mohr's circle → stresses; Mohr's theorems (moment area) → deflection.
Key Concepts for Students
- Other deflection methods: Macaulay, conjugate beam, strain energy, Castigliano, unit load.
- Mohr's circle radius = maximum in-plane shear stress.
- Moment area method is handy for cantilevers and symmetric beams.
Practice more: this is question 10 in Slope and Deflection MCQs – Part 1. Try the whole set and check every answer instantly.