Which of the following is an assumption made in the theory of simple bending?
Try it first: pick an option, then read the explanation.
Correct answer: D. The beam is in equilibrium
Asked in SSC JE 23/09/2019 (Morning)
Detailed Explanation
The bending equation M/I = σ/y = E/R is derived under a set of simplifying assumptions. Three of the options here are simply those assumptions turned upside down.
Why “The beam is in equilibrium” Is Correct
The beam is assumed to be in static equilibrium under the applied moment, so that the internal resisting moment equals the external bending moment.
| Assumption of simple bending | Why it is needed |
|---|---|
| Material is homogeneous and isotropic | Same E everywhere and in every direction |
| Hooke's law holds (stress within elastic limit) | Stress is proportional to strain |
| E is the same in tension and compression | Neutral axis passes through the centroid |
| Plane sections remain plane after bending | Strain varies linearly with y |
| Beam initially straight, radius of curvature large compared with depth | Simple geometry of bending |
| Beam in equilibrium under pure bending (no shear, no axial force) | Only M acts on the section |
| Each layer expands or contracts freely | Layers act independently |
Why the Other Options Are Wrong
- A. The value of Young's modulus varies in tension and compression: The theory assumes E is the same in tension and compression.
- B. The material of the beam is not homogeneous: The material is assumed homogeneous and isotropic.
- C. Beam material within the elastic limit does not obey Hooke's law: The material is assumed to obey Hooke's law within the elastic limit.
Key Point
Simple bending: homogeneous, isotropic, Hooke's law, equal E in tension and compression, plane sections plane, beam in equilibrium.
Key Concepts for Students
- If E differs in tension and compression, the N.A. no longer passes through the centroid.
- Composite (flitched) beams are handled with the modular ratio.
- Pure bending means zero shear force over the length.
Practice more: this is question 13 in Bending and Shear Stress MCQs – Part 1. Try the whole set and check every answer instantly.