Pick the correct statement:
Try it first: pick an option, then read the explanation.
Correct answer: D. All of these
Asked in SSC JE 24/01/2018 (Morning)
Detailed Explanation
Across a beam section the bending stress varies linearly from zero at the neutral axis, while the shear stress (for a rectangle) varies parabolically from zero at the outer fibres to a maximum at the neutral axis.
Why “All of these” Is Correct
Each statement holds. In particular, at the outer fibre the shear stress is zero, so the only stress is the normal bending stress — a stress acting on a plane with no shear is by definition a principal stress. Hence all of these.
| Level in section | Bending stress σ | Shear stress τ | Principal stress |
|---|---|---|---|
| Outer fibre | Maximum | Zero | σ itself |
| Neutral axis | Zero | Maximum | ±τ (pure shear) |
| In between | σ | τ | σ/2 ± √((σ/2)² + τ²) |
Why the Other Options Are Wrong
- A. The bending stress in a section is zero at its neutral axis and maximum at the outer fibres: True, but not the only true statement.
- B. The shear stress is zero at the outer fibres and maximum at the neutral axis: True for common sections, but not the only true statement.
- C. The bending stress at the outer fibres is a principal stress: True, but not the only true statement.
Key Point
Outer fibre: τ = 0 ⇒ bending stress is principal. Neutral axis: σ = 0, τ max.
Key Concepts for Students
- Principal planes carry no shear stress.
- At the neutral axis the element is in pure shear: principal stresses ±τ at 45°.
- This question links beam stresses with chapter 4.
Practice more: this is question 44 in Slope and Deflection MCQs – Part 3. Try the whole set and check every answer instantly.