In a beam, at a section carrying a shear force F, the shear stress is maximum at the:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2012
Detailed Explanation
The first moment of the area above a layer, Aȳ, grows as the layer moves down from the top and is largest when the layer reaches the neutral axis.
Why “neutral surface” Is Correct
For rectangular, circular and I-sections the shear stress peaks at the neutral surface, and is zero at the top and bottom fibres. Mid-depth is the same place only for sections symmetric about the horizontal axis; the general answer is the neutral surface. (A triangle is an exception: its peak is at mid-height.)
Why the Other Options Are Wrong
- B. topmost fibre: The top fibre is a free surface: shear stress is zero there.
- C. bottommost fibre: The bottom fibre is also a free surface with zero shear stress.
- D. mid-depth: Mid-depth coincides with the N.A. only for symmetric sections; the general answer is the neutral surface.
Key Point
Shear stress is maximum at the neutral axis and zero at the extreme fibres (triangle: maximum at h/2).
Key Concepts for Students
- Bending stress is zero exactly where shear stress is maximum.
- τmax = 1.5τavg (rectangle), 4/3 τavg (circle).
- Horizontal shear causes sliding of layers — the reason glued timber beams fail at mid-depth.
Practice more: this is question 25 in Bending and Shear Stress MCQs – Part 2. Try the whole set and check every answer instantly.