A beam has an angle (L) section with one leg vertical and the other leg horizontal at the top. Which of the following cross-sections has the same nature of shear stress distribution as the angle section?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 11/10/2023 (9 am–11 am)
Detailed Explanation
Shear stress at any level is τ = VAȳ/(Ib). It depends on the area above the level, its moment about the neutral axis, and the width b at that level. Sliding the horizontal leg sideways (angle versus T) changes none of these quantities.
Why “T-section” Is Correct
Both the angle and the T have a single wide flange at the top and a single narrow stem below. In both, τ rises from zero at the top, jumps up where the width drops from the flange to the stem, peaks at the neutral axis and falls parabolically to zero at the bottom tip. So the angle section behaves like the T-section.
Why the Other Options Are Wrong
- A. Cross (+) section: In the cross section the wide part is at mid-depth, so the stress drops near the neutral axis — a very different shape.
- C. I-section: The I-section has two flanges and two jumps, symmetric about the neutral axis.
- D. Triangular section: A triangle has no sudden width change, so its diagram is a smooth curve.
Key Point
Same width-versus-depth profile ⇒ same shear stress diagram (angle ≡ T).
Key Concepts for Students
- A sudden change in width produces a sudden jump in shear stress.
- τ at a junction is inversely proportional to the width there.
- For unsymmetric sections like angles, the load must pass through the shear centre to avoid twisting.
Practice more: this is question 4 in Bending and Shear Stress MCQs – Part 1. Try the whole set and check every answer instantly.