Pick the incorrect statement. The intensity of horizontal shear stress at a layer of a beam section is directly proportional to:
Try it first: pick an option, then read the explanation.
Correct answer: D. the moment of inertia of the beam section about its neutral axis
Asked in SSC JE 23/01/2018 (Evening)
Detailed Explanation
Read each quantity off the formula τ = VAȳ/(Ib) and see whether it is in the numerator or the denominator.
\[ \tau = \frac{V\,A\,\bar y}{I\,b} \]
Why “the moment of inertia of the beam section about its neutral axis” Is Correct
I is in the denominator, so τ is inversely proportional to the moment of inertia. Statement (d) is the incorrect one.
Why the Other Options Are Wrong
- A. the shear force: Correct statement: τ ∝ V.
- B. the area of the section beyond the layer: Correct statement: τ ∝ A (area beyond the layer).
- C. the distance of the C.G. of that area from the neutral axis: Correct statement: τ ∝ ȳ.
Key Point
τ = VAȳ/(Ib): directly ∝ V, A, ȳ; inversely ∝ I and b.
Key Concepts for Students
- A stiffer (larger I) section has lower shear stress for the same V.
- Aȳ = first moment of area.
- Horizontal and vertical shear stresses at a point are equal (complementary).
Practice more: this is question 63 in Bending and Shear Stress MCQs – Part 5. Try the whole set and check every answer instantly.