Consider the following statements regarding the distribution shear stress assumptions : 1. For all values of y, q is uniform across the width of the cross-section, irrespective of its shape. 2. ‘F = (dM/dx)’ is derived from the assumption that bending stress varies non-linearly across the section and is not zero at the centroid. 3. The material is homogenous and isotropic and the value of E is the same for tension as well as compression. Which of the above statements is/are correct ?
- A1 and 2 only
- B2 and 3 only
- C1 and 3 onlyCorrect
- D1, 2 and 3
Solution
Concept
Assumptions behind τ = VAȳ / Ib
Formula
τ = V A ȳ / (I b)
Step-by-step solution
1. The shear stress is assumed uniform across the width at a given level (statement 1 true). 2. The flexure formula assumes bending stress varies linearly and is zero at the neutral axis (statement 2 false). 3. The material is homogeneous and isotropic with equal E in tension and compression (statement 3 true).
Explanation
The usual derivation of the shear stress formula rests on linear bending stress, a uniform shear across the width, and an elastic, homogeneous material.
Why the other options are wrong
Statement 2 contradicts the linear distribution of bending stress.
Shortcut
Bending stress: linear, zero at NA.
Common mistake
Accepting non-linear stress.
Correct answer: C) 1 and 3 only