The maximum shear stress at the neutral axis due to a shear force F on a rectangular section of area A is:
Try it first: pick an option, then read the explanation.
Correct answer: C. 3F/2A
Asked in SSC JE 04/03/2017 (Evening)
Detailed Explanation
The average shear stress is F/A. In a rectangle the parabolic distribution makes the peak 50 % higher than the average.
\[ \tau_{max} = \frac{3}{2}\cdot\frac{F}{A} \]
Why “3F/2A” Is Correct
The maximum shear stress is 3F/(2A), at the neutral axis.
Why the Other Options Are Wrong
- A. F/A: F/A is the average shear stress, not the maximum.
- B. F/2A: F/2A is half the average.
- D. 2F/3A: 2F/3A is the inverse factor — smaller than the average.
Key Point
Rectangle: τmax = 3F/(2A).
Key Concepts for Students
- Circle: τmax = 4F/(3A).
- Shear stress is zero at the top and bottom.
- IS 800 uses average web shear for rolled I-sections.
Practice more: this is question 30 in Bending and Shear Stress MCQs – Part 2. Try the whole set and check every answer instantly.