Question

If the maximum shear stress in a rectangular beam cross section is 120 N/mm$^2$, then the average shear stress is

• A. 40 N/mm$^2$
• B. 80 N/mm$^2$
• C. 90 N/mm$^2$
• D. 180 N/mm$^2$

Hint:

Memorize the relationship between max and average shear stress for common shapes:
- Rectangle: $\tau_{max} = 1.5 \times \tau_{avg}$
- Circle: $\tau_{max} = \frac{4}{3} \times \tau_{avg} \approx 1.33 \times \tau_{avg}$
- I-Beam: $\tau_{max} \approx \tau_{avg}$ (in the web, where most shear is carried)

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Rectangular beam, τ_max=120 N/mm². Find τ_avg.

Step 2: Key Formula (Alternate):
For rectangle: τ_max = 1.5 × τ_avg. So τ_avg = τ_max/1.5.

Step 3: Detailed Explanation:
τ_avg = 120/1.5 = 80 N/mm². Parabolic distribution: zero at edges, max at center.

Step 4: Final Answer:
Average shear stress is 80 N/mm².