Question

A point in a circular beam of diameter D is subjected to a shear force of F. The ratio of average shear stress to maximum shear stress is

• A. 0.75
• B. 1.33
• C. 1.50
• D. 0.67

Hint:

Be careful with the wording of the ratio.
- Max to Average for a circle is $\tau_{max} / \tau_{avg} = 4/3 \approx 1.33$.
- Average to Max for a circle is $\tau_{avg} / \tau_{max} = 3/4 = 0.75$.
Read the question carefully to provide the correct ratio.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
Circular beam: ratio τ_avg/τ_max = ?

Step 2: Key Formula (Alternate):
For circle: τ_max = (4/3)×τ_avg. So τ_avg/τ_max = 3/4.

Step 3: Detailed Explanation:
3/4 = 0.75. Compare: rectangle has ratio 2/3≈0.667. Triangle has ratio 2/3. Circle has highest avg-to-max ratio among common shapes.

Step 4: Final Answer:
0.75.