The maximum shear stress τmax for a beam of circular section is (where A is cross-sectional area and V is shear force.)
- A5V / 3A
- B3V / 4A
- C3V / 5A
- D4V / 3ACorrect
Solution
Concept
Maximum shear stress for common sections
Formula
τmax = (4/3) τavg (circle); (3/2) τavg (rectangle)
Step-by-step solution
1. For a circular section the maximum shear stress occurs at the neutral axis. 2. τmax = (4/3) × V/A = 4V/3A.
Explanation
The maximum shear stress is 4/3 times the average shear stress for a solid circular section. It is 3/2 times for a rectangle.
Why the other options are wrong
3V/4A, 5V/3A and 3V/5A are not the multiples of the average stress for a circle.
Shortcut
Circle 4/3, rectangle 3/2, triangle 3/2.
Common mistake
Using 3/2.
Correct answer: D) 4V / 3A