What is the ratio of maximum shear stress to the average shear stress for a beam of rectangular cross-section?
- A1.25
- B1.5Correct
- C2.0
- D4.0
Solution
Concept
Shear stress distribution in a rectangle
Formula
τmax = 1.5 τavg
Step-by-step solution
1. τ = V A ȳ / (I b) is parabolic across the depth. 2. At the neutral axis τmax = 3V/2bd = 1.5 × (V/bd).
Explanation
In a rectangular section the maximum shear stress occurs at the neutral axis and is 1.5 times the average value.
Why the other options are wrong
1.25 is not a standard ratio, 2.0 is not for any common section, and 4/3 (1.33) is for a circle.
Shortcut
Rectangle 1.5, circle 4/3.
Common mistake
Using 4/3.
Correct answer: B) 1.5