Question

The ratio of the maximum shear stress and the average shear stress in a circular section is

• A. \(\dfrac{3}{4}\)
• B. \(\dfrac{4}{3}\)
• C. \(\dfrac{2}{3}\)
• D. \(\dfrac{3}{2}\)

Hint:

Maximum shear stress: \[ \boxed{ \begin{aligned} \text{Rectangle} &: \tau_{\max}=1.5\,\tau_{\text{avg}}\\ \text{Circle} &: \tau_{\max}=\frac{4}{3}\tau_{\text{avg}} \end{aligned} } \]

Answer 1

The Correct Option is B

Step 1: Recall how shear stress is distributed over a circular cross section.
Unlike a rectangle, the width of a circle changes as you move away from the centre, so the shear stress does not follow the same parabolic curve there and the peak works out to a different multiple of the average value.
Step 2: Recall the average shear stress.
\[ \tau_{avg} = \frac{V}{A}. \]
Step 3: Recall the known result for the maximum stress in a solid circular section.
For a circular section, the maximum shear stress at the neutral axis works out to \[ \tau_{max} = \frac{4}{3}\tau_{avg}. \]
\[ \boxed{\frac{4}{3}} \]