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 the shear stress distribution. For a solid circular section, \[ \tau_{\max} = \frac{4}{3}\tau_{\text{avg}}, \] where \[ \tau_{\text{avg}} = \frac{V}{A}. \]

Step 2: Determine the required ratio. Therefore, \[ \boxed{ \frac{\tau_{\max}}{\tau_{\text{avg}}} = \frac{4}{3} } \] Hence, \[ \boxed{(B)} \] is the correct answer.