Question

The maximum shear stress \((q_{\max})\) in a rectangular beam is ____

• A. \(1.25\) times the average
• B. \(1.50\) times the average
• C. \(1.75\) times the average
• D. \(2.0\) times the average

Hint:

For common sections: \[ \boxed{ \begin{aligned} \text{Rectangular section: }& \tau_{\max}=1.5\,\tau_{\text{avg}}\\ \text{Circular section: }& \tau_{\max}=\frac{4}{3}\tau_{\text{avg}} \end{aligned} } \]

Answer 1

The Correct Option is B

Step 1: Recall the shear stress distribution in a rectangular section. The shear stress varies parabolically across the depth of a rectangular beam. The maximum shear stress occurs at the neutral axis.

Step 2: Use the standard relation. \[ \tau_{\max} = \frac{3}{2}\tau_{\text{avg}} = 1.5\,\tau_{\text{avg}} \] Hence, \[ \boxed{\tau_{\max}=1.5\,\tau_{\text{avg}}} \] Therefore, \[ \boxed{(B)} \] is the correct answer.