Discussion
Ratio of maximum shear stress to the average shear stress in a rectangular beam subjected to torsion is ________.
Answer: B
The Board's key is 1.5, the standard textbook ratio for a rectangular section.
For a rectangular beam of width \(b\) and depth \(d\) carrying a shear force \(V\), the shear stress varies parabolically across the depth. It is zero at the top and bottom faces and largest at the neutral axis.
\[ \begin{aligned} \tau_{avg} &= \frac{V}{bd} \\ \tau_{max} &= \frac{3V}{2bd} \end{aligned} \]
\[ \frac{\tau_{max}}{\tau_{avg}} = 1.5 \]
The stem says the beam is subjected to torsion, but the 1.5 ratio belongs to transverse shear in bending; a twisted rectangular bar has a different stress pattern with no such simple average. The item is therefore best read as the transverse shear case, and 1.5 is the only option that matches it. A solid circular section gives 4/3 and a thin-walled circular tube gives 2, so those values do not describe a rectangle.
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