Question

A beam having rectangular cross section is subjected to transverse loading. The ratio of maximum shear stress developed in the beam to the average shear stress is:

• A. 1.50
• B. 1.25
• C. 1.33
• D. 1.66

Hint:

In rectangular beams, the maximum shear stress is 1.5 times the average shear stress. This ratio is critical when designing beams to resist shear forces.

Answer 1

The Correct Option is A

The maximum shear stress \( \tau_{\text{max}} \) in a rectangular beam subjected to transverse loading occurs at the neutral axis (the middle of the beam). The average shear stress \( \tau_{\text{avg}} \) is the total shear force divided by the cross-sectional area of the beam. For a rectangular cross-section, the relationship between the maximum and average shear stress is given by the formula: \[ \frac{\tau_{\text{max}}}{\tau_{\text{avg}}} = \frac{3}{2} = 1.5. \] Thus, the ratio of the maximum shear stress to the average shear stress is 1.5, and the correct answer is \( (A) 1.50 \). Final Answer: 1.50