Question

A simply supported beam of span \( L \) and constant width \( b \) carries a point load \( W \) at mid span. The depth of the beam required at the mid span to make the beam of uniform strength for maximum extreme fibre stress \( \sigma \) is

• A. \( d = \frac{3WL}{2bp} \)
• B. \( d = \frac{\sqrt{3WL}}{2bp} \)
• C. \( d^2 = \frac{3WL}{2bp} \)
• D. \( d = \frac{2WL}{3bp} \)

Hint:

In problems involving bending stress, the depth of the beam is critical for maintaining uniform strength under loading. Always apply the correct formula based on material properties and loading conditions.

Answer 1

The Correct Option is B

To determine the required depth \( d \) of the beam, we apply the principle of uniform strength, which relates the bending stress to the beam's cross-sectional dimensions. The formula for the depth \( d \) of the beam for maximum fibre stress is derived as: \[ d = \frac{\sqrt{3WL}}{2bp} \] Thus, the correct answer is \( d = \frac{\sqrt{3WL}}{2bp} \).