Question

The maximum bending moment of a simply supported beam of span \( l \) and carrying a point load \( W \) at the centre of the beam is

• A. \( \dfrac{Wl}{2} \)
• B. \( \dfrac{Wl}{4} \)
• C. \( Wl \)
• D. \( 2Wl \)

Hint:

For a simply supported beam with a central point load, maximum bending moment always occurs at mid-span.

Answer 1

The Correct Option is B

Step 1: Understanding the loading condition.
A simply supported beam carries a concentrated load \( W \) at its mid-span. Due to symmetry, the reactions at both supports are equal.
Step 2: Calculating support reactions.
Each support reaction is: \[ R = \frac{W}{2} \]
Step 3: Finding maximum bending moment.
Maximum bending moment occurs at the centre of the beam: \[ M_{\max} = R \times \frac{l}{2} = \frac{W}{2} \times \frac{l}{2} \] \[ M_{\max} = \frac{Wl}{4} \]
Step 4: Conclusion.
The maximum bending moment is \( \dfrac{Wl}{4} \).