Topic: Strength of Materials
A simply supported beam carries a load 'P' through a bracket as shown in the figure. The maximum bending moment in the beam is
- A. $\frac{Pl}{2}$
- B. $\frac{Pl}{2}+\frac{aP}{2}$
- C. $\frac{Pl}{2}+aP$
- D. $\frac{Pl}{2}-aP$
Answer: C. $\frac{Pl}{2}+aP$
Explanation: The load P on the bracket creates both a vertical load P at the center of the beam and a concentrated moment $M = P \times a$. Taking moments about support C to find the reaction at A: $R_{A} \times l + Pa = P \times \frac{l}{2}$, yielding $R_{A} = \frac{P}{2} - \frac{Pa}{l}$. The reaction at C is $R_{C} = P - R_{A} = \frac{P}{2} + \frac{Pa}{l}$. The mathematical calculation for the maximum bending moment evaluates to $M_{max} = (\frac{P}{2} - \frac{Pa}{l})\frac{l}{2} + Pa = \frac{Pl}{4} + \frac{Pa}{2} = \frac{1}{2}(\frac{Pl}{2} + Pa)$, which strictly points to option (b). However, the official ISRO answer key selected option (c).