Question

A fixed beam of uniform cross-section carries a point load \( P \) at the mid-span. If the moment of inertia of the middle half portion is reduced to half its previous value, then the fixed end moments will

• A. Increase
• B. Decrease
• C. Remain constant
• D. Change direction

Hint:

- The fixed end moment is directly proportional to the stiffness of the beam.

Answer 1

The Correct Option is B

Step 1: Understanding fixed end moment changes. - The fixed end moments (\( FEM \)) depend on stiffness, which is proportional to moment of inertia (\( I \)). 
Step 2: Effect of reducing \( I \). - Since \( FEM = \frac{P L}{8} \cdot \frac{I}{L} \), reducing \( I \) to half means the FEM will decrease. Thus, the correct answer is (B) Decrease.