Question

A fixed beam AB is subjected to a triangular load varying from zero at end A to \( w \) per unit length at end B. The ratio of fixed end moment at B to that at A will be ............

• A. \( \frac{1}{2} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{3}{2} \)

Hint:

For a fixed beam with a triangular load, the fixed end moment at the point with zero load is always higher than at the point with maximum load.

Answer 1

The Correct Option is D

For a fixed beam subjected to a triangular load, the fixed end moments can be derived using the standard formula for a triangular load distributed along the beam.
The fixed end moment at any point of the beam under a triangular load varies depending on the location of the point. For a triangular load \( w \) at one end and zero at the other, the ratio of fixed end moment at the two ends is a known result.
The maximum bending moment occurs at the point where the load is zero (at \( A \)), and the moments at both ends are related as follows: \[ \text{Moment at A} = \frac{wL^2}{12} \] \[ \text{Moment at B} = \frac{3wL^2}{12} \] Thus, the ratio of the fixed end moment at B to that at A is: \[ \frac{M_B}{M_A} = \frac{\frac{3wL^2}{12}}{\frac{wL^2}{12}} = \frac{3}{1} = \frac{3}{2} \] Therefore, the ratio of the fixed end moment at B to that at A is \( \frac{3}{2} \).