Question

A massless beam is fixed at one end and supported on a roller at other end. A point force \(P\) is applied at the midpoint of the beam as shown in figure. The reaction at the roller support is 

• A. \(\frac{5P}{16}\)
• B. \(\frac{2P}{3}\)
• C. \(\frac{4P}{9}\)
• D. \(\frac{9P}{25}\)

Hint:

For problems involving beams with point loads at the center, use symmetry and moment balance about the fixed support to solve for reactions.

Answer 1

The Correct Option is A

- This problem can be solved by using the concept of equilibrium and taking moments about the fixed end. The total force applied on the beam is \(P\), and the reaction at the roller support is unknown. Let \(R\) be the reaction at the roller. The force distribution is symmetrical because the point load is applied at the midpoint.
- By applying the equilibrium condition of moments, the reaction at the roller support is \(R = \frac{5P}{16}\).