Question

The truss shown is subjected to a force \( P \). All members of the truss have the same length \( L \). The reaction at A and force in member AB are 

• A. \( \frac{\sqrt{3}}{4}P \) and \( \frac{P}{2} \)
• B. \( \frac{\sqrt{3}}{8}P \) and \( \frac{\sqrt{3}}{4}P \)
• C. \( \frac{\sqrt{3}}{4}P \) and \( \frac{P}{4} \)
• D. \( P \) and \( \frac{P}{4} \)

Hint:

For truss analysis, use equilibrium equations to solve for reactions and forces in the members. Consider the geometry and symmetry of the truss.

Answer 1

The Correct Option is A

In this truss problem, we need to analyze the reaction at point A and the force in member AB under the applied force \( P \). Using static equilibrium equations, we can solve for the forces.

Step 1: Determine the reaction at A.
The reaction at A can be determined by resolving the forces in the vertical direction, considering the geometry of the truss. After applying equilibrium equations, we find the reaction at A to be \( \frac{\sqrt{3}}{4}P \).

Step 2: Calculate the force in member AB.
Next, we calculate the force in member AB by considering the force components and applying equilibrium conditions. The force in AB is \( \frac{P}{4} \).

Step 3: Conclusion.
Thus, the reaction at A is \( \frac{\sqrt{3}}{4}P \), and the force in member AB is \( \frac{P}{4} \).

Final Answer: \text{(C) \( \frac{\sqrt{3}}{4}P \) and \( \frac{P}{4} \)}