Question

A plane truss PQRS (PQ = RS, and \( \angle PQR = 90^\circ \)) is shown in the figure. The forces in the members PR and RS, respectively, are \(\underline{\hspace{2cm}}\) 

• A. \( F \sqrt{2} \) (tensile) and \( F \) (tensile)
• B. \( F \sqrt{2} \) (tensile) and \( F \) (compressive)
• C. \( F \) (compressive) and \( F \sqrt{2} \) (compressive)
• D. \( F \) (tensile) and \( F \sqrt{2} \) (tensile)

Hint:

In truss problems, use symmetry and equilibrium equations to solve for forces in individual members. Use the method of joints or sections depending on the given problem.

Answer 1

The Correct Option is B

Given the plane truss PQRS with \( \angle PQR = 90^\circ \), and knowing that the truss is in static equilibrium, we apply the method of joints or method of sections to solve for the forces in the members PR and RS.

Step 1: Identify the forces acting on the joints
- The truss is symmetric, so we can apply symmetry to simplify calculations.
- The force in member PR can be found using the geometry of the truss and equilibrium equations.

Step 2: Calculate the forces
- The force in member RS can be determined using the fact that the angle \( \angle PQR = 90^\circ \), and by using the trigonometric relations in the truss.

We find that:
- The force in PR is \( F \sqrt{2} \), and it is tensile.
- The force in RS is \( F \), and it is compressive.

Thus, the correct answer is Option (B).
Final Answer: (B) \( F \sqrt{2} \) (tensile) and \( F \) (compressive)