Discussion
A three-member truss is simply supported at Q and R, and loaded at P by a horizontal force \(F\) as shown. The force in QR is
Answer: B
The force in QR is F (tensile).
R is a roller, so its reaction is vertical. With PQ = QR (the 45-degree angle at R), take moments about Q:
\[ \begin{aligned} F \cdot PQ &= R_{R} \cdot QR \\ R_{R} &= F \ \text{(upward)} \end{aligned} \]
At joint R the forces are \(R_{R}\), the member PR at 45 degrees and the horizontal member QR. Vertical balance needs PR to supply F downward, so PR carries \(\sqrt{2}F\) in compression, pushing on R down and to the right. Its horizontal component F must then be balanced by QR pulling R to the left, toward Q, which is tension F.
\(\sqrt{2}F\) is the force in PR, not QR, and it is compressive. Zero would hold only if R took the horizontal load, which a roller cannot.
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