Question

A two member truss PQR is supporting a load W. The axial forces in members PQ and QR are respectively

• A. 2W tensile and $\sqrt{3}$W compressive
• B. $\sqrt{3}$W tensile and 2W compressive
• C. $\sqrt{3}$W compressive and 2W tensile
• D. 2W compressive and $\sqrt{3}Wtensile$

Answer 1

The correct option is B

$\sqrt{3}$W tensile and 2W compressive

$\sum F_v=0$

$F_{QR}\cos {60}^{\circ }+W=0$

$F_{QR}=-\frac{W}{\cos 60}=-2W$

$=2W\left(\text{compressive}\right)$

$\sum F_H=0$

$\therefore F_{QP}+F_{QR}\cos {30}^{\circ }=0$

$F_{QP}=-F_{QR}\cos {30}^{\circ }$

$=-(-2W)\cos {30}^{\circ }$

$F_{QP}=+2W\times \sqrt{\frac{3}{2}}=+W\sqrt{3}\left(\text{tensile}\right)$