Question F5.11: Determine the force in members GF, GD, and CD of the truss a......
Determine the force in members GF, GD, and CD of the truss and state if the members are in tension or compression.
From the geometry of the truss,
\theta=\tan ^{-1}(1 \mathrm{~m} / 2 \mathrm{~m})=26.57^{\circ}
\phi=\tan ^{-1}(3 \mathrm{~m} / 2 \mathrm{~m})=56.31^{\circ}.
The location of O can be found using similar triangles.
\begin{aligned} \frac{1 \mathrm{~m}}{2 \mathrm{~m}} & =\frac{2 \mathrm{~m}}{2 \mathrm{~m}+x} \\ 4 \mathrm{~m} & =2 \mathrm{~m}+x \\ x & =2 \mathrm{~m} \end{aligned}
⤹ +\Sigma M_{G}=0
26.25 \mathrm{kN}(4 \mathrm{~m})-15 \mathrm{kN}(2 \mathrm{~m})-F_{C D}(3 \mathrm{~m})=0
F_{C D}=25 \mathrm{kN}(\mathrm{T})
⤹ +\Sigma M_{D}=0
26.25 \mathrm{kN}(2 \mathrm{~m})-F_{G F} \cos 26.57^{\circ}(2 \mathrm{~m})=0
F_{G F}=29.3 \mathrm{kN}(\mathrm{C})
⤹+\Sigma M_{O}=0 ; 15 \mathrm{kN}(4 \mathrm{~m})-26.25 \mathrm{kN}(2 \mathrm{~m})
-F_{G D} \sin 56.31^{\circ}(4 \mathrm{~m})=0
F_{G D}=2.253 \mathrm{kN}=2.25 \mathrm{kN}(\mathrm{T})