Question 6.41: Determine the force in members FG, GC and CB of the truss us...
Determine the force in members FG, GC and CB of the truss used to support the sign, and state if the members are in tension or compression.
Method of Sections: The forces in members FG, GC, and CB are exposed by cutting the truss into two portions through section a–a on the upper portion of the free-body diagram, Fig. a. From this free-body diagram, \mathbf{F}_{C B}, \mathbf{F}_{G C}, \text { and } \mathbf{F}_{F G} can be obtained by writing the moment equations of equilibrium about points G, E, and C, respectively
\hookrightarrow + \Sigma M_G=0 ; \quad 900(6)+1800(3)-F_{C B}(3)=0
F_{C B}=3600 \mathrm{~N}=3.60 \mathrm{kN} (\mathrm{T})
\hookrightarrow +\Sigma M_E=0 ; \quad \quad F_{G C}(6)-900(6)-1800(3)=0
F_{G C}=1800 \mathrm{~N}=1.80 \mathrm{kN} (\mathrm{C})
\hookrightarrow +\Sigma M_C=0 ; \quad 900(6)+1800(3)-F_{F G} \sin 26.57^{\circ}(6)=0
F_{F G}=4024.92 \mathrm{~N}=4.02 \mathrm{kN} (\mathrm{C})
