Question 6.3: Determine the forces in members FH, GH, and GI of the roof t...

STRATEGY: You are asked to determine the forces in only three members of the truss, so use the method of sections. Determine the reactions by treating the entire truss as a free body and then isolate part of it for analysis. In this case, you can use the same smaller part of the truss to determine all three desired forces.
MODELING and ANALYSIS: Your reasoning and computation should go something like the sequence given here.
Free Body: Entire Truss. From the free-body diagram of the entire truss (Fig. 1), find the reactions at A and L:

\pmb{\text{A}}=12.50 \text{ kN}\uparrow \quad \quad \quad \pmb{\text{L}}=7.50 \text{ kN}\uparrow

Note that

\tan \alpha=\frac{FG}{GL}=\frac{8 \text{ m}}{15 \text{ m}}=0.5333 \quad \quad \quad \quad \alpha=28.07^\circ

Force in Member GI. Pass section nn vertically through the truss (Fig. 1). Using the portion HLI of the truss as a free body (Fig. 2), obtain the value of F_{GI} :

F_{FH}=-13.81 \text{ kN} \quad \quad \quad F_{FH}=13.81 \text{ kN} \ C

Force in Member GH. First note that

\tan \beta=\frac{GI}{HI}=\frac{5 \text{ m}}{\frac{2}{3}(8 \text{ m})}=0.9375 \quad \quad \quad \beta=43.15 ^\circ

Then determine the value of F_{GH} by resolving the force \pmb{\text{F}}_{GH} into x and y components at point G (Fig. 4) and solving the equation \sum{M_L}=0.

F_{GH}=-1.371 \text{ kN} \quad \quad \quad F_{GH}=1.371 \text{ kN} \ C

REFLECT and THINK: Sometimes you should resolve a force into components to include it in the equilibrium equations. By first sliding this force along its line of action to a more strategic point, you might eliminate one of its components from a moment equilibrium equation.