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Determine the force in each member of the truss and  state if the members are in tension or compression.

 

\( \stackrel{+}\longleftarrow \sum F_{x}=0 \)

\( -A_ x-3=0 \rightarrow-A_ x=3 \)

                     \( =A _x=3 k N\quad\longleftarrow \)

\( +\uparrow \sum F_ y=0 \longrightarrow \quad A_ y+E_ y-10-4-8=0 \quad  \longrightarrow A_ y+E_ y=22 \)

\( \sum M_{A}=0 \quad \longrightarrow \quad E_ y(4)-10(4)-4(2)-3(1.5)=0\quad \longrightarrow\quad ∴ E_y=13.125kN \)

\( ∴ A y=22-13.125=8.875 \mathrm{kN} \uparrow \)

Joint B:

 

 

\( \stackrel{+}\longrightarrow \sum F_{x}=0 \quad \longrightarrow 3-F_{B C}=0 \longrightarrow F_{B C}=3 k N \)

\( +\uparrow \sum F_ y=0 \quad \longrightarrow F_{A B}-8=0 \rightarrow F_{A  B}=8kN \)

Determine the force in each member of the truss and  state if the members are in tension or compression.

 

Joint A

 

\( +\uparrow \Sigma F_{y}=0 \)

\( 8.875-8-F_{A C}\left(\frac{1.5}{2.5}\right)=0 \)

\(∴ F_{A C}=1.46 \mathrm{kN} \quad(c) \)

\( \stackrel{+}{\longrightarrow} \sum F_{x}=0 \quad \longrightarrow F_{A F}-3-F_{A C}\left(\frac{2}{2 . 5}\right)=0 \quad \longrightarrow \quad ∴ F_{A F}=4.17 \mathrm{kN} \)

                                                                                                \( (T) \)

Joint C

 

\( +\uparrow \Sigma F_{y}=0 \quad \longrightarrow F_{C F}-4+1.46\left(\frac{1.5}{2.5}\right)=0 \)

\( ∴ F_{C F}=3.12 \mathrm{kN}(\mathrm{c}) \)

\(\stackrel{+}{\longrightarrow} \sum F_{x}=0 \quad \longrightarrow 3+1.46\left(\frac{2}{2.5}\right)-F_{CD}=0 \longrightarrow ∴ F_{C D}=4.168(c) \)

Determine the force in each member of the truss and  state if the members are in tension or compression.

Joint E

 

\( \stackrel{+}{\longrightarrow} \sum F_{x}=0 \)

\( ∴ F_{ E F}=0 \)

\( +\uparrow \sum F_{y}=0 \quad \longrightarrow 13.125-F_{ED}=0 \longrightarrow F_{ED}=13.125 \mathrm{kN}(\mathrm{c}) \)

Joint D

 

\( +\uparrow \sum F_ y=0 \)

\( 13.125-10- F_{DF }\left(\frac{1.5}{2.5}\right)=0 \)

\( ∴ F_{D F}=5.21 K N(T) \)

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