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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

$+\uparrow \sum F_ y=0$

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

$∴ F_{D F}=5.21 K N(T)$