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

Question

Accepted Answer

[latex] ⤹ +\Sigma M_A=0 ; \quad D_y(30)-1000(20)=0[/latex]

[latex] D_y=666.7 \mathrm{lb}[/latex]

[latex]\overset{+}\longrightarrow {} \Sigma F_x=0 ; \quad A_x=0 \ +↑ \Sigma F_y=0 ; \quad A_y-1000+666.7=0[/latex]

[latex] A_y=333.3 \mathrm{lb}[/latex]

Joint A:

[latex]\overset{+}\longrightarrow {} \Sigma F_x=0 ; \quad F_{A B}-F_{A G} \cos 45^{\circ}=0 [/latex]

[latex]+↑ \Sigma F_y=0 ; \quad 333.3-F_{A G} \sin 45^{\circ}=0 [/latex]

[latex]F_{A G}=471 \mathrm{lb} (\mathrm{C}) [/latex]

[latex]F_{A B}=333.3=333 \mathrm{lb} (\mathrm{T}) [/latex]

Joint B:

[latex] \overset{+}\longrightarrow {} \Sigma F_x=0 ; \quad F_{B C}=333.3=333 \mathrm{lb} (\mathrm{T})[/latex]

[latex] +\uparrow \Sigma F_y=0 ; \quad F_{G B}=0[/latex]

Joint D:

[latex] \overset{+}\longrightarrow {} \Sigma F_x=0 ; \quad-F_{D C}+F_{D E} \cos 45^{\circ}=0[/latex]

[latex]+↑ \Sigma F_y=0 ; \quad 666.7-F_{D E} \sin 45^{\circ}=0[/latex]

[latex]F_{D E}=942.9 \mathrm{lb}=943 \mathrm{lb} (\mathrm{C}) [/latex]

[latex] F_{D C}=666.7 \mathrm{lb}=667 \mathrm{lb} (\mathrm{T})[/latex]

Joint E:

[latex] \overset{+}\longrightarrow {} \Sigma F_x=0 ; \quad-942.9 \sin 45^{\circ}+F_{E G}=0[/latex]

[latex] +↑ \Sigma F_y=0 ; \quad-F_{E C}+942.9 \cos 45^{\circ}=0[/latex]

[latex] F_{E C}=666.7 \mathrm{lb}=667 \mathrm{lb} (\mathrm{T})[/latex]

[latex] F_{E G}=666.7 \mathrm{lb}=667 \mathrm{lb} (\mathrm{C})[/latex]

Joint C:

[latex]+↑ \Sigma F_y=0 ; \quad F_{G C} \cos 45^{\circ}+666.7-1000=0 [/latex]

[latex]F_{G C}=471 \mathrm{lb} (\mathrm{T}) [/latex]

Question 6.126: Determine the force in each member of the truss and state if...