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-3(1.5)-4(2)-10(4)+E_y(4)=0 [/latex]

[latex]E_y=13.125 \mathrm{kN} [/latex]

[latex] +↑ \Sigma F_y=0 ; \quad A_y-8-4-10+13.125=0[/latex]

[latex]A_y=8.875 \mathrm{kN} [/latex]

[latex] +↑ \Sigma F_x=0 ; \quad A_x=3 \mathrm{kN}[/latex]

Joint B:

[latex] \overset{+}\longrightarrow {} \Sigma F_x=0 ; \quad F_{B C}=3 \mathrm{kN} (\mathrm{C})[/latex]

[latex] +↑\Sigma F_y=0 ; \quad F_{B A}=8 \mathrm{kN} (\mathrm{C}) [/latex]

Joint A:

[latex] +↑\Sigma F_y=0 ; \quad 8.875-8-\frac{3}{5} F_{A C}=0[/latex]

[latex] F_{A C}=1.458=1.46 \mathrm{kN} (\mathrm{C})[/latex]

[latex]\overset{+}\longrightarrow {} \Sigma F_x=0 ; \quad F_{A F}-3-\frac{4}{5}(1.458)=0[/latex]

[latex] F_{A F}=4.17 \mathrm{kN} (\mathrm{T})[/latex]

Joint C:

[latex]\overset{+}\longrightarrow {} \Sigma F_x=0 ; \quad 3+\frac{4}{5}(1.458)-F_{C D}=0 [/latex]

[latex] F_{C D}=4.167=4.17 \mathrm{kN} (\mathrm{C})[/latex]

[latex] +↑\Sigma F_y=0 ; \quad F_{C F}-4+\frac{3}{5}(1.458)=0 [/latex]

[latex]F_{C F}=3.125=3.12 \mathrm{kN} (\mathrm{C}) [/latex]

Joint E:

[latex]\overset{+}\longrightarrow {} \Sigma F_x=0 ; \quad F_{E F}=0 [/latex]

[latex] +↑ \Sigma F_y=0 ; \quad F_{E D}=13.125=13.1 \mathrm{kN} (\mathrm{C})[/latex]

Joint D:

[latex] +↑ \Sigma F_y=0 ; \quad 13.125-10-\frac{3}{5} F_{D F}=0[/latex]

[latex] F_{D F}=5.21 \mathrm{kN} (\mathrm{T})[/latex]

[latex]\overset{+}\longrightarrow {} \Sigma F_x=0 ; \quad 4.167-\frac{4}{5}(5.21)=0 [/latex]

Question 6.120: Determine the force in each member of the truss and state if...