Determine the force in members Kl, KD, and CD of the Pratt truss and state if the members

Question

Determine the force in members Kl, KD, and CD of the Pratt truss and state if the members are in tension or compression.

Accepted Answer

From the geometry of the truss,

[latex]\phi= an ^{-1}(3 \mathrm{~m} / 2 \mathrm{~m})=56.31^{\circ}[/latex].

[latex] ⤹ +\Sigma M_{K}=0[/latex];

[latex]33.33 \mathrm{kN}(8 \mathrm{~m})-40 \mathrm{kN}(2 \mathrm{~m})-F_{C D}(3 \mathrm{~m})=0[/latex]

[latex]F_{C D}=62.2 \mathrm{kN}(\mathrm{T})[/latex]

[latex] ⤹ +\Sigma M_{D}=0 ; \quad 33.33 \mathrm{kN}(6 \mathrm{~m})-F_{K J}(3 \mathrm{~m})=0[/latex]

[latex]F_{K J}=66.7 \mathrm{kN}(\mathrm{C})[/latex]

[latex]+\uparrow \Sigma F_{y}=0[/latex]

[latex]33.33 \mathrm{kN}-40 \mathrm{kN}+F_{K D} \sin 56.31^{\circ}=0[/latex]

[latex]F_{K D}=8.01 \mathrm{kN}(\mathrm{T})[/latex]

Question F5.9: Determine the force in members Kl, KD, and CD of the Pratt t......