Question

Use the method of sections to determine the forces in members BC, CD, and DE of the truss.

Use the method of sections to determine the forces in members BC, CD, and DE of the truss.

Answer 1

Take mom ent about point \(A\)

$$ \begin{array}{l} \sum M_{A}=0 \\ -(10 \times 3)-(15 \times 6)+9 E_{y}=0 \\ E_{y}=\frac{120}{9} \\ =13.33 \mathrm{kN} \end{array} $$

Take section vertically between \(B C\) and \(D E\).

Take mom ent about point \(C\).

$$ \begin{array}{l} \sum M_{C}=0 \\ -3 F_{D E}+(13.33 \times 3)=0 \\ F_{D X}=13.33 \mathrm{kN} \end{array} $$

Apply equilibrium equations.

$$ \begin{array}{l} \sum F_{y}=0 \\ -F_{D C} \sin 45^{\circ}-15+13.33=0 \\ F_{D C}=-\frac{1.67}{\sin 45^{\circ}} \\ =-2.36 \mathrm{kN} \\ \sum F_{x}=0 \\ -F_{B C}-F_{D C} \cos 45^{\circ}=0 \end{array} $$

\(F_{B C}=-\left(-2.36 \cos 45^{\circ}\right)\)

$$ =1.67 \mathrm{kN} $$