Question

determine the force in member ef and indicate whether the member is in tension or compression
675 lb in compression;
1200 lb in tension;
540 lb in tension;
675 lb in tension;
540 lb in compression;

Explanation:

Step1: Take moment about point A

$$\sum M_A = 0$$
$$600\times8 + 900\times4 - C\times3 = 0$$
$$4800+3600 - 3C=0$$
$$3C = 8400$$
$$C = 2800\ lb$$

Step2: Use method of sections

Cut the truss through members \(EF\), \(ED\), and \(CD\). Take the left - hand side of the section.
Take moment about point \(D\)
$$\sum M_D=0$$
Let the force in member \(EF\) be \(F_{EF}\)
The vertical distance from \(A\) to \(D\) is \(8\ ft\) and horizontal distance from \(A\) to \(D\) is \(3\ ft\)
$$900\times4 - F_{EF}\times4=0$$
$$F_{EF}=900\times1 = 540\ lb$$
Since the force is positive, the member is in tension.

Answer:

540 lb in tension