**Problem Analysis and Given Data:**

In this problem, we are given a roof truss that is simply supported on purlins. The purlins are attached to the joints of the top chord of the truss. The roof is subjected to uniformly distributed loading, which is transmitted by the purlins as concentrated loads to the truss joints. We need to determine the force in each member of the roof truss.

**Solution:**

To solve this problem, we will use the method of joints. We will consider each joint of the truss and apply the equations of equilibrium to determine the forces in the members.

**Step 1: Identify the External Reactions**

Since the roof is simply supported on purlins, there will be reactions at the supports. These reactions can be determined by taking moments about any point. Let's assume that the left support is at point A and the right support is at point B. Taking moments about point A, we have:

∑M_A = 0
RA * 6 - (w * 6 * 6/2) = 0
RA = (w * 6 * 6/2) / 6
RA = 18w

Similarly, taking moments about point B, we have:

∑M_B = 0
RB * 6 - (w * 6 * 6/2) = 0
RB = (w * 6 * 6/2) / 6
RB = 18w

Therefore, the reactions at points A and B are both equal to 18w.

**Step 2: Solve the Joints**

Now, we will consider each joint of the truss and apply the equations of equilibrium to determine the forces in the members.

Joint 1 (Left End):

At joint 1, there are three unknown forces: AB, AC, and AD. To solve for these forces, we will apply the equations of equilibrium in the x and y directions.

∑F_x = 0:
AB - AC * cos(60°) = 0
AB = AC * cos(60°)

∑F_y = 0:
AD + AC * sin(60°) - RA = 0
AD = -AC * sin(60°) + RA

Joint 2:

At joint 2, there are four unknown forces: BC, BD, CE, and CF. To solve for these forces, we will apply the equations of equilibrium in the x and y directions.

∑F_x = 0:
BC + BD * cos(60°) - CE * cos(60°) = 0
BC = CE

∑F_y = 0:
BD * sin(60°) + CE * sin(60°) - AD = 0
BD = (AD - CE * sin(60°)) / sin(60°)

Joint 3:

At joint 3, there are three unknown forces: DE, DF, and EF. To solve for these forces, we will apply the equations of equilibrium in the x and y directions.

∑F_x = 0:
DE - DF * cos(60°) = 0
DE = DF * cos(60°)

∑F_y = 0:
DF * sin(60°) - CE = 0
DF = CE / sin(60°)