To solve this truss problem, we need to calculate the forces in each member of the truss and determine if they are in tension or compression. The truss is statically determinate, and the external forces are given as 60 N horizontally to the left at point B and 120 N at an angle of 30° to the right at point C. Let me walk through the steps required to solve this:

Step 1: Reaction Forces at Supports

Points $A$ and $D$ are the supports:

• Point $A$ is a roller, which means it can only exert a vertical reaction force ($A_y$).
• Point $D$ is a pinned support, meaning it can exert both horizontal ($D_x$) and vertical ($D_y$) reaction forces.

We can start by applying the equilibrium conditions to the entire truss.

Step 2: Equilibrium Equations

We use the three static equilibrium conditions:

1. Sum of forces in the x-direction: $\Sigma F_x = 0$
2. Sum of forces in the y-direction: $\Sigma F_y = 0$
3. Sum of moments about any point (e.g., point $A$): $\Sigma M_A = 0$

2.1. Horizontal Forces

$\Sigma F_x = 0: \quad D_x - 60 \, \text{N} + 120 \cos(30^\circ) = 0$ Solving this will give the horizontal reaction at $D$.

2.2. Vertical Forces

$\Sigma F_y = 0: \quad A_y + D_y - 120 \sin(30^\circ) = 0$ Solving this will provide the vertical reactions at points $A$ and $D$.

2.3. Moment about Point $A$

Taking moments about point $A$ to eliminate $A_y$: $\Sigma M_A = 0: \quad 60 \times 3 \, \text{m} - D_y \times 6 \, \text{m} + 120 \sin(30^\circ) \times 3 \, \text{m} = 0$ From this equation, we can find $D_y$, and then substitute it back into the vertical force equation to solve for $A_y$.

Step 3: Analyze Each Truss Member

Once the support reactions are known, we can use the method of joints or method of sections to solve for the forces in each member of the truss. Each joint is analyzed using equilibrium equations to find the internal forces.

For example, at joint $C$:

• Apply the equilibrium equations in the x and y directions to solve for the forces in members $BC$ and $CD$.

Repeat the process for other joints until all member forces are determined.

Let me perform the calculations step by step.The reaction forces at the supports are as follows:

• Vertical reaction at $A$ ($A_y$): $60 \, \text{N}$
• Vertical reaction at $D$ ($D_y$): approximately $0 \, \text{N}$ (very small value due to rounding errors, so it can be considered zero)
• Horizontal reaction at $D$ ($D_x$): $-43.92 \, \text{N}$ (to the left)

Next, we'll analyze the forces in each truss member using the method of joints, starting with joints $B$ and $C$, to determine the internal forces in the members.

Would you like me to proceed with the method of joints to determine the forces in the truss members, or would you like more explanation on the calculations so far?

Also, here are some follow-up questions to expand on this:

1. How do we identify whether a member is in tension or compression?
2. What is the significance of reaction forces at different types of supports (roller vs. pin)?
3. How would the solution change if the angle of the force at $C$ were different?
4. Can we use the method of sections instead of the method of joints for this problem? When would it be advantageous?
5. How does a change in the magnitude of the applied forces affect the internal forces in the truss members?

Tip: When analyzing trusses, always start by calculating the reaction forces at the supports before moving on to the internal forces.