A load W=2 kN is applied vertically to joint C of truss ABCDE as indicated. You will use the method of joints to obtain the axial forces in the bars and reactions at the supports A, E .

We start with the classification of the degrees of freedom as "free" or "constrained".

From the geometry of the truss, we see that we have:

Free DOF x and y at B, C, and D.

Constrained DOF x and y at A and E .

Question 1: Use MATLAB to find the axial forces in the bar.

Order the vector {X} of unknown axial forces in the bars as:

To use MATLAB to find the axial forces in the bars of the truss, you need to set up and solve a system of equations. Here's how you can do it step by step:

1. Identify the unknown axial forces in the bars. Let's label the bars as follows:
- Bar AB: F_AB
- Bar BC: F_BC
- Bar CD: F_CD
- Bar CE: F_CE
- Bar DE: F_DE

2. Write the equations for force equilibrium at each joint. Since joint C has a load applied vertically, we can start by analyzing the forces at joint C.

- In the x-direction: F_BC * cos(theta) - F_CD * cos(90 degrees) - F_CE * cos(theta) = 0
- In the y-direction: -W + F_BC * sin(theta) - F_CD * sin(90 degrees) - F_CE * sin(theta) = 0

Here, theta represents the angle formed by the inclined bars BC and CE with the horizontal direction.

3. Next, move on to joint B. We can write force equilibrium equations at joint B as follows:

- In the x-direction: F_AB * cos(theta) - F_BC * cos(theta) = 0
- In the y-direction: -F_AB * sin(theta) + F_BC * sin(theta) = 0

4. Now, let's consider joint D. We can write force equilibrium equations at joint D as follows:

- In the x-direction: -F_CD * cos(90 degrees) + F_DE * cos(theta) = 0
- In the y-direction: -F_CD * sin(90 degrees) - F_DE * sin(theta) = 0

5. Finally, we need to analyze the reactions at supports A and E. Since these supports are fixed, the horizontal and vertical forces at these points should be zero. Therefore, we have:

- At support A: -F_AB - F_DE = 0
- At support E: -F_CE = 0

6. Now, you can rearrange these equations to form a system of equations in the form of AX = B, where X is the vector of unknown axial forces {F_AB, F_BC, F_CD, F_CE, F_DE}. The matrix A and vector B can be constructed based on the coefficients in the equations.

7. Once you have the system of equations, you can solve it using MATLAB's matrix operations. You can use the backslash operator (\) to solve for X in the equation AX = B. Simply type the following command in MATLAB:

X = A \ B

This will give you the vector X, which contains the unknown axial forces in the bars.

Note: Make sure to substitute the appropriate values for W, theta, and any other dimensions or quantities given in the problem before solving the equations.