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 find the axial forces in the bars of the truss using MATLAB, you can follow these steps:
Step 1: Define the given information and the known values:
- Load applied at joint C: W = 2 kN
- Geometry of the truss: joints A, B, C, D, and E
Step 2: Draw the free-body diagram of the truss and label the forces acting on each joint. This will help you identify the forces in each bar.
Step 3: Apply the method of joints to each joint in the truss. The method of joints involves applying force equilibrium equations to each joint to determine the forces in the bars.
Step 4: Set up the equilibrium equations for each joint. Consider both the sum of forces in the x and y directions. If a joint has more than two unknown forces, you may need to use additional equations to solve for all the forces.
Step 5: Solve the system of equations using MATLAB. You can use matrix operations to set up the system of equations based on the equilibrium equations obtained from Step 4. Then, use MATLAB's matrix operations to solve for the unknown axial forces in the bars.
Step 6: Order the vector {X} of unknown axial forces in the bars as per the given instructions. This means arranging the vector in a specific order that matches the labeling of the bars in the truss. The ordering may vary depending on how the bars are labeled in the truss diagram.
Once you have completed these steps, you should be able to find the axial forces in the bars of the truss using MATLAB.