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 solve for the unknown axial forces in the bars of the truss using the method of joints, you can follow these steps:
1. Assign coordinates to each joint: Label the joints A, B, C, D, and E, and assign coordinates to each joint based on the given geometry.
2. Identify the forces acting at each joint: Consider the applied load W and any known reaction forces at the supports A and E. Write the known forces as vectors, and assume the unknown axial forces in the bars as variables.
3. Apply the equilibrium equations to each joint: Apply the equations of equilibrium (ΣF_x = 0 and ΣF_y = 0) to each joint. This will allow you to write an equation for each joint in terms of the unknown axial forces and other known forces.
4. Solve the system of equations: Combine the equations from each joint to form a system of equations. This system can be solved using MATLAB or other computational tools.
5. Determine the unknown axial forces: Once you have solved the system of equations, you will obtain the values of the unknown axial forces in the bars of the truss.
To order the vector {X} of unknown axial forces in the bars, you need to list the axial forces based on the labeling of the bars. The bars can be labeled as AB, AC, BC, CD, and DE. So, the vector {X} of unknown axial forces would be ordered as follows:
{X} = [X_AB, X_AC, X_BC, X_CD, X_DE]
Make sure to substitute the appropriate values for the known forces and coordinates into the equations before solving the system of equations using MATLAB or any other tool for solving simultaneous equations.