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 this problem using the method of joints and MATLAB, you need to follow the below steps:
Step 1: Identify the unknown axial forces in the bars.
In this case, the truss has five bars (AB, BC, CD, DE, and AC), so the vector {X} of unknown axial forces in the bars will have five elements. Let's order the vector {X} as follows:
{X} = [F_AB, F_BC, F_CD, F_DE, F_AC]
Step 2: Write the equilibrium equations for each joint.
Start by analyzing each joint individually and write equilibrium equations for forces in the x and y directions. For each joint, sum the forces in the x and y directions to zero. This will give you a set of simultaneous equations.
Step 3: Write the equations in matrix form.
Convert the simultaneous equations into a matrix equation. The matrix equation will be in the form AX = B, where A is a coefficient matrix, X is the vector of unknowns, and B is the vector of known values.
Step 4: Solve the matrix equation using MATLAB.
Using the matrix equation from step 3, you can solve for the unknowns {X} using MATLAB's matrix operations. Simply input the coefficient matrix A and the vector B into MATLAB and solve for X.
Step 5: Interpret the results.
Once you have obtained the solution vector {X} in MATLAB, you can interpret the results to find the axial forces in the bars and reactions at the supports. Each element of the vector {X} corresponds to a specific bar in the truss.
Remember to input the given load W = 2 kN applied vertically to joint C in the equilibrium equations when solving for the unknowns.
Following these steps, you can use the method of joints and MATLAB to find the axial forces in the bars and reactions at the supports in the truss.