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:
Indicate your specific subject in the "School Subject" box, so those with expertise in the area will respond to the question.
The subject is physics, simonsay is who I wanted to answer it, can you answer it yourself or you don't know?
To find the axial forces in the bars using MATLAB, we first need to understand the truss structure and determine the unknowns.
In this case, we have a truss with joints A, B, C, D, and E. The load W of 2 kN is applied vertically at joint C.
To start, we classify the degrees of freedom (DOF) as "free" or "constrained" for each joint. From the geometry of the truss, we can determine the following:
- Free DOF in both x and y directions at joints B, C, and D.
- Constrained DOF in both x and y directions at joints A and E.
Now we move on to solving the problem using the method of joints. The method of joints involves analyzing each joint of the truss individually.
To begin, we start with joint A. Since joint A is a pin joint, it can only transmit forces along its members. Therefore, we assume that member AB is in tension (positive force) and member AE is in compression (negative force).
Next, we move on to joint B. The unknown forces at joint B are the axial forces in members BA and BC. Since joint B is in equilibrium, the sum of forces in both the x and y directions must be zero. We can write the following equations:
ΣF_x = 0: -F_{BA}*cos(45°) - F_{BC} = 0
ΣF_y = 0: -F_{BA}*sin(45°) + F_W = 0
Where F_{BA} and F_{BC} represent the axial forces in members BA and BC, respectively, and F_W is the vertical load at joint C.
Using MATLAB, you can define these equations as a system of linear equations and then solve for the unknowns F_{BA} and F_{BC}. The order of the vector {X} of unknown axial forces in the bars would be:
{X} = [F_{BA}, F_{BC}]
By solving the system of equations, you can find the values of F_{BA} and F_{BC}, which represent the axial forces in members BA and BC, respectively.