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 .
E4_1?
All the bars in truss ABC have constant cross section and are made of a homogeneous linear elastic material. Under the effect of a 1 kN horizontal load applied at B , the pin at A is observed to displace to the right by 6 cm.
Use the method of joints to obtain the numerical value (in kN) of the axial forces in the bars.
NAB=
kN
unanswered
NBC=
kN
unanswered
NCA=
kN
unanswered
E4_1B
Obtain the numerical value (in kN) of the reactions at the supports.
RAy=
kN
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RCx=
kN
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RCy=
kN
unanswered
E4_1C
Obtain the numerical value (in kN/m) of the stiffness of bar CA .
KCA=
kN/m
unanswered
E4_2: SOLVING TRUSSES WITH MATLAB PART 1: SELECT DEGRESS OF FREEDOM
All the bars of the truss in the figure below have a cross-sectional area of 10 mm2 . We want to determine the axial forces in each of the bars and the Cartesian components of the reactions at supports C and D using the method of joints.
We will soon use MATLAB to solve this problem, but first we need to identify the "free" and the "constrained" degrees of freedom (DOFs) of the joints of the truss. Because this is a 2D problem in the x-y plane, each joint of the truss can only have two (Cartesian) DOFs (i.e., the joint can move only along x and along y). Some joints are hinges directly attached to the wall. These joint/hinges (like joint C in the example above) cannot freely move when the truss is loaded, because the wall prevents it: these DOFs are "constrained". In contrast, a joint like A is not attached directly to the wall, so it is free to move in both Cartesian directions: its DOFs are unconstrained or "free".
For each component below, select "Free" if it is unconstrained and "Fixed" if it is constrained.
Joint A , x component
FreeFixed
Joint A , y component
FreeFixed
Joint B , x component
FreeFixed
Joint B , y component
FreeFixed
Joint C , x component
FreeFixed
Joint C , y component
FreeFixed
Joint D , x component
FreeFixed
Joint D , y component
FreeFixed
Joint E , x component
FreeFixed
Joint E , y component
FreeFixed
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:
I obtained,
X =
4.00
2.00
-2.82
2.00
-2.82
-2.00
but is incorrect, can someone help me please?
To find the axial forces in the bars using the method of joints, you need to analyze the equilibrium of each joint in the truss. Here's how you can approach the problem:
1. Start by analyzing joint A: Since joint A is a pin joint, it can move freely in both the x and y directions. Therefore, it has two degrees of freedom (DOFs) that are unconstrained or "free".
2. Analyze joint B: Again, joint B is a pin joint and has two free DOFs.
3. Analyze joint C: Joint C is a pin joint as well, but it is also affected by the vertical load W applied at joint C. Therefore, there will be a vertical reaction force at joint C. The horizontal load applied at joint B will also result in a horizontal force at joint C. However, since joint C is constrained in the x direction, this force will be transferred to the support at joint A. Therefore, we need to consider the reactions at both joint C and joint A.
4. Analyze joint D: Similar to joint B and joint C, joint D is a pin joint with two free DOFs.
5. Analyze joint E: Joint E is constrained in both the x and y directions, similar to joint A. So, it has two constrained DOFs.
Now, let's determine the axial forces in the bars using MATLAB:
1. Set up the equilibrium equations for each joint by considering the forces acting on it. Apply the equations ΣF_x = 0 and ΣF_y = 0 to each joint.
2. Write down the force balance equations for each joint. Consider the unknown axial forces in the bars as variables and the known forces (such as the applied load W and the reactions at the supports) as constants.
3. Build a system of equations using the force balance equations for each joint.
4. Solve the system of equations using MATLAB's matrix operations or the solve() function. The unknown axial forces in the bars will be the variables to solve for.
5. Once you have solved the system of equations, you will obtain the numerical values of the axial forces in the bars.
If you have already followed these steps and obtained a different result, it might be helpful to double-check your calculations or provide more information about the specific truss configuration and applied loads.