# Method of joints not working on simple truss, supposed to be stable and determinant

In the process of editing the question to put better pictures of my dimensions in, I realized that how I calculated my angles was incorrect, and that is why my answers were yielding inconsistent answers

I am writing a computer program to help me solve for stresses in motorcycle suspension and chassis members. I have a girder front fork that I have simplified into a truss, shown below.

The "Too long, didn't read" version is that when I use the method of joints to solve the axial force in the members starting at point A, then again at point B, then again at point C, I get different answers for the axial force in basically all of the members. If I do the analysis again starting at point D, then again at point B and C, I get different answers as well.

What am I doing wrong? Is there something that conceptually, I am not understanding? The reaction at joint C is a pin joint reaction, and the reaction at point D resists X-forces but not Y-forces.

The dimensions are shown below. Solution Method:

First, I made sure that the structure statically determinant internally from the equation m + r = 2j -> (5 members + 3 reactions) = 2*(4 joints) ; 8 = 8. I also checked to make sure that the structure was stable using a program called itruss. With that in mind, I assumed there shouldn't be any reason why method of joints would not work so I continued my analysis.

Reaction Forces Next, I solved for the reaction forces. I used matrix trick x = A^(-1) * B throughout this analysis. The 3 systems of equations that I got were:

Fx: 534.857 + Rx.d + Rx.c = 0

Fy: 594.286 + Ry.c = 0

Moments positive clockwise about joint C: Rx.d*11.446 - 534.857*24.869 + 594.286*9.259 = 0

Solving the system of equations gave me: Rx.c = -1216.2 lbf; Ry.c = -594.29 lbf; Rx.d = 681.362 lbf (note that there probably will be some rounding error here compared to if somebody did it by hand with the values I gave because the dimensions in the diagram were rounded)

Method of Joints - Joint AThen I used the method of joints on Joint A to solve the axial force in tube a (F.a) and tube b (F.b). Assuming that all tubes are in tension got me the following system of equations:

Fx: 534.857 + F.aCOS(80.44) + F.bCOS(69.58) = 0

Fy: 594.286 + F.aSIN(80.44) + F.bSIN(69.58) = 0

The solution that I got for this system of equations was F.a = 1559.9 lbf; F.b = -2275.5 lbf

Method of Joints - Joint B Next, I used the method of joints to solve for the axial force in tube e and tube c. Assuming that all tubes were in tension got me the following system of equations:

Fx: F.cCOS(57.18) + F.eCOS(9.102) - F.aCOS(80.44) = 0 F.y: F.cSIN(57.18) - F.eSIN(9.102) - F.aSIN(80.44) = 0

The solution for this system of equations was: F.c = 1703.76 lbf and F.e = -672.84 lbf

Method of Joints - Joint C This was where I realized that I wasn't getting consistent answers. I solved the system of equations for joint C as though I did not already know the axial force in tube E and I got a different answer for the axial force in tube E. My system of equations:

Fx: Rx.c + F.dCOS(80.404) - F.eCOS(9.102) - F.b*COS(69.58) = 0

Fy: Ry.c + F.dSIN(80.404) + F.eSIN(9.102) - F.b*SIN(69.58) = 0

The solution to this was F.d = -1452.1193 lbf; F.e = -672.832 lbf

Originally, the calculated values for F.e did not match but now they do after I fixed how I calculated my angles. Sorry about that.

• Welcome to Engineering! I can start by telling you that the method of joints should work in this case. However, in order for us to check your work, it'd help if you could edit your post and change the image with the dimensions, making sure to add them all. There's no reference to B's position (x or y), it's not clear whether the 9.25" is from A to C or D, and there's no horizontal position for whichever other one isn't 9.25". I tried using the angles to help but must've done something wrong because they didn't work, and I don't have time to try again right now. – Wasabi Apr 28 at 15:53
• Hello Wasabi, thank you for taking a look at my post. I used CAD to add better pictures for you. In the process I took a deeper look and noticed that the angles I had calculated were slightly off from the angles in CAD I have been using as verification. I did not think that an error of something in the neighborhood of 0.1 degrees would lead to such inconsistent answers but it sure did. Thanks again for taking a look at my problem and I am sorry if I wasted your time. – FinallyAnEngineer Apr 28 at 18:35
• No worries. I just suggest you keep your original question and then post your solution as an answer. – Wasabi Apr 28 at 19:08