I am trying to calculate the loads in the suspension components of a typical car double wishbone setup. I have found a thread on the www.fsae.com forum, which seems to be exactly the kind of thing I am looking for. It involves considering the assembly as a 3D truss, and building up matrices, containing

  1. the unit vectors and cross products at the mounting points of the struts at the upright
  2. the forces and cross products at the tyre contact patch. Which when the inverse of matrix 1 is multiplied by matrix 2, results in a third matrix containing the loads on the struts.

My question is, can someone give me the name of this method of truss analysis, and any textbooks / resources that specifically cover this method?

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    $\begingroup$ I think most textbooks refer to it as the "matrix method," or something similar. It's really just applying finite element equations to a system. If you haven't had any formal training on the subject, you will probably find it hard to get into. $\endgroup$ – grfrazee Aug 17 '15 at 11:56

Initially after reading your question I thought that it was using the stiffness method but after seeing the image on page 7 of that forum post I don't think that's what it is. This is because the stiffness method relates forces to displacement using the members' stiffness properties. I don't see any of that discussed on the forum.

Instead, it just seems like a force balance in each of the XYZ axes and a moment balance about each of the XYZ axes giving rise to 6 equations. Depending on how your 3D truss is supported you may have 6 or more unknowns. Using matrices is just an efficient way to solve many simultaneous equations. I'm not sure there's a specific name for this given the context of your application. In terms of mathematics it is just linear algebra (i.e. solving a system of linear equations).

Perhaps with more information about what you're trying to achieve (maybe a diagram of your suspension system) we can better guide you. The assembly can be modeled as a 3D Truss like you've stated. Normally you would come up with a Free Body Diagram (FBD) to figure out how the 3D Truss is supported and loaded. From there you would solve for the reaction forces where it is supported. This looks like where the 6x6 matrix comes into play - you'd use that to solve for the reaction forces of the suspension system on the chassis. Then you could use this to find the internal forces of the suspension members if that's what your ultimate goal is.

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    $\begingroup$ Thanks for that Paul, I appreciate your help. From what you have said, and my previous research, Free Body Diagrams are the way to go about this. The text books I am reading on suspension design cover the functional requirements of suspension systems (in terms of wheel control etc) but not necessarily how to consider the forces acting on the components, and I am trying to find an entry point into learning about this. $\endgroup$ – Jim Aug 17 '15 at 19:06

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