Mechanical Engineering Designing/ Analyzing Stress in the beam members of a bicycle This question is for those who are familiar with analytical engineering of bikes (not using Finite element analysis)

Okay guys, I'm trying to do an optimization project on the frame of a bicycle to minimize the weight.  My trouble is that I know I cannot treat the members as two force members (meaning the only force in them occurs axially since there is bending because of the weld joints).  Does anyone know how to go about this? or how to model the weld joints as forces acting on beams so maybe a superposition method can be used.
Anyone know or have a good source for this?
"Lords of the Chainring" might help. It's been a while since I've looked at my copy,  from memory it was more focussed on dynamic balance but I vaguely recall a section on basic frame analysis. The fact that people spent a long time trying to come up with simple(ish) equations for forces on a bike frame and failed repeatedly suggests to me that once you get past very simple approximations you're probably not going to succeed at all. Hence the popularity of FEA and iterative prototyping.

The forces on a frame are quite complex, and I'm not sure there's any part of the frame that could be analysed as two force member. The Slingshot bike had a cable downtube but that was an interesting bike to ride (twisting the handlebars visibly moved the front wheel sideways). Remember that there's torsion as well and bending and tension going on in most joints.

Looking at carbon fibre layup patterns will probably give you a better idea of the forces because fibre has very directional strength and is laid to resist the actual forces. Metals are homomorphic and gain a lot of unnecessary strength in a bike frame from being thick enough to deal with highly directional forces.