Mechanical Engineering Designing/ Analyzing Stress in the beam members of a bicycle
"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.