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Isn't it more the case that because there are a lot of parts that are kinematically constrained (though in complicated ways), the entire system (once you take into account the spokes) becomes massively overdetermined
Yes, if you simplify your model to fix all the joints and treat the materials as inelastic, and as you say if you model it realistically you have to consider that the shape changes under load, and that alters the way the load distributes among the different components. A radially-laced front wheel is neither circular nor radially laced once you load it, whether that's rim brake loads or just pushing down on the axle and up on the tyre contact patch.
gbj_tester-
Yeah, those were called 'second-order effects' when I studied this kind of thing (in a civil engineering context though, and that was in German, so might be called something else in English). If I remember correctly, unless the deformations go beyond a certain limit, it doesn't impact the overall load distribution that much though. The thing is that here, a full model is already difficult to 'solve' fully for a rigid wheel.
SwissChap
Isn't it more the case that because there are a lot of parts that are kinematically constrained (though in complicated ways), the entire system (once you take into account the spokes) becomes massively overdetermined, which is what makes the exact load calculations so difficult?
But then also when you want to get into the details, you need to take into account second order effects because it's not actually a rigid body system, rims and spokes etc. can flex as well.