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There are surely great books out the, which cover the basics. Search for "analysis fibre reinforced composites" or something similar. Sadly, I can't recommend one, because all the basic level literature I've read happend to be in German. While those books will show you how to calculate your beams, you will most likely find no mathematical answer to the load distribution. but I really do think you are making it unnecessarily complicated here. A camper box is no aerospace tec. And it sounds like some kind of expedition, which means that you don't know what exacly will happen to you box, and therefore you have to build it much stronger than the pure mathematics will tell you. Damage resistance against skin delamination caused by impacts will be a far greater issue than pure statics/dynamics. With a 60mm sandwich core a incredible thin carbon skin would be sufficient to drive a car over it. Theoretically. Practically things look different.
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