Example: An exercise bike that can support 250 lb. Does the engineer find a large enough weight that deforms the bike, then take a fraction of that as the amount it can support?
In: Engineering
Your assumption is not wrong, except that instead of testing the “bike”, engineers tested standard geometries using different materials and the engineering community keeps a huge database of those tests. By making use of failure theories, they can predict how desired shapes will behave under different loads and boundary conditions. Naturally, this is the start of the design process.. so it is not trying and error, in the case of a bicycle they will test the end product to validate their calculations, but in the case of a bridge for example, a direct test may not be feasible.
I recommend the following video
Latest Answers