Aircraft structural engineer here.
Firstly, we have material properties. By performing special tests with specimens we could determine how much “force” will hold material regardless of part size and form.
Second, during hundreds of years of strength science humankind has developed various mathematical models, which helps us predict behaviour of various parts under various ideal loadings. So, we could determine how much deformation or force a particular structure will hold up to some failure point. With accuracy less than 1-2%, which is more than enough, because most materials will vary in properties for the same 1-2%.
Third, we could predict under which condition structure will be operated in real world. That really depends on the type of structure or machine, like for the usual chair we knew it should withstand a sitting person but somebody could put on it an anvil or something, which is hard to predict. But for an airplane we had determined the exact condition under which it will be operated. That allows us to make more accurate calculation and less safety margins, therefore lighter structure.
Having this knowledge we could predict behaviour of almost any structure in reality under ideal loading. And to account for some reality, like not an ideal load (not exactly like in a mathematical model), sometimes much greater applied load (anvil on chair) or some discrepancies during production we use “safety factor”. In other words, we just multiply predicted load conditions for some factor, which really depends on the type of machine or structure. So, for the usual chair we could easily make it 5 times heavier than it should to be by mathematical model with ideal load. But for an airplane (or any other structure where we must keep it as light as possible) we have much more accurate load conditions, therefore less safety margin.
So, in summary we have a lot of math models to predict loads and structure behaviour. Finite element modeling is good in concept, but in reality only really good engineers could use it properly and make safe structure.
Thanks for your attention, I will try to answer any questions)
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