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But all one wants to know is how much weight a beam can support or something similar. Surely, there are formulas for this?
There are. But the known equations give the maximum value that the beam can possibly hold. In other words, if you get 1000 N as an answer, it means that it will surely be impossible to exceed that limit … but the value could be less if things are not perfect. And they never are.
How much less? This is where the concept of the safety factor is introduced...