how do architects calculate if a structure like a bridge is stable?
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People are giving great answers, but here’s my five year old response – take a popsicle stick, support it at both ends, and hang a weight from the middle. Let’s say it breaks at 2kg. Now you know the bending strength of a popsicle stick. You can do the same thing to figure out the strength in other orientations. You can even create simple shapes (say a triangle) and do it again. This creates a solid reference library for your material strength. Now use those simple shapes to create a structure, and you can use some math along with your material strength to calculate the strength of the structure. You can test that full structure to verify (or in the case of a large structure, build a scale model).
How do you know if that strength is enough? You come up with load cases. What is the structure going to be used for? How much weight should it hold? What kind of wind do you expect? What if someone uses the structure in an unintended way.
If you want to be extra careful, you design the strength to be 2, 3, 4, etc times stronger than the worst load case. This is called a factor of safety.
This all seems somewhat complicated, but humans have been designing and building structures for a very long time, so there’s a lot of experience to draw on.
Pre-computers, engineers did the designing and math on paper, but now we have computer tools that can help us make things much faster.
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