How do I cope with the responsibility of keeping people safe?

You can analyze a structure until you are sure of it, and that certainty matters because real people stand on what you approve. Carrying the knowledge that lives depend on your care is a serious weight, and the fact that you feel it means you are the right kind of person for the work. But there is a difference between responsibility and dread. Your duty is to do the analysis thoroughly, to check what should be checked, to refuse to sign off on what you have not verified. When you have done that fully, you have met your responsibility. The weight is meant to sharpen your care, not to haunt you after the work is sound. Build a habit that lets you set it down: a final check you trust, a standard you never cut. When you have met it, tell yourself plainly that the work is sound and it is allowed to rest. You keep people up by doing the work well, not by carrying fear forever. Do it right, then let yourself breathe.