Found this gem for tension loads in bolts on a bracket. But what in the world is that calculation/theorem/approximation called? I'd like to read more on it.
The formula you are asking about isn't a named theorem but its based on the fact the joint is statically indeterminate.
The component parts held by the bolts or screws are assumed to be totally ridged and in order to get round the indeterminacy of the bolts its assumed that we have a load per unit length of the members between the applied load, pivot point and bolt positions.
Have a look at the file I up loaded in the thread you referenced it might help.
“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein
This may be a silly question, but which 12" are you using in that file? I wasn't quite sure when I looked at it. Also, did you find this in Bruhn, Peery, or learned it through the course of your career? That is a really helpful trick that should be taught, IMHO.