A conservative method a non-engineer can actually use.

I use Working Stress Design, the system used for reinforced concrete before the 1960s and still completely sound for small projects. It is deliberately conservative: it uses a little more steel, and in return the math is far simpler. There are no ultimate-strength code calculations meant for engineers. High school algebra is enough, every calculation is worked out in full, and a math tutorial is included. No outside tables. No software. A pocket calculator does the rest.