I think Genghis has it pretty well covered but to add some colour, here are a few details from my current job certifying a composite CS-23 / FAR 23 aeroplane:
The regulatory loadings are minima. We have chosen (as have others in the same class) to certify ours to +/-10g which means we will do the certification ultimate load tests, after the fatigue test, to the loads for15g. we will do that at 72 centigrade. The airframe used for all that testing will also incorporate some tens of points of deliberate manufacturing error or deliberate impact damage. In addition, the material properties values we use in calculations for the structure are based on low expectations derived from statistics from multiple sample tests (that's not a very scientific sentence, I am trying to convey the ideas for general readers). Those sample tests are on test pieces that have been conditioned in a hot and humid environment for several weeks. In summary, for composite aircraft, there are multiple layers of pessimism in the calculating and testing of the airframe.
One last thing, for about the last twenty years, seats, which for small aeroplanes tends to mean a big chunk of the front end of the aeroplane as well, have been dynamically tested for occupant injury protection (similar to the crash tests used in car advertising). There are probably videos on the internet if you look for them. Discovery Canada did a good piece on it in the airliner context in 2013 (but I'm only saying that because I was the technical talking head
).
Oh yes, books. I found Cutler and Liber's Understanding Aircraft Structures to be a good introduction.