Hi Adrian,
About 10 years ago when I bought a book "Matrix Analysis of Structures by: Aslam Kassimali". It's a very good book where you can study from the basic Matrix Algebra up to solving some problems like plane trusses, beams, plane frames and space frames. Then from there you can check results from a beam analysis program like Caesar II, Autopipe, Caepipe, and compare your results from manual calculation. You can appreciate more the software you are using if you can do some simple hand calcs and compare it with the result from any program you are using. Basically, the software is a very powerful tool to solve thousands to million of equations simultaneously thru algorithms. And if you feel your hand calcs are almost the same with the software results then you will feel confident to do the more complex ones. As we know Finite Element Analysis now is becoming more common in different industries but as a user it's always good to first validate the results from some simple hand calcs. Then maybe you can trace the 10% to 15% difference, mostly if the problem is non-linear maybe some settings need to set the same for both software. So my suggestion is for you start from a simple linear analysis and step by step you proceed to non-linear analysis and check some settings like Force or displacement tolerances, etc.
Cheers!!!