Hi Nic

In all truthfulness, the golden section is just one element of design vocabulary and its value phi is a first order mathematical curiosity, but phi, whether squared, cubed, rooted, inverted, multiplied or divided, will not alone solve your problem and neither will any other single factor or formula. It will be up to you to find what looks right but barns were built to do right and well, to fill needs and service a farms economy. So I would suggest, fill the need simply and follow old barn patterns and looking good is nearly automatic.

Back to phi:

the math, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

classic design, http://www.aboutscotland.com/harmony/harmony.html

fun with a geometer, http://www.nexusjournal.com/GA-contents.html