Sheds are often a pain because although they seem to be dry they actually capture and hold onto moisture which would otherwise dissipate during the day. I have a mid-80s GT that picked up rust speckling in a shed. I now keep it in a lean-to (and under a blanket to deal with dew) which is better, but, what helps most of all is maintenance. What you need to do is clean the frame with Autosol to remove the rust then use a chrome specific polish designed to protect it. The best I have come across is from an American company called Mothers Chrome Polish. Unfortunately, being in the UK rust is a constant threat and enclosed spaces just exacerbate this problem.