Timber shed. Damp comin from the bottom?

You say it's on a concrete base. How thick is the concrete? Did you put down a damp proof layer under the concrete...a sheet of polythene? Or lay the concrete in two layers with a couple of coats of a compound such as Synthapruf or car body underseal to stop water soaking up through? This will stop damp coming up through the concrete and into the timbers. Does the concrete extend outside the timber walls of the shed? It's possible then for rain to run along the concrete under the walls and into the shed, then up into the timber. Rain will splash up the sides of the shed to about 15 inches...37cm. I always put my sheds on a brick or block wall for this reason as it's always the bottom 30cm or so of a shed that rots first. Have you got gutters on the shed? Are they leaking? Is water leaking in through the window frames possibly?
That's a few ideas for you. I would guess that it's water soaking up through the concrete floor and into the timber. Best of luck!!

Denis Langley
February 2012