Raised beds

I have a new raised bed and have never grown anything in them before.  It is only six inches deep, will this be deep enough for dwarf/runner beans and beetroot.  Any suggestions for what I won't be able to grow in them at that depth?

They are on top of soil, albeit not very good soil

At 6" depth you should be able to grow beetroot and lettuce and any other shallow-rooted veg but, if I were you, I'd double-dig - a spade's depth - and fork over the bottom trench adding compost, manure etc, then back-fill. Then you will be able to grow beans and owt else you want as their roots will be able to grow into the full depth required of deep-rooters.

The soil isn't brilliant as it's under a tree but I did grow leeks there over the winter and the majority didn't turn out too bad.  I will do as you suggest and work the soil, it has already had a fair bit of compost put in when I grew the leeks so if I add some more before I put the raised bed in I think it should be OK.  Thanks for the advice