What's the magnitude and direction of the load? I've had a 2" thick piece of timber sat on a concrete floor for years without moving, and it didn't take any bolts at all :)
It was going to be to run a decking joist along the edge/side of my shed's concrete base instead of having the joist up on posts but the dimensions don't work for bolting it to the concrete anyway.
Fixing a 47mm thick piece of timber to concrete, how long an expansion bolt will I need?