This is the drive circuit for my heated bed; the FET manage up to 50A if I remember well and the design of the circuit is inspired from the ultimaker board. The led and its resistance is optional and is needed only to see when the bed is driven; the Diode in reverse between the heated bed terminals act as freewheel diode. I don’t find the original schematic that I share to Tim, but I redo that and this is identical 
hope this can help:
I was running 12.5v/20A
Seems the SSR gods are just not on my side. Got an SSR 40DD from amazon today and hooked it up. Didn’t explode like the last one but seems to be stuck in a perpetual on position. Bah!
@ stefano, isnt that the same fet stp55 on most ramps? hmmm i didnt know arduino can drive this fet direct 
@3roomlab I think this is a common used MOS and I see it used also on Ultimaker Board. I use this part and the schematic you see in my custom board and I have no problem driving it from arduino, I use it for hot end as well for a 10A heated bed
Just found this post and see its form a long time ago. But want to add 2c to it. The wattage load based on a 12v psu would need double the amps compared to a 24v psu. the SSR’s can run quite abit more voltage just not the amps. If your heat bed can run at a higher voltage that would be the answer.