I've used SketchUp to design before, I didn't use it a lot but it seemed reasonable as I was learning the ropes. If you can save pieces to use as a template/object, then you could make logs of certain thickness/length and add them as needed, but I don't know if that's an option. It is free to use the web version.
Maybe try Weyerhauser's software or check NDS website. Not a lot of free software out there that is worth investing time in to.
If this is a one-time deal I wouldn't fiddle with software. If you want to go far down the rabbit hole then you will need professional level software anyway.
Most timber design manuals are fairly easy to digest and have lots of tables, chrts, etc.