Beefing up support on screen porch for wood storage?

[michaelthomas]

I have a 12x12 attached screen porch and have been storing about a cord at a time during the winter out there. I refill it about 3x a winter. I now have 2 stoves and am anticipating burning 6 cord next year. I would like to store as much as I can at once to decrease the snow removal to the wood stacks, dealing with frozen tarps and icy wood during the refill. I think I can fit 4 cord in there. The screen porch ledger boards are resting on the foundation on one side and the back, and rest on 4x4s every 6 feet on the front and the open side. It is constructed with 2x10 or 12? joists and they span 12 feet without any support in the middle. The decking is 1x6 standard PT decking. the joists run back to front and decking obviously runs opposite. The deck is only 2-2 1/2' off the ground.
If I built a solid wood header (4 or 5 2x4's screwed together and supported by blocks underneath) from side to side midway across the joists, would this support the weight of 4 cord of seasoned hardwood? If not what would?

 

[Backwoods Savage]

Should work. You might also consider cement blocks. You might want to lay a little cement under the blocks, then just stack up the blocks and fill in at the top with wood shims.