I want to build a deck to support a hot tub on the second floor. The total dimensions will be 23' x 16', with the house on one side. My ledger board is set-up for 12" stringers. I only need to support the hot tub on one corner of the deck, while the rest of the deck will be normal traffic. I'm thinking of a 7' x 7' square hot tub. The hot tub specs call out for 2x10's, but I'm thinking of 2x12's at least under the hot tub since I'm set up for them. Could I get by with spanning the entire 16' if I use 2x12's, or would I need to have a cross beam in the middle of the deck area that supports the hot tub? Could I use 2x10's in the rest of the deck?