retro repair subfloor problem
We had our house built in 1984 and all was great until we remodeled the kitchen in 2002. In the kitchen we added granite countertops to the cabinets and a 3'x7'piece of granite to the center island. We also put in a much larger/heavier refrigerator and grade 4 porcelain tiles layed on the diagonal.
I now have cracks in the porcelain tile that run parallel to the joists across the whole kitchen spaced every 4 feet. When I look from the basement, the cracks are in line with a twin line of twisted-type nails protruding through the plywood about 3.5 inches off of the joists. It seems that the top layer of plywood was layed parallel to the joists (the first layer is perpendicular to the joists) and for some reason, the ends are not on the joists. The second layer is nailed only to the first layer. To make matters worse, the plywood on the bottom is only 16/32--I assume that the second layer is the same.
I obviously have a problem with inadequate support for the floor. The joists are 2x10s 16" o.c. and the unsupported span is 13.5'. I think that they are ok but need to support the area under the edges of the top layer of ply. I'm thinking----grind off the protruding nails then glue and screw with 2 1/4"construction screws 2x6s on the flat. I can screw the 2x6s into the closest joist on one side. I can put 2x4s as cross blocking up tight to the flat 2x6s maybe every 16 inches. What do you think? Do you think that the joists are adequate? Any other suggestions besides removing the entire floor and beefing it up from the top.