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Haven’t found anything addressing my situation:
I am remodeling a bath at home and want to put 12″ ceramic tile on the floor. However, everything I’ve read specify floor joists 16″ O.C. Unfortunately, I have a 2×4, 12″ depth, web truss floor system 24″ O.C. with a 3/4″ subfloor. The room dimensions are 4’x7′-8″. Two trusses run parallel to the long dimension and truss span (between supporting walls below) is about 8′-8″. Plumbing prevents adding more floor joists. Bathroom configuration is a shower, toilet and pedestal sink.
One article from a P.E. used a formula for determining floor stiffness. The formula in the article (I = (B x D3 [D-cubed]) divided by 12) basically states cubing the floor depth and multiplying by 8 calculates stiffness. If correct, increasing my floor depth (D) to 2″ would increase my stiffness (I) from 3.37 to 64. I would use a glue & screw method to join another 3/4″ sheet and a 1/2″ sheet of plywood to the existing 3/4″ subfloor. Or I could use one more layer of 3/4″ ply (for a stiffness of 27) and 1/4″ Hardibacker.
The stiffer the better but a thicker floor impacts other aspects of the job. Am I being too technical? Would a 1-1/2″ floor with Hardibacker be sufficient to prevent the ceramic tile from cracking or should I make it 2″? Any suggestions if this wouldn’t work?
Thank you,
Terry
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Terry2- If it were me, I'd tear out the 3/4" subflooring and add new framing with ground support beneath the space. In this way, you can access the areas necessary to supplement your framing needs more easily while working around the restrictions of plumbing. Tile needs as much stability as you can achieve and though it's a small space, it would be worth the extra work to assure you won't be replacing cracked tile in the future. You might also consider going with a smaller tile size because the scale of 12" tile in such a small space will look out of balance while the bigger tile are more prone to cracking due to deflection issues. By supplementing the framing and using a smaller tile, you should be able to simply add 1/2" backer board on the floor without adding so much thickness to the floor that you'll need a ladder to get into the room. I'm a math dunce so your formula (though it might work) is like reading Chinese to me. Others might have better advice so keep checking this thread for other answers. Good luck.
*The formula is a correct formula, but it's not a formula for "stiffness"i per se. The quantity "I" is moment of inertia, which is used in another formula to calculate deflection. Deflection is inversely proportional to I. In other words, if you double I, then the deflection is cut in half. Since I depends on the depth cubed, then you don't need to double the depth to double the thickness. You only need to increase the depth by 1.26 times in order to cut the deflection in half. Unfortunately, the formula for I only applies to beams of rectangular cross section, like solid lumber. It won't work on trusses. Thicker trusses have less deflection, but you can't use the formula you gave to calculate I.However, I think you're looking at the wrong thing. When they say for tile that the maximum joist spacing is 16 inches and you've got 24 they are concerned about the deflection of the plywood between the joists, not the deflection of the joists along their length.Unfortunately, I'm not enough of a tile expert to give advice on how to prepare a floor with 24 inch joist spacing.