Tile Floor and a Plumber's Notch in 2×10 Joists
A 1970s two-story wood-frame apartment building has 2×10 Douglas Fir–Larch No. 2 floor joists at 16 in on center, simply spanning 14 ft between bearing walls, with a ¾ in subfloor and carpet. Properties: E = 1.6×10⁶ psi, I = 98.9 in⁴, S = 21.4 in³, Fb = 875 psi with the repetitive member factor permitted. A remodel replaces the carpet with a bonded mortar bed and ceramic tile, adding about 15 psf dead load. Existing dead load (subfloor, ceiling, MEP, finishes) is 12 psf; live load is 40 psf. The plumber also wants a 3 in deep notch in the top edge of one joist at midspan to pass a new drain line.
1. Are the existing joists adequate for the tile floor? Check both bending and deflection.
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Service loads per joist (tributary 16/12 = 1.333 ft):
- Dead: (12 + 15) × 1.333 = 36 plf = 3.0 lb/in
- Live: 40 × 1.333 = 53.3 plf = 4.44 lb/in
Bending:
- M = wL²/8, L = 14 ft = 168 in
- MD = 36 × 14²/8 = 882 ft-lb = 10,584 in-lb
- ML = 53.3 × 14²/8 = 1,306 ft-lb = 15,672 in-lb
- Total = 26,256 in-lb
- Allowable: Fb′ × S = 875 × 1.15 × 21.4 = 21,530 in-lb
Overstressed by about 22%. Before the tile (12 psf dead) the total was 20,376 in-lb, i.e. just adequate - the mortar bed is what pushes the joists over.
Deflection (Δ = 5wL⁴/384EI, EI = 1.6×10⁶ × 98.9 = 1.58×10⁸ lb-in²):
- Live only: 5 × 4.44 × 168⁴/(384 × 1.58×10⁸) = 0.29 in = L/577
- Total: 5 × 7.44 × 168⁴/(384 × 1.58×10⁸) = 0.49 in = L/344
Ceramic tile over a bonded mortar bed generally needs the total-load deflection held to L/360, so L/344 misses. Both bending and total-load deflection fail; it would be wrong to report this as a deflection-only problem.
2. Is the proposed 3 in top-edge notch at midspan acceptable?
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No. Three separate problems, and the location makes each of them worse:
- Depth limit. Top-edge notches in sawn joists are limited to D/4, i.e. 9.25/4 = 2.3 in. A 3 in notch exceeds it.
- Section loss at the worst place. A 3 in notch leaves 6.25 in of depth, so I drops to (6.25/9.25)³ ≈ 31% of the original - a 69% local loss of stiffness right where the moment is maximum. On a floor that already misses L/360 by a small margin, that is not a detail, it is a failure.
- The pipe will not fit anyway. A drain needs roughly 3½ in of clearance. A hole is limited to D/3 ≈ 3.1 in and must be kept at least 2 in clear of the edges, so a legal round hole does not exist either.
The correct answer is to route the drain below the joists in a soffit or chase, or to reframe: cut out the joist, header off to the neighbors on both sides with a doubled 2×10 header, and hang the drain in the resulting bay. Do not approve a notch here and do not accept 'it's only one joist' - that joist is also the one the tile bed will crack over.
3. What repair would you specify, and how do you confirm it works?
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Two deficiencies to fix separately: strength and stiffness of the field, and the pipe routing.
Joists. Full-length 2×10 sisters, glued and screwed, on every joist in the tiled area:
- S doubles to 42.8 in³ → capacity 43,000 in-lb against 26,256 in-lb, DCR 0.61.
- I doubles to 1.98×10⁸ → total-load Δ = 0.245 in = L/686, comfortably inside L/360 for tile.
- Verify that the sister bears fully at both walls; a sister that stops short of bearing adds stiffness but almost no strength, which is the classic field shortcut.
Alternative if sisters are impractical (plumbing, electrical): a midspan beam cutting the span to 7 ft reduces M and Δ by 4× and 16× respectively, but it needs a new footing and load path through the floor below - usually more intrusive in an occupied apartment.
Pipe. Relocate below the joists or reframe around a header; no notch, no hole larger than D/3.
Verification. Have the contractor confirm the sister bearing and the adhesive used (structural adhesive, not construction adhesive), and photograph before the subfloor goes down. Confirm the tile installer's L/360 requirement in writing so the deflection criterion is documented.