# How do I repair this joist? [duplicate]

Previous homeowner cut a big notch into a joist in the basement to vent a gas water heater. I had the water heater replaced with electric, and now I want to fix the joist. (Photo below, with annotated measurements.) What’s the best way to do that?

One contractor wants to install two steel plates (3”x36”x1/4”) to brace it … which seems like a good move to me.

• Did that contractor have an engineer analyze the situation to come up with the sizing and nail/bolt pattern for the steel plate? Commented Nov 17, 2023 at 21:06
• Commented Nov 17, 2023 at 21:47
• Commented Nov 17, 2023 at 21:47
• Commented Nov 17, 2023 at 21:48
• @popham You mean "Where is this notch located along the length of the span?..." Commented Nov 17, 2023 at 23:39

For sufficiency, you want the 1/2"x3" steel beam to provide the same strength and stiffness as the whole wood section.

Bending Strength

Assuming that there's a 1-1/2" spacer block inside the notch and between the cheek plates (this braces the steel against a failure mode called "lateral torsional buckling"), the AISC Specification for Structural Steel Buildings provides the following bending strength:

Mₙ = (36000psi)(1/4)(0.5in)(3in)² = 40500#-in,

40500#-in <= 1.6(36000psi)(1/6)(0.5in)(3in)² = 43200#-in OK.

Converting the strength to ASD, that's a design strength of

40500#-in / 1.67 = 24300#-in.

For your 2x8 floor joist, I follow Chapter 3 from the National Design Specification and Chapter 4 from its Supplement, conservatively assume #2 grade Southern Pine, and conservatively apply the repetitive use factor of 1.15 to arrive at a design strength of

(1100psi)(1.15)(1/6)(1.5in)(7.5in)² = 20500#-in.

That's a D/C ratio of 20500#-in / 24300#-in = 84%. Fine.

Stiffness

Using Chapter 4 from the NDS Supplement and assuming Douglas Fir instead of the Southern Pine from earlier to remain conservative, I get a flexural rigidity of

EI = (1600000psi)(1/12)(1.5in)(7.5in)³ = 84000000#-in².

For the steel detail, your flexural rigidity is

EI = (29000000psi)(1/12)(0.5in)(3in)³ = 33000000#-in².

That's about half, implying that your floor deflections will be around L/180 assuming that the original joist was sized under the International Residential Code for L/360. If the original joist was sized for L/720 and that's very unlikely, then your steel plates are sufficient for the deflection limits prescribed by the International Residential Code.

Increasing the plate height to 4" works as long as the plates are positioned correctly, with the top edges touching the underside of the floor sheathing. The position is important because the plates work together with the narrow band of wood above the notch to just barely attain sufficient stiffness. Contact with the floor sheathing isn't important.

Fastener Schedule

I looked up 2x8 joists in the IRC's load tables to get a maximum length (16 ft), and I used that maximum length to compute demands. I assumed those hot dip galvanized, 1-1/2" long "10d" nails that Simpson makes (they use the 0.148" diameter of 10d nails, hence the "10d" labeling). Based on those demands and nails, I computed a 3.9" fastener spacing along the full length of the steel plates to join the joist and each 1/4"x4" plate into a composite section. The 12" to the left and right of the notch should be plenty sufficient to load up the steel with its proportion of stresses just in time for the notch to offload the bottom of the joist. The combination of steel plus wood above the notch has the strength and stiffness to replace the missing joist material.

Rounding the 3.9" spacing down to 3", the layout is a staggered pattern with 6" spaces in each line. Each line is offset 1" from its nearest edge with a 2" gap between the lines. 5/32" is a good drill bit size for drilling the steel plates:

``````    |    6"   |    6"   |    6"   |    6"   | ...
--------------------------------------------------  -·-
|                                                    1"
|   ·         ·         ·         ·         ·       -·-
|                                                    2"
|   ·    ·         ·         ·         ·            -·-
|                                                    1"
--------------------------------------------------  -·-
| 3" |    6"   |    6"   |    6"   | ...
``````

Notes

• Be sure to jack a bit of camber into the joist before attaching all of this stuff. It has already deflected under its own weight, so you want to get it parallel with the other joists (or even a bit higher) before locking in the geometry.

• Feel free to cheat a little on the hole layout above the notch if that's what it takes to find sound material for fastening.