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I purchased a pair of Bilco stringers. The instructions say to use standard 2x10s for the treads, so I bought pressure-treated #1 grade Southern Yellow Pine 2x10s. I cut them each to 46.5" and the spans end up being exactly 44". The steps seem sturdy enough, though I only weigh 165 lb. and I wasn't carrying anything.

Then I got to thinking about the safe span for lumber laid flat like that and got concerned. I know normally a staircase like this would have a third stringer, but it's not really an option with the way these Bilco stringers work. I also read somewhere that pressure treating lumber may have reduced its safe capacity by some small amount. Is it considered acceptable to span a 44" gap with a pressure-treated 2x10? I want the steps to be strong enough that people heavier than me can safely use them and sometimes people carry heavy things out of the basement.

If this is too long a span for this wood, what other type of wood would fit the bill?

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  • Particularly with respect to "carry heavy things out" a simple approach is to screw (or glue & screw) a 2x3 or 2x4 on edge to the bottom of each tread to reinforce it. A different approach that is simple or not dependng on how the stairs are installed is to pull them out and lift the heavy things vertically with a portable crane.
    – Ecnerwal
    Commented Mar 13 at 22:28
  • @Ecnerwal Is there a risk of actually introducing a weakness if I screw into the primary board?
    – Eric Marsh
    Commented Mar 13 at 22:36
  • Bilco (the manufacturer) got back to me. They say that a 6' span is safe. That seems ambitious to me...
    – Eric Marsh
    Commented Mar 14 at 21:47

2 Answers 2

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If the pressure treated lumber is incised (with tiny little slits to allow the chemicals to penetrate the wood), then pressure treatment reduces the wood's bending strength by 20%. My understanding is that Southern Pine is absorptive enough to take in the chemicals without incising. In cases of pressure treatment without incising, there's no strength loss. See the incising factor, Ci, in Chapter 4 of the NDS.

The strength of residential stairs must be sufficient for a 40 psf live load. The 1-1/2" thickness of wood adds an additional dead load component of about 5 psf for a total design load of 45 psf. There's also a 300# concentrated load to check. These requirements can be found in Chapter 3 of the International Residential Code.

Note that wood has substantially higher strengths when loaded for short duration. If you're moving a piano or something, I would multiply the 300# strength by 1.6 to get a short term strength of 480# for center-span foot presses. Under grading standards, that 480# represents the 5th percentile of strengths within the grade and species, so there would be a 95% chance for each step that the capacity is greater than the 480#.

Beyond strength, there's also maximum allowable stair deflections in the same chapter of the International Residential Code. The maximum value is (1/240)(45") = 0.19". The stair deflection under the 40 psf live load (without dead load) must be less than this 0.19" value. The 300# concentrated live load (again without dead load) must also cause deflection less than the 0.19".

Only given your grade, #1, I'll otherwise assume the probable worst case in the US: Incised Spruce-Pine-Fir with high moisture content. In this scenario, your stair treads have a demand/capacity ratio of 105% and a maximum deflection of 0.16". Technically the 105% is out-of-bounds for my worst case scenario assumption. Deflections are fine, though.

Other US softwood species (still #1 grade) will bring that 105% down, but if you want to substitute other grades and/or species (with alternative unadjusted Fb values from the NDS Supplement), you gotta be careful for 1.2Fb > 1150 psi. In that case there's a wet service factor of 0.85 that needs to be applied (in place of a 1.0 factor that was applied below) in computing Fb'.

Strength

Pulling Fb = 875 psi from the NDS Supplement and following Chapter 4 of the NDS, the adjusted bending design stress is

Fb' = (875psi)(1.0)(1.0)(1.0)(1.0)(1.1)(1.2)(0.80)(1.0) = 924 psi.

The maximum uniform load is therefore

(924psi)(1/6)(9.5")(1.5")2 / [(45")2/8] = 13 #/in.

Converting that to a psf loading, I get

[(13#/in)/(9.5in)](144in2/ft2) = 197 psf.

That's a demand/capacity ratio of (45psf)/(197psf) = 23%, so the 45 psf is fine.

For the maximum concentrated load, I get

[(924psi)(1/6)(9.5")(1.5")2 - (5psf)(1ft2/144in2)(9.5")(45")2/8] / [(45")/4] = 285#.

That's a demand/capacity ratio of (300#)/(285#) = 105%. Using 44" as the span length is admissible but only brings the 105% down to 103%. I get it down to 102% by using 3 psf dead load instead of the 5 psf, but I can't rationalize using a dry weight like the 3 psf implies. Somebody might do it, though, and still call the analysis "rational."

Deflection

Pulling E = 1400000 psi from the NDS Supplement and applying an incising factor of 0.95, the 40 psf live load causes a deflection of

(40psf)(1ft2/144in2)(9.5in)(5/384)(45")4/[(0.95)(1400000psi)(1/12)(9.5")(1.5")3] = 0.040",

and the 300# concentrated live load causes a deflection of

(300#)(45")3(1/48)/[(0.95)(1400000psi)(1/12)(9.5")(1.5")3] = 0.16".

Both of these are less than the 0.19" constraint.

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  • You're right--I've never seen dimensional SPF incised. Larger items such as posts and landscape timbers sometimes are.
    – isherwood
    Commented Mar 13 at 18:32
  • @isherwood, I treated the SPF above as incised. It's the 0.80 in that blob of factors from the Fb' expression. My local PT Hem-Fir is incised, but even locally I don't understand the ins-and-outs of pressure treatment well enough to make sweeping generalizations. As you transition to worse use categories, does a particular species transition from non-incised to incised? I have no idea. Posts and landscape timbers are bigger, but they're also use categorized for ground contact unlike, maybe, the dimensional lumber.
    – popham
    Commented Mar 13 at 19:11
  • By the way, I just edited the above because I confirmed the type of wood. It's Southern Yellow Pine.
    – Eric Marsh
    Commented Mar 13 at 20:44
  • @Eric Marsh, I'll leave the answer calibrated for SPF for the benefit of others without your higher strength. For your Southern Pine I get Fb' = 1260 psi and E = 1600000 psi. That E provides smaller deflections than computed above (88% of the values above), so that's still within spec. The 1260 psi lowers the 105% to 77%, so that's good. The 480# capacity for short duration loading becomes 630#. The 77% and 630# assume that your Southern Pine hasn't been incised. You may not have even seen incised lumber before. If your stuff is incised, then say so because I just lied about the 77% and 630#.
    – popham
    Commented Mar 13 at 21:36
  • 1
    Is there a yes/no answer somewhere in this wall of text?
    – nobody
    Commented Mar 14 at 0:32
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Yeah, that's too much span, by a substantial margin.

The first red flag is that the documentation states an actual lumber dimension of 1⅝" by 9½". That hasn't been the case for half a century (though swollen treated lumber comes close).

Then, keep in mind that the documentation for those stringers doesn't really concern the specs of the treads--they merely suggest that the stringers are up to the task with just two.

Mostly, though, I can speak from experience. I've replaced several two-stringer stair sets built with conventional (solid) lumber at shorter spans which were springy as heck. The design simply doesn't meet modern load (capacity) or performance (deflection) standards.

In this case I would absolutely reinforce basic 2x10 treads with more lumber underneath. Sistered 2x6 laid flat or 2x4 on edge over 80% or more of the tread span would do well. Position them about a third of the way back from the nosing as there's more load near the front. It's key to fasten them well near the ends, where most of the separation stress occurs.

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  • Were your instances using a single board per tread?
    – popham
    Commented Mar 13 at 16:11
  • They were single 2x10 treads over about 32".
    – isherwood
    Commented Mar 13 at 16:35
  • Deflection doesn't do a very good job of predicting strength. Scaffolding planks are my exhibit A. I had a hard time finding anything formal for tread sizing by putzing around the internet, though. The 2021 IRC's Table R507.7 seems to support you with max span lengths of 24". It's predicated on #2 grade lumber, but there's not much difference between that and the OP's #1 grade. I can only speculate that the table uses a 3.5" or 5.5" board width under the 300# concentrated load, so the 2x10 provides substantial additional strength and stiffness.
    – popham
    Commented Mar 13 at 17:43
  • I'm not sure what you're getting at. I mentioned deflection only with respect to function. A bouncy tread is difficult to descend.
    – isherwood
    Commented Mar 13 at 18:05
  • Except for "The design simply doesn't meet modern load (capacity)...standards," your answer doesn't seem to address strength. The OP has already built the stairs and has confirmed that the deflection performance is within his standards. The question is about strength. If deflection and strength were interchangeable, then I could see your answer as addressing the question.
    – popham
    Commented Mar 13 at 18:21

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