Tag Archives: stair stringers

Structural Design of Stairs With Cutout Stringers

Structural Design of Stairs With Cutout Stringers

Loading requirements for stair stringers are called out for in IBC (International Building Code) Table 1607.1. For one and two family dwellings, uniform live load is 40 psf (pounds per square foot) and 100 psf for all other occupancies. Although not expressly stated, one would assume one and two family dwellings would also incorporate accessory buildings (garage/shop or similar) on a property with a dwelling (basic IRC – International Residential Code) present.

IBC Section 1011.2 requires stairs to be 44 inches in width, with exception 1 allowing for a 36 inch width provided stairs serve an occupant load of less than 50.

IBC Section 1011.5.2 specifies maximum stair rise as 7 inches and minimum run as 11 inches. Exception 3 allows rise to be 7-3/4 inches and run as 10 inches for R-3 occupancies, within dwelling units for R-2 and Group U when an accessory to either of these (basically an IRC qualifying structure). Some jurisdictions have amendments allowing for greater rises and lesser runs.

Stair stringers act as beams, where top is attached to an appropriate member by means of a Simpson LCS bracket (or equivalent) and bottom is resting upon a wood or concrete floor.

Looking at an exception 3 above rise and run, would cut triangles 4-1/2” deep into a 11-1/4 inch 2×12 stringer, leaving 6-3/4” of ‘meat’ remaining.

How far can a 2×12 stringer then span in a residential application?

Checking for bending only:

SQUARE ROOT OF [8 x Sm (Section Modulus of 1.5” x 6.75” x 6.75” / 6 = 11.39) x Fb (Fiberstress in bending, for #2 SYP = 750, SPF = 850, HemFir = 875, DFir = 900)] / (40 psf live load + 10 psf dead load) x 36” width stairs/2 (one stringer on each edge of stair width)

For SYP (Southern Yellow Pine) = 8.71’ (or 8’8”). This span is measured horizontal to ground and is measured from centerline of required bearing area at each end.

Checking for Deflection

Allowable = 104” / 360 = 0.289”

Maximum = (5 x (50 psf/12 x 1.5’) x 104”^4) / (384 x MOE x I)

MOE (Modulus of Elasticity) = 1,400,000 for SPF or SYP; 1,600,000 for DFir; 1,300,000 for HemFir

I = b x d^3 / 12 = 1.5” x 6.75”^3 / 12 = 38.44

(5 x 6.25 pli x 104”^4) / (384 x 1,400.000 x 38.44) = 0.177” <= 0.289” therefor OK

For greater spans, a 2×6 #2 can be applied alongside 2×12. Fb value of lesser member must be used (even though 2×6 has a greater individual strength):

Bending test:

SQUARE ROOT OF [8 x (11.39 + 7.5625) x 750] / (50 x 18”) = 11.24’ (rounding down to 134”)

Checking for Deflection

Allowable = 134” / 360 = 0.372”

Maximum = (5 x (50 psf/12 x 1.5’) x 134”^4) / (384 x MOE x I)

I = b x d^3 / 12 = 1.5” x 6.75”^3 / 12 = 38.44 for notched out 2×12 plus 20.8 for a 2×6

(5 x 6.25 pli x 134”^4) / (384 x 1,400.000 x 59.24) = 0.316” <= 0.372” therefor OK

Need to span even farther? Let’s add another 2×12 with a 2×6 on each side in center of tread. Center stringer supports twice load of outer stringers.

SQUARE ROOT OF [8 x (11.39 + (2 x 7.5625)) x 750 x 1.15] / (50 x 18”) = 14.258’ (171”)

But wait, where did 1.15 come from? When three members are combined or members are 24 inches on center of less, Cr (Repetitive member factor) is equal to 1.15.

Checking for Deflection

Allowable = 171” / 360 = 0.475”

Maximum = (5 x (50 psf/12 x 1.5’) x 171”^4) / (384 x MOE x I) I = 38.44 for notched out 2×12 plus 2 x 20.8 for two 2×6 = 80.04

(5 x 6.25 pli x 171”^4) / (384 x 1,400.000 x 80.04) = 0.621” > 0.475” therefor NOT OK

Even though this combination works for bending, it is beyond deflection limitations. Solution is to place internal stringers at third points.

An Evolution in Laying Out Stair Stringers

An Evolution in Laying Out Stair Stringers

Credit for today’s information to Brian Campbell, a finish carpenter and foreman with Solid, based in St. Paul, Minn.

Most carpenters are familiar with laying out stair stringers by stepping them out with a framing square equipped with stair gauges. A common error source with this method is failing to accurately line up framing square at the board edge board as you move from one step to next. Rounded (eased) boards make it hard to align layout lines from step to step. Minor shifts can compound errors. Savvy carpenters will make a tick mark when laying out each step to accurately define exact points where gauges meet board edges, but it’s still easy to wander off, and results in a stringer set not perfectly matching. Sometimes, boards with waney edges throw off square and you end up having to guess at position.

To avoid these problems, I stopped using stair gauges and made a sliding jig I use with a framing square instead (see photo, below). It’s simple to make on a table saw. Square slides in a kerf cut on each end of a 1×2, and I clamp sides together with small C-clamps when stepping off a stringer.

To improve accuracy, I moved to stepping off stringer with trammel points. I set up my trammel points on a board hypotenuse length of stair’s rise and run (square root of rise squared plus run squared), and at first used this trammel set to step off distance along the board edge.

Instead of working from board’s edge, possibly leading to errors, step off a stair stringer with a trammel set, working off a chalk line snapped near board’s middle.

Eventually this process evolved further by avoiding board edge entirely. Instead, work along a chalk line snapped down the stringer’s length. This line passes through each stair step inside corner. Step distance is exactly the same as edge step distance, but using a straight line down stringer middle helps to keep things more consistent.

Empire’s framing square has a cut-out milled at inside corner making it easy to line up a trammel point at square’s exact inside corner. 

I use this point to define where to snap my line, and after stepping off stair’s inside corners with trammel set, I line square up inscribed trammel points to draw cut lines for each step. This method adds a few movements, but it eliminates minor errors, allowing for a perfect stringer set, even with lumber variations.