Wood stair

One straight flight on sawn lumber stringers with its treads, to NDS 2024 with ASCE 7-22 loads and the stair limits of IBC 2021 1011. LRFD or ASD.

Inputs of the wood stair #

• Flight: the stair's use sets the code limits checked; risers, riser and tread, clear width and headroom. The span on plan is (risers − 1) × tread plus the span beyond the treads, which you enter.
• Stringers: how many, evenly spaced; solid, with the treads on ledgers or housed, or cut in a sawtooth. Species, grade, size, plies.
• Cut stringers and the notch limit: NDS 4.4.3.2, as written, limits interior notches to one-sixth of the depth in the outer thirds and permits none in the middle third. A cut stringer fails that, so the check is on by default. AWC's own deck guide (DCA6) prescribes cut stringers with a 5 in. throat. If you accept that, turn the limit off; the calculation then checks the net section at the throat and says the decision is yours.
• Treads: flat boards of the same species and grade, spanning between stringers. Uniform load is shared by the boards in a tread; the concentrated load is on one board.
• Loads: dead and live load on plan, the concentrated load on a tread, a guard's dead load on an outside stringer. ASCE 7-22 Table 4.3-1 gives 100 psf, 40 psf in one- and two-family dwellings, and 300 lb on a tread, not at the same time as the uniform load. An entered value below the table gets a warning.
• Service conditions: wet service and incising (exterior stairs usually have both), temperature, deflection limits. The tread's L/288 is AWC DCA6's basis, not an IBC limit.

Auto-design (editor toolbar) varies the stringer size, the number of stringers and the tread board. Objective: the least wood across the stair.

Checks performed #

The drawings are the flight elevation, the stringer and tread sections, and the stringer's shear and moment diagrams.

Limitations #

• One straight flight, simply supported on plan. Landings, winders and connections are not designed. The guard is a dead load only.
• Axial force in the stringer is not calculated: with two vertical seats it is zero at midspan, where the moment is largest. A stringer that thrusts against its base needs that checked separately.
• Vibration is not checked.
• A cut stringer is checked braced at every tread.

Verification examples #

Verification status: 14 values compared in 3 examples (0 published, 3 hand calculations from the cited equations): 14 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: partial. Only some provisions were read in the target edition; the rest rests on older editions, examples or summaries.

No free worked example of a wood stair exists. Everything here is a hand calculation from the cited equations, listed on the Verification page, and two comparisons with AWC DCA6-2015, p. 21, which publishes rules and not calculations:

• Table 6's minimum tread of a 2x8 at 36 in., wet and incised, No. 2 Douglas Fir-Larch, 300 lb and L/288. It passes bending at 993 psi against 993.6 and deflection at 0.105 in. against 0.125 in., and a 2x6 fails: the table reads as this calculation does for Douglas Fir-Larch. By hand, Hem-Fir's lower E gives 0.129 in., a little over the limit, though the table lists it with the same 2x8.
• Figure 28's two stringer spans, cut 6 ft with a 5 in. throat and solid 13 ft 3 in., come out at the same bending stress within 5 % on the net section. That is why the net section is offered once the notch limit is turned off.

Neither is a published result to the same basis, so this type should be read as hand verified.