Reinforced Concrete Stair Design (NSCP 2015 / ACI 318): Loads, Effective Span, and Reinforcement with Example

By Engr. Ruel H. Cepeda, Structural Engineer

A reinforced concrete stair is a sloped one-way slab — the waist — carrying triangular steps, spanning between landings or landing beams. Once riser-tread geometry suits comfortable walking, the design follows the same R_n/ρ method as an ordinary one-way slab, with three adjustments: loads convert to the horizontal plan, span runs between landing supports, and bars need careful anchorage at the kink where flight meets landing. This article covers geometry, thickness, loads, span, moment, steel, and kink detailing, then a full worked example per NSCP 2015 and ACI 318.

Stair Geometry: Riser, Tread, and Headroom

Riser (R) and tread (T) are set for safe walking before any structural check. Philippine practice keeps R between 150 and 180 mm, T between 250 and 300 mm, related by the comfort rule:

2R + T ≈ 600–650 mm

Risers per flight = rise ÷ R, rounded to a whole number; treads = risers − 1; going = (risers − 1) × T — not the same as the effective span used later.

Headroom is an architectural/fire-egress check, not a structural one, but it constrains the stairwell layout. Confirm the 2.0 m minimum against the National Building Code of the Philippines; it most often governs where a flight passes beneath another.

Waist Slab Thickness

The waist is the sloped slab carrying the steps, thickness measured perpendicular to the flight. Absent a deflection calculation, practice sizes it as a fraction of the horizontal effective span L:

t = L/25 to L/20

with a practical minimum of about 100 mm for a narrow domestic flight, 125 mm or more for wider or tiled/handrailed ones. Round up to the next 25 mm; the worked example lands on t = L/20. This is a practice band, not a code rule — check it against the deflection-control minimum thickness for one-way slabs in NSCP 2015 Table 407.3.1.1 (ACI 318 Table 7.3.1.1): L/20 simply supported, L/24 one end continuous, L/28 both ends continuous, for Grade 420 steel and normal-weight concrete (multiply by 0.4 + f_y/700 for other grades). A simply supported flight sized thinner than L/20 therefore needs a deflection calculation.

Loads on the Inclined Waist Slab

Every load converts to an equivalent UDL per metre of horizontal plan, carried through M_u = w_uL²/8 (or /10):

Sum rows 1–3 for dead load D; row 4 is live load L. Factor as usual: w_u = 1.2D + 1.6L.

Effective Span Between Landing Beams

Do not confuse the going (Step 1, the length the steps occupy) with the effective span L used for the moment. Where a flight lands on beams top and bottom, L is the horizontal distance between the landing beam supports, just as an ordinary slab's span is taken between its supporting beams. L normally exceeds the going, since the waist continues onto each beam for bearing and anchorage.

Design Moment

For a flight without special continuity detailing, take the conservative simply supported case, M_u = w_uL²/8. Some use M_u ≈ w_uL²/10 instead, reflecting partial restraint from a monolithic landing slab — reliable only if negative (top) steel is detailed over the support; otherwise /10 is unconservative. Default to /8 unless continuity is deliberately designed for.

Main Reinforcement Design (R_n/ρ Method)

Design a 1000 mm strip running up the slope, exactly as for a one-way slab:

R_n = M_u / (φ·b·d²)    ρ = (0.85f′_c/f_y)·[1 − √(1 − 2R_n/0.85f′_c)]    A_s = ρ·b·d

φ = 0.90, b = 1000 mm, d = t − cover − half bar diameter. Main bars run along the slope into the landing — see the kink note below before finalizing the layout. Minimum flexural steel for slabs is the shrinkage-and-temperature amount on the gross section (NSCP 2015 Section 407.6.1 / ACI 318 Section 7.6.1): A_s,min = 0.0018·b·t for Grade 420 bars (0.0020·b·t for f_y below 420 MPa); use whichever of computed A_s or A_s,min is larger. Distribution steel runs transverse at the same ratio: A_s,ts = 0.0018·b·t. Max spacing: 3t or 450 mm (main), 5t or 450 mm (distribution).

Detailing at the Kink — Where Flight Meets Landing

This is the detail most often gotten wrong: at the flight-to-landing junction, a bar under tension behaves like a rope pulled around a corner and wants to straighten out. Simply bent through the kink with nothing holding it, that force pushes outward against the bend's outer cover and can spall it off, destroying anchorage right where moment and shear are significant. Instead, run tension steel straight past the kink into the landing for a full development length, and add supplementary closing or hairpin bars anchored into both flight and landing to resist the outward force directly — the same logic behind the hook, bend, and development provisions of ACI 318-19 Chapter 25 (NSCP 2015 Section 425) and the re-entrant-corner details in standard detailing manuals.

Landing Design Note

Landing slabs are flat, so self-weight is simply t·γ_c, with no /cosθ term and no step wedge. They usually span perpendicular to the flight, between the flanking landing beams, carrying the same live load, and normally see a lower factored load per m² than the flight even though both are often kept at equal thickness for formwork continuity. Design it independently, using the same R_n/ρ method — see the sister one-way slab design article.

Worked Example — Dog-Leg Stair

Given: Dog-leg stair, flight rise H_flight = 1.6 m; R = 160 mm, T = 275 mm, waist t = 150 mm; L = 3.0 m. f′_c = 21 MPa; Grade 415 bars, 20 mm cover, 12 mm main / 10 mm distribution bars; finish (assumed) 1.5 kPa; live load 4.8 kPa.

1. Geometry check

Risers/flight = 1600/160 = 10. Treads = 10−1 = 9. Going = 9×275 = 2475 mm = 2.475 m.
2R+T = 320+275 = 595 mm, within tolerance of the 600–650 mm band.
L (3.0 m) exceeds going (2.475 m) by ≈0.26 m per end: landing-beam width plus bearing.

2. Waist thickness check

L/20 to L/25 = 150 mm to 120 mm. Chosen t = 150 mm = L/20, above the 100–125 mm practical minimum and equal to the Table 407.3.1.1 minimum for a simply supported one-way slab (3000/20 = 150 mm; the Grade 415 factor 0.4 + 415/700 = 0.99 gives 149 mm), so no deflection calculation is required.

3. Loads (per m² of horizontal plan)

hypotenuse = √(275²+160²) = √101,225 = 318.16 mm; cosθ = 275/318.16 = 0.864.
Waist self-weight = 0.150×24/0.864 = 4.165 kPa.
Step self-weight = 0.5×0.160×24 = 1.920 kPa.
Finish = 1.500 kPa. D = 4.165+1.920+1.500 = 7.585 kPa. L = 4.8 kPa.

4. Factored load and design moment

w_u = 1.2(7.585)+1.6(4.8) = 16.782 kN/m.
M_u = 16.782×3.0²/8 = 18.88 kN·m/m (simply supported; /10 would give 15.10 kN·m/m and ≈21% less steel — not used since no negative steel is detailed at the supports).

5. Main steel

d = 150−20−12/2 = 124 mm.
R_n = 18.88×10&sup6;/(0.9×1000×124²) = 1.364 MPa.
ρ = 0.04301×[1−√(1−2(1.364)/17.85)] = 0.00342.
A_s = 0.00342×1000×124 = 425 mm²/m > A_s,min = 0.0018×1000×150 = 270 mm²/m (300 mm²/m at 0.0020) → computed governs.
12 mm bars (A_b = 113.1 mm²): s = 1000×113.1/425 = 266 mm < 450 mm cap → use 12 mm @ 250 mm o.c. (452 mm²/m > 425).

6. Distribution steel

A_s,ts = 0.0018×1000×150 = 270 mm²/m (300 mm²/m if the literal 0.0020 for f_y < 420 MPa is applied).
10 mm bars (A_b = 78.5 mm²): s = 1000×78.5/270 = 291 mm < 450 mm cap → use 10 mm @ 250 mm o.c. (314 mm²/m, satisfying either minimum).

Result: t = 150 mm; main steel 12 mm @ 250 mm o.c.; distribution 10 mm @ 250 mm o.c.

Assumptions & Limitations

• Applies to cast-in-place waist-slab stairs only — not precast, steel stringer, or helical stairs.
• Simply supported (/8) is the conservative default; use /10 only with deliberately detailed negative steel at the support.
• Finish allowance (1.5 kPa) is assumed; confirm against the finish schedule and handrail loads.
• The 0.0018 minimum treats Grade 415 as Grade 420 per common local practice; literally NSCP 2015 gives 0.0020 for f_y below 420 MPa (300 mm²/m here). The bars selected (12 mm @ 250 main = 452 mm²/m, 10 mm @ 250 distribution = 314 mm²/m) satisfy either value.
• One-way shear rarely governs a waist-slab stair of ordinary span; verify for long spans or heavy loads.
• Landing slabs, stringer beams, and handrail anchorages are designed separately; confirm the code edition adopted locally.

Frequently Asked Questions

How do I choose between the simply supported and partially fixed moment coefficients?

Default to simply supported (/8) unless negative steel is specifically detailed through the landing into the flight; without it, /10 understates demand.

Why is stair live load as high as 4.8 kPa when floor live loads are often only 1.9–2.4 kPa?

Stairs are egress routes that can see crowd loading during evacuation, so codes treat them closer to an assembly load. NSCP 2015 Table 205-1 lists 4.8 kPa for exit facilities including stairways; ASCE 7 allows about 1.9 kPa only for stairs within one- and two-family dwellings — confirm which value the governing code and reviewer accept before using the lower figure.

Do I still add the step self-weight term for open-riser stairs?

No. ½·R·γ_c is the solid wedge of a closed riser; open risers have no wedge, so drop it and keep only waist self-weight, finishes, and live load. In the example this cuts dead load by 1.92 kPa; open-riser treads are usually designed as separate elements instead.

Getting the load conversion, span, and kink anchorage right keeps a stair off the rework list. Try the free reinforcement calculator and minimum beam depth calculator, or browse all free web tools. For the underlying procedure, see the one-way slab design article. Offline spreadsheets are on the download page.