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Reinforced concrete staircase to SANS 10100-1

A dog-leg flight of 9 risers on two landings that span across the stair well: geometry, the effective span, loads on plan, bending on the waist, shear, deflection, minimum and top steel, and the landings. The numbers come from the free STATIX staircase calculator.

1. The problem

Input	Value
Stair	Dog-leg flight between two landings that span across the stair well
Steps	9 risers of 170 mm, 8 goings of 250 mm; flight 2 000 mm on plan, 1 530 mm rise
Waist	150 mm, width 1 000 mm; landings 1 000 mm wide, 150 mm thick
Loads	Finishes 1,0 kPa on plan; imposed 1,5 kPa
Materials	f_cu = 30 MPa, f_y = 450 MPa, cover 45 mm (moderate exposure), fire rating 1 h
Bars	Main Y12 @ 150 (bottom), distribution Y10 @ 250, top steel at the ends Y12 @ 200

2. Geometry and effective span (4.9.1)

pitch = tan^-1(170 / 250) = 34,2° · slope factor = √(170² + 250²) / 250 = 1,209

The landings span across the stair, so clause 4.9.1.3.1 lets the flight span to the middle of each landing, but not more than 900 mm into it:

effective span = 2 000 + 1 000/2 + 1 000/2 = 3 000 mm

3. Loads on plan (4.9.1.1)

waist: 0,150 × 24 × 1,209 = 4,35 kPa
steps: 0,170 / 2 × 24 = 2,04 kPa
finishes 1,00 kPa ⇒ g_k = 7,39 kPa on the flight, 4,60 kPa on the landings

SANS 10160-1 gives two ultimate combinations. With this light imposed load, 1,35 G + 1,0 Q governs:

flight: 1,35 × 7,39 + 1,0 × 1,5 = 11,48 kN/m² · landings: 1,35 × 4,60 + 1,5 = 7,71 kN/m²

4. Moment and bending resistance (4.9.2.2, 4.3.3.4.1)

A single span of 3 000 mm with 500 mm of landing load at each end and 2 000 mm of flight load in the middle:

R = (11,48 × 2,0 + 7,71 × 0,5 × 2) / 2 = 15,34 kN/m
M_max = 15,34 × 1,5 − 7,71 × 0,5 × 1,25 − 11,48 × 1,0 × 0,5 = 12,4 kNm/m

The section is the waist measured square to the soffit (4.9.1.4): d = 150 − 45 − 6 = 99 mm. Y12 @ 150 gives 754 mm²/m:

x = 0,87 × 450 × 754 / (0,45 × 30 × 0,9 × 1 000) = 24 mm · z = 99 − 0,45 × 24 = 88 mm
M_u = 0,87 × 450 × 754 × 88 = 26,0 kNm/m ≥ 12,4 (48 %)

5. Shear, deflection and minimum steel

Shear: v = 15,34 / (1 000 × 99) = 0,155 MPa, well under v_c = 0,74 MPa: no links (21 %).
Deflection (4.9.2.3, 4.4.6): L/d = 3 000 / 99 = 30,3 against 20 × 1,15 (stair without stringers, flight over 60 % of the span) × 1,86 (tension steel factor) = 42,8 (71 %).
Minimum steel (table 23): 0,13 % × 1 000 × 150 = 195 mm²/m in both directions; distribution Y10 @ 250 = 314 mm²/m (62 %).
Top steel at the monolithic ends (4.11.7.3.3): at least half the span steel, 377 mm²/m, for max(0,1 l, 45φ) = 540 mm; Y12 @ 200 = 565 mm²/m (67 %).
Fire, 1 h (table 45): thinnest part 150 ≥ 100 mm, cover 45 ≥ 15 mm.

6. The landings

Each landing spans 2 300 mm across the well and carries its own load plus the flight reaction. Its moment is 12,9 kNm/m against 22,5 kNm/m with Y12 @ 150 at d = 87 mm (57 %); its span / depth ratio governs the whole stair at 85 %, and its top steel over the supports at 96 %.

7. Result

Check	Result
Flight bending	12,4 ≤ 26,0 kNm/m (48 %)
Shear, no links	0,155 ≤ 0,74 MPa (21 %)
Flight span / depth	30,3 ≤ 42,8 (71 %)
Landing span / depth	26,4 ≤ 31,1 (85 %)
Landing top steel	377 ≤ 393 mm²/m (96 %), governs

All 31 checks pass. The flight has spare capacity; the landings set the limit, so a thicker or shorter landing is the first place to save or add.

Run this example yourselfThe free STATIX staircase calculator checks to SANS 10100-1 by default. Enter the inputs from step 1 and every number above appears, with each clause and a printable calc sheet.
Open the free staircase calculator

A worked example for learning, not a design. Check every value against the current code and your own project, and have the design checked and signed by a registered professional engineer.

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