Quarter turn stair, 2.1 m by 5 m

Given data and assumptions

• Stairwell (internal): 5 m x 2.1 m; floor-to-floor height $H = 3$ m; stair for a residential building, RCC.
• Assumed riser $R = 167$ mm and tread $T = 240$ mm; flight width $b = 0.9$ m. The narrow 2.1 m width limits the cross flight, so a riser of about 167 mm and a tread of 240 mm (slightly less than the usual 250 mm) are taken; the maximum riser for dwellings is 175 mm.

Design

1. Number of risers $= H/R = 3/0.167 = 18$, adopt 18 risers; exact riser $= 3/18 = 166.7$ mm.
2. Flights: a quarter-turn stair has a square quarter landing. Take flight 1 = 12 risers (11 treads) and flight 2 = 6 risers (5 treads); total 12 + 6 = 18 risers.
3. Goings: flight 1 $= 11 \times 0.24 = 2.64$ m; flight 2 $= 5 \times 0.24 = 1.2$ m.
4. Quarter landing: 0.9 m x 0.9 m at height $= 12 \times 0.1667 = 2$ m.
5. Fit along the length: $2.64 + 0.9 = 3.54$ m $\le 5$ m.
6. Fit along the width: $0.9 + 1.2 = 2.1$ m $\le 2.1$ m.
7. Check: $2R + T = 2 \times 166.7 + 240 = 573$ mm (within 550-650 mm); pitch $= \tan^{-1}(R/T) = 34.8^\circ$ (within 25-40 degrees).
8. Waist slab: effective span about 3.54 m, so depth $\approx$ span/20 $= 177$ mm; adopt a 200 mm thick waist slab (reinforcement to be designed separately). Provide a handrail 0.9 m high, 20-25 mm nosing and a non-slip finish.

Plan and section

 +----+--------------------+
 | F2 |                    |
 | ^  |                    |
 | ^  |      (hall)        |
 +----+--------------------+
 |LAND| <<<<<<<<<<<< F1 UP |
 +----+--------------------+
 F1 = 12 risers (starts at the right end), quarter landing, F2 = 6 risers
 (arrows point up the stair)

 SECTION (not to scale)
                          +---- upper floor 3 m
                    _____|
               ____|   flight 2
        ______|  landing
   ____|  flight 1
 _|
 ground floor +0.00

Summary

Answer: 18 risers of 166.7 mm and treads of 240 mm; flights of 12 and 6 risers; flight width 0.9 m.