Quarter turn stair, 5.5 m by 4.0 m

Stair

A stair is a set of steps (a series of risers and treads) that connects floors at different levels, giving access from one storey to another, usually with landings and a balustrade.

Design of quarter turn stair

Given data and assumptions

• Stairwell (internal): 5.5 m x 4 m; floor-to-floor height $H = 3$ m; stair for a residential building, RCC.
• Assumed riser $R = 150$ mm and tread $T = 250$ mm; flight width $b = 1.1$ m.

Design

1. Number of risers $= H/R = 3/0.15 = 20$, adopt 20 risers; exact riser $= 3/20 = 150$ mm.
2. Flights: a quarter-turn stair has a square quarter landing. Take flight 1 = 12 risers (11 treads) and flight 2 = 8 risers (7 treads); total 12 + 8 = 20 risers.
3. Goings: flight 1 $= 11 \times 0.25 = 2.75$ m; flight 2 $= 7 \times 0.25 = 1.75$ m.
4. Quarter landing: 1.1 m x 1.1 m at height $= 12 \times 0.15 = 1.8$ m.
5. Fit along the length: $2.75 + 1.1 = 3.85$ m $\le 5.5$ m.
6. Fit along the width: $1.1 + 1.75 = 2.85$ m $\le 4$ m.
7. Check: $2R + T = 2 \times 150 + 250 = 550$ mm (within 550-650 mm); pitch $= \tan^{-1}(R/T) = 31^\circ$ (within 25-40 degrees).
8. Waist slab: effective span about 3.85 m, so depth $\approx$ span/20 $= 192$ 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 = 8 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: 20 risers of 150 mm and treads of 250 mm; flights of 12 and 8 risers; flight width 1.1 m.