Dog-legged stair, 5.0 m by 4.0 m

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.

Functional requirements of a good stair

1. Location: easily accessible, centrally placed, well lit and ventilated, and near the main entrance; not reached through rooms.
2. Width: residential at least 0.9-1.0 m, public buildings 1.5 m or more (as per NBC and local building bye-laws), so that two persons can pass.
3. Easy and safe ascent: riser 150-175 mm (public buildings not more than 150 mm), tread 250-300 mm; $2R + T$ about 580-600 mm; all steps in one flight equal.
4. Pitch: between 25 and 40 degrees.
5. Number of steps per flight: not more than 12 and not less than 3.
6. Landings: provided at turns and between flights, with width not less than the stair width.
7. Headroom: at least 2.0-2.2 m clear above every step.
8. Strength and fire resistance: strong enough for the live load; fire-resistant material, with a separate fire-escape stair in tall buildings.
9. Handrails and balustrades: about 0.9 m high, strong and safe for children.
10. Surface: non-slip treads, good lighting and ventilation, durable and pleasing in appearance.

Given data and assumptions

• Stairwell (internal): 5 m x 4 m; floor-to-floor height $H = 3$ m; stair for a public building, RCC.
• Assumed riser $R = 150$ mm and tread $T = 300$ mm; flight width $b = 1.9$ m. Wide flights of 1.9 m (public building) leave a gap of 4.0 - 2 x 1.9 = 0.2 m between the flights.

Design

1. Number of risers $= H/R = 3/0.15 = 20$, adopt 20 risers; exact riser $= 3/20 = 150$ mm.
2. Flights: a dog-legged stair has two equal flights, so each flight has 20/2 = 10 risers and 10-1 = 9 treads (the landing or upper floor acts as the last tread).
3. Going of one flight $= 9 \times 0.3 = 2.7$ m.
4. Width: two flights of 1.9 m side by side need $2b = 3.8$ m; the remaining $W - 2b = 4 - 3.8 = 0.2$ m is the gap between the flights.
5. Landing: a half-space landing 1.9 m x 4 m (full stairwell width) at height $= 10 \times 0.15 = 1.5$ m.
6. Length check: going + landing $= 2.7 + 1.9 = 4.6$ m $\le 5$ m, so it fits; the spare 0.4 m is kept as entry/exit space.
7. Check: $2R + T = 2 \times 150 + 300 = 600$ mm (within 550-650 mm); pitch $= \tan^{-1}(R/T) = 26.6^\circ$ (within 25-40 degrees).
8. Waist slab: effective span about 4.6 m, so depth $\approx$ span/20 $= 230$ mm; adopt a 250 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

 +------------------------+---------+
 | FLIGHT 2  <<<<<<  UP   |         |
 | 9 treads               | LANDING |
 +------------------------+ (b x W) |
 | FLIGHT 1  >>>>>>  UP   |         |
 | 9 treads               |         |
 +------------------------+---------+
 <-------- going -------> <-- b -->
 (entry at left end of flight 1; 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 300 mm; 2 flights x 10 risers; flight width 1.9 m.