RCC stair, 2.1 m by 4.5 m room

Given data and assumptions

• Stairwell (internal): 4.5 m x 2.1 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 $b = 1$ m.

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 $= 9 \times 0.25 = 2.25$ m.
4. Width: two flights of 1 m side by side need $2b = 2$ m; the remaining $W - 2b = 2.1 - 2 = 0.1$ m is the gap between the flights.
5. Landing: a half-space landing 1 m x 2.1 m (full stairwell width) at height $= 10 \times 0.15 = 1.5$ m.
6. Length check: going + landing $= 2.25 + 1 = 3.25$ m $\le 4.5$ m, so it fits; the spare 1.25 m is kept as entry/exit space.
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 3.25 m, so depth $\approx$ span/20 $= 162$ mm; adopt a 175 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 250 mm; 2 flights x 10 risers; flight width 1 m.