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Dog-legged stair, 4.8 m by 2.25 m

Short answer

A staircase is a series of steps linking floors. With 3.6 m height in 4.8×2.25 m: 24 risers at 150 mm, tread 280 mm; two flights of 12 risers, 11 treads, flight width 1.05 m, waist slab 225 mm.

Define staircase. For a given space of 4.8m × 2.25m with floor height of 3.6m, design a RCC dog-legged staircase.

A staircase 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.

Given data and assumptions

  • Stairwell (internal): 4.8 m x 2.25 m; floor-to-floor height H=3.6H = 3.6 m; stair for a residential building, RCC.
  • Assumed riser R=150R = 150 mm and tread T=280T = 280 mm; flight width b=1.05b = 1.05 m. Gap between the flights = 2.25 - 2 x 1.05 = 0.15 m.

Design

  1. Number of risers =H/R=3.6/0.15=24= H/R = 3.6/0.15 = 24, adopt 24 risers; exact riser =3.6/24=150= 3.6/24 = 150 mm.
  2. Flights: a dog-legged stair has two equal flights, so each flight has 24/2 = 12 risers and 12-1 = 11 treads (the landing or upper floor acts as the last tread).
  3. Going of one flight =11×0.28=3.08= 11 \times 0.28 = 3.08 m.
  4. Width: two flights of 1.05 m side by side need 2b=2.12b = 2.1 m; the remaining W−2b=2.25−2.1=0.15W - 2b = 2.25 - 2.1 = 0.15 m is the gap between the flights.
  5. Landing: a half-space landing 1.05 m x 2.25 m (full stairwell width) at height =12×0.15=1.8= 12 \times 0.15 = 1.8 m.
  6. Length check: going + landing =3.08+1.05=4.13= 3.08 + 1.05 = 4.13 m ≤4.8\le 4.8 m, so it fits; the spare 0.67 m is kept as entry/exit space.
  7. Check: 2R+T=2×150+280=5802R + T = 2 \times 150 + 280 = 580 mm (within 550-650 mm); pitch =tan⁡−1(R/T)=28.2∘= \tan^{-1}(R/T) = 28.2^\circ (within 25-40 degrees).
  8. Waist slab: effective span about 4.13 m, so depth ≈\approx span/20 =206= 206 mm; adopt a 225 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   |         |
 | 11 treads              | LANDING |
 +------------------------+ (b x W) |
 | FLIGHT 1  >>>>>>  UP   |         |
 | 11 treads              |         |
 +------------------------+---------+
 <-------- going -------> <-- b -->
 (entry at left end of flight 1; arrows point up the stair)

 SECTION (not to scale)
                          +---- upper floor 3.6 m
                    _____|
               ____|   flight 2
        ______|  landing
   ____|  flight 1
 _|
 ground floor +0.00

Summary

ItemAdopted
Riser150 mm (24 nos.)
Tread280 mm
Flights2 flights x 12 risers
Width of flight1.05 m
Waist slab225 mm

Answer: 24 risers of 150 mm and treads of 280 mm; 2 flights x 12 risers; flight width 1.05 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

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