RCC dog-legged stair for office building

Reasons for the size of riser and tread

• Riser 150 mm: an office building has heavy traffic of people of all ages, so the riser is kept at the lower limit (150 mm) for comfortable climbing; the floor height of 3.6 m divides exactly into 24 equal risers.
• Tread 280 mm: a wide tread (250-300 mm) gives safe foot placing; $2R + T = 2 \times 150 + 280 = 580$ mm, which is within the usual comfort range of 550-650 mm.
• The riser and tread are kept equal throughout so that people do not trip.

Given data and assumptions

• Stairwell (internal): 4.8 m x 3 m; floor-to-floor height $H = 3.6$ m; stair for an office building, RCC.
• Assumed riser $R = 150$ mm and tread $T = 280$ mm; flight width $b = 1.45$ m. Stair size 4.8 m x 3.0 m x 3.6 m (length x width x height). Gap between flights = 3.0 - 2 x 1.45 = 0.1 m.

Design

1. Number of risers $= H/R = 3.6/0.15 = 24$, adopt 24 risers; exact riser $= 3.6/24 = 150$ 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 $= 11 \times 0.28 = 3.08$ m.
4. Width: two flights of 1.45 m side by side need $2b = 2.9$ m; the remaining $W - 2b = 3 - 2.9 = 0.1$ m is the gap between the flights.
5. Landing: a half-space landing 1.45 m x 3 m (full stairwell width) at height $= 12 \times 0.15 = 1.8$ m.
6. Length check: going + landing $= 3.08 + 1.45 = 4.53$ m $\le 4.8$ m, so it fits; the spare 0.27 m is kept as entry/exit space.
7. Check: $2R + T = 2 \times 150 + 280 = 580$ mm (within 550-650 mm); pitch $= \tan^{-1}(R/T) = 28.2^\circ$ (within 25-40 degrees).
8. Waist slab: effective span about 4.53 m, so depth $\approx$ span/20 $= 226$ 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   |         |
 | 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

Answer: 24 risers of 150 mm and treads of 280 mm; 2 flights x 12 risers; flight width 1.45 m.

Details to be drawn

• Plans at ground floor and first floor with UP/DN arrows, flight width and landing.
• Section showing the 150 mm riser, 280 mm tread, waist slab, landing slab, nosing (25 mm) and balustrade (0.9 m high).
• Reinforcement: main bars along the slope (e.g. 12 mm dia at 150 c/c), distribution bars 8 mm at 200 c/c, concrete M20, steel Fe415 (to be designed separately).