RCC stair for 6.0 m by 4.2 m lobby

Data: lobby 6.0 m x 4.2 m, floor height 4.5 m, slab thickness 150 mm, riser 150 mm, not more than 12 steps per flight.

Given data and assumptions

• Stairwell (internal): 6 m x 4.2 m; floor-to-floor height $H = 4.5$ m; stair for a public building, RCC.
• Assumed riser $R = 150$ mm and tread $T = 300$ mm; flight width $b = 1.4$ m. Since 30 risers cannot be put in flights of at most 12, a three-flight (zig-zag) stair with two landings is adopted.

Design

1. Number of risers $= H/R = 4.5/0.15 = 30$, adopt 30 risers; exact riser $= 4.5/30 = 150$ mm.
2. Flights: at most 12 risers per flight are allowed, so the 30 risers are divided into three equal flights of 10 risers (9 treads each), arranged side by side in a zig-zag with two half-space landings (one at each end).
3. Going of one flight $= 9 \times 0.3 = 2.7$ m.
4. Width: three bays of 1.4 m give $3b = 4.2$ m $\le 4.2$ m.
5. Landings: two landings, each 1.4 m x 2.8 m (covering two bays), at heights 1.5 m and 3 m.
6. Length check: landing L1 + going + landing L2 $= 1.4 + 2.7 + 1.4 = 5.5$ m $\le 6$ m, so it fits; the spare 0.5 m is kept at the entry.
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). Headroom above landing L1 $= 4.5 - 1.5 - 0.15$ (slab) $= 2.85$ m $> 2.1$ m, OK.
8. Waist slab: effective span about 4.1 m (going + one landing), so depth $\approx$ span/20 $= 205$ mm; adopt a 225 mm thick waist slab, with the given 150 mm slab for the floors (reinforcement to be designed separately). Provide a handrail 0.9 m high, 20-25 mm nosing and a non-slip finish.

Plan and section

 far end
 +-------------------+---------+
 |    LANDING L1     | arrival |
 |    (+1.50 m)      | (upper  |
 |                   |  floor) |
 +---------+---------+---------+
 |   F1    |   F2    |   F3    |
 |   ^     |   v     |   ^     |
 |   ^     |   v     |   ^     |
 +---------+---------+---------+
 |  start  |    LANDING L2     |
 |         |    (+3.00 m)      |
 +---------+-------------------+
 near end   (arrows point up the stair)

 SECTION (not to scale)
                                  +---- upper floor +4.50
                            _____|  flight 3
                      _____|  landing L2 +3.00
                _____|  flight 2
          _____|  landing L1 +1.50
     ____|  flight 1
 ___|
 ground floor +0.00

Summary

Answer: 30 risers of 150 mm and treads of 300 mm; 3 flights x 10 risers; flight width 1.4 m.