Fitting a Stair into a Fixed Stairwell
An architect must fit a staircase between two floors 3.30 m apart. The stairwell available is 2.60 m wide and 4.20 m long; one end opens to a corridor and the space under the flight is wanted for storage. The local bylaw allows risers of 150–190 mm and treads of 250–300 mm, requires 2R + T to lie between 550 and 700 mm, a clear headroom of at least 2100 mm, and a flight width of at least 1000 mm.
The client wants a single straight flight so that 'it reads as one gesture' and the under-stair storage forms a clean wedge. The first sketch uses 18 risers and a 250 mm tread, which the draughtsman calls 'close enough'. A contractor has already priced the stringers on that basis. Before signing the drawing, the architect must check the numbers properly, decide whether the client's single-flight wish can be met at all, and set out an alternative that satisfies width, going, comfort and headroom.
1. Determine the minimum permissible number of risers, then test whether a single straight flight of 18 risers fits the 4.20 m going. Is 'close enough' defensible?
Read the worked answer
Riser count. N ≥ 3300/190 = 17.4, so at least 18 risers. With 17 risers, R = 3300/17 = 194.1 mm, which breaches the 190 mm cap; 18 risers give R = 3300/18 = 183.3 mm, inside 150–190.
Goings. A straight flight of 18 risers has 17 goings. At the minimum permitted tread of 250 mm the going is 17 × 250 = 4250 mm, against 4200 mm available - over by 50 mm before a single wall finish, skirting or nosing projection is counted. Any comfortable tread makes it worse: 17 × 275 = 4675 mm, 17 × 300 = 5100 mm.
Comfort check. 2R + T = 2(183.3) + 250 = 616.6 mm, comfortably inside 550–700, so the section is fine - the failure is purely in plan.
Is 'close enough' defensible? No. The 50 mm deficit is not a rounding issue; it means the flight physically does not fit, so either the stairwell wall moves, the flight is cut short (making the last tread non-conforming), or the design changes. A contractor pricing stringers off a non-fitting layout is a variation claim waiting to happen, and the draughtsman's phrase hides a dimensional failure behind a tolerance word. The architect should stop the pricing, issue a revised layout, and record the check - including the bylaw clauses relied on - on the drawing sheet.
2. Design the compliant alternative and verify width, tread, comfort and going.
Read the worked answer
Configuration. An 18-riser dog-leg: two flights of 9 risers, with a half-space landing at mid-height. Each flight has 8 goings.
Tread and going. Take T = 275 mm: going per flight = 8 × 275 = 2200 mm. Landing depth 1200 mm. Total plan length = 2200 + 1200 = 3400 mm ≤ 4200 mm, leaving 800 mm of slack - enough to raise the tread to 300 mm (8 × 300 + 1200 = 3600 mm) if a more generous tread is preferred.
Comfort. 2R + T = 2(183.3) + 275 = 641.6 mm, inside 550–700. With T = 300 mm it becomes 666.6 mm, still compliant and more comfortable for descent.
Width. Two flights of 1000 mm plus a 100 mm well = 2100 mm, against 2600 mm available; landing width 2100 mm. Both exceed the 1000 mm minimum with room to spare, and the extra 500 mm can absorb the handrail zone and wall build-up.
What the client loses. The single-gesture straight flight is geometrically impossible here - 18 risers cannot compress into 4.20 m at any legal tread. The dog-leg keeps the riser, the comfort ratio and the headroom, and converts the under-stair wedge into two smaller storage volumes. If the reading as one continuous flight is a hard design driver, the only honest routes are extending the stairwell into the adjacent room or changing the floor-to-floor height; neither is available, so the dog-leg is the answer and should be presented to the client that way, with the arithmetic, rather than as a preference.
3. Check headroom for the dog-leg. Where is the critical location, and what does that imply for the under-stair storage and the corridor?
Read the worked answer
Requirement. Clear headroom ≥ 2100 mm, measured vertically from the pitch line of the flight below to the underside of the obstruction above.
Where it is fine. The upper flight springs from the half-space landing, so above the lower flight the obstruction is the upper flight itself, which rises away from the lower flight much faster than the lower flight descends. Along the walked path the clearance is generous, typically well over 2 m by the second or third riser of the lower flight.
Where it fails. Beneath the half-space landing the clear height is exactly the height of one flight: 9 × 183.3 = 1650 mm. That is 450 mm short of 2100 mm. It is not a drawing error and cannot be finessed - it is a direct consequence of splitting the height in two.
Judgement. Three consequences follow. (1) The corridor must not pass under the half-space landing; place the landing at the far end of the stairwell, away from the corridor opening, so the 1650 mm zone is never a route. (2) That zone becomes the storage volume the client wanted, but it must be a lockable cupboard entered from outside the stair, not a walk-in space - nobody may be able to walk into a 1650 mm void by mistake. (3) If a through-route under the landing is unavoidable, the only compliant fixes are a different flight division (for example a quarter-turn with winders) or raising the landing by adding a riser, both of which change the scheme. Check headroom at the lowest headroom point, not at mid-flight, and mark the dimension on the section drawing.