Stair Set-Out With a Fixed Floor-to-Floor Height
You are setting out a straight flight of timber stairs in a renovation. The finished floor-to-floor height is 2710 mm. The stairwell opening in the upper floor is fixed at 2400 mm long and 900 mm wide, and the headroom above the flight must not be less than 2000 mm at any point. The client wants a rise that feels comfortable and a going that is as generous as the opening allows. The upper floor joists run across the stairwell and cannot be moved. The lower floor is timber, so the bottom of the stringer can be fixed to a bearer rather than the slab.
1. Work out a riser and going that satisfies the height and the opening, and explain how you checked headroom.
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Start with the total rise: 2710 mm. A comfortable domestic rise is usually around 170-190 mm. Dividing 2710 by 16 gives 169.4 mm; by 15 gives 180.7 mm. Sixteen risers of 169 mm is the better fit because it keeps the rise under 170 mm and gives 15 goings.
Going: the opening is 2400 mm long. The flight must fit within it plus the floor thickness at the top. If the going is 250 mm, 15 goings need 3750 mm of horizontal run, which will not fit in a 2400 mm opening. That tells you the flight must either be steeper or the opening is too short for a straight flight. Check the geometry: with a 2400 mm opening and a 2710 mm rise, a straight flight at a comfortable pitch will not clear the upper floor edge.
The judgement is to test the headroom. Headroom is measured vertically from the nosing line to the underside of the floor above. At the point where the flight passes under the upper floor edge, the height of the nosing line above the lower floor is the number of risers climbed times the riser height. If the opening starts 2400 mm back from the top nosing, the flight reaches the opening edge after roughly 2400/going steps. With a 250 mm going that is about 9.6 steps, so the nosing line is about 9.6 x 169 = 1620 mm above the lower floor. The underside of the upper floor is at 2710 mm minus the floor depth, say 240 mm, so about 2470 mm. Headroom is 2470 - 1620 = 850 mm, which fails badly.
The answer is that a straight flight does not fit this opening with a comfortable going. Options: reduce the going (steeper, less comfortable), introduce a winder or landing to turn the flight, or enlarge the opening. The exam wants you to show the arithmetic and to conclude that the opening governs, not to force a number that fails headroom.
2. The client insists on a straight flight and will not move the joists. What design change would you propose, and how would you check it?
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If the joists cannot move and the opening stays 2400 mm, the straight flight has to be steeper. Work backwards from the opening. The flight must pass under the upper floor edge with at least 2000 mm headroom. Underside of upper floor is about 2470 mm, so the nosing line at the opening edge must be no higher than 470 mm above the lower floor. That is only about 2.8 risers at 169 mm, meaning the opening edge must be reached very early in the flight, which is impossible for a flight that climbs 2710 mm in a 2400 mm run.
So a straight flight within a 2400 mm opening cannot meet 2000 mm headroom at any comfortable pitch. The honest answer is that the constraint set is infeasible as stated. Propose either a dog-leg with a landing (which turns the flight and uses the width rather than the length), a winder at the bottom or top, or enlarging the opening by trimming one or two joists and adding a trimmer. A trimmer is usually the cheapest structural change and is the one to put to the client first.
Check the proposal by drawing the nosing line to scale, marking the 2000 mm headroom envelope, and confirming the flight stays below it. Also check the going is not below the minimum the client will accept, because a steeper flight trades comfort for fit. The judgement is to recognise an infeasible brief early rather than build a stair that fails inspection.