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Tread width
The tread width of a step cannot be chosen at random. It is determined by the average step size of grown-up people.
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The average step size to be considered for calculations is 630 mm! |
Any new staircase to be built, which is not tied to fixed points like stair-aprons, is calculated to the step size formula.
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Sm = a + 2s |
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Sm = step size |
(Formula 2) |
Figure 9 - Representation of
the dependence of the height of rise and of the tread width on the step size -
a tread width, s height of rise, Sm step size
Since the tread width depends, to a great extent, on the height of rise, the step size of 630 mm can be taken care of. Thus the step size may vary between 615 mm and 645 mm. Stairs built in this ratio of rise and tread are easy to step on.
Height of rise
The height of rise is the vertical distance between the surfaces of the steps (treads).
The height of rise cannot be chosen at random.
For floor-to-floor staircases in dwelling houses it should be between 165 mm and 190 mm.
The height of rise takes priority for the determination of the ratio of rise and tread because the head steps of the flights must be flush with (have the same height as) the surfaces of the stair landings and the heights of rise within one flight must be of the same size.
The height of rise is calculated by means of the following formula:
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Lh = flight height |
(Formula 3) |
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ns = number of rises | |
In order to calculate the height of rise for a flight, the number of rises must be known first. The number of rises can be determined by assuming any height of rise between 165 mm and 190 mm and completing the formula by it.
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(Formula 4) |
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sg = height of rise chosen (assumed) | |
If the result is a decimal fraction, it must be rounded off to bring it up or down to an integer number.
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When rounding down, the height of rise will become greater than
the one assumed! |
Such rounded-off figure is applied to the formula (3) to get the height of rise for the staircase.
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The ideal height of rise is 170 mm! |
For stairs in ancillary rooms the height of rise may be up to 220 mm.
Ratio of rise and tread
The ratio of rise and tread is expressed by formula (5).
m = ratio of rise and tread
a = tread
s = height of rise
The ideal ratio of rise and tread is:
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Any staircase must be built to a ratio of rise and tread to be determined in advance. |
The height of rise takes priority for the determination of the ratio of rise and tread.
Even if drawings are available for stairs to be built, you should not rely on such drawings only.
Generally, all dimensions for the manufacture of a staircase should be taken from the stairwell and be compared with the drawing.
In most cases, the dimensions taken from the stairwell differ from the dimensions in the drawing. Therefore, the ratio of rise and tread is to be calculated anew for each staircase.
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The dimensions taken from the stairwell are binding for the calculation of the ratio of rise and tread! |
What is the meaning of "ratio of rise and tread" of a staircase?
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Flight line of stairs
The flight line is an imaginary line running over the front edges of the steps in the centre of the stair flight. In the plan view it is represented by an arrow showing the flight direction of the stairs (see Fig. 11).
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The ratio of rise and tread is determined at the flight line shown in the plan view. |
Flight length of stairs
The flight line shown in the plan view corresponds to the real length of the stair flight.
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The flight length of stairs is the horizontal distance between the front edge of the bottom step and the front edge of the head step. |
The stair flight is the inclined part of the stairs and consists of a number of treads of equal width.
Figure 10 - Connection between
stair flight length and stair flight height - a tread width, s
height of rise, 1 stair flight line, - L stair flight length, Lh
stair/light height, a angle of inclination of the
stair flight 1 - 4 in "L " direction is the number of treads 1 - 5 in "Lh"
direction is the number of rises
Figure 11 - Layout (plan view)
of the stair flight 1 stair foot (bottom step) at the stair
flight line, 2 stair head (head step) at the stair flight line, 3
stair flight line, B stair flight width
The flight length is calculated to the formula:
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L = na · a | |
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L = flight length of stairs |
(Formula 6) |
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na = number of treads | |
One flight of stairs should consist of not more than 15 treads. If more than 15 treads are required for a staircase, a landing should be included.
More than 15 treads in one flight of stairs would require much physical effort of the user of such stairs. If the tread width is required for the calculation of the ratio of rise and tread, formula (6) is to be conversed to give the tread width as under:
This formula is required when the flight length is limited by built-in stair-aprons (see Fig. 12).
Flight height of stairs
The flight height of stairs consists of a number of heights of rise of equal size (see Fig. 10).
The flight height of stairs is the vertical distance between the surfaces of the two landings.
In this respect it is important that the distance between the surfaces of the finished floor is to be measured. That means, the construction of the floor must be known!
The flight height of stairs decides how many rises are to be included in a flight of stairs because the height of rise cannot be chosen at random.
The flight height is calculated to the formula:
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Lh = ns · s |
(Formula 8) |
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The flight height of stairs is riot in any case equal to the height between floors. |
Figure 12 - Connection between
floor-to-floor height (height between floors) and the stair flight height - 1
main top landing, 2 main bottom landing, 3 half-landing, 4 floor-to-floor
height, 5 staircase (stairwell) wall with access to flat, 6 access
to flat (door), 7 staircase window, 8 staircase
(stairwell) wall (mostly outer wall), Lh
stair flight height, GL stairwell length
The height between floors is the vertical distance between the surfaces of the main landings! In stairmaking it is important to know that each flight of stairs always has one rise more than treads!
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ns = na + 1 |
(Formula 9) |
What is the flight line of stairs important for in
stairmaking?
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What is the "flight length of
stairs"?
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What is the "flight height of
stairs"?
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Landings
Stair landings are resting places for people who, for health or age reasons, have difficulties in climbing stairs. Without landings the flight of stairs would not be accessible!
The length of main landings must correspond to the flight width. Half-landings must have a minimum length of three times the tread width.
Figure 13 - Representation of
the lengths of the main landing and half-landing - 1 main landing,
half-landing, 3 outer string, 4 surface - main landing (surface -
flooring), 5 wall string, 6 rosette, 7 surface half-landing (surface
flooring), B stair flight width
A stair landing need not always be clearly visible, the half-landing for example. It may pass into the floor ceiling with no noticeable transition point. With wooden stairs, the landings support the flight of stairs. The bottom landing must resist and distribute horizontal and vertical forces, the top landing horizontal forces only.
Figure 14 - Distribution of
forces in the bottom and top landings - 1 lower stair-apron, 2 upper
stair-apron, 3 stair string, 4 load on the stairs by user, 5 acting force by
user, 6 force acting horizontally, 7 force acting vertically, 8 force acting
diagonally between the two landings
Stairwell
The stairwell is the space intended for building-in the staircase.
Figure 15 - Representation of
the stairwell - 1 lower floor-ceiling, 2 upper floor-ceiling, 3 stairwell, 4
opening in the upper floor-ceiling, 5 stairs with half-landing to be built
in
It is limited in length by the existing opening in the upper floor-ceiling and in the height by the surfaces of the floor ceilings.
The width depends on the type of stairs to be built in. The height between floors decides on the type of stairs to be built in.
The dimensions for the stairs to be built are to be taken from the stairwell and to be compared with the existing drawing.
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The stairwell height is always based on the surface of the finished floors! |
In order to compare the dimensions taken with the drawing, a hand-sketch is to be drawn and completed by the dimensions taken.
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In the case of mortised stairs, 40 mm are to be deducted from the stairwell length to prevent the necessary riser from contacting the stair-apron! |
The stair strings only must contact the stair-apron (see Fig. 16).
What does the term "stairwell"
mean?
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Drawing floor
In order to build a straight wooden staircase, only the top and bottom connections to landings need to be drawn (scale 1: 1) on the drawing floor.
It is not necessary to take into account the measured flight length and flight height.
The required angle of inclination of the flight is obtained by drawing (scale 1:1) two treads and two heights of rise at the top stair-apron.
Figure 16 - Drawing of the top
and bottom string connections at the stair-aprons - (1) bottom connection (2)
top connection - 1 lower (bottom) stair-apron, 1 upper
(top) stair-apron, 3 floor construction of the top landing, 4
floor construction of the bottom landing, 5 stair head (head
step), 6 stair foot (bottom step), 7 step, 8 string top, 9
string bottom, 10 riser, - a tread width, s height of rise,
u false tread, hW string height
The angle of inclination can be laid off to the bottom connection by means of a bevel protractor.
A flat, clean plate is used as drawing floor.
It is also possible to use clean boards nailed onto supporting strips.
Figure 17 -
Representation of a drawing floor - (1) flat, clean plate (2) drawing floor
made from boards - 1 boards, 2 supporting strings, 3 nails
Stair strings
The stair strings carry the steps in 20 mm deep mortises. The string height can be measured from the drawing floor (see Fig. 16).
The string length can be determined by means of the approximation formula
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Lw = (ns + 0.5) c |
(Formula 10) |
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Lw = length of the posts for the stair string | |
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c = size between the front edges of the steps. | |
Figure 18 - Sketch for
determining the stair string length - a tread width, s
height of rise, ns number of rises,
Lw length of posts for the stair string, c length at a
rise triangle
The size "c" can be measured from the drawing floor. The thickness of the string should be at least 50 mm. It is recommended to plane the posts for the stair string on four sides prior to scribing, making sure that they are in parallel. The dimensional tolerances in thickness and height may be ± 1 mm.
Steps
The steps must all be cut to the same length (B + 2 · 20 mm).
"B" is the clear width of the stair flight (see Fig. 13). They must all have the same length to be uniformly fixed (clamped) when the stair strings are drawn together by the screw rods.
If some steps are not fixed (clamped) by drawing together, they will squeak when stepped on.
The steps are surfaced on one small side and one wide side and then thicknessed.
After that the width is scribe-marked. For width scribing it is important that the width of the steps must have the size of the tread width (go width) plus false tread.
For sawing-out of the steps, 2 mm are to be added and will be removed by planing after sawing-out (see
Figure 19 - Connection between
rough-step size and finished-step size - (1) rough step (2) finished and
scribe-marked step - a tread width from the calculation, u false
tread, - 1 wide side of the step, 2 left side of the step, 3 small side of
the step, 4 length of the step, 5 scribed line for sawing to width of step, 6
scribed line of exact width of step, 7 right side of the step
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When preparing the steps it is to be considered that the left side of the wood is to be stepped on! |
How deep should the steps be mortised into the stair
string?
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Risers
The risers are to be cut 4 mm shorter than the steps. They must not be clamped by drawing together of the stair strings. The risers must have a slight cove upwards of approx. 2 mm to provide good support to the steps in the flight line when being stepped on. For preparing and planing of the risers the same working steps are required as for the steps.
Stair railing
The railing protects the user of the stairs from falling down at the side. It consists of the bottom post, the head post and the hand-rail.
Figure 20 - Stair railing with
vertical railing bars - 1 outer string, 2 bottom step, 3 head step, 4 bottom
post, 5 head post, 6 hand-rail, 7 vertical railing bar
Protection between the hand-rail and the outer string can be achieved by unprofiled or profiled vertical railing bars. The railing bars are mortised into the hand-rail. At the bottom end, the railing bars can be mortised directly into the outer string. But it is also possible to use a baseboard for the railing bars to be mortised into. The tenon in the railing bar is spot-faced to avoid back-mortising in the hand-rail, outer string or baseboard.
Figure 21 - Representation of
the mortise-and-tenon joints of the railing bars - 1 outer string, 2
hand-rail, 3 underside of the handrail, 4 railing bar (profiled),
5 tenon of the railing bar, 6 mortise in the hand-rail
The hand-rail is to be designed so as to permit easy gripping of it and convenient sliding on it. Side-protection at the outer string can also be achieved by bars which are in parallel with the hand-rail.
Figure 22 - Stair
railing with parallel bars - 1 outer string, 2 bottom stepp, 3 bottom post, 4
handrail, 5 railing bars, 6 head post
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The distance between the railing bars is to be chosen so that children cannot slip through the bars. |
The bottom and head posts can be connected with the outer string by a simple lap joint.
Figure 23 - Lap joint
between railing post and outer string - 1 outer string, 2 railing post, 3
bottom step, 4 machine screw, 5 lap joint
For better stability of the railing posts, they can also be connected with the outer string by a slit-and-tongue-joint.
Figure 24 - Slit-and-tongue
joint between railing post and outer string - 1 outer string, 2 railing post,
3 bottom step, 4 machine screw, 5 slit-and-tongue joint
The railing posts can be glued or screwed to the outer string. The screw heads can be covered by rosettes.
What is the purpose of stair
railings?
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