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Example 1:
A staircase of saddle stairs with a flight width of 1250 mm is to be built in. What perpendicular height must the string bottom have when the height of rise is 190 mm?
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Required: |
hu |
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Known: |
s = 190 mm | |
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Wd = 65 mm (Table 2) | |
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Formula: |
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(Formula 1) |
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Calculation: |
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hu = 169.9 mm |
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hu = 200 mm chosen |
The string bottom must have a perpendicular height of 200 mm.
Example 2:
A staircase has a tread width of 288 mm and a height of rise of 171 mm. What is the ratio of rise and tread of this staircase?
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Required: |
m | |
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Known: |
a = 288 mm | |
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s = 171 mm | |
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Formula: |
m = |
(Formula 5) |
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Calculation: |
m = |
(Don't work out, just delete the unit of measurement!) |
| |
m = | |
The ratio of rise and tread of the stairs is 
Example 3:
A tread width of 286 mm and a height of rise of 172 mm have been measured at inserted stairs. What is the step size for climbing such stairs?
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Required: |
Sm | |
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Known: |
a = 286 mm | |
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s = 172 mm | |
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Formula: |
Sm = a + 2s |
(Formula 2) |
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Calculation: |
Sm = 286 mm + 2 · 172 mm |
Sm = 630 mm |
The step size is 630 mm.
Example 4:
A vertical distance of 1750 mm has be measured between two landings. The stairs to be built in shall have a height of rise of 170 mm.
How many rises will such stair flight have?
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Required: |
ns |
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Known: |
Lh = 1750 mm |
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|
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sg = 170 mm | |
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Formula: |
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(Formula 4) |
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Calculation: |
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ns = 11 |
The stair flight will have 11 rises.
Example 5:
For mortised stairs with 10 rises the stair flight height is 1680 mm. What is the height of rise for such stairs?
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Required: |
s | |
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Known: |
Lh = 1680 mm |
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|
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ns = 10 | |
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Formula: |
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(Formula 3) |
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Calculation: |
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s = 168 mm |
The height of rise of such stairs is 168 mm.
Example 6:
A stair flight has 12 treads. The tread width is 283 mm. What is the length of such stair flight?
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Required: |
L | |
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Known: |
na = 12 |
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|
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a = 283 mm | |
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Formula: |
L = na · a |
(Formula 6) |
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Calculation: |
L = 12 · 283 mm |
L = 3396 mm |
The stair flight length is 3396 mm.
Example 7:
A stair flight length of 3124 mm is available for mortised wooden stairs. The stairs shall have 11 treads. What is the tread width of the stair steps?
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Required: |
a | |
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Known: |
L = 3124 mm |
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|
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na = 11 |
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Formula: |
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(Formula 7) |
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Calculation: |
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a = 284 mm |
The tread width of the stair steps must be 284 mm.
Example 8:
What is the stair flight height of stairs having 8 rises with a height of rise of 175 mm?
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Required: |
a | |
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Known: |
ns = 8 |
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|
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s = 175 mm | |
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Formula: |
Lh = ns · s |
(Formula 8) |
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Calculation: |
Lh = 8 · 175 mm |
Lh = 1400 mm |
The stair flight height is 1400 mm.
Example 9:
A stair flight height of 1215 mm has been measured at the stairwell. The stairs to be built in shall be climbable with a step size of 630 mm.
What is the ratio of rise and tread for climbing such stair flight?
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Required: |
m | |
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Known: |
Sm = 630 mm |
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|
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Lh = 1215 mm |
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|
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sg = 190 mm |
(Formula 5) |
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Formula: |
m = a/s | |
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a = Sm - 2s |
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Calculation: |
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ns = 7 |
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s = 173.5 mm |
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a = 630 mm - 2 · 173.5 mm |
a = 283 mm |
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The ratio of rise and tread of the flight is 
Exercise 1
Mortised stairs shall be calculated to the step size. A stair flight height of 1344 mm has been measured.
a) How many treads must be available?
b) What is the tread
width of the stairs?
c) What is the consequent ratio of rise and tread of
such stairs?
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a) Required: |
na |
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Known: |
|
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Lh = 1344 mm |
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sg = 180 mm |
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Formula: |
na = ns - 1 |
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Calculation: |
na = |
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b) Required: |
a | |
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Known: |
Sm = 630 mm |
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|
|
| |
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Lh = 1344 mm |
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|
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ns = 8 |
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Formula: |
a = sm - 2 s |
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Calculation: |
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a = |
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c) Required: |
m | |
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Known: |
a = 294 mm | |
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s = 168 mm | |
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Formula: |
| |
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Calculation: |
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m = |
Exercise 2
Saddle stairs shall be built in with a stair flight width of 1300 mm and a height of rise of 170 mm. What height must the string bottom have?
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Required: |
hu |
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Known: |
s = 170 mm | |
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Wd = 70 mm (Table 2) | |
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Formula: |
| |
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Calculation: |
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hu chosen = mm |
Exercise 3
A single-flight staircase has 15 treads with a ratio of rise and tread of 278/176.
What length does this stair flight have?
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Required: |
L |
L = na · a |
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Known: |
na = 15 |
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|
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a = 278 mm | |
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Formula: |
L = na · a | |
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Calculation: |
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L = mm |
Exercise 4
A floor-to-floor height of 2656 mm has been measured at the stairwell. A straight staircase with two opposed branches of flights (180 degrees turn) and landing shall be built in. The length of landing is 800 mm. The height of rise shall not exceed 172 mm. The two stair flights shall have the same length.
a) How many rises will one stair flight have?
b) What length
must the stairwell have if the stairs are to be built to the step size?
a) Required: ns
Known:
Formula:
Calculation: ns =
____________________
b) Required: GL
Known:
Formula:
Calculation: GL
=____________________ mm
Exercise 5
A staircase with inserted stairs has 8 treads with a tread width of 290 mm. What is the stair flight height of such stairs?
Required:
Known:
Formula:
Calculation: L =
____________________mm
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