So, how do professionals advise performing calculations in XXI century?
Staircase design can be done in various ways. Each one is based on optimal sizes flight of stairs necessary for comfortable and safe movement.
Naturally, the most convenient there will be a gentle and not narrow staircase, but, as a rule, practical circumstances dictate restrictions on the choice key parameters which include: view stairs, lifting height, plan area, inclination angle, number of steps, width and height of each.
These indicators interconnected and cannot be determined individually. For example, for a simple one-flight staircase, the height of the rise and the angle of inclination rigidly determine the area in plan and, on the contrary, knowledge of the area in plan and height will leave no doubt about the angle of inclination of the staircase.
In this article we we won't consider exotic options, like stairs with elements of three-dimensional curvature, but let’s focus on the familiar and feasible home handyman designs on stringers and scarves.
Step size
These are perhaps one of the main characteristics of the staircase. It depends on them how much comfortable and safe household members will be able to go up to the second floor and go down.
Master Novitsky Oleg Vadimovich in the book “ Modern stairs. Design, manufacturing, installation.” ( Best wishes to the author and this amazing work) mentions recommended and repeatedly tested values for lifting ( h) and tread ( a) steps:
h×a = 150×300, 160×300, 170×290 mm.
These sizes are good, but unfortunately cannot be used, if the house has already been built and the total height of the stairs ( H) is not a multiple of a single step ( h). In this case, we can turn to calculation formulas.
Widely known convenience formula:
a - h = 12 cm.
According to this ratio, the stairs will be the most convenient.
The stairs count safe if the sum of sizes ( With) the width of the tread and the height of the riser is equal to 45 cm:
30+15; 27+18; 25+20 .
Accordingly, this equation is called safety formulas :
c = a + h = 45 cm.
The difficulty is that the formulas are applicable in small range sizes and it is not always possible to realize the required proportion in practice. In this case, you should “get” into the indicated proportions with minimal deviation or use a universal Blondel's formula, which takes into account the average step of a person. More on this below.
| Floor height, m | Number of stages n | Step height h, mm | Step width b, mm | Slope h:b |
| 2.25 for basements | 12 | 118 | 260 | 1:1,38 |
| 13 | 173 | 260 | 1:1,50 | |
| 2,50 | 14 | 179 | 260 | 1:1,45 |
| 14 | 179 | 290 | 1:1,62 | |
| 2,75 | 15 | 183 | 260 | 1:1,42 |
| 16 | 172 | 260 | 1:1,51 | |
| 16 | 172 | 290 | 1:1,69 | |
| 3,00 | 17 | 176 | 290 | 1:1,65 |
| 18 | 167 | 290 | 1:1,74 |
Please note: in single-flight staircases, as well as in one flight of two- and three-flight staircases within the first floor, no more than 18 rises (steps). Limit height steps - 220 mm ( SNiP 21-01-97).
To design a simple wooden staircase on stringers measure the height between floors(vertical distance from the floor of the lower floor to the floor of the upper).
By the way height between floors- this is the most “sick” size. In houses made of stone, deviations from the design are often encountered. 4-5 cm, and wooden ones are subject to shrinkage and shrinkage (up to 15 cm per floor). Ideally, you should wait several years for the log structure to dry out completely.
Also dimensions for calculating stairs it is better to remove when the finished floors are laid or you will have to clearly set horizontal levels heights
So let height in our case:
Choose riser height:
Dividing the height between floors by the height of the risers, we get required quantity steps:
270: 18 = 15 pieces.
To determine the optimal step width, use convenience formula:
a - h = 12, h = 18 cm.
Convenient tread width:
a = 12 + h = 30 cm.
So it is necessary 15 steps width 30 cm and length depending on the width of the opening in interfloor covering. Checking the stairs safety formula:
a + h = 46 + 3 cm
In this case:
18 + 30 = 48 cm.
Ladder safe and easy to use.
This example of calculations is given by Stolyarov A.N. in the book " We build stairs».
The French architect and engineer was still in the distant 1672 proposed the following ratio:
Where S is the average step of a person that is within 600-640 mm.
Can be converted into an inequality:
Nizhny an acceptable result for practice would be minimum lift steps:
h = 120 mm, a = 400 mm, slope 17 degrees.
With a smaller angle, it is no longer a staircase, but a ramp (ramp) - a gently sloping platform.
Upper step rise:
h = 220 mm, a = 200 mm, slope 48 degrees.
At the upper limit of the formula it turns out not the most comfortable a ladder suitable for use only when moving facing the steps.
Going down the stairs is more dangerous than going up, hence the ease of use evaluate on downward movement. An example of a master's thoughts according to Blondel's formula:
We measure the height between floors:
H = 3050 mm.
Determining the rise of steps h by division H for the possible number of ascents ( n). Value options:
With 17 lifts: h = H / n = 3050 / 17 = 179.4 mm.
At 18: h = H / n = 3050/18 = 169.4 mm.
At 19: h = H / n = 3050/19 = 160.5 mm.
A = 5000 mm.
The length of the course line should not be less than the height between floors ( H), otherwise the stairs will be impractically steep. In our example:
A (5000) > H (3050).
At n = 18 tread a = 5000 / (n - 1) = 294 mm.
Actual number of steps per 1 less than the calculated value. This fact is easy to accept if the first step is considered to be at floor level.
Step parameter according to Blondel:
169 × 2 + 294 = 632 mm.
Hence, size is acceptable, is organic and lies within the average human step. We have determined the width of the tread and the height of the riser for easy movement, but this is not enough to build a comfortable and safe staircase.
Walking line and middle marching line
Stroke line (A) is a horizontal projection of a person’s imaginary movement along the steps. Passes in the distance 300-500 mm from the inner edge of the stairs. This average size determines comfort of using the handrail. The children will go closer to the railings, adults - further.
Sometimes for direct march this size is neglected, since the edges of the steps parallel.
If the width of the stairs is up to 1000 mm, then the line of movement will coincide with the middle line of the march. If more 1000 mm, then the stroke line shifts towards the handrail. The calculation algorithm is as follows:
Using chalk or a plumb line draw the intended line on the floor(or lines) of the move. Record the size with a tape measure and correlate it with the height of the stairs. It's great if the line more, than the height in 1,7 times - that means the slope will be 30 °.
All obtained tread size indicators calculate using Blondel's formula to determine the optimal one.
Relative magnitude of rise of march (elevation angle)
In construction practice, the elevation angle is usually in the range from 20 to 50 degrees, but the most convenient are stairs with an angle from 30 to 45 degrees.
Dependency table size of steps depending on the angle of inclination:
Choice inclination angle determines the distance margin (critical height) of at least 2000 mm from any step to the ceiling or any protruding element of the building (beam, parapet):
Critical altitude convenient to check by drawing the calculated steps on any sheet material or directly on the wall. As design practice shows, very often a line drawn from the ceiling or a dangerous protrusion will be less than the desired value.
It is for this reason that it is not possible to design a staircase that is shallow enough. As the angle of inclination increases, comfort decreases, therefore, with the low average height of all households, sometimes this size is underestimated.
In the already mentioned work of Novitsky O.V. “Modern stairs. Design, manufacturing, installation.” considered real practical case, in which as many as 6 options for the location of stairs in the room.
In any case, the final result is usually golden mean between many conflicting arguments.
March width
March width is determined by the capacity of the staircase (the number of people per minute in the narrowest place) and assumes the comfortable movement of an adult.
For indoor staircases building codes determine this value (the size from the wall to the railing or between two railings on the left and right side) at least in 900 mm, in luxury houses 1250-1600 mm.
Provided exceptions for width flight of stairs ( 0,8 m) some types of stairs (for example, in garden houses), but when designing a staircase you should focus on this size only in conditions of severe lack of free space in the room.
Width less than 0.8 m can afford auxiliary structures, for example, stairs to the basement or attic.
Standard elements
Every good owner knows how to count money. The construction of stairs is no exception. Can good savings, if the staircase details at the design stage work out adjust to standard preparations accepted on the territory RF.
Economic Considerations can become the key argument that will allow the owner to choose the only option for the location of the stairs from several possible ones.
1. Stage standards.
Available with fillet R 12.5. Invitations steps:
| № | Size, mm |
| 1 | H 220×400×1200, R200 |
| 2 | H220×400×1400, R200 |
Triangular winder step custom size to order it is calculated as a rectangular one (the necessary one is simply cut out of it). Because it is advisable to order rectangular. The cost is identical, and the trimmings will be useful in the work.
Large steps can be made from furniture board sizes:
| № | Dimensions (H×W×D), mm |
| 1 | 38×400×2000 |
| 2 | 38×500×1500 |
| 3 | 38×500×2000 |
| 4 | 38×700×1500 |
| 5 | 38×1000×1000 |
| 6 | 38×1100×1100 |
| 7 | 38×1200×1200 |
2. Risers.
| № | Dimensions (H×W×D), mm |
| 1 | 18×180×900 |
| 2 | 18×180×1000 |
| 3 | 18×180×1100 |
| 4 | 18×180×1200 |
| 5 | 18×180×1300 |
| 6 | 18×180×1400 |
| 7 | 18×120×900 |
| 8 | 18×120×1000 |
| 9 | 18×120×1100 |
| 10 | 18×120×1200 |
| 11 | 18×120×1300 |
| 12 | 18×120×1400 |
3. Cladding board.
| № | Dimensions (H×W×D), mm |
| 1 | 18×200×2000 |
| 2 | 18×300×2000 |
| 3 | 18×350×1000 |
| 4 | 18×350×1500 |
| 5 | 18×350×2000 |
| 6 | 18×350×2500 |
| 7 | 18×350×3000 |
| 8 | 18×350×3500 |
4. Beam.
| № | Dimensions (H×W×D), mm |
| 1 | 80×80×1200 |
| 2 | 80×80×2000 |
| 3 | 80×80×2500 |
| 4 | 80×80×3000 |
| 5 | 100×100×1200 |
| 6 | 100×100×2000 |
| 7 | 100×100×2500 |
| 8 | 100×100×3000 |
5. Bowstrings.
| № | Dimensions (H×W×D), mm |
| 1 | 40×350×2500 |
| 2 | 40×350×3000 |
| 3 | 40×350×3500 |
| 4 | 40×400×4000 |
| 5 | 50×300×3500 |
| 6 | 50×350×3500 |
| 7 | 50×400×4500 |
6. Handrails.
The length of the handrails can vary from 3500 to 6000 mm. And here are the sizes sections are constant:
| № | Section (W×H), mm |
| 1 | 40×70 |
| 2 | 45×70 |
| 3 | 45×80 |
| 4 | 45×90 |
| 5 | 60×60 |
| 6 | 70×70 |
| 7 | 70×90 |
| 8 | 80×100 |
7. Balusters.
Diameter round balusters - 30 or 47 mm. Length all varieties - up to 900 mm. Sections square products:
| № | Section (W×H), mm |
| 1 | 40×40 |
| 2 | 45×45 |
| 3 | 50×50 |
| 4 | 60×60 |
| 6 | 70×70 |
| 7 | 80×80 |
| № | Diameter, mm |
| 1 | 75 |
| 2 | 95 |
| 3 | 115 |
| 4 | 140 |
| 5 | 145 |
More at the calculation stage You should check the price list of the nearest supplier within walking distance.
So, it is not the gods who burn the pots. We hope that we were somewhat successful dispel the myth that the design and construction of stairs is available only to a select few. Read the articles, literature that we referred to in this text, take measurements, sketches and drawings.
Task bottom line looks simple: based on the layout of the house, the location of the stairs, the aesthetic preferences of the owners, you need perform parameter calculations given in the article. All that remains is to organically fit the indicators into the standards of comfortable and safe traffic country house or multi-level apartment.
We wish you comfort and goodness in your home.
Private country houses residential buildings and dachas in two or more floors- have long ceased to seem like a curiosity. This approach to planning their estates allows owners to achieve the maximum possible usable area housing even on “modest” sized construction sites. It is clear that both the design of a building with several levels and its construction become seriously more complicated. In particular, in addition to the usual architectural and interior elements typical of any house, it is necessary to think through the creation of interfloor transitions. Most often, stairs play this role. And if we consider the statistics of individual construction, then the undisputed “leaders” in popularity are
Nowadays there is no shortage of finished projects staircase structures. You can also find special applications on the Internet that conduct necessary calculations. But it is quite possible to independently calculate the wooden staircase to the second floor. For many, this will be even more interesting and understandable, since during the calculation the owner of the house delves into many of the nuances of such a structure, trying them on for his property.
In this publication, let's go step by step through the stages of basic staircase calculations. You will see that everything is not so prohibitively complicated.
Basic structural elements of a wooden staircase
First of all, what are they like - wooden stairs?
- The simplest option is a single-flight straight staircase. Such designs are relatively simple to calculate and install, and are characterized by high reliability and ease of use.
A significant disadvantage of such a staircase is that it “eats up” a lot of usable space in the room. And a decrease in its size (meaning its projection onto the floor plane) leads to an increase in the steepness of the ascent and descent. Which, in turn, makes the flight of stairs inconvenient and even unsafe for movement, especially for children or people with physical disabilities.
- If the space available in the room does not allow for a single-flight staircase, or it turns out to be too steep, it is divided into two or more flights, changing their direction to perpendicular or opposite.
It is clear that the total length of the marches, with the same height of ascent and its steepness, will not become less. But this approach allows, so to speak, to optimize the space. For example, flights of stairs are located in the corner part of the room along the walls, and it does not clutter the room. Or, a small separate room is allocated for the interfloor passage, turning it into a compact staircase with opposing marches.
- Stairs with two or more straight flights may also vary. And this difference lies in the features of ensuring a change in direction of movement. So, between the marches there can be a horizontal transition platform. Another option - the marches are connected by a curved section with a smooth change in direction, with steps of a characteristic trapezoidal shape. Such steps are called winder steps.
A staircase with a winder, of course, looks more elegant in the interior. And due to the fact that the rise does not “stop” anywhere, including at a turn, there is a gain in the overall dimensions of the structure. But a winder staircase is much more complicated in calculations, design and installation, and in operation it is not as convenient and safe as a similar one, but with a transition platform. So it’s better to weigh all its advantages and disadvantages in advance.
Prices for wooden stairs
wooden staircase
- The design allows you to place the interfloor passage literally “on the spot”. And one cannot but agree that such a staircase in the interior looks very vintage (pardon the pun). But, however, this is where its advantages are limited.
But she has more than enough shortcomings. The complexity of calculations and installation largely limits the possibilities for independent creativity - the construction of such structures is still the lot of professionals. Moreover, many models use curved, bent parts, which cannot be manufactured on our own without special equipment and without knowledge of technology - it is completely impossible. From the point of view of convenience and safety of moving along spiral steps, the staircase generally loses to all its “brothers”. And one more thing - just imagine that you need to lift some large piece of furniture or household appliances to the second floor (or lower it down)!
- On the inside, the steps can be covered with riser panels (item 5). However, this element is not mandatory, and often risers are not installed either for the sake of giving the structure visual lightness, or so as not to create an obstacle for placing one’s foot (this is typical for stairs with a significantly steep rise).
To make risers, use a board with a thickness of at least 20 mm (30 mm is recommended). This part can be positioned and fastened in different ways, and this must be taken into account in advance, since its position often affects the “working” width of the tread.
The picture above, just as an example, shows two different principles connections between treads and risers. It is quite obvious that on the left fragment the position of the riser does not affect the width of the step. But on the right, where the riser is installed in the selected grooves, you will have to make an adjustment to the width of the tread panel so that the calculated width of the step does not decrease.
Prices for stair steps
- The first stage of the lower flight (item 6) may be no different from all the others. But sometimes its configuration is varied (while trying not to change the height), made wider, with rounded edges, so as to make it easier to approach the flight of stairs from the left or right side. This step is called frieze.
- An important element of any wooden staircase is the design of the railing. This provides both security and an additional decorative “highlight” of the interfloor passage. The basis for installing the fence are powerful posts (item 7), which should be placed at the beginning and end of each flight. At the transition site, such a column becomes common to both marches. If the entrance to the staircase is made with a frieze, then the lower pillar can be shifted to the second or even third step.
Between the pillars, with equal spacing, which should not be more than 150÷180 mm, (item 8), forming a common balustrade. There are railings (handrails) (pos. 9) running from pillar to pillar, which rest on the upper ends of the balusters along the march.
As a rule, pillars and balusters are given a beautiful configuration - the details are turned into lathe. There is now no shortage of offers for such products, and it is quite possible to order a set from a carpentry workshop. The railings will also be made there. the desired shape in cross section. Some recommendations for the shapes and sizes of the staircase railing design parts are clearly shown in the diagram.
By the way, it is the position of the fencing system that determines the width of the flight of stairs - it is calculated between the wall and the handrails, or between the handrails on both sides. From the point of view of convenience, a flight of width from 900 to 1000 mm is considered optimal from the point of view of convenience for indoor stairs - not too wide so as not to “eat up” the space, and quite convenient for moving one person and carrying furnishings. However, the upper limit in width is not indicated anywhere - this is at the discretion of the owners. But minimum size- strictly stipulated by fire safety rules. In any case, the staircase is considered as one of the escape routes, and its width cannot be less than 800 mm.
It is clear that staircase models can combine various elements, including those that were not shown in the proposed diagram. But since our article is intended for beginners (experienced craftsmen have long known all the intricacies of calculation and installation), it is better not to waste time, but to limit ourselves to analyzing the most available options.
The basic structure of the staircase is considered. You can choose the type of structure that is most suitable for specific conditions and proceed to calculations.
The main stages of calculating a wooden staircase
Stairs can be classified as structures increased complexity However, for a real owner, nothing is impossible. The main thing is that the design being created is convenient and safe in everyday use, and is highly reliable and durable. Plus, no one, as a rule, ever discounts the aesthetic component, since the staircase should fit well into the intended interior.
And they begin the calculations by assessing the place where the stairs are supposed to be installed. The steepness of its rise directly depends on this.
Calculations basic general linear parameters of the staircase structure
Although the owner is free to “experiment” within his home, he will, one way or another, have to adhere to certain rules when creating a staircase design. And above all, this concerns the steepness of the flight of stairs, that is, the angle between the direction of ascent and the horizontal plane.
The staircase should be both convenient to use and safe. Therefore, there are certain limits to its steepness. So, the rise should not be too gentle - this is both inconvenient for a person and will take up too much space in the room. Staircases in residential buildings are not designed with a slope of less than 20 degrees, but it is still better to consider 24 degrees as the permissible lower limit of steepness, although this is also a bit too small.
The most optimal the range is considered to be approximately 27 to 33 degrees - such marches are the most comfortable and safe. But often in cramped conditions at home it is difficult to achieve such values, and stairs are made with a slope of up to 40 degrees. Well, the top one. The critical limit for a staircase in constant use to the second floor can be considered an angle of 45 degrees. But for individual family members, this bias is already becoming quite difficult to overcome.
It is clear that the flatter the staircase, the more space required for its installation. Therefore, it seems appropriate to take the first step to evaluate the steepness of the march and the size of the horizontal projection - how it will “fit” into the space of the room that can be allocated for its installation.
So, we consider the interdependence of the steepness of the stairs and the space required for its installation.
This dependence is expressed by the trigonometric relation:
D=H/tga
Below is an online calculator, which already includes this trigonometric function. And if you approach the calculation, with a known lifting height (and it is calculated “from floor to floor,” that is, taking into account the thickness of the ceiling), you can do it in two ways:
- It is planned to create a staircase with a precisely selected angle of flight steepness. The calculation will show how much space she will have to allocate in the room.
- The dimensions of the area for the stairs are strictly regulated - you need to determine what angle the flight will have and whether it will fall within the permissible range. For this calculation, you just need to vary the slope in the input field to achieve the required value of the projection length at the output - all this will take a few seconds.
If there is not enough space for a single-flight staircase (and this most often happens in a small private house), then it should be divided into two flights, as mentioned above. In this case, for each of the marches you can carry out your own calculation, changing the height of the transition platform. But at the same time, not forgetting that the slope angle must be maintained the same for all marches. This is a strict rule that cannot be broken!
Calculator for analyzing the relationship between the slope of a staircase and the size of its horizontal projection
When calculating the load-bearing capacity, the staircase elements are divided into statically definable beams - cantilever or single-span, and are calculated using the appropriate formulas. Since stairs are subject to dynamic loads, increased demands are placed on the rigidity of the load-bearing elements: their deflection should not exceed 1/400 of the span. Loads acting on flights of stairs and landings must be collected by adding the dead weight of the structures and temporary loads: in residential buildings - 300 kg/m².
When lifting, a person expends approximately twice as much energy as when moving horizontally (Fig. 2). Practice has established: a staircase is comfortable and safe if twice the height of the riser, added to the width of the step (tread), is equal to the average human step. The length of a person's stride on a plane is approximately 600–640 mm. Based on this, the tread and rise are determined by the formula: 2a+b = 600…640 mm.
Fig.2. Calculation of the height and width of ordinary steps
As an alternative, you can use another, easier to remember, formula: a+b = 450 ± 20 mm, where a is the height of the step (riser), b is the width of the step (tread).
The width of the tread should ensure that the foot rests with the full foot, that is, it should be no less than 200 and no more than 320 mm. The optimal height of the riser is 150, and the width of the tread is 300 mm. If the tread width increases too much, you will certainly lose your step, and if the tread width decreases too much, descending will be difficult. When designing winder steps, it must be taken into account that the minimum width of the steps at the narrow end should be at least 100 mm, and the overhang of the tread over the bottom step should be no more than 50 mm. Also, the overhang of the upper step over the lower one is done when other methods fail to increase the width of the tread; in this case, the amount of overhang should not exceed 30 mm for wooden and 50 mm for reinforced concrete steps.
The most convenient staircase angles are in the range from 23 to 37°. The steeper the staircase, the less space it needs to be installed in the house, and accordingly, the more positioned the staircase is, the more space needs to be provided for it. If the angle is less than 23°, the staircase can be replaced with a ramp (a flat inclined platform); if it is more than 45°, then the staircase becomes an attached or folding one (Fig. 3). The optimal angle of rise of spiral staircases is 25–35°. The most difficult process when the flight of stairs is steeper than 40° is descending from the stairs, and at angles greater than 45° the descent can only be done backwards.
rice. 3. Standard dependence of the size of steps on the steepness of the stairs The number of steps depends on the height of the floor and the angle of inclination of the stairs. Knowing the location of the staircase in the plan and the height of the room, the number of steps can (and is easier) be determined graphically, and then, using safety formulas, determine the width of the tread.
To graphically construct a staircase on graph paper or checkered paper, you need to draw a flight of stairs to scale (Fig. 4), measuring it with the height of the floor.
rice. 4. An example of a graphical calculation of the number of steps and riser height. Height table for steps in buildings with standard floor heights The height of the floor is the difference in the elevations of the finished floor levels of the lower and upper floors, that is, the thickness of the floor coverings must be included in the size of the floor height. For example, the floor of the lower floor is tiled ceramic tiles, and the floor of the upper floor is laid with parquet along the joists and a plywood “subfloor”. When calculating the floor height, all layers of these floor structures must be included: below - the thickness of the leveling screed, tile adhesive and tiles; at the top - the thickness of the logs, plywood and parquet. In Russia, since the existence of the USSR, floor height has been a regulated value. Typically, the standard floor height is 2.8 or 3 m, less often - 2.7 or 3.3 m, which allows you to design a room height (distance from floor to ceiling) of at least 2.4 m. This floor height allows you to easily fit a staircase with step sizes that meet the requirements of the safety calculation formula (Fig. 4, Table 2). If your floor height differs from the standard and is not a multiple of 3, then the height of the steps must be calculated (rounded) with an accuracy of one millimeter, but so that the heights of all risers are the same. It is better to distribute the calculation error resulting from the rounding of heights onto the lower frieze step, and make the remaining steps of the flight of the same height.
Steps of different heights lead to the construction of a dangerous staircase. This staircase becomes especially dangerous when descending at night. When going down the stairs, muscle memory tells us that there should be a step. The weight of the body is transferred to the leg, but there is no step under it... It is lower! And only two or three tens of millimeters, but they twisted their leg... and it’s still good if they didn’t roll head over heels.
In houses with a non-standard floor height, in order to equalize the height of the steps, it is allowed to lower the level of the finished floor of the upper floor landing a little lower relative to the level of the finished floor of the rest of the floor. It is better not to make a threshold, but to make the floor of the floor area in the form of a ramp, that is, inclined. To adjust the height of the steps, you will only need a few millimeters so that the slope is unlikely to be very noticeable. Alternatively, if the landing is enclosed by walls with doors, the floors between these rooms can be made with a small threshold. This solution is well known to everyone: the level of floor areas in apartment buildings, as a rule, below the level of clean floors in apartments. We don’t break our legs here - we’re used to it.
Table 1, Figure 3 shows the dimensions of the steps for “compacted” stairs, suitable for country houses. Often, in the layouts of these houses, so little space is left for stairs that in order to make the stairs shorter, one has to sacrifice the width of the tread. So, for example, in a staircase with a riser height of 200 mm, the tread width is 250 mm. An adult cannot rest his full foot on such a tread and he has to go down the stairs sideways or backwards. Table 2 of Figure 4 shows the dimensions of the riser heights for standard floor heights. Calculating the width of the tread using safety formulas is not difficult. But there is another way to determine the size of the steps - graphically.
This ergonomic method is based on the fact that a person, freely taking a step of 620 mm on a horizontal plane, can with the same ease raise his leg to a height equal to only half of this value, that is, 310 mm. Therefore, if on the horizontal axis of the graph (Fig. 5) we put known number parts, each equal to one step (620 mm), and on the vertical axis - equal to the height of the leg rise of 310 mm, then this construction makes it possible to obtain the dimensions of the rise and width of the steps for stairs with any inclination. To do this, you need to plot the slope of your staircase on the graph (its height and length are known) and draw perpendiculars at the points of intersection with the graph grid. This is the optimal height and width of the step for a given flight of stairs. Moreover, you can use this method and build a staircase specifically “for yourself”. For example, by setting the step to 600, and the lift, respectively, 300 mm, or by setting the step length to whatever you consider necessary.
rice. 5. Graphical method for selecting the optimal size of steps (dimensions in mm) When you undertake work such as a metal staircase with your own hands, calculations in this matter are extremely important. On the one hand, it may seem that calculating the design parameters for ascent and descent is not so difficult, but in practice, during the manufacture of stairs, a lot of serious defects may be revealed that cannot be corrected. And then you will have to re-do not only all the calculations, but also the resulting design.
Quite often used for tasks such as calculation metal stairs a program called a calculator. It greatly facilitates the calculation of parameters. But even when using it, do not forget that it is better to master the technology according to which the calculation is carried out thoroughly yourself in order to be able to control and correct the data obtained if they do not fully correspond to the existing conditions of your premises.
Parameters used in calculations
The calculation of a metal staircase to the second floor, as well as the structure and any other material, is carried out on the basis of special formulas where the main parameters are used.
Before you begin the calculations, you should decide on the location of the structure in your house, the location of the landing and other nuances.
- It is best if your design connects exactly those rooms where there is high level pedestrian load. For example, it would be most advantageous to place the entrance to the second floor next to the corridor or hallway.
- Structures with one or two flights will occupy a fairly large area. Therefore, installation of such stairs in small rooms is undesirable. In order to save space, it is more advisable to install a spiral staircase or a prefabricated one in a small room.
- The calculation of the metal staircase and its placement must be done so that the exit to the second floor is located in the most convenient place. It is impossible for there to be a sloping roof directly above the exit, as happens if your house has an attic floor, since dark time days, you risk getting injured when moving up stairs.
- In its upper and lower parts, the structure must be equipped with free platforms, the minimum width of which must be at least 0.8 m. This factor has a significant impact on the choice of location for the stairs, because not every room allows the installation of large structures.
Pay attention! Usage sliding stairs or folding type designs can be called an additional option. In order to obtain a stable and reliable design and at the same time save space, it is better to give preference to a spiral staircase.
Main design parameters
Calculation metal frame stairs are the first thing you have to do. Of course, using modern calculators, you can plan your design much faster, but the effectiveness of this approach is lower, since the programs do not always take into account the relationship between the key parameters of the staircase.
The width of the frame depends on the purpose of the staircase:
- basement and attic spaces usually not used as often as residential ones, so you can afford to save on space and take a staircase that is only 0.8 m wide;
- the structure for the second floor in a residential area must have a minimum width of 1 m; if you are planning a main staircase with an exit from the living room, then you can make a frame 1.5 m wide, provided that the area of your room allows the installation of such a large structure;
- double-flight structures are placed as closely as possible; you can take a frame 0.75 m wide.
Now you can proceed to calculating the height parameter of the structure.
Pay attention! This indicator depends on such an element of the general design as clearance. Therefore, in your calculations you should definitely build on it.
When calculating the height it is necessary to take into account:
- lifting height should be measured from flooring on the first floor to the same level on the second floor;
- clearance, which is the distance from the surface of the step to an obstacle located above it, as a rule, such an obstacle can be the ceiling of the upper floor;
- The minimum clearance size should be 1.9 m or more, otherwise you will have to expand the passage to the second floor or make the structure more flat.
Pay attention! Clearance size requirements for basements and attic stairs not so rigid, since such structures are used very rarely.
Planning steps and landings
When you are calculating a metal staircase, the platform plays an important role, because it allows you to make small corrections to the angle of elevation.
This method works under the following conditions:
- having the same number of steps, with equal parameters, and the length of the flight, you can use this element to reduce the angle of rise of the structure;
- using a simple design option to facilitate your calculations, you can consider the platform as a large step, and you have the opportunity to increase the flight of stairs due to it;
- The most optimal placement of the site is strictly in the middle of the march.
Pay attention! The staircase requires more reliable and durable fastening than other steps.
You can use special programs and applications that help you design and calculate the stairs.
Suitable for such purposes free apps, of which quite a lot can be found on the Internet.
Such a design stage as calculating the steps of a metal staircase is carried out last. Such calculations are based on the average width of a human step, as a rule, it is 60-60.5 cm. The formula used for calculations looks like this: Z + 2M = 60-60.5 cm, where M is the riser height indicator, and as Z – indicator of tread width.
If we summarize the parameters of the steps for standard projects, then the height is approximately 15-20 cm and the width is 25-35 cm.
Pay attention! You should not deliberately increase the width of the tread, since such a staircase will not be comfortable and you will constantly lose your step.
The overhang of the step should also not be made too large; 5 cm will be enough.
Screw design parameters
To calculate a spiral metal staircase, you need to take basic measurements, which are taken in the same way as in the case of conventional structures.
Let's look at the example of calculating a staircase with the following parameters:
- opening width – 2 m;
- floor height – 2.5 m;
- twist angle – 2,700.
Basic calculations:
- The diameter should always be less than the width of the opening, so it is calculated in our case as follows: 2 m – 0.2 m = 1.8 m.
- To calculate the length of the step, you need to take half the diameter, that is, the radius: 1.8 m: 2 = 0.9 m.
- Using the formula L = 2PR, you can calculate the circumference. With our parameters it should be: 2x3.14x0.9 = 5.65 m.
Pay attention! A spiral staircase cannot be called a complete circle, so the result obtained is multiplied by 3/4 (this figure corresponds to 2700). The resulting length of the staircase is 4.24 m (outer radius). If the rotation angle is 1800, then this indicator is divided in two.
- You can calculate the estimated length of the stairs based on the indicator of a convenient line of movement, which is located at a distance from the center - 2/3R. The calculations look like this: 4.24 m x 2/3 = 2.83 m.
- With a floor height of 2.5 m, you can calculate the number of steps (step 15-20 cm). Formula: 250:17 = 14.7.
- To find out the exact step height, we round the previously obtained figure (14.7) to 15, and according to the formula we get: 250:15 = 16.75 cm.
Pay attention! If, after calculating the exact step height, you do not get a whole number, you can round this figure to tenths (in our case it will be 16.7 cm), and taking this into account, you can simply make the first step of the staircase lower.
To do this, a calculation is performed: 250–14x16.7 = 16.2 cm.
Working with a calculator
The calculator for calculating a metal staircase will allow you to calculate the most important parameters designs. Even the most standard application can cope with this task. At the first stage, you just need to enter all the initial data into the program.
Source data includes:
- the height of your opening;
- length of the lifting part of the stairs;
- the planned number of flights in the structure and steps on each of them;
- step parameters (tread, overhang, etc.).
As a result, the program will provide you with the necessary drawing, which shows all the dimensions necessary for the manufacture of the stairs.
In order to make your home as comfortable as possible, you need not only to hire builders, but also to delve into engineering calculations yourself. The main modular design of the house is. It is this that gives the interior that unique luxury that many people dream of. You can arrange flights of stairs and install steps in different ways. Online staircase calculation will help you design optimal design and calculate material consumption.
Various types of staircase designs: photo gallery
There are a lot of options for placement and execution of stairs. You can easily choose an interesting design that will make the interior individual and unique.
Wooden structures with a platform significantly save space:
Screw structures can become a real interior decoration:
It may also be a good choice for staircase structures:
Metal structures have increased strength and reliability. They can be combined with both wood and glass:
Designs from can become the central link of the hall:
It is important when planning the design of stairs to take into account the age of the residents. If there are small children, the main criterion is safety both in the structure of the steps and. It will be difficult for older people to get used to the screw design; the slope should be less steep.
Related article:
How to create comfortable and stylish ones yourself - read our publication. You will learn not only possible design options and their advantages and disadvantages, but also design styles and the secrets of installing a staircase yourself.
Determination of basic technical parameters for online calculation of stairs
Building a staircase is not a designer’s flight of fancy. Certain standards for optimal ratios and permissible loads have been developed, compliance with which is important primarily for the safety and comfortable movement of others. Small deviations are allowed within acceptable limits, otherwise the design will simply become dangerous for people.
- lifting height (risers);
- tread (step) width;
- slope of the stairs.
A slope angle of more than 45° is considered steep; this design is not suitable for every family or for daily use. However, if the layout or area of the house does not allow the installation of another structure, you need to consider reliable railings to make walking up the stairs easier.
This is interesting! The slope of a staircase is the ratio of the height of the rise to the width of the step. The wider the step, the less steep the flight of stairs will be.
In addition to the main parameters, the design of the staircase is also influenced by:
- length of flight of stairs;
- dimensions of the staircase opening;
- distance between finished floor marks of the 1st and 2nd floors;
- number of steps. Regulatory documents define from 3 to 18 units.
Deviation from standard or acceptable parameters will, at best, cause discomfort when moving. At worst, it can provoke a number of diseases.
Main types of staircase structures
Stairs indoors can be made in the following variations:
- flight of stairs;
- screw;
- combined option.
The choice depends on the area and layout of the premises. It is important what role it will play in the interior of the house; the feasibility of installing a particular model depends on this.
Let's take a closer look at each design.
Flight of stairs
This design has increased reliability and ease of execution. Depending on the height of the room and the width of the steps, you can install one or more flights. The number of steps in each should not exceed 16.
Flights of stairs can be classified according to the following criteria:
| According to installation form | straight |
| with a platform between marches | |
| rotary | |
| By location | L-shaped |
| U-shaped | |
| T-shaped | |
| By mounting method | mounted |
| monolithic | |
| on the bowstrings | |
| on a frame | |
| on stringers | |
| combined |
Screw
It involves installing steps in a spiral around the main axis. This design can be installed in order to save usable space. It will not take up more than 1 m². The main feature of a spiral staircase is the ability to be installed almost anywhere in the room. The structures consist of steps, supports, balusters and railings.
With its installation, the interior is transformed with a completely unique design. She may look absolutely weightless. For example, glass steps with wooden railings and aluminum balusters. You can choose the material to suit any style direction of the room.
Combined
An arched staircase is usually called combined. It combines elements of a screw design with a flight of stairs. To install it, you need to allocate some area. Elements can be made in the form of straight sections, in the shape of an ellipse, circle or semicircle.
The main materials used for the manufacture of stairs and the nuances of their calculation
The material from which the staircase will be made must fit into the interior and meet all safety requirements. When choosing it, you need to pay attention to the origin and environmental friendliness, and check the material’s certificates for compliance with quality standards.
Most often used:
- wooden structures;
- metal stairs;
- glass;
- plastic elements.
The design may include combined options execution. For classic interiors or ethno-style would be suitable, forging would look appropriate in the Gothic style. In modern directions, you can use nickel-plated or galvanized steel in combination with aluminum or glass.
Calculation of wooden stairs
The base of the structure is subject to greater load, so hard types of wood are suitable for it. For fencing elements, you can choose a material of medium hardness or soft varieties; it is easier to process.
To calculate a wooden staircase, you will need the following parameters:
- Room height (from finished floor to ceiling);
- opening length (the horizontal projection of the length from the edge of the opening to the first tread is measured);
- number of steps;
- the width of an average person's step;
- width of the flight of stairs, optimal size taking into account railings and handrails – 100 cm;
- step depth;
- step height (underwall);
- the height of the fence, including the railings, should be about 100 cm;
- thickness of the approach - this parameter depends on the type of tree.
One of the main calculation parameters is the thickness of the stringer, which takes the main load. Steps in a wooden structure can be made with or without a protrusion. It just depends on personal preference.
Calculation of metal stairs
The design of a metal staircase is made of a channel, corrugated metal steps, steel “fillies” and brackets. The elements are secured by welding. The elements are calculated using a general formula, taking into account comfortable ascent and descent.
In addition, for a metal structure it is necessary to calculate the strength and rigidity parameters:
- Useful standard load per 1 sq. m of stairs is considered 300 kg. When calculating, it is necessary to take into account the overload factor equal to 1.4;
- When calculating the load on the railing, an overload factor of 1.3 k should be taken into account standard parameter from 50 to 100 kg 1 linear meter.
When calculating a flight of stairs, the distance between opposite walls is taken into account. They must be planned 20 centimeters larger than the width of the march.
Determining the required geometric dimensions of the stairs
Before starting structural calculations, it is important to take into account the geometric parameters of the room:
- distance from the floor level of the 1st and 2nd floors;
- design features of the location of the walls;
- installation locations for doors and windows;
- area of premises;
It may be necessary to make changes to the specific installation and repair work of the premises when performing calculations.
Calculating the size of staircase steps in a private house using an online calculator
First of all, it is necessary to calculate the steps of the stairs so that their height is the same. The width of the flight of stairs should not differ from the width of the landing. The length of the march should be within 1.5÷3 m.
- The size of the step depends on the length of the flight of stairs and the number of steps. When calculating the width, the total throughput, while the standard is 0.7 m per person;
- The height of the steps is also calculated taking into account comfortable ascent and descent. Optimal height– 12÷20 cm;
- The depth of the step depends on the size of the person’s foot. Parameters from 28 to 30 cm are considered standard;
- To calculate the number of steps, you need to divide the height of the stairs by the height of the step, which should be selected from the table, taking into account the comfortable angle of inclination of the structure. If the parameter does not turn out to be even, adjustment should be made at the size of the first step.
It is generally accepted that the width of two steps plus the height of the step should be within 60÷64 cm. These are the most comfortable dimensions of staircase steps for ascent and descent. When planning a structure with marches located in the opposite direction, it is necessary to leave an opening of at least 50 cm between them.
