Compact spiral staircase dimensions. How to calculate a spiral staircase - the dimensions of the flight of stairs and steps. Materials for manufacturing
Rice. 1 General drawing of stairs
- H - the height of the stairs - usually determined by the height of the floors of your house D1 - the diameter of the stairs - the dimension of the stairs, depends on how much space you can allocate in your house for the stairs D1 - the inner diameter - the dimension of the rod to which the steps are mounted A - the angle of rotation - depends on mutual placement of the beginning of the stairs and the “receiving” platform of the upper floor Z - the thickness of the steps - the geometric parameter of the material (for example, boards) from which you plan to build the stairs C - the number of steps - how many steps will it take you most comfortably to move from floor to floor
2 Black and white drawing of a staircase It is advisable to use this function in two cases: If you are used to working with standard GOST drawings, and, accordingly, perceive graphics without color filling better. If you are going to print the results of calculating a spiral staircase online. Then you will spend less paint / toner and the visual perception of the drawings on paper will be better. And, of course, this function is used when printing on a black-and-white printer. The main result of this calculator is a drawing and calculation of helical steps. According to this drawing, parts are made from which the structure is assembled.
Rice. 3 An example of a step drawing All other drawings show the final view of the structure after joining the steps with the rod. How to make the transition to the second and third floors spectacular? Pay attention to the spiral staircases of different sizes and shapes that you can assemble with your own hands or entrust their manufacture to professionals in their field.
The calculation of spiral staircases to the second floor with the help of our service will allow not only to clarify the cost of the future product, but also to decide on the choice of parameters. An online calculator for calculating the spiral staircase to the second floor will help you to independently equip the house with stairs, and if you entrust this work to professionals, then all the list of works will be completed without your participation, but taking into account all your requirements and wishes. It is important to note that in comparison with other types of stairs, it is the spiral one that will cost less, and in design and reliability it will not be inferior to the others. It can be made from wooden or metal steps, but in the same style as the interior design.
Calculation of the spiral staircase to the second floor
The decision to make a staircase on your own should begin with a calculation of the features of the future product, marches, the size and shape of the steps and other nuances that will eventually paint the big picture. A convenient online spiral staircase calculator will help you calculate absolutely all the important parameters and determine the amount of material that will be needed during the implementation of this project, as well as see the parameters in the drawings.
A spiral staircase is an option popular with owners of small spaces, as its design allows for significant space savings.
According to most beginners in matters of construction and repair, making such a staircase is much more difficult than a marching one. This is not true. It is necessary to study in detail the design features of such a structure and adhere to the recommended procedure for its construction in order to obtain a reliable and durable result.
Design rules
For the safe operation of the ladder, its parameters must be selected in a special way:
The optimal width should be at least 80 cm.
This will allow one person to pass freely. The average width of the step (tread) should vary between 25-30 cm. This value is based on data on the average width of the step of a person. The height of the riser should correspond to the interval 15-20 cm. This value is also based on the average width of the step step. The most convenient angle of inclination, at which the design does not become too cumbersome, is 30-40 °.
It is necessary to take into account the features of spiral staircases. In such structures, the upper part is above the person.
So that he does not have to constantly bend down, it is not recommended to choose the height of the risers less than 17 cm. It is more convenient to use the staircase that contains an odd number of steps. Safe railings should be between 90 cm and 120 cm.
It is necessary to check the parameters of the stairs according to the following ratio: a-b=12-14 cm, a+b=45-47 cm, where a is the width of the tread, b is the height of the riser.
Geometric calculation method
Before carrying out calculations, it is required to determine the location of the stairs, the entry point on the lower floor and the exit point on the upper floor.
The main nuance that must be taken into account at this stage is the height of the passage. A person should calmly rise and fall without having to bend his head.
The first stage of calculations is the determination of the height of the steps. First, their number is determined.
To do this, divide the floor height by the recommended riser height. If the result is 2.8 m, then the following calculations are carried out: 280/17=16.47. It is recommended to install structures with an odd number of steps, so their number is taken as 17.
Accordingly, the height of each will be equal to 16.47 cm. The resulting value is rounded up to 16.5 cm. All steps, except for the lower one, will be equal to 16.5 cm (in height), and the first - 16 cm.
Next, the width of the tread is calculated. At this stage of the calculation, it should be taken into account that the person is walking at a distance of 1/3 of the width from the outer edge of the stairs. With a width of 1 m, a person walks in one ascent (or descent) a distance (L) equal to the circumference (its diameter is 100 cm * 2/3).
L=2*3.14*100*2/3=418.7 cm.
This distance should be divided by the number of steps, reduced by 1, since the top step will be located flush with the platform of the upper floor. It will turn out: 418.6 / 16 \u003d 26.2 cm. This value falls into the indicated recommended interval, therefore it is taken as the calculated one.
With such a width of tread, the exit on the upper platform is strictly above the entrance below. However, this is not possible in all locations. Therefore, the calculations will need to be adjusted, taking into account the degree of rotation of the spiral staircase.
After correcting the data obtained as a result of the calculation, it remains only to perform the installation of the structure. Its installation is also carried out according to certain norms and rules.
The invention of the spiral staircase is one of the most successful in the construction industry.
They are compact, comfortable, always organically fit into the interior, being its original element. Their dimensions and design are very diverse - from stone heavy lifts in ancient towers to airy interesting solutions in modern buildings. At first glance, it seems that such a design is too complicated for self-production, but in fact, building such a staircase with your own hands is not such a difficult task.
Spiral staircases have been invented for a long time.
They fit perfectly into any interior and are distinguished by a wide variety of shapes, sizes and designs. Before you start building a spiral staircase, you need to calculate it correctly. You will have to remember the school geometry course. Steps are equal sectors of a circle, located in height at the same distance and rotated relative to each other by the same angle. When calculating a staircase - any, not just a spiral one - it is necessary to take into account the accepted ergonomic standards, since it must be easy to use and safe.
Ergonomics rules for design
As ergonomic calculations show, the ladder will be comfortable and safe if its design parameters correspond to the average width of a person's step and the length of his foot.
Its width in the living room should be sufficient for the passage of one person, this size must be taken at least 80 cm.
The width of the tread (actually the steps) is 25-30 cm, the best size is 28 cm. This indicator is especially important when moving down. If the width is less than 25 cm, then a person will be able to step on it not with a full foot, but only with a heel, which can lead to a fall during the descent.
The height of the riser is taken within 15-20 cm.
This value corresponds to the average stride length of an adult. If the lift height is less than 15 cm, then you will have to step too often, which is not very convenient. And if the height is made more than 20 cm, then it will be difficult to climb such a ladder - you will have to raise your leg too high.
The angle of inclination is 30-40º.
A steeper staircase is inconvenient to use, and a more gentle one takes up more space. In the case of a screw structure, one must also take into account the fact that when lifting, the upper steps can be directly above the person’s head, so a too small height of the riser is unacceptable. Its optimal size is 17 cm.
For ease of use, it is necessary that the number of steps be odd, and the height of the railing be within 90-120 cm.
To check how the staircase meets the requirements of convenience and safety, you can use the following formulas:
where a is the width of the tread, b is the height of the riser.
It is advisable to take into account the recommended dimensions given at the design stage of the house, but if the house has already been built, and the staircase has not been previously calculated, then its dimensions will have to be adjusted to the finished premises, but if possible, ergonomic requirements should be taken into account.
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First you need to determine where the entrance to the stairs will be located and how the exit from it will be located on the top floor. It must not be overlooked that when lifting a person should not rest his head on the upper platform.
Do-it-yourself staircase calculation begins with determining the height of the steps. To do this, the floor height is divided by the recommended riser height.
For example, the height between the floor of the first and second floors is 2.8 m. Do not forget that the number of steps must be odd. With a simple selection, you can determine that with a riser height of 16.5 cm, 17 steps are obtained.
17x16.5=280.5 cm.
Graphic calculation of a spiral staircase.
The extra 0.5 cm is subtracted from the height of the first step. All other steps must be the same height, including the last one, which is also the floor level of the second floor or the landing of the stairs.
So, we got 17 lifts of 16.5 cm, which meets the requirements of ergonomics. We proceed to the calculation of the width of the tread.
When calculating a spiral staircase, it must be taken into account that a person passes at a distance of 2/3 of the width from the center of the stairs. Make a calculation for a passage width of 1 m. The path (L) that a person walks is equal to the length of a circle with a radius equal to 100x2/3 cm.
L=2πR2/3=2*3.14*100*2/3=418.7 cm.
Divide the resulting value by the number of steps minus one step, since the top one, as already noted, is the platform of the second floor.
418.7/16=26.2 cm.
But it doesn't always work out that way. With a narrower passage, the steps would have been smaller in width, which would have been inconvenient when descending the stairs. In this case, you need to reduce the number of steps and, in accordance with this, increase the risers.
For example, the width of the stairs is 90 cm with the same floor height. Then the length of the path will be
L=2*3.14*90*2/3=376.8 cm.
Rules for the construction of steps and risers.
With the same number of steps, their width turns out to be 376.8 / 16 \u003d 23.5 cm. You can leave this size, but for greater convenience and safety, it is still better to increase it to 25 cm.
Then the number of lifts will change: 376.8/25=15. In this case, the height of the riser will be 280/15 = 18.7 cm, which also corresponds to the rules of ergonomics. It should be recalled that if the height of the stairs is not divided entirely by the size of the riser, then the lower step is made smaller, and all the rest are equal in height.
If your project provides for a spiral staircase with a turn not of 360º, but less, then you need to take into account that the overall height decreases as you climb, and if you make the top platform 3-4 steps wide, then when you enter the stairs you will have right over your head. For example, with a riser of 16.5 cm and a floor height of 2.8 m on the fourth rise, the height will decrease by 66 cm, more than 2 m will remain in stock, which means that in this case it is possible to make a platform 4 steps wide.
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When calculating spiral staircases, it is difficult to adhere to strict rules. Usually, different options are calculated, while in addition to convenience and safety, factors such as layout, aesthetic parameters, and the properties of the material from which the staircase will be made are taken into account.
More stringent requirements are imposed on the selection of the height of the steps.
The width of the treads in this case is less important, since the design of the steps is such that their width is not the same along the length. In addition, each person will ascend and descend along different trajectories - someone will walk closer to the center, someone will prefer to walk closer to the edge, where the steps are wider. And if we take into account the fact that with the left and right foot a person will inevitably step on sections of different widths, it becomes clear that in this case the width of the tread is a rather arbitrary value.
Therefore, when designing a spiral staircase, they calculate several different options for the height of the steps, determine how many of them are obtained, and choose the one in which the results obtained are most consistent with accepted standards.
It should be noted that the dimensions of any structure must comply with the overall style and layout of the building. Wooden interior elements should be of sufficient size so as not to look too lightweight and fragile, and forged metal products should be airy enough so as not to burden the space of the room.
Stairs- this is one of the most important structures in any private house, as it is the basis for free movement between floors. When choosing a project, craftsmen are often guided only by the economic and aesthetic side of the problem, often neglecting construction and design norms and rules. However, ignoring such an important component in many cases leads to the fact that the product is unstable, unsafe and uncomfortable.
The efficient construction service KALC.PRO offers to perform an automated calculation of stairs online on a 3D calculator, as a result of which you will receive everything you need to mount the structure: a comprehensive estimate, a complete set of drawings and an interactive model for a better visual experience. The stair design software calculates the parameters of all elements and provides some recommendations based on the provisions of SNiP, GOST and TU which are used for the manufacture of wooden structures.
The program is easy to use and does not require special engineering skills - all fields of the calculator are intuitive, and the help includes illustrations with the notation of individual elements. Each calculation is accompanied by an assessment of the resulting structure and if incorrect values are entered - in case of critical deviations, the calculation will stop and a pop-up window will show in which field the error was made, if the deviation is insignificant, recommendations will be provided where to apply the correction.
Use the calculator for calculating the wooden stairs to the second floor to create a really reliable and convenient design. For 5 years of work, we have helped to realize over 3000 projects for residents of Russia, the CIS and Europe.
Why are our stair calculators better?
Close cooperation with ladder manufacturers
Highest detail drawings and 3D models
Final report with a list of required materials
Ready estimate for the manufacture of the structure by the contractor
Technical support helps when working with the calculator
Positive feedback and a large number of completed projects
Unlike other online staircase calculator sites, our project has a number of undeniable advantages and these are not empty words, since you can personally verify all these statements in practice.
- Constructor functionality. You can design a structure of any type and choose the features of fastening elements. If invalid values are entered, the calculation stop and a warning with an error will be displayed, on other resources - the calculation will be made in any case.
- Recommendations. Our calculator provides recommendations for many structural elements, for example, you will find out the optimal parameters: the angle of inclination, the height of the steps, the width of the step board, the width of the tread, the width of the stairs, the width of the stringers (upper, intermediate, lower). On other sites - tilt angle only .
- . Our development department works closely with real ladder manufacturers, so we pay more attention to detailing and fixing individual components. Professionals and private companies use our tool everywhere .
- Ready estimate. As a result of the calculation, the user receives a final report, which contains all the necessary drawings, a 3D model in the selected projection and a ready estimate for the manufacture of stairs, with a detailed description quantities of materials . On other sites - only the dimensions of the elements.
- Graphic arts. Most visitors choose our site, including because of the presence of high-quality well-designed graphics. In addition to the fact that the drawings are as close as possible to the standards of technical documentation, the projection of individual elements on the diagram is selected in such a way that when cutting, the fiber direction wood (seam of glued boards).
- . If you are having difficulty using the calculator or have questions regarding the resulting calculation, we will look into the situation and we will try to answer for any constructive questions 24/7.
- Personal Area. Also on our website there is a convenient personal account in which the results of the calculation of stairs or any other structure are saved - you never lose your project, and you can also download the download at any time, regardless of the time of the operation.
Every month we receive dozens of positive feedback and thanks from the users of the KALC.PRO project. On the page " Reviews» there are ready-made designs of structures made on the basis of the calculations of our tools.
Constructor Features
The service provides a large number of proven tools, using which you can create a convenient, reliable and safe design. In its calculations, the 3D staircase designer algorithm takes into account the data of SNiP 21-01-97 (SP 112.13330.2011) "Fire safety of buildings and structures", SNiP 31-02-2001 (SP 55.13330.2010) "Single-apartment residential houses", SNiP 2.08 .01-89 "Residential buildings", SNiP 2.08.02-89 (SP 118.13330.2011) "Public buildings and structures", SNiP 2.01.07-85 (SP 20.13330.2010) "Loads and impacts", GOST 23120-78 "Mid-flight stairs, platforms and steel railings", etc.
At the moment, the calculation of the following types of wooden structures is available in the program:
- straight staircase (on stringers, on bowstrings);
- stairs with winder steps at 90 ° (two-flight);
- stairs with winder steps at 180° (two-flight);
- stairs with winder steps 180 ° (three-flight);
- stairs with a 90° turntable (two-flight);
- stairs with a 180° turntable (two-flight);
- stairs with a 180° turntable (three-flight).
In addition, we also have calculation of metal stairs- perhaps you will be interested in the design on a broken stringer (zigzag) ?!
Among the main features of the calculator, it is necessary to highlight ( - only on KALC.PRO) :
- Units. Ability to select units of measurement (mm, cm, m, inches, feet), as well as their automatic translation in calculator fields and results without recalculation by the user.
- Drawing color. Possibility to choose color or monochrome rendering of drawings. It can be useful for persons with disabilities and, if necessary, to increase the contrast of individual elements.
- Ladder option. Possibility to choose the side of entry to the stairs (right or left).
- Mounting of rotary steps. Possibility to choose the type of fastening of the rotary steps to the support column (thorn-groove connection, connection with a section of the support column).
- opening parameters. Classic fields for entering the parameters of the opening (height, length, width).
- Opening definition. In calculators, it is possible to select the direction (segment) along the outer edge of the stairs (upper, intermediate or lower flight), which will be taken as the length of the opening. The characteristics of the stairs directly depend on this parameter.
- Step calculationstairs. Depending on the calculator, you need to enter the number of upper, intermediate and lower steps, their thickness and protrusion. It is also necessary to specify whether to consider the upper step below the level of the second floor or not.
- risers. It is possible to indicate whether the installation of risers is required and, if so, what thickness they will have.
- Kosoura(for stairs on the stringer). You must enter the thickness and width of the stringer.
- bowstring(for ladders on a bowstring). You must enter the thickness and width of the bowstring. We also take into account the stock of the heel and the stock of the width of the bowstring (front, back), and the drawings are presented in two projections.
- Support beams. You must enter the thickness and width of the stiffening beams.
- Support pillars. You must enter the value of the section side of the support column.
- Stair railing. Fields for entering the parameters of the enclosing elements of the stairs: handrails (thickness, width, height), balusters (section side).
- Floor slab. Fields for entering floor parameters (protrusion above the opening, offset from the wall, thickness).
- Wall. Optional field, necessary for better visual perception.
A well-executed staircase project to the second floor in a private house will save a significant amount of time and money on the manufacture of the structure.
Calculation results
As a result of calculating the stairs online, you get a comprehensive estimate with the optimal consumption of materials (quantity, volume) and detailed characteristics of each structural element. However, the most important thing is that the convenience of the building will be assessed according to the following parameters: the angle of inclination of the stairs, the width of the stairs, the number of steps, the height of the steps, the depth of the tread, the minimum width of the kosour / bowstring); after which you can adjust the parameters and make the final decision on the need to use this type of stairs.
Calculations are based on classical mathematical logic using simple geometric formulas, so calculation errors are minimized, however, it should be taken into account rounding numbers when displaying dimensions on drawings. There is a direct relationship that determines that the accuracy of displaying the calculation result is higher when using units of lower order, that is, for millimeters, the error will be no more than 0.1 mm, and when choosing centimeters - ~ 1 mm, etc.
It should also be noted some features when transferring dimensions from drawings to a real design. First, it is necessary to take into account the thickness of the cut, which has physical dimensions and is several millimeters wide. Secondly, we must not forget about the cumulative error, an example of which can be demonstrated as follows.
A staircase was calculated (in centimeters) with 10 steps with an opening height of 162.5 cm - as a result, in the drawings, the height of each step turned out to be 16.3 cm. However, you can see if you make a reverse calculation by steps, you get 16.3 cm × 10 = 163 cm, which is actually 0.5 cm higher than the height of the opening. This situation arises due to the fact that when drawing on the drawings, the values \u200b\u200bare rounded to the first decimal place, i.e. under the number 16.3 cm, the value 16.25 cm was “hidden”. To reduce such errors to a minimum should be calculated in millimeters however, in some situations it will still be necessary to adjust the outermost elements of the structure when mounting in height.
Staircase drawing with dimensions
Stair drawings are an essential component of any project documentation, as they allow you to fix the design features of the elements and their connections. They also provide an opportunity to pre-evaluate the parameters of individual components of the structure in practice. That is, by making templates from cheaper materials, such as cardboard or paper, you can eliminate error initially and save a significant amount of money on materials.
However, you should not assume that you can draw a staircase diagram yourself without proper experience in drawing and designing. Without special training, you are unlikely to be able to withstand the dimensions of the drawings, maintain accuracy down to a fraction of millimeters, and at the same time be accurate, while maintaining the readability of each element. Professional computer programs AutoCAD, Compass-3D, CorelDRAW, etc. cost a considerable amount of money, in addition, without proper work skills, it will take a lot of time to at least learn the basics.
The KALC.PRO service eliminates unnecessary difficulties and provides ready-made drawings of wooden stairs based on the user's entered data. Our schemes are distinguished by excellent elaboration of individual nodal connections and the whole picture as a whole, you can independently evaluate the high quality of graphics and compare it with other services.
3D model
A 3D staircase model allows you to view the resulting structure in real proportions and evaluate the prospects for using the current project. Unlike drawings, a 3D model is not designed to produce structural elements, but it is able to visually convey the general idea of an object down to the smallest detail.
On our website, the rendering of a 3D staircase project is based on the user's entered data with absolute accuracy. without any distortion or error. Scaling and camera control is done with the mouse - the left and right keys, respectively. A three-dimensional model can be downloaded in the selected projection on the stairs calculator tab in PNG format, there is also the possibility of downloading graphics in OBJ format (supported by Autodesk 3ds Max, AutoCAD, ArchiCAD, PC LIRA ...) for further editing.
How to calculate the stairs online on the calculator?
To perform the calculation of stairs with drawings on the online calculator, you must go to the tab of the corresponding design and fill in all the fields, based on the available parameters of the opening. However, first we recommend that you familiarize yourself with the proposed video, which describes in detail all the steps of working in the program and provides professional advice, who is engaged in the manufacture of stairs personally.
Calculation of stairs online on the calculator from KALC.PRO is confidence in the quality of the structures being built due to the high accuracy of the operations performed.
How to make a comfortable staircase?
The choice of staircase design depends to a greater extent on the parameters of the opening and to a lesser extent on one's own preferences, since in the majority of private houses redevelopment is excluded and one has to adapt to existing conditions. At the same time, the main task of the master is reduced to the most rational use of the available space in order to achieve the optimal characteristics of the stairs, which will ensure high ergonomics of the structure as a whole.
Accordingly, it is possible to single out some directly proportional dependence, the arguments of which are the area of \u200b\u200bthe structure in projection onto the surface of the floor / ceiling and the conditional coefficient of convenience. The correlation occurs according to the principle - the larger the occupied area, the greater the comfort a person will experience when moving between levels. In descending order of comfort, sorting looks like this:
- stairs are straight;
- stairs with a platform;
- winder stairs;
- combined stairs;
- spiral stairs.
Thus, mid-flight stairs are recognized as the best structures, then combined ones and, lastly, spiral ones.
In the case of choosing classic designs on a stringer or bowstring, it is necessary to pay increased attention to the overall slope of the stairs, the calculation of the steps, the height of the fences, etc. The list of all recommendations and rules is quite extensive, but among the most significant it is worth noting the following values:
- angle of inclination of stairs from 30° to 45°;
- the number of steps per march should vary from 3 to 16 and be odd so that the first and last steps are on one foot;
- recommended step height - 12-20 cm, optimal - 15-18 cm;
- width (depth) of steps - 27-30 cm;
- the height of the railing should not be less than 90 cm, in the presence of children it is better to increase it to 150 cm;
- the safe interval for installing balusters is 10-15 cm.
Compliance with these and other recommended parameters is extremely important - comfort during movement and safety, minimization of the occupied area, compliance with fire safety requirements, and the capacity of the staircase structure depend on them. Each online stair calculation calculator from KALC.PRO evaluates structures and provides some recommendations that can be viewed in the corresponding block of the report.
Rice. 1 General drawing of stairs
- H - the height of the stairs - usually determined by the height of the floors of your house
- D1 - the diameter of the stairs - the dimensions of the stairs, depends on how much space you can allocate in your house for the stairs
- D1 - inner diameter - the dimension of the rod to which the steps are mounted
- A - angle of rotation - depends on the mutual placement of the beginning of the stairs and the "receiving" platform of the upper floor
- Z - the thickness of the steps - the geometric parameter of the material (for example, boards) from which you plan to build a staircase
- C - the number of steps - how many steps will it take you most comfortably to move from floor to floor
"Black and white drawing:" function
Rice. 2 Black and white drawing of stairs
It is useful to use this function in two cases:
- If you are used to working with standard GOST drawings, and, accordingly, better perceive graphics without color content.
- If you are going to print the results of the calculation of the spiral staircase online. Then you will spend less paint / toner and the visual perception of the drawings on paper will be better. And, of course, this function is used when printing on a black and white printer.
The main result of this calculator is the drawing and calculation of helical steps.
According to this drawing, the parts from which the structure is assembled are made.
Rice. 3 Step drawing example
All other drawings show the final view of the structure after joining the steps with the rod.
How to make a spectacular transition to the second and third floor? Which of the design options to choose so that your home gets its zest? Pay attention to the spiral staircases of different sizes and shapes that you can assemble with your own hands or entrust their manufacture to professionals in their field. The calculation of spiral staircases to the second floor with the help of our service will allow not only to clarify the cost of the future product, but also to determine the choice of parameters.
An online calculator for calculating the spiral staircase to the second floor will help you to independently equip the house with stairs, and if you entrust this work to professionals, then the entire list of works will be completed without your participation, but taking into account all your requirements and wishes. It is important to note that in comparison with other types of stairs, it is the spiral one that will cost less, and in design and reliability it will not be inferior to the others. It can be made from wooden or metal steps, but in the same style as the interior design.
Calculation of the spiral staircase to the second floor
The decision to make a staircase on your own should begin with a calculation of the features of the future product, marches, the size and shape of the steps and other nuances that will eventually paint the big picture. A convenient online spiral staircase calculator will help you calculate absolutely all the important parameters and determine the amount of material that will be needed during the implementation of this project, as well as see the parameters in the drawings.
The calculation of a spiral staircase is a little more complicated than a marching staircase, but in general, if you remember the formula for the circumference of a circle, there is nothing difficult in it. We will use the following notation (Figure 1):
- H is the distance from the floor of the second floor to the floor of the first floor;
- H1 is the distance from the step surface to the ceiling. Should not be less than 200 cm;
- H2 - overlap thickness;
- h is the step height. It lies in the range from 14 cm to 20 cm. The optimal value is 15 cm;
- R1 is the outer radius of the stairs;
- R is the radius of the stairs along the line of motion;
- r is the radius of the support (the inner radius of the stairs);
- L1 - the length of the stairs along the outer edge;
- L - the length of the stairs along the line of motion;
- L2 - the length of the stairs along the inner edge;
- l - the depth of the step along the line of motion, should lie in the range from 25 cm to 32 cm, the optimal value is 30 cm;
- l1 - step depth along the outer edge;
- l2 - step depth along the inner edge. Should not be less than 9 cm;
- K is the total (calculated) number of steps;
- k is the actual number of steps (usually one less than K, explained below);
- S - step width.
Picture 1
spiral staircase safety
For a spiral staircase, unlike other stairs in the interior of the house, risers (vertical parts of the steps) are not made. Restrictions on the depth and height of steps are imposed for reasons of convenience and safety of the stairs. You can check how comfortable the stairs are using the formula 2h + l. For optimal values h = 15, 1= 30:
2h + l \u003d 2 * 15 + 30 \u003d 60.
This is exactly the average step length of a person, therefore, the closer this value is for the steps of your stairs in the number 60, the more convenient it is. It is believed that for public stairs the value 2h + l can lie in the range from 58 cm to 65 cm.
Calculation of a spiral staircase on an example
Suppose that the inner support has a radius r = 30 cm, and the width of the steps S = 100 cm. Thus, the outer radius of the stairs is R1 = 130 cm (100 + 30). Let's calculate the spiral staircase with the following parameters: the distance from the floor of the first floor to the floor of the second H = 300 cm, the thickness of the ceiling H2 = 20 cm, with the height of the steps h = 15 cm.
Let's calculate the number of steps:
K \u003d H: h \u003d 300: 15 \u003d 20
This is a calculated value, but since the last step will coincide with the floor of the second floor, then in fact there will be one less step on our stairs, that is, k = 19.
In general, as practice shows, the most confusion when calculating a spiral staircase arises precisely with the last step, so you need to clearly imagine what it is. It helps a lot in this case, the contemplation of a real staircase, for example, in your own entrance. Count how many steps and risers are on it, and everything will fall into place.
Now let's decide on the size of the stairwell. The distance from the floor of the first floor to the ceiling is:
H1 \u003d H - H2 \u003d 300 - 20 \u003d 280 cm.
When ascending each step, this value decreases by 15 cm. For the fifth step:
H1 \u003d H - H2 - 5h \u003d 300 - 20 - 5 * 15 \u003d 205 cm,
what else is within the acceptable range (does not exceed 200 cm). But for the sixth step, H1 = 190 cm, and a tall person, climbing the stairs, can hit the ceiling with his head. Therefore, only 5 steps can be under the ceiling, and the horizontal projection of the stairs looks like that shown in Figure 1b.
The depth of the steps of a spiral staircase is not constant and changes, increasing towards the outer edge of the staircase. It is believed that the most intensively used area is located at a distance of a third of the outer radius of the stairs from its edge. We, after all, do not go close to the railing or strictly above the wall, but try to move in the middle or closer to the outer edge of the spiral staircase. This is the so-called line of movement, at which the depth of the steps should be optimal. The radius R corresponding to the line of motion is equal to 2/3 of the outer radius of the stairs R1. In our case:
R \u003d 130 * 2/3 \u003d 86.7 cm.
As a rule, for a comfortable ascent to a height of H = 300 cm, a 360 degree rotation angle is required, that is, a full circle. Then the imaginary end of the 20th step in the projection coincides with the beginning of the first. Since the 20th step is, in fact, the floor of the second floor, it is quite possible to combine its beginning with the beginning of the first step. True, this will slightly reduce the size of the second floor area, and the horizontal projection of the stairs will look like in Figure 2:
Figure 2
We see that now the full circle is 19 steps, and the imaginary 20th step is strictly above the first. Let's calculate their sizes and check whether they coincide with the optimal ones. First you need to calculate the width of the steps on the line of motion. According to the circumference formula 2pR, where n = 3.14, we determine the length L of the line of motion:
L \u003d 2nR \u003d 2 * 3.14 * 86.7 \u003d 544.5 cm.
Dividing the resulting value of the length of the movement line by 19, we get:
l \u003d 544.5: 19 \u003d 28.7 cm.
This, of course, is not the optimal value, but it is within the normal range. If you want to bring your staircase to perfection and slightly increase the depth of the step, there are three ways to go:
- Increasing the angle of the stairs.
- Increasing the radius of the stairs.
- Reducing the number of steps, and at the same time increasing their height.
With an increase in the turn angle, the depth of the steps will increase, their height will remain the same, but the dimensions of the landing will decrease, which may not be very convenient. By reducing the number of steps, you will have to increase their height, which is also not always desirable.
If convenience and safety are at the forefront when calculating a spiral staircase (and in the case of a spiral staircase, which is not a very convenient design, it is advisable to do so), then it is better to increase the outer radius of the staircase, for example, by 5 cm. In this case, the radius R corresponding to the line of motion will be:
R=135*2*3=90 cm.
Then the length of the ladder L along the line of motion:
L \u003d 2 * 3.14 * 90 \u003d 565.2
Depth of steps on the line of movement:
l \u003d L / k \u003d 565.2 / 19 \u003d 29.8 cm.
L1 \u003d 2nR1 \u003d 2 * 3.14 * 135 \u003d 847.8 cm l1 \u003d L1 / k \u003d 44.6 cm
L2 \u003d 2p r \u003d 2 * 3.14 * 30 \u003d 188.4 cm 12 \u003d L2 / k \u003d 9.9 cm
So, in the calculation example, the spiral staircase has the following parameters:
- the number of steps on the stairs k = 19 (the 20th step coincides with the floor of the second floor, do not forget about it!);
- depth of steps along the line of motion l = 29.8 cm;
- step depth along the outer edge l1 = 44.6 cm;
- depth of steps along the inner edge l2 = 9.9 cm;
- step height h = 15 cm;
- outer radius R = 135 cm;
- step width S = 105 cm.
The step drawing will look like this:
Figure 3
Strictly speaking, we calculated the lengths of the arcs shown by the dotted line, and the depth of the steps will be slightly less. In order not to delve into complex mathematical calculations, this small difference in size can be neglected. However, especially meticulous builders can find the formula for the length of the chord and calculate the exact values.
Spiral staircases deservedly attract the attention of private homeowners. This beautiful design will give any home solidity and attractiveness. The technology for making a spiral staircase with your own hands is quite simple. Given the availability of a variety of building materials in our time, any owner who has certain knowledge in carpentry can make such a staircase. The only point that causes difficulty in creating this original interior element is the determination of the correct dimensions of the spiral staircase in the manufacture of drawings. In this article, we will explain how to calculate the spiral staircase for your home in a quick and practical way.
The main parameters of the stairs: we calculate the steps
The first thing to start with the calculation of a spiral staircase is the correct calculation of the dimensions of the steps of the structure. To do this, you need to navigate in the conventions of the parameters presented below:
- H is the height of the structure. It is determined by the sum of the distance from the floor to the ceilings, taking into account their thickness;
- H1 is the interturn distance;
- h is the height of the steps;
- h1 - tread;
- R is the outer radius of the step;
- R1 - radius along the point of the main line of descent-ascent.
These symbols will later be used in calculations and drawings. It must be remembered that the design of spiral staircases is not an amateur activity. Their parameters, such as diameter, width, or the dimensions of the steps already mentioned, must clearly fit into the existing GOSTs and SNiP norms. Compliance with all requirements for the size of the steps and their other parameters will ensure the safety and strength of the staircase structure. Therefore, in the manufacture of drawings of steps, the following points are always taken into account:
Design subtleties: how to calculate a flight of stairs
The calculation of a spiral staircase is a procedure that requires perseverance. Only 100% correct calculations will turn your idea into a beautiful and safe design. For convenient work on a spiral staircase project, it is advisable to draw up a preliminary diagram with its dimensions, and already carry out all calculations on it. In carrying out such work, special construction calculators can be a good helper - programs that allow you to qualitatively make all calculations of a spiral staircase, even online. They are easy to use, have an intuitive interface and make working on a project a real pleasure.
If online programs are not available to you, you can purchase a disk with such licensed software. This profitable purchase will allow using a computer to create high-quality drawings of building structures according to the specified parameters of width, height, diameter, and other indicators that are entered in special program windows.
The calculation of the flight of stairs should begin with the calculation of the area of \u200b\u200bthe site allotted for the arrangement of the interfloor structure. This important indicator is the main one for determining the minimum diameter of a spiral staircase, as well as for further calculations of the dimensions of the structure.
After that, you should proceed to determine the height of the interior element (H). To do this, as already indicated in the table, measure the distance from the flooring of the first floor to the second, taking into account the thickness of the floor. Here you should also decide on the entry-exit points, which will allow you to determine in the drawing the angle at which the flight of stairs will twist.
Having completed these preliminary measurements, the number of steps should be calculated. For example, we use the conditional calculation of a spiral staircase with a diameter of 2000 mm (radius - 1000 mm), a height of 3500 mm and a vertical angle of twist of 360 degrees. We get: R = 1000; H = 3500; ω=360°.
It is important to note that all measurements and calculations of parameters for drawings using formulas are made exclusively in millimeters!
The calculation algorithm is as follows:
Based on the fact that risers are usually not used in screw structures, it is possible to adjust the distance between the steps in the direction of increasing the gaps. During the adjustment, it should be checked for compliance with the results obtained with the reference dimensions, according to which the double height of the step in total with its depth should fit into the interval from 60 to 65 cm.
We calculate the diameter of the stairs and the width of the landing
At this stage, everything is quite simple. The diameter should always be slightly smaller than the dimensions of the spiral staircase opening. An exception is the option when balusters are installed along the outer edge of the steps. In this case, the width of the stairway may coincide with the diameter of the structure.
For example calculations, let's take the diameter as 220 cm and reduce it to 200 cm (220-20 = 200), taking into account only the part of the tread intended for walking. In this case, the length of the step will be equal to the radius: 200/2 = 100 cm. In this case, the width of the spiral staircase will be 1/2 less than the thickness of the support beam, but this will not affect the calculations.
The calculation of the width of the upper platform is made by calculating the loss of height when moving along the steps. In the case of our stairs with a 360-degree turn of the march, when climbing one step, the distance to the platform will decrease by 22 cm. Having climbed 5 steps, the height loss will be about 110 cm. If we take into account the thickness of the ceiling (hp = 20 cm), then in there is still more than 2 meters left. Thus, the width of the top platform can be within the width of 5 steps. If it is increased to 6, then the two-meter margin will disappear, and the head of the climber will cling to the upper structures.
To check the calculations, you can use the formula:
- H1 = H-5h-hp = 350-110-20 = 220 cm (good result).
By substituting your options into this formula, you can calculate the most suitable sizes.
As you can see, the exact calculation of all the parameters of spiral staircases for the further production of drawings is a laborious task, but simple and interesting. Using the acquired skills or resorting to help, you can easily prepare a quality project and bring it to life.
