Calculation of a spiral staircase made of metal calculator. Geometric calculation of a spiral staircase. Dimensions of typical spiral staircases
With a lack of living space, it is often necessary to choose such a design of an interfloor staircase that takes up a minimum of space. The best option in such cases is a screw or spiral design. To build it with your own hands, first of all, you need to make a calculation of the spiral staircase, decide on its shape and dimensions.
In this article, we will consider an example of such a calculation for a structure with a central support column as in the picture above.
As with determining the parameters of a conventional straight staircase, we will need to measure some existing dimensions and draw up a project. Below is a short guide to help you with this.
The size of the opening (clearance) in the ceiling of the second floor
The opening can be round or square. If it has not yet been made, then during its manufacture it should be taken into account that the diameter of the future staircase will be approximately 20 cm less than the width of the gap - 10 cm on each side must be left for the railing.
Floor height
Measured between the "clean" floor of the lower and upper levels.
Advice. The easiest way to determine the height of the floor is to lower the plumb bob as shown in the picture above and measure the length of the string with the load.
Entry and exit points
In addition, you need to determine the place of entry to the first step and exit from the last on the second floor. This will give us the opportunity to find out the angle of twist of the structure and, accordingly, calculate its length. You need to choose the entrance and exit taking into account the position of the stairs in the room and the presence of obstacles that interfere with comfortable movement.
For example, if it is located in a corner or against a wall, there are not so many options for the position of the first stage. And if the second floor is an attic type with a sloping ceiling, the upper step should be in such a place that, when exiting, the distance between the platform and the ceilings is greater than human height.
By drawing up a drawing and marking the entry and exit points on it, you can determine the angle of twist.
Calculation example
Let's assume that after all the measurements and definitions we have the following data:
- opening width 200 cm;
- Floor height 250 cm;
- Twisting angle 270 0 .
Based on this, we begin the calculation of spiral staircases.
Stair diameter and step length
- As mentioned above, the diameter should be slightly less than the width of the opening. However, if you attach balusters under the handrails to the edge of the steps, the overall diameter can not be reduced. But for calculations, we still take it equal to 180 cm (200 - 20 \u003d 180), because it is the working, running gear of the tread that is important to us.
- The length of the step will be equal to the radius or half the diameter: 180: 2 = 90 cm. In this case, the running gear (the width of the flight of stairs) will be less than half the thickness of the support post. But this does not affect the calculations.
Ladder length
To simplify the calculations, you need to get a development of the screw structure, determining its length along the outer contour and along the line of motion.
To do this, we use formulas known to everyone from the school curriculum.
- Circumference L = 2PR. Substituting the known value of the radius into the formula, we get: 2 x 3.14 x 90 = 565 cm. But our design in terms of plan is not a complete circle, so the resulting value must be multiplied by ¾, which corresponds to 270 0. As a result, we get the length of the stairs along the outer radius of 424 cm.
Attention!
If you need to calculate a semi-spiral staircase (with a rotation angle of 180 0), the resulting circumference should be divided by 2.
If at the same time the half-helical structure is part of a two-flight turning staircase, straight and turning sections are calculated separately.
- Since the most convenient line of movement along such a staircase passes at a distance of 2/3R from its center, the estimated length we need will be 424 x 2/3 = 283 cm.
Thus, we obtained data corresponding to the direct single-flight design of the stairs and allowing us to calculate the number of steps and their dimensions.
Definition of the main parameters
250: 17 = 14,7 .
Round the resulting value to an integer and get the exact step height:
250: 15 = 16.67 cm.
The figure turned out to be not very convenient, since in the manufacture of risers it will be necessary to take measurements every time, taking into account hundredths of a centimeter. To avoid this, round it up to tenths (16.7 cm), and make the first step lower:
250 - (14 x 16.7) = 16.2 cm.
As a result, we get the height of the first step 16.2 cm, the height of all the others - 16.7 cm. There are 15 of them in total. It remains to calculate the width of the tread along the line of motion. It should fall into the "fork" of 20-40 cm.
Divide the length of this line by the number of treads, i.e. by 14, since the last step is already the floor of the second floor. We get:
283: 14 = 20.2 cm.
This is enough for the foot to fully rest on the tread during descent and ascent.
- h is the height of the step already known to us;
- b is its width.
We substitute the obtained data into the formula: 2 x 16.7 + 20.2 = 53.6 cm. We see that we do not fall into the recommended values. So, you need to increase either the height of the step, or the length of the line of motion. But it is easier to reduce the number of steps, for example, to 12 (plus one climb to the top platform = 13).
We calculate again:
- Step height 250: 13 = 19.2 cm;
- Tread width 283: 12 = 23.6 cm;
- 2 x 19.2 + 23.6 = 62 cm.
Now everything is in order: all values correspond to the normative ones, which is very important. The price of the issue is your safety and ease of movement.
Note. The data of the final calculations are rounded off, they must be brought into line with the actual ones, as described above.
Determining the shape of the steps
We determined the width of the tread only along the line of motion. But it is not rectangular, so we need the dimensions of the narrowest and widest part of it.
The width of the narrow part depends on the diameter of the support post, on which the steps are strung and fixed in a predetermined position. That is, in this place the tread will have a hole. To ensure the required strength, its width must be increased by two hole diameters.
Those. if the diameter of the support post is 5 cm, then the width of the narrow part is at least 15 cm.
On the outer edge, the width of the tread is calculated simply: the circumference is divided by the number of steps: 424: 12 \u003d 35.3 cm.
Conclusion
As you can see, the calculation consists mainly in the selection of the parameters of the steps based on the existing design data. They must fit into the recommended standards, corresponding to the size of the foot and the length of the step of a person. By changing the number and height of rises, you can find the most optimal form of steps.
In the presented video in this article you will find additional information on this topic.
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.
A spiral staircase is a rather complex structure and at the same time the best and most elegant solution for multi-storey buildings. Installing wooden or metal spiral staircases is the most optimal and compact solution at home. This is a structure that does not require special costs and a lot of space, and you can do it yourself. There is a fairly diverse selection of materials, design and interior. Which one is right for you, consider below.
Varieties of spiral staircases
Spiral staircases have always given a certain charm to the house. With the right calculation of the place and space, this kind of stairs can be the most beloved and beautiful design in the house. There are so many varieties of these structures that each house needs an individual solution. Mostly distinguish four types:
- Spiral staircases that are surrounded by special supports or walls. Supports can be either wood or metal. And in the middle they are attached to a wooden post or stone column. These poles and columns can be finished in materials of your choice and taste.
- Spiral staircases that do not have special supports. They are usually located in the middle of the room, thus not leaning against the walls. In the middle they are attached to a support post.
- Spiral staircases that do not have a support in the middle, but professionally made railings serve as support. This design gives the impression of a certain soaring lightness. This, as a rule, is the most optimal and beautiful solution for a home, but it requires professional calculation and a special approach to business.
- External spiral staircases supported by steel pipes with a diameter of at least 50 mm. This type is also very common, as it does not require special skills and knowledge for installation. A spiral staircase of this kind is the most optimal solution for summer residents who are going to do everything with their own hands.
Calculation of spiral staircases. The size
When calculating the size of a spiral staircase, you need to take into account all the main aspects of this design, such as the height of the railing, as well as the width of the staircase itself. If we talk about the practice of using this kind of stairs, then the optimal span size is 0.90 m. In this case, we are dealing with this size with a design with a diameter of 2-2.2 m .
How to calculate a spiral staircase?
When calculating the size of a screw structure, you must first calculate the width of the opening. The opening or clearance to the second floor can be rounded or square. When making an opening, you need to take into account that its width should be 20 cm more than the diameter of the stairs (you need to take into account the railing, 10 cm on both sides).
The third step is to calculate the angle of twist of the stairs. To do this, you need to determine the entry point to the first stage and exit from the last stage. When calculating the last step, you need to take into account the height to the ceiling. It is necessary that from the last step to the ceiling there should be more space than the height of a person, so as not to hit the ceiling with his head when lifting. To calculate the angle of twist, you need to make a preliminary drawing of a spiral staircase. These sketches can help you visualize the whole structure.
Calculation of a spiral staircase on an example
For example, with a floor height of 2.5 m, a twist angle of 270 ° and an opening width of 2 m, we begin to calculate the size of a spiral staircase.
First we must calculate the diameter of the entire structure. As already mentioned, the diameter of our structure should be less than the width of the opening. Because opening width is 2 m, then the diameter of the spiral staircase should be 1.8 m. Accordingly, the length of the step or running gear is 0.90 m, which is the best option.
After determining the diameter of the structure, you need to calculate the length of the stairs. To do this, we use the well-known school formula for measuring the circumference of a circle.
Circle length (L) = 2*P(3.14)*Radius(R).
In our example, L \u003d 2 * 3.14 * 90 \u003d 565 cm.
But we have an incomplete circle of 360°, but 270°. Therefore, we multiply our length by 0.75.
565*0.75=424cm
Now we know the length of the ladder. It is 4.24 m.
The next step is to determine the number of steps. Since the recommended height of each step is between 15 and 20 cm, we take 17 cm as the fixed height of our step. So, we know the height of each step (17 cm) and the height of the floor (2.5 m).
So, we have number of steps. Round up to 15 the number of steps and calculate the exact height of each step.
250/15=16.67 cm
To avoid some shortcomings when using hundredths, we will make the first step a little lower than 16.2 cm, and the rest 16.7 cm.
Now you need to calculate the width of the tread. It is known that the width of the tread should accommodate the entire foot. The most convenient size is 20 - 25 cm. We take 23 cm. We have a rectangular step. But we need the dimensions of the narrowest and widest part of it. Its narrow part is equal to the diameter of the support that supports the entire structure. Here the tread will have a hole. To achieve the greatest strength, it is necessary that the diameter of the tread be 2 times larger than the support pipe.
A spiral staircase is a rather complex design and requires a lot of diligence, although it seems quite simple at first glance. Therefore, the help of professionals in their field is very appropriate here. Although the calculations are given above, it is difficult for a beginner to build such a structure on his own. Experience plays an important role here.
Material and design of spiral staircases. Calculation
For the manufacture of a spiral staircase suitable for all materials, be it wood and metal or even concrete. The support pipe or stand is usually made of metal. But it can also be made of durable wood, natural stone or concrete, as long as it is durable. After all, the whole structure rests on it.
Railings also play an important role. As a rule, railings are made of decorative materials, mainly wrought iron. Openwork materials, beautifully crafted from iron, give the interior the most auspicious look.
When installing spiral staircases, it is necessary to take into account, first of all, the convenience and durability of the structure. Adhering to the following guidelines will help you install the most durable and safe design:
- Installing a screw structure on a special concrete "cushion" is the safest solution. After all, a spiral staircase is a large and heavy structure. Often the floor cannot withstand such a load. It is necessary to take into account the weight of the structure itself and the people who will move along it. Therefore, in order to extend the service life of your structure, it is necessary to calculate all this and, if necessary, make the appropriate optimal solution.
- The ideal height of the passage is 2m, so that when lifting, you do not touch any elements of your structure with your head.
- When installing this structure, you need to take into account that the width of the steps should be no less than your feet, so that it is most convenient to move around the structure. Each turn must be equipped with at least 12 steps.
- To ensure maximum safety, it is necessary that adjacent steps are additionally fastened to each other.
And in conclusion we present the most important details, which you need to know when installing spiral staircases. Why do we give preference to this type of structure, and what do you need to know?
- The spiral staircase is an element of originality and style. Therefore, it can suit any interior of the house.
- Does not require a lot of space - 1.5-2 square meters. m is more than enough for you to realize any idea.
- It is cheaper than the usual stairs.
- It is enough to have minimal skills in the calculation and installation.
Of course, you need to know the safety rules and follow them when moving around this structure. Walking fast on them is not recommended, as the rather steep angle of inclination is a source of danger. But reliable railings can be more useful than ever in such cases. Therefore, the best option is a spiral staircase, having 30-40 degrees tilt angle. And the height of the railing is recommended from 0.90 to 1.2 m. An odd number of steps and twisting counterclockwise is also recommended by professionals, since many people usually enter the first step with their right foot.
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.
