How to calculate the stairs - spiral, rotary, wooden, single-flight. Rules for the design of stairs in private houses, drawings and calculations of the stairs of a private house Calculation of the width of the stairs
When building a private house, you almost always have to resort to making stairs - in order to save usable area site modern building private houses in most cases are the construction of two-story mansions. Stairs in private house the price can have the most diverse, depending on the size, cost of the material of manufacture and the materials used for decoration. The design of the stairs of a private house can be a classic mid-flight, with a lack of space, the installation of a spiral staircase is often used. Recently, bolt ladders have become increasingly popular, the construction of which uses hidden fastenings on bolts or pins.
Features of design and calculation
Proper design and calculation of an object under construction very often turns out to be extremely important and significant for the further trouble-free operation of the building, for example, incorrectly calculated ceilings can lead to the destruction of the building, and violations in the design of stairs threaten the impossibility of comfortable use and increase the risk of injury for residents of the house. The base moment in building stairs is the stage of its calculation and design, experts recommend paying due attention to it.
When building a house without a professional project, the issue of calculating the stairs can cause some difficulties, the reason for this is the lack of the necessary knowledge in engineering science. In this article we will try to recall the requirements and standards that should be followed when creating stairs in a private house.
How to determine the size of marches and landings
It is generally accepted that optimal width stairs in a private house should be 1.2 m, but given that the area for its installation can be very limited, it is allowed to reduce the width to 0.9 m. The gap between parallel marches should not be less than 0.1 m. The sum of these indicators will be the width of the future landing. Please note that the selection is minimal. allowable sizes will lead to the fact that the stairs will be very narrow and it will be extremely difficult to carry furniture or other large items along it. This is especially undesirable if the marches are located relative to each other at an angle of 180 degrees. If the angle is 90 - the site will be square.
If there is enough space to determine the width of the stairs, you will need to decide on its purpose, the planned throughput, the dimensions of the site allocated for the construction of the stairs. The staircase for descending to the basement or ascending to the attic can be 0.8 m wide. The width of a comfortable staircase in a private house can be from 1 to 1.5 m, of course, if the area allows. It will be convenient for residents to move along it. The width of the opening is measured from the wall to the railing or between opposite railings, the width of the steps is usually slightly larger.
Calculate the number of steps
Calculating the number of steps will require the use of accurate floor height measurements. They are obtained by measuring the distance from the floor of the first floor to the floor level of the second. If, when calculating the size of a staircase in a private house, you only have a distance to the floor level, then you should first decide on the design of the future floor and take into account the thickness of the insulation and finishing material or others structural elements. Such accurate calculations required for the reason that the height of the steps must be the same.
The recommended value for the height of the stair step is 0.15 m, however, in practice it often turns out that this size is adjusted design features Houses. Often, developers install stairs not with standard sizes steps 0.3x0.15 m, and 0.31x0.16 m or 0.29x0.17 m, which is also acceptable, because dimensions are not out of range.
In one march, the number of steps should not be more than 18. Such a number allows you to create a staircase with a height of 2.7 m. But given that the width of the step should be 0.3 m, the length of the stairs will be 5.4 m. rational option there will be a creation of a staircase with two flights of 9 steps.
The calculation of the number of steps may also depend on the dimensions. staircase, the smaller its area, the higher the steps will have to be designed.
Pay attention to the height of the ceiling above the intermediate platform; it should not be less than 2 m.
Stairs in a private house can have a variety of projects, but the number of steps will be determined as follows: divide the height of the entire staircase by the recommended height of one step. For example, with a staircase height of 3 m and a step height of 0.15 m, the number of steps will be 20. Since the last step will turn out by itself, the required number of steps for the stairs is 19.
If the calculation results in indicators that do not correspond to the recommended ones, in particular, the height and width of the steps, then the design indicators should be slightly changed within reasonable limits until an optimal result is achieved, as close as possible to the recommended standards.
Calculation of a curved profile staircase
Independent implementation of such a calculation will require the use of deeper knowledge. If the rotary options for stairs in a private house are calculated independently, then you should remember:
the minimum width of the narrow part of the wedge-shaped step cannot be less than 0.1 m, along the central axis - not less than 0.2 m,
the maximum step width at the far, wide end should not exceed 0.4 m
the turning radius of the narrow part of the stairs cannot be less than 0.3 m.
When constructing a staircase, it is allowed that its vertical surface hangs 0.03-0.05 m above the horizontal one, this will significantly increase the width of the steps and avoid increasing the length of the stairs.
Factors affecting the calculation of the stairs
The result of the calculation of the stairs will be influenced by:
- the number of landings and their dimensions, the height of flights of stairs and their number,
- the area that can be allocated for the construction of stairs,
- material from which it will be made stairs and decoration.
When calculating, one should not forget about such an important indicator as clearance. This is the height from the steps to the nearest upper barrier, for example, the ceiling of the second floor. The clearance should have a height such that a person tall could calmly, without touching the ceiling with his head, walk up the stairs, on average this figure should not be less than 1.9 - 2 m.
Stair steepness
The steepness of the future stairs, or in other words - the angle of its inclination, should facilitate comfortable movement along it and be in the range from 22 to 40 degrees. At an angle less than 22 degrees, you can get by with the construction of a ramp, but its construction will require very big square, in private houses its construction is impractical. A slope greater than 40 degrees will be acceptable for attic stairs or leading to the basement, more than 75 - only for firefighters.
The higher the steepness of the stairs, the less area required for its construction.
Consider how in practice you can calculate the angle of inclination. A right angle should be drawn on a sheet of paper, on its horizontal side, mark on a scale of 1:10 the length of the floor section allocated for the flight of stairs, along the vertical side - the height flight of stairs. By connecting the segments marked on the sides of the corner, we get a triangle, the hypotenuse of which will be equal to the length of the string of the stairs. The angle formed with respect to the horizontal line is the angle of inclination of the march; its value can be measured using a protractor.
Calculation of the height and width of steps
The calculation of the stairs in a private house also involves determining the width and height of the steps. To do this, you can use a simple formula 2a + b = 0.6 - 0.64 m, and - this is the height of the step, its recommended value is 0.15 m, but in reality it can be in the range from 0.14 to 0.17 m. It is not desirable to increase the indicator to 0.2 m or more. b is the overhang, or tread width. This indicator should be in the range from 0.2 to 0.32 m, it will be difficult to walk on wider steps - the step will go astray. Too narrow steps will be very inconvenient when going down. 0.6-0.64 m is an indicator of the average step of an adult.
The second formula that can be used in the calculation:
a + b \u003d 0.45 - 0.46 m. Everything is also extremely simple in it: if a is equal to the standard indicator of 0.15 m, then b will be equal to 0.3 - 0.31 m.
The top step should not hang over the bottom step by more than 0.05 m.
In our age of limited living space and rational use In residential areas, the importance of stairs is steadily increasing - they play the role of a connecting element between floors, between separate buildings, serve as the supporting structures of the building. Functional purpose stairs have long been complemented by a significant decorative element- due to the variety of shapes of stairs and the materials from which they are made, they can become a real highlight of the interior. However, as before, the correct calculation of the stairs remains the main requirement for its construction. Otherwise, the most luxurious or most elegant staircase can become a potential health hazard for the people who use it.
The main elements of the stairs are steps, consisting of risers and treads, which are attached to wide bowstrings or stringers made of wood or metal. In order to make the design more convenient and safe, a railing made of balusters, called a balustrade, is installed on the stairs, on top of which a handrail is attached. There are some more additional elements, which are used depending on the configuration and design of stairs.
Given the steep angle of this ladder, it can be assumed that climbing it will be difficult, and the nearby wall will limit maneuvering when lifting large objects.
Great amount construction teams today offers their services, but their professionalism will be visible only during the work. Moreover, as advertising on many sites, ready-made stairs are presented that have obvious defects in their design. Therefore, it does not bother the customer to know how to calculate the stairs in order to be able to control building process and, if the builders make a mistake, ask them to correct it in a timely manner.
During the construction of multi-storey residential buildings, the standards for calculating stairs are observed very strictly, because the safety of all residents depends on this. Owner country house or a cottage is not so limited in the choice of shapes, sizes and steepness of the stairs that will be built in it. And yet, in order for the ladder to be convenient and safe to use, it is better to adhere to existing norms.
Example of parameter calculation
The calculation of the stairs to the second floor is based on the following data: the height between floors and free space allocated under the stairs. First of all, it is worth deciding on the shape of the stairs. The most convenient is considered a single-flight staircase - a straight march, starting at the level of one floor and ending at the level of another. This option is suitable for those rooms where the height between levels is relatively small (from 2.5 to 3.5 meters), and free space enough to install the stairs.
Before you decide on the shape of the stairs, you should clarify whether there is enough free space where it is planned to be installed.
Compliance with the rules when calculating the stairs ensures that it will be easy to use
The optimal ratio of the length and height of the stairs is considered to be a ratio of 2: 1, that is, with a distance between floors of 3 meters, the length of the stairs will be 6 meters.
Slope index
An important indicator is also the steepness of the stairs, which determines the angle of the structure. How to calculate the angle of inclination of the stairs so that it does not pose a danger to others, is easy to use and harmoniously fits into the interior?
On such a ladder you can easily move large items
Optimal steepness stairs is in the range of 30-40 degrees, although in country houses most often this indicator is determined by the preferences of the owner
Optimal angle the slope of the stairs is considered to be an angle of 30 degrees. A smaller angle will turn the stairs into a sloping ramp, bulky and uncomfortable, and an angle of more than 40 degrees makes the stairs dangerous to use not only for the elderly and children, but also for adult residents of the house.
One of the varieties of a single-flight wooden staircase - the goose-walk staircase - saves space, but it is obvious that its steepness is far beyond the established norms.
Width and height of steps
The calculation of the steps of the stairs is carried out according to two parameters and depends on the length of the average step of a person, which ranges from 57 to 64 centimeters. You can use the formula in which the sum of the width of the tread (A) and twice the height of the riser (B) should not go beyond the length of the average step of a person. In mathematical display, it looks like this: A + 2B \u003d 57-64 cm.
To use the stairs was convenient and safe, do not neglect established norms height and width of steps
There are other calculation options, for example, the convenience formula: A-B \u003d 12cm. Whatever method of calculating the steps is used, it must be remembered that climbing stairs with a step height of more than 17 centimeters for the elderly will not be associated with comfort and safety.
Important! All steps of the stairs must be of the same width and height, even slight deviations are not allowed. This is due to the fact that a person performs many actions automatically, such actions include climbing stairs. Having determined the width and height of the steps, a person then switches to other thoughts, and the slightest discrepancy between the end of the stairs and its beginning can lead to accidents.
Usage intensity setting
There are two more important parameters to consider when designing stairs. Before you calculate the size of the stairs, you need to decide on the number of people who will use it at the same time, and the purpose of the stairs. The width of the structure depends on these parameters. If the stairs are used simultaneously by two and more people moving in opposite directions, then its width must be at least 120 centimeters. The same width will be optimal if bulky items (equipment or furniture) are to be moved up the stairs.
Even without measurements, it is clear that the width of the steps does not meet the standards, and descending and ascending these stairs can turn into a dangerous journey.
Usually, stairs of this width are not needed in private houses; for comfortable operation, a staircase of 90 cm wide is quite suitable. If the dimensions of the room are limited, then the width of the stairs can be reduced to 70 centimeters - the minimum allowable width.
Calculation of a wooden staircase
The calculation of a wooden staircase is carried out according to the same parameters as stairs made of another material, but there is a nuance - given that wood, compared to metal or concrete, is less durable material, on a wooden staircase with a width of more than 90 centimeters, it is advisable to install an average bowstring. This support beam will add strength to the wooden stairs and avoid possible deflection of the steps.
How to calculate the spiral staircase
Stairs of a different shape, for example, spiral or rotary, are calculated a little differently. The calculation of a spiral staircase depends on its purpose: if this staircase serves as an element of the decor of the room and will be used occasionally, then its parameters can be slightly adjusted in favor of the aesthetic component and at the expense of comfort.
This spiral staircase was not built to save space, so climbing it will be convenient and safe.
If the stairs are supposed to be used all the time, to carry heavy dimensional objects from floor to floor, then you need to know how to calculate the spiral staircase correctly and you should follow the generally accepted rules. The outer diameter of a spiral staircase depends on the space it is given, the inner diameter depends on the diameter. load-bearing structure.
The steps of a spiral staircase are most reminiscent of a cone in shape, so special requirements are also imposed on them: in the central part, the recommended width is 20-25 centimeters, in the widest part - no more than 40 centimeters. But the requirements for the height of the riser for spiral staircases more democratic: they can reach 18 centimeters.
The nuances of calculating the turning stairs
Another way to rationally use space is to install turning stairs. It is a bit like a two-flight staircase with an intermediate platform, with the only difference being that the platform here is replaced by several steps, so the calculation of the turning staircase is not much different from the calculation of a conventional staircase.
A properly designed staircase with turning steps will take up little space and will successfully complement the interior of the room.
The calculation of a staircase with turning steps is based on the height of the rise, the length of the stair opening, the total number of steps and the number turning steps (best option- no more than three).
General mandatory rules for settlement
- the distance from the upper surface of the stairs to the ceiling or the upper steps of a spiral or turning staircase must be at least 2 meters, otherwise head injuries may occur;
- the number of steps in one flight of stairs can be no less than three and no more than 16, a deviation from this indicator is a violation of safety regulations;
- a staircase is considered comfortable for walking if its steepness is in the range of 30-40 degrees.
If a attic space, according to the ideas of the owners of the house, serves as a full-fledged residential, then, as a rule, a full-fledged staircase is being built, which must meet all the requirements for safety and comfort of moving along it. But quite often the attic is a utility room, that is, they do not rise there so often, only as needed. But at the same time, of course, it will be much more convenient if the possibility of entering the attic does not depend in any way on the season or weather, that is, the stairs to it will still be located inside the house, and not outside.
There are many options for arranging such an interfloor transition. So, the installation of folding systems is practiced, from the simplest to the most complex, which are brought “on alert” only as needed. Another approach is the installation of stationary structures, which they try to build so that they occupy a minimum of usable living space. In any case, whether a ready-made kit is purchased, or manufacturing and installation attic stairs will take place on their own, without information on her main parameters. The proposed calculators for calculating the length and steepness of the stairs to the attic can help in this matter.
A few necessary explanations will be given below.
ORTHODOX GYMNASIUM
NAMED AFTER REPRED SERGIUS OF RADONEZH
FESTIVAL OF SCIENTIFIC AND CREATIVE PROJECTS
"HARMONY OF THE UNIVERSE"
K R U T I Z N A
L E S T N I C S
Serova Maria, 6th grade.
HEAD: Sterlyagova Galina Gennadievna,
mathematic teacher.
Sergiev Posad
2015
Everyone probably knows the special staircase in our utility block, which leads from the second floor to the third. The steps of the stairs are halves of ordinary steps and they are located symmetrically with respect to the line of travel. Why? We decided to look into this issue and the concept of “steepness of the stairs”, which we met in a mathematics lesson, helped us in this.
But first, a little history.
The staircase has long become a familiar, traditional attribute of our Everyday life. It facilitates the path of a person to the upper floors, while striking people with its beauty and grace. Stairs meet us literally at every step - in country houses, in administrative and public buildings, apartment buildings and on industrial facilities. But, of course, the question is very interesting, when and where did the staircase first appear?
The history of stairs begins with the first human settlements. No one knows what the first staircase was. It could be tree branches tied with bunches of grass or steps hewn with stone axes. Perhaps, noting that it is more convenient to climb the mountain along the goat path, which looks like a clumsy ladder, primitive people adopted this experience from the animal world.
Stairs, reminiscent of modern ones, were made millennia ago. The first mention of the technology of building stairs was found in Egyptian manuscripts of the 4th-1st millennium BC. Building numerous temples and amphitheaters, the ancient Greeks and Romans also could not do without massive stairs and stepped structures. Egyptian pyramids are huge stairs leading to heaven.
Stairs in the temples of the ancient Greeks had steps no less than human height. In the Middle Ages, the development of "staircase" was stimulated by the construction of knightly castles with high walls and defensive towers.
Over time, staircase structures became more and more complex, gradually taking on an aesthetic function. During the Middle Ages, when city streets were very narrow and houses grew mostly strictly vertically, . Such designs also became widely used in castles. But the greatest impetus to the development of staircase structures was given during the Renaissance, when great attention began to be paid to decorative decoration. Stairs began to be endowed large quantity whimsical, openwork elements to give them high aesthetic qualities. As a result, they have become an integral part interior decoration and architectural design of buildings. The ancient staircases that were installed in the luxurious front rooms were a real work of art.
And so, the ladder serves to climb to a height. And important for the characteristics of the stairs is itssteepness (slope) .
In a mathematics textbook for grade 6 (author N.Ya. Vilenkin and others), the following definition is given:
The steepness of a staircase is the ratio of the height of a step to its width.
slope = height: width
According to the slope of the stairs are divided into steep and gentle. With a steepness of less than 0.78 (slope 38 °), stairs are consideredgentle , and from 0.78 to 1 (slope from 38° to 45°) -cool .
We measured the steepness of various stairs, and found among them both gently sloping and very steep.
1. Every day when we come to our gymnasium, we climb the stairs in two steps. The steepness of this staircase is 0.36 (slope 20°).
2. And the students primary school In our gymnasium, they climb stairs with a steepness of 0.54 (slope 28 °).
3. The steepness of the stairs in the building of our gymnasium is 0.45 (slope 24°).
4. The steepness of the stairs leading to the second floor in the utility block is 0.67 (slope 34°).
5. AT tall buildings, where there is little space, and the lifting height is high: in towers, mills, bell towers, etc., stairs with great steepness are used. Stone stairs with a steepness of 0.92 (slope42°) leads up the bell tower of the Assumption Church, which is located on Bolotnaya Street.
6. And at the very top of the bell tower of the Assumption Church, in order to climb to the bells, there is a ladder with a steepness of 1.05 (slope46°).
7. We found the steepest staircase in the same bell tower. The wooden span of the stairs of the bell tower has a steepness of 2.6 (slope69°)!
And now let's return to the special ladder in our utility block. We learned that these types of stairs are called "duck step".The duck step ladder is also known as the goose step, samba, and Japanese tread. All these names are very suitable for this design. Remember the gait of geese and ducks, they shift weight from one foot to another, while their body sways from side to side, if you climb these steps, your gait will look like a duck or goose. There is another option that explains the funny name - the shape of the steps is similar to the paws of a goose or duck. The name “samba” is also logical: the dance and climbing the stairs must be started with a certain step, not to stray from the rhythm.
Such designs found their application ten centuries ago in Europe. They were used in high bell towers and used to be called "monk's stairs". The goose step staircase has one great advantage- because of her unusual design takes up little space, almost two times less than a conventional staircase.
We measured the steepness of the stairs in the utility block, and it turned out to be 1.2 (slope50°).
And now let's get acquainted with the most beautiful and famous stairs in the world.
Potemkinskaya stairs
Boulevardstairsleading to the seaOdessa . An architectural structure in the style of classicism, which is an architectural monument of the first half of XIX century and one of the main attractions of the city. From the top stepsstairsopens a wide panorama seaport. To date, the staircase consists of 192 steps (initially there were exactly two hundred of them, but eight steps were lost when the port was expanded) and a dozen spans. The length of the Potemkin stairs is 142 meters, it was created perspectively - its base (21.7 m wide) is much wider than the upper part (12.5 m), which is why, when viewed from above, the stairs give the impression of the same width along its entire length.
Staircase over the sea in Spain
On the tiny Spanish island of Gastelugatx, there is a luxurious staircase. It leads high up the mountain, to a hermitage built in the 20th century. Walking 237 steps, enjoying the silence and picturesque nature, is best in spring or autumn. In summer it is crowded.
Spiral staircase taihan, china
These steps will certainly appeal to extreme sportsmen. Their height is 91.5 m. There is a staircase near the Tiaihan Mountain in Lingzhou, China. Climbing such a staircase is a pleasure: you can feel the full force of the wind, admire the birds flying by, and feel the slight creak of the steps under your feet.
Staircase as a work of art, Germany
This 21 m high staircase is verylooks like a rollercoaster . You can walk along it, but you can’t go around the whole circle, because in the middle of the attraction"loop" .
Tourists nicknamed the stairs the Tiger and the Turtle. And she is inDuisburg , Germany.
Chand Baori well, India
In the Indian village of Abaneri, near the city of Jaipur, there is an interesting building - Chand Baori, built in 800. The giant well has 3,500 steps that go 30 meters underground.
The well was built to preserve as much as possible more water because this area is very dry. At the bottom of Chand Baori, the temperature is 5-6 ° C lower, so on especially hot days locals come here to relax.
Livraria Lello - this staircase leads to book heaven
located in Porto, Portugal. Here is the most beautiful wooden staircase in the most beautiful bookstore in the world. The absolutely amazing interior of the store is richly decorated walls, intricate carvings and an intricately curved red staircase crowned with a stained-glass ceiling.
Musical staircase at Odenplan metro station in Stockholm.
At the initiative of the Volkswagen concern, a staircase appeared at one of the Stockholm metro stations, not only reminiscent of piano keys, but also publishing real musical sounds. The idea of the project was to inspire people to take the stairs, and it worked, the number of those who preferred the steps increased by 66%.
Moses Bridge stairs. Netherlands.
Fort de Ruver, built in the early 17th century, is surrounded by a moat and was originally built without a bridge. However, during a recent restoration program, it was decided to build a bridge providing access to the fort.Out of respect for the fort's original island status, the Netherlands built the "Moses Bridge Ladder", an inconspicuous "flooded" bridge that sits flush with the line of soil and water. The result is an almost invisible bridge that partially submerges people walking on it into the moat.
In conclusion, I would like to note that it was interesting for us to find the application of our school knowledge in the life around us.
List of information sources used :
1. Article:History of stairs. Access mode:centersi. spb. en/ flattery- art1. html .
2. Article: The Potemkin Stairs is one of the most beautiful stairs in the world. Access mode:lifeglobe. net/ blogs/ details? id=134
3. Article: Most beautiful stairs peace. Access mode:
18.09.2017
In order not to have to fix an uncomfortable and dangerous staircase, already at the design stage for the drawing, special attention should be paid to the steepness future design. The optimal angle of elevation is 34-41 degrees. In order to calculate the steepness, you will need:
- Determine the place in the house where the product will stand.
- Determine the distance from the second floor to the first step.
- Then calculate the height in a straight line, from the second to the first floor.
- You will get a right triangle, the degree of the angle will be the degree of inclination.
In order not to strain with mathematics, you can load the data into a special program for calculating. It will be faster and more accurate.
How to fix a steep staircase to the second floor
If the mistake was nevertheless made, and access to the second floor is inconvenient, and the descent from the stairs is too dangerous, then the structure will have to be corrected. Unfortunately, there is no single instruction on how to do this. In any case, to correct the miscalculation, you will have to redo the entire structure. Installing a goose step staircase will help, but it will take some getting used to as the steps are not evenly sized.