The roof in the building is designed to hold external loads and redistribute them to load-bearing walls or supporting structures. Such loads include the weight of the roofing pie, the mass of the structure itself, the weight of the snow cover, and so on.
The roof is located on the truss system. This is the name of the frame structure on which the roof is fixed. It accepts all external loads, distributing them over the supporting structures.
The gable roof truss system includes the following elements:
- Mauerlat;
- Struts and braces;
- Side and ridge runs;
- Rafter legs.
A truss truss is a construction that includes all of the listed elements with the exception of the Mauerlat.
Calculation of the loads of a gable roof
Permanent loads
The first type is called such loads that always act on the roof (in any season, time of day, and so on). These include the weight of the roofing cake and various equipment installed on the roof. For example, the weight of a satellite dish or aerator. It is necessary to calculate the weight of the entire truss structure along with fasteners and various elements. Professionals for this task use computer programs, as well as special calculators.
The calculation of a gable roof is based on the calculation of the loads on the rafter legs. First of all, you need to determine the weight of the roofing pie. The task is quite simple, you just need to know the materials used, as well as the dimensions of the roof.
As an example, let's calculate the weight of a roofing cake with ondulin material. All values are approximate, high precision is not required here. Typically, builders calculate the weight per square meter of the roof. And then this figure is multiplied by the total area of \u200b\u200bthe roof.
The roofing pie consists of ondulin, a waterproofing layer (in this case, polymer-bitumen-based insulation), a thermal insulation layer (the weight of basalt wool will be calculated) and a crate (the thickness of the boards is 25 mm). We calculate the weight of each element separately, and then add all the values.
Calculation of the roof of a gable roof:
- A square meter of roofing material weighs 3.5 kg.
- A square meter of waterproofing layer weighs 5 kg.
- A square meter of insulation weighs 10 kg.
- A square meter of the crate weighs 14 kg.
Now let's calculate the total weight:
3.5 + 5 + 10 + 14 = 32.5
The resulting value must be multiplied by the correction factor (in this case it is 1.1).
32.5 * 1.1 = 35.75 kg
It turns out that a square meter of roofing cake weighs 35.75 kg. It remains to multiply this parameter by the area of \u200b\u200bthe roof, then it will be possible to calculate a gable roof.
Variable roof loads
Variables are called such loads that act on the roof not constantly, but seasonally. A prime example is snow in winter. Snow masses settle on the roof, creating an additional impact. But in the spring they melt, respectively, the pressure decreases.
Variable loads include wind. This is also a weather phenomenon that does not always work. And there are many such examples. Therefore, it is important to take into account variable loads when calculating the length of gable roof rafters. When calculating, you need to take into account many different factors affecting the roof of the building.
Now let's take a closer look at snow loads. When calculating this parameter, you need to use a special card. There is marked the mass of snow cover in different regions of the country.
To calculate this type of load, the following formula is used:
Where Sg is the terrain indicator taken from the map, and µ is the correction factor. It depends on the slope of the roof: the stronger the slope, the lower the correction factor. And here there is an important nuance - for roofs with a slope of 60 o it is not taken into account at all. After all, snow will simply roll off them, and not accumulate.
The whole country is divided into regions not only by the mass of snow, but also by the strength of the winds. There is a special map on which you can find out this indicator in a certain area.
When calculating roof rafters, wind loads are determined by the following formula:
Where x is the correction factor. It depends on the location of the building and its height. And W o - the parameter selected on the map.
Calculation of the dimensions of the truss system
When the calculation of all types of loads is over, you can proceed to the calculation of the dimensions of the truss system. The execution of the work will differ depending on which roof structure is planned.
In this case, a double slope is considered.
Section of the rafter leg
The calculation of the rafter leg is based on 3 criteria:
- Loads from the previous section;
- Remoteness of the railing;
- Rafter length.
There is a special table of cross-sections of rafter legs, in which you can find out this indicator based on the criteria described above.
The length of the rafters in the gable roof
When calculating manually, basic knowledge of geometry will be required, in particular, the Pythagorean theorem. The rafter is the hypotenuse of a right triangle. Its length can be found by dividing the length of the leg by the cosine of the opposite angle.
Consider a specific example:
It is required to calculate the length of the gable roof rafters for a house with a width of 6 m, in which the slope of the slopes is 45 o. Let L be the length of the rafters. Substitute all the data in the formula.
L = 6 / 2 / cos 45 ≈ 6 / 2 / 0.707 ≈ 4.24 meters.
To the value obtained, you need to add the length of the visor. It is approximately 0.5 m.
4.24 + 0.5 = 4.74 meters.
This completes the calculation of the length of the rafters for a gable roof. It was a manual way of doing the task. There are special computer programs designed to automate this process. The easiest way is to use Arkon. This is a completely free program that even a person who is poorly versed in computers can easily understand.
It is enough just to specify the input parameters based on the size of the house. The program will independently perform calculations and show the required section, as well as the length of the gable roof rafters.
The roof is one of the most important structural elements of a private house, as it prevents the penetration of precipitation, melt water and cold air masses into the premises. If you know how to correctly calculate the height of the roof and ridge, its device will allow gravity to remove moisture from the roof surface without increasing the load on the rafter system.
The need to calculate the height of the roof
Home ownership will look harmonious, provided that the appearance of the roof complements its architectural design. To do this, you need to correctly calculate the height of the roof in relation to the width of the house.
In accordance with the accepted terminology, the height of the ridge is the distance between the middle of the base of the roof structure and its highest point.
The following characteristics depend on the value of this parameter:
- The slope angle. The greater the height of the ridge, the steeper the slope of the roof of the household turns out. In regions where a large amount of snow falls in winter or heavy rains often occur during the year, the angle of inclination of the slopes should be 20 - 50 degrees.
- roof surface area. The higher the roof, the larger the area of \u200b\u200bthe slopes, which means that the cost of installation increases. This is due to the large number of building materials required for the construction of the truss system.
- Bearing capacity of the roof frame. With an increase in height, the weight of the structure increases, as does the load from the layers of the "pie". For this reason, there is a need to strengthen the frame by installing additional elements.
There are 2 methods for finding out the height of the roof:
- calculate the desired value depending on the size of the desired slope,
- first decide on this parameter, and then only calculate what the slope of the slopes should be.
Selecting the height of the structure
When designing, it is necessary to know the height of the roof, since this value has a significant impact on its performance.
Possession of information on how to determine the height of the roof of a house will help to calculate and create its project, which will meet the climate of the region and the purpose of the building. As a result, the roof will last much longer and require less maintenance.
When designing a roof structure, consider the following:
- Average annual rainfall. The higher this indicator, the higher the skate should be made.
- wind load. In areas with strong winds, low-rise buildings with a sloping low roof are usually built.
- The purpose of the building. If the project of the house provides for the arrangement of a residential attic space, then the height of the ridge must be at least 2.5 meters.
How to correctly calculate and determine the height of the roof, in relation to the width of the house
The technique for calculating the height of the roof and ridge is simple. When carrying out calculations, it is considered that the vertical section of the roof is an isosceles triangle, in which the base is equal to the width of the pediment. In this case, mathematical formulas are used.
- The width of the structure is divided by 2.
- To determine the slope, you need to choose the angle between the base and the surface of the roof slope.
- Further, according to the Bradis table, the tangent of this angle is determined.
- Multiply half of the width value by the tangent of the angle and get the height of the ridge.
Usually this parameter is chosen so that the slope of the roof is 25-45 degrees.
The classic roof of a Russian hut is a gable roof. The rafter system for it is quite simple, and this has ensured great popularity for this type of roof. A hip roof (four-pitched), for example, is geometrically more complex. It is more difficult to calculate and build, so let's take up the calculation of a symmetrical roof with two slopes.
Its calculation consists in determining the length of the rafters that form pairs. Each of these pairs is attached to the adjacent roof trusses with the help of a crate. The ends of the roof are triangular gables. The length of the rafters, like the height of the roof, will be determined by its angle. How to choose it correctly? This will tell the weather prevailing in the area.
Skate height selection
Those who have been to the Baltic countries or Scandinavia could notice that the roofs of village houses there are pointed. This is due to the high amount of precipitation, which, in turn, is explained by the predominance of the maritime and temperate climate. Water immediately flows from such a roof, and snow does not linger at all. However, the neighborhood with forested hills reliably protects these settlements from strong winds, so the large windage of such roofs is not of great importance.
Arab houses had flat roofs because the rainfall in the desert was minimal. But strong dry winds in such parts happen.
In the same place where the winds rage in the middle lane, you can find houses with completely different roofs - almost flat or arched, because the lack of windage or good streamlining plays a big role.
And if earlier such houses were built intuitively, based on the experience of generations, today sets of rules have been created for different regions of Russia that describe wind and snow loads on the roof. In particular, this is SP20.13330.2011, developed on the basis of SNiP 2.01.07-85* "Loads and Impacts". In the central region of the country, for example, it is recommended to choose the height of the ridge so that the angle of inclination of the slopes is approximately 30–45 °. It is this angle that will make it possible to calculate both the height of the roof ridge and the length of the rafters.
Roof height calculation
Let's turn to school geometry. Our roof must be presented in the form of a triangle, in fact, which is each of its gables. Such a triangle will be obtuse. We divide it along the axis of symmetry into two right-angled triangles. We received two legs, one of which (a) is known to us - this is half the width of the house. The second leg (b), which is not yet known, is the height of our roof.
b = a * tan α, where:
α is the angle of the roof, taken from the set of rules.
The tangent of this angle can be calculated on an engineering calculator or use mathematical tables. The resulting leg b is the height of the roof.
Knowing both legs, we can calculate the value of the hypotenuse. This is the approximate length of the rafters. However, since the roof often extends beyond the walls of the house, hanging over them, the length of the rafters can be increased. It all depends on the architecture of a particular building.
Knowing the length of the rafters and the length of the roof itself, which in this dimension can also protrude beyond the edges of the house, hanging like a visor over the gables, we can already calculate its area, and therefore the amount of roofing material.
Calculation example
Let's say the house has a width of 6 m. Divide it in half and get 3 m. This is our leg a. The slope angle recommended for building a house in this area is 45 °.
b = 3 * tan 45° = 3 * 1
But even without using this formula, one can guess that with an inclination angle of 45 °, our right triangle will turn out to be equilateral. That is, even without tables and a calculator, it will become clear that the height of the roof will be 3 m, that is, half the width of the house.
Accurate calculation of the height of a gable roof
For a classic gable roof of a Russian hut, the calculation is to determine the length of the rafters that form pairs. Each of these pairs is connected with a crate.
How to calculate the height of the roof: calculating the height of the ridge of the house
The roof is the first protective barrier of the house, which prevents the penetration of cold air, melt or rain moisture into the living space. If you correctly calculate and then correctly determine the height of the roof ridge, it will independently remove atmospheric moisture, snow mass from the surface of the slope, preventing an increase in the load on the rafter system. In this article, we will tell you how easy it is to calculate the height of the roof of a house, as well as how this parameter affects the quality of the roof structure.
Definition and functions
In order for the appearance of the roof to be harmonious and organically complement the architectural design of the house, it is necessary to correctly calculate the ratio of the width and length of the building. According to construction terminology, the height of the ridge is the distance from the middle of the base of the roof to its highest point. The following design qualities depend on this parameter:
- Roof slope angle. The higher the ridge, the steeper the slope of the roof of the house should be. On the territory of central Russia, which is famous for its large amount of winter precipitation, prolonged downpours in autumn, it is recommended to choose the angle of inclination of the slopes within 20-50 degrees.
- Area of slopes. The higher the roof, the larger the slopes have, which increases the cost of roofing, as well as the material for the manufacture of the truss frame.
- load bearing capacity of the frame. With an increase in the height of the roof, the weight increases, and, consequently, the load from the roofing pie, which is why it is necessary to strengthen the frame of the structure with additional elements.
Important! There are 2 methods for calculating the height of the roof: you can calculate this parameter based on the value of the desired slope, or, conversely, determine the height of the roof, and then calculate what angle of inclination of the slopes needs to be done for this.
Factors affecting the choice
The height of the roof of the house has a significant impact on the technical characteristics, performance characteristics of the structure. If you correctly calculate and then make a roof project that meets the climatic conditions, the nature of the use of the structure, then it will last longer, will need less care and maintenance. When designing the roof of a house, the following factors are taken into account:
- The amount of precipitation. The higher the average annual rainfall in the construction region, the higher the peak should be.
- The strength and direction of the wind. In windy regions, it is recommended to build low-rise buildings with a low, sloping roof so that it is not torn off by swift gusts of air.
- The nature of the use of the premises. If the project of the house provides for the construction of a residential attic, then the height of the ridge should be at least 2.5 m.
Note! The height and slope of the roof are calculated before the project is drawn up, since these indicators have a strong influence on the design of the truss frame and the choice of roofing.
Calculation procedure
Calculating the height of the roof is quite simple, even if you do not have a special calculator program at hand. The calculation is based on the fact that the vertical section of the roof is an isosceles triangle, the base of which corresponds to the width of the pediment. Knowing the geometric formulas, we can find the height of the ridge using the calculation formula that is valid for a triangle:
- First we need to measure the width of the structure, and then divide this value by 2.
- Then you need to determine the slope of the slope, that is, calculate the angle between the base of the roof and the surface of the slope.
- The next step is, using the Bradis table or using an engineering calculator, we determine the tangent of the angle formed by the base of the roof and the slope.
- Then we multiply half the width of the overlapped structure by the tangent of the angle between the slope and the base of the roof, getting the height of the ridge.
How to calculate roof height - 3 factors of influence and a running formula
The basis of any construction has always been, is and will be a competent calculation. Without it, at best, the owner will pay extra money, and at worst, the structure will simply collapse. It is relatively simple to calculate the height of a ridge for any truss system, but one formula is not enough, here you need to take into account a number of factors and then we will analyze 3 main factors, plus you will get the same calculation formula.
Roof configurations.
Three factors affecting the height of the roof
First of all, let's deal with the terminology. It is customary to call the roof ridge the upper line of the connection of the slopes of this very roof. Moreover, the skate is exactly a horizontal line. If, for example, a hipped hipped roof does not have a horizontal line, then the height of the upper point of the connection of the slopes is calculated.
Most types of roofs can be decomposed into right triangles.
The calculation of the gable roof of the building is considered the simplest, there we have a triangle. If we draw a vertical line from the ridge to the base, then we get 2 right-angled triangles, which are the main characters in the calculations.
But almost all complex types of structures, upon closer examination, can be decomposed into the same right triangles.
The gable design is the simplest in terms of calculation.
The only exception is vaulted structures, but the construction of such a structure with your own hands and without preparation is unlikely, so we will leave the vaulted roof alone and deal with the factors affecting the height of triangular roofs.
Factor #1: You can't argue with nature
In this case, we are talking only about atmospheric phenomena, that is, wind, rain and snow. Because the stability of the house during earthquakes has nothing to do with the height of the ridge.
Competing with the elements is at least stupid, so you need to adapt to it:
- in areas characterized by frequent hurricane winds, it is recommended to make the roof slope no more than 10º, maximum 15º, but fortunately we have few such places. In the steppe and moderately windy regions, the maximum is about 40 degrees,Atmospheric phenomena are considered to be one of the most important factors in calculations.
All of the above data can be found in the regional meteorological service or use two relevant documents. The first document is SNiP 23-01-99, and the second is a collection of synoptic maps for the regions of SP 20.13330.2011.
Factor #2: roofing material
The slope of the slopes directly affects the choice of material with which you plan to cover the roof. Often, most materials will have a recommended tilt range written on them, but this information has yet to be found, so it's easier to remember a few general guidelines.
The height of the ridge and the type of roof are related.
- If the material is piece, for example, ceramic or bituminous tiles, then the angle of inclination should be as large as possible, because there are too many hooks on such a plane, according to precipitation, there will be something to hold on to,
- On gentle slopes, smooth and large sheets are in priority. If earlier it was slate, now in terms of sliding characteristics it has been significantly overtaken by metal tiles and corrugated board. There is also a seam roof, but it is more expensive, so it is used less often,
- Heavy materials, such as ceramic tiles, love steep slopes, because on gentle slopes they need to mount a much more powerful truss system under them.
The angle of inclination affects the type of roofing material.
The angle of inclination of the slope also affects the amount of roofing material and, accordingly, the cost of it. The steeper the roof, the more expensive it will cost. So a roof with a slope of 10º will be 2 times cheaper than a roof with a slope of 60º.
Factor #3: Attic
Roof structures are attic and without attic. In the first case, the attic is separated from the lower floor, and in the second, they form a single whole. Without an attic roof, it is more convenient for windy areas, while with an attic there is the possibility of arranging additional living space.
There are attic and non-attic roofs.
Attic structures come with a residential and non-residential attic. So, if the attic is not residential, then the fire minimum for the height of the interior under the ridge is 1.6 m.
Calculation of usable space for a gable attic.
In windy areas, the height of residential attics can be increased due to the side "attic" walls, which is considered an excellent way out.
The useful area of the attic can be increased by attic walls.
In aesthetic terms, if the house is one-story, then the optimal ratio of the height of the ridge to the height of the first floor is 1:1. If you do more, then the house will look like a mushroom, and if you do less, then it will visually grow into the ground.
Roof Height Formula
The first and perhaps the easiest way is to use a calculator program. Under the article (in the "basement" of the site) you will find the "construction calculators" section, there are such programs.
You know the width of the house, you also know the desired parameters, the rest will be prompted by the program and the technical support service of the site.
As mentioned, most roofs can be decomposed into simple right triangles, where one leg is the vertical from the ridge to the base, and the second leg is the horizontal along the base, our hypotenuse is the roof slope.
To find out the height of the leg vertically, we need to multiply the leg horizontally by the tangent of the angle of inclination of the roof (we take the tangent from the Bradis table).
The essence of the mathematical method.
By the way, the angle of inclination of the slope can be indicated in degrees, percentages or as a decimal fraction. In the numerator of such a fraction is the height of the ridge, and in the denominator is the horizontal leg of our triangle. So, builders usually use the fractional definition of the angle of inclination, which is much more convenient.
Fractional determination of the angle of the roof is considered more practical.
Designing any roof is a rather painstaking task, since most of the impacts of bad weather - snow, rain and strong winds fall primarily on the roof slopes and truss frame. Even though, in terms of stability and strength, a gable roof is considered the best option for any low-rise building.
Specialists have to repeatedly calculate the height of the ridge of a gable roof in order to find the golden mean between the angle of inclination of the slope, the volume of the under-roof space and the windage of the building.
What affects the height of the skate
Any person who is unfamiliar with the features of the layout and calculation of a gable roof can intuitively guess that the height of the ridge cannot be selected. It really is. The height at which the line of joining of two slopes is located depends on two main factors that determine the viability and price of the roof truss frame:
- Rafter length. The higher the ridge is raised, the longer the rafters;
- With an increase in the height of the ridge, the cost of beams, strut boards and struts increases;
- The higher the ridge, the greater the consumption of roofing, film steam and waterproofing, insulation, lining material;
- The windage of the building increases, if the height of the ridge exceeds the limit value determined by the calculation, a situation is possible when the box of the building is not able to hold the roof.
In calculating the parameters of the roof, the factor of the influence of atmospheric phenomena is taken as one of the most important. An equally important characteristic depends on the height of the ridge - the angle of inclination of the roof slopes, the higher the ridge, the greater the slope.
Note! A gust of wind of medium intensity creates a dynamic pressure along the normal to the surface of the roofing cake, reaching 20 kg per square meter.
Increasing the angle of inclination by 5° will mean that the height of the ridge and the length of the roof slope will increase by almost 10%, respectively, for 10° the increase will be almost 30%. It would seem that the drainage of rainwater has improved and the volume of the heat-insulating under-roof space has increased. But at the same time, the force of wind pressure increased by 30%. The calculation shows that the pressure of the high-speed air flow on the plane of an ordinary gable roof measuring 8x8 m is more than 1200 kg, which in itself is quite a lot, given the strength of the rafters. Under these conditions, an additional 400 kg can be fatal for the roof Mauerlat.
Builders don't like high skates. This usually means that the rafters will have to be purchased at an inflated price. It turns out that the greater the height of the ridge, the more expensive the material for a gable roof. For a bar longer than 6 m, the price per meter grows almost in arithmetic progression. In addition, truss beams have to be spliced, and due to changes in proportions, they become overly flexible. To prevent too much deflection, it is necessary to perform a control calculation of the deformation of each beam and be sure to use braces.
The height of the ridge cannot be increased arbitrarily also for reasons of stability of the roofing. Before calculating the height of the gable roof ridge, it is necessary to determine the type of roofing. Most manufacturers give recommendations on the optimal slope of a gable roof for a particular type of roofing material. For example, flexible tiles cannot be laid on a roof slope with a slope of less than 16 ° and more than 40 °, and ondulin and metal tiles are not used on slopes with an angle of inclination of 60-65 °.
The positive aspects of increasing the height of the ridge
There are only three main advantages with a plus sign that arise when the height of the ridge is increased:
- Reducing the pressure of the snow cover;
- Increased usable attic space due to higher ceilings;
- Improving ventilation of the under-roof space, reducing the risk of rainwater leaking under the roofing pie, reducing the cost of insulation due to a more voluminous air cushion.
A roof with a high ridge is ideal for dense urban development, in the presence of a large amount of precipitation in the form of snow, rain and fog. Such a roof is often not even equipped with full-fledged thermal insulation, since the air pocket of the attic reduces heat loss 3-4 times more efficiently. But for gable roofs with a high ridge, a special design of gables will be required. A more effective solution would be to replace the gable roof with a half-hip Danish scheme.
Before choosing which angle for a gable roof is best suited, it would be appropriate to compare the advantages and disadvantages that an increase in the height of the ridge entails.
For example, how important is a large attic space for the owners. A simple geometric calculation shows that an attempt to equip a living space on the second floor of a building with a conventional gable roof is, as a rule, inefficient. In this case, less than half of the working space is used.
Note! If the height of the walls of the attic room of a gable roof exceeds 120 cm from the level of the ceiling, the building inspectorate may qualify it as a second floor and prohibit construction or refuse to register the building.
At the same time, the cost of building a roof truss system due to the additional amount of lumber and insulation will increase by more than 70%. It will be necessary to calculate the estimate again, calculate the cost of the services of workers, and most importantly, recalculate the strength of the rafters for the new height of the ridge.
As a result, it turns out that a gable roof with a ridge height of more than two building wall heights is beneficial primarily for summer cottages, when the attic is not insulated and is used only as a utility room. But even in this case, the height of the ridge for a gable roof must be calculated according to science.
How is the height of the skate determined?
If the choice of the type of roofing has already been made, then in order to determine the height of the ridge, it will be necessary to make a calculation or assessment of the resistance of the roof to the effects of weather factors in a given climatic zone.
You may not have to independently check the stability of the truss frame at different ridge heights, this is the lot of professional designers. But you need to know that the calculation is performed based on the statistics of the meteorological service for three determining factors:
- Predominant direction and average wind speed near the earth's surface and at a height of 7-10m;
- Average and maximum thickness of snow cover in a given area over the past 70 years;
- Average daily, maximum plus and minus temperatures in the area.
The calculation will require tabular data from the set of rules SP 20-13330-2011, according to which the country's territory is divided into eight zones, with an approximately equal amount of snow falling maximum during the winter control period. The first belt includes a snow load of 80 kg / m 2, for the last, eighth belt, the amount of snow on one square can reach 560-600 kg.
If we compare the pressure of snow on the roof and the dynamic pressure of the wind, it becomes clear that the calculation of the height of the ridge and the angle of inclination of a gable roof should be carried out primarily according to the snow load. For snowy areas, the height of the ridge is chosen so that the angle of inclination of the gable roof is in the range of 30-60 °. At large angles, snow pressure can be ignored.
But this does not mean that the dynamic pressure of the wind can not be taken into account at all. For example, consider the system of gables of a gable roof. With a ridge height of 3 m and a base width of 6 m, the surface area of one gable is 9 m 2. According to the calculation, at a wind speed of 10-12 m / s, a horizontally applied force of 200 kg will act on the roof gable. This means that even with a small ridge height, the rafter system has a chance to be folded like a house of cards if the frame calculation does not provide for the installation of struts and wind boards.
The geometry of the gable roof ridge
Often, for everyone who first comes into contact with the topic of calculating a gable roof, a logical question arises - why do you need to calculate the height of the ridge if the main characteristics are determined by the angle of inclination of the slopes?
In fact, the angle of inclination is used primarily to take into account external climatic factors, and the height of the ridge is a purely structural value. From the selected height of the ridge, the length of the rafters and the length of the struts and posts holding the ridge beam are determined.
To calculate the height of the ridge, two methods are used:
- Using trigonometric functions;
- Tabular method, according to pre-calculated lengths of rafters and bases.
If the gable roof is made according to a symmetrical scheme, then for the calculation it is enough to know the laying length or half of the roof base and the angle of inclination. Next, by the tangent, we determine the height of the ridge, as in the diagram.
It is clear that trigonometric functions are very inconvenient and, most importantly, not visual for practical work. Therefore, in construction reference tables, you can see the designation of the angle of inclination, as 5:10. It doesn’t matter how many degrees it is, for the calculation it is enough for the master to know that 5 is the height of the ridge, and 10 is the length of the laying.
In addition, the height of the ridge can be determined by a graphical or practical method. In the first case, drawings or exact sketches of the design of the future gable truss frame are used. For construction calculations, sometimes it is enough to simply measure with a ruler and recalculate the values on the scale of the drawing. Despite external primitiveness, this is the most reliable and proven method of calculation. In the second case, you have to climb onto the roof with a tape measure and a plumb line and measure the height of the ridge in practice.
For example, when assembling a gable frame, it is necessary to accurately cut the length of the rafter and wash it down under the support pads on the ridge beam and on the Mauerlat. In practice, the data of the theoretical calculation of the length is used only as a reference. To perform the sawing, the master climbs to the roof, measures the height of the ridge and the length of the base with a plumb line and a tape measure, and only after that he calculates the place to wash down.
Conclusion
With the development of software systems for the development and design of roof truss frames, it is possible to obtain a complete detail of all structural elements of the truss system with dimensions and materials. But the practical skills of performing height and size calculations are always useful, if only to check the results produced by the machine.
The aesthetic indicators, architectural specifics and technical characteristics of the house depend on the height of the roof ridge. It is extremely important when developing a project to correctly determine the correct size of the structure.
To get the perfect result, we invite you today to figure out how to calculate the height of the ridge of a gable roof, and which method is better to use in independent calculations.
A ridge is called a horizontal edge of a gable roof, formed at the junction of the vertices of its inclined planes. Without the slightest doubt, we will attribute the height of the ridge to the most significant parameters that set the proportions of the roof.
Both underestimation and overestimation of it can lead not only to a violation of the architectural picture, but also to problems in operation. The ardent desire of the owner of the house to realize his own ideas often runs counter to technical regulations, familiarization with which will help to avoid serious mistakes.
In order to make the process of studying the value under study easier and more understandable, let's imagine the future roof in the form of an equilateral triangle. This is the most common option. In addition to it, there are asymmetrical gable roofs with slopes that differ in area.
However, the angle of inclination of both structural components is most often equal, therefore the height of the ridge is calculated according to the standard scheme.
For convenience, we divide an equilateral triangle into two symmetrical parts. The line passing from the top of the triangle to its base is the axis of symmetry of the figure presented by us, it is also the leg of the right triangle and the height of the ridge.
Landmark #1: Atmospheric Phenomena
There is no point in arguing with climate reality, it is necessary to adapt to its inexorable dictation and adapt. Atmospheric phenomena that affect the choice of ridge height include:
. In areas where the weather conditions are characterized by frequent gusty winds, it is customary to build flat and low-pitched roof structures with an inclination angle of up to 10º. In regions with weak and moderate winds, the height of the ridge can be any.The indicated characteristics will be prompted by the local meteorological service. You can independently find them in the collection with rules and tables on building climatology SNiP 23-01-99 or according to the zoning maps given in SP 20.13330.2011.
Landmark number 2: The presence of an attic
In the gable roof family, there are attic and non-attic representatives. In the first case, the attic space is separated from the box of the house by a ceiling. They are also called "separate", which confirms the architectural independence of the premises between the roof structure and the ceiling.
Attic representatives are residential and non-residential. The height of the ridge of residential roofs is set by ease of movement. Structures with an operated attic are built mainly according to, involving the construction of a truss system of two tiers.
The height of the ridge of an exploited attic roof consists of two values: the height of the lower part of the roof and the height of the top of the roof, erected on the lower tier. The height dimension of the lower tier is usually taken from 2.0 to 2.3 m.
It is calculated by adding the growth of the tallest of the future owners and a margin of 30 - 40 cm, necessary for the convenience and safety of movement. The size of the top of the sloping roof is arbitrary, depending on the taste preferences of the owners.
The height of the ridge of non-residential attics is determined by fire regulations. In addition, the size of the attic space should not create obstacles for maintenance. The building code regulations indicate that in the attic there should be a through passage along the entire roof of at least 1.6 m in height and 1.2 m in length. In short sections of a composite structure, the width and height of the through passage can be reduced by 40 cm in both directions.
In the second "non-attic" case, the space under the roof is not separated from the box by a ceiling. It is usually located below: at the level of the ceiling system of the previous floor. Non-attic roofs are called "combined", which just indicates the connection of the space under the roof with part of the space of the foot.
Bright representatives of structures without an attic belong to. They are erected according to the usual gable scheme, but the Mauerlat is laid on walls with a height of at least 1.4 m. The height of the ridge of the half attic is measured from the lower edge of the Mauerlat.
The practicality of building a semi-mansard roof in regions with high wind load is difficult to overestimate. Thanks to its construction, the minimum lateral load acts on the roof, and the owners receive a comfortable and very spacious additional floor.
Without an attic and an attic floor, low, small household buildings and warehouses are being built. Covering in such situations is neither economical nor reasonable in terms of access for maintenance.
Landmark #3: Type of roofing
We have already represented the gable roof as an equilateral triangle. And the height of the skate was represented by the leg of its rectangular counterpart, obtained by dividing the structure into two symmetrical parts. In the geometric figure we created, all components are interconnected, including angles and side lengths.
We, as roof designers, are interested in the angle of its slope, because. it is directly dependent on the type and technical characteristics of the roofing. It will help to determine the optimal height of the designed structure.
There are several rules for selecting roofing material, taking into account the height of the ridge and the steepness of the roof, these are:
- The smaller the piece elements of the roof, the greater must be the angle of inclination of the pitched planes. Numerous joints of piece coatings create the prerequisites for the penetration of moisture under the roof, so it is necessary to accelerate the precipitation.
- The lower the roof, the fewer joints and seams should be on the floor. The priority for the arrangement of large-sheet and roll roofs.
- The heavier the coating, the steeper the roof should be built. The weight of massive elements will be distributed in projection per unit area of the base. As a result, the higher the ridge, the less the load puts pressure on the rafter system and the ceiling.
True, the arrangement of a steep roof with a high ridge will cost more. The construction of a structure with a slope of 45º will take 1.5 times more material than covering a flat roof with a steepness of up to 7 - 10º. And if the slopes are tilted at an angle of 60º, the costs will double.
Typically, the range of suitable angles of inclination is indicated by roofing manufacturers in the instructions. The recommendations of the manufacturers should be followed in the name of the long-term service of the structure.
Knowing the recommended angle of inclination, the width of the cornice overhangs and the dimensions of the house box, it is possible to find the height of the ridge in the course of simple geometric constructions. However, in the design of roofs, not only the graphic method is used.
The slope of the slopes is indicated by degrees, percentages or decimal fractions, in the numerator of which the height of the ridge is indicated, in the denominator - half of the overlapped span. All three slope expressions are interrelated, but on a construction site it is more convenient to use the latter option.
There are few who want to postpone the angle of inclination of the ramp with a construction protractor at the facility. Moreover, the process of installing layered rafters, for example, is carried out on an already installed ridge run. Those. you need to know the height of the ridge run ahead of time. This is another one of the good reasons that stimulates interest in calculating the height of the skate.
To the percentage expression of the slope of the roof, there was a general attitude both among the masters and among the home craftsmen. Percentages will only help to confuse. The most acceptable method of displaying the slope is the ratio of the height of the ridge to half the span to be covered. It is most often used on the construction site.
Knowing the height of the ridge, you can not peep every minute in the project documentation. Simply by measuring, the middle of the gable wall is determined. At the point obtained, a bar or pole is nailed strictly vertically. From the upper face of the Mauerlat pre-installed on the wall, the size we are studying is laid upwards. It is guided by the construction of the truss system.
Ways to determine the height of the ridge
To calculate the height of the ridge of a gable roof, the area of \u200b\u200bplanes and other dimensions of the designed structure, there are a significant number of calculator programs on the network. All calculations are carried out automatically, the speed and simplicity of the procedure pleases. True, it is difficult to check the results of the calculations without a visual representation of the planned roof configuration. And if you accidentally enter an erroneous number, it will be possible to detect “amazing” sizes only at the construction site. Therefore, it is better to understand in advance the features of construction and calculations, so that a banal flaw does not cause super-high costs.
Independent designers will need memories of a school trigonometry course and a desire to build diagrams to scale using a monitor or a regular paper sheet.
Mathematical and graphic methods
To determine the height of the ridge of the roof structure, the following methods are used:
- Mathematical. It consists in calculating the size according to the formula for calculating the length of one of the sides of a right triangle.
- Graphic. It consists in building a roof scheme on a scale to obtain the height of the ridge.
For the production of mathematical calculations, the formula a \u003d b × tgα is used, where a is the desired height of the ridge; b - half the width of the span; tgα is the slope angle chosen by the owner of the house on the basis of technical regulations and recommendations from the roofing manufacturer.
Graphically, the height of the ridge is determined at the intersection of the axis of symmetry of the roof and the line of the slope, laid out at a given angle from the extreme point of the cornice overhang. Let's analyze one of the illustrative examples of graphical construction to get an idea of the process.
Let's note an important nuance. The described methods calculate the rise of the roof, and not the total height of the ridge. The real value depends on the technology of fastening the top of the rafters. In hanging systems, the height of the ridge remains unchanged. Similarly, in layered versions, if the top of the rafter does not protrude above the line of the ridge run.
If the tops of the rafter legs rise above the run, then 2/3 of the thickness of the board or timber used in the construction of the rafter system should be added to the roof rise. It is believed that the depth of the cut reduces the thickness of the material by a third.
The crate built over the rafters and the thickness of the roofing are usually neglected in the calculations. It is practically impossible to avoid slight deviations during the construction of the roof, in fact, 5-7 cm of the roof with the crate have almost no effect on anything.
Practical Calculation Example
Let us analyze the procedure for calculating the height of the ridge using a specific example. This is how North American carpenters specializing in the construction of low-rise frame houses calculate the dimensions of a gable roof. Fundamentally, the process is no different from the actions of masters in other countries.
In the example, there is a purely technological specificity: the attachment point of the lower heels of the rafter legs to the base is attached with a notch. The rafters rest on a ridge board. If this is not taken into account when drawing up the diagram and performing calculations, the slope will change, which is highly undesirable when choosing the limit value of the slope angle recommended by the coating manufacturer.
At the heart of independent constructions is the same equilateral triangle, divided into two symmetrical halves. We know the width of the span of the house box and the angle of inclination, because it is selected in accordance with the type of roofing.
The algorithm for calculating the height of the ridge is reduced to a number of the following actions:
- Let's build a scaled diagram and put on it the exact dimensions of the equipped box. The most convenient and understandable scale is 1: 100, according to which 1 cm displays on a scale of 1 m. If working with such a decrease is uncomfortable, you can choose a smaller or larger scale.
- Let's find the middle of the span and draw an axis of symmetry of the roof from the obtained point upwards.
- From the corner of the box, we set aside with a protractor the angle of the slope of the projected roof. We draw a slope line according to the marked angle.
- The intersection of the axis of symmetry of the roof and the line of the slope of the slopes, i.e. diagonal, will give us the opportunity to estimate at what height the board of the ridge run will be located.
- We outline schematically the outline of the ridge run and the support post on which the run will be laid. Their axis of symmetry must coincide with the axis of symmetry of the roof. You just need to set aside half the thickness of the ridge board on both sides of the axis and draw arbitrary lines.
- The line of the base of the triangle, the diagonal and the nearby side face of the ridge run, together with the rack, determine the desired triangle, the vertical leg of which is the rise of the roof.
- We reduce the rise by 1/3 of the thickness of the board, i.e. to the depth of the cut of the lower node of the rafters.
- From the resulting height, we set aside the width of the ridge board and draw the ridge run, then the ridge rack.
- On a scale, we draw the rafter leg, not forgetting that it will sink 1/3 of the width due to the cut. To simplify work, we draw a straight line parallel to the diagonal at a distance of 2/3 of the thickness of the rafter board.
Simply put, the height of the ridge is the sum of the rise of the roof and 2/3 of the thickness of the rafter board. In practice, there will still be no impeccable accuracy, but the error can be considered insignificant and quite acceptable according to the construction standards for the construction of wooden structures, prescribed in the collection of joint ventures 64.13330.2011. Ideally, the processes of compression and crushing of the wooden parts of the system should be taken into account.
Video example of a skate device
The video will acquaint you with the option of building a gable roof ridge, similar to the design described in the example:
A well-designed roof with a properly calculated ridge height will look great. Its components will not create conditions for leakage and premature wear of the structure. It is not difficult to master the calculation methods proposed by us.
Specify the required dimensions in millimeters
X- house width
Y- roof height
C- overhang size
B- roof length
Y2- additional height
X2- additional width
Reference
The program is designed to calculate the building materials of the roof: the amount of sheet material (ondulin, nulin, slate or metal tiles), roofing material (glassine, roofing material), the number of boards and rafters.You can also calculate some useful dimensions of the roof.
The program works in two modes: in the mode of a simple gable roof and a roof with two side gables (side roofs), type 1 and type 2.
Attention! If you have a roof with one side gable, then use type 1 for the calculation, then type 2. And from the data obtained, calculate the amount of building materials: rafters, sheathing boards, roofing and sheet materials.
Otherwise, there may be an error in the calculation. After all, the program takes into account cutouts in the main roof under the roofs of the side gables.
In the calculation, you will see several numbers: the size or volume of the building material of half the roof and in brackets - the full size or volume.
In the calculation of an additional roof - the full size and volume, and in brackets are two numbers: the size and volume of one and two additional roofs.
Attention! When calculating sheet roofing material, consider what the program calculates by the roof area.
For example, 2.8 rows multiplies 7.7 sheets per row. In real construction, 3 rows are laid.
For a more accurate calculation of the number of roofing sheets, it is necessary to reduce the height of the sheet in the calculation until an integer number of rows is obtained.
Don't forget to set the amount of overlap more accurately.
When calculating the material volume of the main roof rafters, in type 2 mode, the program does not take into account the cutout for the side gable. This is due to some implementation difficulties in the program.
Maybe I will solve it in the future.
However, excess rafter material is unlikely to disappear or make some adjustments to your calculations.
There will also be a separate program for a more intelligent calculation of sheet roofing materials.
And do not forget that you need to buy building materials with some margin for waste.
