We calculate the length of the rafters and overhangs of the gable roof. Calculation of a gable roof: area, rafters, height Calculate the pitch of the rafters
The rafter system is the main part of the blood, which takes all the loads acting on the roof and resists them. To ensure the high-quality functioning of the rafters, a correct calculation of the parameters is required.
How to calculate the rafter system
To make the calculation of the materials used in the rafter system on their own, simplified calculation formulas are presented in order to increase the strength of the system elements. This simplification increases the number of materials used, but if the roof is small, then such an increase will be imperceptible. Formulas allow you to calculate the following types of roofs:
- single-slope;
- gable;
- attic.
Video: calculation of the rafter system
Calculation of the load on the rafters of a gable roof
For the construction of a sloped roof, a strong supporting frame is required, to which all other elements will be attached. When developing a project, the required length and cross-sectional area of the rafter bar and other parts of the rafter system are calculated, which will be subject to variable and constant loads.
To calculate the system, you need to take into account the peculiarities of the local climate Loads that act constantly:
- the mass of all elements of the roof structure, such as roofing material, lathing, waterproofing, thermal insulation, lining of the attic or attic;
- a mass of equipment and various items that are attached to the rafters inside the attic or attic.
Variable loads:
- load caused by wind and precipitation;
- the mass of a worker who performs repairs or cleaning.
Variable loads also include seismic loads and other types of special loads that place additional requirements on the roof structure.
The angle of inclination of the slope depends on the wind load In most regions of the Russian Federation, the problem of snow load is acute - the rafter system must take up the fallen mass of snow without deforming the structure (the requirement is most relevant to single-pitched roofs). With a decrease in the angle of inclination of the roof, the snow load increases. The arrangement of a shed roof with a close to zero slope angle requires the installation of rafters with a large cross-sectional area, with a small pitch. You will also need to constantly clean it. This also applies to roofs with an inclination angle of up to 25 °.
Snow load is calculated by the formula: S = Sg × µ, where:
- Sg is the mass of snow cover on a flat horizontal surface with a size of 1 m 2. The value is determined according to the tables in SNiP "Roof systems" based on the required area in which the construction is being carried out;
- µ - coefficient taking into account the angle of inclination of the roof slope.
At an angle of inclination of up to 25 0, the value of the coefficient is 1.0, from 25 o to 60 o - 0.7, over 60 o - the value of snow loads is not involved in the calculations.
Precipitation affects roof calculation Wind load is calculated by the formula: W = Wo × k, where:
- Wo - the value of the wind load, determined according to the tabular values, taking into account the nature of the area where the construction is underway;
- k is a coefficient that takes into account the height of the building and the nature of the terrain.
With a building height of 5 m, the value of the coefficients is kA = 0.75 and kB = 0.85, 10 m - kA = 1 and kB = 0.65, 20 m - kA = 1.25 and kB = 0.85 ...
Roof rafter section
It is not difficult to calculate the size of the rafter beam, given the following point - the roof is a system of triangles (applies to all types of roofs). Having the overall dimensions of the building, the value of the angle of inclination of the roof or the height of the ridge and using the Pythagorean theorem, the length of the rafters from the ridge beam to the outer edge of the wall is determined. The length of the eaves is added to this size (in the case when the rafters protrude beyond the wall). Sometimes the cornice is made by mounting fillies. When calculating the roof area, the lengths of the filly and rafters are summed up, which allows you to calculate the required amount of roofing material.
The cross-section of the timber for the rafters depends on many parameters. To determine the section of the timber used for the construction of any type of roof, in accordance with the required length of the rafter, the step of its installation and other parameters, it is best to use reference books.
The range of rafter bar sizes ranges from 40x150 to 100x250 mm. The length of the rafter is determined by the angle of inclination and the distance between the walls.
An increase in the slope of the roof entails an increase in the length of the rafter beam, and, accordingly, an increase in the cross-sectional area of the beam. This is necessary in order to provide the necessary structural strength. At the same time, the level of snow load is reduced, which means that the rafters can be installed with a large step. But by increasing the step, you increase the total load that will act on the rafter.
When making a calculation, be sure to take into account all the nuances, such as humidity, density and quality of sawn timber, if a roof is built from wood, the thickness of the used rolled metal - if the roof is made of metal.
The basic principle of calculations is as follows - the amount of load acting on the roof determines the size of the cross-section of the timber. The larger the cross-section, the stronger the structure, but the greater its total mass, and, accordingly, the greater the load on the walls and foundation of the building.
How to calculate the length of the gable roof rafters
The rigidity of the structure of the truss system is a mandatory requirement, and its provision excludes deflection when exposed to loads. The rafters bend in the event of errors in the design calculations and the step size with which the rafter is installed. In the case when this defect is detected after the end of the work, it is necessary to strengthen the structure with the help of struts, thereby increasing its rigidity. With a rafter length of more than 4.5 m, the use of struts is mandatory, since the deflection will in any case be formed under the influence of the beam's own weight. This factor must be taken into account when performing calculations.
The length of the rafters depends on their location in the system Determining the distance between rafters
The standard step with which the installation of rafters in a residential building is carried out is about 600-1000 millimeters. Its value is influenced by:
It is not recommended to artificially decrease or increase the step of the rafters. The determination of the required number of rafters is taking into account the step with which they will be installed. For this:
- The optimal installation step is selected.
- The length of the wall is divided by the selected step and one is added to the resulting value.
- The resulting number is rounded to the nearest whole.
- The length of the wall is divided again by the resulting number, thereby determining the desired step of mounting the rafters.
Truss system area
When calculating the area of a gable roof, you need to take into account the following factors:
- The total area, which consists of the area of two slopes. Based on this, the area of one slope is determined and the resulting value is multiplied by the number 2.
- In the case when the sizes of the slopes differ among themselves, the area of each slope is determined individually. The total area is calculated by adding the values obtained for each slope.
- In the case when one of the slope angles is greater or less than 90 °, in order to determine the area of the slope, it is "divided" into simple figures and their area is calculated separately, and then the results are added.
- When calculating the area, the area of chimneys, windows and ventilation ducts is not taken into account.
- The area of gable and cornice overhangs, parapets and firewall walls is taken into account.
The calculation of the rafter system depends on the type of roof For example, a house is 9 m long and 7 m wide, the rafter is 4 m long, the eaves overhang is 0.4 m, and the pediment overhang is 0.6 m.
The value of the area of the ramp is found by the formula S = (L dd + 2 × L fs) × (L c + L ks), where:
- L dd - wall length;
- L fs - the length of the gable overhang;
- L c - the length of the rafter bar;
- L ks - the length of the eaves overhang.
It turns out that the area of the slope is S = (9 + 2 × 0.6) × (4 + 0.4) = 10.2 × 4.4 = 44.9 m 2.
The total roof area is S = 2 × 44.9 = 89.8 m 2.
If a tile or a soft covering in rolls is used as a roofing material, then the length of the slopes will be 0.6–0.8 m less.
The size of the gable roof is calculated in order to determine the required amount of roofing material. With an increase in the angle of inclination of the roof, the consumption of material also increases. The stock should be about 10-15%. It is caused by overlapping stacking. To determine the exact amount of material, taking into account the slope of the slopes, it is best to use reference books.
Video: gable roof truss system
How to calculate the length of the rafters of a hip roof
Despite the variety of types of roofs, their structure consists of the same elements of the truss system. For hip type roofs:
Video: hip roof truss system
What affects the angle of inclination of the rafters
For example, the slope of a pitched roof is about 9–20 о, and depends on:
- type of roofing material;
- climate in the region;
- functional properties of the structure.
In the case when the roof has two, three or four slopes, then in addition to the geography of construction, the purpose of the attic space will also have an impact. When the purpose of the attic is to store various property, then a large height is not required, and if used as a living space, equipment of a high roof with a large angle of inclination will be required. Hence it follows:
- the appearance of the front of the house;
- used roofing material;
- influence of weather conditions.
Naturally, for areas with strong winds, the best choice would be a roof with a small slope angle - to reduce the wind load on the structure. This also applies to regions with hot climates, where rainfall is often minimal. In areas with a large amount of precipitation (snow, hail, rain), a maximum angle of inclination of the roof is required, which can be up to 60 °. This angle of inclination minimizes the snow load.
The angle of inclination of the slope of any roof largely depends on the characteristics of the climate. As a result, for the correct calculation of the angle of inclination of the roof, it is necessary to take into account all the above factors, therefore the calculation will be carried out in the range of values from 9 o to 60 o. Very often, the result of calculations shows that the ideal angle of inclination lies in the range from 20 o to 40 o. At these values, the use of almost all types of roofing materials is allowed - corrugated board, metal tiles, slate and others. But it should be borne in mind that each roofing material also has its own requirements for the construction of roofs.
Without the dimensions of the rafters at your disposal, you cannot begin the construction of the roof. Take this issue seriously. Do not limit yourself only to the calculations of the rafter system, the choice of its design and the determination of the acting loads. Building a house is a solid project in which everything is interconnected. In no case should you consider separately such elements as the foundation, the supporting structure of the walls, rafters, roofing. A high-quality project necessarily takes into account all factors in an integrated manner. And if you plan to build housing for your own needs, then the best solution would be to contact specialists who will solve pressing issues and carry out design and construction without errors.
The roof in a building is designed to hold external loads and redistribute them to load-bearing walls or support structures. These loads include the weight of the roofing cake, the weight of the structure itself, the weight of the snow cover, and so on.
The roof is located on the rafter system. This is the name of the frame structure on which the roof is fixed. It takes all external loads, distributing them over the supporting structures.
The rafter system includes the following elements:
- Mauerlat;
- Braces and braces;
- Side and ridge runs;
- Rafter legs.
A truss is a structure that includes all of the listed elements with the exception of the Mauerlat.
Calculation of gable roof loads
Constant 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 the 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 rafter structure, together with fasteners and various elements. Professionals for this task use computer programs, as well as special calculators.
The calculation of the 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 cake. 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 taken approximately; high accuracy is not required here. Usually builders perform calculations of the weight per square meter of the roof. And then this indicator is multiplied by the total roof area.
The roofing pie consists of ondulin, a layer of waterproofing (in this case, insulation on a polymer-bitumen basis), a layer of thermal insulation (the weight of basalt wool will be calculated) and lathing (the thickness of the boards is 25 mm). Let's 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 battens 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 roof area, then it will turn out to calculate the gable roof.
Variable roof loads
Variables are those loads that act on the roof not constantly, but seasonally. Snow in winter is a prime example. Snow masses settle on the roof, creating an additional impact. But in the spring they melt, respectively, the pressure decreases.
Wind also belongs to variable loads. This is also a weather phenomenon that does not always work. And there are a lot of such examples. Therefore, it is important to take into account variable loads when calculating the length of the gable roof rafters. When calculating, you need to take into account many different factors affecting the roof of a 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 a mass of snow cover in various regions of the country.
To calculate this type of load, the following formula is used:
Where Sg is an indicator of the terrain taken from the map, and µ is a 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 amount 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 is the parameter selected from the map.
Calculation of the dimensions of the rafter system
When the calculation of all types of loads is over, you can proceed to calculate the dimensions of the rafter system. The performance of the work will differ depending on what kind of roof structure is planned.
In this case, a gable is considered.
Rafter leg section
The calculation of this indicator is based on 3 criteria:
- Loads from the previous section;
- Remoteness of the railings;
- The length of the rafters.
There is a special table of sections of rafter legs, in which you can find out this indicator based on the above criteria.
The length of the rafters in the gable roof
When calculating manually, you will need a basic knowledge of geometry, in particular, the Pythagorean theorem. The rafter is the hypotenuse of a right triangle. You can find out its length by dividing the length of the leg by the cosine of the opposite angle.
Let's consider a concrete example:
It is required to calculate the length of the rafters of a gable roof 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. Let's put all the data into the formula.
L = 6/2 / cos 45 ≈ 6/2 / 0.707 ≈ 4.24 meters.
The length of the visor must be added to the resulting value. It is approximately equal to 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 figure out.
It is enough to simply 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.
How to calculate the length of the rafters of a gable roof: roof calculation, load and design rules
We calculate the length of the rafters and overhangs of the gable roof
When designing a private house, many different parameters must be taken into account. If they are calculated incorrectly, then the strength of the structure will be in great doubt. The same goes for the roof of the house. Here, even before the start of construction, you need to find out the height of the ridge, and the area of \ u200b \ u200bthe roof and much more, including calculating the length of the rafters. And how to make the last calculations will be discussed in this article. 
What type of roof
How to calculate the length of the rafters? This question will interest everyone who builds a house on their own. But in order to answer it, it is worthwhile to first find out many other parameters. First of all, it is worth deciding on the type of roof, because the length of the slope and rafters will depend on this. The most common option is considered to be a gable design. But here there are several options, namely:
You can consider even more complex designs, such as multi-level ones. These roofs will look very attractive. But to make a calculation, and especially to build a rafter system, in this case it will be almost impossible without the help of professionals. Therefore, in most cases, they are limited to the three above-mentioned options for a gable roof.
System type
The calculation of the length of the gable roof rafters will also depend on the system used. Here experts distinguish the following two main types:
- Hanging system. This is the easiest option. In this case, the rafter legs rest only on the Mauerlat. Their upper part is simply connected to each other. This system is used if the width of the house is small. In this case, the length of the rafters should not exceed six meters. The hanging option is undesirable for use with an asymmetrical gable roof.
- The rafter system is a more durable rafter system. It is used if there is an axial load-bearing wall in the middle of the house. In this case, supports and a ridge girder are installed, on which the upper part of the rafter legs is attached.
You can also use a combined option. It is often used in the construction of houses with complex geometry. Here it will be more difficult to calculate the length of the rafters and other parameters of the system. If you have this particular option, then it is better to entrust everything to a specialist to calculate. In this case, there will be fewer mistakes, which means that the roof will last longer and will not cause you problems during operation. 
What else needs to be considered
The type of roof and the system used are not all the parameters that will be required in order to calculate the length of the gable roof rafters. Before calculating everything, you need to find out a lot more information, namely:
In addition, when calculating the length of the rafters, you should find out what the overhangs should be. More than one roof can do without this "additional" element. Overhangs play the role of protection, which protects the walls of the house and its foundation from being washed away by water flowing from the roof.
They can be a continuation of the rafters or made as independent elements. In the latter case, boards called "filly" are attached to the main structure. At their core, they are an extension of the rafters.
How long to choose overhangs is up to the owners of the house. According to existing building codes, this parameter should be in the range from 50 to 60 centimeters. Do not do less, otherwise the walls and foundation may suffer. Sometimes overhangs are made more than one meter. In this case, a small canopy is obtained along the wall, which can be used for resting or storing things. 
Making calculations
How is the length of the rafters calculated? If the roof has a symmetrical shape, then it is not difficult to calculate this parameter. For this, the formula of the Pythagorean theorem is used, namely: C is equal to the square root of A squared plus B squared, where:
- C is the desired length of the rafter;
- A is the height at which the ridge is located (from the base of the roof);
- B is half the width of the house.
Moreover, using this formula, you can calculate the length of the rafters only up to the Mauerlat. The length of the overhangs is not taken into account here. If they are a continuation of the rafters, then their length must be added to the calculated parameter.
And how to make a calculation if the roof is asymmetrical? In this case, the slopes will be different. But even here you can use the Pythagorean theorem. You can calculate the rafters on the roof using the same formula, but first find out the value of the "B" parameter (in the first case, it is equal to half the width of the house). If the roof is asymmetrical, then even at the design stage you will calculate at what distance the ridge will be located from the walls. It is this value that is taken as the "B" parameter. As a result of the calculation, you will receive the length of each of the rafter legs (for the left and right slope). As you can see, there are no problems with calculations here either. 
There is another way to calculate the rafters. In this case, the slope angle of the ramp is used. This formula is a little more complicated than the previous one. The length of the rafters (for a gabled symmetrical roof) will be equal to the sum of 0.5 and the height from the base of the roof to the ridge divided by the cosine of the slope angle.
In whatever way the calculation is made, the main thing is to do it correctly and accurately. The strength of the entire rafter system will depend on this. If you cannot calculate the length of the rafters to an integer, then it is better to round up. It is better to cut off the excess a little during the installation itself.
Calculation of the length of the rafters of a gable roof, depending on the type of roof (symmetric, asymmetric, broken) and the type of rafter system (hanging, layered). Basic nuances and calculations.
The roof is not only the protection of the house from the external environment, but also a kind of decorative element that gives the structure a finished look. That is why developers are building today the most unusual roofs with complex structures of rafter systems.
The rafter system is the most important element in the arrangement of any roof. It accounts for the weight of the coating and precipitation. Therefore, the correct implementation of such a system, taking into account all the rules of the building art, is a guarantee of the reliability and durability of the roof. It is very important to correctly determine the length of the rafters and other structural elements. In this case, it is necessary to take into account such climatic features as:
What the rafter system consists of
Any structure of this kind is performed in the form of interconnected elements that strictly correspond to the previously made calculations. As part of this system, the following elements can be distinguished:
- slant legs, which are also called rafters;
- stops, sprengels and other fasteners that give the structure the necessary rigidity;
- vertical type racks;
- wives.
Note! It is necessary to take special responsibility in calculating the length of the rafters - any, albeit insignificant, error can lead to deformation of the geometry of the roof and, accordingly, its collapse.
If you do not understand the features of the roofing structure, then it is better to contact qualified specialists. For self-calculation, use special calculators and tables - this will help you avoid mistakes.
Varieties of rafter system
Varieties of rafter system
Rafter systems are divided into two groups depending on the material used:
- wooden structures;
- metal structures.
There are also reinforced concrete rafter systems, but they are used mainly in industrial buildings. In any case, whether the rafters are metal, wood or concrete, they must be firmly attached to the walls of the house.
Often, for the construction of rafters in country houses, wood is used, mainly of conifers. Compared to metal, wood is easier to handle and install. Moreover, even if an error occurs in the calculations, the wooden parts are easy to replace.
Before you start calculating, first measure the width of the house. The fact is that although small slant legs do not need additional build-up, in some cases, the special geometry of the roof requires reinforcement of the rafters, even if the house is small in size.
According to the design features, the rafters are divided into:
In the construction of country houses, inclined rafters are often used, but often builders combine both. As mentioned, an extension of the nipple legs may be required. It depends on the roofing material used in the construction. So, slate or ceramic tiles, due to their high weight, can only be installed on a rafter system of increased strength.
Types of gable rafter systems
The cross-section of the boards used in the construction of rafters can be 20x6 cm or 15x5 cm.But if the structure is reinforced, then you can pick up a beam with b O with a larger section (there is another way of strengthening - by splicing the boards).
And now - directly to the calculations.
What you need to consider when calculating rafters
First, let's define the fundamental points.
- The type and shape of the roof directly affects the functional features of the rafter system. The fact is that the calculations for hipped and gable roofs will differ from each other, because they need to be carried out according to different methods. Moreover, asymmetrical roofs (for example, broken) need additional stabilizing elements - crossbars, sleepers, struts, etc.
- Future loads on the structure, mainly snow and wind, are also very important in the calculations. For example, in the snow-covered regions of the country it is quite difficult to build a roof with a slope of less than 45 °, and if the slope or height of the structure is increased, the wind load will increase. In a word, it is necessary to determine the very "golden mean", but not to the detriment of attractiveness. Very often only true masters can solve such a problem.
- Another important point in the calculation is the coating material. Many of these materials require specific conditions. So, flexible tiles are laid exclusively on a solid surface (in extreme cases - a frequent crate). Ceramic tiles need a reinforced frame.
- Size and area - these are the main indicators that affect the choice of a particular type of roof. If the area is large, then the pitch of the rafters increases and, accordingly, the distance between them. Because of this, the cross section of the used timber increases.
Note! The distance between load-bearing walls is called a run. With an increase in the girder, the number of design changes increases, in particular, the number of stabilizing and reinforcing elements.
How to calculate the roof rafters
Now that you have familiarized yourself with the starting points, you can take paper, a ruler and a pencil and start calculating.
First step. Roofing cake weight
First, determine how much the roof itself will weigh. This is very important, because the rafter system must withstand this weight for a long time. It is very easy to calculate: find out the weight per square meter of each of the layers, sum up the obtained data and add a correction 10%.
Here is an example of such calculations.
- A square meter of lathing weighs 15 kg.
- The roof covering will be, say, an ondulin weighing 3.5 kg.
- A square meter of bituminous waterproofing weighs another 6 kg.
- The weight of a 10 cm layer of mineral wool is approximately 10 kg per square meter.
Let's see what happens.
We add a correction 10%, it turns out 37.95 kg. It is this figure that is an indicator of the weight of the roofing cake.
Note! In most cases, this weight does not exceed 50 kg, but experienced specialists are sure that the calculations should be based on this value - "for the reserve".
It turns out that the weight of the roofing cake should be 50 + 10% = 55 kg / m².
It is very important to take into account the snow load, because snow can accumulate on the roof in a fairly large amount. Use a special formula to determine this load:
S in this case, this is the snow load that you need to calculate;
µ - correction depending on the slope of the slope;
For a flat roof, the slope of which does not exceed 25 °, the correction will be equal to one; if the slope of the slope is more than 25 °, but does not exceed 60 °, then the correction will be 0.7. If a very steep roof is built, then snow loads for it can not be calculated at all.
S ᶢ Is the weight per square meter of snow cover. This indicator depends on the climatic characteristics of a particular region, you can find out about it in SNiP.
Let's say the slope of the roof will be 25 °, and the snow mass will be 200 kgf / m².
Use the formula below to calculate the wind load on the rafters.
Wᵒ in this case, it is a normative indicator that you must determine from the table (it all depends on which region you live in);
TO Is an amendment that takes into account the height of the house and the type of terrain.
Stage four. Calculation of the pitch and length of the rafters
The choice of the section and length of the rafter leg
To calculate the length of the rafters, you can recall the geometry at school, namely the famous Pythagorean theorem. After all, a rafter structure is, in fact, a right-angled triangle and its diagonal is very easy to measure. But do not forget to take into account when calculating:
- the strength of the bars;
- the possibility of deformation - what kind of load the system can withstand without breaking.
Note! According to GOST, the rafters should not bend by more than 1/250 of their length. For example, if the length of the rafters is 5m, then multiply this number by 0.004 - so you get the ultimate deflection, namely 2 cm.
Basic material requirements
According to GOST, wood must meet the following requirements:
- its moisture content should not exceed 18%;
- the number of knots should not exceed three pieces per running meter of timber;
- blind cracks can be, but their length should not exceed half of the total length;
- wood must be treated with an antiseptic, fire retardant and biological protection agent.
In addition, when buying bars, pay attention to:
- manufacturer;
- date of manufacture;
- product name, standard;
- quality of performance of individual parts;
- size and moisture content of products;
- wood species.
Special computer programs
Judging by the above, for calculating the rafters, you need to have not only a sufficient supply of knowledge, but also the skills of drawing and drawing. Of course, not all of us can boast of all this.
Fortunately, today there are many computer utilities designed to facilitate calculations. There are professional ones among them, such as, for example, AutoCAD, but you can find simpler options. So, in the program "Arkon" you can easily create various projects, as well as clearly see how the future roof will look like.
Note! In such utilities there is also a calculating calculator, which was mentioned earlier. With its help, you can calculate the length, pitch and section of the rafters with extreme accuracy.
Such calculators are also available online, but all the data that can be obtained with their help are of a recommendatory nature and will not replace the full-fledged preparation of a project.
As a conclusion
One of the most important stages in the construction of a roof is the calculation of the rafter system. Of course, it is better to entrust this business to professionals, but preliminary measurements can be made on your own - this will help you understand the finished drawing.
Video - Installing rafters
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Find out how to calculate roof rafters! What data are needed for calculations, step-by-step guide, tables, photo + video.
The strength of the roof directly depends on how accurately the calculation of the rafter system is made, in which both the angle of inclination of the slopes and the length, as well as the cross-section of the beams, matter.
Choosing a rafter structure
The strength of the roof is determined not only by the material from which the rafter legs are made, but also by the scheme of their assembly. For example, someone may decide that metal trusses will be the most reliable solution for roofing, but remember that this will create additional stress on the walls and foundation, which will have to be reinforced. Therefore, lumber is often used for rafters, among which beams, boards, as well as strips of different sections for the lathing can be distinguished. Round timber is less commonly used.
The wood is strong enough, but it is very important to commensurate the roof area with the length and cross-section of the supporting elements. That is why the Mauerlat (supporting horizontal beams along the upper edge of the walls along the entire perimeter of the house) is chosen with a large margin of safety. In addition, all parts are designed so that they can support their own total weight together with the roof and additional temporary load (long-term or short-term). All this should be taken into account directly in the project of the house.
Regardless of the design, only certain elements are used in it, namely: rafter legs, racks, braces installed at an angle, ridge beam. Crossbars and under-beams are also needed, which provide the rigidity of the roof frame. But since the fundamental factor is the area of the roof and its slope, calculations are carried out only with respect to the rafters: their length, section and angle to the horizon, as well as the distance between them. It is known that the triangle resists the loads best, therefore it is this figure that is formed with the help of crossbars installed as crossbars between the rafters of a gable roof.
Rafter system. Calculation of rafters and floor beams. Before proceeding with the construction of a roof, of course, it is desirable that its rafter system be designed for strength. Immediately after the publication of the last article "Do-it-yourself gable roof of a house", I began to receive questions in the mail regarding the choice of the section of rafters and floor beams. Yes, it is really quite difficult to understand this issue on the vastness of our beloved Internet. There is a lot of information on this topic, but, as always, it is so scattered and sometimes even contradictory that an inexperienced person, who in his life may not even have encountered such a subject as "Strength" (someone was lucky), can easily get confused in these wilds. I, in turn, will now try to draw up a step-by-step algorithm that will help you independently calculate the rafter system of your future roof and finally get rid of constant doubts - and suddenly it will not stand, but suddenly it will fall apart. I must say right away that I will not delve into the terms and various formulas. Well, why? There are so many useful and interesting things in the world that you can fill your head with. We just need to build a roof and forget about it. The whole calculation will be described using the example of a gable roof, which I wrote about in the last article. So, Step # 1: Determine the snow load on the roof. For this we need a map of snow loads of the Russian Federation. To enlarge the picture, click on it with the mouse. Below I will give a link where you can download it to your computer. Using this map, we determine the number of the snow region in which we are building the house and from the following table we select the snow load corresponding to this region (S, kg / m²): If your city is located on the border of regions, choose a higher load value. It is not necessary to correct the resulting figure depending on the angle of inclination of the slopes of our roof. The program we are going to use will do it itself. Let's say in our example we are building a house in the suburbs. Moscow is located in the 3rd snow region. The load for it is 180 kg / m². Step # 2: Determine the wind load on the roof. For this we need a map of the RF wind loads. It can also be downloaded from the link below. Using this map, we also select the corresponding region number and determine the value of the wind load for it (the values are shown in the lower left corner): Next, the resulting figure must be multiplied by the correction factor "k", which in turn is determined from the table: Here, column A - open coasts seas, lakes and reservoirs, deserts, steppes, forest-steppe and tundra; column B - urban areas, woodlands, etc. terrain evenly covered with obstacles. It should be noted that in some cases the type of terrain may differ in different directions (for example, the house is located on the outskirts of a settlement). Then we select values from column "A". Let's go back to our example. Moscow is located in the 1st wind region. The height of our house is 6.5 meters. Suppose that it is being built in a settlement. Thus, we take the value of the correction factor k = 0.65. That is, the wind load in this case will be equal to: 32x0.65 = 21 kg / m². Step # 3: You need to download to your computer a calculation program made in the form of an Excel table. Further we will work in it. Here is the download link: "Calculation of the rafter system". It also contains maps of snow and wind loads of the Russian Federation. So, download and unpack the archive. Open the file "Calculation of the rafter system", while we get into the first window - "Loads": Here we need to change some values in the cells filled with blue. All calculations are done automatically. Let's continue to consider our example: - in the "Initial data" plate we change the angle of inclination by 36 ° (what angle you will have, write this, well, I think everyone understands this); - we change the step of the rafters, to the one we chose. In our case, this is 0.6 meters; - Load. roofing (load from the own weight of the roofing material) - we select this value from the table: For our example, we select a metal tile with a weight of 5 kg / m². - Snow. area - here we enter the sum of the values of snow and wind loads that we received earlier, ie 180 + 21 = 201 kg / m²; - Insulation (mans.) - we leave this value unchanged if we lay insulation between the rafters. If we make a cold attic without insulation, we change the value to 0; - enter the required dimensions of the crate into the “Crate” plate. In our case, for metal tiles, we will change the pitch of the lathing by 0.35 m and the width by 10 cm. Leave the height unchanged. All other loads (from the own weight of the rafters and lathing) are automatically taken into account by the program. Now let's see what we've got: We see the inscription "The load-bearing capacity of the crate is provided!" We do not touch anything else in this window, there is even no need to understand what the numbers are in other cells. If, for example, we choose another step of the rafters (more), it may turn out that the bearing capacity of the lathing will not be provided. Then it will be necessary to select other dimensions of the crate, for example, to increase its width, etc. n. In general, I think you will figure it out. Step # 4: Click at the bottom of the working screen on the "Sling 1" tab and go to the rafter calculation window with two support points. Here, all the incoming data we entered earlier have already been substituted by the program automatically (this will be the case in all other windows). In our example from the article "Do-it-yourself gable roof of a house", the rafters have three points of support. But let's imagine that there are no intermediate racks and make a calculation: - change the length of its horizontal projection on the rafter diagram (the cell is filled with blue). In our example, it is 4.4 meters. - in the plate "Calculation of rafters" we change the value of the thickness of the rafters B (set) to the one chosen by us. We put 5 cm. This value must necessarily be greater than that indicated in the Ttr cell (stable); - now in the line "Accept H" we need to enter the selected rafter width in centimeters. It must be greater than the values indicated in the lines "Ntr. (Strength)" and "Ntr. (Deflection)". If this condition is met, all the inscriptions at the bottom under the rafter scheme will look like "Condition met". The line "H, (by grade)" indicates the value that the program itself offers us to choose. We can take this figure, or we can take another. Usually we select the sections available in the store. So, what we got is shown in the figure: In our example, in order to comply with all the strength conditions, it is necessary to choose rafters with a section of 5x20 cm.But the roof scheme shown by me in the last article has rafters with three points of support. Therefore, to calculate it, we proceed to the next step. Step 5: Click at the bottom of the working screen on the tab "Lanyard 2" or "Lanyard. 3 ″. This opens a window for calculating rafters with 3 support points. The choice of the tab we need is made depending on the location of the middle support (rack). If it is located to the right of the middle of the rafter, i.e. L / L1<2, то пользуемся вкладкой «Строп.2″. Если стойка расположена левее середины стропила, т. е. L/L1> 2, then we use the "Lanyard 3" tab. If the rack is exactly in the middle, you can use any tab, the results will be the same. - on the rafter diagram, we forward the dimensions in the cells filled with blue (except for Ru); - according to the same principle as described above, we choose the dimensions of the rafter section. For our example, I took the dimensions 5x15 cm. Although 5x10 cm could have been. I just got used to working with such boards, and the margin of safety will be more. Now it is important: from the figure obtained during the calculation, we will need to write down the value of the vertical load acting on the rack (in our example (see the figure above) it is 343.40 kg) and the bending moment acting on the rack (Mop. = 78.57 kghm). We will need these figures further when calculating the racks and floor beams. Further, if you go to the "Arch" tab, the window for calculating the rafter system will open, which is a ridge arch (two rafters and a tightening). I will not consider it, it will not fit our roof. We have too large a span between the supports and a small angle of inclination of the slopes. There you will get rafters with a section of about 10x25 cm, which is certainly unacceptable for us. For smaller spans, such a scheme can be used. I am sure whoever understood what I wrote above will figure it out on his own with this calculation. If you still have questions, write in the comments. And we move on to the next step. Step 6: Go to the "Rack" tab. Well, everything is simple here. - the previously determined values of the vertical load on the rack and the bending moment are entered in the figure, respectively, in the cells "N =" and "M =". We have them written in kilograms, we enter them in tons, while the values are automatically rounded; - also in the figure we change the height of the rack (in our example it is 167 cm) and set the dimensions of the section we have chosen. I chose a 5x15 cm board. Below, in the center, we see the inscription "Central provided!" and “Vnecenter. provided ”. So everything is all right. The safety factors "Kz" are very large, so you can safely reduce the cross-section of the racks. But we will leave it as it is. The result of the calculation in the figure: Step 7: Go to the "Beam" tab. A distributed load and a concentrated load act on the floor beams at the same time. We need to consider both. In our example, beams of the same cross-section cover spans of different widths. Of course, we make calculations for a wider span: - in the “Distributed load” plate we indicate the step and span of the beams (from the example we take 0.6 m and 4 m, respectively); - we take the values of Load. (normal) = 350 kg / m² and Load (calc.) = 450 kg / m². The values of these loads in accordance with SNiP are averaged and taken with a good margin of safety. They include the load from the own weight of the floors and the operating load (furniture, people, etc.); - in the line "B, given" we enter the selected width of the section of the beams (in our example, it is 10 cm); - in the lines "H, strength" and "H, deflection" the minimum possible section heights of the beams will be indicated at which it will not break and its deflection will be acceptable. We are interested in the largest of these numbers. We take the height of the beam section proceeding from it. In our example, a beam with a section of 10x20 cm is suitable: So, if we did not have racks resting on the floor beams, the calculation would be over. But there are racks in our example. They then create a concentrated load, so we continue to fill in the plates "Concentrated load" and "Distribution + concentrated": - in both plates we enter the dimensions of our spans (here I think everything is clear); - in the "Concentrated load" plate, we change the values of Load (normal) and Load (calculated) by the figure that we received above when calculating rafters with three support points - this is the vertical load on the rack (in our example, 343.40 kg) ; - in both plates we enter the accepted width of the section of the beam (10 cm); - the height of the section of the beam is determined by the plate "Distribution + concent.". Focusing on a higher value again. For our roof, we take 20 cm (see the picture above). This completes the calculation of the rafter system. I almost forgot to say: the calculation program we use is applicable for roof systems made of pine (except for Weymouth), spruce, European and Japanese larch. All used wood is of the 2nd grade. When using other woods, some changes will need to be made to the program. Since other types of wood are rarely used in our country, I will not describe now what needs to be changed. Read more.
-> Calculation of the rafter systemThe main element of the roof, which perceives and resists all types of loads, is rafter system... Therefore, in order for your roof to reliably withstand all environmental influences, it is very important to make the correct calculation of the rafter system.
For self-calculation of the characteristics of the materials required for the installation of the rafter system, I give simplified calculation formulas... Simplifications are made in the direction of increasing the strength of the structure. This will cause some increase in lumber consumption, but on small roofs of individual buildings, it will be insignificant. These formulas can be used when calculating gable attic and mansard, as well as pitched roofs.
Based on the calculation methodology below, programmer Andrey Mutovkin (Andrey's business card - Mutovkin.rf) for his own needs has developed a program for calculating the rafter system. At my request, he generously allowed to post it on the site. You can download the program.
The calculation method is based on SNiP 2.01.07-85 "Loads and Impacts", taking into account the "Changes ..." from 2008, as well as on the basis of the formulas given in other sources. I developed this technique many years ago, and time has confirmed its correctness.
To calculate the rafter system, first of all, it is necessary to calculate all the loads acting on the roof.
I. Roof loads.
1. Snow loads.
2. Wind loads.
The rafter system, in addition to the above, is also affected by the load from the roof elements:
3. Roof weight.
4. Weight of subfloor and battens.
5. The weight of the insulation (in the case of an insulated attic).
6. Weight of the rafter system itself.
Let's consider all these loads in more detail.
1. Snow loads.
To calculate the snow load, we will use the formula:
Where,
S - the required value of the snow load, kg / m2
µ is a coefficient depending on the slope of the roof.
Sg - standard snow load, kg / m².
µ is a coefficient depending on the slope of the roof α. Dimensionless quantity.
You can approximately determine the slope angle of the roof α by dividing the height H by half the span - L.
The results are summarized in the table:
Then, if α is less than or equal to 30 °, µ = 1;
if α is greater than or equal to 60 °, µ = 0;
if 30 ° is calculated by the formula:
μ = 0.033 * (60-α);
Sg - standard snow load, kg / m².
For Russia, it is accepted according to map 1 of the mandatory appendix 5 SNiP 2.01.07-85 "Loads and Impacts"
For Belarus, the standard snow load Sg is determined
Technical Code STANDARD PRACTICE Eurocode 1. EFFECTS ON STRUCTURE Part 1-3. General influences. Snow loads. TKP EN1991-1-3-2009 (02250).
For example,
Brest (I) - 120 kg / m²,
Grodno (II) - 140 kg / m²,
Minsk (III) - 160 kg / m²,
Vitebsk (IV) - 180 kg / m².
Find the maximum possible snow load on a roof with a height of 2.5 m and a span of 7 m.
The building is located in the village. Babenki, Ivanovo region RF.
According to map 1 of compulsory Appendix 5 SNiP 2.01.07-85 "Loads and Impacts", we determine Sg - the standard snow load for the city of Ivanovo (IV region):
Sg = 240 kg / m²
Determine the angle of the roof slope α.
To do this, divide the roof height (H) by half the span (L): 2.5 / 3.5 = 0.714
and from the table we find the slope angle α = 36 °.
Since 30 °, the calculation µ is produced by the formula µ = 0.033 · (60-α).
Substituting the value α = 36 °, we find: μ = 0.033 · (60-36) = 0.79
Then S = Sg · µ = 240 · 0.79 = 189kg / m²;
the maximum possible snow load on our roof is 189kg / m².
2. Wind loads.
If the roof is steep (α> 30 °), then due to its windage, the wind presses on one of the slopes and tends to overturn it.
If the roof is flat (α, then the lifting aerodynamic force arising from the wind around it, as well as turbulence under the overhangs tend to raise this roof.
According to SNiP 2.01.07-85 "Loads and Impacts" (in Belarus - Eurocode 1 IMPACTS ON STRUCTURE Part 1-4. General effects. Wind effects), the standard value of the average component of the wind load Wm at a height Z above the earth's surface should be determined by the formula :
Where,
Wo is the standard value of the wind pressure.
K is a coefficient that takes into account the change in wind pressure along the height.
C is the aerodynamic coefficient.
K is a coefficient that takes into account the change in wind pressure along the height. Its values, depending on the height of the building and the nature of the terrain, are summarized in Table 3.
C - aerodynamic coefficient,
which, depending on the configuration of the building and the roof, can take values from minus 1.8 (the roof rises) to plus 0.8 (the wind presses on the roof). Since our calculation is simplified in the direction of increasing strength, the value of C is taken to be 0.8.
When building a roof, it must be remembered that wind forces that tend to lift or tear off the roof can reach significant values, and, therefore, the bottom of each rafter leg must be properly attached to the walls or to the mats.
This is done by any means, for example, using an annealed (for softness) steel wire with a diameter of 5 - 6 mm. With this wire, each rafter leg is screwed to the matrices or to the ears of the floor slabs. It's obvious that the heavier the roof, the better!
Determine the average wind load on the roof of a one-story house with a ridge height from the ground - 6 m. , slope angle α = 36 ° in the village of Babenki, Ivanovo region. RF.
According to map 3 of Appendix 5 in "SNiP 2.01.07-85" we find that the Ivanovo region belongs to the second wind region Wo = 30 kg / m²
Since all buildings in the village are below 10m., The coefficient K = 1.0
The value of the aerodynamic coefficient C is taken equal to 0.8
standard value of the average component of the wind load Wm = 30 · 1.0 · 0.8 = 24kg / m².
For information: if the wind blows at the end of this roof, then a lifting (tearing) force of up to 33.6 kg / m² acts on its edge
3. Roof weight.
Different types of roofing have the following weight:
1. Slate 10 - 15 kg / m²;
2. Ondulin (bituminous slate) 4 - 6 kg / m²;
3. Ceramic tiles 35 - 50kg / m²;
4. Cement-sand tiles 40 - 50 kg / m²;
5. Bituminous shingles 8 - 12 kg / m²;
6. Metal tiles 4 - 5 kg / m²;
7. Decking 4 - 5 kg / m²;
4. Weight of subfloor, battens and truss system.
Rough flooring weight 18 - 20 kg / m²;
Lathing weight 8 - 10 kg / m²;
The weight of the actual rafter system is 15 - 20 kg / m²;
When calculating the final load on the rafter system, all of the above loads are added together.
And now I will tell you a little secret. Sellers of some types of roofing materials note their lightness as one of the positive properties, which, according to their assurances, will lead to significant savings in lumber in the manufacture of the truss system.
As a refutation of this statement, I will give the following example.
Calculation of the load on the rafter system when using various roofing materials.
Let's calculate the load on the rafter system when using the heaviest (Cement-sand tile
50 kg / m²) and the lightest (metal 5 kg / m²) roofing material for our house in the village of Babenki, Ivanovo region. RF.
Cement-sand tile:
Wind loads - 24kg / m²
Roof weight - 50 kg / m²
Lathing weight - 20 kg / m²
Total - 303 kg / m²
Metal tile:
Snow loads - 189kg / m²
Wind loads - 24kg / m²
Roof weight - 5 kg / m²
Lathing weight - 20 kg / m²
The weight of the rafter system itself is 20 kg / m²
Total - 258 kg / m²
Obviously, the existing difference in design loads (only about 15%) will not lead to any tangible savings in sawn timber.
So, we figured out the calculation of the total load Q acting per square meter of the roof!
I would like to draw your attention to the following: when calculating, carefully follow the dimension !!!
II. Calculation of the rafter system.
Rafter system consists of separate rafters (rafter legs), therefore, the calculation is reduced to determining the load on each rafter leg separately and calculating the section of an individual rafter leg.
1. Find the distributed load per running meter of each rafter leg.
Where
Qr - distributed load per linear meter of rafter leg - kg / m,
A - distance between rafters (rafter pitch) - m,
Q - total load acting on a square meter of the roof - kg / m².
2. Determine the working section of the maximum length Lmax in the rafter leg.
3. Calculate the minimum cross-section of the rafter leg material.
When choosing a material for rafters, we are guided by the table of standard sizes of sawn timber (GOST 24454-80 Sawn softwood. Sizes), which are summarized in Table 4.
| Board thickness - section width (B) | Board width - section height (H) | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 16 | 75 | 100 | 125 | 150 | |||||
| 19 | 75 | 100 | 125 | 150 | 175 | ||||
| 22 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | ||
| 25 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 32 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 40 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 44 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 60 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 75 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 100 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 | |
| 125 | 125 | 150 | 175 | 200 | 225 | 250 | |||
| 150 | 150 | 175 | 200 | 225 | 250 | ||||
| 175 | 175 | 200 | 225 | 250 | |||||
| 200 | 200 | 225 | 250 | ||||||
| 250 | 250 |
A. We calculate the cross-section of the rafter leg.
We arbitrarily set the section width in accordance with the standard dimensions, and the section height is determined by the formula:
H ≥ 8.6 Lmax sqrt (Qr / (B Rben)), if the roof slope α
H ≥ 9.5 Lmax sqrt (Qr / (B Rben)), if the roof slope is α> 30 °.
H - section height cm,
B - section width cm,
Rben - bending resistance of wood, kg / cm².
For pine and spruce, Rben is equal to:
1st grade - 140 kg / cm²;
2nd grade - 130 kg / cm²;
3rd grade - 85 kg / cm²;
sqrt - square root
B. We check whether the deflection value is within the standard.
Standardized material deflection under load for all roof elements should not exceed L / 200. Where, L is the length of the working area.
This condition is satisfied if the following inequality is true:
3.125 · Qr · (Lmax) ³ / (B · H³) ≤ 1
Where,
Qr - distributed load per linear meter of rafter leg - kg / m,
Lmax - the working area of the rafter leg of the maximum length, m,
B - section width cm,
H - section height cm,
If the inequality is not met, then we increase B or H.
Condition:
Roof slope angle α = 36 °;
Rafter pitch A = 0.8 m;
The working section of the rafter leg of the maximum length Lmax = 2.8 m;
Material - 1 grade pine (Rben = 140 kg / cm²);
Roof - cement-sand tiles (Roof weight - 50 kg / m²).
It has been calculated that the total load per square meter of the roof is Q = 303 kg / m².
1. Find the distributed load per running meter of each rafter leg Qr = A · Q;
Qr = 0.8303 = 242 kg / m;
2. Let's choose the thickness of the board for the rafters - 5cm.
We calculate the cross-section of the rafter leg with a cross-sectional width of 5 cm.
Then, H ≥ 9.5 Lmax sqrt (Qr / B Rben), since the roof slope α> 30 °:
H ≥ 9.5 2.8 sqrt (242/5 140)
H ≥15.6 cm;
From the table of standard sizes of sawn timber, select the board with the closest section:
width - 5 cm, height - 17.5 cm.
3. Check if the deflection value is within the standard. For this, the inequality must be observed:
3.125 · Qr · (Lmax) ³ / B · H³ ≤ 1
Substituting the values, we have: 3.125 · 242 · (2.8) ³ / 5 · (17.5) ³ = 0.61
Meaning 0.61, which means the cross-section of the material of the rafters is chosen correctly.
The cross-section of the rafters, installed with a pitch of 0.8 m, for the roof of our house will be: width - 5 cm, height - 17.5 cm.
Russian language reference
Breathing in incense - meaning
Pointing Particles: Examples