Rafter load calculation calculator. How to calculate the truss system: calculation algorithm, formulas, examples

The roof of the house is a load-bearing structure that takes on all the external load (the weight of the roofing pie, its own weight, the weight of the snow cover, etc.) and transfers it to all the load-bearing walls of the house or to internal supports.

In addition to its aesthetic and load-bearing functions, the roof is an enclosing structure, separating the attic from the external environment.

The basis of the roof of any house is the truss system.

This is the frame to which the roof is attached.

It is this skeleton that takes all the loads.

The truss system consists of:

rafter legs;
Mauerlat;
side runs and ridge run;
braces, diagonal ties, braces.

When all these elements (except for the Mauerlat) are interconnected, a truss truss is obtained.

The basis of such a farm is a triangle, which is the most rigid of the geometric shapes.

The main element of the roof frame are the rafters.

Rafter calculation

Before you directly start calculating the rafters, you should find out what loads will affect the roof of the house.

That is, on rafter legs.

The loads acting on the roof frame are usually divided into constant and variable.

Constants are those loads that act constantly, regardless of the time of day, season, etc.

This is the weight of the entire roofing pie, the weight of additional equipment that can be installed on the roof (fencing, snow guards, aerators, antennas, etc.).

Variable loads appear at certain times of the year.

For example, snow.

When snow falls on the roof, this is a very decent weight.

In any case, it should be taken into account.

The same with the wind.

It is not always there, but when a strong wind blows, a fairly large wind force acts on the roof frame.

And an inexperienced person is unlikely to succeed.

Although it's worth a try.

Just when calculating, you need to remember a large number of different factors that affect the roof.

At least the weight of the truss system itself with all the elements and fasteners.

Therefore, professionals use special computer programs and calculators to calculate rafters.

How to find out the load on the rafter legs?

The collection of loads should begin with determining the weight of the roofing cake.

If you know what materials will be used and the area of \u200b\u200bthe slopes, then it is not difficult to calculate everything.

It is customary to calculate how much 1 square meter of roof weighs.

And then multiply by the number of squares.

For example, let's calculate the weight of a roofing pie.

The roofing material is ondulin:

Ondulin. A square meter of ondulin has a weight of 3 kg.
Waterproofing. If polymer-bitumen insulation is used, then it weighs 5 kg / square meter.
Insulation. The weight of one square of basalt wool is 10 kg.
Crate. Boards 2.5 cm thick. Weight per square meter 15 kg.

We summarize all weights: 3+5+10+15= 33 kg.

Then the value obtained as a result of the calculations should be multiplied by a factor of 1.1.

This is a correction factor.

It turns out 34.1 kg.

How much does 1 sq. meter of our roofing cake.

And if the total area of our roof is 100 squares, then it will weigh 341 kg.

Snow load calculation

There is a map of snow loads.

It shows the amount of snow cover in each region.

We calculate the snow load using the following formula: S = Sg x µ.

Sg is the mass of snow cover.

µ is a correction factor.

And this coefficient depends on the angle of inclination of the slopes of your roof.

The larger this angle, the smaller the value of this coefficient.

At angles of inclination greater than 60 degrees, it is not used at all.

Since snow does not collect on the roof.

Calculate wind load

Just as the whole country is divided into regions according to the mass of snow, so it is also divided according to the strength of the winds.

And there is also a special map on which the strength of the wind is indicated in each area.

The following formula is used to calculate wind loads:

Wo - an indicator taken from the map.

k is a correction factor depending on the type of terrain where the building is located and its height.

We calculate the cross section of the rafter leg

The cross section of the rafters depends on three factors:

from the length of the rafter;
from the distance between the railings;
from the loads acting on the roof.

Knowing these parameters, it is easy to determine from the table.

How to calculate the length of the rafter legs of a shed roof

Of all the types of roofs, pitched roofs are the simplest.

There are no complex elements in it at all.

And its installation is carried out on load-bearing walls, which have different heights.

Such a roof is arranged on garages, baths, utility rooms.

To calculate what will be the length of the rafters of a shed roof, you should determine the angle of inclination.

And the angle of inclination of the slope depends, first of all, on the type of roofing material that you want to use.

In the case when it is corrugated board, then the optimal angle of inclination is 20 degrees.

But it is forbidden to make an angle less than 8 degrees!

Otherwise, in the cold season, under the weight of the snow cover, the roof will not withstand and simply fail.

If you will lay metal tiles, then the minimum angle of inclination increases to 25 degrees.

When using slate - 35 degrees.

If the roof is folded, then the angle of inclination can be different: 18 - 35 degrees.

After you figured out the angle of the slope, you need to raise the back wall to such a height that you get the desired angle.

The most difficult thing in such calculations is to find the sine and tangent.

But for this they use this sign:

Roof slope angle, degrees	Tangent tgA	sine sinA
5	0,09	0,09
10	0,18	0,17
15	0,27	0,26
20	0,36	0,34
25	0,47	0,42
30	0,58	0,5
35	0,7	0,57
40	0,84	0,64
45	1,0	0,71
50	1,19	0,77
55	1,43	0,82
60	1,73	0,87

For example, let's find the length of the rafter and the height of the elevation of the facade wall for a house 5 meters long.

The tilt angle is 25 degrees.

To determine the height of the front wall rise Lbc x tg 25 = 5 x 0.47 = 2.35 meters.

Accordingly, the length of the rafter leg Lc = 2.35 x 0.42 = 5.6 meters.

And do not forget to add the length of the front and rear overhangs to the resulting length, which are necessary in order to provide the walls of the building with protection from slanting rain.

On average, the length of one overhang is 0.5 meters.

If required, this length can be longer.

But less than 0.5 meters is impossible.

This means that 1 meter should be added to the length of the rafter: Lc \u003d 5.6 + 1 \u003d 6.6 meters.

Calculation for a gable roof

The truss system of a gable roof is much more complicated than the truss system of a shed roof.

There are more elements, and the principle of its operation is somewhat different.

To calculate the length of the rafter leg, we use the Pythagorean theorem.

If you look at the right triangle shown in the figure, you can see that the hypotenuse b is our rafter.

And its length is equal to the length of the leg, divided by the cosine of a specific slope angle.

For example, if the width of the house is 8 meters, and the slope of the slopes is 35 degrees, then the rafter leg will have a length of:

b \u003d 8 / 2 / cos 35 \u003d 8 / 2 / 0.819 \u003d 4.88 meters.

Now it remains to add the length of the visor, about 0.5 meters, to get the desired length of the rafters.

It should be said that these are simplified versions of the calculations of rafters.

In order to get the most accurate data, it is best to use special programs.

For example, the free Arkon program.

The built-in calculator, according to the parameters you set, will automatically calculate both the cross section of the rafter leg and the length of the rafter.

Video about the rafter calculation program.

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 rafter 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 this indicator 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.

How to calculate the length of the gable roof rafters: roof calculation, load and design rules

We calculate the length of the rafters and overhangs of a gable roof

When designing a private house, it is necessary to take into account many different parameters. If they are calculated incorrectly, then the strength of the structure will be in great doubt. The same applies to 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 to answer it, you should 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 two-slope design. But here there are several options, namely:

You can consider even more complex structures, for example, multi-level ones. Such roofs will look very attractive. But to make a calculation, and especially to build a truss system, in this case, without the help of professionals, it will be almost impossible. Therefore, in most cases, they are limited to the three options listed above 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 varieties:

Hanging system. This is the easiest option. In this case, the rafter legs rest only on the Mauerlat. The upper part of them simply connects to each other. Such a 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 to use with an asymmetric gable roof.
The layered system is a more durable truss system. It is used in the event that an axial load-bearing wall passes in the middle of the house. In this case, supports and a ridge run are installed, on which the upper part of the rafter legs is attached.

You can also use a combined version. 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 option, then it is better to entrust everything to calculate to a specialist. In this case, there will be fewer errors, which means that the roof will last longer and will not cause you problems during operation.

What else to consider

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 you calculate everything, you need to know a lot more information, namely:

In addition, when calculating the length of the rafters, you should find out what overhangs should be. Not 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 "fillies" are attached to the main structure. At their core, they are an extension of the rafters.

What length to choose overhangs is up to the owners of the house to decide. According to existing building codes, this parameter should be in the range from 50 to 60 centimeters. You should not do less, otherwise the walls and foundation may suffer. Sometimes overhangs make more than one meter. In this case, a small canopy is obtained along the wall, which can be used for rest or storage.

Making calculations

And 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.

At the same time, using this formula, you can calculate the dyne 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 asymmetric? In this case, the slopes will be different. But here you can use the Pythagorean theorem. You can calculate the rafters on the roof using the same formula, only first find out the value of the parameter "B" (in the first case it is equal to half the width of the house). If the roof is asymmetric, then at the design stage you will calculate at what distance from the walls the ridge will be located. It is this value that is taken as the parameter "B". As a result of the calculation, you will get the length of each of the rafter legs (on 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 is used. This formula is a little more complicated than the previous one. The length of the rafters (for a gable 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.

No matter how the calculation is made, the main thing is to make it correctly and accurately. The strength of the entire truss 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 saw off a little excess during the installation itself.

Calculation of the length of the rafters of a gable roof, depending on the type of roof (symmetrical, asymmetric, broken) and the type of truss system (hanging, layered). Basic nuances and calculations.

The roof is not only the protection of the house from the external environment, but also a certain decorative element that gives the building a finished look. That is why developers are building today the most unusual roofs with complex designs of truss 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 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 is the rafter system

Any construction of this kind is carried out in the form of interconnected elements that strictly correspond to the calculations made earlier. This system includes the following elements:

sloping legs, which are also called rafters;
stops, sprengels and other fasteners that give the structure the necessary rigidity;
vertical type racks;
conjurers.

Note! It is necessary to take special responsibility when calculating the length of the rafters - any, albeit insignificant, error can lead to deformation of the roof geometry and, accordingly, its collapse.

If you do not understand the features of the roof 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 the truss system

Rafter systems are divided into two groups depending on the material used:

wooden structures;
metal structures.

There are also reinforced concrete truss systems, but they are used mainly in industrial buildings. In any case, whether the rafters are metal, wooden 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 coniferous species. Compared to metal, wood is easier to handle and install. Moreover, even if an error occurs during the calculations, then the wooden parts are easy to replace.

Before proceeding with the calculations, first measure the width of the house. The fact is that although small slanted legs do not need additional extension, in some cases the special geometry of the roof requires reinforcement of the rafters, even if the house is of small size.

According to the design features, the rafters are divided into:

In the construction of country houses, inclined rafters are more often used, but often builders combine both. As already mentioned, it may be necessary to build up the oblique legs. It depends on the roofing material used in the construction. So, slate or ceramic tiles, due to their large weight, can only be installed on a rafter system of increased strength.

Types of gable truss systems

The cross section of the boards used in the construction of the rafters can be 20x6 cm or 15x5 cm. But if the structure is strengthened, you can pick up a beam with b about large section (there is another way to strengthen - by splicing the boards).

And now - directly to the calculations.

What to consider when calculating rafters

First, let's define the fundamentals.

The type and shape of the roof directly affect the functional features of the truss 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 ones) need additional stabilization elements - crossbars, sleepers, struts, etc.
Very important in the calculations and future loads on the structure, mainly snow and wind. For example, in the snowy regions of the country it is quite difficult to build a roof with a slope of less than 45 °, and if you increase the slope or height of the structure, then 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 need certain 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 timber used increases.

Note! The distance between the bearing walls is called the run. With an increase in the run, the number of changes in the design increases, in particular, the number of stabilizing and reinforcing elements.

How to calculate the rafters on the roof

Now, having familiarized yourself with the starting points, you can take paper, a ruler and a pencil and proceed with the calculations.

First stage. Roofing cake weight

First, determine how much the roof itself will weigh. This is very important, because the truss 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, summarize the data obtained and add a correction of 10%.

Here is an example of such calculations.

A square meter of the crate weighs 15 kg.
The roofing will be, say, ondulin with a weight of 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 metre.

Let's see what happens.

We add correction 10%, it turns out 37.95 kg. It is this figure that is an indicator of the weight of the roofing pie.

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 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 load of snow that you need to calculate;

µ - correction depending on the slope 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 ramp is greater than 25°, but does not exceed 60°, then the correction will be 0.7. If a very steep roof is being built, then snow loads for it can not be calculated at all.

Sᶢ is the weight per square meter of snow cover. This indicator depends on the climatic features 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 mass of snow will be 200 kgf / m².

Use the formula below to calculate the wind load on the rafters.

Wᵒ in this case, it is a standard indicator that you must determine from the table (it all depends on which region you live in);

To- This is an amendment that takes into account the height of the house and the type of terrain.

Fourth stage. Calculation of the pitch and length of the rafters

The choice of section and length of the rafter leg

To calculate the length of the rafters, you can remember the geometry at school, namely the famous Pythagorean theorem. After all, the truss structure is, in fact, a right triangle and it is very simple to measure its diagonal. But do not forget to take into account when calculating:

the strength of the bars;
the possibility of deformation - what load the system can withstand without breaking.

Note! According to GOST, rafters should not bend more than 1/250 of their length. For example, if the length of the rafters is 5 m, then multiply this number by 0.004 - so you get the maximum deflection, namely 2 cm.

Basic material requirements

According to GOST, wood must meet the following requirements:

its humidity should not exceed 18%;
the number of knots should not exceed three pieces per linear meter of timber;
there may be non-through cracks, but their length should not exceed half of the total length;
wood must be treated with an antiseptic, flame retardant and biological protection agent.

In addition, when buying bars, pay attention to:

manufacturer;
date of manufacture;
product name, standard;
quality of execution of individual parts;
dimensions and humidity of products;
tree species.

Special computer programs

Judging by everything that has been said above, for calculating rafters, you need to have not only a sufficient stock of knowledge, but also drawing and drawing skills. 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 Arkon program, you can easily create various projects, as well as visually see how the future roof will look like.

Note! In such utilities there is also a calculation calculator, which was mentioned earlier. With its help, you can calculate the length, pitch and cross section of the rafters with extreme accuracy.

Such calculators are also available online, but all the data that can be obtained with their help is advisory in nature and will not replace a full-fledged drafting.

As a conclusion

One of the most important stages in the construction of the roof is the calculation of the truss system. Of course, it is better to entrust this matter to professionals, but preliminary measurements can be made on your own - this will help you understand the finished drawing.

Video - Installation of rafters

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Learn how to calculate the rafters on the roof! What data is needed for calculations, a step-by-step guide, tables, photos + videos.

Beautiful and reliable.

And what is the basis of any roof?

From how correctly the calculation of the parameters of the elements of the truss system will be carried out, it will depend on how strong and reliable the roof will be.

Therefore, even at the stage of drawing up a building project, a separate calculation of the truss system is performed.

Factors taken into account when calculating rafters

It is impossible to perform the calculation correctly if you do not take into account the intensity of the various loads that will affect the roof of the house in different periods.

The factors affecting the roof are usually classified into:

Constant loads. This category includes those loads that constantly affect the elements of the rafter system. Regardless of the time of year. These loads include the weight of the roof, lathing, waterproofing, heat and vapor barrier and all other roof elements that have a fixed weight and constantly create a load on the rafter system. If you plan to install any equipment on the roof (snow guards, satellite TV antenna, ethernet antenna, smoke exhaust and ventilation systems, etc.), then the weight of such equipment must be added to constant loads.
Variable loads. These loads are called variables due to the fact that they load the truss system only at some certain period of time, and at other times this load is minimal or not at all. Such loads include the weight of the snow cover, the load from blowing winds, the load from people who will serve the roof, etc.
Special type of loads. This group includes loads that occur in areas where hurricanes very often occur or seismic effects occur. In this case, the load is taken into account in order to add an additional margin of safety to the structure.

The calculation of the parameters of the truss system is quite complicated.

And it is difficult for a beginner to make it, since there are a lot of factors that affect the roof that must be taken into account.

Indeed, in addition to the above factors, it is also necessary to take into account the weight of all elements of the truss system and fasteners.

Therefore, special programs for calculation come to the aid of calculators.

Determining the load on the rafters

Roofing cake weight

To find out the load on the rafters of our house, you must first calculate the weight of the roofing cake.

It is not difficult to make such a calculation if you know the total area of \u200b\u200bthe roof and the materials that are used to create this very pie.

First, consider the weight of one square meter of the pie.

The mass of each layer is summed up and multiplied by the correction factor.

This coefficient is equal to 1.1.

Here is a typical example of calculating the weight of a roofing pie.

Let's say you decide to use ondulin as a roofing material.

And that's right!

After all, ondulin is a reliable and inexpensive material. It is for these reasons that it is so popular among developers.

So:

Ondulin: its weight is 3 kg per 1 square meter.
Waterproofing. Polymer-bitumen material is used. One square meter of it weighs 5 kg.
insulation layer. Mineral wool is used. The weight of one square is 10 kg.
Lathing, boards 2.5 cm thick. Weight 15 kg.

We summarize the data obtained: 3+5+10+15= 33 kg.

Now the result must be multiplied by 1.1.

Our correction factor.

The final figure is 34.1 kg.

This is the weight of one square meter of roofing cake.

The total area of the roof, for example, 100 sq. meters.

So, it will weigh 341 kg.

This is very little.

This is one of the advantages of ondulin.

We calculate the snow load

The moment is very important.

Because in many areas in our winter a fairly decent amount of snow falls.

And this is a very large weight, which must be taken into account!

The snow load map is used to calculate the snow load.

Determine your region and calculate the snow load using the formula

In this formula:

— S is the desired snow load;

— Sg - mass of snow cover.

The weight of snow per square meter is taken into account. meter.

This indicator is different in each region.

It all depends on the location of the house.

A map is used to determine the mass.

— µ is the correction factor.

The indicator of this coefficient depends on the angle of inclination of the roof.

If the slope angle is less than 25 degrees, then the coefficient is 1.

At an angle of inclination of 25 - 60 degrees, the coefficient is 0.7.

If the angle of inclination is greater than 60 degrees, then the coefficient is not taken into account.

For example, a house was built in the Moscow region.

The slopes have an angle of inclination of 30 degrees.

The map shows us that the house is located in the 3rd district.

The mass of snow per 1 square. meter is 180 kg.

We perform the calculation, not forgetting the correction factor:

180 x 0.7 \u003d 126 kilograms per 1 sq. roof meter.

Determination of wind loads

To calculate wind loads, a special map is also used, broken down by zones.

Use this formula:

Wo is a normative indicator determined by the table.

Each region has its own wind tables.

And the k indicator is a correction factor that depends on the height of the house and the type of terrain.

We count wooden rafters

Rafter length

The calculation of the length of the rafter leg is one of the simplest geometric calculations.

Since you only need two dimensions: width and height, as well as the Pythagorean theorem.

To make the calculation more clear, look at the figure below.

We know two distances:

- a is the height from the bottom to the top of the inside of the rafters.

First leg;

- b is a value equal to half the width of the roof.

Second catheter.

c is the hypotenuse of the triangle.

c² \u003d (2 x 2) + (3 x 3).

Total s²=4+9=13.

Now we need to get the square root of 13.

You can, of course, take the Bradis tables, but it’s more convenient on a calculator.

We get 3.6 meters.

To this number, now you need to add the length of the take-out d to get the desired length of the rafters.

We calculate and select the section of the elements of the truss system

The cross section of the boards that we will use for the manufacture of rafters and other elements of the rafter system depends on how long the rafters are, with what step they will be installed and on the snow and wind loads that exist in a particular region.

For simple structures, a table of typical board sizes and sections is used.

If the design is very complex, then it is better to use special programs.

We calculate the step and the number of rafter legs

The distance between their bases is called.

Experts believe that the minimum distance should be 60 cm.

And the optimal distance is 1 meter.

We calculate the distance between the rafters:

we measure the length of the slope along the eaves;
then the resulting figure should be divided by the estimated pitch of the rafters. If the step is planned to be 60 cm, then it should be divided by 0.6. If 1 meter, then divided by 1. About the preliminary choice of the step will be further;
then 1 should be added to the received result and the resulting value should be rounded up. Thus, we get the number of rafters that can be installed on the roof of your house;
the total length of the slope must be divided by the number of rafters to get the pitch of the rafters.

For example, the length of the roof slope is 12 meters.

Pre-select a rafter pitch of 0.8 meters.

12/0.8 = 15 meters.

We add a unit 15+1=16 rafters.

If it were a fractional number, then we would round it up.

Now from 12 meters should be divided by 16.

As a result, 1216 = 0.75 meters.

Here is the optimal distance between the rafters on one slope.

The table discussed earlier can also be used.

We calculate wooden floor beams

For wooden beams, the optimal span is from 2.5 to 4 meters.

The optimal section is rectangular.

The ratio of height and width is 1.4:1.

The beam should go into the wall by at least 12 cm.

Ideally, the beams are attached to anchors that are pre-installed in the wall.

Waterproofing of beams is carried out "in a circle".

When calculating the section of the beams, the load from its own weight (usually 200 kg / sq. Meter), and the operational live load are taken into account.

Its value is equal to the constant load - 200 kg / sq. meter.

Knowing the span and the installation step of the beams, their cross section is calculated from the table:

Span (m) / Installation pitch (m)	2.0	2.5	3.0	4.0	4.5	5.0	6.0
0.6	75x100	75x150	75x200	100x200	100x200	125x200	150x225
1	75x150	100x150	100x175	125x200	150x200	150x200	175x250

If a more accurate calculation is required, then use the Romanov calculator.

Calculation of shed roof rafters

Shed roof - the simplest version of the roof.

But this option is not suitable for every building.

And the calculation of the rafters is required in any case.

Shed roof calculations begin with determining the angle of inclination.

And it depends on, first of all, what material you plan to use for the roof.

For example, for corrugated board, the minimum angle is 8 degrees.

The optimum is 20 degrees.

Settlement programs

If online calculators perform simple calculations, then special software can calculate everything you need.

And there are quite a few such programs!

The most famous of them are 3D Max and AutoCAD.

Such programs have only two drawbacks:

to use them, you must have certain knowledge and experience;
such programs are paid.

There are a number of free programs.

Most programs can be downloaded to your computer.

Or use them online.

Video about the calculation of rafters.

The roof and the frame of the house are two complementary structures that are responsible for the strength, reliability and durability of the building. The construction of a roof is unthinkable without the construction of a truss system - a frame made of boards and beams, on which the layers of the roofing pie are fixed. To build a solid roof, you need to correctly calculate the truss system and select the elements suitable for it. This is what causes most of the difficulties in building a house. In this article, we tried to cover all the nuances associated with this task.

The rafter frame is responsible for the rigidity of the roof and evenly distributes the load of the pie along the external and internal supports. The strength and reliability of the roof, as well as its ability to resist various influences, depends on the correct calculation. There are quite a few of these impacts, ranging from the weight of all materials laid on the rafters, ending with external factors.

To calculate the roof truss system, all loads exerted on the structure should be taken into account. Only after that, you can find the optimal parameters and select elements that can withstand the total impact of these loads. But it should be taken into account that the calculation scheme turns out to be “idealized” every time. This means that the roof is experiencing a uniformly distributed load, but in reality everything happens quite differently - somewhere there was more snow, from some side the wind blows stronger, etc.

Loads on the truss system:

Variables - snow, wind, hail and other weather phenomena.
Regular - the weight of roofing materials and equipment installed on the roof.
Atypical (special) - hurricane winds, seismic tremors.

All load calculations are described in the relevant SNiP, therefore, in the process of work, you should constantly check with the approved documentation. The same applies to determining the optimal angle of inclination of the roof, the pitch of the rafters and the choice of materials. After drawing up a detailed diagram, taking into account all the required parameters, you can make adjustments and proceed with installation.

Wind loading can seriously damage an improperly designed roof. The same goes for the large amount of snow that has accumulated on the surface. Correctly selected angle of inclination of slopes will help to avoid troubles.

To determine the degree of snow load in a horizontal projection, use the following formula: S=Sg* µ.

Sg is the weight of snow per 1 m² of area, and µ is the coefficient of dependence on the angle of inclination. So, for roofs with a slope of less than 25 °, it will be 1.0, for roofs with a slope of 25 ° to 60 °, the coefficient will be 0.7, and for very steep slopes of more than 60 °, it is generally possible not to take into account the snow load - snow on such a surface simply will not be able to resist.

To find the wind load, use another formula: W=Wₒ*k.

Wₒ here is a standard value that can be selected depending on the wind area (indicated in SNiP), and k is a coefficient that determines the dependence of the wind force on the height of the house and its location. This relationship can be traced in the table below:

If the angle of inclination of the roof is more than 30 °, the calculation of the truss system should be corrected for the wind. Also, for the calculation, you need to know the constant wind direction in the area where the house is being built.

The wind, depending on the angle of inclination of the roof, will tend to either lift it or overturn it, so in both cases the rafters should be attached to the support beam very firmly. Mounting methods will also differ depending on the effects of the wind. But what can be said with certainty is that the heavier the roof, the better - the wind will not be able to cope with a heavy structure.

Let's give an example of calculating the snow and wind load on the roof of a house being built in central Russia, say, in the Moscow region. Therefore, in order to view the calculated values, you will need SNiP 2.01.07-85 on "Loads and Impacts". The angle of inclination of the slopes is 22 °. Since the house is located in the third snow region, the calculated load for it will be 180 kg / m², and the dependence coefficient will be 1.0. We multiply these two values \u200b\u200beach other and get a snow load of 180 kg / m². If the pitched roof coefficient is less, say, 0.7, then the load will decrease to 126 kg / m².

An important point: In the event of a snowdrift on the roof, the load increases to 400-500 kg / m².

As for the wind load for our house in the Moscow region, for this region it is 32 kg / m². Let's say the area of \u200b\u200bthe house is 10 m², then it is very easy to calculate the degree of wind exposure: 32 * 0.65 \u003d 20.8 kg / m².

You need to calculate the roof truss system taking into account all the materials that you will lay on it: waterproofing, insulation, elements of the ventilation system, roofing material, equipment, etc. The choice of roofing material depends on the angle of inclination of the slopes and directly affects the strength requirements of the components of the truss system.

Weight of common roofing materials per 1 m²:

ceramic tiles - 35-50 kg;
cement tiles - 40-50 kg;
slate - 10-15 kg;
shingles - 8-12 kg;
bitumen slate - 4-6 kg;
corrugated board and metal tiles - 4-5 kg.

The rough flooring for the layers of the roofing cake weighs from 18 to 20 kg / m², the lathing - from 8 to 10 kg / m², and the entire rafter system gives a load of 15 to 20 kg / m². Summarize all this data and you will understand that the roof exerts serious pressure on the walls of the house and the foundation. By the way, if the house is built on a lightweight foundation or has weak walls, then a roof covered, for example, with ceramic or cement tiles, is out of the question.

Useful advice: Many sellers of roofing materials focus on the lightness of products, they say, this will save on the truss system by building it from thinner and cheaper elements. But we already know that the heavier the roof, the more difficult it is for the wind to overturn or tear it off, so you should not blindly believe such arguments.

Rafter section

As you already understood, the section (thickness) of the rafters should be chosen depending on the load on the roof, more precisely, the sum of all the loads listed above. When building a gable or four-pitched roof, many different elements are used. The length of standard rafters can vary from 4.5 to 6 m. If necessary, they can be shortened or extended.

Before choosing a beam section, you need to know the length of the rafters, the step of their installation and the load on them. The table below shows the necessary data for calculating the roofing system. However, these values are only suitable for the Moscow region and take into account the climatic features of this particular region.

But the "skeleton" of the roof consists not only of rafters - it has a support beam (Mauerlat), struts, crossbars and many other elements. Below are the recommended sections for each of them:

mauerlat is the most powerful element of the system, so it needs a large cross section of 100x100 mm, 100x150 mm or 150x150 mm;
runs also perform a supporting function and must be strong - 100x100 mm, 100x150 mm or 100x200 mm;
valleys and diagonal rafter legs - 100x200 mm;
struts and crossbars - 100x150 mm or 150x150 mm;
hemming boards - 25x100 mm;
puffs - 50x150 mm.

When the length, thickness and pitch of the rafters are selected, their number can be determined. You need to do this, focusing on the length of the house. In the design process, it is also necessary to calculate the deflection, correlating the load on the rafters and the possible deflection of the wooden elements under it. For a mansard roof truss system, the deflection will not exceed 1/250 of the length of the segment on which pressure is applied.

In other words, five-meter rafters will bend a maximum of 2 cm. With an increase in length or load, the roof may deform.

On 1 running meter of material there should not be more than 3 knots up to 3 cm long (if the knot is larger, then the rafter will be weak).
The presence of non-through cracks is acceptable, but only if they do not exceed half the length of the entire timber.
The wood must be well dried. The permissible moisture level of the bars is 18% or less. If you build a truss system from raw elements, it will deform very soon.

Useful advice: Before installing the structure of the truss system, be sure to treat each wooden element with an antiseptic and flame retardant. This should be done before installation, not after.

Calculation of the truss system

The calculation of the truss system will depend, first of all, on the design features of the roof and its type: single-pitched, gable, hip, etc. In this chapter, we will consider the calculation features for the most common types of roofs.

shed roof

A shed roof is very simple in execution and it will not be difficult to calculate the rafters for it. However, the biggest disadvantage of this design is its strong exposure to snow and wind loads. A lot of snow will constantly accumulate on a large flat area, so the rafter system must be powerful enough. This is especially true if you can not regularly clean the roof. Perhaps, in such a situation, it is worth thinking about choosing a different type of roof, for example, the simplest gable. The small angle of inclination of a shed roof requires not only a powerful frame, but also the use of reinforced waterproofing due to the high risk of leaks.

To make a calculation of the truss system of a shed roof, you first need to set the angle of inclination (on what it depends, we already found out in the previous chapter). To create the necessary slope, it is necessary to organize the correct difference in height - place the supports of the appropriate height.

The length of the overlapped span determines the complexity of the truss system:

To cover a small length, only rafter legs can be used.
With a span length of 4.5 to 6 m, it is necessary to install struts at the bottom of the slope.
To close a span longer than 6.5 m, you will need vertical racks - they will not allow the roof to bend under loads.

Let's give an example of calculating the frame of a shed roof for a garage with an area of 4x5 m with a slope of 25 °. First you need to find out the height of the roof in order to understand how much to raise one of the load-bearing walls of the garage. To do this, multiply the slope tangent by the length of the side wall: tg25*5=2.35 m.

To find the length of the rafter leg, we divide the height of the roof by the sine of the slope and add the double length of the overhang to the result obtained: 2.35 / sin25 + 2 * 0.5 \u003d 6.6 m.

Calculation of the truss system of a gable roof

The gable roof has been popular for thousands of years, and even today, with an abundance of design solutions, many prefer this classic option. This can be explained not only by aesthetic appeal, but also by the simplicity of construction and the practicality of the design.

The slope of the gable roof truss system can vary from 5° to 90° depending on the climate zone and regular loads. Of course, design preferences also play an important role here. If you are building a house in a favorable climate zone, where there are no strong winds and snowfalls, but you want to decorate your home with a gabled roof, no one can forbid you to do this. The most common option is roofs with a slope of 35° to 45°. They do not block the view, succinctly fit the house into the natural landscape and leave enough free space in the attic.

The device of the truss system of such a roof differs in terms of the use of supports for the rafters. They can be hanging or layered. The former are used in cases where the distance between the supports does not exceed 6-6.5 m. Layered elements are relevant for structures that have a load-bearing central wall or internal columnar supports.

After determining the total load per 1 m² of the system (wind, snow, weight of the roofing cake, etc.), the cross section of the rafters can be determined. To make the task easier, break the roof into several geometric shapes, for example, into 2 trapezoid slopes. Calculate the load for each of them and add up the results. The same principle can be used to calculate the truss system of a hipped roof.

hipped roof

There are several types of hip roof designs, but the most popular are hip and hip roofs. Hipped roofs consist of 4 triangles, the upper corners of which are reduced to one ridge knot. Hip-type roofs are 2 trapeziums connected by a ridge beam along the upper faces and 2 triangles on the sides. There are also broken roofs with a complex structure, but it is possible to calculate a truss frame for them only if you have extensive experience and qualifications.

The hip roof is best suited for residential buildings, as it allows you to create a fairly spacious attic space. It can be insulated and turned into a living room: bedroom, study or workshop. However, the calculation of the hip truss system requires patience and time.

Special tables greatly facilitate the task. So, the image below shows the coefficients of dependence of the length of the corner and intermediate rafters on the angle of inclination of the slopes.

With the help of tables of cross-section, wind load, mass of roofing material, you can quickly collect all the necessary information for your project. Geometric parameters and roof area are measured in square meters.

If you are inexperienced or not confident in your mathematical abilities, it is better to use an online calculator or one of the special programs for calculating the truss system. In the latter case, you only need to enter the necessary data, and the program will do all the calculations and generate the result. Errors are thus minimized. Below you will find a video on the calculation of the truss system using one of these programs:

The height of the roof (h) and the distance between the center of the base and its nearest edge (b \ 2) corresponds to the slope tangent (tg α). So, knowing the angle of inclination of the ramp, you can find the height by the formula: h \u003d (b * tg α) \ 2.

Knowing the cosine of the angle of inclination, you can also find the length of the side rafters (e): e \u003d b \ (2 cos α).

To find the length of the hip rafters (d), the Pythagorean theorem is useful:

Keep in mind that diagonal rafters are longer than usual and will be supported by shorter elements, so it is important to ensure their strength and rigidity. This can be done by choosing a harder wood and properly building up the timbers if necessary.

Calculations and design are a colossally time-consuming and responsible task, whether it is a truss system of a gable simple roof, hip or tent. In order to correctly complete the task, it is necessary to clearly understand what each element is for and how the roof “feels” during operation. If you doubt that you can do it, it is better to practice creating rafters for a garage or gazebo, and then move on to a residential building. You can also use the services of specialists - you can save on construction, but not at the expense of design. To make it easier for you, we have prepared several diagrams of truss systems.

Rafter system: photo

snow thickness;
the amount of summer precipitation;
wind power.

Any construction of this kind is carried out in the form of interconnected elements that strictly correspond to the calculations made earlier. This system includes the following elements:

sloping legs, which are also called rafters;
stops, sprengels and other fasteners that give the structure the necessary rigidity;
vertical type racks;
conjurers.

Note! It is necessary to take special responsibility when calculating the length of the rafters - any, albeit insignificant, error can lead to deformation of the roof geometry and, accordingly, its collapse.

If you do not understand the features of the roof structure, then it is better to contact a qualifiedm specialists. For self-calculation, useUse special calculators and tables - this will help you avoid mistakes.

Rafter systems are divided into two groups depending on the material used:

wooden structures;
metal structures.

According to the design features, the rafters are divided into:

oblique;
hanging.

The cross section of the boards used in the construction of the rafters can be 20x6 cm or 15x5 cm. But if the structure is strengthened, you can pick up a beam with babout large section (there is another way to strengthen - by splicing the boards).

And now - directly to the calculations.

What to consider when calculating rafters

First, let's define the fundamentals.

The type and shape of the roof directly affect the functional features of the truss 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 ones) need additional stabilization elements - crossbars, sleepers, struts, etc.
Very important in the calculations and future loads on the structure, mainly snow and wind. For example, in the snowy regions of the country it is quite difficult to build a roof with a slope of less than 45 °, and if you increase the slope or height of the structure, then 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 need certain 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 timber used increases.

Note! The distance between the bearing walls is called the run. With an increase in the run, the number of changes in the design increases, in particular, the number of stabilizing and reinforcing elements.

Now, having familiarized yourself with the starting points, you can take paper, a ruler and a pencil and proceed with the calculations.

First stage. Roofing cake weight

Here is an example of such calculations.

A square meter of the crate weighs 15 kg.
The roofing will be, say, ondulin with a weight of 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 metre.

Let's see what happens.

15 + 3.5 + 6 + 10 = 34.5 kg.

We add correction 10%, it turns out 37.95 kg. It is this figure that is an indicator of the weight of the roofing pie.

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 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:

µ x S ᶢ = S, where

Sin this case, this is the load of snow that you need to calculate;

µ - correction depending on the slope 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 ramp is greater than 25°, but does not exceed 60°, then the correction will be 0.7. If a very steep roof is being built, then snow loads for it can not be calculated at all.

Sᶢis the weight per square meter of snow cover. This indicator depends on the climatic features of a particular region, you can find out about it in SNiP.

Calculation example

Let's say the slope of the roof will be 25 °, and the mass of snow will be 200 kgf / m².

0.7 x 200 = 140 kgf / m²

This is the planned load of snow on the truss system.

Use the formula below to calculate the wind load on the rafters.

K x Wᵒ = W, where

Wᵒin this case, it is a standard indicator that you must determine from the table (it all depends on which region you live in);

To- This is an amendment that takes into account the height of the house and the type of terrain.

Table 1. Wind loads in Russia

Table 2. Norms of the correction factor.

House height, m
	0,75
		0,65
	1,25	0,85

In this case, A is open areas, and B is areas evenly covered with obstacles.

Calculation example

Let's say you want to build a five-meter-high house in the Moscow region. This region is located in I windy area, so the wind load here is 25 kgf/m². Correction - 0.5. Let's see what happens:

0.5 x 23 = 11.5 kgf / m²

Fourth stage. Calculation of the pitch and length of the rafters

the strength of the bars;
the possibility of deformation - what load the system can withstand without breaking.

Note! According to GOST, rafters should not bend more than 1/250 of their length. For example, if the length of the rafters is 5m, then multiply this numbero by 0.004 - so you get the ultimate deflection, namely 2 cm.

Use the table below to calculate the cross section.

Table 3. Calculation of the section of the truss system

Rafter length, m	Distance between rafters, m	Required beam section, cm
Less than 3		8x10
Less than 3		9x10
Less than 4		8x16
Less than 4		8x18
Less than 4		9x18
Less than 6		8x20
Less than 6		10x20

Calculation example

Let's say the length of the rafter is 4 m. From the table we see that for such a length there are three options for the section, depending on the pitch of the rafters. If this step is, for example, 14 m, then for work you will need a beam with a section of 8x18 cm.

Basic material requirements

According to GOST, wood must meet the following requirements:

its humidity should not exceed 18%;
the number of knots should not exceed three pieces per linear meter of timber;
there may be non-through cracks, but their length should not exceed half of the total length;
wood must be treated with an antiseptic, flame retardant and biological protection agent.

In addition, when buying bars, pay attention to:

manufacturer;
date of manufacture;
product name, standard;
quality of execution of individual parts;
dimensions and humidity of products;
tree species.

Special computer programs

Note! In such utilities there is also a calculation calculator, which was mentioned earlier. With its help, you can calculate the length, pitch and cross section of the rafters with extreme accuracy.

Such calculators are also available online, but all the data that can be obtained with their help is advisory in nature and will not replace a full-fledged drafting.