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Calculate the truss system of a gable roof calculator. Gable roof rafter calculator. Choosing a truss structure


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The calculation of the truss system should be done not after the construction of the box of the house, but even at the stage of manufacturing the building project. It must be remembered that for very responsible and prestigious buildings, it is recommended to order such work from professional architects, only they will be able to perform correct calculations and guarantee the duration and safety of the operation of the facility.

Although it is one of the most simple types systems for residential buildings, there are several types of construction. Diversity allows you to increase the options for using roofs in the construction of houses according to standard or individual exclusive projects.

Type of truss system gable roof Architectural features and brief description

The most commonly used option has two completely identical slopes rectangular shape. The loads between the individual elements are distributed evenly, regardless of their location. The number of additional stops is not limited, a specific decision is made depending on the plans for the use of attic space. Calculations can be done using free programs hosted on construction sites.

The skate is shifted to one side of the house or slopes with different angles tilt. The roof truss system is more complex for calculations. If in a simplified version one slope can be calculated and the data obtained automatically applied to the second, then this option cannot be used for an asymmetric truss system. Advantages - original appearance. Disadvantages - the complexity of calculations and installation and a decrease in the used attic space.

Most often used during the construction of attic spaces, it allows you to significantly increase the volume of attic spaces. Calculations on complexity belong to the middle category. Rafter system with an external break. Rarely there are systems with an internal break, except for the original appearance, they have no advantages.

Structural elements of the truss system

We will give a list of all the elements that need to be calculated for each specific case.

The simplest element of the truss system can be made from timber 150 × 150 mm, 200 × 200 mm or boards 50 × 150 mm and 50 × 200 mm. On small houses, it is allowed to use paired boards with a thickness of 25 mm or more. Mauerlat is considered an irresponsible element, its task is only to evenly distribute point forces from the rafter legs along the perimeter of the facade walls of the building. It is fixed to the wall on a reinforcing belt using anchors or large dowels. Some truss systems have large bursting forces, in these cases the element is calculated for stability. Accordingly, select best ways fixing the mauerlat to the walls, taking into account the material of their masonry.

Bar prices

They form the silhouette of the truss system and perceive all the existing loads: from wind and snow, dynamic and static, permanent and temporary.

They are made from boards 50x100mm or 50x150mm, they can be solid or extended.

The boards are calculated according to the resistance to bending, taking into account the data obtained, the species and types of wood, the distance between the legs, and additional elements to increase stability are selected. Two connected legs are called a truss, in the upper part they may have puffs.

Puffs are calculated for stretching.

Runs

One of the most important elements of the gable roof truss system. They are calculated for maximum bending forces, they are made of boards or timber of the section corresponding to the loads. A ridge run is installed at the highest point, side rails can be mounted on the sides. Run calculations are quite complex and must take into account a large number of factors.

They can be vertical and inclined. Inclined work in compression, attached at right angles to the rafters. The lower part rests against floor beams or concrete slabs, options for resting on horizontal beds are acceptable. Due to the stops, it is possible to use thinner lumber for the manufacture of rafter legs. Vertical stops work in compression, horizontal stops in bending.

lying down

They are laid along the attic, rest against several load-bearing walls or interior partitions. Purpose - simplification of the manufacture of a complex truss system, the creation of new points of transfer of loads from various types stops. For beds, beams or thick boards can be used, the calculation is made according to the maximum bending moment between the support points.

crate

The type of crate is selected taking into account technical parameters roofing and does not affect the performance of the truss system.

What crate is needed for corrugated board? When to mount wooden, and when metal? How to choose the right step of the crate and what factors should be taken into account?

Prices for building boards

Building boards

Stages of calculating a gable roof

All works consist of several stages, each of which has a great influence on the stability and durability of the structure.

Calculation of the parameters of the rafter legs

Based on the data obtained, the linear parameters of lumber and the truss pitch are determined. If the loads on the rafters are very large, then vertical or angular stops are installed to evenly distribute them, the calculations are repeated taking into account new data. The direction of the impact of forces, the magnitude of torque and bending moments change. During the calculations, three types of loads should be taken into account.

  1. Permanent. These loads include the weight of roofing materials, lathing, insulation layers. If the attic is in use, then the mass of all finishing materials of the inner surfaces of the walls should be taken into account. Data on roofing materials are taken from their specifications. The lightest of all metal roofs, the heaviest of all are natural slate materials, ceramic or cement-sand piece tiles.

  2. Variable loads. The most difficult to calculate efforts, especially at the present time, when the climate is changing dramatically. For calculations, data are still taken from reference books of SNiP of an outdated model. For his tables, information was used fifty years ago, since then the height of the snow cover, the strength and the prevailing direction of the wind have changed significantly. Snow loads can be several times higher than those in the tables, which has a significant impact on the reliability of calculations.

    Moreover, the height of the snow changes not only taking into account the climatic zone, but also depending on the location of the house on the cardinal points, the terrain, the specific location of the building, etc. Data on the strength and direction of the wind are just as unreliable. Architects have found a way out of this difficult situation: data is taken from outdated tables, but a safety factor is used in each formula to ensure reliability and stability. For critical roof systems on residential buildings, the standard is 1.4. This means that all linear parameters of the system elements increase by 1.4 times, and this increases the reliability and safety of the structure operation.

    The actual wind load is equal to the figure in the region where the building is located, multiplied by the correction factor. The correction factor characterizes the features of the location of the building. The same formula is used to determine the maximum snow load.

  3. individual loads. This category includes specific efforts affecting truss system gable roof during an earthquake, tornado and other natural disasters.

The final values ​​are determined taking into account the probability of the simultaneous action of all the above loads. The dimensions of each element of the truss system are calculated using a safety factor. According to the same algorithm, not only rafter legs are designed, but also lintels, stops, stretch marks, girders and other roof elements.


For low-rise buildings, a rafter roof is perfect. It will decorate the facade of the house, and with a sufficient slope, snow does not accumulate on such a roof, unlike a flat structure.

One of the types of roof rafters - gable. This is a fairly simple system, which is formed by two slopes. The slope of the roof is the entire inclined plane, with the help of which a drain is provided.

The structure rests on two parallel walls. Such a roof forms two triangular side pediments. A pediment is the end of a building's facade.

Advantages of a gable system

  1. Ease of Design.
    Calculation of the bearing capacity and necessary materials for the installation of such a roof is quite simple, since there are few options for the types and sizes of supporting structures;
  2. Ease of installation.
    A gable roof does not have complex structural elements. A small number of standard sizes allows you to quickly install all the elements of the roof;
  3. Ease of use.
    The fewer different breaks the roof has, the more reliably it protects the home. In the simplest version, a gable roof has only one break - a ridge. Such a roof is easier to repair in case of defects;
  4. Free space.
    For the arrangement of the attic, a gable roof is preferable, since it “eats up” space less. For comparison, consider a 6x6 m house with an attic. At the outer walls, the height from the floor of the room to the roof is 1.5 m, at the ridge - 3 m. For a gable roof under such conditions, the volume of the room will be 81 cubic meters, and for a hip roof with four slopes, 72 cubic meters. For large sizes building volume loss will increase.

Construction types

There are four main types of gable roofs:

  1. symmetrical.
    Reliable, stable, easy to perform, based on an isosceles triangle;
  2. Asymmetrical.
    The ridge is not located in the center, the roof slopes have different slopes;
  3. Polyline symmetrical.
    Roof slopes are broken. Significantly increases the height of the room;
  4. Polyline asymmetrical.
    The attic or attic room is smaller than in the previous case. The roof has a very unusual appearance.

The choice of the type of gable roof depends on the purpose of the room located directly under it and the architectural appearance of the building.

General principles for calculating the truss system

The most important load-bearing parts of the gable roof truss system of a building are the mauerlat, crossbar and rafters. Mauerlat works in compression, so its cross section can be taken conditionally.

The crossbar and rafter legs experience a bending moment.

The calculation of such structures is carried out in terms of strength and stiffness. For small buildings, you can choose their cross section approximately, but for serious buildings, for safety and material saving purposes, the calculation of the truss system should be performed by a professional.

Roof self-weight load

To perform the calculation, you need to know the load per 1 sq.m. roofs.

To do this, you need to add the masses of 1 sq.m. all roofing materials:

  1. filing(if it is, it is most often performed from drywall);
  2. rafter legs. To calculate how much weight of the rafters falls on square meter roofing, you need to find the mass of the running meter of the rafter leg and divide this number by the pitch of the rafters in meters. For the calculation, you can take the approximate cross section of the rafter, the area of ​​\u200b\u200bthis section must be multiplied by the density of the wood;
  3. heater (if any). The density of the insulation must be indicated by the manufacturer, it must be multiplied by the thickness;
  4. crate. To ensure a margin, a continuous crate can be taken into account. For example, 1 sq.m. lathing from a board 32 mm thick will weigh approximately 25 kilograms;
  5. roofing material. Weight 1 sq.m. coatings are usually specified by the manufacturer.

Snow load

The snow load for each area is different and is equal to the weight of the snow cover on a horizontal plane.

On the territory of Russia, it can take values ​​from 80 to 560 kilograms per square meter. On the Internet, you can easily find a snow load distribution map and select the right number based on the construction area.

Roof pitch

The angle of inclination of the roof is quite easy to calculate, knowing the geometry and having an engineering calculator or a standard calculator on a personal computer at hand.

If we divide the height of the roof rise by the distance from the ridge to the cornice in the plan, we get the slope of the roof in fractions or the tangent of the angle of inclination. In order to calculate the angle, it is enough just to find the arc tangent.

If using an engineering calculator is difficult, the arc tangent can be found using an online calculator.

Rafter step calculation

Rafter step mansard roof should be chosen for reasons of ease of installation of insulation. Mats usually have a width of 60 centimeters, so the pitch of the rafters should be chosen so that the distance between them in cleanliness is 58 or 118 centimeters. Two centimeters will allow you to install the insulation boards very tightly, which will allow it to stick between the rafters and improve thermal insulation.

Rafter leg length

Leg length is easy to calculate using the formula:
L/cosα,
where L is the distance from the roof ridge to the inner surface outer wall in plan, and cosα is the cosine of the angle of inclination of the roof. With rigid fastening, you need to add the size of the notch.

Section of the rafter leg

The cross section of the rafter leg must be selected as a multiple of the size of the boards and timber.

An example of a simple calculation of the section of the rafter leg:

  1. we find the load per 1 linear meter of the rafter.
    q =(1.1*weight of 1 sq.m. of roof*cosα + 1.4*normative snow load*cosα2)* rafter spacing;
  2. find W.
    W= q * 1.25 * flight of rafters / 130;
  3. solve the equation:
    W= b*h2/6.
    In this equation, b is the width of the section of the rafter leg, and h is the height.

To solve, you need to ask for the width and find the height by solving a simple quadratic equation. The width can be set to 5 cm, 7.5 cm, 10 cm, 15 cm. For small spans, a width of 15 cm is impractical.

To calculate the truss systems, there are all kinds of tables, programs, online calculators.

The main elements of the roof

The main elements of a gable roof, like any other roof truss, are:


Rafter roof with attic

To fully use the space under the roof, you can design an attic.

Attic floor- This is the floor in the attic space. The facade of the attic is completely or partially formed by the roof surfaces. According to regulatory documents, in order for a room to be considered an attic, the line of intersection of the roof plane and the outer wall should not be higher than 1.5 m from the floor level. If this requirement is not met, the space will be considered a normal floor.

The roof of the attic floor differs from the roof of the attic floor by the presence of a heater in its design. Mostly for insulation. mansard roof mineral wool boards are used.

Lighting of the attic space can be carried out in three ways:

  1. window openings in the gables;
  2. dormers;
  3. roof windows.

dormer window – this is a window structure that has a frame mounted simultaneously with the truss system. This frame is made of wood. The dormer has its own small roof, which can be gable or cylindrical. The double-glazed window is installed vertically.

roof window- This is a window specially designed for use on a rafter roof. It is installed in the plane of the slope in an inclined position. The roof window must withstand the calculated snow load. It is better not to use this type of windows in roofs with a slight slope.

The choice of roofing material

After the appearance of the roof is determined, you can proceed to the choice of material. There are several types of modern coatings. In the list below, material options are listed in descending order of average market value.

  1. Ceramic tiles.
    Ceramics as a roofing material has a long history. The ceramic roof is reliable and durable. The disadvantages of this material are the price and the large mass. Under the roof of ceramic tiles, you will have to arrange a reinforced truss system and crate;
  2. Cement-sand tiles.
    It has almost all the characteristics of ceramic, but costs a little less;
  3. Flexible shingles.
    It has good soundproofing characteristics. Thanks to the rough surface, the tiles are able to prevent snow from moving off the roof. Requires a continuous crate, usually a layer is used moisture resistant plywood. Cannot be used on roofs with large slopes;
  4. Metal tile.
    Compared to previous coatings, it is lighter in weight. Easy to mount. minus metal roofing is that it can be too noisy when it rains.
  5. seam roof.
    The most attractive option in terms of cost. It requires special qualifications during installation, since it will be difficult for a non-professional to make high-quality connections. Installation is more laborious than that of metal and shingles. The same "noisy" as metal tiles.

The material of the roof depends entirely on the desires and capabilities of the customer. The exception is roofs with too much or too little slope, since all materials have limits on the slope of the slope.

Types of truss systems

Structural roof truss systems can be of three types:

  1. Rafters.
    The rafters rest on two sides. From below - on the Mauerlat, from above - on the crossbar. Racks and struts can be used as intermediate supports. Most often used in buildings with a small distance between the ends or, if possible, put racks or a wall in the middle of the attic.
    With large spans of rafters (large distances between the longitudinal walls), racks, struts or puffs can be additionally used.
    Laminated rafters are easy to calculate.
    Usually the most powerful element of such a system is the crossbar, which bears half the load of the entire roof structure.
  2. Hanging rafters.
    In the absence of the possibility of using a crossbar as an upper support, it is reasonable to use this truss system.
    Hanging rafters rest only on the Mauerlat, and at the top point they are interconnected with the help of an overlay.
    This truss system works like a truss under load. The greatest pressure falls on the outer walls. There is a horizontal force - thrust, which can lead to displacement of the walls. In the design of hanging rafters, the expansion force is perceived by a puff, which tightens the rafter legs and prevents them from moving apart.
    Hanging rafters are classified depending on the location of the puff:
    1) Triangular three-hinged arch.
    The puff and rafters form a triangle. The puff is located at the level of the overlap;
    2) Triangular three-hinged arch with suspension.
    With a large span of rafters, the tightening may not pass according to the deflection requirements. To prevent it from sagging, the puff is suspended from the ridge. But with such a system, as well as with a system of layered rafters, a row of racks is formed in the middle of the attic;
    3) Triangular three-hinged arch with a raised puff.
    The puff is most often located at the level of the ceiling of the attic room. Such a scheme is less beneficial from the point of view of the design. The higher the puff is located, the greater the thrust it perceives.
    Hanging rafters must be considered as a triangular truss, which complicates the calculation.
  3. Combined rafters.
    The combined system includes spacer layered rafters. They need both bolt installation and tightening. Unlike the previous options, in which the rafters are hinged to the Mauerlat, here the rafter leg is rigidly attached, so there is a thrust in the system. For such a system, the Mauerlat must be securely attached to the wall, and the wall itself must be strong and thick. An excellent option would be to run a reinforced concrete belt around the perimeter.

Installation of the truss system

Installation takes place in the following order:

  1. mauerlat laying;
  2. installation of a crossbar (if any);
  3. layout of rafters;
  4. insulation (if any);
  5. crate;
  6. roofing material.

Attaching the rafter leg to the Mauerlat can be rigid and articulated.

Hinged fastening

It makes it possible to compensate for the expansion of wood under the influence of humidity and temperature changes.

Fastening can be done in several ways:

  1. using special fasteners, a metal "sled";
  2. using a mounting plate;
  3. washed down on the rafter leg. The junction of the rafter leg and the Mauerlat is fixed with nails.

Rigid fastening

The rafter is attached to the Mauerlat with a notch and securely fixed with nails hammered at an angle with respect to each other. One nail is driven vertically into the surface of the Mauerlat. Such a connection excludes displacement in any plane.

The gable truss system has undeniable advantages. You can design and install it yourself, you just need to take this issue responsibly and think through everything to the smallest detail.

Rafter system. Calculation of rafters and floor beams. Before proceeding with the construction of the roof, it is of course desirable that its truss 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, understanding this issue in the vastness of our beloved Internet is really quite difficult. There is a lot of information on this subject, but as always, it is so scattered and sometimes even contradictory that it is easy for an inexperienced person who in his life may not even have come across such a subject as "Sopromat" (lucky someone), it is easy to 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 truss system of your future roof and finally get rid of constant doubts - what if it doesn’t stand up, but suddenly it falls 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 a previous article. So Step #1: Determine the snow load on the roof. To do this, we need a map of the 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 a house and from the table below select the snow load corresponding to this region (S, kg / m²): If your city is located on the border of regions, choose greater value loads. It is not necessary to correct the resulting figure depending on the angle of inclination of the slopes of our roof. The program that we will use will do it itself. Let's say in our example we are building a house in the suburbs. Moscow is in the 3rd snow region. The load for it is 180 kg / m². Step #2: Determine the wind load on the roof. To do this, we need a map of the wind loads of the Russian Federation. It can also be downloaded from the link below. On this map, we also select the corresponding number of the region and determine the value of the wind load for it (the values ​​\u200b\u200bare 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-steppes and tundras; column B - urban areas, forests and other areas evenly covered with obstacles. It should be taken into account that in some cases the type of terrain may differ in different directions (for example, a house stands on the outskirts of a settlement). Then select the 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 accept the value of the correction factor k=0.65. That is, the wind load in this case will be equal to: 32x0.65 \u003d 21 kg / m². Step number 3: You need to download to your computer a calculation program made in the form of an Excel table. We will continue to work on it. Here is the download link: "Calculation of the truss system". Also here are maps of snow and wind loads of the Russian Federation. So, download and unpack the archive. We open the file "Calculation of the truss system", while we get into the first window - "Loads": Here we need to change some values ​​in the cells of the filled blue color. All calculations are done automatically. Let's continue to consider our example: - in the plate "Initial data" we change the angle of inclination to 36 ° (what angle you will have, write like that, well, I think everyone understands this); - change the pitch of the rafters to the one we have chosen. 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. district - here we enter the sum of the values ​​\u200b\u200bof the snow and wind loads that we received earlier, i.e. 180 + 21 \u003d 201 kg / m²; - Insulation (mans.) - we leave this value unchanged if we lay the insulation between the rafters. If we do cold attic without insulation - change the value to 0; - in the plate "Crate" we enter the required dimensions of the crate. In our case, for a metal tile, we will change the crate step by 0.35 m and the width by 10 cm. We 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 got: We see the inscription "The load-bearing capacity of the crate is ensured!" We don’t touch anything else in this window, we don’t even need to understand what the numbers are in other cells. If, for example, we choose a different rafter pitch (larger), it may turn out that the load-bearing capacity of the crate will not be ensured. Then it will be necessary to select other sizes of the crate, for example, increase its width, etc. In general, I think you will figure it out. Step number 4: Click on the tab "Sling.1" at the bottom of the working screen and go to the window for calculating rafters with two support points. Here, all the incoming data entered by us earlier is already 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 equal to 4.4 meters. - in the plate "Calculation of rafters" we change the value of the thickness of the rafter B (given) to the one we have chosen. We set 5 cm. This value must be greater than that indicated in the cell Vtr (stable); - now in the line "Accept H" we need to enter the selected rafter width in centimeters. It must necessarily be greater than the values ​​​​specified 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 "N, (by sort)" indicates the value that the program itself offers us to choose. We can take this figure, or we can take another. Usually we choose the sections available in the store. So, what we got is shown in the figure: In our example, in order to comply with all 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 support points. Therefore, to calculate it, we proceed to the next step. Step number 5: Click at the bottom of the working screen on the tab "Sling.2" or "Sling. 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 tab "Line 3". If the rack is exactly in the middle, you can use any tab, the results will be the same. - on the scheme of rafters, we transfer the dimensions in the cells filled with blue (except for Ru); - according to the same principle as described above, we select the dimensions of the section of the rafters. For our example, I took the dimensions of 5x15 cm. Although it was possible and 5x10 cm. I just got used to working with such boards, and there will be more safety margin. Now it is important: from the figure obtained during the calculation, we will need to write out the value of the vertical load acting on the rack (in our example (see figure above) it is equal to 343.40 kg) and the bending moment acting on the rack (Mop. = 78.57 hmmm). We will need these figures later when calculating racks and floor beams. Further, if you go to the "Arch" tab, a window for calculating the rafter system, which is a ridge arch (two rafters and a puff), will open. I will not consider it, it will not work for 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 cross section of the order of 10x25 cm, which is of course unacceptable for us. For smaller spans, this scheme can be used. I am sure whoever understood what I wrote above will deal with this calculation himself. 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=". They were recorded in kilograms, we enter them in tons, while the values ​​\u200b\u200bare 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 board 5x15 cm. At the bottom in the center we see the inscriptions “Central provided!” and "Off-center. secured." So everything is in order. The safety factors "Kz" are very large, so you can safely reduce the section of the racks. But we will leave it as is. The result of the calculation in the figure: Step No. 7: Go to the "Beam" tab. Floor beams are affected simultaneously by a distributed load and a concentrated load. We need to consider both. In our example, beams of the same section cover spans of different widths. Of course, we make a calculation for a wider span: - in the “Distributed load” plate, we indicate the step and span of the beams (we take 0.6 m and 4 m, respectively, from the example); - accept 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 operational load (furniture, people, etc.); - in the line "B, given" we enter the width of the section of the beams we have chosen (in our example it is 10 cm); - in the lines "N, strength" and "N, deflection" the minimum possible heights of the beam section 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 based on it. In our example, a beam with a section of 10x20 cm is suitable: So, if we did not have racks resting on floor beams, the calculation would be completed. 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 + concentration”: - in both plates we enter the dimensions of our spans (here I think everything is clear); - in the “Concentrated load” plate, change the values ​​of Load (normal) and Load (calc.) to the figure that we received above when calculating the 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 beam section (10 cm); - the height of the beam section is determined by the plate "Distribution + concentrator". Again, we focus on a larger value. For our roof, we take 20 cm (see the figure above). This completes the calculation of the truss system. I almost forgot to say: the calculation program we use is applicable for truss systems made of pine (except Weymouth), spruce, European and Japanese larch. All wood used is 2nd grade. When using other wood, 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.

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:

  1. Symmetrical - This is the most common type of gable roof. Its popularity is due to the simplicity of the design and the simple calculation of all the necessary parameters. Another plus is the even distribution of loads on the truss system. But there are also disadvantages. Not a very rational use of space. This is especially important if you are planning to. A large number of sharp corners creates a lot of "blind" zones, which cannot be rationally used.
  2. Asymmetrical. In this case, the slopes are located at different angles. As a result, the rational area increases. But even here it was not without drawbacks. Such a gable roof requires more complex calculations. If done with a mistake, then the structure may not withstand loads that are not evenly distributed.
  3. A broken line is the most efficient design if you want to make attic floor. In this case, the rafter legs will “break” at a certain distance from the ridge. As a result, under the roof you will get more free space, and the entire area will be used more rationally. In this case, it will be even more difficult to calculate the parameters of the rafters, including their length.

    4. 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. 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:

    1. . 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.
    2. - This is a more durable truss system. It is used if there is an axial line in the middle of the house. bearing wall. In this case, supports and a ridge run are installed, on which the top part rafter legs.

    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.

Moreover, using this formula, you can calculate the rafter length only up to. 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.

-> Calculation of the truss system

The main element of the roof, perceiving and resisting all types of loads, is rafter system. Therefore, in order for your roof to reliably resist all influences environment, it is very important to make the correct calculation of the truss system.

For self-calculation characteristics of the materials necessary for the installation of the truss 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 the consumption of lumber, but on small roofs of individual buildings it will not be significant. These formulas can be used when calculating gable attic and mansard, as well as shed roofs.

Based on the calculation methodology below, programmer Andrey Mutovkin (Andrey's business card - Mutovkin.rf) developed a truss system calculation program for his own needs. At my request, he generously allowed me to post it on the site. You can download the program.

The calculation methodology was compiled on the basis of SNiP 2.01.07-85 "Loads and impacts", taking into account the "Changes ..." of 2008, as well as on the basis of 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. Loads acting on the roof.

1. Snow loads.

2. Wind loads.

On the truss system, in addition to the above, the load from the roof elements also acts:

3. Roof weight.

4. The weight of the rough flooring and lathing.

5. The weight of the insulation (in the case of an insulated attic).

6. The weight of the rafter system itself.

Let's consider all these loads in more detail.

1. Snow loads.

To calculate the snow load, we use the formula:

Where,
S - the desired value of the snow load, kg / m²
µ is a coefficient depending on the slope of the roof.
Sg - normative snow load, kg/m².

µ - coefficient depending on the slope of the roof α. Dimensionless value.

You can approximately determine the angle of the roof slope α by the result of 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 - normative snow load, kg/m².
For Russia, it is accepted according to map 1 of mandatory annex 5 of SNiP 2.01.07-85 "Loads and impacts"

For Belarus, the normative snow load Sg is determined
Technical code of GOOD PRACTICE Eurocode 1. EFFECTS ON STRUCTURES Part 1-3. General impacts. Snow loads. TCH 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 the mandatory annex 5 of SNiP 2.01.07-85 "Loads and impacts", we determine Sg - the standard snow load for the city of Ivanovo (IV district):
Sg=240 kg/m²

We determine the angle of the roof slope α.
To do this, we divide the height of the roof (H) by half the span (L): 2.5 / 3.5 \u003d 0.714
and according to the table we find the slope angle α=36°.

Since 30° , calculation µ will be produced according to the formula µ = 0.033 (60-α) .
Substituting the value α=36° , we find: µ = 0.033 (60-36)= 0.79

Then S \u003d Sg µ \u003d 240 0.79 \u003d 189 kg / m²;

the maximum possible snow load on our roof will be 189kg/m².

2. Wind loads.

If the roof is steep (α > 30°), then because of 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 that occurs when the wind bends around it, as well as turbulence under the overhangs, tend to raise this roof.

According to SNiP 2.01.07-85 "Loads and actions" (in Belarus - Eurocode 1 IMPACTS ON STRUCTURES Part 1-4. General actions. Wind actions), the standard value of the average component of the wind load Wm at a height Z above the ground should be determined by the formula :

Where,
Wo - normative value of wind pressure.
K is a coefficient that takes into account the change in wind pressure along the height.
C - 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, we take the value of C equal to 0.8.

When building a roof, it must be remembered that wind forces tending 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 annealed (for softness) steel wire with a diameter of 5 - 6 mm. With this wire, each rafter leg is screwed to the mats 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 one-story house with the height of the ridge from the ground - 6m. , 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, coefficient K= 1.0

Meaning 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 = 24 kg / 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 tiles 8 - 12 kg/m²;
6. Metal tile 4 - 5 kg/m²;
7. Decking 4 - 5 kg/m²;

4. The weight of the rough flooring, lathing and truss system.

Draft flooring weight 18 - 20 kg/m²;
Lathing weight 8 - 10 kg/m²;
The weight of the rafter system itself is 15 - 20 kg / m²;

When calculating the final load on the truss system, all of the above loads are summed up.

And now I will reveal to you little secret. Sellers of certain types of roofing materials as one of the positive properties they note their lightness, 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 truss system when using various roofing materials.

Let's calculate the load on the truss system when using the heaviest (Cement-sand tile
50 kg / m²) and the lightest (Metal tile 5 kg / m²) roofing material for our house in the village of Babenki, Ivanovo region. RF.

Cement-sand tiles:

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 truss system itself is 20 kg / m²
Total - 258 kg/m²

Obviously, the existing difference in design loads (only about 15%) cannot lead to any tangible savings in lumber.

So, with the calculation of the total load Q, acting on a square meter of the roof, we figured it out!

I especially draw your attention: when calculating, carefully follow the dimension !!!

II. Calculation of the truss system.

truss system consists of separate rafters (rafter legs), so the calculation is reduced to determining the load on each rafter leg separately and calculating the section of a separate rafter leg.

1. We find the distributed load per linear meter of each rafter leg.

Where
Qr - distributed load per linear meter of the rafter leg - kg / m,
A - distance between rafters (rafter pitch) - m,
Q - total load acting on a square meter of roof - kg / m².

2. We determine in the rafter leg the working section of the maximum length Lmax.

3. We calculate the minimum cross section of the material of the rafter leg.

When choosing a material for rafters, we are guided by a table of standard sizes of lumber (GOST 24454-80 Lumber conifers. Dimensions), which are summarized in Table 4.

Table 4. Nominal dimensions of thickness and width, mm
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 set the width of the section arbitrarily in accordance with the standard dimensions, and the height of the section is determined by the formula:

H ≥ 8.6 Lmax sqrt(Qr/(B Rbend)), if the slope of the roof α

H ≥ 9.5 Lmax sqrt(Qr/(B Rbend)), if the roof pitch α > 30°.

H - section height cm,


B - section width cm,
Rizg - resistance of wood to bending, kg / cm².
For pine and spruce Rizg is equal to:
Grade 1 - 140 kg / cm²;
Grade 2 - 130 kg / cm²;
Grade 3 - 85 kg / cm²;
sqrt - square root

B. We check whether the deflection value fits into the standard.

The normalized deflection of the material under load for all roof elements should not exceed the value 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 the rafter leg - kg / m,
Lmax - working section of the rafter leg of maximum length m,
B - section width cm,
H - section height cm,

If the inequality is not met, then increase B or H .

Condition:
Roof slope angle α = 36°;
Rafter pitch A = 0.8 m;
The working section of the rafter leg is maximum length Lmax = 2.8 m;
Material - pine 1 grade (Rizg = 140 kg / cm²);
Roof - cement-sand tiles (Roof weight - 50 kg / m²).

As it was calculated, the total load acting on a square meter of the roof is Q \u003d 303 kg / m².
1. We find the distributed load per linear meter of each rafter leg Qr=A·Q;
Qr=0.8 303=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 section width of 5 cm.

Then, H ≥ 9.5 Lmax sqrt(Qr/B Rbend), since the slope of the roof α > 30°:
H ≥ 9.5 2.8 sqrt(242/5 140)
H ≥15.6 cm;

From the table of standard lumber sizes, select a board with the nearest section:
width - 5 cm, height - 17.5 cm.

3. We check whether 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, then the cross section of the material of the rafters is chosen correctly.

The cross section of the rafters, installed in increments of 0.8 m, for the roof of our house will be: width - 5 cm, height - 17.5 cm.