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The rafter system is a structure that provides the strength of the roof and serves as the basis for installation roofing material... She is shown in the photo.

The roof is a load-bearing structure that performs the following functions:

• gives the structure a beautiful appearance;
• takes over external loads;
• protects the attic from the outside world;
• transfers the load from the battens and the material on it to the walls of the building and internal supports.

The main elements of the roof include lathing, rafters and Mauerlat. Also, the supporting structure includes additional fasteners - crossbars, racks, rafter struts, spacers, etc. The reliability and strength of the roof is most influenced by the rafter system. The rafters are the main load-bearing part of the roof. The rafter system accounts for the weight of not only the roofing, but also the snow cover, wind pressure. It must withstand all these influences, therefore, the calculation is made taking into account the type of roofing material and the climatic characteristics of the region.

The structure of the rafter system

Joining the rafters to each other stiffens the roof frame, resulting in a strong rafter structure. The load on the rafters can be quite significant, for example, during strong winds, so the frame is tightly tied to the frame of the building.

In the construction of private houses and cottages, wooden truss systems are usually used, which are easy to manufacture and install. If mistakes were made during the construction of the walls, these products can be easily processed: shorten, increase, hang, etc.

During installation, fasteners are used. rafter system: bolts, screws, clamps, nails, staples. They are also used to reinforce the load-bearing roof structure. The interconnected elements of the roof create a truss truss, which is based on triangles, which are the most rigid geometric figure.

When choosing a material for making a system from rafters, it is necessary to take into account the structural and architectural nuances of the project. Do not forget about antiseptic and fireproof impregnation for them, as this affects the durability of the roof.

The system consists of rafter legs. Install the rafters at an angle of inclination of the roof slopes. The lower sections of the rafter legs rest on external walls with the help of a Mauerlat, which contributes to an even distribution of the load. The upper ends of the rafters are supported on a bar under the ridge or on intermediate fittings. The strut system transfers the load to the load-bearing internal walls.

Types of rafters

The structure transfers a significant horizontal expansion force to the walls. In order to reduce the load, a stretch is used, with the help of which the rafter legs are connected. They do it either at the base of the rafters, or on greater height... The stretch at the base of the rafters is at the same time the floor beam - this is important when creating mansard roofs. With an increase in the height of the brace location, it is necessary to increase its power and make sure that it is securely attached to the rafters.

Part layered rafters includes: rafter leg, mauerlat, headstock, brace, tightening. This type of rafter is installed in buildings in which there is a middle load-bearing wall or intermediate supports in the form of pillars. Elements of this design work only for bending, performing the function of the heads. The slab rafter system is lighter and requires less materials and is therefore less expensive than a hanging system.

Installation of a layered system is done if the supports are no more than 6.5 meters apart from each other. If there is an additional support, the rafters sometimes overlap the width of 12 meters, and if there are two supports, up to 15 meters.

Rafter legs are most often based not on the walls of the building, but on a special beam - the Mauerlat. This element can be located along the entire length of the house or be placed only under the rafter legs. If the structures are wooden, a log or timber is taken for the Mauerlat, which is the upper crown of the log house.

At brickwork Mauerlat walls are a bar installed flush with the inner surface of the walls, fenced off from the outside by a masonry ledge. A layer of waterproofing is laid between this element and the brick - for example, roofing material can be put in two layers.

If the width of the rafters is small, they can sag over time. To prevent this from happening, use a lattice consisting of a rack, a crossbar and struts. At the top of the structure, a girder is laid, which connects the rafters or trusses. This is done regardless of the type of roof. Subsequently, on this run, the roof ridge is made. In places where there are no load-bearing walls, the heels of the rafters rest against the side girders - longitudinal beams significant power. The dimensions of these parts depend on the expected load.

In the construction of private houses, log rafters are used - they are lighter. To create roofs on multi-storey residential buildings and industrial buildings, metal rafters are used.

Installation of roof systems

The slope angles of the slopes are selected based on the type of building and the purpose of the attic space. The amount of slope is also influenced by the material chosen to create the roofing.

If roll products are to be stacked, the angle of inclination should be 8-18 degrees. For tiles, the required angle is 30-60 degrees, for roofing steel or asbestos-cement sheets - 14-60 degrees.

The installation of the rafter system begins after the erection of the load-bearing walls of the house (for more details: ""). The design of the rafters of a wooden log house differs significantly from the systems for houses made of foam-gas concrete, brick, frame wooden or panel houses. The differences are significant even with the same shape, type and type of roof. As for how to treat the rafter system, it is necessary to use antiseptic and fire-fighting agents so that the roof will last for a long time.

The main elements of the supporting structure are the lathing. The roof is the outer part of the roof, which is laid on a supporting structure consisting of battens and rafters.

For the production of rafters, material of a certain size is taken. So, the thickness of the rafters (section) is most often 150x50 and 200x50 millimeters. For the lathing, they usually take beams and boards measuring 50x50 and 150x25 millimeters. The distance between the rafter legs is on average 90 centimeters. If the slope of the roof is more than 45 degrees, this step is increased to 100-130 centimeters, and if a huge amount of snow falls in the region, then it is reduced to 60-80 centimeters.

To make more accurate calculations regarding the gap between the construction legs, you need to take into account their cross section, the step between the supports (struts, ridge run, uprights), and the type of roofing material.

The floating rafter system is attached with special brackets that allow the rafters to "sit down" together with the shrinkage of the gables and not hang over the ridge log.

In mountainous areas, the chalet rafter system is popular (in more detail: ""). A feature of this design is the significant roof protrusion beyond the bearing walls. Sometimes such a ledge reaches two to three meters, and the angle of the roof slope is small. Snow does not linger on such a roof, so it serves for a long time. But the best option is a 1-1.5 meter roof overhang (also read: "Roof Characteristics and Construction: Rafter Systems").

The installation of the rafter system must be carried out, strictly observing all the requirements. If you do not have experience in construction, it is better to entrust the construction of the roof to specialists, since this is not an easy task, and the slightest mistakes can lead to its collapse.

Let the construction of the rafter system seem quite simple, but it requires accurate mathematical calculations. Correct dimensions elements of the supporting structure will not allow the roof to be fragile and save the owner of the house from excessive spending.

Calculation of the parameters of the rafter system

The rafter system is formed not only by the rafter legs. The design includes a Mauerlat, struts, struts and other elements, the dimensions of which are strictly standardized. The fact is that the components of the rafter system are supposed to withstand and distribute certain loads.

Elements of the truss system simple gable roof- these are rafters, a run (ridge board), racks, a bed, a mauerlat and rafter legs (struts)

It is a four-bar structure that connects brick, concrete or metal walls of a house to a timber supporting structure of the roof.

The Mauerlat bar should occupy 1/3 of the space at the top of the wall. The optimal section of this lumber is 10x15 cm.But there are others suitable options, for example, 10x10 or 15x15 cm.

The main thing is not to take bars less than 10 cm wide to create a Mauerlat, as they will greatly fail in terms of strength. But lumber with a width of more than 25 cm in reliability will not cause doubts, however, it will put pressure on the house so that it will soon begin to collapse.

Mauerlat must be narrower than the walls, otherwise it will exert excessive pressure on the walls

The ideal length of the base for the truss system is equal to the length of the wall. It is not always possible to comply with this condition, therefore, it is permissible to construct a Mauerlat from segments completely or at least approximately the same in length.

Lezhen acts as an element of the rafter system, which is in a recumbent position and serves as the basis for the rack (headstock) of the roof supporting structure.

A bar of the same section as the Mauerlat is usually taken as a bed. That is optimal size horizontal element on the internal load-bearing wall - 10x10 or 15x15 cm.

The size of the bed does not differ from the Mauerlat

Ridge bar

Due to the size of the ridge beam, against which the rafters abut with the upper end, the weight of the roof should not go beyond the permissible limits. This means that for the ridge it is required to take a beam that is quite strong, but not heavy, so that other elements of the roof supporting structure do not bend under its pressure.

The most suitable pine lumber for the ridge of the roof is a beam with a section of 10x10 cm or 20x20 cm, as in the structure racks.

The ridge girder should not be thicker than the rafter system

Filly

A filly is a board that extends the rafter if it is unacceptably short.

When using fillies, the rafter legs are cut flush with outside wall... And the boards that lengthen them are selected in such a way that they form the necessary overhang of the roof and are not thicker than the rafters themselves.

An extra 30-50 cm must be added to the length of the filly, which will go to combine the rafters with an additional board and make the connection of the frame and the roof overhang as strong as possible.

In thickness, the filly is inferior to the rafter leg

Racks

The stand is the same as the center support. Height vertical bar in the rafter system, it is customary to find by the formula h = b 1xtgα - 0.05. h is the height of the post, b 1 is half the width of the house, tgα is the tangent of the angle between the rafter and the mauerlat, and 0.05 is the approximate height of the ridge beam in meters.

The main requirement for the racks is stability, therefore, as they are chosen thick, like a bed, beams

A brace is an element of the rafter system, which at an angle of at least 45 ° (with respect to the horizontal cut of the walls) is mounted on one end on the rafter, and on the other - on a tightening, laid in the direction from one wall of the house to another, close to the vertical rack.

The length of the brace is determined by the cosine theorem, that is, by the formulaa² =b² +c² - 2xbxcxcosα for a flat triangle. a is the length of the brace, b is part of the length of the rafter, c is half the length of the house, and α is the angle opposite side a.

The length of the brace depends on the length of the rafter and the house

The width and thickness of the braces must be identical to the same dimensions for rafter leg... This will greatly facilitate the task of securing the element in the roof frame.

The brace is installed at the base of the rafter system and plays the role of a floor beam. The length of this element is determined by the length of the building, and its section does not differ from the parameter of the rafter legs.

The tightening in another way can be called a ceiling lag

A sliding support or element of the rafter system that allows it to adapt to a change in configuration must be characterized by the following parameters:

• length - from 10 to 48 cm;
• height - 9 cm;
• width - 3-4 cm.

The size sliding bearing should allow good fixation of the rafters on the base of the roof

Rafter boards or beams

The size of the boards that will become the roof rafters with symmetrical slopes is not difficult to determine. This will help the formula from the Pythagorean theorem c² = a² + b², where c acts as the required length of the rafter leg, a denotes the height from the base of the roof to the ridge beam, and b - ½ part of the width of the building.

The parameters of the rafters, differing in asymmetry, are also recognized by the Pythagorean formula. However, the indicator b in this case will no longer be half the width of the house. This value will have to be measured separately for each slope.

Using the Pythagorean formula, you can calculate both the length of the rafters and the height of the rack

Rafters are usually boards with a thickness of 4 to 6 cm. The minimum parameter is ideal for utility buildings, such as garages. And the truss system of ordinary private houses is created from boards 5 or 6 cm thick. The average width of the main elements of the supporting structure of the roof is 10-15 cm.

With a large step and considerable length, the cross-section of the rafters will certainly increase. For example, when the distance between the legs of the roof supporting structure reaches 2 m, a section of 10 × 10 cm is chosen for the rafters.

The length of the rafter is influenced by the degree of inclination of the roof and the length of the space between the walls located opposite each other. With an increase in the slope of the roof, the length of the rafter leg increases, as does its section.

The size of the rafters is due to the size of the gap between them.

Table: correspondence of the length of the rafter leg to its thickness and step

Rafter angle

The value of the rafter angle is determined by the formula α = H / L, where α is the angle of inclination of the roof, H is the height of the ridge beam, and L is half the span between the opposite walls of the house. The resulting value is converted into percentages according to the table.

How the rafters are tilted depends on two indicators - the height of the ridge and the width of the house.

Table: determining the angle of the rafters in percent

Video: calculating the size of the rafter legs

For each element of the rafter system, there is an average size data. They can be guided by, however, it is better to calculate the parameters of racks, struts and other components of the supporting structure of the roof in special programs on a computer or using complex geometric formulas.

The calculation of the rafter system must be carried out with the utmost accuracy, guided by the characteristics of the construction site, the planned load on the rafter system, the size and configuration of the building, as well as the materials used to overlap the roof. This article will discuss how to calculate the length of the roof rafters.

Loads experienced by rafters

For a pitched roof, a strong frame must be created, which is its supporting structure. Even during the design, the rafter leg must be calculated in order to determine the length and section of the elements that will bear the main loads.

The loads that act constantly are created by the roofing cake itself, which includes the outer roofing material, lathing, heat, steam and waterproofing material, as well as inner lining attic or attic. These loads also include the weight of various objects that will be located on the roof or fixed on the inside of the rafter system.

Variable loads consist of effects that are generated by wind, precipitation, and seismic activity. This also includes the weight of a person who will carry out repairs, scheduled maintenance or cleaning the roof in the future.

Calculation of the mass of the roofing cake

Before calculating the length of the rafter leg, you will need to calculate the mass roofing cake... To do this, you will need to take a simple formula by which you need to add the masses of one square meter of all layers of roofing materials, and the result is multiplied by 1.1 - the correction factor, which will improve the reliability of the structure by 10%.

It turns out that the usual calculation of the mass of the roof can be expressed as follows: (mass of 1 m 2 of lathing + mass of 1 m 2 of roofing material + mass of 1 m 2 of waterproofing coating + mass of 1 m 2 of insulation layer) × 1.1 = mass of roofing cake, which includes correction factor. If you plan to lay one of the common roofing, then the load on the rafter system will not go beyond 50 kg / m 2.

When creating a project of a shed or gable roof, it is enough to rely only on the mass of the roofing cake, equal to 50 kg / m 2. According to this principle, a roof frame of increased strength can be built so that in the future it is possible to change the type of roofing material without recalculating the rafter system.

Snow and wind loads by example

The length of the rafter leg should be selected in such a way that the roof can withstand heavy loads of snowfall. The snow will press on the roof the stronger, the smaller the slope angle it has. If an almost flat single-pitched roof is being erected, then the cross-section of the rafter legs should be as large as possible, and their step should be as small as possible. In addition, if the slope of the roof is less than 25º, it will need to be cleaned systematically.

• Sg is the value of snow cover per 1 m 2, which is selected from the SNiP tables, and is determined by the region in which the house is being built;

• µ - correction factor, which depends on the angle of inclination of the roof: for a slope with a slope of up to 25 ° - 1.0; and for a slope with slopes of 25-60 ° - 0.7.

For those slopes, the angle of inclination of which is more than 60 °, snow loads are not taken into account.

Wind loads can be calculated using the formula W = Wo × k, where:

• Wo is a reference value for your region (can be found in reference tables);

• k is a correction factor, which is determined by the height of the building and the type of terrain - open type (field, steppe or coast), or closed (forest, building).

Dependence of the length of the rafter leg and the section

For example, the calculation of the rafter leg will be easier if you imagine that almost the entire roof consists of triangles. Having the length of the walls of the building, the slope of the slope or the height of the ridge, and using the Pythagorean theorem, you can determine the length of the rafter leg from the wall to the ridge. To the result obtained, you will need to add the value of the eaves overhang. Sometimes the eaves overhang is created by mounting fillies - boards to increase the length of the rafters. The length of the fillies will also be added to the length of the rafters when calculating the roof area - this is necessary to obtain the exact amount of material needed to install the roofing pie.

In order to understand what section a board or timber is needed, you need to take a special table of standards, which will indicate the dependencies of such parameters as the thickness, length and step of the rafter leg.

As a rule, the cross-section of the rafters ranges from 40 × 150 mm to 100 × 250 mm. Before determining the length of the rafters, you need to take into account that it depends on the slope of the ramp and the length of the span between opposite walls. The greater the slope of the slope, the longer the rafters should be, which means that their cross-section should also be sufficient to give the structure the necessary strength. With this approach, the load from snowfall will decrease, and the step between the rafters can also be increased. It must also be remembered that the smaller the step between the rafters, the greater the load the rafter leg will experience.

Each master, whom you ask to give an example of calculating rafters, will tell you that in order for the roof frame to be as strong as possible, you need to take into account the characteristics of the wooden elements and the thickness of the metal nodes.

The load-bearing part of the roof must be rigid enough so that it does not buckle due to loads. Deflections can appear if during the design the wrong sections of the roofing elements and the step of installing the rafters were selected. If it turns out that the deflection appeared after installing the roof, you can install additional struts in order to make the structure more rigid. With a rafter leg length of more than 4.5 m, without installing struts, deflection may appear when using rafter legs of any section. This must be taken into account in any case, when determining how to calculate the length of the rafter.

In general, being determined with the thickness of the timber, they are repelled from the total load on the roof. The thicker it is, the stronger the roof will be, and there will be no need to worry about sagging. However, this leads to an increase in the total mass of the rafter system, therefore, the loads on the entire structure and foundation will be higher.

When constructing residential buildings, the step between the rafters is from 60 to 100 cm and is determined by:

• calculated load;
• cross-section of rafters;
• the type of roofing used;
• slope of the slopes;
• the width of the thermal insulation layer.

The number of installed rafter legs depends, first of all, on the step of their installation. First, the desired step is determined, after which the length of the wall is divided by the obtained value, one is added to the result and rounded. The result of dividing the length of the wall by the resulting number will be the step we are looking for between the rafters. Given the required number of rafters on one slope, you need to take into account the distance between the axes of the rafter legs.

Metal truss systems

When building a private house, he rarely resorts to the use of a metal rafter system, because the metal frame must be installed using welding, and this somewhat complicates the process. Naturally, the manufacture of the structure can also be carried out at production facilities, but in this case one cannot do without the involvement of special equipment. Project metal roof must be created with maximum accuracy, observing the exact dimensions of all elements, since during the construction process they must be adjusted to required sizes the opportunity will no longer be presented.

Metal rafter systems have many advantages. During operation, there is no deflection of the rafters, even on large spans and without the installation of additional nodes to improve strength and reliability. Steel rafters can be laid on spans exceeding 10 m, while under the design loads, deflection will not occur.

When calculating a rafter system made of steel profiles, take into account the mass of the material itself, the load on the entire structure and foundation. The high strength of the rafters made of such a material, which allows the structure to not bend, makes it possible to reduce the number of nodes in comparison with elements made of wood.

In addition, it is necessary to calculate the steel frame for the roof based on the data on the strength of structural elements, which is determined by their shape and thickness. Consider also the length of the spans and the slope of the slopes. The Mauerlat steel for the rafter system must be carefully fixed to the top of the wall.

The above material will allow you to understand in detail how to calculate the rafter leg, so that you can complete everything without any problems construction works at this stage, and you will have your own example of calculating the rafter system.

Design and competent calculations of elements truss structure- the key to success in the construction and subsequent operation of the roof. She is obliged to staunchly resist the combination of temporary and permanent loads, while making the building as heavy as possible.

For the production of calculations, you can use one of the many programs laid out on the network, or do everything manually. However, in both cases, it is required to clearly know how to calculate the rafters for the roof in order to thoroughly prepare for the construction.

The rafter system determines the configuration and strength characteristics of the pitched roof, which performs a number of significant functions. It is a responsible enclosing structure and an important component of the architectural ensemble. Therefore, in the design and calculations of rafter legs, flaws should be avoided and try to eliminate shortcomings.

As a rule, in design development, several options are considered, from which the optimal solution is selected. Choice best option does not mean at all that you need to compose a certain number of projects, perform accurate calculations for each and, in the end, prefer the only one.

The very course of determining the length, mounting slope, section of the rafters consists in scrupulous selection of the shape of the structure and the size of the material for its construction.

For example, in the formula for calculating the bearing capacity of a rafter leg, the parameters of the section of the most suitable material for the price are initially entered. And if the result does not meet technical standards, then the size of the lumber is increased or decreased until they achieve maximum compliance.

Slope search method

Determining the slope angle of a pitched structure has architectural and technical aspects. In addition to the proportional configuration, the most suitable for the style of the building, an impeccable solution must take into account:

• Snow load indicators. In areas with abundant precipitation, roofs are erected with a slope of 45 degrees or more. Snow deposits do not linger on slopes of such steepness, due to which the total load on the roof is noticeably reduced, and the building as a whole is stalled.
• Wind load characteristics. In areas with choppy strong winds, coastal, steppe and mountainous areas, erect low-pitched structures of a streamlined shape. The steepness of the slopes there usually does not exceed 30º. In addition, the winds prevent the formation of snow deposits on the roofs.
• Weight and type of roofing. The more weight and finer the elements of the roof, the steeper you need to build the truss frame. This is necessary in order to reduce the likelihood of leaks through the joints and to reduce the specific gravity of the coating per unit of the horizontal projection of the roof.

In order to choose the optimal angle of inclination of the rafters, the project must take into account all the listed requirements. The steepness of the future roof must correspond to the climatic conditions of the area selected for construction and the technical data of the roofing.

True, property owners in the northern calm areas should remember that with an increase in the angle of inclination of the rafter legs, the consumption of materials increases. Building and equipping a roof with a steepness of 60 - 65º will cost approximately one and a half times more than erecting a structure with an angle of 45º.

In areas with frequent and strong winds, do not cut the slope too much in order to save money. Excessively sloping roofs lose in architectural terms and do not always contribute to lower costs. In such cases, reinforcement of the insulating layers is most often required, which, contrary to the expectations of the economist, leads to an increase in the cost of construction.

The slope of the rafters is expressed in degrees, as a percentage, or in dimensionless units, reflecting the ratio of half the span of the span to the installation height of the ridge girder. It is clear that the degrees delineate the angle between the line of the ceiling and the slope line. Percentages are rarely used because of the complexity of their perception.

The most common method of designating the angle of inclination of rafter legs, used by both designers of low-rise buildings and builders, is dimensionless units. They represent the ratio of the length of the span to be covered to the height of the roof in shares. At the facility, it is easiest to find the center of the future gable wall and install a vertical rail in it with a ridge height mark than to postpone corners from the edge of the slope.

Calculation of the length of the rafter leg

The length of the rafters is determined after the angle of inclination of the system has been selected. Both of these values ​​cannot be attributed to the number of exact values, since in the process of calculating the load, both the steepness and following it, the length of the rafter leg may change somewhat.

The main parameters affecting the calculation of the length of the rafters include the type of eaves overhang, according to which:

1. The outer edge of the rafter legs is trimmed flush with the outer surface of the wall. The rafters in this situation do not form a cornice overhang that protects the structure from precipitation. To protect the walls, a drain is installed, fixed on a cornice board nailed to the end edge of the rafters.
2. The rafters, cut flush with the wall, are built up by fillets to form a cornice overhang. The filly is fastened to the rafters with nails after the construction of the rafter frame.
3. The rafters are initially cut taking into account the length of the eaves. In the lower segment of the rafter legs, cuttings are chosen in the form of an angle. To form the cuts, they retreat from the lower edge of the rafters to the width of the eaves. The cuts are needed to increase the support area of ​​the rafter legs and for the device of support nodes.

At the stage of calculating the length of the rafter legs, it is required to think over the options for attaching the roof frame to the Mauerlat, to the bypasses or to the upper crown of the log house. If you plan to install the rafters flush with the outer contour of the house, then the calculation is carried out along the length of the upper edge of the rafter, taking into account the size of the tooth, if it is used to form the lower connecting node.

If the rafter legs are cut taking into account the eaves, then the length is calculated along the upper edge of the rafters together with the overhang. Note that the use of triangular cuts significantly accelerates the pace of construction of the rafter frame, but weakens the elements of the system. Therefore, when calculating the bearing capacity of rafters with a selected angle of cuttings, a coefficient of 0.8 is used.

The traditional 55 cm is recognized as the average width of the eaves removal. However, the spread can be from 10 to 70 and more. The calculations use the projection of the eaves on the horizontal plane.

There is a dependence on the strength characteristics of the material, on the basis of which the manufacturer recommends limit values. For example, slate manufacturers advise against extending the roof beyond the wall contour for a distance of more than 10 cm, so that the snow mass accumulating along the roof overhang cannot damage the edge of the cornice.

It is not customary to equip steep roofs with wide overhangs, regardless of the material, the cornices are not made wider than 35 - 45 cm. But structures with a slope of up to 30º can perfectly complement a wide cornice, which will serve as a kind of canopy in areas with excessive sunlight. In the case of designing roofs with eaves of 70 cm or more, they are reinforced with additional support posts.

How to calculate the bearing capacity

In the construction of truss frames, lumber made of coniferous wood is used. The harvested timber or board must not be lower than the second grade.

Rafter legs pitched roofs work on the principle of compressed, curved and compressed-curved elements. The second-class wood copes with the tasks of resistance to compression and bending excellently. Only if the structural element will work in tension is the first grade required.

Rafter systems are arranged from a board or a bar, they are selected with a margin of safety, focusing on the standard dimensions of the lumber produced in-line.

Calculations of the bearing capacity of rafter legs are carried out in two states, these are:

• Estimated. A condition in which a structure collapses as a result of an applied load. Calculations are carried out for the total load, which includes the weight of the roofing cake, the wind load, taking into account the number of storeys of the building, the mass of snow, taking into account the slope of the roof.
• Normative. A condition in which the rafter system bends, but the destruction of the system does not occur. It is usually impossible to operate the roof in this state, but after carrying out repair operations, it is quite suitable for further use.

In a simplified design, the second state is 70% of the first value. Those. to obtain the standard indicators, the calculated values ​​must be corny multiplied by a factor of 0.7.

The loads, depending on the climatic data of the construction region, are determined according to the maps attached to SP 20.13330.2011. The search for standard values ​​on maps is extremely simple - you need to find the place where your city, cottage village or other nearest settlement is located, and take readings about the calculated and standard value from the map.

The average information about snow and wind loads should be adjusted according to the architectural specifics of the house. For example, the value taken from the map must be distributed along the slopes in accordance with the wind rose compiled for the area. You can get a printout from your local weather service.

On the windward side of the building, the mass of snow will be much less, therefore, the calculated indicator is multiplied by 0.75. On the leeward side, snow deposits will accumulate, so multiply here by 1.25. Most often, in order to unify the material for building a roof, the leeward part of the structure is constructed from a paired board, and the windward part is arranged with the rafters of their single board.

If it is not clear which of the slopes will be on the leeward side, and which is the opposite, then it is better to multiply both by 1.25. The safety margin does not hurt at all, if it does not increase the cost of the lumber too much.

The calculated snow weight indicated by the map is also adjusted depending on the steepness of the roof. From the slopes set at an angle of 60º, the snow will immediately slide without the slightest delay. In the calculations for such steep roofs, the correction factor is not applied. However, with a lower slope, snow can already be trapped, therefore, for slopes of 50º, an additive is used in the form of a coefficient of 0.33, and for 40º it is the same, but already 0.66.

The wind load is determined in the same way according to the corresponding map. The value is adjusted depending on the climatic specifics of the area and on the height of the house.

To calculate the bearing capacity of the main elements of the projected rafter system, it is required to find the maximum load on them, summing up the temporary and constant values. No one will strengthen the roofs before the snowy winter, although in the country it would be better to put safety vertical struts in the attic.

In addition to the mass of snow and the pressing force of the winds in the calculations, it is necessary to take into account the weight of all elements of the roofing pie: the sheathing installed on top of the rafters, the roof itself, insulation, inner lining, if used. The weight of vapor and waterproofing films with membranes is usually neglected.

Information on the weight of materials is indicated by the manufacturer in the technical data sheets. The data on the mass of the bar and the board are taken as an approximation. Although the mass of the lathing per meter of projection can be calculated based on the fact that a cubic meter of sawn timber weighs on average 500 - 550 kg / m 3, and a similar volume of OSB or plywood from 600 to 650 kg / m 3.

The load values ​​given in SNiPs are indicated in kg / m 2. However, the rafters perceive and hold only the load that directly presses on this linear element. In order to calculate the load on the rafters, the set of natural tabular values ​​of the loads and the mass of the roofing cake is multiplied by the step of installing the rafter legs.

The load value reduced to linear parameters can be reduced or increased by changing the step - the distance between the rafters. By adjusting the load collection area, its optimal values ​​are achieved in the name of the long service life of the pitched roof frame.

Determination of the cross-section of the rafters

The rafter legs of roofs of various steepness do an ambiguous job. The bending moment acts mainly on the rafters of shallow structures; on the analogs of steep systems, a compressive force is added to it. Therefore, in the calculations of the cross-section of the rafters, the slope of the slopes must be taken into account.

Calculations for structures with a slope up to 30º

Only bending stress acts on the rafter legs of the roofs of the specified steepness. They are calculated for the maximum bending moment with the application of all types of load. Moreover, temporary, i.e. climatic loads are used in calculations based on maximum values.

For rafters that have only supports under both their own edges, the point of maximum bend will be in the very center of the rafter leg. If the rafter is laid on three supports and is composed of two simple beams, then the moments of maximum bending will fall in the middle of both spans.

For a solid rafter on three supports, the maximum bend will be in the area of ​​the central support, but since there is a support under the bending section, then it will be directed upward, and not, as in the previous cases, downward.

For normal operation of the rafter legs in the system, two rules must be followed:

• The internal stress formed in the rafter during bending as a result of the load applied to it must be less than the calculated value of the bending resistance of the sawn timber.
• The deflection of the rafter leg must be less than the normalized deflection value, which is determined by the ratio L / 200, i.e. the element is allowed to bend only one two hundredth of its real length.

Further calculations consist in the sequential selection of the dimensions of the rafter leg, which, as a result, will satisfy the specified conditions. There are two formulas for calculating the cross section. One of them is used to determine the height of a board or timber by an arbitrary specified thickness. The second formula is used to calculate the thickness at an arbitrary height.

In calculations, it is not necessary to use both formulas, it is enough to apply only one. The result obtained as a result of the calculations is checked according to the first and second limit state... If the calculated value turned out with an impressive margin of safety, an arbitrary indicator entered into the formula can be reduced so as not to overpay for the material.

If the calculated value of the bending moment is greater than L / 200, then the arbitrary value is increased. Selection is carried out in accordance with standard sizes commercially available lumber. This is how the section is selected until the moment when the optimal version is calculated and obtained.

Let's consider a simple example of calculations using the formula b = 6Wh². Suppose h = 15 cm, and W is the ratio M / R out. We calculate the M value using the formula g × L 2/8, where g is the total load vertically directed to the rafter leg, and L is the span length equal to 4 m.

R iz for sawn softwood is taken in accordance with technical standards 130 kg / cm 2. Suppose we calculated the total load in advance, and we got it equal to 345 kg / m. Then:

M = 345 kg / m × 16m 2/8 = 690 kg / m

To convert to kg / cm, divide the result by 100, we get 0.690 kg / cm.

W = 0.690 kg / cm / 130 kg / cm 2 = 0.00531 cm

B = 6 x 0.00531 cm x 15 2 cm = 7.16 cm

We round the result as it should be in the big direction and we find that for the device of rafters, taking into account the load given in the example, a beam of 150 × 75 mm is required.

We check the result for both states and make sure that the material with the cross section calculated now is suitable for us. σ = 0.0036; f = 1.39

For roof systems with a slope over 30º

The rafters of roofs with a steepness of more than 30º are forced to resist not only bending, but also the force compressing them along their own axis. In this case, in addition to checking the bending resistance described above and by the amount of bending, it is necessary to calculate the rafters by internal stress.

Those. actions are performed in a similar order, but there are slightly more verification calculations. In the same way, an arbitrary height or arbitrary thickness of the lumber is set, with its help the second parameter of the section is calculated, and then a check is carried out for compliance with the above three technical conditions, including the compression resistance.

If it is necessary to increase the bearing capacity of the rafters, the arbitrary values ​​entered into the formulas are increased. If the safety margin is large enough and the standard deflection significantly exceeds the calculated value, then it makes sense to perform the calculations again by reducing the height or thickness of the material.

To select the initial data for the production of calculations, a table will help, which summarizes the generally accepted sizes of lumber we produce. It will help you choose the section and length of the rafter legs for the initial calculations.

Video about the calculations of rafters

The video clearly demonstrates the principle of performing calculations for the elements of the rafter system:

Calculating the load-bearing capacity and rafter angle is an important part of the roof frame design. The process is not easy, but it is necessary to understand it both for those who make calculations manually and for those who use the calculation program. You need to know where to get tabular values ​​and what the calculated values ​​give.