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

One of the types of rafter roofing is gable. This is a fairly simple system, which is formed by two slopes. The roof slope is everything inclined plane, with the help of which drainage is provided.

The structure rests on two parallel walls. This roof forms two triangular side gables. The pediment is the completion of the facade of the building.

Advantages of a gable system

1. Ease of design.
   Calculation bearing capacity and the necessary materials for installing such a roof are quite simple, since there are options for types and sizes load-bearing structures A little;
2. Easy to install.
   A gable roof does not have complex structural elements. A small number of standard sizes allows you to quickly install all roof elements;
3. Ease of use.
   The fewer different kinks a roof has, the more reliably it protects the home. In its simplest design, a gable roof has only one break - the ridge. Such a roof is easier to repair in case of defects;
4. Free space.
   For arranging an attic, a gable roof is preferable, since it “eats up” less space. 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 gable roof under such conditions, the volume of the room will be 81 cubic meters, and for a hip room with four slopes, 72 cubic meters. For large sizes building volume losses will increase.

Types of structures

There are four main types of gable roofs:

1. Symmetrical.
   Reliable, stable, easy to implement, based on an isosceles triangle;
2. Asymmetrical.
   The ridge is not located in the center, the roof slopes have different slopes;
3. Broken symmetrical.
   The roof slopes have a kink. Significantly increases the height of the room;
4. Broken asymmetrical.
   The attic or attic space turns out to be 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 below it and the architectural appearance of the building.

General principles for calculating the rafter system

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

The crossbar and rafter legs experience a bending moment.

Such structures are calculated based on strength and rigidity. For small buildings, you can choose their cross-section approximately, but for serious buildings, for the sake of safety and saving material, the calculation of the rafter system should be performed by a professional.

Load from the roof's own weight

To perform the calculation you need to know the load per 1 square meter. roofs.

To do this, you need to add up masses of 1 square meter. all roofing materials:

1. binder(if it exists, it is most often made of plasterboard);
2. rafter legs. To calculate the weight of the rafters square meter roofing, you need to find the mass per linear meter rafter leg and divide this number by the pitch of the rafters in meters. For calculation, you can take the approximate cross-section of the rafters; the area of ​​this cross-section must be multiplied by the density of the wood;
3. insulation (if any). The density of the insulation must be indicated by the manufacturer, it must be multiplied by the thickness;
4. sheathing. To ensure a reserve, you can take into account a continuous sheathing. For example, 1 sq.m. sheathing made from boards 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 is different for each area and is equal to the weight of the snow cover on a horizontal plane.

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

Roof angle

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 hand. personal computer.

If you divide the height of the roof by the distance from the ridge to the eaves in plan, you get the slope of the roof in fractions or the tangent of the angle of inclination. In order to calculate the angle, you just need to find the arctangent.

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

Calculation of rafter pitch

Rafter pitch mansard roof should be chosen for 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 clear distance between them is 58 or 118 centimeters. Two centimeters will allow you to install the insulation boards very tightly, which will allow it to stay between the rafters and improve thermal insulation.

Rafter leg length

Leg length can be easily calculated using the formula:
L/cosα,
here L is the distance from the roof ridge to inner surface outer wall in plan, and cosα is the cosine of the roof inclination angle. For rigid fastening, you need to increase 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 beams.

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

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

To solve, you need to set 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 not practical.

To calculate rafter systems, there are all kinds of tables, programs, and online calculators.

Basic roof elements

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

Rafter roof with attic

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

Attic floor- This is a floor in the attic space. The attic façade is formed entirely or partially 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 regular floor.

The roof of the attic floor differs from the roof of the attic in the presence of insulation in its design. Most often for insulation mansard roof mineral wool boards are used.

Lighting attic space can be done in three ways:

1. window openings in gables;
2. dormer windows;
3. attic windows.

Dormer window – This window design, which has a frame mounted simultaneously with the rafter system. This frame is made of wood. The dormer window has its own small roof, which can be gable or cylindrical. The glass unit itself is installed vertically.

Dormer window- This is a window specifically designed for use on rafter roofs. 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 window in roofs with a slight slope.

Selection of roofing material

Once the appearance of the roof has been determined, you can begin to select the material. There are several types modern coatings. In the list below, material options are listed in descending order of average market cost.

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 large mass. Under a roof made of ceramic tiles, you will have to install a reinforced rafter system and sheathing;
2. Cement-sand tiles.
   It has almost all the characteristics of ceramic, but costs a little less;
3. Flexible bitumen shingles.
   Has good soundproofing characteristics. Thanks to the rough surface, the tiles are able to prevent snow from moving off the roof. Requires continuous sheathing, a layer of moisture-resistant plywood is usually used. Cannot be used on roofs with large slopes;
4. Metal tiles.
   Compared to previous coatings, it is lighter in weight. Easy to install. Minus metal roofing is that when it rains it can be too noisy.
5. Seam roofing.
   The most attractive option in terms of cost. Requires special qualifications during installation, since it will be difficult for a non-professional to make high-quality connections. Installation is more labor-intensive than metal and flexible tiles. The same “noisy” as metal tiles.

The roofing material completely depends on the wishes and capabilities of the customer. The exception is roofs with too large or too small a slope, since all materials have limitations on the angle of inclination of the slope.

Types of rafter systems

Structural roof truss systems can be of three types:

1. Layered rafters.
   The rafters rest on two sides. From below - on the mauerlat, from above - on the crossbar. As intermediate supports Racks and struts can be used. Most often used in buildings with a small distance between the ends or where it is possible to place racks or a wall in the middle of the attic.
   For large rafter spans (large distances between longitudinal walls), racks, struts or tie rods can be additionally used.
   Layered rafters are easy to calculate.
   Typically, the most powerful element of such a system is the crossbar, which carries half the load of the entire roof structure.
2. Hanging rafters.
   If it is not possible to use the crossbar as an upper support, it is reasonable to use this rafter system.
   The hanging rafters rest only on the mauerlat, and at the top point they are connected to each other using an overlay.
   This rafter system operates under load like a truss. The greatest pressure occurs on the outer walls. A horizontal force arises - thrust, which can lead to displacement of the walls. In the design of hanging rafters, the spacer force is absorbed by the tightening, which tightens the rafter legs and prevents them from moving apart.
   Hanging rafters are classified depending on the location of the tie:
   1) Triangular three-hinged arch.
   The tie and rafters form a triangle. The tightening is located at the ceiling level;
   2) Triangular three-hinged arch with suspension.
   With a large span of rafters, the tightening may not meet the deflection requirements. To prevent it from sagging, the tie is suspended from the ridge. But with such a system, just as with the system of layered rafters, a row of racks is formed in the middle of the attic;
   3) Triangular three-hinged arch with a raised drawstring.
   The tightening is most often located at the ceiling level of the attic room. This scheme is less beneficial from the point of view of the operation of the structure. The higher the tightening is located, the more thrust it absorbs.
   Hanging rafters must be treated as a triangular truss, which complicates the calculation.
3. Combined rafters.
   TO combined system can be attributed to spacer layered rafters. They require both bolt installation and tightening. Unlike previous options, in which the rafters are hinged to the mauerlat, here the rafter leg is rigidly attached, so a thrust appears 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 build around the perimeter of a reinforced concrete belt.

Installation of the rafter system

Installation occurs in the following order:

1. laying the Mauerlat;
2. installation of a crossbar (if there is one);
3. rafter layout;
4. insulation (if any);
5. sheathing;
6. roofing material.

Attaching the rafter leg to the mauerlat can be rigid and hinged.

Hinge fastening

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. A cut is made 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 is securely fixed with nails driven at an angle relative to each other. One nail is driven vertically onto the surface of the Mauerlat. This connection eliminates displacement in any plane.

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

Rafters are the basis of any roof. They bear the main load associated with the weight of the roof, wind and snow pressure. For long-term and trouble-free operation of the roof, it is important to make accurate calculations of these loads, determine the strength characteristics of the rafters, their cross-section, length, quantity, as well as the volume of material required for the arrangement roof frame. All these calculations can be done independently.

Calculation of rafters using online programs

The easiest way to calculate rafters is with an online calculator. You specify the initial data, and the program calculates the necessary parameters. Existing programs vary in their functionality. Some of them are complex in nature and calculate many parameters of the rafter system, others are much simpler and involve the calculation of one or two indicators. Among the comprehensive services, we should highlight the Stroy-calc series of construction calculators for calculating the parameters of roof rafters with one and two slopes, an attic and hips.

The Stroy-calc calculator is used to calculate the parameters of roof rafters with one, two slopes, an attic and hips

The program also takes into account roofing material, i.e., together with the calculation of the rafter system, you can obtain data on the required quantity finishing coating from:

• ceramic tiles;
• cement-sand tiles;
• bitumen shingles;
• metal tiles;
• slate (asbestos-cement slabs);
• steel seam roofing;
• bitumen slate.

In order to obtain the required result, the following information is entered:

• roof characteristics: roofing material, base width, base length, rise height, overhang length;
• rafter characteristics: rafter pitch, type of wood for rafters;
• characteristics of the sheathing: width, board thickness, distance between rows;
• snow load on rafters: select the region of snow load on the map.

The program contains drawings of roof types, which show data entry parameters in graphical form. The result displays information on:

• roof - angle of inclination, surface area, approximate weight of roofing material;
• rafters - length, minimum cross-section, quantity, volume of timber for rafters, their approximate weight, layout (drawing);
• lathing - number of rows, distance between boards, number of boards, their volume, approximate weight.

Online calculators, of course, cannot take into account the design features of rafters in all situations. To obtain accurate data for a specific roof option, all calculations must be done manually. We offer you methods for calculating loads on rafters (snow, wind, roofing pie), as well as determining rafter parameters (section, length, quantity, pitch). Based on these data, it will also be possible to calculate the amount of wood required for arranging the rafter system.

Calculation of the load on the rafters

The rafters hold up the roof. Therefore, loads are transferred to them both from external natural factors, and on the weight of the roofing pie (sheathing, insulation, hydro- and vapor barrier). The main external loads are associated with the effects of snow and wind.

Snow load

Snow load is determined by the formula: S =μ ∙ S g, where:

• S is the desired load value;
• μ - coefficient determined by the slope of the roof (the greater the slope, the lower this coefficient, since the snow will melt, so its pressure will be less);
• S g is the norm of snow pressure in a specific area of ​​the country (kg/m2), calculated based on the results of long-term observations.

The angle of the roof is calculated from its main triangle

To determine the coefficient μ, it is necessary to know the angle of inclination of the slope. It often happens that the width and height of the roof are given, but the angle of inclination is unknown. In this case, it must be calculated using the formula tg α = H/L, where H is the height of the ridge, L is half the width of the building (on the gable side), tg α is the tangent of the desired angle. Next, the value of the angle itself is taken from special tables.

Table: the value of the slope angle according to its tangent

tan α	α, deg
0,27	15
0,36	20
0,47	25
0,58	30
0,70	35
0,84	40
1,0	45
1,2	50
1,4	55
1,73	60
2,14	65

Let's assume that the house has a width of 8 m and a height at the ridge of 2.32 m. Then tg α = 2.32/4 = 0.58. From the table we find that α = 30 o.

The coefficient μ is determined using the following method:

• at slope angles up to 25 o μ = 1;
• for angles from 25 to 60 o μ = 0.7;
• for steeper slopes μ = 0, i.e. the snow load is not taken into account.

Thus, for the structure under consideration μ = 0.7. The S g value is selected based on the location of the region in which construction is taking place on the snow load map.

The snow load map allows you to determine the snow pressure on the roof in different regions of Russia

Having determined the region number on the map, the value of the standard snow load can be found using the corresponding table.

Table: standard snow load by region

Region No.	I	II	III	IV	V	VI	VII	VIII
S g, kg/m 2	80	120	180	240	320	400	480	560

Let's assume that our house is located in the Moscow region. This is the third region in terms of snow load. S g here is equal to 180 kg/m 2. Then the total snow load on the roof of the house will be S = 0.7 ∙ 180 = 126 kg/m2.

Wind load

Wind load depends on the area of ​​the country where the house is built, the height of the house, the characteristics of the terrain and the slope of the roof. It is calculated by the formula: W m = W o ∙ K ∙ C, where:

• W o - standard value of wind pressure;
• K is a coefficient that takes into account changes in wind pressure at altitude;
• C - aerodynamic coefficient, taking into account the shape of the roof (with flat or steep slopes).

The standard value of wind pressure is determined from the wind load map.

The wind load map allows you to determine the wind pressure on the roof in different regions of Russia

Table: standard wind load by region

Region No.	1 a	1	2	3	4	5	6	7
W o , kgf/m 2	24	32	42	53	67	84	100	120

In terms of wind loads, the Moscow region is in the first zone. Therefore, the standard value of wind pressure W o for our case is 32 kg/m2.

The K value is determined using a special table. The higher the house and the more open the area it is built, the greater the value of K.

Table: coefficient taking into account wind pressure at height

Let's take the average height of a house - from 5 to 10 m, and we will consider the area closed (this type corresponds to most areas where suburban construction). This means that coefficient K in our case will be equal to 0.65.

The aerodynamic coefficient can vary from -1.8 to 0.8. A negative coefficient means that the wind is trying to lift the roof (usually with gentle slopes), while a positive coefficient means it is trying to tip it over (with steep slopes). For reliability, let’s take the maximum value of this coefficient, equal to 0.8.

Wind affects roofs with steep and gentle slopes differently

Thus, the total wind load on the house we are considering will be equal to W m = 32 ∙ 0.65 ∙ 0.8 = 16.6 kg/m 2.

Roofing cake weight

The total weight of a square meter of roofing cake will be equal to the sum specific gravity all its constituent elements:

• lathing from coniferous species wood (8 – 12 kg);
• roofing(for example, we take corrugated sheeting - 5 kg);
• waterproofing made of a polymer membrane (1.4 – 2.0 kg);
• vapor barrier made from reinforced film(0.9 – 1.2 kg);
• insulation (mineral wool - 10 kg).

The weight of other types of roofing can be determined using a special table.

Table: weight of various types of roofing

For greater reliability, we take the maximum weight values ​​of the roofing pie components: P = 12 + 5 + 2 + 1.2 + 10 = 30.2 kg/m2. We add a reserve of 10% in case of installing any additional structures or non-standard types coating: P = 30.2 ∙ 1.1 = 33.2 kg/m 2.

Total load on the rafters

The total load on the rafters is calculated by the formula: Q = S+W m +P, where:

P is the weight of the roofing pie.

Let us recall that the calculation is carried out for the Moscow region, the roofing is corrugated sheeting, the roof inclination angle is 30°: Q = 126 + 16.6 + 33.2 = 175.8 kg/m2. Thus, the total load per square meter of rafters is 175.8 kg. If the roof area is 100 m2, then the total load is 17580 kg.

It is a mistaken belief that reducing the weight of the roofing significantly reduces the load on the rafters. Let's take cement-sand tiles (50 kg/m2) as a coating. Then the weight of the roof will increase by 45 kg/m2 and will be not 33.2, but 76.4 kg/m2. In this case, Q = 126 + 16.6 + 76.4 = 219 kg/m2. It turns out that with an increase in the mass of the roofing covering by 10 times (from 5 to 50 kg/m2), the total load increased by only 25%, which can be considered not such a significant increase.

Calculation of rafter parameters

Knowing the magnitude of the loads on the roof, we can calculate the specific parameters of the material required for installation of the rafter system: cross-section, length, quantity and pitch.

Selection of rafter cross-section

The cross-section of the rafters is calculated according to the formula: H = K c ∙ L max ∙ √Q r /(B ∙ R bend), where:

• K c - coefficient equal to 8.6 at an angle of inclination less than 30 o, and 9.5 at a greater slope;
• L max - the largest rafter span;
• B is the thickness of the rafter section in meters;
• R bend - bending resistance of the material (kg/cm 2).

The meaning of the formula is that the required section size increases with an increase in the largest span of the rafter and the load on its linear meter and decreases with an increase in the thickness of the rafter and the bending resistance of the wood.

Let's calculate all the elements of this formula. First of all, let's determine the load per linear meter of rafters. This is done according to the formula: Q r = A ∙ Q, where:

• Q r - calculated value;
• A - the distance between the rafters in meters;

The logic of the calculation is quite simple: the sparser the rafters are located and the fewer there are, the greater the load per linear meter will be.

We have already calculated the total load per 1 square meter of rafters. For our example, it is equal to 175.8 kg/m 2. Let's assume that A = 0.6 m. Then Q r = 0.6 ∙ 175.8 = 105.5 kg/m. This value will be required for further calculations.

Now let’s determine the cross-sectional width of the lumber according to GOST 24454–80 “Softwood lumber”. Let's look at what sections the wood is cut into - these are standard values.

Table: determination of standard values ​​for the width of the board depending on its thickness

Board thickness - section width, mm	Board width - section height, mm
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

Let's decide on the thickness of the board (B). Let it correspond to the most commonly used edged lumber - 50 mm or 0.05 m.

Next, we need to know the largest rafter span (L max). To do this, you need to turn to the project and find a drawing roof truss, where all its dimensions will be indicated. In our case, let us take Lmax equal to 2.7 m.

The largest span of the rafter (Lmax) is an important component for calculating its cross-section and is determined from the drawing of the truss

The amount of bending resistance of the material (R bend) depends on the type of wood. For the first grade it is 140 kg/cm2, the second - 130 kg/cm2, the third - 85 kg/cm2. Let's take the value for the second grade: it is not very different from the first, but the second grade of wood is cheaper.

We substitute all the obtained values ​​into the above formula and get H = 9.5 ∙ 2.7 ∙ √ (105.5)/(0.05x130) = 103.4 mm. With a rafter thickness of 50 mm no standard value width is 103.4 mm, so we take the one closest to it higher value from the table above. It will be 125 mm. Thus, the sufficient cross-section of lumber with a rafter pitch of 0.6 m, a maximum span of 2.7 m and a roofing load of 175.8 kg/m2 is equal to 50x125 mm.

• Mauerlat - 100x100, 100x150, 150x150;
• rafter legs and valleys - 100x200;
• crossbars - 100x150, 100x200;
• racks - 100x100, 150x150.

These are sections with a margin. If you want to save material, you can use the above method.

Video: calculation of loads on rafters and their cross-section

Rafter length

When making rafters, in addition to the cross-section, their length is also important. It depends, in particular, on the slope with which the roof will be built. The roof slope angle usually varies between 20 and 45 degrees, but varies depending on the roofing material used, since not every roofing material can be used with a roof of any slope.

The influence of the type of roofing material on the roof pitch angle

Permissible roof slope angles for roofing materials:

• roll coverings - flat and low-slope roofs (up to 22 o);
• bitumen roofing and folded metal sheets - any slope;
• fiber cement sheets, corrugated sheets - from 4.5 o;
• metal tiles, bitumen, ceramic tiles, slate - from 22 o;
• high-profile piece tiles, slate - from 25 o.

Permissible roof slope angles are determined by the roofing material used

Despite the fact that the permissible roof slope angles can be very small, we still recommend making them large to reduce the snow load. For corrugated sheeting they can be from 20 o, metal tiles - 25 o, slate - 35 o, seam roofing - 18 - 35 o.

Rafter length different types roofs are considered differently. Let's show how this is done for a single slope and gable roof.

Calculation of the length of the rafters of a pitched roof

The length of the rafter leg is calculated by the formula L c = L bc / sin A, where L bc is the amount by which the wall needs to be raised, and A is the roof slope angle. To understand the meaning of the formula for calculating L c, recall that the sine of an angle of a right triangle is equal to the ratio of the opposite leg to the hypotenuse. Thus, sin A = L bc /L c. The value of L bc can be calculated using the formula: L bc = L cd ∙ tg A, where L cd is the length of the wall of the house.

All formulas for calculating the rafter system pitched roof taken from a right triangle, which is a projection of the under-roof space onto the pediment

The easiest way to find the values ​​of tg A and sin A is from the table.

Table: determining the values ​​of trigonometric functions based on the roof slope angle

Roof pitch angle, degrees	tg A	sin A	cos A
5	0,09	0,09	1,00
10	0,18	0,17	0,98
15	0,27	0,26	0,97
20	0,36	0,34	0,94
25	0,47	0,42	0,91
30	0,58	0,50	0,87
35	0,70	0,57	0,82
40	0,84	0,64	0,77
45	1,00	0,71	0,71
50	1,19	0,77	0,64
55	1,43	0,82	0,57
60	1,73	0,87	0,50

Let's look at an example.

1. Let's take the length of the house wall to be 6 m and the roof slope to be 30 degrees.
2. Then the height of the wall is L bc = 6 ∙ tg 30 o = 6 ∙ 0.58 = 3.48 m.
3. Length of the rafter leg L c = 3.48 / sin 30 o = 3.48 / 0.5 = 6.96 m.

Calculation of the length of the rafters of a gable roof

A gable roof can be imagined as an isosceles triangle formed by two slopes and a transverse ceiling beam.

A graphical representation of a gable roof in the form of an isosceles triangle allows you to determine the length of the rafter leg in two different ways

The length of the rafter leg (a) can be determined in two different ways.

1. If the width of the house b and the angle of inclination of the roof A are known. Then a = b/ (2 ∙ cos A). Let's assume that the width of the house is 8 m, and angle A is 35 o. Then a = 8 /(2 ∙ сos 35 o) = 8/(2 ∙ 0.82) = 4.88. We add 0.5 m to the overhangs and get the length of the rafter leg equal to 5.38 m.
2. If the width of the roof b and its height at the ridge h are known. In this case, a = √b 2 + h 2 . Let's assume that the height of the ridge is 2.79 m. Then a = √4 2 +2.79 2 = √16 + 7.78 = √23.78 = 4.88. We add 0.5 m to the overhang and as a result we have the same 5.38 m.

It must be borne in mind that the standard length of timber lumber is 6 meters. If they are longer, they will need to be either spliced ​​or special ordered, which, naturally, will be more expensive.

Video: calculation of rafters

Calculation of rafter pitch

The pitch is the distance between adjacent rafters. It determines how many rafters we need for the roof. The step size is usually set to be from 60 cm to 1 m. To calculate a specific step size you need to:

1. Select an approximate step.
2. Determine the length of the slope. Typically this value is specified by the project.
3. Divide the length of the ramp by the approximately selected step size. If the result is a fractional number, then the result is rounded up and 1 is added (this adjustment is necessary because there must be rafters along both boundaries of the slope).
4. Divide the length of the slope by the number obtained in the previous paragraph.

For clarity, we will show the progress of the calculation using a specific example.

Let's assume that the approximate step is 1 m and the length of the slope is 12 m.

1. We divide the length of the slope by the approximately selected step size: 12 / 1 = 12.
2. We add 1 to the resulting number, we get 13.
3. We divide the length of the slope by the resulting number: 12 / 13 = 0.92 m.

It is necessary to understand that the obtained value is the distance between the centers of the rafter joists.

The pitch between the rafters can also be determined from the table based on the given cross-section and the length of the rafter leg.

Table: calculation of rafter pitch depending on the length of the rafter leg and the section of the beam

Rafter pitch, m	Rafter leg length in meters
	3,0	3,5	4,0	4,5	5,0	5,5	6,0
0,6	40x150	40x175	50x150	50x150	50x175	50x200	50x200
0,9	50x150	50x175	50x200	75x175	75x175	75x200	75x200
1,1	75x125	75x150	75x175	75x175	75x200	75x200	75x200
1,4	75x150	75x175	75x200	75x200	75x200	100x200	100x200
1,75	75x150	75x200	75x200	100x200	100x200	100x250	100x250
2,15	100x150	100x175	100x200	100x200	100x250	100x250	-

Using the same table, you can determine the permissible cross-section of the rafters, knowing the size of the step and its length. So, with a step of 0.9 m and a length of 5 m, we obtain a section of 75x175 mm.

If the thickness of the rafter beams is greater than usual, the distance between the rafters can also be made larger.

Table: calculation of the pitch of rafters made of thick beams and logs

Distance between the rafters, m		Maximum length of rafter leg, m
		3,2	3,7	4,4	5,2	5,9	6,6
1,2	timber	9x11	9x14	9x17	9x19	9x20	9x20
	log	11	14	17	19	20	20
1,6	timber	9x11	9x17	9x19	9x20	11x21	13x24
	log	11	17	19	20	21	24
1,8	timber	10x15	10x18	10x19	12x22	-	-
	log	15	18	19	22	-	-
2,2	timber	10x17	10x19	12x22	-	-	-
	log	17	19	22	-	-	-

Calculation of the number of rafters

1. Depending on the load on the rafter system, we select the section of the rafter leg.
2. Calculate the length of the rafters.
3. Using the table, select the pitch of the rafters.
4. We divide the width of the roof by the pitch of the rafters and get their number.

For example, let’s calculate the number of rafters for a gable roof 10 m wide with a rafter leg length of 4 m and its cross-section 50x150 mm.

1. We set the step to 0.6 m.
2. Divide 10 m by 0.6 m, we get 16.6.
3. Add one rafter to the edge of the roof and round it up. We get 18 rafters per slope.

Calculation of the amount of wood required for the manufacture of rafters

Coniferous wood is most often used to construct rafters. Knowing how many rafters are required for the roof and how much wood is contained in one beam, we calculate required volume wood Let's assume that we have made a full calculation of the rafter system and found that 18 units of timber measuring 150x150 mm are needed. Next, look at the table.

Table: amount of timber per cubic meter of lumber

Size timber, mm	Number of beams 6 m long 1 m 3 lumber, pcs.	Volume of one beam 6 m long, m 3
100x100	16,6	0,06
100x150	11,1	0,09
100x200	8,3	0,12
150x150	7,4	0,135
150x200	5,5	0,18
150x300	3,7	0,27
200x200	4,1	0,24

The volume of one beam 150 x 150 mm is 0.135 m 3. This means that the volume of lumber for 18 rafters will be 0.135 m 3 ∙ 18 = 2.43 m 3.

Video: calculation of material for gable roof rafters

Correct calculation of the main parameters allows you to make the rafter system safe, reliable and durable. Knowledge required volume wood allows you to save money on arranging rafters. Online calculators greatly facilitate the calculation of all technical characteristics of a roofing frame, save time on calculations and increase their accuracy.

Specify the parameters of wooden rafters:

B– width of the rafters, important parameter determining the reliability of the rafter system. The required cross-section of the rafter (in particular the width) depends on: loads (constant - the weight of the sheathing and roofing pie, as well as temporary - snow, wind), the material used (quality and its type: board, timber, laminated veneer lumber), the length of the rafter leg, distances between rafters. You can determine the approximate cross-section of the beam for the rafters using the table data (the width value is the larger value from column 3, for example, with a rafter length of up to 3000 mm and a pitch of 1200 mm, the desired width value is 100 mm). When choosing the width of the rafters, be sure to take into account the recommendations given in SP 64.13330.2011 “Wooden Structures” and SP 20.13330.2011 “Loads and Impacts”.

Rafter length, mm	Rafter pitch, mm	Rafter section, mm
Up to 3000 mm	1200	80x100
Up to 3000 mm	1800	90x100
Up to 4000 mm	1000	80x160
Up to 4000 mm	1400	80x180
Up to 4000 mm	1800	90x180
Up to 6000 mm	1000	80x200
Up to 6000 mm	1400	100x200

Y– roof height, distance from the ridge to the attic floor. Affects the angle of inclination of the roof. If you plan to equip a non-residential attic, you should choose a small height (you will need less material for rafters, waterproofing and roofing), but sufficient for inspection and maintenance (at least 1500 mm). If it is necessary to equip a living space under a roof arch, to determine its height, you must focus on the height of the tallest family member plus 400-500 mm (approximately 1900-2500 mm). In any case, you must also take into account the requirements of SP 20.13330.2011 (updated edition of SNiP 2.01.07-85*). It should be remembered that on the roof with small angle slope (small height) precipitation can be retained, which negatively affects its tightness and durability. However, a high roof becomes more vulnerable to strong wind gusts. The optimal tilt angle is between 30-45 degrees.

X– The width of the roof (without overhangs) is determined by the width of the outer perimeter of your house.

C– the size of the overhang, an important structural element of the roof that protects the walls and foundation from precipitation, is determined taking into account the climatic conditions of your region (SP 20.13330.2011) and the general architectural idea. For one and two-story houses without organizing external water flow of at least 600 mm. If you arrange a drainage system, you can reduce it to 400 mm (SNB 3.02.04-03). According to the requirements of IRC-2012, paragraph R802.7.1.1 (International Building Code for 1-2 unit individual residential buildings) the maximum length of the free overhang of the rafters, which does not require the installation of additional support struts, is 610 mm. The optimal overhang size is considered to be 500 mm.

Z– this is the distance from the top edge of the rafter to the cut. Size Z is related to the width of the rafter by a simple ratio - no more than 2/3 of its width (neglecting this rule significantly reduces the load-bearing capacity of the rafter). The cut is necessary to attach the rafters to the mauerlat - a support that takes the load from the roof and redistributes it to the load-bearing walls.

By checking the “Black and white drawing” item, you will receive a drawing close to GOST requirements and will be able to print it without wasting colored paint or toner.

Calculation results:

Length to rafter overhang– this size should be used to mark the cut of the rafters to the mauerlat.

Overhang length will show how far it is necessary to extend the rafter beyond the perimeter of the house to obtain a given roof overhang ( WITH) protecting from bad weather.

Having calculated total length of rafters and overhang it's not hard to find out required amount lumber required length and estimate how many reagents are needed to treat wood against rotting.

Calculation of the angle and section of the rafters: The cut angle is the angle at which the ends of the rafters must be cut to connect to each other. The beginning of the cut should be measured at the same angle to the edge of the rafter. To maintain the same cutting angle on all rafters, it is advisable to use a template.

Design and competent calculations of truss structure elements are the key to success in the construction and subsequent operation of the roof. It must firmly resist a combination of temporary and permanent loads, while adding minimal weight to the structure.

To perform calculations, you can use one of the many programs available on the Internet, or do everything manually. However, in both cases, you need to clearly know how to calculate the rafters for the roof in order to thoroughly prepare for construction.

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

As a rule, in design developments Several options are being considered from which to choose optimal solution. Choice the best option does not mean at all that you need to create a certain number of projects, perform accurate calculations for each and ultimately choose the only one.

The very process of determining the length, installation slope, and cross-section of the rafters lies in the scrupulous selection of the shape of the structure and the dimensions of the material for its construction.

For example, in the formula for calculating the load-bearing capacity of a rafter leg, the cross-sectional parameters of the most suitable material are initially introduced. And if the result does not meet technical standards, then increase or decrease the size of the lumber until maximum compliance is achieved.

Inclination angle search method

Determining the slope angle pitched design there are architectural and technical aspects. In addition to the proportional configuration that best suits the style of the building, an impeccable solution should take into account:

• Snow load indicators. In areas with heavy rainfall, roofs with a slope of 45º or more are erected. Snow deposits do not linger on slopes of such steepness, due to which the total load on the roof, footings and the building as a whole is significantly reduced.
• Wind load characteristics. In areas with gusty strong winds, coastal, steppe and mountainous areas, low-slope, streamlined structures are built. The steepness of the slopes there usually does not exceed 30º. In addition, winds prevent the formation of snow deposits on roofs.
• Weight and type of roofing covering. The greater the weight and the smaller the roof elements, the steeper the rafter frame needs to be constructed. This is necessary in order to reduce the likelihood of leaks through connections and reduce the specific weight of the coating per unit of 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 chosen for construction and the technical data of the roofing covering.

True, property owners in northern windless areas should remember that as the angle of inclination of the rafter legs increases, the consumption of materials increases. The construction and arrangement of a roof with a slope of 60 - 65º will cost approximately one and a half times more than the construction of a structure with an angle of 45º.

In areas with frequent and strong winds, you should not reduce the slope too much in order to save money. Excessively sloping roofs are disadvantageous in architectural terms and do not always help reduce costs. In such cases, strengthening of the insulating layers is most often required, which, contrary to the expectations of the economist, leads to higher construction costs.

The slope of the rafters is expressed in degrees, as a percentage, or in the format of dimensionless units that display the ratio of half the span to the installation height ridge girder. It is clear that the angle between the ceiling line and the slope line is delineated in degrees. Percentages are rarely used because they are difficult to perceive.

The most common method of indicating the angle of inclination of rafter legs, used by both designers of low-rise buildings and builders, is dimensionless units. They convey in fractions the ratio of the length of the covered span to the height of the roof. On site, the easiest way is to find the center of the future gable wall and install a vertical rail in it with a mark for the height of the ridge, rather than putting corners away 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 is selected. Both of these values ​​cannot be considered exact values, because in the process of calculating the load, both the steepness and the subsequent length of the rafter leg may change slightly.

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

1. The outer edge of the rafter legs is cut flush with outer surface walls. In this situation, the rafters do not form a cornice overhang that protects the structure from precipitation. To protect the walls, a drain is installed, secured to a cornice board nailed to the end edge of the rafters.
2. The rafters, cut flush with the wall, are extended with fillets to form a cornice overhang. The fillies are attached 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 overhang. In the lower segment of the rafter legs, notches in the form of an angle are selected. To form notches, step back from the lower edge of the rafters to the width of the eaves extension. Notches are needed to increase the supporting area of ​​the rafter legs and to install support units.

At the stage of calculating the length of the rafter legs, it is necessary to consider options for attaching the roof frame to the mauerlat, to the bypasses or to the upper crown of the log house. If it is planned to install the rafters flush with the external contour of the house, then the calculation is carried out according to 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 extension, then the length is calculated along the upper edge of the rafter along with the overhang. Note that the use of triangular notches significantly speeds up the pace of construction of the rafter frame, but weakens the elements of the system. Therefore, when calculating the load-bearing capacity of rafters with selected cutting angles, a coefficient of 0.8 is used.

The average width of the cornice extension is considered to be traditional 55 cm. However, the spread can be from 10 to 70 or more. The calculations use the projection of the cornice extension onto 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 do not advise extending the roof beyond the contour of the walls to a distance of more than 10 cm, so that the snow mass accumulating along the eaves of the roof cannot damage the edge of the cornice.

It is not customary to equip steep roofs with wide overhangs; regardless of the material, the eaves are not made wider than 35 - 45 cm. But structures with a slope of up to 30º can be perfectly complemented by a wide eaves, which will serve as a kind of canopy in areas with excess solar lighting. In the case of designing roofs with eaves extensions of 70 cm or more, they are strengthened with additional support posts.

How to calculate load-bearing capacity

In construction rafter frames Lumber made from softwood is used. The prepared timber or board must be at least second grade.

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

Rafter systems are made from boards or timber, they are selected with a margin of safety, focusing on the standard sizes of lumber produced in-line.

Calculations of the load-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 pie, wind load taking into account the number of floors of the building, and the mass of snow taking into account the roof slope.
• Regulatory. A condition in which the rafter system bends, but the system does not collapse. It is usually impossible to operate a roof in this condition, but after repair operations it is quite suitable for further use.

In a simplified calculation version, the second state is 70% of the first value. Those. To obtain standard indicators, the calculated values ​​need to be multiplied by a factor of 0.7.

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

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 among the slopes in accordance with the wind rose compiled for the area. You can get a printout of it from your local weather service.

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

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

The estimated snow weight indicated by the map is also adjusted depending on the steepness of the roof. From the slopes, installed at an angle of 60º, the snow will immediately slide off without the slightest delay. In calculations for such steep roofs correction factor do not apply. However, at a lower slope, snow can already be retained, so 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.

Wind load is determined in a similar way using the corresponding map. The value is adjusted depending on the climatic specifics of the area and the height of the house.

To calculate the load-bearing capacity of the main elements of the designed rafter system, it is necessary to find the maximum load on them, summing up the temporary and permanent values. Nobody will strengthen the roofs before a snowy winter, although at the dacha it would be better to install vertical safety struts in the attic.

In addition to the mass of snow and the pressing force of the winds, calculations must take into account the weight of all elements of the roofing pie: the sheathing installed on top of the rafters, the roof itself, insulation, and inner sheathing, 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 technical passports. Data on the mass of the block and board are taken as an approximation. Although the mass of the sheathing per meter of projection can be calculated, taking as a basis the fact that a cubic meter of lumber weighs on average 500 - 550 kg/m3, and a similar volume of OSB or plywood from 600 to 650 kg/m3.

The load values ​​given in SNiPs are indicated in kg/m2. However, the rafter perceives and holds only the load that directly presses on this linear element. In order to calculate the load specifically on the rafters, the totality of the natural tabular values ​​of the loads and the mass of the roofing pie are multiplied by the installation step of the rafter legs.

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

Determining the cross section of rafters

The rafters of roofs of varying steepness perform ambiguous work. The rafters of flat structures are affected mainly by a bending moment; on analogues of steep systems, a compressive force is added to it. Therefore, when calculating the cross-section of rafters, the slope of the slopes must be taken into account.

Calculations for structures with a slope of up to 30º

Only bending stress acts on the rafters of roofs of the specified steepness. They are calculated on maximum torque bending 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 of their own edges, the point of maximum bending will be in the very center of the rafter leg. If the rafter is laid on three supports and made up of two simple beams, then the moments of maximum bending will occur 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 downward as in the previous cases.

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 lumber.
• 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 actual length.

Further calculations consist of sequential selection of the dimensions of the rafter leg, which will ultimately 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 beam based on an arbitrarily specified thickness. The second formula is used to calculate the thickness at an arbitrarily specified height.

It is not necessary to use both formulas in calculations; it is enough to use only one. The result obtained as a result of the calculations is checked against the first and second limit states. If calculated value turned out with an impressive margin of strength, the 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 turns out to be greater than L/200, then the arbitrary value is increased. The selection is carried out in accordance with the standard sizes of commercially available lumber. This is how the cross section is selected until the optimal option 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 bend. We calculate the value of M using the formula g×L 2 /8, where g is the total load vertically directed on the rafter leg, and L is the span length equal to 4 m.

R bend for softwood lumber is accepted in accordance with technical standards as 130 kg/cm 2. Let's say we calculated the total load in advance, and it turned out to be 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 × 0.00531 cm × 15 2 cm = 7.16 cm

We round the result up as expected and find that to install the rafters, taking into account the load given in the example, you will need a beam of 150x75 mm.

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

For rafter systems with a slope over 30º

Roof rafters with a slope 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 the bending value, it is necessary to calculate the rafters based on internal stress.

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

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

A table that summarizes the generally accepted sizes of lumber produced by us will help you select the initial data for making calculations. It will help you select the cross-section and length of the rafter legs for initial calculations.

Video about rafter calculations

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

Carrying out load-bearing capacity and rafter angle calculations is an important part of 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 a calculation program. You need to know where to get tabular values ​​and what the calculated values ​​give.

-> Calculation of the rafter system

The main element of the roof, which absorbs and resists all types of loads, is rafter system. Therefore, in order for your roof to reliably withstand all impacts environment, it is very important to make the correct calculation of the rafter system.

To independently calculate the characteristics of the materials required for installing the rafter system, I provide simplified calculation formulas. Simplifications have been made to increase the strength of the structure. This will cause a slight increase in lumber consumption, but on small roofs of individual buildings it will be insignificant. These formulas can be used when calculating gable attic and mansard roofs, as well as single-pitch roofs.

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

The calculation methodology is based on SNiP 2.01.07-85 “Loads and Impacts”, taking into account “Changes...” from 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.

In addition to the above, the rafter system is also subject to loads from roof elements:

3. Roof weight.

4. Weight of rough flooring and sheathing.

5. Weight of 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 - desired value of snow load, kg/m²
µ - coefficient depending on the roof slope.
Sg - standard snow load, kg/m².

µ - coefficient depending on the roof slope α. Dimensionless quantity.

The roof slope angle α can be approximately determined by dividing the height H by half the span - L.
The results are summarized in the table:

Then, if α is less than or equal to 30°, µ = 1 ;

if α is greater than or equal to 60°, µ = 0;

If 30° is calculated using the formula:

µ = 0.033·(60-α);

Sg - standard snow load, kg/m².
For Russia it is accepted according to map 1 of mandatory appendix 5 of SNiP 2.01.07-85 “Loads and impacts”

For Belarus, the standard snow load Sg is determined
Technical code of PRACTICE Eurocode 1. EFFECTS ON STRUCTURES Part 1-3. General impacts. Snow loads. TKP EN1991-1-3-2009 (02250).

For example,

Brest (I) - 120 kg/m²,
Grodno (II) - 140 kg/m²,
Minsk (III) - 160 kg/m²,
Vitebsk (IV) - 180 kg/m².

Find the maximum possible snow load on a roof with a height of 2.5 m and a span of 7 m.
The building is located in the village. Babenki Ivanovo region. RF.

Using Map 1 of Mandatory Appendix 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

Determine the roof slope angle α.
To do this, divide the roof height (H) by half the span (L): 2.5/3.5=0.714
and from the table we find the slope angle α=36°.

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

Then S=Sg·µ =240·0.79=189kg/m²;

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

2. Wind loads.

If the roof is steep (α > 30°), then due to its windage, the wind puts pressure on one of the slopes and tends to overturn it.

If the roof is flat (α, then the lifting aerodynamic force that arises when the wind bends around it, as well as turbulence under the overhangs, tend to lift this roof.

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

Where,
Wo is the standard value of wind pressure.
K is a coefficient that takes into account the change in wind pressure with height.
C - aerodynamic coefficient.

K is a coefficient that takes into account the change in wind pressure with 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 mats.

This can be 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 matrices or to the ears of the floor slabs. It's obvious that The heavier the roof, the better!

Determine the average wind load on the roof one-story house with the height of the ridge from the ground - 6 m. , slope angle α=36° in the village of Babenki, Ivanovo region. RF.

According to map 3 of Appendix 5 in “SNiP 2.01.07-85” we find that the Ivanovo region belongs to the second wind region Wo= 30 kg/m²

Since all buildings in the village are below 10m, coefficient K= 1.0

The value of the aerodynamic coefficient C is taken equal to 0.8

standard value of the average component of the wind load Wm = 30 1.0 0.8 = 24 kg/m².

For information: if the wind blows at the end of a given 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 (bitumen slate) 4 - 6 kg/m²;
3. Ceramic tiles 35 - 50kg/m²;
4. Cement-sand tiles 40 - 50 kg/m²;
5. Bitumen shingles 8 - 12 kg/m²;
6. Metal tiles 4 - 5 kg/m²;
7. Corrugated sheeting 4 - 5 kg/m²;

4. Weight of rough flooring, sheathing and rafter system.

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

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

And now I'll tell you little secret. Sellers of certain types of roofing materials as one of the positive properties note their lightness, which, according to them, will lead to significant savings in lumber in the manufacture of the rafter system.

To refute this statement, I will give the following example.

Calculation of the load on the rafter system when using various roofing materials.

Let's calculate the load on the rafter system when using the heaviest one (Cement-sand tiles
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
Sheathing weight - 20 kg/m²

Total - 303 kg/m²

Metal tiles:
Snow load - 189kg/m²
Wind loads - 24kg/m²
Roof weight - 5 kg/m²
Sheathing weight - 20 kg/m²
The weight of the rafter system itself is 20 kg/m²
Total - 258 kg/m²

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

So, we figured out the calculation of the total load Q acting per square meter of roof!

I especially draw your attention: when making calculations, pay close attention to the dimensions!!!

II. Calculation of the rafter system.

Rafter system consists of separate rafters (rafter legs), so the calculation comes down to determining the load on each rafter leg separately and calculating the cross-section of an individual rafter leg.

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

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

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

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

When choosing material for rafters, we are guided by the table standard sizes lumber (GOST 24454-80 Softwood lumber. 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 arbitrarily set the width of the section in accordance with standard dimensions, and determine the height of the section using the formula:

H ≥ 8.6 Lmax sqrt(Qr/(BRben)), if the roof slope α

H ≥ 9.5 Lmax sqrt(Qr/(BRben)), if the roof slope α > 30°.

H - section height cm,


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

B. We check whether the deflection value is within the standard.

The normalized deflection of the material under load for all roof elements should not exceed L/200. Where, L is the length of the working section.

This condition is satisfied if the following inequality is true:

3.125 Qr (Lmax)³/(B H³) ≤ 1

Where,
Qr - distributed load per linear meter of rafter leg - kg/m,
Lmax - working section of the rafter leg with maximum length m,
B - section width cm,
H - section height cm,

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

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

As it was calculated, the total load acting on a square meter of roof is Q = 303 kg/m².
1. Find the distributed load per linear meter of each rafter leg Qr=A·Q;
Qr=0.8·303=242 kg/m;

2. Choose the thickness of the board for the rafters - 5cm.
Let's calculate the cross-section of the rafter leg with a section width of 5 cm.

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

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

3. We check whether the deflection value is within the standard. To do this, the following inequality must be observed:
3.125 Qr (Lmax)³/B H³ ≤ 1
Substituting the values, we have: 3.125·242·(2.8)³ / 5·(17.5)³= 0.61
Meaning 0.61, which means the cross-section of the rafter material 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.