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How to calculate the rafter system of a gable roof using an online calculator. Roof calculator: calculation of the roof, rafter system, lumber Program for calculating the rafter system

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 carry out exact calculations these loads, determine strength characteristics rafters, their cross-section, length, quantity, as well as the volume of material required for 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. A number of them are complex in nature and calculate many parameters 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 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 graphically show data entry parameters. The result displays information on:

• roof - angle of inclination, surface area, approximate weight 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). Basic external loads associated with exposure to 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 roof slope (than more slope, the smaller 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

Total weight square meter there will be a roofing pie equal to the sum specific gravity all its constituent elements:

• lathing from coniferous species wood (8 – 12 kg);
• roofing covering (for example, we take corrugated sheeting - 5 kg);
• waterproofing from 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 of 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 required size cross-section increases along with the increase in the long span rafters and loads on it linear meter and decreases with increasing rafter thickness and wood bending resistance.

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/m2. 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, there is no standard width value of 103.4 mm, so we take the closest larger 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 roof load of 175.8 kg/m2 is 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 seamed 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 two pitched roof.

Calculation of the length of the rafters of a pitched roof

Length 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 the angle right triangle 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 kept in mind that standard length 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, the result is rounded to big side and 1 is added (this adjustment is needed 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 according to a 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 produced full payment 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

Greetings! My name is Mikhail. I am 59 years old. Education - higher. I work as a sales consultant in a company for the manufacture and installation of metal-plastic structures. I love my job and hope that my experience and knowledge will be of interest to you.

In this article we'll talk about the simple program "Rafters". It is intended for calculating a two-span wooden beam. The software will provide data on the maximum moment, deflection and bearing capacity. Let's take a closer look at the representative.

"Rafters" does not require installation, you just need to run the file from the archive. All functionality is in one window. You will need to enter required parameters about spans, inclination angles, height and width in lines and press the button "Calculation", so that the calculation results are displayed below. Please note that there are three types of wood and two calculation modes, this helps to determine the most accurate parameters.

Advantages

• The program is distributed free of charge;
• Does not require installation;
• Russian language is available;
• Simple interface.

Flaws

• Minimal functionality.

"Rafters" provides minimum set tools needed to calculate the roof. However, it fully copes with its task and provides accurate information about the parameters of a two-span beam. The software is easy to use and does not require special skills.

Rate the program:

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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 do correct calculation rafter system.

For self-calculation I provide the characteristics of the materials required for installation of the rafter system 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. Bituminous 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 their assurances, 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. Determine the working area in the rafter leg maximum length Lmax.

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(Roof 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 - 5 cm.
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.

One of the most important parts of a pitched roof is the rafter system, consisting of strong and reliable beams. It is the rafters that form the basis for the roof. It is important that the materials used can easily withstand not only the roof structure, but also the pressure of snow or ice masses in winter period, as well as wind loads throughout the year. In this regard, before proceeding with the installation of rafters, you should necessary calculations, taking into account all possible factors and nuances. Of course, you can order rafter calculations in various construction companies, however, such a service will cost a fairly decent amount, so the best option may become an independent calculation. So, how to calculate the roof truss system correctly? Of course, before moving on to the main question, it is worth studying the features of the rafters and the types of construction.

Features of the rafter system

To make a calculation of the rafter system, you should understand what it is. So, the rafters are load-bearing structure roof, which takes on all external loads, in the form of snow drifts, heavy rains or gusty winds. Its main elements are:

• vertical posts - necessary for maximum stability of the rafter system;
• rafter inclined legs - determine the slope of the roof slope and its general appearance;
• purlins - there are lateral and ridge varieties of purlins, the elements are necessary for fastening and supporting the rafter legs;
• tightening bolts, crossbars – fixing elements;
• struts - diagonal supporting beams that give stability to the rafters;
• ridge - an upper beam laid at the junction of two roof slopes;
• fillies - an element that allows you to increase the length of insufficiently long rafters in the case of installing a roof overhang;
• truss - a set of posts, braces, sheathing and other elements that form the basis of the roofing system.



When starting to calculate the rafters, you should calculate each individual element. It is also important to comply with the requirements for the rafter system; this will help you choose the right material, as well as create the most durable and long-lasting roof.

Basic requirements when choosing rafter material

Today, quite a few home owners prefer wood roofs. As a rule, the rafter system is made from coniferous trees tree species. In this case, the timber should have a moisture content of no more than 20%. This is the so-called air-dried wood, which is characterized by the necessary strength and lightness. In addition to the humidity percentage, when choosing a tree, the following conditions should be observed:

• the presence of a minimum number of knots, cracks and other possible defects, for this you should choose grade 1 or 2 wood. When choosing grade 3 wood, you should pay attention that per 1 m of board or beam there are no more than 3-4 knots up to 3 cm high, and if there are cracks, their length and depth should be small;
• for load-bearing, capital elements, such as rafters, mauerlat, ridge, and so on, it is recommended to use timber with a thickness of more than 5 cm; it is optimal to use products with square or rectangular cross-section from 10 to 20 cm;
• when choosing coniferous boards, product lengths up to 6.5 m are allowed, and if used hardwoods, then the length of the lumber should not exceed 4.5 m. As a rule, hardwood is used for such structural parts as purlins and mauerlat. It is also worth giving preference to hard rocks.



Important! The entire constructed system must have rigidity and strength. That is finished design must have a reliable fixation and be motionless. If at least one element does not meet this requirement, then there is a high probability that the roof may be destroyed by hurricane winds or heavy snow, and it will not matter how correctly the wooden roof rafters are calculated. In the most dire situation, not only the roof, but also the walls of the building will be destroyed. It is also worth keeping in mind that the rafter system should be made light, especially when wooden load-bearing walls. In order to be able to use strong and reliable beams, but not make the structure heavier, it is recommended to choose lumber with a low percentage of moisture, that is, about 10-15%. Also, don’t forget about processing wooden elements antiseptics, fire retardants, water repellents and other protective drugs. Before getting down to the question of how to correctly calculate the rafter system, you should get an idea of ​​the types of rafters.

Video on the topic:


Types of rafters

The specific type of rafters depends on the type of roof and when calculating the rafter system, this should be taken into account. For example, the roof can be gable or hipped, and accordingly the rafters will be calculated differently. At the same time, the presence structural elements and the principle of their installation remains practically unchanged. Today it is customary to distinguish 2 main types of rafter systems.

1. Layered rafters - in this case, the rafter legs rest on the walls of the building, and their middle is supported intermediate support. A similar system is installed if necessary, if spans are longer than 5-7 m. Each additional support can increase the span length by 3-4 m.
2. – are installed when the distance between the external walls on which the rafter system is installed is no more than 6.5 m.

Having chosen a specific type of roof, as well as a type of rafter system, you can proceed to the implementation of all necessary calculations, that is, calculating the cross-section of the rafters, the load, the length and height of the beams, and so on.

Calculation of the load on the rafters

When calculating the roof rafters yourself, it is recommended to take increased parameters, so that you can have a certain margin of safety for the roof. Of course, this will increase the consumption of building materials, however, home safety issues should still be given top priority. So, the first step is to take into account all possible loads that will affect the roof structure. In particular, such loads include snow and wind loads. Also, when calculating the load on the rafter system, it is worth taking into account quite a few features. Including factors such as:

• weight of roofing material;
• sheathing weight;
• weight of insulation, hydro- and vapor barrier;
• weight of the rafter system.

Only by calculating each point can you calculate the rafter system. For example, the formula for calculating snow load would look like this:

S = Scalc·μ,
where S is the desired parameter, Scalc. is the value of the weight of snow per 1 sq.m, which should be taken from the SNiPs in force in a certain territory, and μ is a coefficient calculated from the angle of inclination of the roof. To calculate the wind load, you can also use the formula:

Wm = Wo·k·c,
where Wo is the standard parameter of wind pressure, determined according to SNiPs in force in the region, k is the coefficient of wind pressure, depending on the height of the roof above the ground, and c is the aerodynamic coefficient, which depends on the shape of the roof. Knowing all the initial values, making calculations is not difficult. However, today it is not at all necessary to carry out all the necessary measurements and calculations in manual mode. After all, special programs have been created for these purposes, for example, a program for calculating a rafter system or a program for calculating rafters and trusses. Such programs include:

• Stropila;
• AutoCAD;
• Arkon;
• Online calculation services (construction calculators).

What is the operating principle of such software? It is quite simple, you need to enter all the parameters from SNiPs or the building plan into the appropriate windows or lines, then click the “calculate” button and the program will display the result. As a rule, these resources include all the necessary calculations, that is, wind and snow loads, as well as calculation of the total load, calculation of the distributed load, calculation of the rafter system, and so on. The programs also contain maps with wind pressure and snow weight in all regions. Even untrained users will be able to make calculations in such applications, and all parameters will be the most accurate. In addition, it should be borne in mind that certain parameters are constant and can be found in the instructions for building materials or on the Internet.

Type of roofing and its weight

Depending on what roofing material you plan to use, the load on the rafter systems also changes. Almost all types of coatings have a fixed weight, making calculations quite easy. Let's consider the weight of the main varieties roofing coverings, which are provided by manufacturers during manufacture.

As for the mass of the rough flooring, rafter system and sheathing, these values ​​are considered to be standard. In particular, draft roof structure will have a weight of 18-20 kg/sq.m, wooden sheathing– 8-10 kg/sq.m and rafters – 15-20 kg/sq.m. By summing up all the values, you can easily find the desired load parameter on the rafter system.

Calculation of rafters

Once the load has been determined, you can move on to a point such as calculating the rafter system. It is necessary to determine the load on each rafter leg in order to understand what cross-section the rafters should have, their strength and how much timber will be required for the rafters in each specific case. The formula for calculating the load on each rafter leg is as follows:

Qr=A·Q,
where Qr is the desired value, measured in kg/m, A –, measured in meters and Q is the total load acting on 1 sq.m of roof, measured in kg/sq.m (this is the value that was found in the calculations made by previously). The load can also be calculated automatically, using programs. Various applications allow you to calculate the cross-section of rafters, their number, height and many other parameters. Important! When calculating the rafter system, you should always round the parameters up, as this allows you to increase the strength of the roof structure.

Making the necessary calculations yourself is not at all difficult. Of course, if knowledge in this matter is not enough, you can always turn to specialists. However, a huge variety of automated programs can help you cope with the calculation of the rafter system without much hassle. It is important to remember that not only the strength and reliability of the roof, but also the safety of the residents of the house depends on the correctness of the calculations.

Beautiful and reliable.

What is the basis of any roof?

How strong and reliable the roof will be will depend on how correctly the parameters of the rafter system elements are calculated.

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

Factors taken into account when calculating rafters

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

Factors influencing the roof are usually classified into:

1. Constant loads. This category includes those loads that are constantly exposed to the elements of the rafter system, regardless of the time of year. These loads include the weight of the roof, sheathing, waterproofing, heat and vapor barrier and all other roof elements that have a fixed weight and constantly create a load on the rafter system. If you plan to install any equipment on the roof (snow guards, satellite TV antenna, Internet antenna, smoke removal and ventilation systems, etc.), then the weight of such equipment must be added to the constant loads.
2. Variable loads. These loads are called variable due to the fact that they load the rafter system only during a certain period of time, and at other times this load is minimal or non-existent. Such loads include the weight of the snow cover, the load from blowing winds, the load from people who will service the roof, etc.
3. Special type of loads. This group includes loads that occur in areas where hurricanes often occur or seismic impacts occur. In this case, the load is taken into account in order to build an additional margin of safety into the structure.

Calculating the parameters of the rafter system is quite complicated.

And it is difficult for a beginner to do it, since many factors that affect the roof must be taken into account.

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

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

Determining the load on the rafters

Roofing cake weight

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

This calculation is not difficult to make if you know the total area of ​​the roof and the materials that are used to create this very pie.

First, calculate the weight of one square meter of cake.

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

This coefficient is equal to 1.1.

Here typical example calculating the weight of the roofing pie.

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

And that's true!

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

So:

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

Let's sum up the data obtained: 3+5+10+15= 33 kg.

Now the result must be multiplied by 1.1.

Our correction factor.

The final figure is 34.1 kg.

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

The total roof area is, for example, 100 square meters. meters.

This means that she will weigh 341 kg.

This is very little.

This is one of the advantages of ondulin.

Calculating the snow load

The moment is very important.

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

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

To calculate the snow load, a snow load map is used.

Determine your region and calculate the snow load using the formula

In this formula:

— S is the desired one snow load;

— Sg is the mass of snow cover.

The weight of snow per 1 square meter is taken into account. meter.

This indicator is different in each region.

It all depends on the location of the house.

A map is used to determine the mass.

— µ is the correction factor.

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

If the angle of inclination of the slopes is less than 25 degrees, then the coefficient is equal to 1.

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

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

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

The slopes have an inclination angle of 30 degrees.

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

Mass of snow per 1 sq. meter is 180 kg.

We carry out the calculation, not forgetting about the correction factor:

180 x 0.7 = 126 kilograms per 1 sq. meter of roof.

Determination of wind loads

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

Use this formula:

Wo is a standard indicator determined from the table.

Each region has its own wind tables.

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

Calculating wooden rafters

Rafter length

Calculating the length of the rafter leg is one of the simplest geometric calculations.

Because you only need two dimensions: width and height, and the Pythagorean theorem.

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

We know two distances:

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

First leg;

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

Second leg.

- c is the hypotenuse of the triangle.

c²=(2 x 2)+(3 x 3).

Total c²=4+9=13.

Now we need to get the square root of 13.

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

We get 3.6 meters.

To this number you now need to add the extension length d to get the required rafter length.

We calculate and select the cross-section of the rafter system elements

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

For simple designs use a table of typical board sizes and sections.

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

We calculate the pitch and number of rafter legs

The distance between their bases is called.

Experts believe that the minimum distance should be 60 cm.

And the optimal distance is 1 meter.

We calculate the distance between the rafters:

• We measure the length of the slope along the cornice;
• then the resulting figure should be divided by the expected rafter pitch. If the step is planned to be 60 cm, then it should be divided by 0.6. If it is 1 meter, then divided by 1. We will talk about the preliminary selection of the step later;
• then you should add 1 to the obtained result and round the resulting value up. Thus, we get the number of rafters that can be installed on the roof of your house;
• the total length of the slope must be divided by the number of rafters to obtain the rafter pitch.

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

We first select a rafter pitch of 0.8 meters.

12/0.8 = 15 meters.

We add the unit 15+1=16 rafters.

If the result was a fractional number, we would round it up.

Now 12 meters should be divided by 16.

As a result, 1216 = 0.75 meters.

Here optimal distance between the rafters on the same slope.

The table mentioned earlier can also be used.

Calculating wooden floor beams

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

The optimal cross-section is rectangular.

Height to width ratio 1.4:1.

The beam must extend into the wall at least 12 cm.

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

Waterproofing of beams is carried out “in a circle”.

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

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

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

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

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

Calculation of rafters for a pitched roof

A pitched roof is the simplest roofing option.

But this option is not suitable for every building.

And rafter calculations are required in any case.

Calculations pitched roof begin with determining the angle of inclination.

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

For example, for corrugated sheets minimum angle equals 8 degrees.

And the optimal temperature is 20 degrees.

Calculation programs

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

And there are quite a lot of such programs!

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

Such programs have only two drawbacks:

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

There are a number of free programs.

Most programs can be downloaded to your computer.

Or use them online.

Video about calculating rafters.