Calculation of the thickness of rafters for the roof. Calculation of the rafter system of a gable roof. The pitch of the beams of the supporting roof structure

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 the strength characteristics of the rafters, their cross-section, length, quantity, as well as the volume of material required for the construction of the 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 the required amount of 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 from 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 required 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/m 2.

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:

• laths made of coniferous 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 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 on one square meter 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;

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, 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 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. The length of rafters for different types of roofs is calculated 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
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

cos A

1. Let's look at an example.
2. Let's take the length of the house wall to be 6 m and the roof slope to be 30 degrees.
3. Then the height of the wall is L bc = 6 ∙ tg 30 o = 6 ∙ 0.58 = 3.48 m.

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

1. The length of the rafter leg (a) can be determined in two different ways.
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 show the progress of the calculation on 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 get 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. Knowing the required volume of wood allows you to save money on arranging rafters. Online calculators make it much easier to calculate everything technical characteristics roofing frame, save time on calculations and increase their accuracy.

Most of the construction is already behind you, and your future home is pleased with a strong foundation and smooth walls? It's time to start building a roof that will protect your home comfort from dampness and bad weather. But the first thing to do is to design and calculate the entire structure down to the very last detail.

Remember that at height all work is more difficult, and therefore it is better not to redo anything. Moreover, the calculation of the rafter system itself gable roof It’s not complicated – now you’ll see for yourself! By the way, a gable roof is also called a gable roof.

• Mauerlat is the foundation of the roof, usually represented by a horizontal beam, on which the rafters rest.
• Ridge beam.
• Inclined beams and rafters.
• Vertical racks.
• Lathing and additional parts that give the necessary rigidity to the frame.

Nothing complicated - the gable roof is just what makes us happy:

Standard and sloping gable roof

The project of a standard gable rafter system consists of two rectangular inclined planes and smooth vertical ends on the sides, called pediments. Such a roof is one of the simplest structures, the construction of which can be successfully completed by even inexperienced specialists.

But the sloping gable roof has a different architecture. Here, the upper flatter roof is usually built with a slope of 30°, and the lower steep roof with a slope of 60°.

A broken gable roof is good because snow and ice hardly stay on it, but the attic space turns out to be much more convenient and cozy. Moreover, in the lower plane of such a roof it is rational to install dormer windows, which on flatter planes usually become a problem of leaks and dampness - rainwater lingers on them longer.

Note that one of the most best options for buildings 6-8 m wide. Moreover, it will be easier for you to assemble a broken profile - for this you just need to mount the necessary components directly on the ground, and simply cut all the posts and rafters according to the template:

How to calculate a gable rafter system?

So, the first thing when designing and calculating is to decide usable area attic, and based on this data, decide how high the vertical racks will be. And the attic is usually built in such a roof - it’s convenient.

For convenience, we suggest understanding the concepts:

We calculate the angle of inclination of the slopes

Now we calculate the slope of the slopes. So, if your house has a standard width of 6-8 m, then a slope angle of 45° will leave too little space for the attic living space. Do 60° - this is the best option, although it will cost you more. In addition, already with a 45° slope you can use any roofing materials.

It is rare, but it happens when a gable roof is initially planned to be asymmetrical - if only so that there is room in the attic space for arranging a residential attic. But in any case, calculate the angle of inclination of a standard gable roof based on the wind and snow loads of your region.

But keep in mind that as the angle of inclination of the slopes increases, the consumption of materials will also increase, although the performance characteristics of such a roof will also be higher:

Gable roofs with unequal slope angles are also built to express original design. It has many shortcomings, and therefore we advise you to still plan a symmetrical roof, at the base of which there are isosceles triangles.

Deciding on the type of rafters

A gable roof has only two of them.

Hanging rafters

A distinctive feature of this type of rafter system is that the support here is only on the side walls of the structure, i.e. the rafters are simply hanging. This process in construction is considered negative, because Such design leads to a bursting load on the roof and over time the walls may even become deformed. And over the decades, it even becomes skewed. That is why, for a more harmonious and safe distribution of the load, consider additional and auxiliary elements - tightening, headstock, and bevels.

But the hanging rafter system also has its advantages:

• The installation work of such a roof is quite simple.
• There are no complex components or other elements for system reliability.
• All truss structure– high degree of rigidity.

Layered rafters

The layered rafter system is characterized by the presence of an internal supporting partition, which is located at the same distance from the opposite walls. The entire roof rests on it, and therefore you cannot do without a layered system if the roof has a serious weight or size.

Distributing the load of the rafters

Now it is important to redistribute the load of all rafters onto the floor beams as much as possible. If the rafters need to be strengthened, then add additional linings to the project or a larger section of the beam than planned.

Weight of the rafter system and roofing covering

We calculate everything using the following tables:

The project may also have inclined racks that strengthen the rafter system. Next, the gabled roof truss will need to be reinforced with a headstock - a central post that will connect the ceiling and ridge beams.

In addition, it is important that the roof can easily survive climatic dissonances. It is easiest to calculate and design roofs in small countries where the climate is the same throughout the entire territory. That is why the Irish tend to build some structures, in hot countries - others, and the Swedes - others. It’s just that in such areas, building traditions have been developing for centuries, which have actually been tested in practice by more than one generation.

But in Russia, such traditions are ambiguous: somewhere they build flat, low roofs and houses almost in the ground, and somewhere, on the contrary, high sharp slopes near the same high towers. The fact is that the climate in our country is varied (naturally, due to its vast territory), and in some areas they are trying to cope with tons of snow, while in others they are trying to prevent a stray wind from tearing off all the roofs in the village. Therefore, still focus on the experience of your region and do not make too radical decisions in calculating the rafter system. Wind load

So, the force of the wind exerts lateral pressure on the roof. When faced with an obstacle, the wind is divided into two flows: down to the foundation and up, under the eaves. If you calculate everything correctly, your roof will serve you faithfully until your great-grandchildren, and if you make a mistake with the calculations, the consequences will be sad. Moreover, if the wind tears off the roof in the literal sense of the word, some minor repairs will not be enough - you will have to rebuild the entire rafter system.

Therefore, in the construction world it is customary to pay special attention to the so-called aerodynamic coefficient of the roof. It depends on its angle of inclination: the steeper it is, the greater the load will be and it will be easier for the wind to overturn the roof. The lower you go, the more difficult it is, but here the wind will act as a lifting force, trying to catch it on the cornice and tear it off like a mushroom cap. Therefore, the ideal roof for windy regions is one with a slight angle of inclination and a minimal eaves. And certainly not with hanging rafters.

Another dangerous point: in such areas, the wind often breaks branches from trees and carries other objects. And the higher the roof, the more likely it is that all this debris will collide with it. A couple of scratches and corrosion is guaranteed. Therefore, the metal coating will also have to be abandoned. In addition, if there are strong winds in your area, lay the mauerlat close to the edge outer wall It is not recommended that gusts of wind could disrupt it.

Snow load

Snow cover in winter periods actually puts quite a bit of pressure on the roof. And the further north the area, the more such precipitation there is, and the greater the threat of a roof failure, especially at a low angle of inclination. Therefore, this final element of the building must be designed and calculated carefully, taking into account all the subtleties and nuances.

It is especially difficult to design a reliable roof in areas where periodic temperature changes are the norm. The fact is that the constant melting of snow and its freezing the next day has a bad effect on any roofing. As a result, the entire rafter system is deformed, waterproofing and insulation are destroyed, and constant roof leaks lead to unpleasant dampness and regular repairs. Do you have similar weather conditions? Place your bet on maximum roof protection!

The formula for calculating the roof slope angle in this case is simple: the higher the slope, the less snow is retained. In snowy regions, also forget about complex roof shapes and numerous elements. Just count simple design with a high angle of inclination, on which it will be necessary to install snow holders (so that precipitation does not destroy the drainage system).

Modern programs for calculating a gable roof

Naturally, it is quite difficult to draw the entire rafter system with your own hands, as in the official design documentation, unless you are trained as an architect. But it is quite enough to have the theoretical knowledge that this article gives you and at least make a sketch so that you can already purchase construction material. And you can go another way - use modern 3D programs. It will be difficult to figure out things like AutoCAD and 3D Max, but in Arkon all the necessary calculations and sketches are easy to do.

Also, if you still have questions, you will always find on our website who will quickly perform all the necessary calculations.

A simple online calculator will accurately calculate the length of the rafters, the length of the overhang of the rafters, and the cutting angle of the rafters. Start calculating rafters right now!

DIY rafter system

This calculator is indispensable for those who decide to make DIY rafters. A smart online calculator will accurately calculate the length to the overhang of the rafters, the length of the overhang, the angle of cut and the distance from the edge of the rafter to the beginning of the cut. Online calculator suitable for calculating the rafters of a gable roof and a single-pitched roof.

The permissible range of roof inclination angle is from 20° to 60°, than smaller angle, the less lumber is needed for the farm, but the larger the angle, the more spacious it will be under the roof of the second floor of the house. If you choose an angle of 30°, then for a building width of 10 m, the elevation of the ridge above the top floor will be 2.5 m. The length of the rafter legs will be 7 meters, of which 6.2 are above the house, and the rest extends beyond the roof. The minimum overhang size is usually taken to be 50 cm for safety from bad weather. Rafters 7 meters long are considered the maximum permissible for an inclined design to the roof ridge, if the length of the rafters is more than 7 meters, additional reinforcement of the gable roof in the form of beams is required. When calculating rafters for a gable roof the step between individual lags is 80-130 cm. The exact pitch size depends on the weight of the roof, the amount of precipitation and wind load in your region of construction. All rafter blanks must be treated with antiseptic and fire-fighting compounds.

The gable roof has long become a classic of architecture. The list of its advantages includes ease of installation, low cost maintenance and practicality in terms of natural removal of rainwater and snow. To fully experience these benefits, you need to carefully think through the roof design and calculate the dimensions. This is the only way to make the structure durable and maintain its attractive appearance. appearance for many years.

Basic parameters of a gable roof

Selection optimal size roofs are a complex process of finding a compromise between the desired appearance of a building and its safety requirements. In a properly designed roof, all proportions are close to ideal. The main parameters of a gable roof include the angle of inclination, the height of the ridge, the width of the roof and its overhangs.

The slope of the roof is the value that determines the position of the slope relative to the horizon line. The choice of this indicator is carried out at the design stage of the structure. Traditionally, both slopes of a gable roof are made with the same angles of inclination, but asymmetrical varieties are also found.

The most common roofs have a slope of 20° to 45°

The unit of measurement for slope is degrees. For roofs, the accepted range is 1 0 -45 0. How higher figure, the more acute the structure, and vice versa, as the degree decreases, the roof becomes sloping.
Depending on the slope, there are several types of roofs:

• flat (less than 5°), the advantages of which are low consumption of materials and ease of maintenance, and the disadvantages are the mandatory presence of a good waterproofing system and measures to prevent snow accumulation;
• flat (up to 30°), allowing the use of all existing materials as roofing, but more expensive than flat;
• steep (more than 30°), capable of self-cleaning, but not resistant to wind loads.

The tool for measuring the slope angle is an inclinometer. Modern models are equipped with an electronic display and bubble level. When the device is oriented horizontally, “0” is displayed on the scale.

Manufacturers offer to purchase inclinometers with laser sensors that allow measurements to be taken at a distance from the object

Photo gallery: roofs with different slope values

The load on a roof with a slope of 45° degrees is 5 times higher than on a roof with an angle of 11°
Steep slopes, due to the large slope, drain precipitation well
A multi-slope roof is erected if it is necessary to connect walls of different heights or an adjacent extension to the house
The minimum slope angle recommended by builders is 14°

In a number regulatory documents, for example, SNiP II-26–76 “Roofs”, the slope is indicated as a percentage. There are no strict recommendations for a single parameter designation. But the value in percentage is very different from the option in degrees. So, 1 0 equals 1.7%, and 30 0 equals 57.7%. For error-free and quick conversion of one unit of measurement to another, special tables have been created.

Table: relationship between slope units

Slope, 0	Slope, %	Slope, 0	Slope, %	Slope, 0	Slope, %
1	1,7	16	28,7	31	60,0
2	3,5	17	30,5	32	62,4
3	5,2	18	32,5	33	64,9
4	7,0	19	34,4	34	67,4
5	8,7	20	36,4	35	70,0
6	10,5	21	38,4	36	72,6
7	12,3	22	40,4	37	75,4
8	14,1	23	42,4	38	78,9
9	15,8	24	44,5	39	80,9
10	17,6	25	46,6	40	83,9
11	19,3	26	48,7	41	86,0
12	21,1	27	50,9	42	90,0
13	23,0	28	53,1	43	93,0
14	24,9	29	55,4	44	96,5
15	26,8	30	57,7	45	100

Ridge height

Another important roof parameter is the height of the ridge. The ridge is the top point of the rafter system, located at the intersection of the planes of the slopes. It serves as a support for the rafters, giving the roof the necessary rigidity and allowing the load to be evenly distributed over the entire structure. Structurally, it is a horizontal rib made of wooden beam. If you imagine a gable roof in the form of a triangle, then the height of the ridge is the distance from the base to the top of the figure.

According to the rules of geometry, the height of the ridge is equal to the length of the leg of the right triangle

Overall roof width and overhang width

The overall width of the roof is determined by the width of its box (the size of the rafter system) and the width of the eaves overhangs.

The overhang is the part of the roof protruding beyond the walls. The width of the overhang is the distance from the intersection load-bearing wall from the roof to the bottom of the roofing sheet. Despite its modest dimensions and small specific percentage of the total area, the overhang plays a key role in the operation of the house. The cornice protects the external walls from precipitation, keeping their coating in its original form. He creates a shadow in local area V summer heat and shelters people during snowfall. In addition, the overhang facilitates the drainage of rainwater from the roof.

The required size of the eaves overhang B is obtained by lengthening or building up the rafter legs

There are 2 types of overhangs, differing in location and width:

• pediment - a small section of the roof slope located on the pediment side;
• eaves - a wider overhang that is located along the roof.

To protect the lower surface, the overhang is sheathed edged board, siding or soffits

Photo gallery: roofs with different overhang widths

The optimal width of the cornice is in the range of 50–60 cm
The edge of the roof ends at the top line of the gable or wall
Houses built in the Mediterranean style have narrow overhangs and a slight slope angle
The wide cornice gives monumentality to the entire building

Factors influencing roof parameters

The first stage of roof construction is the development and preparation of a technical plan. It is necessary to take into account all the nuances that will affect the life of the roof. Design parameters are determined by considering a group of factors: climatic features of the region, the presence of an attic and the type of roofing material.

Depending on the area in which the building is located, it may be influenced by various natural forces and loads. These include wind pressure, snow pressure and water exposure. You can determine their meaning by contacting a special construction organization carrying out similar research. For those who are not looking for simple ways, there is an option to determine the parameters yourself.

Wind load

The wind creates significant pressure on the walls and roof of the building. The air flow, encountering an obstacle on its way, is divided, rushing in opposite directions: towards the foundation and the roof overhang. Excessive pressure on the overhang can cause the roof to fall off. To protect the building from destruction, the aerodynamic coefficient is estimated, depending on the angle of inclination of the slope.
The steeper the slope and the higher the ridge, the stronger the wind load per 1m2 of surface. In this case, the wind tends to overturn the roof. Hurricane winds have a different effect on flat roofs - the lifting force lifts and carries away the crown of the house. Therefore, for areas with low to moderate wind strength, roofs can be designed with any ridge height and pitch angle. And for places with strong gusts of wind, low-slope types from 15 to 25° are recommended.

In addition to the horizontal impact, the wind exerts pressure in the vertical plane, pressing the roofing material against the sheathing

Calculation of wind load on a gable roof

The calculated wind load is the product of two components: the standard value of the parameter (W) and the coefficient (k), which takes into account the change in pressure depending on the height (z). The standard value is determined using a wind load map.

The country's territory is divided into 8 zones with different nominal wind load values

The height coefficient is calculated from the table below based on the corresponding type of terrain:

1. A - coastal areas of bodies of water (seas, lakes), deserts, steppes and tundra.
2. B - urban area with obstacles and buildings 10–25 m high.
3. C - urban area with buildings from 25 m in height.

Table: coefficient for calculating wind load

Height z, m	Coefficient k for different types terrain
	A	IN	WITH
up to 5	0,75	0,50	0,40
10	1,00	0,65	0,40
20	1,25	0,85	0,55
40	1,50	1,10	0,80
60	1,70	1,30	1,00
80	1,80	1,45	1,15
100	2,00	1,60	1,25
150	2,25	1,90	1,55
200	2,45	2,10	1,80
250	2,65	2,30	2,00
300	2,75	2,50	2,20
350	2,75	2,75	2,35
480	2,75	2,75	2,75

Let's look at an example. It is necessary to determine the estimated wind load and draw a conclusion about the acceptable roof slope. Initial data: region - the city of Moscow with terrain type B, the height of the house is 20 m. We find Moscow on the map - zone 1 with a load of 32 kg/m 2. By combining the rows and columns of the table, we find that for a height of 20 m and type of terrain B, the required coefficient is 0.85. By multiplying the two numbers, we determine that the wind load will be 27.2 kg/m2. Since the obtained value is not large, it is possible to use a slope of 35–45°, otherwise you need to take a slope angle of 15–25°.

Snow load

Snow masses accumulating on the roof exert a certain pressure on the roof. The larger the snowdrifts, the greater the load. But not only the pressure of the snow is dangerous, but also its melting when the temperature rises. The average weight of newly fallen snow per 1 m 3 reaches 100 kg, and in its raw form this figure increases threefold. All this can cause deformation of the roof, a violation of its tightness, and in some cases lead to the collapse of the structure.

The greater the slope angle, the easier it is for snow deposits to be removed from the roof. In areas with heavy snowfall, the maximum slope slope should be 60º. But the construction of a roof with a slope of 45º also contributes to the natural removal of snow.

Under the influence of heat coming from below, the snow melts, increasing the risk of leaks.

Calculation of snow load on a gable roof

The snow load value is obtained by multiplying the average load (S), characteristic of a certain type of terrain, and a correction factor (m).

The average value of S is found from the snow load map of Russia.

The territory of Russia includes 8 snow regions

• The correction factor m varies depending on the roof slope:
• at a roof angle of up to 25 0 m is equal to 1;
• the average value of m for the range 25 0 –60 0 is 0.7;

for steeply sloped roofs with an angle of more than 60 0, the coefficient m is not included in the calculations. Let's look at an example. Need to determine snow load

for a house with a slope angle of 35 0, located in Moscow. From the map we find that the required city is located in zone 3 with a snow load of 180 kg/m2. The coefficient m is taken equal to 0.7. Therefore, the desired value of 127 kg/m2 will be obtained if we multiply these two parameters.

The total load, consisting of the weight of the entire roof, snow and wind loads, should not be more than 300 kg/m2.

Otherwise, you should choose a lighter roofing material or change the slope angle.

Roof type: attic or non-attic

There are 2 types of gable roofs: attic and non-attic. Their names speak for themselves. Thus, an attic (separate) roof is equipped with a non-residential attic, and a non-attic (combined) roof is equipped with a usable attic. If you plan to use the space under the roof to store items that are not used in everyday use, then there is no point in increasing the height of the roof ridge. Conversely, when planning a living room under the roof, the height of the ridge should be increased.

The height of any type of roof must be sufficient for interior repairs

Until recently, the construction market offered only a few types of roofing materials. It was traditional slate and galvanized steel sheet. Now the range has been significantly expanded with new products. When choosing a roofing material, several rules should be considered:

1. When reducing the dimensions of piece roofing materials, the angle of inclination is increased. It's connected with big amount joints that are potential places leak. Therefore, they try to make the precipitation disappear as quickly as possible.
2. For roofs with a low ridge height, it is preferable to use rolled roofing materials or large-sheet sheets.
3. The more the roofing material weighs, the steeper the roof slope should be.

The range of possible slopes is described in the manufacturer’s instructions for roof installation

Material type	Minimum slope, 0	Note
Metal tiles	22	Theoretically, installation on a roof with an angle of 11 0 –12 0 is possible, but for better sealing, choose a larger slope
Corrugated sheet	5	When the angle of inclination changes upward, the overlap of one sheet onto another increases
Asbestos cement slate	25	If the slope is less than recommended, snow will accumulate on the roof, under the weight of which the roofing material will collapse
Soft roll roofing (roofing felt, ondulin)	2	The minimum slope angle depends on the number of layers: for one layer 2 0, and for three - 15 0
Seam roofing	7	For roofs with a slight slope, it is recommended to purchase a double standing seam

Cost of a gable roof

It is logical that as the slope of the slope increases, the roof area increases. This leads to increased consumption of lumber and roofing materials and components (nails, screws) for securing them. The cost of a roof with a 60° angle is 2 times more than the creation flat roof, and a slope of 45° will cost 1.5 times more.

The greater the total load on the roof, the larger the section of timber used for the rafter system. With a slight roof slope, the sheathing pitch is reduced to 35–40 cm or the frame is made solid.

Accurate calculation of roof dimensions will save the family budget

Video: rafter system and roof parameters

Calculation of roof parameters

To quickly calculate roof dimensions, you can use an online calculator. The initial data (dimensions of the building’s base, type of roofing material, lift height) are entered into the program fields, and the result is the required value of the rafter slope, roof area, weight and quantity of roofing material. A small minus is that the calculation steps are hidden from the user.

For greater understanding and clarity of the process, you can carry out independent calculations of the roof parameters. There is a mathematical and graphical method for calculating the roof. The first is based on trigonometric identities. A gable roof is represented in the form of an isosceles triangle, the dimensions of which are the parameters of the roof.

Using trigonometry formulas you can calculate roof parameters

Calculation of the slope angle of roof slopes

The initial data for determining the slope angle is the selected roof height and half of its width. As an example, consider a classic gable roof with symmetrical slopes. We have: ridge height 3 m, wall length 12 m.

Dimensions c and d are usually called roof pitch

Sequence of slope calculation:

1. We divide the conditional roof into 2 right triangles, for which we draw a perpendicular from the top to the base of the figure.
2. Consider one of the right triangles (left or right).
3. Since the structure is symmetrical, the projections of slopes c and d will be the same. They are equal to half the length of the wall, i.e. 12/2 = 6 m.
4. To calculate the slope angle of slope A, we calculate its tangent. From the school course we remember that tangent is the ratio of the opposite side to the adjacent side. The opposite side is the height of the roof, and the adjacent side is half the length of the roof. We find that the tangent is 3/6 = 0.5.
5. To determine what angle the resulting tangent has, we use the Bradis table. Having found the value 0.5 in it, we find that the slope angle is 26 0.

To convert tangents or sines of angles into degrees, you can use simplified tables.

Table: determining the slope of the slope through the tangent of the angle for the range 5–60 0

Tilt angle roofs, 0	Tangent angle A	Sinus angle A
5	0,09	0,09
10	0,18	0,17
15	0,27	0,26
20	0,36	0,34
25	0,47	0,42
30	0,58	0,5
35	0,7	0,57
40	0,84	0,64
45	1,0	0,71
50	1,19	0,77
55	1,43	0,82
60	1,73	0,87

Calculation of the rise of a gable roof and the height of the ridge

The height of the roof is closely related to the steepness of the slope. It is determined in the reverse way to the method for obtaining the slope. The calculation is based on the angle of inclination of the roof, which is suitable for the given area depending on the snow and wind load, and the type of roof.

The greater the slope, the more free space under the roof

Procedure for calculating roof lift:

1. For convenience, we divide our “roof” into two equal parts, the axis of symmetry will be the height of the ridge.
2. We determine the tangent of the selected roof slope angle, for which we use Bradis tables or an engineering calculator.
3. Knowing the width of the house, we calculate the size of its half.
4. We find the height of the slope using the formula H = (B/2)*tg(A), where H is the height of the roof, B is the width, A is the slope angle of the slope.

Let's use the given algorithm. For example, it is necessary to set the height of a gable roof of a house with a width of 8 m and an angle of inclination of 35 0. Using a calculator we find that tangent 35 0 is equal to 0.7. Half the width of the house is 4 m. Substituting the parameters into the trigonometric formula, we find that H = 4 * 0.7 = 2.8 m.

A well-calculated roof height gives the house a harmonious look

The above procedure relates to determining the rise of the roof, i.e. the distance from the bottom of the attic floor to the support point of the rafter legs. If the rafters protrude above the ridge beam, then the full height of the ridge is determined as the sum of the roof rise and 2/3 of the thickness of the rafter beam.

Thus, the total length of the ridge for a roof with a rise of 2.8 m and a beam thickness of 0.15 m is equal to 2.9 m.

In places where ledges are cut for assembly with a ridge girder, the rafters are reduced by 1/3

Calculation of rafter length and roof width

1. To calculate the length of the rafters (hypotenuse in a right triangle), you can go in two ways:
2. Calculate the size using the Pythagorean theorem, which states: the sum of the squares of the legs is equal to the square of the hypotenuse.

Use the trigonometric identity: the length of the hypotenuse in a right triangle is the ratio of the opposite leg (the height of the roof) to the sine of the angle (the slope of the roof).

Let's consider both cases. Let’s say we have a roof rise height of 2 m and a span width of 3 m. We substitute the values ​​into the Pythagorean theorem and find that the desired value is equal to the square root of 13, which is 3.6 m.

Knowing the two legs of a triangle, you can easily calculate the hypotenuse or the length of the slope

The second way to solve the problem is to find the answer through trigonometric identities. We have a roof with a slope angle of 45 0 and a rise height of 2 m. Then the length of the rafters is calculated as the ratio of the number of rises of 2 m to the sine of the slope 45 0, which is equal to 2.83 m.

The width of the roof (Lbd in the figure) is the sum of the length of the rafters (Lc) and the length of the eaves overhang (Lкc). And the length of the roof (Lcd) is the sum of the length of the house wall (Ldd) and two gable overhangs (Lfs).

For a house with a box width of 6 m and overhangs of 0.5 m, the roof width will be 6.5 m.

Building codes do not regulate the exact length of the slope; it can be selected in a wide range of sizes Calculation of roof area. Let's look at a specific example. Let the roof of the house have a width of 3 m and a length of 4 m. Then the area of ​​one slope is 12 m 2, and the total area of ​​the entire roof is 24 m 2.

Incorrect calculation of the roof area can lead to additional costs when purchasing roofing material

Calculation of materials for the roof

To determine the amount of roofing materials, you need to arm yourself with the roof area. All materials are overlapped, so when purchasing you should make a small margin of 5–10% of the nominal calculations.

Correct calculation of the amount of materials will significantly save the construction budget.

1. General rules for calculating lumber:
2. Dimensions and cross-section of the Mauerlat. The minimum possible cross-section of the timber is 100×100 mm. The length corresponds to the perimeter of the box, the margin for connections is set around 5%. The volume of the beam is obtained by multiplying the cross-sectional dimensions and length. And if you multiply the resulting value by the density of wood, you will find the mass of lumber.
3. Size and number of rafters. The calculation is based on the total load on the roof (pressure from the roofing pie, snow and wind). Let's assume that the total load is 2400 kg/m2. The average load per 1 m of rafters is 100 kg. Taking this into account, the footage of the rafters will be equal to 2400/100 = 24 m. For a rafter length of 3 m, we get only 8 rafter legs or 4 pairs. The cross-section of the rafters is taken from 25x100 mm and above.

Volume of material for sheathing. It depends on the type of roofing: for bitumen shingles, a continuous sheathing is constructed, and for corrugated sheets or asbestos-cement slate, a sparse sheathing is constructed.

Let's look at the calculation of roofing materials using metal tiles as an example. This is sheet material mounted on the roof in one or several rows.

1. Calculation sequence:
2. Determination of the total area. To determine the total area of ​​the roofing material, the number of sheets is multiplied by the total area (the product of the total width and length) of one sheet. In our case, 8 * (1.18 m * 5 m) = 47.2 m 2. For gable structures, the result is multiplied by two. We find that the entire roof area is 94.4 m2.
3. Determining the amount of waterproofing. Standard roll waterproofing material has an area of ​​65m2 without overlap. The number of rolls is obtained by dividing the total roof area by the area of ​​the film, i.e. 94.4 m2 /65 m2 = 1.45 or 2 full rolls.
4. Determining the quantity of fasteners. There are 6–7 self-tapping screws per 1 m2 of roofing. Then, for our situation: 94.4 m 2 * 7 = 661 screws.
5. Determining the number of extensions (skates, wind bars). The total footage of the planks is 2 m, and work zone- 1.9 m due to partial overlap. Dividing the length of the ramp by the working length of the planks, we obtain the required number of additions.

Video: calculating materials for a gable roof using an online calculator

A graphical method for determining roof parameters is to draw it on a reduced scale. For it you will need a piece of paper (plain or graph paper), a protractor, a ruler and a pencil. Procedure:

1. The scale is selected. Its optimal value is 1:100, i.e. for every 1 cm of paper sheet there is 1 m of structure.
2. A horizontal segment is drawn, the length of which corresponds to the base of the roof.
3. The middle of the segment is located, from the point of which a perpendicular is drawn upward (a vertical line at an angle of 90 0).
4. Using a protractor, the required roof angle is plotted from the boundary of the roof base and an inclined line is drawn.
5. The intersection of the inclined line with the perpendicular gives the height of the roof.

Video: manual calculation of materials for a gable roof

The first thing people pay attention to is the visual appearance of the roof. Architects make sure that the roof is harmoniously combined with the facade of the building. But beauty alone is not enough. It is important to correctly calculate the parameters so that the design is durable and functional. Neglecting snow and wind loads or installing rafters at the wrong angle can cause roof destruction. And incorrect determination of the roof area will lead to additional costs for the purchase of missing materials. Therefore, you should approach calculations responsibly, paying attention to all the nuances.

The rafter system is the main part of the blood, which absorbs all the loads acting on the roof and resists them. To ensure high-quality functioning of rafters, correct calculation of parameters is required.

How to calculate the rafter system

To make calculations of the materials used in the rafter system on your own, simplified calculation formulas are presented in order to increase the strength of the system elements. This simplification increases the number of materials used, but if the roof has small dimensions, then such an increase will be unnoticeable. Formulas allow you to calculate the following types of roofs:

• single-pitched;
• gable;
• attic.

The service life of the roof largely depends on correct calculation

Video: calculation of the rafter system

Calculation of the load on the rafters of a gable roof

To build a sloping roof, you need a strong supporting frame to which all other elements will be attached. When developing a project, the required length and cross-sectional area of ​​the rafter beam and other parts of the rafter system that will be subject to variable and constant loads are calculated.

To calculate the system, you need to take into account the features of the local climate

Loads that act continuously:

• the mass of all elements of the roof structure, such as roofing material, sheathing, waterproofing, thermal insulation, interior lining attic or attic;
• a lot of equipment and various items that are attached to the rafters inside the attic or attic.

Variable loads:

• load created by wind and precipitation;
• the mass of the worker who performs the repair or cleaning.

Variable loads also include seismic loads and other types of special loads that place additional demands on the roof structure.

The angle of inclination of the slope depends on the wind load

In most areas Russian Federation The problem of snow load is acute - the rafter system must absorb the fallen mass of snow without deforming the structure (the requirement is most relevant for pitched roofs).

As the roof slope decreases, the snow load increases. The arrangement of a pitched roof with a slope close to zero requires the installation of rafters with a large cross-sectional area, with a small pitch. It will also need to be cleaned regularly. This also applies to roofs with an angle of up to 25 degrees.

• Sg is the mass of snow cover on a flat horizontal surface measuring 1 m 2. The value is determined according to the tables in SNiP “Rafter systems” based on the required area in which construction is being carried out;
• µ - coefficient taking into account the angle of inclination of the roof slope.

At an angle of inclination up to 25 0 the value of the coefficient is 1.0, from 25 o to 60 o - 0.7, over 60 o - the value of snow loads is not included in the calculations.

The amount of precipitation affects the calculation of the roof

Wind load is calculated using the formula: W = Wo × k, where:

• Wo is the magnitude of the wind load, determined according to the table values, taking into account the nature of the area where construction is taking place;
• k is a coefficient that takes into account the height of the building and the nature of the terrain.

With a building height of 5 m, the value of the coefficients is kA=0.75 and kB=0.85, 10 m - kA=1 and kB=0.65, 20 m - kA=1.25 and kB=0.85 .

Section of the rafters on the roof

Calculating the size of the rafter beam is not difficult if you take into account the following point - the roof is a system of triangles (applies to all types of roofing). Using the overall dimensions of the building, the angle of inclination of the roof or the height of the ridge, and using the Pythagorean theorem, the length of the rafters from the ridge beam to the outer edge of the wall is determined. The length of the cornice is added to this size (in the case where the rafters protrude beyond the wall). Sometimes the cornice is made by installing fillies. When calculating the roof area, the lengths of the fillies and rafters are summed up, which allows you to calculate the required amount of roofing material.

The cross-section of timber for rafters depends on many parameters

To determine the cross-section of the timber used when constructing any type of roof, in accordance with the required length of the rafters, the pitch of its installation and other parameters, it is best to use reference books.

The range of rafter beam sizes ranges from 40x150 to 100x250 mm. The length of the rafter is determined by the angle of inclination and the distance between the walls.

An increase in the slope of the roof entails an increase in the length of the rafter beam, and, accordingly, an increase in the cross-sectional area of ​​the beam. This is necessary in order to ensure the necessary structural strength. At the same time, the level of snow load is reduced, which means that rafters can be installed in larger increments. But by increasing the step, you increase the total load that will affect the rafter beam.

When making calculations, be sure to take into account all the nuances, such as humidity, density and quality of lumber if the roof is made of wood, and the thickness of the rolled steel used if the roof is made of metal.

The basic principle of calculations is as follows - the magnitude of the load acting on the roof determines the cross-sectional size of the beam. The larger the cross section, the stronger design, but the greater its total mass, and accordingly the greater the load on the walls and foundation of the building.

How to calculate the length of the rafters of a gable roof

The structural rigidity of the rafter system is a mandatory requirement, and its provision eliminates deflection when exposed to loads. Rafters bend if errors are made in the calculations of the structure and the size of the step with which the rafter beam is installed. If this defect is identified after completion of the work, it is necessary to strengthen the structure with the help of struts, thereby increasing its rigidity. When the length of the rafter beam is more than 4.5 m, the use of struts is mandatory, since deflection will be formed in any case under the influence of the beam’s own weight.

This factor must be taken into account when performing calculations.

The length of the rafters depends on their location in the system

Determining the distance between rafters

The standard step with which rafters are installed in a residential building is about 600–1000 millimeters. Its value is influenced by:

beam section;

roof characteristics;

roof angle;

width of insulation material.

It is not recommended to artificially reduce or increase the pitch of the rafters

1. Determining the required number of rafters takes into account the step with which they will be installed. For this: Selected optimal step
2. installations.
3. The length of the wall is divided by the selected step and one is added to the resulting value.
4. The resulting number is rounded to the nearest whole number.

The length of the wall is again divided by the resulting number, thereby determining the required installation step of the rafters.

Area of ​​the rafter system

1. When calculating the area of ​​a gable roof, the following factors must be taken into account:
2. The total area, which consists of the area of ​​two slopes. Based on this, the area of ​​one slope is determined and the resulting value is multiplied by the number 2.
3. In the case when one of the angles of the slope is more or less than 90°, in order to determine the area of ​​the slope, it is “divided” into simple figures and their area is calculated separately, and then the results are added up.
4. When calculating the area, the area of ​​chimney pipes, windows and ventilation ducts.
5. The area of ​​gable and eaves overhangs, parapets and firewalls is taken into account.

The calculation of the rafter system depends on the type of roof

For example, a house is 9 m long and 7 m wide, the rafter beam is 4 m long, the eaves overhang is 0.4 m, and the gable overhang is 0.6 m.

The value of the slope area is found by the formula S = (L dd +2×L fs) × (L c +L ks), where:

• Ldd – wall length;
• L fs – length of the pediment overhang;
• L c – length of the rafter beam;
• L ks is the length of the eaves overhang.

It turns out that the area of ​​the slope is S = (9+2×0.6) × (4+0.4) = 10.2 × 4.4 = 44.9 m2.

The total roof area is S = 2 × 44.9 = 89.8 m2.

If tiles or soft covering in rolls, the length of the slopes will become 0.6–0.8 m less.

The size of a gable roof is calculated to determine the required amount of roofing material. As the angle of inclination of the roof increases, material consumption also increases. The margin should be about 10–15%. It is caused by overlapping laying. To determine the exact amount of material taking into account the slope of the slopes, it is best to use reference books.

Video: gable roof rafter system

How to calculate the length of hip roof rafters

Despite the variety of roof types, their design consists of the same elements of the rafter system. For hip roofs:

Video: hip roof rafter system

What affects the angle of the rafters

For example, the slope of a pitched roof is about 9–20°, and depends on:

• type of roofing material;
• climate in the region;
• functional properties of the structure.

In the case when the roof has two, three or four slopes, then in addition to the geography of construction, the purpose will also have an impact attic space. When the purpose of the attic will be to store various property, then a large height is not required, but if used as a living space, a high roof with a large angle of inclination will be required. This is what follows:

• appearance of the front part of the house;
• roofing material used;
• influence of weather conditions.

Naturally, for areas with strong winds optimal choice there will be a roof with a small angle of inclination - to reduce the wind load on the structure. This also applies to regions with hot climates, where precipitation is often minimal. In areas with high precipitation (snow, hail, rain), a maximum roof slope is required, which can be up to 60 degrees. This angle of inclination minimizes the snow load.

The slope angle of any roof largely depends on the climate

As a result, to correctly calculate the angle of inclination of the roof, it is necessary to take into account all the above factors, so the calculation will be carried out in the range of values ​​​​from 9 o to 60 o. Very often the result of calculations shows that perfect angle the inclination ranges from 20° to 40°. With these values, the use of almost all types of roofing materials is allowed - corrugated sheets, metal tiles, slate and others. But it should be noted that each roofing material also has its own requirements for roof construction.

Without having the dimensions of the rafters at your disposal, you cannot start building a roof. Take this issue seriously. Do not limit yourself only to the calculations of the rafter system, the choice of its design and the determination of the operating loads. Building a house is an integral project in which everything is interconnected. In no case should elements such as the foundation, load-bearing structure of walls, rafters, and roof be considered separately. A high-quality project must take into account all factors comprehensively. And if you plan to build housing for your own needs, then the best solution will turn to specialists who will solve pressing issues and carry out design and construction without errors.