Calculation of the length of the rafters of a gable multi-level roof. Gable roof rafter calculator. Type of roofing and its weight

Building a roof on your own is a very real task. Of course, this requires a certain amount of knowledge, and first of all it concerns truss system- the main element of the roof, which perceives and resists all types of loads.

The truss system actually provides the rigidity of the roof structure, since it distributes the load from the lathing with the laid roofing material to the external and internal supports. Therefore, the reliability of the roof, its ability to withstand all influences, depends on how to calculate the truss system.

How to correctly calculate the truss system

The calculation of the elements of the truss system is performed in order to determine the optimal design parameters that ensure its ability to withstand the impact of the total weight of the roof, including coating and thermal insulation, under conditions of maximum exposure to external loads, wind and snow. In this regard, the question naturally arises of how to calculate the truss system for the total impact possible loads. For example, the weight of the coating, interior decoration ceilings, hail, wind, ice on the roof during the period, etc. The calculations use reliability factors, say, 1.1 and 1.4. The first increases the strength of the calculated roof by 10%, and the second - by 40%.

As a rule, the calculation scheme that is accepted in the calculations is “idealized”. It is believed that the roof is under the influence of a uniformly distributed load, that is, it experiences the same and even force, which evenly affects all slopes. In fact, such a picture is almost never found. For example, when the wind sweeps snow bags onto one slope, it simultaneously blows it off another. The force of impact on the slopes, therefore, is uneven.

Loads on rafters

Rafters experience two types of impact - temporary and permanent. The second includes the weight of the roof elements, including the roof, lathing, girders and rafters. The second is snow and wind. Temporary - also include useful, if any.

snowy

This type of impact can be a serious hazard to the reliability of the structure, since large volumes of snow accumulated on the roof have a significant effect on it. The amount of snow load is determined in horizontal projection by the formula:

S=Sg*µ ,

• Sg is the mass of snow cover per unit area of ​​the horizontal plane. This parameter depends on the location of the building.
• µ is a coefficient expressing the dependence on the angle of the roof. For example, for flat roofs up to 25⁰ - 1.0, for pitched with a slope of more than 25 ⁰< α < 60⁰ – 0,7. При крутом уклоне, свыше 60°, снеговая нагрузка не учитывается.

wind

To calculate the average wind load at a given height, the following formula is used:

W=W o x k,

wherein

• W o - standard value, it is selected according to the table, according to the wind region;
• k - coefficient of dependence of wind pressure on height, it differs depending on the area where the construction is carried out:

The correction for the wind in the calculation of the rafters is made only when the roof slope is more than 30 °.

The choice of type of terrain depends on the direction of the wind, which is used in the calculation.

How to calculate taking into account wind and snow

Let us calculate the climatic loads using the example of the Moscow Region, which is part of middle lane RF. Design values ​​are selected from SNiP 2.01.07-85*, namely "Loads and impacts".

Let's say the slope of the roof is 22⁰. This is the third snow region, for which the calculated value is 180 kg / m 2, and µ \u003d 1.0, then 180 x 1.0 \u003d 180 kg / m 2. For pitched roofs with a coefficient µ=0.7, this value is reduced to 126 kg/m 2 .

With the formation of a snow bag, the value of this indicator can increase to 400-500 kg / m 2.

The calculated wind load for the same region is 32 kg/m 2 . If we assume that we are talking about a 10-meter house, then the magnitude of the wind effect will be equal to 32 x 0.65 \u003d 20.8 kg / m 2.

Other

• The load created by the under-roof structure and the roof itself is calculated according to the size of the structure and the volume of materials used.
• Useful is taken into account for structures "associated" with roof trusses. For example, ceilings suspended from them, ventilation chambers or water tanks located on farms, etc.

When designing a roof, two types of calculations are carried out:

• by strength, which excludes damage to the rafter legs;
• by deformation, which determines the maximum degree of deflection of such a beam. So, the calculation of the truss system broken roof should take into account that the deflection of the rafters for such a construction should not be more than 0.004 of the length of the section, that is, for example, the maximum deflection of a 6-meter beam reaches 2 cm. At first glance, it may seem that this is not so much, however, if even slightly exceed the amount of deformation, it will become visually noticeable. And large deflections will make the roof look like a Chinese pagoda.

Calculation of elements

The design of the system is determined taking into account the following parameters:

• roof pitch,
• span span,
• section of rafters and purlins,
• total load from roofing, wind and snow,
• the distance between the rafters, its optimal value is determined by the limit method, that is, the value upon reaching which partial or complete destruction can be expected.

The cut (section) of the rafters is selected based on their length and the magnitude of the loads experienced.

The values ​​\u200b\u200bgiven in this table, of course, are not the result of a full-fledged calculation, they are only recommended for use when carrying out rafter work for simple structures.

A full-fledged calculation of the system is possible with sufficient theoretical knowledge, certain drawing and drawing skills. Fortunately, the task of designing today is greatly facilitated, thanks to convenient computer programs designed specifically for the development of projects of various building elements. They are suitable not only for professionals, but also for private users.

Example of calculation using programs

Step 1. Calculation of loads

At the first stage, the “Loads” window is selected in the menu and the necessary changes are made to the cells of the blue tables:

"Initial data"

• Change the slope of the slope and the pitch of the rafters to the intended ones. The next line of the table "Load. Roofs "fill in with data from the table below.

• The sum of pre-calculated loads from wind and snow is entered in the next cell. Next comes " Warming (mans.)"- the cell is left unchanged for a warm attic or enter 0 - for a cold one.
• The values ​​​​in the table "Crate" are also corrected.

If the filled in data is correct, the message "The bearing capacity of the crate is ensured!" should appear in the lower part of the window. Otherwise, you will need to change the dimensions of the crate or the distance between the rafters.

Step 2 Double Post Rafter

At this stage, they work with the “Sling” tab. one".

Starting from this tab, the data already entered into the table will be automatically inserted into the cells by the program.

What edits are made at this stage?

• They make changes to the value of the value of the horizontal projection of the rafters on the diagram and proceed to fill in the table " Calculation of rafters".
• The value of the thickness of the rafter, which is entered in the cell "In (given)" Must be greater than the specified "Vtr (stable)".
• The width of the rafters entered in the line “Accept H”, must exceed the values ​​\u200b\u200bspecified in the lines “Ntr., (deflection)" and "Ntr., (strength)". If all values ​​are substituted correctly, then the program under the scheme will “write”: “The condition is met”.

The line "N, (by sort)" is filled in by the program itself, but you should know that you can change the data yourself.

Step 3 Three-Post Rafter

Such rafters are calculated on the tab " Sling. 2" or " Sling. 3".

Which one to choose depends on the location of the intermediate support. The tabs differ in the location of the middle rack (support). In the case of L/L1<2, иначе говоря, она находится правее середины стропила, пользуются «Строп.2 », в противном случае – «Строп.3 ». Стойка может располагаться точно посередине, тогда не принципиально, какую из них выбрать – результат будет тот же. С этими вкладками работают аналогично «Строп. 1 ».

Step 4 Rack

The magnitude of the bending moment of the rack and the vertical impact on it is entered (in tons), respectively, in the cells "M =" and "N =". The inscriptions "Out-of-center. provided” and “Central provided!” in the center means admission to the next stage.

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

Calculation of rafters using online programs

It is easiest to calculate the rafters using an online calculator. You set the initial data, and the program calculates the necessary parameters. Existing programs are different in their functionality. A number of them are complex in nature and calculate many parameters of the truss system, others are much simpler and involve the calculation of one or two indicators. Among the complex services, it is worth highlighting the Stroy-calc series of construction calculators for calculating the parameters of roof rafters with one, 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 the roofing material, i.e., together with the calculation of the truss system, you can obtain data on the required amount of finishing coating from:

• ceramic tiles;
• cement-sand tiles;
• bituminous tiles;
• metal tiles;
• slate (asbestos-cement slabs);
• steel seam roof;
• bituminous slate.

In order to obtain the desired 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;
• lathing characteristics: width, board thickness, distance between rows;
• snow load on the rafters: selection of the snow load region on the map.

The program contains drawings of types of roofs, which graphically show the data entry parameters. As a result, information is displayed on:

• roof - slope angle, surface area, approximate weight of the roofing material;
• rafters - length, minimum section, quantity, volume of timber for rafters, their approximate weight, layout (drawing);
• crate - the number of rows, the distance between the boards, the 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 the loads on the rafters (snow, wind, roofing cake), as well as determining the parameters of the rafters (section, length, quantity, pitch). Based on these data, it will also be possible to calculate the amount of wood needed to equip the truss 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 cake (battens, insulation, hydro and vapor barriers). 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 - the desired value of the load;
• 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 - the norm of snow pressure in a particular region of the country (kg / m 2), calculated from 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 by the formula tg α \u003d H / L, where H is the height of the ridge, L is half the width of the building (along the gable side), tg α is the tangent of the desired angle. Further, the value of the angle itself is taken from special tables.

Table: slope angle value according to its tangent

Suppose the house is 8 m wide and 2.32 m high at the ridge. Then tg α = 2.32/4 = 0.58. According to the table, we find that α \u003d 30 o.

The coefficient μ is determined by the following method:

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

Thus, for the considered structure μ = 0.7. The value of S g is selected based on the location of the region in which construction is being carried out on the map of snow loads.

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

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

Table: normative snow load by region

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 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

The wind load depends on the region 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 according to the formula: W m \u003d W about ∙ K ∙ C, where:

• W about - standard value of wind pressure;
• K - coefficient taking into account the change in wind pressure at altitude;
• C - aerodynamic coefficient, taking into account the shape of the roof (with gentle or steep slopes).

The normative value of wind pressure is determined from the map of wind loads.

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

Table: standard wind load by region

According to the level of wind loads, the Moscow Region is in the first zone. Therefore, the standard value of wind pressure W about for our case is 32 kg/m 2 .

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

Table: coefficient taking into account wind pressure at altitude

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

The aerodynamic coefficient can range from -1.8 to 0.8. A negative coefficient means that the wind is trying to raise the roof (usually with gentle slopes), a positive coefficient means that it is tilting (with steep slopes). For reliability, we take the maximum value of this coefficient equal to 0.8.

The wind affects the roofs with steep and gentle slopes in different ways.

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 per square meter of the roofing cake will be equal to the sum of the specific gravity of all its constituent elements:

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

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

Table: weight of various types of roofing

For greater reliability, we take the maximum values ​​​​of the weight of the components of the roofing cake: P \u003d 12 + 5 + 2 + 1.2 + 10 \u003d 30.2 kg / m 2. We add a margin of 10% in case of 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 \u003d S + W m + P, where:

Recall that the calculation is carried out for the Moscow region, the roofing is corrugated board, the angle of inclination of the roof is 30 °: Q = 126 + 16.6 + 33.2 = 175.8 kg / m 2. Thus, the total load per square meter of rafters is 175.8 kg. If the roof area is 100 m 2, then the total load is 17580 kg.

It is erroneous to believe that reducing the weight of the roofing significantly reduces the load on the rafters. Let's take cement-sand tiles (50 kg / m 2) as a coating. Then the weight of the roof will increase by 45 kg / m 2 and will not be 33.2, but 76.4 kg / m 2. In this case, Q \u003d 126 + 16.6 + 76.4 \u003d 219 kg / m 2. It turns out that with an increase in the mass of the roofing by 10 times (from 5 to 50 kg / m 2), the total load increased by only 25%, which can be considered a not so 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 the installation of the truss system: section, length, quantity and pitch.

Selection of the cross section of the rafters

The cross section of the rafters is calculated by the formula: H \u003d K c ∙ L max ∙ √Q r / (B ∙ R izg), where:

• K c - coefficient equal to 8.6 at an angle of inclination less than 30 about, and 9.5 at a greater slope;
• L max - the largest span of the rafter;
• 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 resistance of wood to bending.

Let's calculate all the elements of this formula. First of all, we determine the load per linear meter of the rafter. This is done according to the formula: Q r \u003d A ∙ Q, where:

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

The logic of the calculation is quite simple: the less often the rafters are located and the smaller they are, the greater the load per linear meter will be.

We have already calculated the total load per 1 square meter of rafters. It is equal to 175.8 kg / m 2 for our example. Let us 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 width of the sawn timber section according to GOST 24454–80 "Softwood lumber". We look at what sections the wood is sawn - these are standard values.

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

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 span of the rafter (L max). To do this, you need to turn to the project and find a drawing of a truss truss, where all its dimensions will be indicated. Let us take in our case L max equal to 2.7 m.

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

The value of the resistance of the material to bending (R bend) depends on the type of wood. For the first grade, it is 140 kg / cm 2, the second - 130 kg / cm 2, the third - 85 kg / cm 2. 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 ​​\u200b\u200bin the above formula and get H \u003d 9.5 ∙ 2.7 ∙ √ (105.5) / (0.05x130) \u003d 103.4 mm. With a rafter thickness of 50 mm, there is no standard width value of 103.4 mm, so we take the nearest larger value from the table above. It will be 125 mm. Thus, a 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 / m 2 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

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

Influence of the type of roofing material on the angle of the roof slope

Permissible roof slope angles for roofing materials:

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

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 board, they can range from 20 o, metal tiles - 25 o, slate - 35 o, seam roof - 18 - 35 o.

The length of the rafters of different types of roofs is considered differently. We will show how this is done for a single-pitched and gable roof.

Calculation of the length of the rafters of shed roofs

The length of the rafter leg is calculated according to the formula L c \u003d L bc / sin A, where L bc is the amount by which the wall must be raised, and A is the angle of the roof slope. To understand the meaning of the formula for calculating L c, recall that the sine of the angle of a right triangle is equal to the ratio of the opposite leg to the hypotenuse. Thus, sin A \u003d L bc / L c. The value of L bc can be calculated by applying the formula: L bc \u003d L cd ∙ tg A, where L cd is the length of the wall of the house.

All formulas for calculating the truss system of a shed roof are taken from a right triangle, which is the projection of the under-roof space onto the gable

It is easiest to find the values ​​\u200b\u200bof tg A and sin A using the table.

Table: determination of the values ​​​​of trigonometric functions by the angle of the roof slope

Consider an example.

1. Let's take the length of the wall of the house, equal to 6 m, and the angle of inclination of the roof of 30 o.
2. Then the height of the wall rise L bc = 6 ∙ tg 30 o = 6 ∙ 0.58 = 3.48 m.
3. The length of the rafter leg L c \u003d 3.48 / sin 30 o \u003d 3.48 / 0.5 \u003d 6.96 m.

Calculation of the length of the gable roof rafters

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

The 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 \u003d b / (2 ∙ cos A). Let's say that the width of the house is 8 m, and the angle A is 35 o. Then a \u003d 8 / (2 ∙ cos 35 o) \u003d 8 / (2 ∙ 0.82) \u003d 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 in the ridge h are known. In this case a = √b 2 + h 2 . Let us 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 sawn wood is 6 meters. With a longer length, they will either need to be spliced ​​or made to order, which, of course, will be more expensive.

Video: rafter calculation

Rafter step calculation

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

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

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

Suppose that the approximate step is 1 m, and the length of the ramp is 12 m.

1. We divide the length of the slope by the approximately selected step size: 12 / 1 \u003d 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 \u003d 0.92 m.

It must be understood that the value obtained is the distance between the centers of the rafter logs.

The step between the rafters can also be determined from the table for a given cross section and the length of the rafter leg.

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

According to the same table, you can determine the permissible cross-section of the rafter, 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.

With the thickness of the beam of the rafter legs more than usual, the distance between the rafters can also be made larger.

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

Calculation of the number of rafters

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

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

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

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

For the construction of rafters, coniferous wood is most often used. Knowing how many rafters are required for the roof and how much wood is contained in one bar, we calculate the required amount of wood. Suppose that we have made a complete calculation of the truss system and received that 18 units of timber with a size of 150x150 mm are needed. Let's look at the table below.

Table: the amount of timber in a cubic meter of lumber

The volume of one bar 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: material calculation for gable roof rafters

The correct calculation of the main parameters allows you to make the truss system safe, reliable and durable. Knowing the required volume of wood allows you to save money on arranging rafters. Online calculators greatly facilitate the calculation of all the technical characteristics of the roof frame, save time on calculations and increase their accuracy.

The roof is an important structural part of the house, performing a number of the most important functions. It protects against atmospheric adversity and removes precipitation, provides insulation and makes a solid contribution to the formation of its own building style. In order for such a significant structure to "excellently" cope with the entrusted work, it is necessary to thoroughly think over the project and scrupulously figure out the dimensions.

Careful analysis and calculation of a gable roof is required for both independent craftsmen and owners of suburban property who resort to the services of construction organizations. Let's figure out how to do it right.

The roof, resembling an inverted V in a section, leads the list of pitched structures for a reason. In terms of simplicity of construction and economy, a gable roof has practically no rivals. For centuries, proven in practice, they are the basis for the construction of most roofing structures.

Unpretentious pitched planes do not require complex cutting of the coating and other materials, which results in an impressive amount of waste. No specific tricks are needed to implement intricate configurations. Precipitation does not linger on sloping surfaces, so there is no need to strengthen the waterproofing. As a result, the installation of a gable roof is often cheaper than a shed roof.

A roof with two slopes can be an independent object or part of a complex of structures of a similar or different form. Its simplest version does not have built-in dormer windows and canopies over the entrance porch, i.e. there are no additional fractures, ridges and accompanying valleys.

The absence of convex and concave corners deprives the master of "pleasure" to suffer with a number of difficult operations. Again, the owners will not get imaginary pleasure from leaks, which often appear at the joints of the pitched roof elements.

In principle, no one bothers fans of bizarre architecture to equip two ramps with numerous built-in structures. True, there are climatic limitations: in areas with a high volume of winter precipitation, the construction of roofs with numerous components is undesirable. In the grooves formed by excesses, favorable conditions are created for the accumulation of snow deposits. They will have to be cleaned faster than usual, and excessive zeal in the field of snow removal can cause damage to the coating with all the consequences.

However, adherents of simple and clear forms should not relax either. The corner roof configuration must be perfectly matched and calculated, otherwise it will not be able to perform the entrusted work flawlessly.

Despite the deceptive elementarity, there are tricks in determining the optimal form of the structure. It is impossible to overcome and get around them without knowing the technological subtleties, because all the parameters of the structure are interconnected:

• The width of the gable roof depends on the dimensions of the box and the type of coating, which in turn affects the selection of the steepness of the slopes.
• The slope of the roof depends on the climatic features of the construction area and on the type of roofing material.
• The combination of the above circumstances, width and slope, determines the height of the structure, which in the end may not meet architectural requirements and aesthetic considerations.

The impeccably designed roof has all the proportions perfectly matched. Its width and height determine the rise and slope necessary for the removal of precipitation in a particular area. Lower is impossible for technical reasons, higher is expensive and unreasonable, unless the unique architecture requires it.

Note that, coupled with an increase in steepness, the construction budget also increases. According to the slope, roofing material is selected. Focusing on its weight and specifics, design and calculate the truss frame. The calculation of the truss frame is carried out taking into account the listed parameters and taking into account the loads acting from the outside on the structure.

The interdependence of the proportions of the roof, the complexity of the construction of the truss frame and the nuances of the selection of the coating makes it necessary to determine the best shape through a banal selection. If something does not fit, replace or strengthen the supporting structures. Fortunately, the assortment on the construction market is now plentiful, and all kinds of methods have been developed to strengthen the structure.

If the upcoming calculations and shuffling of data are scary, it is better to resort to a win-win solution - a typical project. It is not for nothing that abroad all the houses of one settlement are equipped with roofs of equal height and covered with material of the same color and characteristics. Typification allows you to maintain landscape identity and reduce design costs.

However, even a typical design solution is not a panacea for technical troubles and aesthetic shortcomings. We must not forget about the individual dimensions of the box over which it is planned to build a roof. Compatriots deny leveling in height and steepness, therefore it is still desirable for us to deal with the proportions of the roof structure.

Step by step calculations

The configuration and dimensions of any pitched roof are set by the truss frame. On the edges of the rafter legs, slopes are laid, forming a dihedral angle. They construct truss systems from rolled metal and wood, use industrial structures and lumber in construction.

Let's look at the options available for the efforts of an independent master, i.e. construction method of erecting a roof frame from lumber.

Stage # 1 - choosing the type of truss system

The method of constructing a gable roof is indirectly related to the dimensions, but without taking into account the difference in the arrangement of structures, it will be difficult to understand the geometric parameters.

In the construction of gable roofs, two traditional technologies are used:

• Layered, according to which the top and bottom of the rafters have a strong fulcrum. The walls of the house, equipped with a Mauerlat, serve as the lower support. The top of the layered rafter legs rests on a running beam that forms a ridge. The girder is supported on a support system built specifically for it, on the inner wall or on the stone gables of the box, erected to the roof. The layered method is mainly used in the arrangement of large houses with an internal load-bearing wall or a row of columns.
• hanging, according to which the tops of the rafters rest only against each other. The walls serve as a support for the bottom, as in the previous case. Hanging rafter legs form an equilateral triangle, the base of which is called a puff. Taken together, such a system does not create thrust, i.e. does not transfer the bursting load to the walls of the box. Rafter triangles are installed either ready for installation, i.e. assembled on the ground, or constructed from separate rafters on site. The absence of an upper support makes adjustments to the scope of use: the hanging method is used in the arrangement of only small buildings with small spans.

Schemes of truss systems of both types include a minimum of structural elements when overlapping boxes up to 8-10m wide.

When arranging spans larger, there is a danger of deformation of the rafter legs. To eliminate sagging and deflection of wooden parts made of lumber, reinforcing elements are installed: struts, contractions, side runs, etc.

Additional details provide rigidity and stability of a large structure, but increase the load. How the total load is determined and produced, we have already analyzed.

Step #2 - Width Calculation

Both types of wooden truss systems are built along the floor beams or along the Mauerlat. How the width of the roof is calculated depends on the type of base:

• When mounted on floor beams, it is they who form the cornice overhang, i.e. determine the dimensions of the roof.
• When installed on a Mauerlat, the width of the roof is determined by adding three values. You need to sum up the width of the box and two projections of the width of the cornice overhang. However, only the bearing part of the width of the roof, equal to the width of the box, is used in the calculations.

The function of the Mauerlat in frame buildings is performed by the upper trim, which at the same time connects the disparate elements into a single frame. In wooden construction, the upper crown, folded with a bar or log, serves as a Mauerlat.

In the case of using the "beam" scheme of the device, the so-called matrices are used - bars or logs laid under the upper crown of the foot as an overlap.

Eaves overhangs of roofs installed on the Mauerlat can be formed directly by rafter legs, fillies sewn to them or a brick ledge. The latter option, of course, is used in the construction of brick walls. The choice of the width of the overhang is dictated by the type of roofing and the material from which the walls are composed.

• For a slate roof no more than 10cm;
• For bituminous tiles in the range of 30-40cm;
• For metal tiles 40-50cm;
• For profiled sheet 50cm;
• For ceramic tiles 50-60cm.

Walls made of logs and timber require enhanced protection from slanting rains, therefore the overhangs above them are usually increased by 10-15 cm. If the limit value of the overhang width recommended by the manufacturer is exceeded, it is necessary to provide for measures to strengthen it.

It is possible to install external struts on the walls or support pillars, which can simultaneously play the role of structural elements of the terrace, porch, veranda.

Stage # 3 - determining the slope

The angle of inclination of the slopes is allowed to vary within the widest limits, on average from 10º to 60º with permissible deviations in both directions. Traditionally, both planes of a gable roof have equal angles of inclination.

Even in asymmetric structures for residential buildings, they are mainly placed at an equal angle, and the effect of asymmetry is achieved by constructing different-sized slopes. Most often, differences in the slope of the main parts of the roof are observed during the construction of country houses and domestic facilities.

The procedure for determining the optimal steepness of a gable roof is significantly influenced by three factors:

• The type of coating, coupled with the weight of the crate intended for it. The type of roofing material determines the installation technology and the method of arranging the base for its fastening. The denser the roof is, the lower the value of the slope can be. The fewer overlaps and joints between the elements of the coating, the lower the roof is allowed to be. And vice versa.
• Roof weight with. A heavy coating located at an angle to the horizon presses on the base only with its projection. In short, the higher the slope, the less mass is transferred to the floor. Those. under a heavy roof you need to build a steep roof.
• Climatic specificity of the region. The high slope helps to quickly drain snow and water, which is highly desirable in areas with significant rainfall. However, high slopes are very sensitive to the effects of winds that tend to overturn them. Therefore, in regions with characteristic strong winds, it is customary to build gently sloping structures, and in areas with abundant rainfall, roofs with a high slope.

In the regulatory documentation used in calculating the angles for the construction of gable roofs, there are units that can confuse inexperienced home builders in roofing. The simplest value is expressed in dimensionless units, the most understandable - in degrees.

The second version conveys the ratio of the height of the roof to half its width. To determine it, a line is drawn from the central point of overlap to the top of the roofing triangle. The real line is drawn on the diagram of the house, imaginary at the facility. The value is indicated either as a percentage, or as a mathematical ratio such as 1: 2.5 ... 1: 5, etc. In percentages, it is wiser and more inconvenient.

Stage # 4 - determining the height of the skate

A roof with two slopes, at the request of the owner, may or may not have an attic. In the attic spaces of gable roofs, it is not supposed to arrange useful premises. There is for this. However, the height of the attic used for servicing and inspecting roofs at an angle is not arbitrary.

According to the requirements of the fire service from the top to the ceiling should be at least 1.6 m. The upper limit is dictated by the aesthetic beliefs of the designers. They argue that if the height of the roof is greater than the height of the box, then it seems to “press” on the building.

The height of the ridge top for hanging roofs arranged on beams is easiest to determine by the drawing method:

• We draw a diagram of the box of the house on a scale.
• We are looking for the middle of the upper floor.
• From the middle up we lay the axis of symmetry.
• On either side from the middle, we set aside half the width of the roof - we get the extreme point of the overhang.
• With the help of a protractor, from the extreme point of the overhang, we draw a straight line at an angle recommended by the roofing manufacturer. The point of its intersection with the axis will be the top of the roof. We measure the distance from the top to the overlap, we get the height.

To get a complete picture, on the diagram you need to draw a second slope in a similar way. Parallel to the lines of the drawn slopes, two more lines must be drawn at a distance equal to the thickness of the rafter legs on the same scale.

If the configuration of the roof does not suit you, you can "play" with the height on paper, changing the position of the vertex point and the slope of the roof within reasonable limits. The same manipulations can be carried out in one of the drawing programs.

When drawing the outline of a roof constructed using layered technology, the thickness of the running beam should be taken into account. With impressive power, it will slightly shift the position of the slopes.

Craftsmen believe that the calculations of the elements of the truss system for the construction of a gable roof can generally be reduced to calculating only the section of the run. This is the most loaded element, all the others have the right to be thinner. For example, if calculations show that a 100 × 150 mm material is required for a ridge run, then a 50 × 150 mm board is enough for rafters, supports, struts.

The process of finding the height of structures with overhangs formed by filly is slightly different from the described method. It’s just that the slope angle is drawn not from the extreme point of the overhang, but from the lower attachment point of the rafter to the Mauerlat. In any case, it is better to choose variations with the steepness and dimensions of the gable roof planned for construction on “paper” than on the construction site.

Stage # 5 - calculation of material consumption

A normal owner thinks ahead of time about the construction budget. True, in the preliminary estimate, by definition, there will be inaccuracies. The process of erecting a gable roof will impose its own adjustments on the initial calculation of the material, but it will help to find out the amount of basic expenses.

The preliminary estimate should include:

• Beam for the Mauerlat device. In residential construction, lumber with a cross section of 100 × 150 mm to 200 × 200 mm is used. The footage is calculated around the perimeter of the box with a 5% margin for processing and connections. A similar material is purchased for the bed device, if it is designed.
• Board for the manufacture of rafters. Most often, for the manufacture of rafter legs, material is used with a cross section from 25 × 150 mm to 100 × 150 mm. The footage is determined by multiplying the length of the outer edge by the number. The material is purchased with a margin of 15-20%.
• A board or bar for making struts, puffs and supports with a section of 50 × 100, 100 × 100 mm, depending on the project. You also need a margin of about 10%.
• Material for the device of the crate. Its consumption depends on the type of finish coating. The crate is constructed either solid, if it will be produced, or sparse for corrugated board, metal tiles, ordinary tiles, slate, etc.
• Roll waterproofing, the footage of which determines the type of roof and the steepness. High roofs are covered with a waterproofing carpet only along the overhangs, the ridge and in convex or concave corners. Gentle ones are covered with a continuous carpet.
• Finish coating. Its amount is calculated by summing the area of ​​​​the slopes. If there are embedded dormer windows, then their areas are also calculated. Only calculated as a rectangle, not in fact. The amount of laying stock is recommended by the coating manufacturers.
• Material for sheathing gables and overhangs.
• Corners, plates, self-tapping screws, staples, nails. We need anchors and studs, their number will tell the project.

You will also need shaped elements for arranging through passages through the roof, valleys, overhangs, ridge. The cost estimate presented is valid for a cold design. For an insulated roof, it will be necessary to purchase insulation and a vapor barrier film, a bar for a control batten and material for roof sheathing from the inside.

The gable roof has long been a classic of architecture. The list of its advantages includes ease of installation, low maintenance costs and practicality in terms of the natural removal of rainwater and snow. In order to fully experience these advantages, it is necessary to correctly think over the roof project and calculate the dimensions. This is the only way to make the structure durable and maintain an attractive appearance for many years.

The main parameters of the gable roof

The selection of the optimal roof size is a complex process of finding a compromise between the desired appearance of the building and the requirements for its safety. 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 a value that determines the position of the slope relative to the horizon. 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 there are also asymmetric varieties.

Most often there are roofs with a slope of 20 ° to 45 °

The unit of measure for slope is degrees. For roofs, the range 1 0 -45 0 is accepted. The larger the number, the sharper the structure, and vice versa, as the degree decreases, the roof becomes sloping.
Depending on the slope, several types of roofs are distinguished:

• 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;
• gently sloping (up to 30 °), allowing the use of all existing materials as roofing, but more expensive in cost than flat;
• steep (more than 30°), capable of self-cleaning, but not resistant to wind loading.

An inclinometer is used to measure the slope angle. Modern models are equipped with an electronic scoreboard and a 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° is 5 times higher than on a roof with an angle of 11°
Steep slopes, due to the large slope of the slope, drain precipitation well
A multi-slope roof is erected if necessary to connect walls of different heights or a neighboring extension to the house
The minimum slope angle recommended by builders is 14°

In a number of 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 percentage value is very different from the variant in degrees. So, 10 equals 1.7%, and 300 equals 57.7%. For error-free and quick conversion of one unit of measure to another, special tables have been created.

Table: relationship between slope units

Skate height

Another important parameter of the roof is the height of the ridge. The ridge is the top point of the truss 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 allows you to evenly distribute the load on the entire structure. Structurally, it is a horizontal rib made of a wooden beam. If we 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 a right triangle

Total roof width and overhang width

The total width of the roof is determined by the width of its box (the size of the truss system) and the width of the eaves.

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

The required size of the cornice 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 side of the pediment;
• eaves - a wider overhang that is along the roof.

To protect the lower surface, the overhang is sheathed with edged boards, siding or spotlights.

Photo gallery: roofs with different widths of overhangs

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.
A wide cornice gives monumentality to the entire building

Factors affecting 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. The design parameters are determined by considering a group of factors: the 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 can be influenced by various natural forces and loads. Among them - wind, snow pressure and the impact of water. You can determine their value by contacting a special construction organization that performs such surveys. 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, which meets an obstacle on its way, is divided, rushing in opposite directions: to the foundation and the overhang of the roof. Excessive pressure on the overhang can cause the roof to fall off. To protect the building from destruction, the aerodynamic coefficient is estimated, which depends on the angle of inclination of the slope.
The steeper the slope and the higher the ridge, the stronger the wind load per 1 m 2 of the surface. In this case, the wind tends to topple the roof. Hurricane winds have a different effect on sloping roofs - the lifting force lifts and carries away the crown of the house. Therefore, for areas with weak or moderate wind strength, roofs with any ridge height and angle of inclination can be designed. And for places with strong gusts of wind, low-slope species 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 crate

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 the wind load map.

The territory of the country is divided into 8 zones with different nominal values ​​of wind load

The height factor is calculated from the table below based on the respective terrain type:

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

Table: coefficient for calculating the wind load

Consider an example. It is necessary to determine the design wind load and draw a conclusion about the acceptable slope of the roof. Initial data: region - the city of Moscow with a view of the terrain 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 obtain that for a height of 20 m and terrain type B, the required coefficient is 0.85. Multiplying two numbers, we determine that the wind load will be 27.2 kg / m 2. Since the value obtained is not large, it is possible to use a slope of 35–45 °, otherwise it is necessary to take a slope angle of 15–25 °.

Snow load

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

The greater the slope of the slope, the easier the snow deposits are removed from the roof. In areas with heavy snowfalls, a maximum slope of 60º should be taken. But the construction of a roof with a slope of 45º 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 the correction factor (m). The average value of S is found on the snow load map of Russia.

The territory of Russia includes 8 snow regions

The correction factor m varies depending on the slope of the roof:

• with a roof angle of up to 25 0 m equals 1;
• the average value of m for the range 25 0 -60 0 is 0.7;
• for steep roofs with an angle of more than 60 0, the coefficient m is not included in the calculations.

Consider an example. It is necessary to determine the snow load for a house with a slope angle of 35 0 located in Moscow. On the map we find that the required city is located in zone 3 with a snow load of 180 kg/m 2 . The coefficient m is taken equal to 0.7. Therefore, the desired value of 127 kg / m 2 will be obtained by multiplying these two parameters.

The total load, consisting of the weight of the entire roof, snow and wind loads, should not exceed 300 kg / m 2. Otherwise, you should choose a lighter roofing material or change the slope of the slope.

Roof type: attic or non-attic

There are 2 types of gable roofs: attic and non-attic. Their names speak for themselves. So, the attic (separate) roof is equipped with a non-residential attic, and the non-attic (combined) roof is equipped with an exploited attic. If you intend to use the space under the roof for storing items that are not used in everyday life, then it makes no sense to increase 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 to carry out internal repairs.

For non-residential roofs, the height of the ridge is determined by fire safety rules. Building codes state that the attic must contain a through passage 1.6 m high and 1.2 m long. For residential roofs, the height is set based on their convenience of living and trouble-free placement of furniture.

Type of roofing material

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

1. With a decrease in the dimensions of piece roofing materials, the angle of inclination is increased. This is due to the large number of joints, which are potential places for leaks. Therefore, they try to make the rainfall as fast 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 interval of possible slopes is described in the manufacturer's instructions for installation of the roof.

The cost of a gable roof

It is logical that with an increase in the slope of the slope, the roof area increases. This leads to an increased consumption of sawn and roofing materials and components (nails, self-tapping screws) for their fastening. The cost of a roof with an angle of 60° is 2 times more than the creation of a flat roof, and a slope of 45° will cost 1.5 times more.

The greater the total load on the roof, the greater the cross section of the beam is used for the rafter system. With a slight slope of the roof, the step of the crate 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 the dimensions of the roof, you can use the online calculator. Initial data are entered into the program fields (building base dimensions, type of roofing material, lifting height), and the result is the required value of the slope of the rafters, roof area, weight and amount of roofing material. A small minus - the calculation steps are hidden from the user.

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

Using trigonometry formulas, you can calculate the parameters of the roof

Calculation of the slope angle of the 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: the height of the ridge is 3 m, the length of the wall is 12 m.

Dimensions c and d are usually called the laying of the roof

Slope calculation sequence:

1. We divide the conditional roof into 2 right-angled 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 design is symmetrical, the projections of the 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 the tangent is the ratio of the opposite leg to the adjacent one. The opposite side is the height of the roof, and the adjacent side is half the length of the roof. We get that the tangent is 3/6 = 0.5.
5. To determine which angle the resulting tangent has, we will use the Bradis table. Finding a value of 0.5 in it, we find that the slope angle is 26 0.

Simplified tables can be used to convert tangents or sines of an angle to degrees.

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

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 slope method. The calculation is based on the angle of inclination of the roof, which is suitable for the area, depending on the snow and wind load, the type of roof.

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

The procedure for calculating the rise of the roof:

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 according to the formula H \u003d (B / 2) * tg (A), where H is the height of the roof, B is the width, A is the angle of the slope 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 the tangent of 35 0 is 0.7. Half the width of the house is 4 m. Substituting the parameters into the trigonometric formula, we find that H \u003d 4 * 0.7 \u003d 2.8 m.

Properly calculated roof height gives the house a harmonious look

The above procedure refers to determining the rise of the roof, that is, the distance from the bottom of the attic floor to the fulcrum 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 rise of the roof and 2/3 of the thickness of the rafter beam. So, 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 2.9 m.

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

Calculation of the length of the rafters and the width of the roof

To calculate the length of the rafters (the hypotenuse in a right triangle), you can go in two ways:

1. Calculate the size using the Pythagorean theorem, which says: the sum of the squares of the legs is equal to the square of the hypotenuse.
2. Use the trigonometric identity: the length of the hypotenuse in a right triangle is the ratio of the opposite leg (roof height) to the sine of the angle (roof slope).

Let's consider both cases. Let's say we have a roof height of 2 m and a span of 3 m. We substitute the values ​​\u200b\u200binto the Pythagorean theorem and we get 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 of 2 m. Then the length of the rafters is calculated as the ratio of the rise number of 2 m to the slope sine of 45 0, which equals 2.83 m.

The width of the roof (in the figure Lbd) is the sum of the length of the rafters (Lc) and the length of the eaves overhang (Lkc). And the length of the roof (Lcd) is the sum of the length of the wall of the house (Ldd) and two gable overhangs (Lfs). For a house with a box width of 6 m and overhangs of 0.5 m, the width of the roof will be 6.5 m.

Building codes do not regulate the exact value of the slope length, it can be selected in a wide range of sizes

Roof area calculation

Knowing the length of the slope and the width of the roof, you can easily find its area by multiplying the indicated dimensions. For a gable roof, the total roof area is equal to the sum of the areas of both surfaces of the slopes. Let's take a look at a specific example. Let the roof of the house be 3 m wide and 4 m long. Then the area of ​​​​one slope is 12 m 2, and the total area of ​​\u200b\u200bthe 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, it is necessary to arm yourself with the area of ​​\u200b\u200bthe roof. All materials are overlapped, so when buying, you should make a small margin of 5-10% of the nominal calculations. The correct calculation of the amount of materials will significantly save the construction budget.

General rules for calculating lumber:

1. Dimensions and section of the Mauerlat. The minimum possible cross-section of a beam is 100 × 100 mm. The length corresponds to the perimeter of the box, the margin for connections is set in the region of 5%. The volume of the beam is obtained by multiplying the dimensions of the section and the length. And if you multiply the obtained value by the density of wood, then there is a mass of lumber.
2. The size and number of rafters. The calculation is based on the total load on the roof (pressure of the roofing cake, snow and wind). Let's assume that the total load is 2400 kg/m 2 . The average load per 1 m of rafters is 100 kg. Given this, the footage of the rafters will be 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.
3. The amount of material for the crate. It depends on the type of roofing: for bituminous tiles, a continuous crate is constructed, and for corrugated board or asbestos-cement slate, a sparse one.

Consider the calculation of roofing materials using the example of a metal tile. This is sheet material mounted on the roof in one or more rows.

Calculation sequence:

1. Determining the number of sheets. The metal tile sheet has a total width of 1180 mm and a working width of 1100 mm. The latter is smaller than the real one and is not taken into account in the calculation, since it goes to overlap the joints. The number of sheets is defined as the ratio of the total width of the roof (together with overhangs) to the useful width of the sheet. Moreover, the result of the division is rounded up to the nearest whole number. So, for a roof with a slope width of 8 m and a Monterrey metal tile sheet 1.1 m wide, the number of sheets is found by the formula: 8 / 1.1 \u003d 7.3 pcs, and taking into account rounding, 8 pcs. If the canvas is laid in several vertical rows, then the length of the slope is divided by the length of the roofing sheet, taking into account the overlap between the sheets up to 15 cm. Considering that the roof is gable, the value is doubled, that is, 16 sheets are required in total.
2. Determination of the total area. To determine the total area of ​​\u200b\u200bthe 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) \u003d 47.2 m 2. For gable structures, the result is multiplied by two. We get that the entire roof area is 94.4 m 2.
3. Determining the amount of waterproofing. A standard roll of 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 m 2 / 65 m 2 = 1.45 or 2 full rolls.
4. Determining the amount of fasteners. There are 6-7 self-tapping screws per 1 m 2 of the roof. Then, for our situation: 94.4 m 2 * 7 = 661 self-tapping screws.
5. Determination of the number of extensions (skates, wind bars). The total footage of the planks is 2 m, and the working area is 1.9 m due to partial overlap. Dividing the length of the slope by the working length of the slats, we obtain the required number of extensions.

Video: calculation of materials for a gable roof using an online calculator

The graphical method for determining the parameters of the roof is to draw it on a reduced scale. For him, you will need a piece of paper (plain or millimeter), 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 a paper sheet, there is 1 m of the 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 found, from the point of which a perpendicular is drawn upward (a vertical line at an angle of 90 0).
4. With the help of a protractor, the required angle of the roof is laid off from the border 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 they pay attention to is the visual appearance of the roof. Architects make sure that the roof is in harmony 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. Neglect of snow and wind load, installation of rafters at the wrong angle can cause the destruction of the roof. And an incorrect determination of the roof area will lead to additional costs for the purchase of missing materials. Therefore, one should responsibly approach calculations, paying attention to all the nuances.

Online calculator produces exact calculation of rafters online(calculates the dimensions of the rafters for the roof: the length of the rafters, the length of the overhang, the angle of the cut, the distance to the gash). Drawings and dimensions of rafters are generated in real time.

The calculator provides an online calculation of the length of the rafters gable roof. Calculate the rafters of a shed roof with another calculator.

In the "Specify dimensions" block, you must enter the roof data, after selecting the units of measurement that suit you. The image clearly shows all the necessary parameters.

The dimensions required for calculating the rafters:

• roof height- the distance from the level of the "floor" of the attic to the ridge of the roof.
• roof width- the distance between the support points of the rafters. Usually this is the edge of the Mauerlat on the outside of the wall.
• Eaves is the distance from the edge of the wall to the edge of the roof.
• Rafter Width- the width of the rafter board (usually 10 - 15 cm).
• Rafter thickness- thickness of the rafter board (usually 5 cm)
• Washed down depth- the distance from the edge of the board to the extreme point of the gash (you can not do more than 1/3 of the width of the rafter board)

The distance from the edge of the rafter board to the cut should be marked only at the angle of the cut, which the rafter calculation calculator gives you.

The calculated dimensions of the rafters may differ slightly during construction due to the presence of errors at the construction site. Please consider this nuance and before making the entire truss system, make one rafter, which you will use later as a template.

On the tab " 3D viewing"A three-dimensional model of the finished rafter is presented, which can be viewed from all sides: rotate, move, zoom in, reduce. To move the rafter model, first move the cursor over the model, hold down the right mouse button, then move. The rafter model is rotated by holding the left mouse button. To move the rafter model, zoom in/out scroll the mouse wheel.

The thickness of the rafter is determined from the loads on the rafter system, from the step between the rafters, from the length of the rafter, etc. To determine the thickness of the rafters, use the useful article on our website Correct calculation of the truss system.

The gable roof rafter calculator will help to greatly simplify independent calculations, determine the main required dimensions, as well as the amount of material required for the construction of gable roof rafters.