Gable roof rafter calculator. Calculation of rafters: execution methodology, examples, automation. Calculation of wind load on a gable roof

The main element of the roof, perceiving and resisting all types of loads, is rafter system. Therefore, in order for your roof to reliably resist all influences environment is very important to do correct calculation rafter system.

For self-calculation of the characteristics of the materials necessary for the installation of the truss system, I give simplified formulas calculation. Simplifications are made in the direction of increasing the strength of the structure. This will cause some increase in lumber consumption, however, small roofs individual buildings, it will be insignificant. These formulas can be used when calculating gable attic and mansard, as well as shed roofs.

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

The calculation methodology was compiled on the basis of SNiP 2.01.07-85 "Loads and impacts", taking into account the "Changes ..." of 2008, as well as on the basis of formulas given in other sources. I developed this technique many years ago, and time has confirmed its correctness.

To calculate the rafter system, first of all, it is necessary to calculate all the loads acting on the roof.

I. Loads acting on the roof.

1. Snow loads.

2. Wind loads.

On the truss system, in addition to the above, the load from the roof elements also acts:

3. Roof weight.

4. The weight of the rough flooring and lathing.

5. The weight of the insulation (in the case of an insulated attic).

6. The weight of the rafter system itself.

Let's consider all these loads in more detail.

1. Snow loads.

To calculate the snow load, we use the formula:

Where,
S - the desired value of the snow load, kg / m²
µ is a coefficient depending on the slope of the roof.
Sg - normative snow load, kg/m².

µ - coefficient depending on the slope of the roof α. Dimensionless value.

You can approximately determine the angle of the roof slope α by the result of dividing the height H by half the span - L.
The results are summarized in the table:

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

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

if 30° is calculated by the formula:

µ = 0.033 (60-α);

Sg - normative snow load, kg/m².
For Russia, it is accepted according to map 1 of mandatory annex 5 of SNiP 2.01.07-85 "Loads and impacts"

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

For example,

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

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

According to map 1 of the mandatory annex 5 of SNiP 2.01.07-85 "Loads and impacts", we determine Sg - the standard snow load for the city of Ivanovo (IV district):
Sg=240 kg/m²

We determine the angle of the roof slope α.
To do this, we divide the height of the roof (H) by half the span (L): 2.5 / 3.5 \u003d 0.714
and according to the table we find the slope angle α=36°.

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

Then S \u003d Sg µ \u003d 240 0.79 \u003d 189 kg / m²;

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

2. Wind loads.

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

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

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

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

K is a coefficient that takes into account the change in wind pressure along the height. Its values, depending on the height of the building and the nature of the terrain, are summarized in Table 3.

C - aerodynamic coefficient,
which, depending on the configuration of the building and the roof, can take values ​​from minus 1.8 (the roof rises) to plus 0.8 (the wind presses on the roof). Since our calculation is simplified in the direction of increasing strength, we take the value of C equal to 0.8.

When building a roof, it must be remembered that wind forces tending to lift or tear off the roof can reach significant values, and, therefore, the bottom of each rafter leg must be properly attached to walls or mats.

This is done by any means, for example, using annealed (for softness) steel wire with a diameter of 5 - 6 mm. With this wire, each rafter leg is screwed to the mats or to the ears of the floor slabs. It's obvious that the heavier the roof, the better!

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

According to map 3 of application 5 in "SNiP 2.01.07-85" we find that Ivanovo region refers to the second wind region Wo= 30 kg/m²

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

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

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

For information: if the wind blows at the end of this roof, then a lifting (tearing) force of up to 33.6 kg / m² acts on its edge

3. Roof weight.

Different types of roofing have the following weight:

1. Slate 10 - 15 kg/m²;
2. Ondulin (bituminous slate) 4 - 6 kg/m²;
3. Ceramic tiles 35 - 50kg/m²;
4. Cement-sand tiles 40 - 50 kg/m²;
5. bituminous tiles 8 - 12 kg/m²;
6. Metal tile 4 - 5 kg/m²;
7. Decking 4 - 5 kg/m²;

4. The weight of the rough flooring, lathing and truss system.

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

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

And now I will reveal to you little secret. Sellers of certain types of roofing materials as one of the positive properties they note their lightness, which, according to their assurances, will lead to significant savings in lumber in the manufacture of the truss system.

As a refutation of this statement, I will give the following example.

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

Let's calculate the load on the truss system when using the heaviest (Cement-sand tile
50 kg/m²) and the lightest (Metal tile 5 kg/m²) roofing material for our house in the village of Babenki, Ivanovo region. RF.

Cement-sand tiles:

Wind loads - 24kg/m²
Roof weight - 50 kg/m²
Lathing weight - 20 kg/m²

Total - 303 kg/m²

Metal tile:
Snow loads - 189kg/m²
Wind loads - 24kg/m²
Roof weight - 5 kg/m²
Lathing weight - 20 kg/m²
The weight of the truss system itself is 20 kg / m²
Total - 258 kg/m²

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

So, with the calculation of the total load Q, acting on a square meter of the roof, we figured it out!

I especially draw your attention: when calculating, carefully follow the dimension !!!

II. Calculation of the truss system.

truss system consists of separate rafters (rafter legs), so the calculation is reduced to determining the load on each rafter leg separately and calculating the section of a separate rafter leg.

1. Find the distributed load on running meter each rafter leg.

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

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

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

When choosing a material for rafters, we are guided by the table standard sizes lumber (GOST 24454-80 Lumber conifers. Dimensions), which are summarized in Table 4.

A. We calculate the cross section of the rafter leg.

We set the width of the section arbitrarily in accordance with the standard dimensions, and the height of the section is determined by the formula:

H ≥ 8.6 Lmax sqrt(Qr/(B Rbend)), if the slope of the roof α

H ≥ 9.5 Lmax sqrt(Qr/(B Rbend)), if the roof pitch α > 30°.

H - section height cm,


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

B. We check whether the deflection value fits into the standard.

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

This condition is satisfied if the following inequality is true:

3.125 Qr (Lmax)³/(B H³) ≤ 1

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

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

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

As it was calculated, the total load acting on a square meter of the roof is Q \u003d 303 kg / m².
1. We find the distributed load per linear meter of each rafter leg Qr=A·Q;
Qr=0.8 303=242 kg/m;

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

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

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

3. We check whether the deflection value is within the standard. For this, the inequality must be observed:
3.125 Qr (Lmax)³/B H³ ≤ 1
Substituting the values, we have: 3.125 242 (2.8)³ / 5 (17.5)³ = 0.61
Meaning 0.61, then the cross section of the material of the rafters is chosen correctly.

The cross section of the rafters, installed in increments of 0.8 m, for the roof of our house will be: width - 5 cm, height - 17.5 cm.

Beautiful and reliable.

And what is the basis of any roof?

From how correctly the calculation of the parameters of the elements of the truss system will be carried out, it will depend on how strong and reliable the roof will be.

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

Factors taken into account when calculating rafters

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

The factors affecting the roof are usually classified into:

1. Constant loads. This category includes those loads that constantly affect the elements of the rafter system. Regardless of the time of year. These loads include the weight of the roof, lathing, waterproofing, heat and vapor barrier and all other roof elements that have a fixed weight and constantly create a load on the rafter system. If you plan to install any equipment on the roof (snow guards, satellite TV antenna, ethernet antenna, smoke exhaust and ventilation systems, etc.), then to constant loads be sure to add the weight of such equipment.
2. Variable loads. These loads are called variables due to the fact that they load the truss system only at some certain period of time, and at other times this load is minimal or not at all. Such loads include the weight of the snow cover, the load from blowing winds, the load from people who will serve the roof, etc.
3. Special type of loads. This group includes loads that occur in areas where hurricanes very often occur or seismic effects occur. In this case, the load is taken into account in order to add an additional margin of safety to the structure.

The calculation of the parameters of the truss system is quite complicated.

And it is difficult for a beginner to make it, since there are a lot of factors that affect the roof that must be taken into account.

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

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

Determining the load on the rafters

Roofing cake weight

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

This calculation is easy to do if you know total area roofing and materials that are used to create this very cake.

First consider the weight of one square meter pirogue.

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

This coefficient is equal to 1.1.

Here typical example calculation of the weight of the roofing pie.

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

And that's right!

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

So:

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

We summarize the data obtained: 3+5+10+15= 33 kg.

Now the result must be multiplied by 1.1.

Our correction factor.

The final figure is 34.1 kg.

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

The total area of ​​the roof, for example, 100 sq. meters.

So, it will weigh 341 kg.

This is very little.

This is one of the advantages of ondulin.

We calculate the snow load

The moment is very important.

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

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

The snow load map is used to calculate the snow load.

Determine your region and calculate the snow load using the formula

In this formula:

— S is the desired snow load;

— Sg - mass of snow cover.

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

This indicator is different in each region.

It all depends on the location of the house.

A map is used to determine the mass.

— µ is the correction factor.

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

If the slope angle is less than 25 degrees, then the coefficient is 1.

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

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

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

The slopes have an angle of inclination of 30 degrees.

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

The mass of snow per 1 square. meter is 180 kg.

We perform the calculation, not forgetting the correction factor:

180 x 0.7 \u003d 126 kilograms per 1 sq. roof meter.

Determination of wind loads

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

Use this formula:

Wo is a normative indicator determined by the table.

Each region has its own wind tables.

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

We count wooden rafters

Rafter length

The calculation of the length of the rafter leg is one of the simplest geometric calculations.

Since you only need two dimensions: width and height, as well as the Pythagorean theorem.

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

We know two distances:

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

First leg;

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

Second catheter.

c is the hypotenuse of the triangle.

c² \u003d (2 x 2) + (3 x 3).

Total s²=4+9=13.

Now we need to get the square root of 13.

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

We get 3.6 meters.

To this number, now you need to add the length of the take-out d to get the desired length of the rafters.

We calculate and select the section of the elements of the truss system

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

For simple designs use table standard sizes and board sections.

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

We calculate the step and the number of rafter legs

The distance between their bases is called.

Experts believe that the minimum distance should be 60 cm.

And the optimal distance is 1 meter.

We calculate the distance between the rafters:

• we measure the length of the slope along the eaves;
• then the resulting figure should be divided by the estimated pitch of the rafters. If the step is planned to be 60 cm, then it should be divided by 0.6. If 1 meter, then divided by 1. About the preliminary choice of the step will be further;
• then 1 should be added to the received result and the resulting value should be rounded up. Thus, we get the number of rafters that can be installed on the roof of your house;
• the total length of the slope must be divided by the number of rafters to get the pitch of the rafters.

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

Pre-select a rafter pitch of 0.8 meters.

12/0.8 = 15 meters.

We add a unit 15+1=16 rafters.

If it were a fractional number, then we would round it up.

Now from 12 meters should be divided by 16.

As a result, 1216 = 0.75 meters.

Here optimal distance between rafters on one slope.

The table discussed earlier can also be used.

We calculate wooden floor beams

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

The optimal section is rectangular.

The ratio of height and width is 1.4:1.

The beam should go into the wall by at least 12 cm.

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

Waterproofing of beams is carried out "in a circle".

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

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

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

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

Calculation of shed roof rafters

Shed roof - the simplest version of the roof.

But this option is not suitable for every building.

And the calculation of the rafters is required in any case.

Calculations pitched roof start with determining the angle of inclination.

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

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

The optimum is 20 degrees.

Settlement programs

If online calculators perform simple calculations, then a special software able to calculate everything you need.

And there are quite a few such programs!

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

Such programs have only two drawbacks:

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

There are a number of free programs.

Most programs can be downloaded to your computer.

Or use them online.

Video about the calculation of rafters.

When designing the roof rafters of a private house, you need to be able to correctly calculate the angle of the roof. How to navigate in various units of measurement, what formulas to calculate and how the angle of inclination affects the wind and snow load of the roof, we will talk in this article.

The roof of a private house built according to individual project, can be very simple or surprisingly whimsical. The slope angle of each slope depends on architectural solution the whole house, the presence of an attic or attic, the roofing material used, climate zone, in which is located household plot. In a compromise of these parameters, you need to find optimal solution combining the strength of the roof with beneficial use roof space and appearance house or building complex.

Roof angle units

The angle of inclination is the value between the horizontal part of the structure, slabs or floor beams, and the roof surface or rafters.

In reference books, SNiP, technical literature, there are various units for measuring angles:

• degrees;
• aspect ratio;
• interest.

Another unit for measuring angles - radians - is not used in such calculations.

What are degrees, everyone remembers from the school curriculum. The ratio of the sides of a right-angled triangle, which is formed by the base - L, height - H (see the figure above) and the roof deck is expressed as H: L. If α = 45°, the triangle is equilateral and the ratio of sides (legs) is 1:1. In the case when the ratio does not give a clear idea of ​​the slope, they speak of a percentage. This is the same ratio, but calculated in shares converted to percentages. For example, with H = 2.25 m and L = 5.60 m:

• 2.25 m / 5.60 m 100% = 40%

The digital expression of some units through others is clearly shown in the diagram below:

Formulas for calculating the angle of inclination of the roof, the length of the rafters and the area covered by the roofing material

To easily calculate the dimensions of the elements of the roof and truss system, you need to remember how we solved problems with triangles at school, using the basic trigonometric functions.

How does this help in calculating the roof? Breaking down complex elements into simple right triangles and find a solution for each case using trigonometric functions and the Pythagorean theorem.

More complex configurations are more common.

For example, you need to calculate the length of the rafters of the end part hip roof, which represents isosceles triangle. From the vertex of the triangle we lower the perpendicular to the base and get right triangle, whose hypotenuse is middle line end of the roof. Knowing the width of the span and the height of the ridge, from a structure divided into elementary triangles, you can find the angle of the hip - α, the angle of the roof - β and get the length of the rafters of a triangular and trapezoidal slope.

Calculation formulas (length units must be the same - m, cm or mm - in all calculations to avoid confusion):

Attention! The calculation of the lengths of the rafters according to these formulas does not take into account the size of the overhang.

Example

The roof is hipped, hipped. Ridge height (CM) - 2.25 m, span width (W / 2) - 7.0 m, depth of inclination of the end part of the roof (MN) - 1.5 m.

Having obtained the values ​​of sin(α) and tg(β), you can determine the value of the angles using the Bradis table. A complete and accurate table with an accuracy of up to a minute is a whole brochure, and for rough calculations, which in this case valid, you can use a small table of values.

Table 1

For our example:

• sin(α) = 0.832, α = 56.2° (obtained by interpolating neighboring values ​​for angles of 55° and 60°)
• tg(β) = 0.643, β = 32.6° (obtained by interpolation of neighboring values ​​for angles of 30° and 35°)

Remember these numbers, they will be useful to us when choosing a material.

To calculate the amount of roofing material, you will need to determine the area of ​​\u200b\u200bcoverage. The area of ​​​​the slope of a gable roof is a rectangle. Its area is the product of the sides. For our example - a hip roof - this comes down to determining the areas of a triangle and a trapezoid.

For our example, the area of ​​​​one end triangular slope with CN = 2.704 m and W / 2 = 7.0 m (the calculation must be performed taking into account the extension of the roof beyond the walls, we take the length of the overhang - 0.5 m):

• S \u003d ((2.704 + 0.5) (7.5 + 2 x 0.5)) / 2 \u003d 13.62 m 2

The area of ​​one side trapezoidal slope at W = 12.0 m, H c = 3.905 m (trapezoid height) and MN = 1.5 m:

• L k \u003d W - 2 MN \u003d 9 m

We calculate the area, taking into account overhangs:

• S \u003d (3.905 + 0.5) ((12.0 + 2 x 0.5) + 9.0) / 2 \u003d 48.56 m 2

The total area covered by four slopes:

• S Σ \u003d (13.62 + 48.46) 2 \u003d 124.16 m 2

Roof slope recommendations depending on the purpose and material

An unused roof can have a minimum slope angle of 2-7°, which provides immunity to wind loads. For normal snow melting, it is better to increase the angle to 10 °. Such roofs are common in construction outbuildings, garages.

If the under-roof space is supposed to be used as an attic or attic, the slope of a single or gable roof must be large enough, otherwise a person will not be able to straighten up, and effective area will be "eaten" by the truss system. Therefore, it is advisable to apply in this case broken roof, for example, attic type. Minimum Height ceilings in such a room should be at least 2.0 m, but it is desirable for a comfortable stay - 2.5 m.

Options for arranging the attic: 1-2. Double pitched roof classic. 3. Roof with a variable angle of inclination. 4. Roof with remote consoles

Taking this or that material as roofing, it is necessary to take into account the requirements for the minimum and maximum slope. Otherwise, there may be problems that require repair of the roof or the entire house.

table 2

The tilt angles obtained in our example are in the range of 32-56°, which corresponds to slate roof, but does not exclude some other materials.

Determination of dynamic loads depending on the angle of inclination

The design of the house must withstand static and dynamic loads from the roof. Static loads are the weight of the truss system and roofing materials, as well as the equipment of the under-roof space. This is a constant value.

Dynamic loads are variable values ​​depending on the climate and season. In order to correctly calculate the loads, taking into account their possible compatibility (simultaneity), we recommend studying SP 20.13330.2011 (sections 10, 11 and Appendix G). AT in full this calculation, taking into account all possible factors in a particular construction, cannot be presented in this article.

The wind load is calculated taking into account the zoning, as well as the location features (leeward, windward side) and the angle of the roof, the height of the building. The calculation is based on wind pressure, the average values ​​​​of which depend on the region of the house under construction. The remaining data are needed to determine the coefficients that correct a relatively constant value for the climatic region. The larger the angle of inclination, the more serious wind loads the roof experiences.

Table 3

Snow load, unlike wind load, is related to the angle of the roof in the opposite way: the smaller the angle, the more snow lingers on the roof, the lower the probability of snow cover convergence without the use of additional means, and the greater the load the structure experiences.

Table 4

Approach the issue of determining loads seriously. The calculation of sections, designs, and hence the reliability and cost of the truss system depends on the values ​​obtained. If you are not confident in your abilities, it is better to order a load calculation from specialists.

The gable roof is formed on the basis of a frame that combines the elementary nature of the device and unsurpassed reliability. But the backbone of the roof in two rectangular slopes can boast of these advantages only in the case of a careful selection of rafter legs.

Parameters of the gable roof truss system

Calculations should be started if you understand that the rafter system gable roof- This is a complex of triangles, the most rigid frame elements. They are assembled from boards, the size of which plays a special role.

Rafter length

The formula will help determine the length of durable boards for the truss systema²+b²=c², derived by Pythagoras.

The length of the rafter can be found by knowing the width of the house and the height of the roof

The parameter "a" denotes the height and is self-selected. It depends on whether the under-roof space will be residential, and also has certain recommendations if an attic is planned.

Behind the letter "b" is the width of the building, divided in two. And "c" represents the hypotenuse of the triangle, that is, the length of the rafter legs.

Let's say that the width of half of the house is three meters, and it was decided to make the roof two meters high. In this case, the length of the rafter legs will reach 3.6 m (c=√a²+b²=4+√9=√13≈3.6).

To the figure obtained from the Pythagorean formula, 60–70 cm should be added. Extra centimeters will be needed to take the rafter leg out of the wall and make the necessary cuts.

The six-meter rafter is the longest, therefore it is suitable as a rafter leg

The maximum length of the beam used as a rafter leg is 6 m. If a strong board of greater length is required, then they resort to the method of fusion - nailing a segment from another beam to the rafter leg.

Section of rafter legs

For various elements of the rafter system, there are standard sizes:

• 10x10 or 15x15 cm - for Mauerlat timber;
• 10x15 or 10x20 cm - for the rafter leg;
• 5x15 or 5x20 cm - for running and brace;
• 10x10 or 10x15 cm - for the rack;
• 5x10 or 5x15 cm - for lying down;
• 2x10, 2.5x15 cm - for purlins.

Thickness of each piece load-bearing structure roofing is determined by the load that it will experience.

A beam with a section of 10x20 cm is ideal for creating a rafter leg

The section of the rafter legs of a gable roof is affected by:

The pitch of the rafters affects the cross section of the rafter legs most significantly. Increasing the distance between the beams entails increased pressure on the supporting structure of the roof, and this obliges the builder to use thick rafter legs.

Table: cross-section of rafters depending on length and pitch

Variable impact on the truss system

The pressure on the rafter legs is constant and variable.

From time to time and with varying intensity, wind, snow and precipitation affect the supporting structure of the roof. In general, the roof slope is comparable to a sail, which is under pressure natural phenomena may break.

The wind tends to overturn or raise the roof, so it is important to make all the calculations correctly.

The variable wind load on the rafters is determined by the formula W \u003d Wo × k x c, where W is the wind load indicator, Wo is the value of the wind load characteristic of a certain section of Russia, k is a correction factor determined by the height of the structure and the nature of the terrain, and c is the aerodynamic coefficient.

The aerodynamic coefficient can range from -1.8 to +0.8. A minus value is typical for a rising roof, and a positive value is for a roof that is being pressed by the wind. At simplified calculation with a focus on improving strength, the aerodynamic coefficient is considered equal to 0.8.

Calculation of wind pressure on the roof is based on the location of the house

The standard value of wind pressure is recognized from map 3 of Appendix 5 in SNiP 2.01.07–85 and a special table. The coefficient that takes into account the change in wind pressure with height is also standardized.

Table: standard value of wind pressure

Table: value of coefficient k

The wind load is not only affected by the terrain. Great importance has a housing area. Behind the wall of tall buildings, the house is almost in no danger, but in open space the wind can become a serious enemy for it.

The snow load on the rafter system is calculated by the formula S = Sg × µ, that is, the weight of the snow mass per 1 m² is multiplied by a correction factor, the value of which reflects the degree of slope of the roof.

The weight of the snow layer is indicated in the SNiP "Truss Systems" and is determined by the type of area where the building was built.

Snow load on the roof depends on where the house is located

The correction factor, if the roof slopes heel less than 25 °, is equal to one. And in the case of a roof slope of 25–60 °, this figure decreases to 0.7.

When the roof is tilted more than 60 degrees, the snow load is discounted. Still, snow rolls down from a steep roof quickly, not having time to negative impact on the rafters.

Permanent loads

Continuous loads are considered to be the weight of the roofing pie, including the lathing, insulation, films and Decoration Materials for the attic.

Roofing cake creates constant pressure on the rafters

The weight of a roof is the sum of the weights of all the materials used in the construction of the roof. On average, it is 40–45 kg / sq.m. According to the rules, 1 m² of the truss system should not account for more than 50 kg of the weight of roofing materials.

So that there is no doubt about the strength of the rafter system, 10% should be added to the calculation of the load on the rafter legs.

Table: weight of roofing materials per 1 m²

Number of bars

How many rafters will be needed to equip the frame of a gable roof is set by dividing the width of the roof by a step between the bars and adding one to the resulting value. It indicates an additional rafter that will need to be placed on the edge of the roof.

Suppose it is decided to leave 60 cm between the rafters, and the length of the roof is 6 m (600 cm). It turns out that 11 rafters are needed (taking into account the additional timber).

The gable roof truss system is a construction of a certain number of rafters

The step of the beams of the supporting structure of the roof

To determine the distance between the beams of the supporting structure of the roof, you should pay close attention to such points as:

• weight of roofing materials;
• the length and thickness of the beam - the future rafter leg;
• degree of slope of the roof;
• level of wind and snow loads.

After 90-100 cm, it is customary to place the rafters in the case of choosing a light roofing material

A step of 60–120 cm is considered normal for rafter legs. The choice in favor of 60 or 80 cm is made in the case of the construction of a roof inclined by 45˚. The same small step should be, if desired, to cover wooden frame roofs with heavy materials such as ceramic tiles, asbestos-cement slates and cement-sand tiles.

Table: rafter pitch depending on length and section

Formulas for calculating the truss system of a gable roof

The calculation of the truss system comes down to setting the pressure on each beam and determining the optimal section.

When calculating the truss system of a gable roof, they act as follows:

1. According to the formula Qr \u003d AxQ, they find out what is the load per linear meter of each rafter leg. Qr is the distributed load per linear meter of the rafter leg, expressed in kg/m, A is the distance between the rafters in meters, and Q is the total load in kg/m².
2. They proceed to the determination of the minimum cross-section of the beam-rafter. To do this, study the data of the table listed in GOST 24454–80 “Softwood lumber. Dimensions".
3. Focusing on the standard parameters, choose the width of the section. And the height of the section is calculated using the formula H ≥ 8.6 Lmax sqrt (Qr / (B Rbend)) if the roof slope α< 30°, или формулу H ≥ 9,5·Lmax·sqrt(Qr/(B·Rизг)), когда уклон крыши α >30°. H is the height of the section in cm, Lmax is the working section of the rafter leg of maximum length in meters, Qr is the distributed load per linear meter of the rafter leg in kg / m, B is the section width cm, Rbend is the resistance of wood to bending, kg / cm². If the material is made from pine or spruce, then Rizg can be equal to 140 kg / cm² (wood grade 1), 130 kg / cm² (grade 2) or 85 kg / cm² (grade 3). Sqrt is the square root.
4. Check whether the deflection value complies with the standards. It should not be more than the figure that results from dividing L by 200. L is the length of the working area. The compliance of the deflection value with the L / 200 ratio is feasible only if the inequality 3.125 Qr (Lmax)³ / (B H³) ≤ 1 is true. Qr indicates the distributed load per linear meter of the rafter leg (kg / m), Lmax is the working section of the rafter leg maximum length (m), B is the width of the section (cm), and H is the height of the section (cm).
5. When the above inequality is violated, the indicators B and H increase.

Table: nominal dimensions of thickness and width of lumber (mm)

An example of the calculation of the supporting structure

Assume that α (roof pitch) = 36°, A (rafter spacing) = 0.8 m, and Lmax (maximum rafter length) = 2.8 m. , which means that Rizg \u003d 140 kg / cm².

Cement-sand tiles were chosen for the roof covering, and therefore the weight of the roof is 50 kg/m². The total load (Q) experienced by each square meter is 303 kg/m². And for the construction of the truss system, bars 5 cm thick are used.

From this follow the following computational steps:

1. Qr=A·Q= 0.8·303=242 kg/m - distributed load per linear meter of rafter beam.
2. H ≥ 9.5 Lmax sqrt(Qr/B Rbend).
3. H ≥ 9.5 2.8 sqrt(242/5 140).
4. 3.125 Qr (Lmax)³/B H³ ≤ 1.
5. 3.125 242 (2.8)³ / 5 (17.5)³ = 0.61.
6. H ≥ (approximate height of the rafter section).

In the table of standard sizes, you need to find the height of the rafter section, close to 15.6 cm. A suitable parameter is 17.5 cm (with a section width of 5 cm).

This value is quite consistent with the deflection in normative documents, and this is proved by the inequality 3.125 Qr (Lmax)³/B H³ ≤ 1. Substituting the values ​​(3.125 242 (2.8)³ / 5 (17.5)³) into it, we find that 0.61< 1. Можно сделать вывод: сечение пиломатериала выбрано верно.

Video: detailed calculation of the truss system

The calculation of the gable roof truss system is a whole complex of calculations. In order for the bars to cope with the task assigned to them, the builder needs to accurately determine the length, quantity and cross section of the material, find out the load on it and find out what the step between the rafters should be.

The roof is not only the protection of the house from external environment, but also a certain decorative element that gives the building a finished look. That is why developers are building today the most unusual roofs with complex structures truss systems.

The rafter system is the most important element in the arrangement of any roof. It accounts for the weight of the coating and precipitation. That's why correct execution such a system, taking into account all the rules of building art, is a guarantee of the reliability and durability of the roof. It is very important to correctly determine the length of the rafters and other structural elements. In this case, it is necessary to take into account such climatic features as:

• snow thickness;
• the amount of summer precipitation;
• wind power.

Any construction of this kind is carried out in the form of interconnected elements that strictly correspond to the calculations made earlier. This system includes the following elements:

• sloping legs, which are also called rafters;
• stops, sprengels and other fasteners that give the structure the necessary rigidity;
• vertical type racks;
• conjurers.

Note! It is necessary to take special responsibility when calculating the length of the rafters - any, albeit insignificant, error can lead to deformation of the roof geometry and, accordingly, its collapse.

If you are not familiar with the features roof structure, it is better to consult a qualifiedm specialists. For self calculation SpanishUse special calculators and tables - this will help you avoid mistakes.

Rafter systems are divided into two groups depending on the material used:

• wooden structures;
• metal structures.

There are also reinforced concrete truss systems, but they are used mainly in industrial buildings. In any case, whether the rafters are metal, wooden or concrete, they must be firmly attached to the walls of the house.

Often for the construction of rafters in country houses use wood, mainly coniferous species. Compared to metal, wood is easier to handle and install. Moreover, even if an error occurs in the calculations, then wooden details easy to replace.

Before proceeding with the calculations, first measure the width of the house. The fact is that although small slanted legs do not need additional extensions, but in individual cases the special geometry of the roof requires reinforcement of the rafters, even if the house is of small size.

According to the design features, the rafters are divided into:

• oblique;
• hanging.

In construction country houses inclined rafters are more often used, but often builders combine both. As already mentioned, it may be necessary to build up the oblique legs. It depends on the roofing material used in the construction. So, slate or ceramic tiles in view heavy weight can only be installed on a rafter system of increased strength.

The cross section of the boards used in the construction of the rafters can be 20x6 cm or 15x5 cm. But if the structure is strengthened, you can pick up a beam with babout large section (there is another way to strengthen - by splicing the boards).

And now - directly to the calculations.

What to consider when calculating rafters

First, let's define the fundamentals.

1. The type and shape of the roof directly affect functional features rafter system. The fact is that the calculations for hipped and gable roofs will differ from each other, because they need to be carried out according to different methods. Moreover, asymmetrical roofs (for example, broken ones) need additional stabilization elements - crossbars, sleepers, struts, etc.
2. Very important in the calculations and future loads on the structure, mainly snow and wind. For example, in the snowy regions of the country it is quite difficult to build a roof with a slope of less than 45 °, and if you increase the slope or height of the structure, then the wind load will increase. In a word, it is necessary to define the very golden mean", but not to the detriment of attractiveness and. Very often only true masters can solve such a problem.
3. Another important point in the calculation is the coating material. Many of these materials need certain conditions. So, flexible tile it is laid exclusively on a solid surface (in extreme cases, a frequent crate). Ceramic tiles need a reinforced frame.
4. Size and area - these are the main indicators that affect the choice of a particular type of roof. If the area is large, then the pitch of the rafters increases and, accordingly, the distance between them. Because of this, the cross section of the timber used increases.

Note! distance between bearing walls called a run. With an increase in the run, the number of changes in the design increases, in particular, the number of stabilizing and reinforcing elements.

Now, having familiarized yourself with the starting points, you can take paper, a ruler and a pencil and proceed with the calculations.

First stage. Roofing cake weight

First, determine how much the roof itself will weigh. This is very important, because the truss system must withstand this weight for a long time. It is very easy to calculate: find out the weight per square meter of each of the layers, summarize the data obtained and add a correction of 10%.

Here is an example of such calculations.

1. A square meter of the crate weighs 15 kg.
2. The roofing will be, say, ondulin with a weight of 3.5 kg.
3. Square meter bituminous waterproofing weighs another 6 kg.
4. Weight of 10 cm layer mineral wool is approximately 10 kg per square meter.

Let's see what happens.

15 + 3.5 + 6 + 10 = 34.5 kg.

We add correction 10%, it turns out 37.95 kg. It is this figure that is an indicator of the weight of the roofing pie.

Note! In most cases, this weight does not exceed 50 kg, but experienced specialists are sure that the calculations should be based on this value - “for reserve”.

It turns out that the weight of the roofing cake should be 50 + 10% = 55 kg / m².

It is very important to take into account the snow load, because snow can accumulate on the roof in sufficient in large numbers. Use a special formula to determine this load:

µ x S ᶢ = S, where

Sin this case, this is the load of snow that you need to calculate;

µ - correction depending on the slope slope;

At flat roof, the slope of which does not exceed 25°, the correction will be equal to one; if the slope of the ramp is greater than 25°, but does not exceed 60°, then the correction will be 0.7. If a very steep roof is being built, then snow loads you can't count on it at all.

Sᶢis the weight per square meter of snow cover. This indicator depends on climatic features specific region, you can find out about it in SNiP.

Calculation example

Let's say the slope of the roof will be 25 °, and the mass of snow will be 200 kgf / m².

0.7 x 200 = 140 kgf / m²

This is the planned load of snow on the truss system.

Use the formula below to calculate the wind load on the rafters.

K x Wᵒ = W, where

Wᵒin this case, it is a standard indicator that you must determine from the table (it all depends on which region you live in);

To- This is an amendment that takes into account the height of the house and the type of terrain.

Table 1. Wind loads in Russia

Table 2. Norms of the correction factor.

In this case, A is open areas, and B is areas evenly covered with obstacles.

Calculation example

Let's say you want to build a five-meter-high house in the Moscow region. This region is located in I windy area, so the wind load here is 25 kgf/m². Correction - 0.5. Let's see what happens:

0.5 x 23 = 11.5 kgf / m²

Fourth stage. Calculation of the pitch and length of the rafters

To calculate the length of the rafters, you can remember the geometry at school, namely the famous Pythagorean theorem. After all roof structure is, in fact, a right triangle and it is very easy to measure its diagonal. But do not forget to take into account when calculating:

• the strength of the bars;
• the possibility of deformation - what load the system can withstand without breaking.

Note! According to GOST, rafters should not bend more than 1/250 of their length. For example, if the length of the rafters is 5m, then multiply this numbero by 0.004 - so you get the ultimate deflection, namely 2 cm.

Use the table below to calculate the cross section.

Table 3. Calculation of the section of the truss system

Calculation example

Let's say the length of the rafter is 4 m. From the table we see that for such a length there are three options for the section, depending on the pitch of the rafters. If this step is, for example, 14 m, then for work you will need a beam with a section of 8x18 cm.

Basic material requirements

According to GOST, wood must meet the following requirements:

• its humidity should not exceed 18%;
• the number of knots should not exceed three pieces per linear meter of timber;
• there may be non-through cracks, but their length should not exceed half of the total length;
• wood must be treated with an antiseptic, flame retardant and biological protection agent.

In addition, when buying bars, pay attention to:

• manufacturer;
• date of manufacture;
• product name, standard;
• quality of execution of individual parts;
• dimensions and humidity of products;
• tree species.

Special computer programs

Judging by everything that has been said above, for calculating rafters, you need to have not only a sufficient stock of knowledge, but also drawing and drawing skills. Of course, not all of us can boast of all this.

Fortunately, today there are many computer utilities designed to facilitate calculations. There are professional ones among them, such as, for example, AutoCAD, but you can find more simple options. So, in the Arkon program, you can easily create various projects, as well as visually see what the future roof will look like.

Note! These utilities include calculation calculator, which was mentioned earlier. With its help, you can calculate the length, pitch and cross section of the rafters with extreme accuracy.

Such calculators are also available online, but all the data that can be obtained with their help is advisory in nature and will not replace a full-fledged drafting.

As a conclusion

One of milestones roof construction is the calculation of the truss system. Of course, it is better to entrust this matter to professionals, but preliminary measurements can be made on your own - this will help you understand the finished drawing.

Video - Installation of rafters