Online calculator for calculating the rafter leg. Do-it-yourself rafters for a gable roof: calculation and installation. How to calculate the length of the gable roof rafters
For low-rise buildings, a rafter roof is perfect. It will decorate the facade of the house, and with a sufficient slope, snow does not accumulate on such a roof, unlike a flat structure.
One of the types of roof rafters - gable. This is a fairly simple system, which is formed by two slopes. The slope of the roof is the entire inclined plane, with the help of which a drain is provided.
The structure rests on two parallel walls. Such a roof forms two triangular side pediments. A pediment is the end of a building's facade.
Advantages of a gable system
- Ease of Design.
The calculation of the bearing capacity and the necessary materials for the installation of such a roof is quite simple, since there are few options for the types and sizes of supporting structures; - Ease of installation.
A gable roof does not have complex structural elements. A small number of standard sizes allows you to quickly install all the elements of the roof; - Ease of use.
The fewer different breaks the roof has, the more reliably it protects the home. In the simplest version, a gable roof has only one break - a ridge. Such a roof is easier to repair in case of defects; - Free space.
For the arrangement of the attic, a gable roof is preferable, since it “eats up” space less. For comparison, consider a 6x6 m house with an attic. At the outer walls, the height from the floor of the room to the roof is 1.5 m, at the ridge - 3 m. For a gable roof under such conditions, the volume of the room will be 81 cubic meters, and for a hip roof with four slopes, 72 cubic meters. For larger building sizes, volume loss will increase.
Construction types
There are four main types of gable roofs:
- symmetrical.
Reliable, stable, easy to perform, based on an isosceles triangle; - Asymmetrical.
The ridge is not located in the center, the roof slopes have different slopes; - Polyline symmetrical.
Roof slopes are broken. Significantly increases the height of the room; - Polyline asymmetrical.
The attic or attic room is smaller than in the previous case. The roof has a very unusual appearance.
The choice of the type of gable roof depends on the purpose of the room located directly under it and the architectural appearance of the building.
General principles for calculating the truss system
The most important load-bearing parts of the gable roof truss system of a building are the mauerlat, crossbar and rafters. Mauerlat works in compression, so its cross section can be taken conditionally.
The crossbar and rafter legs experience a bending moment.
The calculation of such structures is carried out in terms of strength and stiffness. For small buildings, you can choose their cross section approximately, but for serious buildings, for safety and material saving purposes, the calculation of the truss system should be performed by a professional.
Roof self-weight load
To perform the calculation, you need to know the load per 1 sq.m. roofs.
To do this, you need to add the masses of 1 sq.m. all roofing materials:
- filing(if it is, it is most often performed from drywall);
- rafter legs. To calculate the weight of the rafters per square meter of the roof, you need to find the mass of the running meter of the rafter leg and divide this number by the pitch of the rafters in meters. For the calculation, you can take the approximate cross section of the rafter, the area of \u200b\u200bthis section must be multiplied by the density of the wood;
- heater (if any). The density of the insulation must be indicated by the manufacturer, it must be multiplied by the thickness;
- crate. To ensure a margin, a continuous crate can be taken into account. For example, 1 sq.m. lathing from a board 32 mm thick will weigh approximately 25 kilograms;
- roofing material. Weight 1 sq.m. coatings are usually specified by the manufacturer.
Snow load
The snow load for each area is different and is equal to the weight of the snow cover on a horizontal plane.
On the territory of Russia, it can take values from 80 to 560 kilograms per square meter. On the Internet, you can easily find a snow load distribution map and select the right number based on the construction area.
Roof pitch
The angle of inclination of the roof is quite easy to calculate, knowing the geometry and having an engineering calculator or a standard calculator on a personal computer at hand.
If we divide the height of the roof rise by the distance from the ridge to the cornice in the plan, we get the slope of the roof in fractions or the tangent of the angle of inclination. In order to calculate the angle, it is enough just to find the arc tangent.
If using an engineering calculator is difficult, the arc tangent can be found using an online calculator.
Rafter step calculation
The pitch of the rafters of the attic roof should be chosen for reasons of ease of installation of the insulation. Mats usually have a width of 60 centimeters, so the pitch of the rafters should be chosen so that the distance between them in cleanliness is 58 or 118 centimeters. Two centimeters will allow you to install the insulation boards very tightly, which will allow it to stick between the rafters and improve thermal insulation.
Rafter leg length
Leg length is easy to calculate using the formula:
L/cosα,
here L is the distance from the roof ridge to the inner surface of the outer wall in plan, and cosα is the cosine of the roof pitch angle. With rigid fastening, you need to add the size of the notch.
Section of the rafter leg
The cross section of the rafter leg must be selected as a multiple of the size of the boards and timber.
An example of a simple calculation of the section of the rafter leg:
- we find the load per 1 linear meter of the rafter.
q =(1.1*weight of 1 sq.m. of roof*cosα + 1.4*normative snow load*cosα2)* rafter spacing; - find W.
W= q * 1.25 * flight of rafters / 130; - solve the equation:
W= b*h2/6.
In this equation, b is the width of the section of the rafter leg, and h is the height.
To solve, you need to ask for the width and find the height by solving a simple quadratic equation. The width can be set to 5 cm, 7.5 cm, 10 cm, 15 cm. For small spans, a width of 15 cm is impractical.
To calculate the truss systems, there are all kinds of tables, programs, online calculators.
The main elements of the roof
The main elements of a gable roof, like any other roof truss, are:
Rafter roof with attic
To fully use the space under the roof, you can design an attic.
Attic floor- This is the floor in the attic space. The facade of the attic is completely or partially formed by the roof surfaces. According to regulatory documents, in order for a room to be considered an attic, the line of intersection of the roof plane and the outer wall should not be higher than 1.5 m from the floor level. If this requirement is not met, the space will be considered a normal floor.
The roof of the attic floor differs from the roof of the attic floor by the presence of a heater in its design. Most often, mineral wool boards are used to insulate the attic roof.
Lighting of the attic space can be carried out in three ways:
- window openings in the gables;
- dormers;
- roof windows.
dormer window - this is a window structure that has a frame mounted simultaneously with the truss system. This frame is made of wood. The dormer has its own small roof, which can be gable or cylindrical. The double-glazed window is installed vertically.
roof window- This is a window specially designed for use on a rafter roof. It is installed in the plane of the slope in an inclined position. The roof window must withstand the calculated snow load. It is better not to use this type of windows in roofs with a slight slope.
The choice of roofing material
After the appearance of the roof is determined, you can proceed to the choice of material. There are several types of modern coatings. In the list below, material options are listed in descending order of average market value.
- Ceramic tiles.
Ceramics as a roofing material has a long history. The ceramic roof is reliable and durable. The disadvantages of this material are the price and the large mass. Under the roof of ceramic tiles, you will have to arrange a reinforced truss system and crate; - Cement-sand tiles.
It has almost all the characteristics of ceramic, but costs a little less; - Flexible shingles.
It has good soundproofing characteristics. Thanks to the rough surface, the tiles are able to prevent snow from moving off the roof. Requires a continuous crate, usually a layer of moisture-resistant plywood is used. Cannot be used on roofs with large slopes; - Metal tile.
Compared to previous coatings, it is lighter in weight. Easy to mount. The disadvantage of a metal roof is that it can be too noisy when it rains. - seam roof.
The most attractive option in terms of cost. It requires special qualifications during installation, since it will be difficult for a non-professional to make high-quality connections. Installation is more laborious than that of metal and flexible tiles. The same "noisy" as metal tiles.
The material of the roof depends entirely on the desires and capabilities of the customer. The exception is roofs with too much or too little slope, since all materials have limits on the slope of the slope.
Types of truss systems
Structural roof truss systems can be of three types:
- Rafters.
The rafters rest on two sides. From below - on the Mauerlat, from above - on the crossbar. Racks and struts can be used as intermediate supports. Most often used in buildings with a small distance between the ends or, if possible, put racks or a wall in the middle of the attic.
With large spans of rafters (large distances between the longitudinal walls), racks, struts or puffs can be additionally used.
Laminated rafters are easy to calculate.
Usually the most powerful element of such a system is the crossbar, which bears half the load of the entire roof structure. - Hanging rafters.
In the absence of the possibility of using a crossbar as an upper support, it is reasonable to use this truss system.
Hanging rafters rest only on the Mauerlat, and at the top point they are interconnected with the help of an overlay.
This truss system works like a truss under load. The greatest pressure falls on the outer walls. There is a horizontal force - thrust, which can lead to displacement of the walls. In the design of hanging rafters, the expansion force is perceived by a puff, which tightens the rafter legs and prevents them from moving apart.
Hanging rafters are classified depending on the location of the puff:
1) Triangular three-hinged arch.
The puff and rafters form a triangle. The puff is located at the level of the overlap;
2) Triangular three-hinged arch with suspension.
With a large span of rafters, the tightening may not pass according to the deflection requirements. To prevent it from sagging, the puff is suspended from the ridge. But with such a system, as well as with a system of layered rafters, a row of racks is formed in the middle of the attic;
3) Triangular three-hinged arch with a raised puff.
The puff is most often located at the level of the ceiling of the attic room. Such a scheme is less beneficial from the point of view of the design. The higher the puff is located, the greater the thrust it perceives.
Hanging rafters must be considered as a triangular truss, which complicates the calculation. - Combined rafters.
The combined system includes spacer layered rafters. They need both bolt installation and tightening. Unlike the previous options, in which the rafters are hinged to the Mauerlat, here the rafter leg is rigidly attached, so there is a thrust in the system. For such a system, the Mauerlat must be securely attached to the wall, and the wall itself must be strong and thick. An excellent option would be to run a reinforced concrete belt around the perimeter.
Installation of the truss system
Installation takes place in the following order:
- mauerlat laying;
- installation of a crossbar (if any);
- layout of rafters;
- insulation (if any);
- crate;
- roofing material.
Attaching the rafter leg to the Mauerlat can be rigid and articulated.
Hinged fastening
It makes it possible to compensate for the expansion of wood under the influence of humidity and temperature changes.
Fastening can be done in several ways:
- using special fasteners, a metal "sled";
- using a mounting plate;
- washed down on the rafter leg. The junction of the rafter leg and the Mauerlat is fixed with nails.
Rigid fastening
The rafter is attached to the Mauerlat with a notch and securely fixed with nails hammered at an angle with respect to each other. One nail is driven vertically into the surface of the Mauerlat. Such a connection excludes displacement in any plane.
The gable truss system has undeniable advantages. You can design and install it yourself, you just need to take this issue responsibly and think through everything to the smallest detail.
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 an individual project can be very simple or surprisingly bizarre. The slope angle of each slope depends on the architectural solution of the whole house, the presence of an attic or attic, the roofing material used, the climatic zone in which the plot is located. In a compromise of these parameters, it is necessary to find the optimal solution that combines the strength of the roof with the beneficial use of under-roof space and the appearance of the house or complex of buildings.
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 basic trigonometric functions.
How does this help in calculating the roof? We break complex elements into simple right-angled 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 of the hip roof, which is an isosceles triangle. From the top of the triangle we lower the perpendicular to the base and get a right triangle, the hypotenuse of which is the midline of the end part of the roof. Knowing the width of the span and the height of the ridge, from the 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 are acceptable in this case, you can use a small table of values.
Table 1
| Roof pitch, in degrees | tg(a) | sin(a) |
| 5 | 0,09 | 0,09 |
| 10 | 0,18 | 0,17 |
| 15 | 0,27 | 0,26 |
| 20 | 0,36 | 0,34 |
| 25 | 0,47 | 0,42 |
| 30 | 0,58 | 0,50 |
| 35 | 0,70 | 0,57 |
| 40 | 0,84 | 0,64 |
| 45 | 1,00 | 0,71 |
| 50 | 1,19 | 0,77 |
| 55 | 1,43 | 0,82 |
| 60 | 1,73 | 0,87 |
| 65 | 2,14 | 0,91 |
| 70 | 2,75 | 0,94 |
| 75 | 3,73 | 0,96 |
| 80 | 5,67 | 0,98 |
| 85 | 11,43 | 0,99 |
| 90 | ∞ | 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 the construction of outbuildings, garages.
If the 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 the person will not be able to straighten up, and the usable area will be “eaten up” by the truss system. Therefore, it is advisable to use in this case a sloping roof, for example, a mansard type. The minimum ceiling height 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
| roof type | Range of permissible mounting angles, in degrees | Optimum roof slope, in degrees |
| Roofing with roofing | 3-30 | 4-10 |
| Tole roof, two-layer | 4-50 | 6-12 |
| Zinc roofing with double standing seams (zinc strips) | 3-90 | 5-30 |
| Tole roof, simple | 8-15 | 10-12 |
| Sloping roof covered with roofing steel | 12-18 | 15 |
| Groove tile with 4 grooves | 18-50 | 22-45 |
| shingle roof | 18-21 | 19-20 |
| Grooved tiles, normal | 20-33 | 22 |
| Decking | 18-35 | 25 |
| Corrugated Asbestos Cement Sheet | 5-90 | 30 |
| artificial slate | 20-90 | 25-45 |
| Slate roof, double layer | 25-90 | 30-50 |
| Slate roof, normal | 30-90 | 45 |
| glass roof | 30-45 | 33 |
| Roof tiles, two-layer | 35-60 | 45 |
| Grooved Dutch tile | 40-60 | 45 |
The slope angles obtained in our example are in the range of 32-56°, which corresponds to a 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). 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.
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:
- 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 the weight of such equipment must be added to constant loads.
- 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.
- 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.
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 of the roofing cake.
It is not difficult to make such a calculation if you know the total area of \u200b\u200bthe roof and the materials that are used to create this very pie.
First, consider the weight of one square meter of the pie.
The mass of each layer is summed up and multiplied by the correction factor.
This coefficient is equal to 1.1.
Here is a typical example of calculating the weight of a roofing pie.
Let's say you decide to use ondulin as a roofing material.
And that's right!
After all, ondulin is a reliable and inexpensive material. It is for these reasons that it is so popular among developers.
So:
- Ondulin: its weight is 3 kg per 1 square meter.
- Waterproofing. Polymer-bitumen material is used. One square meter of it weighs 5 kg.
- insulation layer. Mineral wool is used. The weight of one square is 10 kg.
- 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 structures, a table of typical board sizes and sections is used.
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 is the optimal distance between the 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:
| Span (m) / Installation pitch (m) | 2.0 | 2.5 | 3.0 | 4.0 | 4.5 | 5.0 | 6.0 |
| 0.6 | 75x100 | 75x150 | 75x200 | 100x200 | 100x200 | 125x200 | 150x225 |
| 1 | 75x150 | 100x150 | 100x175 | 125x200 | 150x200 | 150x200 | 175x250 |
If a more accurate calculation is required, then use 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.
Shed roof calculations begin 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, the minimum angle is 8 degrees.
The optimum is 20 degrees.
Settlement programs
If online calculators perform simple calculations, then special software can 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.
Most of the construction is over, and your future home pleases with a strong foundation and even walls? It's time to start building a roof that will protect your home comfort from dampness and bad weather. But the first thing to do is to design and calculate the entire structure down to the very last detail.
Remember that at height all work is more difficult, and therefore it is better not to redo anything. Moreover, the calculation of the gable roof truss system itself is not complicated - now you will see for yourself! By the way, a gable roof is also called a gable roof.
- Mauerlat is the foundation of the roof, usually represented by a horizontal beam, on which the rafters rest.
- Skate beam.
- Inclined beams and rafters.
- Vertical racks.
- Lathing and additional details that give the necessary rigidity to the frame.
Nothing complicated - a gable roof is just what pleases:
Standard and broken gable roof
The project of a standard gable truss system consists of two inclined rectangular planes and smooth vertical ends on the sides, called gables. Such a roof is one of the simplest structures, the construction of which can be successfully completed even by inexperienced specialists.
But the broken gable roof has a different architecture. Here, the upper more gently sloping roof is usually built with a slope of 30°, and the lower one is steep with a slope of 60°.
A broken gable roof is good because snow and ice almost do not linger on it, but the attic room turns out to be much more convenient and cozy. Moreover, it is rational to make dormer windows in the lower plane of such a roof, which on flatter planes usually become a problem of leaks and dampness - rainwater lingers on them longer.
Note that one of the best options for buildings 6-8 m wide. Moreover, it will be easier for you to assemble a broken profile - for this you just need to mount the necessary nodes directly on the ground, and we simply cut all the racks and rafters according to the template:
How to calculate a gable truss system?
So, first of all, when designing and calculating, decide on the useful area of \u200b\u200bthe attic, and based on these data, decide how high the vertical racks will be. And the attic is usually made in such a roof - it’s convenient, after all.
We offer for convenience to understand the concepts:
We calculate the angle of inclination of the slopes
Now we calculate the slope of the slopes. So, if your house has a standard width of 6-8 m, then a 45 ° slope angle will leave too little space for attic living space. Do 60 ° - this is the most successful option, although it will cost you more. In addition, already with a 45° inclination, you can use any roofing materials.
Rarely, but it happens when a gable roof is initially planned asymmetrical - if only for the sake of having a place in the attic space for arranging a residential attic. But in any case, calculate the angle of inclination of a standard gable roof based on the wind and snow loads in your region.
But keep in mind that with an increase in the angle of inclination of the slopes, the consumption of materials will also increase, although the operational characteristics of such a roof will also be higher:
They also build gable roofs with unequal slope angles to express the original design. It has many shortcomings, and therefore we advise you to plan a symmetrical roof after all, at the base of which there are isosceles triangles.
Decide on the type of rafters
There are only two of them on a gable roof.
hanging rafters
A distinctive feature of this type of truss system is that the support here goes only to the side walls of the structure, i.e. the rafters just hang. This process in construction is considered negative, because. such a design leads to a bursting load of the roof and over time the walls can even deform. And with decades - even warp. That is why, for a more harmonious and safe distribution of the load, consider additional and auxiliary elements - puffs, grandmas, cuts.
But the hanging truss system also has its advantages:
- Installation work of such a roof is quite simple.
- There are no complex nodes and other elements for the reliability of the system.
- The entire truss structure has a high degree of rigidity.
Rafters
The layered truss system is characterized by the presence of an internal supporting partition, which is located at the same distance from opposite walls. The entire roof rests on it, and therefore it is impossible to do without a layered system if the roof is of serious weight or size.
We distribute the load of the rafters
And now it is important to redistribute the load of all rafters on the floor beams as much as possible. If the rafters need to be strengthened, then add additional overlays to the project or a larger section of the beam than planned.
The weight of the truss system and roofing
We calculate everything according to the following tables:
The project may also have inclined posts that reinforce the truss system. Further, the gabled roof truss will need to be reinforced with a headstock - a central pillar that will connect the ceiling and ridge beams.
In addition, it is important that the roof can easily survive climatic dissonances. It is easiest to calculate and design roofs in small countries where the climate is the same throughout the territory. That is why it is customary for the Irish to build some structures, in hot countries - others, and the Swedes the third. It's just that in such areas, building traditions have been developing for centuries, which have actually been tested in practice by more than one generation.
But in Russia, such traditions are ambiguous: somewhere they build sloping low roofs and houses almost in the ground, but somewhere on the contrary - high sharp slopes near the same high towers. The fact is that the climate in our country is diverse (naturally, because of its vast territory), and in some areas they are trying to cope with tons of snow, while in others they are trying to prevent a crazy wind from tearing off all the roofs in the village. Therefore, anyway, be guided by the experience of your region and do not make too radical decisions in calculating the truss system. Wind load
So, the force of the wind exerts lateral pressure on the roof. Faced with an obstacle, the wind is divided into two streams: down to the foundation and up, under the eaves. If you calculate everything correctly, your roof will serve you faithfully until your great-grandchildren, and if you make a mistake with the calculations, the consequences will be sad. Moreover, if the wind rips off the roof in the literal sense of the word, some minor repairs cannot be done here - you will have to rebuild the entire truss system.
Therefore, in the construction world, it is customary to pay special attention to the so-called roof aerodynamic coefficient. It depends on its angle of inclination: the steeper, the greater such a load will be and it will be easier for the wind to overturn the roof. The lower, the more difficult, but here already the wind will act as a lifting force, trying to hook on the cornice and rip it off like a mushroom cap. Therefore, the ideal roof for windy regions is with a small angle of inclination and a minimal eaves. And certainly not with hanging rafters.
Another dangerous moment: in such areas, the wind often cuts off branches from trees and carries other objects. And the higher the roof, the more likely it is that all this debris will collide with it. A couple of scratches - and corrosion is guaranteed. Therefore, the metal coating will also have to be abandoned. In addition, if there are strong winds in your area, it is not recommended to lay the mauerlat close to the edge of the outer wall so that gusts of wind cannot rip it off.
Snow load
Snow cover during winter periods actually puts a lot of pressure on the roof. And the further north the area, the more such precipitation there, and the greater the threat of a roof break, especially at a low angle of inclination. Therefore, it is necessary to design and calculate this finishing element of the building carefully, taking into account all the subtleties and nuances.
It is especially difficult to think over a reliable roof in those areas where periodic temperature changes are the norm. The fact is that the constant melting of snow, and its freezing the next day, is bad for any roofing. As a result, the entire rafter system is deformed, waterproofing and insulation are destroyed, and constant roof leaks entail unpleasant dampness and regular repairs. Do you have similar weather conditions? Bet the maximum security of the roof!
The formula for calculating the angle of inclination of the roof in this case is simple: the higher the slope, the less snow lingers. In snowy regions, also forget about complex roof shapes and multiple elements. Count only on a simple structure with a high angle of inclination, on which you will definitely need to put snow holders (so that precipitation does not destroy the drainage system).
Modern programs for calculating a gable roof
Naturally, it is quite difficult to draw the entire truss system with your own hands, as in the official design documentation, unless you have an architect's education. But it is quite enough to have the theoretical knowledge that this article gives you and at least make a sketch so that you can already purchase building material. And you can go one more way - to use modern 3D programs. It will be difficult to deal with such as AutoCAD and 3D Max, but in Arkon all the necessary calculations and sketches are easy to do.
Also, if you still have questions, you will always find on our website who will quickly perform all the necessary calculations.
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
It is worth starting the calculations if you understand that the truss system of a gable roof is a complex of triangles, the most rigid elements of the frame. 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 a 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.
The thickness of each part of the supporting structure of the roof 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 slope of the roof is comparable to a sail, which can break under the pressure of natural phenomena.
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 area of \u200b\u200bRussia, 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. In a 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. The housing area is of great importance. 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 off a steep roof quickly, without having time to have a negative impact on the rafters.
Permanent loads
Loads that act continuously are considered to be the weight of the roofing pie, including the lathing, insulation, films and finishing materials for arranging 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
| Type of roof finish | Weight in kg per 1 m² |
| Rolled bitumen-polymer sheet | 4–8 |
| Bitumen-polymer soft tile | 7–8 |
| Ondulin | 3–4 |
| metal tile | 4–6 |
| Decking, seam roofing, galvanized metal sheets | 4–6 |
| Cement-sand tiles | 40–50 |
| Ceramic tiles | 35–40 |
| Slate | 10–14 |
| slate roof | 40–50 |
| Copper | 8 |
| green roof | 80–150 |
| Draft flooring | 18–20 |
| crate | 8–10 |
| The truss system itself | 15–20 |
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˚. An equally small step should be if you want to cover the wooden frame of the roof with heavy materials like ceramic tiles, asbestos-cement slate 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:
- 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.
- 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".
- 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.
- 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).
- When the above inequality is violated, the indicators B and H increase.
Table: nominal dimensions of thickness and width of lumber (mm)
| Board thickness - section width (B) | Board width - section height (H) | ||||||||
| 16 | 75 | 100 | 125 | 150 | - | - | - | - | - |
| 19 | 75 | 100 | 125 | 150 | 175 | - | - | - | - |
| 22 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | - | - |
| 25 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 32 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 40 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 44 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 60 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 75 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 100 | - | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 125 | - | - | 125 | 150 | 175 | 200 | 225 | 250 | - |
| 150 | - | - | - | 150 | 175 | 200 | 225 | 250 | - |
| 175 | - | - | - | - | 175 | 200 | 225 | 250 | - |
| 200 | - | - | - | - | - | 200 | 225 | 250 | - |
| 250 | - | - | - | - | - | - | - | 250 | - |
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 foot 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:
- Qr=A·Q= 0.8·303=242 kg/m - distributed load per linear meter of rafter beam.
- H ≥ 9.5 Lmax sqrt(Qr/B Rbend).
- H ≥ 9.5 2.8 sqrt(242/5 140).
- 3.125 Qr (Lmax)³/B H³ ≤ 1.
- 3.125 242 (2.8)³ / 5 (17.5)³ = 0.61.
- 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 index in the regulatory documents, and this is proved by the inequality 3.125 Qr (Lmax)³ / B H³ ≤ 1. Substituting into it the values (3.125 242 (2.8)³ / 5 (17, 5)³), it turns out 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.
