It is known that the roof is the upper enclosing element of the building, which is designed to protect it from precipitation, wind, sunlight, ultraviolet radiation and other types of aggressive external influences. During the repair or construction of a house, everyone is wondering how to calculate the material for the roof, and for good reason, because it depends on its architectural form, which can be attic and combined. It is necessary to know the parameters of the structure being erected in order not only to monitor the correctness of the drafting of the project, but also to evaluate how the roof can withstand the materials with which it is covered, as well as precipitation and possible overloads.
Most often, the need for calculations arises when repairs are carried out on their own, without the involvement of third-party organizations. A combined roof is usually used for outbuildings, and not for residential buildings. It is only possible to calculate the area of \u200b\u200bthe roof by multiplying its width by its length. There are several types of attic structures: single and gable, half-hip, hip and multi-pinch. In the construction of residential buildings, gable roofs are mainly used.
The calculation of the roof first of all begins with determining the angle of inclination. Theoretically, it can be 11-70 degrees, but it’s still not worth doing more than 45 degrees. This is especially true in dry and warm climates, where a large slope is not required at all. During cold and snowy winters, a 45-degree angle of inclination will relieve the roof from snow load, but the wind pressure will increase, which will require strengthening the battens and rafters. Also, for a large slope of the roof, more material is needed.
The choice of material depends on the slope of the roof. The climate must also be taken into account.
If there is a large amount of precipitation in the region, then the angle of inclination should be greater, if there is little precipitation, then less. Basically it is 10-60 degrees.
If the house is gable, then it is easy to calculate the material for the roof. Let's denote the angle of inclination a, half of the span to be covered by the letter b, height - h. The formula by which we will carry out the calculation is tga=h/b. The values of h and b are known to us, therefore, using the Bradis table or using a calculator that calculates inverse trigonometric functions, we can find a=arctg(h/b). By multiplying b by the length of the roof, you can find the area of \u200b\u200beach slope.
Calculation of the roof structure and the amount of materials
The main materials for rafters are mainly timber and board. To determine the height of the roof, one should take into account the factor that it is now problematic to find a high-quality beam with a section of 150x100 or 100x100 mm with a length of more than 4 meters, and it is expensive. Working with it requires good skills. When building a roof, it is better to use boards with a section from 150x50 to 250x50 mm, which are much cheaper. With an increase in the length of the span, the width of the board will be just as large, this must be remembered in the calculations.
To build a small-sized bath roof 3x4 m, you should use a board with a section of 150x50 mm. Permissible dimensions are 100x50 mm, then some design adjustments will be required. For the construction of the roof of a house measuring 10x6 m, boards of 250x50 mm are needed.
Note! To facilitate construction, edged lumber is used, which makes it possible to erect a roof of any configuration. Cutouts in the form of spikes and overhead metal plates make it much easier to firmly connect parts.
Calculation of a gable roof
This is how the truss system of a gable roof looks like. It is distinguished by simple installation and low cost, in contrast to the four-slope
Initial data: Gable type of roof, the length of the slopes is 5 linear meters, and the ridges are 8.5 linear meters. Let's calculate the area: 5 x 8.5 x 2 = 85 m². In the future, for the calculation, you need the length and width of the sheet of metal.
These parameters depend on the type of interprofile:
- Single-wave interprofile - length is 0.35, width - 1.1 m;
- Three-wave - 1.05 and 1.1 m, respectively;
- Six-wave - 2.1 and 1.1 m;
- Ten-wave - 3.5 and 1.1 m.
Now let's calculate how many sheets are required for the width of the slopes, for which we divide the length of the ridge 8.5 mm by 1.1 m, i.e., by the width of the sheet. The result is 8.5 / 1.1 = 7.73 sheets.
Now you should calculate the number of sheets that are required for the lengths of the slopes, using the example of a single-wave interprofile. Divide 5 meters by 0.35, that is, by the value of the length of the sheet. As a result, we get 14.29 sheets. The value is rounded down, that is, 14 should come out. The remainder is covered with an unused extreme overlap.
The final length number in sheets will be: 0.35 x 14 x 0.29 = 1.42. This value should be multiplied by 2, since the calculations are carried out for a gable structure.
Calculation of a hipped roof
If you are calculating a four-slope structure, then it will be useful to apply your knowledge of geometry. As a rule, such a roof has 2 trapezoids and 2 triangles if it is hipped, or 4 triangles if it is hipped.
A four-pitched roof is more suitable for rectangular residential buildings.
Recall the formula for calculating the area of an equilateral triangle:
S= 0.5ah, where a is the base and h is the height of the figure.
So, we have calculated one of the sides S. They are all the same for a hipped roof, so you need to multiply the result by 4:
However, all the same sides of the building and the undersides of the roof are rare. Therefore, it is advisable to calculate the roof of the house as follows: calculate the area of \u200b\u200beach slope using the above formula and add the results:
Stot = S1 + S2 + S3 + S4
The area of the hip roof is somewhat more complicated, because it consists of different figures: two trapezoids and two triangles. First, we determine the area of the trapezoid. It is equal to:
S = h(a + b)/2, where a is the length of the top of the trapezoid, b is the base, h is the height of the trapezoid.
Stotal \u003d 2Striangles + 2Strapezoids
For a more accurate result, you should calculate the area of each triangle and trapezoid separately, and then add the results.
Thanks to the correct calculation of the location of the ridge on the hip roof relative to parallel and transverse walls and the step for the rafters of triangular side trusses, the construction of the hip roof takes place without errors and it has an ideal shape
General remarks
All the above calculations are an obligatory part of roof design. Before you start building it, you need to know how much money you will spend. For this, the area of \u200b\u200bthe entire structure and coverage with various roofing materials is calculated. It is possible that the calculations will force you to change something in the project.
As you already understood, some knowledge of geometry is required to calculate the area of \u200b\u200bthe roof. After all, all you see is a view of the roof from above, located at a certain angle. The best way to calculate is to break it mentally into separate geometric shapes: triangles, trapezoids, parallelepipeds and rectangles. Using the appropriate formulas for each figure, you can calculate the area of \u200b\u200ball sections of the roof.
Please note that the area is always calculated not at the edges of the building, but at the eaves. The amount of material for it will always be more than the area, since the roofing overlaps, therefore, trimming and intersections will occur. A simple form of roofing will require an increase of 10% of the material to the total amount, and a complex one - from 15 to 20%. When installing a hipped roof, there will always be a lot of waste. To be sure, it is better to entrust the calculation of materials to professionals, providing the exact dimensions of your roof.
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