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August 12, 2017 18:06

How to calculate the angle of inclination of the roof

projects constructed suburban mansions can consider many requirements, preferences and even quirks or "whims" of the owner of their respective owners.But always their "native" common feature - without a solid roof never do any of their buildings.And in the foreground should go not only architectural delights the customer's specific requirements as to the structure element in this regard.This reliability and stability of the entire truss system and roofing, roof, full implementation of its direct purpose - protection against moisture penetration (and in some cases, in addition, also thermal and acoustic insulation), if necessary - the functionality located directly under the roof of the premises.

How to calculate the angle of inclination of the roof

How to calculate the angle of the roof

design of the roof structure - it is extremely responsible and quite difficult, especially for complex configuration.The most sensible thing would be to entrust this work to professionals who own methods of carrying out the necessary calculations and related softwa

re to do this.However, the home owner may also be interested in some of the theoretical aspects.For example, it is important to know how to calculate the angle of the roof of their own, even approximately - to start.

This will give the opportunity to immediately estimate the opportunity to realize their "copyright prikidok" - conceived by matching actual conditions of the region, on the "architecture" to the roof, for the proposed roofing material on the use of the attic.To some extent, the calculated angle of slope of the roof will make a preliminary calculation of the parameters and the amount of timber for the roof system, the total area of ​​the roofing.

In what quantities it is more convenient to measure the angle of the roof?

Article Contents

  • 1 In what quantities it is more convenient to measure the angle of the roof?
    • 1.1 Calculator steepness of the ramp on the known value of the height of the ridge
  • 2 dependence of the type of roof covering on the steepness of the ramp
  • 3 Dependence of height of the ridge on the angle of the roof
    • 3.1 Calculator roof slope lengththe known value of the height of the ridge
  • 4 dependence attic room size of the angle of slope of the roof
  • 5 dependence of external loads on the angle of the roof
    • 5.1 Snow load
    • 5.2 Wind load
    • 5.3 Calculator total, snow and wind loads to determine the required cross-section trusses
  • 6 Video: calculation and installation of a gable roof system

would seem - completely unnecessary question, since all at school know,that the angle measured in degrees.But clarity is still needed, because in the technical literature, and reference tables, and in the usual everyday life of some skilled craftsmen are not uncommon, and other units of measurement - interest or relative aspect ratio.

And one necessary clarification - that is taken as the angle of the roof?

What is meant by roof pitch ?

What is meant by roof pitch?

angle of inclination - the angle formed by the intersection of two planes: the horizontal and the plane of the roof slope.In the figure it is shown by the letter of the Greek alphabet α.

of interest are acute angles (obtuse rays can not be simply defined) lies in the range from 0 to 90 °.Ramps steeper than 50 ÷ 60 ° in "pure" form are extremely rare and, as a rule, for the decoration of roofs - in the construction of pointed towers in the Gothic style.However, there are exceptions - such steep slopes may be the bottom row of the rafters of the roof mansard.

The lower roof rafters mansard may be located at a very high angle

Lower rafter roof mansard may be located at a very high angle

Yet often we have to deal with the stingrays lying in the range from 0 to 45 °

C degrees is clear - everything, probably, are transportedits divisions.A ka to be with other units of measurement?

Too big deal.

relative aspect ratio - is the most simplified fraction showing the ratio of the height of lifting ramp (shown above designated Latin H ) to the projection of the roof on the horizontal plane (on the scheme - L ).

L - it may be, depending on the roof structure, half span (with a symmetrical gable roof), span completely (if the roof lean-to) or, for complex configurations of the roof, really linear section defined drawn to the horizontal projection.For example, in the diagram mansard roof a lot good shows - on the horizontal beam from the angle to the vertical pillar extending from the top of the lower rafters.

slope angle and written, shot, for example « 1: 3 ».

However, in practice it often happens that to use the value of the slope angle in such a representation would be extremely inconvenient if, for example, the number of fractions obtained in non-circular and irreducible.For example, there is little to say inexperienced builder ratio 3: 11 .In this case it is possible to use another value measurement roof pitch - percent.Located

this value is extremely easy - you just need to find the result of dividing the already mentioned fractions and then multiply it by 100. For example, in the above example 3: 11

3: 11 = 0.2727 × 100 = 27,27%

Thus, the value obtained by the slope of the roof slope, expressed as a percentage.

What to do if you want to switch from degrees to percent, or vice versa?

can remember such a relationship.100% - the angle 45 degrees when the legs of the right triangle equal to each other, i.e. in this case the ramp height equal to the length of its horizontal projection.

In this case, 45 ° / 100 = 0,45 ° = 27' .One deviation percentage is 27 arc minutes.

If you come from the other side, the 100/45 ° = 2,22%. That is, we find that one degree - a 2, 22% slope.

For ease of transfer values ​​from one to the other, you can use the table:

value in degrees value in% value in degrees value in% value in degrees value in%
1 ° 2,22% 16 ° 35,55% 31 ° 68,88%
2 ° 4,44% 17 ° 37,77% 32 ° 71,11%
3 ° 6,66% 18 ° 40,00% 33 ° 73,33%
4 ° 8,88% 19 ° 42,22% 34 ° 75,55%
5 ° 11,11% 20 ° 44,44% 35 ° 77,77%
6 ° 13,33% 21 ° 46,66% 36 ° 80,00%
7 ° 15,55% 22 ° 48,88% 37 ° 82,22%
8 ° 17,77% 23 ° 51,11% 38° 84,44%
9 ° 20,00% 24 ° 53,33% 39 ° 86,66%
10 ° 22,22% 25 ° 55,55% 40 ° 88,88%
11 ° 24,44% 26 ° 57,77% 41 ° 9111%
12 ° 26,66% 27 ° 60,00% 42 ° 93,33%
13 ° 28,88% 28° 62,22% 43 ° 95,55%
14 ° 31,11% 29 ° 64,44% 44 ° 97,77%
15 ° 33,33% 30 ° 66,66% 45 ° 100,00%

For clarity would be helpful to bring a flowchart that shows the relationship very accessible allmentioned linear parameters of the angle of slope, and the magnitude of its dimension.

Diagram A. Interdependence Unit Roof slope angle and allowable types of roofing

Scheme A. Interdependence Unit Roof slope angle and allowable types of roofing

to this figure yet to return, when will be considered types of roofing.

Even easier would be to calculate the slope and angle of the slope.if you use the built-in calculator placed below:

Calculator steepness of the ramp on the known value of the height of the ridge

Enter the height of the ridge N and the length of the horizontal projection of the ramp L.

After I click "Calculate angleof slope roof "
height of the ridge N (m)
horizontal projection length of the slope L (meters)

dependence of the type of roof covering on the steepness of the ramp

planning the construction of your own home, the owner of the site probably already spends "estimates" and its head, and with family members - will look like their future housing.The roof in this matter, of course, is one of paramount importance.And here it is necessary to take into account the fact that not every roofing material can be used on different roof slope steepness.In order to avoid misunderstandings later is required in advance to provide this relationship.

roofs distribution diagram on the steepness of the ramp

diagram distribution roofs on the steepness of the ramp

Roofs on the angle of slope can be divided into flat (slope up to 5 °), full low-slope (6 to 30 °) and krutouklonnye, respectively, with an angle of slope of more than 30°.

Each of roof types have their advantages and disadvantages.For example, flat roofs have a minimum area, but require special waterproofing measures.On steep roofs are not late snow masses, but they are more susceptible to wind load because of its "sail".And roofing material - because of their own technological and operational features has certain restrictions on the use of rays with different slopes.

turn to the already discussed earlier figure ( scheme A ).Black circles with arc-shaped arrows and blue numerals indicate the scope of the various roofing (arrowhead indicates minimum allowable value steepness of slope):

1 - is shingle, wood chips, natural shingles.In the same area is the use and still used in the southern edges of reed roofs.

2 - natural, pieces with tile, bitumen-polymer tiles, slate tiles.

3 - roll materials on bituminous basis, at least four layers, with the outer pebbled, recessed into the layer of molten mastic.

4 - similar to paragraph 3, but the reliability of the roof only three layers of roll material.

5 - similar to the above-described web materials (at least three layers), but without outer protective pebbled.

6 - roll roofing materials, affixed to the hot mastic not less than two layers.Metal, corrugated board.

7 - corrugated asbestos cement sheets (slate) unified profile.

8 - clay roofing tiles cover

9 - asbestos cement sheets reinforced profile.

10 - roofing sheet steel with flare connections.

11 - slate covering the usual profile.

Thus, if you want to cover the roof of a certain type of roofing material, the angle of the ramp slope should be planned in the framework of the above.

Dependence of height of the ridge on the angle of the roof

For those readers who remember well the course of high school trigonometry, this section may seem uninteresting.They can just skip it and go on.But forgotten is the need to refresh the knowledge of the interdependence of angles and sides in a right triangle.

What is it?In this case, the construction of the roof is always in the calculations are repelled from the right triangle.Two of his leg - the length of the projection of the ramp onto the horizontal plane (the length of the span, half span, etc. - depending on the type of roof) and the ramp height at the highest point (at the ridge or in the transition to the upper rafters - the calculation of the lower rafters atticroof).It is clear that there is one constant - a span length.But the height can be changed by varying the angle of inclination of the roof.

two main dependence expressed by the sine and tangent of slope angle shown in the table.There are other dependencies (via the cosine or cotangent) but in this case we need only these two trigonometric functions.

Graphic scheme basic trigonometric ratios
Figure n2 H - the height of the ridge
S - roof slope length
L - half-lengthspan (for symmetrical gable roof) and span length (with pent roof)
α - roof pitch
tg α = H / L N = L × tg α
sin α = H / S S = H / sin α

Knowing these trigonometric identities, we can solve almost all the problems on the preliminary design of truss construction.

For clarity - the triangle attached to the roof of the house

For clarity - the triangle attached to the roof

So, if you want to "dance" on the clearly defined lifting height ridge, the ratio tg α = H / L It is not difficult to determine the angle.According

obtained by dividing the number of tangents in the table are in degrees.The trigonometric functions are often laid in engineering calculators, they are mandatory in Exel tables (for those who know how to work with this handy app. However, the calculation is carried out there is not in degrees and in radians).But to our readers do not have to be distracted by the search for the right table are tangent value in the range from 1 to and 80 °.

angle The tangent angle The tangent angle The tangent angle The tangent
tg (1 °) 0.01746 tg(21 °) 0.38386 tg (41 °) 0.86929 tg (61 °) 1.80405
tg (2 °) 0.03492 tg (22 °) 0.40403 tg (42 °) 0.9004 tg (62 °) 1.88073
tg (3 °) 0.05241 tg (23 °) 0.42447 tg (43 °) 0.93252 tg (63 °) 1.96261
tg (4 °) 0.06993 tg (24 °) 0.44523 tg (44 °) 0.96569 tg (64 °) 2.0503
tg (5 °) 0.08749 tg (25 °) 0.46631 tg (45 °) 1 tg (65 °) 2.14451
tg(6 °) 0.1051 tg (26 °) 0.48773 tg (46 °) 1.03553 tg (66 °) 2.24604
tg (7 °) 0.12278 tg (27 °) 0.50953 tg (47 °) 1.07237 tg (67 °) 2.35585
tg (8 °) 0.14054 tg (28 °) 0.53171 tg (48 °) 1.11061 tg (68 °) 2.47509
tg (9 °) 0.15838 tg (29 °) 0.55431 tg (49 °) 1.15037 tg (69 °) 2.60509
tg (10 °) 0.17633 tg (30 °) 0.57735 tg (50 °) 1.19175 tg (70°) 2.74748
tg (11 °) 0.19438 tg (31 °) 0.60086 tg (51 °) 1.2349 tg (71 °) 2.90421