The question of how to calculate the angle of inclination of a roof with a lean-to structure is challenging task, for those craftsmen who are just beginning to master the basics of roofing craftsmanship. This is due to the selection of parameters that determine the difference in the roof structure. Let's look at its main components:
- rafter system and additional accessories;
- sheathing;
- roof threshold made of layers of thermal insulation, waterproofing and vapor barrier;
- roofing material.
It must be taken into account that a large angle of inclination will require the use of significantly more building materials, thereby increasing the cost of roofing by up to 20%. When building in regions with high wind loads, the design is used pitched roof with a slight angle of inclination, which in most cases is located towards the windward side. This provides significant resistance to wind loads. For this reason, proper calculation of the angle of inclination contributes to a high level of savings in roofing materials while complying with all building codes and regulations. The determining factors are:
- climatic features of the area in which construction is taking place;
- roofing material;
- purpose of the building.
Dependence of the angle of inclination on the type of roofing material
When choosing a roofing material, it should be taken into account that it has a direct impact on the structure being built and its cost. Calculation of the slope angle should be carried out taking into account the type of roofing material. To do this, it is recommended to use the table below.
The table shows that the roofing material is the determining factor in the calculations.
When using a soft roof, the angle of inclination is significantly less compared to slate.
The calculation must also take into account the atmospheric features of the area where construction is taking place. One of the features of roofs with a slope angle of 300 is the accumulation of snow on the leeward side and an increase in the load on the roofing materials, and rafter system.
Formula for correct calculation of required parameters
Since a pitched roof rests on walls of different heights, the angle of inclination is formed during the construction of walls with different height levels. In construction documentation, it is allowed to take an angle of inclination in the range from 5 to 60°. For areas with increased precipitation in the winter, the calculated value lies in the range from 45 to 60°. When calculating the angle of inclination of the slopes, the load is taken into account atmospheric precipitation, which is due to the design features of pitched roofs and mechanical strength roofing materials. In general, the formula has the following form:
where L of the wall is the height of the wall pediment;
L length – length of the house wall;
A is the angle of inclination.
To build a pitched roof, you should calculate the length of the rafters, which is determined by the following formula:
To find sinA and tgA, use the special tables below:
Calculation example
House wall length: L length = 5 meters;
Roof angle: A=25°;
Let's determine the height of the wall: L wall =5×tg25°=5×0.47=2.35 meters;
Let's determine the length of the rafters: L rafters =2.35÷sin25°=2.35÷0.42=5.6 meters.
To obtain reliable calculation results, add the length of the front and rear overhang to the length of the rafter leg. They will serve as optimal protection for your home from precipitation.
Proper calculation of the roof is associated with the aesthetic appearance that it will have as a result of completion of construction. Most owners modern houses They prefer high roofs, giving the building a slender, classic look. Another advantage is the possibility of creating a spacious attic. But, from a financial point of view, the construction of a flat roof is much cheaper than its peaked counterparts.
Advantages of a pitched roof
A pitched roof has many advantages that make it the most popular option when arranging premises and structures for domestic purposes. Its main advantages include:
- simple design;
- the design of a pitched roof requires significantly less building materials than its other varieties;
- simple and easy installation;
- low construction costs;
- high resistance to wind loads;
- short construction time.
Disadvantages of a pitched roof structure
In addition to the advantages, a pitched roof has the following disadvantages::
- during its construction there is no opportunity to equip a comfortable attic; it's connected with design features roofs;
- reduced level of thermal insulation, which is due to the minimum amount of free space under the roof.
Calculation of the roof slope angle allows even at preliminary preparatory stage obtain reliable data on the amount of materials required for the construction of a pitched roof. Application correct technique obtaining calculated data provides an optimal ratio between the cost of constructing a roof and its performance characteristics. To save financial resources during construction, it is not at all necessary to reduce the reliability of the roof or refuse to use high-quality materials. It is important to carry out a competent and correct calculation in a timely manner, which will reflect the true cost of construction.
Calculation of the angle of inclination of a pitched roof. Learn to find the slope of a pitched roof using the slope angle formula
We determine the optimal and minimum slope of a pitched roof
Roofs with one slope are becoming fashionable. There are many reasons for this, including their practicality, low cost and distinctive appearance. The slope of shed roofs in most cases differs from gable and hip roofs: it is smaller. Let us consider what the optimal depends on and what is limited by minimum slope pitched roof.
What the standards say: we study SNiP “Roofs”
The updated version of SNiP II-26-76 “Roofs”, updated within the framework of SP 17.13330.2011, indicates that the slope of a flat roof should be from 2° to 12°. It is logical to assume that the standards assume a value for a pitched roof of over 12°. However, SNiP does not contain any information about the slope of a pitched roof. A value of 12 degrees is optional. In fact, the boundary between a flat and a pitched roof is not fixed by regulation and is more often determined “by eye”.
One of the factors indicating that the roof is pitched is the use of roofing material intended for pitched roofs (all types of tiles, sheet materials, corrugated sheets, etc.). Flat roofs have an average slope of 3° and are covered, with rare exceptions, with rolled bitumen materials. Roll bitumen roofing Can also be successfully installed on pitched roofs.
Determining the optimal slope angle
The optimal slope of a pitched roof is dictated by the architectural and planning features of the building. If the slope is the same as a gable roof, the ridge of a shed roof will be twice as high, which is why shed roofs are flatter. For a barn, garage, veranda, in most cases 10-15° will be enough. A shed roof is economical, especially for small buildings. As a rule, a slope of 10-15° is sufficient.
A pitched roof is of little use for organizing an attic in the classic form: one part of the room will be too low, the other too high, such a volume is difficult to use rationally. Even with the device attic floor It is unlikely that you should make a slope of more than 30°. A roofless shed roof, relatively flat, (10-20°) allows you to equip rooms with different ceiling heights on the floor. They are carried to a higher part living rooms, in the low - bathrooms, utility rooms, stairs.
If the layout provides for offset floor levels, a steep pitched roof with a slope of 20-35° would be rational.
Calculate the minimum slope
The limiting factor for the minimum and maximum slope is the manufacturer's recommendations for specific types of roofing materials. Shed roofs are quite flat; we will be more interested in the minimum values.
Roll fused bitumen roofing allows you to cover any roof, including flat ones. Only the maximum angle is limited to 25°, although it is better not to go beyond 15° so as not to complicate installation. Bitumen-polymer materials are the most durable and reliable, upper layer has a sprinkle of stone chips. Rolled materials are hot glued to bitumen mastic.
Asbestos-cement corrugated sheets (slate) require a fairly large slope. For reinforced profile sheets it must be at least 25°, for regular profiles - 35°. It should be noted that the amount of overlap of the sheets of the top row is taken depending on this value. The higher it is, the greater the overlap.
The so-called “Euro slate” is less demanding on surface steepness; a minimum of 6° is allowed. When installing corrugated bitumen sheets, not only the amount of overlap, but also the design of the sheathing depends on the slope: at 6-10° it should be continuous, at 10-15° the pitch of the bars or boards is 45 cm along the axes, with a larger value 60 cm is sufficient.
Metal tiles can theoretically be laid with a slope of 10°. But with a parameter of 10-20°, you will have to seal all the joints of the sheets, and this is not an easy task. Rational decision There will be the use of metal tiles for roofs with a slope of over 20° without additional sealing.
Corrugated sheeting can serve as a roofing covering for roofs with a slope of 5°. At 10° the overlap is increased and sealing tape is placed at the joints.
Seam roofing, both from standard elements with a factory seam, and when seams are made on galvanized steel sheets directly at the construction site, is used for bases with a slope of 8°. Provided the seam joints are sealed, the value can be reduced to 3°.
Flexible bituminous tiles are used on slopes of at least 11°. At a value of up to 18°, the lining layer must be continuous; at a higher value, it is enough to roll out the rolls only along the outer contours of each of the roof planes and additionally insulate the holes.
Ceramic and concrete tiles require a slope of 22°. It can be reduced to 10° if an additional waterproofing layer is installed under the tiles. The tiles are quite heavy and are not often used for pitched roofs.
The data provided is not completely accurate. Each roofing material manufacturer sets its own requirements; they may differ slightly. In addition, the slope largely depends on the snow load for a particular area. The less snow, the flatter the roof can be. There are territorial standards that establish minimum requirements depending on the climatic characteristics of the area.
We found out that the angle of inclination of a pitched roof is determined by the architecture of the building and is limited by technical requirements. The calculation of the rafter system to ensure the necessary strength with rational consumption of materials should be entrusted to specialists.
We calculate minimum angle tilting the pitched roof for optimal results
The angle of inclination of a shed roof is significantly lower than that of a gable roof. What factors are decisive in design, which limits the minimum slope
Features of calculating the angle of inclination of a pitched roof
The pitched roof has gained considerable popularity due to the relative ease of installation and financial profitability. This type of roofing is becoming a common choice when constructing country houses. With the help of a pitched roof you can reliably protect the building from the wind and negative influence other weather phenomena, if the angle of inclination of the pitched roof in relation to the windy side is correctly calculated.
A pitched roof will last longer and will more reliably protect the building from exposure weather conditions, if its rafters rest on walls of different heights, and they will be less affected by gusts of wind.
According to experts, even a person without special skills can install a pitched roof. They claim that it is enough to comply with everything necessary measures safety and theoretically familiarize yourself with the features of the progress of work. This ease of installation and the minimal amount of materials used are the primary advantages that attract many consumers who are building country houses today.
To ensure maximum safety when installing a pitched roof, you should use the most reliable ladders and do not forget to wear rescue belts.
The design features of a pitched roof make it possible to completely avoid
An example of calculating the angle of inclination of a pitched roof
irrational use of indoor space. A pitched roof does not provide for an attic and few comfortable attics.
In addition to country premises, garages, sheds, outbuildings for various purposes, and quite often residential buildings are equipped with pitched roofs. IN residential buildings a roof of this type helps to create a more unique room design. Also, the installation of a pitched roof in a residential building often requires the characteristics of the area. This way, you can minimize the amount of rainwater and melted snow flowing onto the roadway.
Types of pitched roofs
Depending on whether roof ventilation is provided in the room, there are two types of pitched roofs:
- Ventilated. Typically used in building construction closed type. The angle of inclination of a pitched roof in this case ranges from 5 to 20%. Ventilations are specially designated spaces for air passage between the waterproofing and thermal insulation layers of the roof. This allows you to significantly increase the service life of the building's roof.
When installing a pitched roof with a ventilation system provided, it is necessary to make holes on the sides of the building at roof level. This will ensure constant air exchange regardless of wind direction.
- Not ventilated. Most often used in the construction of terraces. The angle of inclination in this case is within 3-6%. Open type premises requires special care, especially in winter.
There is also a combined version of pitched roofs with and without ventilation. In this case, thermal insulation ensures a slight slope of the pitched roof. At the same time, there are significant savings in the creation of the structure, but they create certain inconveniences during operation. So, in winter, when there is a large amount of snow that has fallen, it is necessary to constantly clean the roof, reducing the load on it.
What are the advantages of pitched roofs?
In addition to the minimum volume of materials used and ease of installation, as mentioned earlier, a number of other advantages can be identified due to which a pitched roof is chosen when constructing buildings for various purposes.
- If in the region where the construction of the building is planned, wood is a scarce material, a pitched roof will be the most profitable option for the developer from a financial point of view. Its installation involves the use of a minimum of wood.
- The minimum slope of a pitched roof significantly reduces the windage rate. Thus, the space under the roof will be used most rationally, and there will be no need to equip the least comfortable and least functional attic.
- This type of roof can be easily used in commercial buildings with walls of different heights.
- If there is a roadway on one side of the building, a pitched roof will avoid dumping large amounts of snow and rainwater onto the road.
To eliminate the possibility of damage to the roof by strong wind gusts, it is necessary to install a special curb on the drainage side, reinforced with galvanized iron or tiles.
Rafter system for pitched roofs
The roof truss system is, in fact, its skeleton. That is why its primary task is to evenly distribute the mass of the roofing material onto the supports on which it is attached. Also, when forming a rafter system, the strength of the influence of winds and precipitation in a given area should be taken into account.
It is imperative to increase the expected load on the rafter system, calculating it, as they say, with a margin.
When developing a pitched roof, you should take into account the plan of the walls acting as a support, the characteristics of the attic floor and interior partitions, external parameters of the building, as well as the distance of the largest span.
The angle of the roof and the ease of its installation depend on the type of connection of the rafter system to the supports. So, there are three types of fastening:
- Hanging rafters are used if it is not possible to provide support for the rafters in the distance between the side supports. In this case, the trusses are assembled on the ground, and then the finished structures are carefully transferred to the outer supports. This process takes the most time and effort. It is complicated by the presence of large spans. Load-bearing roof elements are usually made of wood coniferous species, metal and reinforced concrete. The most suitable rafter section is 5*15 centimeters. The bars for the sheathing should have a cross-section of 5 * 5 centimeters.
- Inclined rafters require support on external walls leading elements at an angle. In the upper part of this type, the rafters rest on a beam secured with the help of struts and racks. The support for the struts is the partitions. External load-bearing walls can also serve as supports. The length of the distance between rafter systems can vary between 60 and 140 centimeters. This distance depends on the thickness of the wood and the parameters of the roofing material used. The structure is supported by walls of different heights. Most often, inclined rafters are chosen when arranging the roof of commercial buildings.
Do not forget about turning the roof slope relative to the windy side.
- Sliding rafters a log in a ridge is used as a support. When connecting the rafters to the walls, in this case, special elements called “sliders” are used. Sliding rafters are most often used when arranging roofs in log buildings. Thanks to the use of this type of rafters, it is possible to compensate for the rather large shrinkage of the log house, preventing damage to the building at the junction of its main elements.
Materials used in the formation of pitched roofs
When wondering how to determine the angle of inclination of the roof, first of all it is necessary to take into account the material from which it is planned to create the roof. So, there are certain limits of permissible tilt for different types roofing material:
- The slope of a corrugated roof can vary from 8 to 20 degrees.
- If metal tiles are chosen as the roofing material, minimum slope it can be 25 degrees.
- For slate roofing, the minimum slope angle increases to 35 degrees.
- The seam roof can be at an angle within 18-35 degrees.
Do not try to make the angle of inclination less than eight degrees, since such a roof can fail even under the weight of snow and with high levels of precipitation.
Once the most suitable roof angle for a particular building has been determined, it will be necessary to raise the front wall of the building so that its height in relation to the rear wall forms the established slope. In such calculations one simply cannot do without using certain trigonometric formulas, so often for correct calculations You should contact experienced specialists in drawing up projects of this kind.
Slope angle of a pitched roof: minimum and optimal roof slope - how to calculate?
The article slope angle of a pitched roof will tell you how to calculate the slope angle of a roof, which slope angles are minimal and optimal for various types of roofing coverings, as well as calculation examples and factors influencing the choice and calculation of a roof angle.
How to correctly calculate the angle of inclination and height of a pitched roof
In everything globe there are thousands and thousands of architectural traditions in terms of the appearance of roofs. But modern architects have completely changed the idea of the culture of suburban construction, introducing pitched roof forms as ideally combined with landscape design and diverse in execution. Of course, this new fashionable tone was set by the residents of Australia, where the absence of snow at all is like natural phenomenon allows them to create with architecture residential buildings everything that fantasy dictates. But in the snowy regions of Russia such a roof can be built, but with the appropriate slope and in the right direction. In a word, the main parameter of functionality is the angle of inclination of a pitched roof, which we will now teach you how to calculate.
Step 1. Calculate permanent and dynamic loads
First of all, calculate the loads on a pitched roof. They are usually divided into constant and dynamic. The first is the weight of the roofing covering, which is always located on the roof, installations such as antennas and dishes, a chimney, etc. Those. everything that will be on the roof both day and night.
And dynamic loads, or, as they are also called, variable loads, are those that happen from time to time: snow, hail, people, repair materials and tools. And also the wind, which really loves to tear off pitched roofs due to their windage.
Snow loads
So, if you make a pitched roof slope of 30°, in winter the snow will press on it with a force of 50 kg per square meter. Just imagine having one person per meter sitting on your roof! This is the load.
And if you raise the roof to above 45°, the snow will most likely not be able to stay at all (this also depends on the roughness of the roofing). But for central Russia, where snowfalls are moderate, it is enough to make a pitched roof within the range of 35-30°:
The minimum angle that must be so that snow can slide off a pitched roof on its own is 10°. And the maximum is 60°, because there is no point in making the roof steeper. The same applies to snow, which clings even more to such a roof.
That's why owners of lean-to outbuildings In winter they often take up a shovel. The only thing that saves is the coverage area: the smaller it is, the less likely it is that the snow will be able to bend the material.
Wind loads
But in windy regions it is impossible to build roofs with steep slopes at all. For comparison: a pitched roof slope of 11° experiences exactly 5 times more wind force than a slope of 45°. In view of this, please note that a pitched roof is always made with the low part towards the leeward side.
Combined loads
And be sure to calculate for a pitched roof a value such as the combination of the most unfavorable permanent and temporary loads. Those. that critical point that the rafter system must be able to withstand. By the way, this is often forgotten! They think the roof can withstand the snow and the wind too...
What if you and a friend have to climb out onto the roof during a heavy storm and snowfall? Is the design designed to withstand snow, wind, and the legs of at least two people at the same time? This is how trouble happens.
Step 2. Select the roof slope
The slope of a pitched roof is in a fairly wide range: from 6° to 60°. It all depends on the area in which you are planning to build: if you need to successfully dump tons of snow every winter, then make the slope steeper; if you plan to protect yourself from the wind, then make it flatter. And also from many other factors, including aesthetic ones.
Steep pitched roofs
The greater the angle of such a roof, the faster water flows down it into the gutters. Neither leaves nor dirt will linger here, and therefore the roofing itself will last much longer. In addition, on such a roof the visual aesthetics of the selected flexible tiles or metal profiles are more visible, which often plays a big role for the owners.
Low-slope pitched roofs
The speed of flowing rain and melt water on low-slope slopes is much lower, and therefore there is a risk of water stagnation, dirt collecting and ice getting stuck. On such roofs, moss quickly develops and leaves stick to it. Especially if the roof covering is rough.
As for rainwater, the main requirement for the roof is that the water on it, when the snow melts or after rain, does not remain on the surface of the roofing material, but rolls off easily. If it has too low a slope (for a certain area), then the liquid will sit for a long time in all the irregularities and seams. And the longer, the more chances it has to penetrate inside and create many problems in the form of dampness, deteriorated insulation and corrosion of the metal elements of the roof:
But, if such a building rises big roof at home, then it’s okay:
But there is still a plus here: the smaller the angle of inclination of the pitched roof, the closer the geometry of the interior is to a traditional cube. And, therefore, it is perceived more easily and used with greater benefit.
Therefore, the lower the angle of inclination of such a roof, the more you need to take care of its waterproofing, so that thawed and rainwater could not penetrate the rafter system. Therefore, roofing coverings such as membranes, roll insulation or solid sheets are already needed here.
With a standard slope angle, a pitched roof is built as follows:
Minimum pitched roof angle
A pitched roof, the angle of which is only 3-5%, is often made inverse. Those. they subject it to certain additional loads: they walk on it, grow a garden on it, or even use it as an open terrace. Like here:
In addition, at a certain angle, a pitched roof directs the air flow in the desired direction, capturing precipitation and dispersing it. Remember this!
Step 3. Determine the slope requirements
In functional terms, pitched roofs are divided into three main types: ventilated, non-ventilated and combined. Let's consider each option in more detail.
Ventilated design
These are installed in closed buildings. Ventilation is provided by vents and special voids between the insulating layers, through which air passes, capturing droplets of moisture from the insulation and carrying them outside.
If such ventilation is not provided, then moisture will remain inside the insulation (and it still gets into it, albeit little by little), and the insulation will begin to become damp and deteriorate. And as a result, the entire roofing pie will gradually collapse.
But a ventilated pitched roof has its limitations. So, its inclination angle can only be in the range from 5% to 20%, otherwise the air will not be able to pass through the vents effectively.
Non-ventilated design
This type of pitched roof is advantageously built on terraces and outbuildings. Typically, the angle of such a roof is in the range of only 3-6%, although there are no restrictions on it.
Ventilation in such roofs is not needed because the air in a room without walls or with wide doors often open (as in the case of a garage) itself ventilates well, carrying any water vapor outside. Which, by the way, are not particularly formed in such buildings:
Combined design
Such roofs combine the design of both previous types. Here, the required roof slope is achieved through thermal insulation. It turns out to be economical, but in winter you will have to constantly clear off the snow.
But the structure of such a pitched roof is already different, because dynamic and dynamic loads are now added to the variable and static loads. And usually everything looks like this: there is corrugated board underneath, two layers of insulation on it and good waterproofing.
The angle of a pitched roof also depends on parameters such as the type of connection of the rafters to the mauerlat or walls. Let's take a closer look.
Step 4. Calculate the exact angle of the slope
The angle of a shed roof is usually called the angle at which the rafters and roof slope are inclined to the horizontal plane of the ceiling. Moreover, take this scheme seriously if you want to provide your roof with the correct mechanical strength:
The angle of inclination of the slopes is measured in percentages and degrees. But, if degrees are more or less clear (thanks to the school geometry course), then what are percentages? Percentage is the ratio of the difference in the height of the ridge and cornice to the horizontal of the slope, multiplied by 100.
There is one more interesting point: many architects specifically calculate the angle of a pitched roof so that it is equal to angle the elevation of the sun in a given area in mid-spring. Then you can calculate down to the millimeter when and what kind of shadow there will be, which is important for planning terraces in front of the house and other recreation areas.
Step 5. Limiting the choice of roofing covering
Modern roofing materials also have their own requirements for the minimum and maximum angle of inclination of a pitched roof:
- Profiled sheeting: min 8° - max 20°.
- Seam roofing: min 18° - max 30°.
- Slate: min 20°- max 50°.
- Soft roof: min 5° - max 20°.
- Metal tiles: min 30° - max 35°.
Of course, the smaller the angle, the cheaper materials you can use: roofing felt, corrugated sheets and the like.
You will be surprised, but today, especially for low-slope roofs, the same types of roofing coverings are being developed that are usually used with a slope of at least 30°. For what? This is the fashion in Germany, which has reached us: the pitched roof is almost flat, and the roof is stylish. But how? It’s just that manufacturers are improving the quality of locks, making the overlap area larger and thinking more carefully about protection from dirt. That's all the tricks.
Step 6. Deciding on the rafter system
And based on the selected angle of inclination of the roof and the loads planned for it, we determine the type of fastening of the rafters to the walls. So, there are three types in total: hanging rafters, layered and sliding.
Hanging rafters
Hanging rafters are the only option when the connection must be rigid, but there is no way to support the rafters between the side supports.
Simply put, you only have external load-bearing walls, and no partitions inside. Let's say this is a rather complex rafter system, and its construction must be approached responsibly. The whole problem is the large spans and the pressure that is exerted on the walls:
Or like in this project:
Layered rafters
Here the entire roof presses on at least three supports: two external walls and one internal. And the rafters themselves are dense, with a section of at least 5x5 cm bars and 5x15 cm rafter legs.
Sliding rafters
In this rafter system, a log in the ridge serves as one of the supports. And to connect the rafters to it, special elements such as “slippers” are used. This metal elements, which help the rafters move forward a little when the walls shrink to avoid cracks. Very little! And thanks to this device, the roof easily tolerates even quite noticeable shrinkage of the log house, without any damage.
The point is simple: the more nodes there are in the rafter system, the more flexible and durable it is. The more a pitched roof can withstand the pressure of the weight of the roofing and snow without breaking. But there are rafter systems where the connection is generally static:
Step 7. Calculate the height of the pitched roof
Here are the three most popular ways to accurately calculate the desired height future roof.
Method number 1. Geometric
A pitched roof has the shape of a right triangle. The length of the rafter leg in this triangle is the hypotenuse. And, as you remember from school course geometry, the length of the hypotenuse is equal to the root of the sum of the squares of the legs.
Method number 2. Trigometric
Another option for calculating the length of the rafter legs is this:
- Let us denote by A the length of the rafter beams.
- Let us denote by B the length of the rafters from the wall to the ridge, or the length of part of the wall in this area (if the walls of your building are of different heights).
- Let X denote the length of the rafters from the ridge to the edge of the opposite wall.
In this case, B = A * tgY, where Y is the angle of inclination of the roof, and the length of the slope is calculated as follows:
In fact, all this is not difficult - just substitute required values, and you will receive all the parameters of the future roof.
Method No. 3. Online calculators
By the way, calculate desired angle Modern online calculators will also help you with a pitched roof. Usually they are configured to comply with the current SNiPs - “Load and Impact” TKP 45-5.05. But this method can only be used as an additional one.
Have you figured it out? Now let's move on to the construction of the roof itself:
We hope you figured it out easily!
Angle of inclination, height and slope of a pitched roof: how to calculate
Simple step by step instructions, convenient tables and clear calculation schemes. A step-by-step guide to calculating the pitch angle of a pitched roof.
When designing the roof rafters of a private house, you need to be able to correctly calculate the angle of inclination of the roof. We will discuss in this article how to navigate different units of measurement, what formulas to use for calculations, and how the angle of inclination affects the wind and snow load of the roof.
The roof of a private house built according to individual project, can be very simple or surprisingly fancy. The slope angle of each slope depends on architectural solution the entire house, the presence of an attic or attic, the roofing material used, the climatic zone in which the garden plot is located. In a compromise between these parameters, it is necessary to find the optimal solution that combines roof strength with useful use 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, and technical literature there are various units of measurement for angles:
- degrees;
- aspect ratio;
- interest.
Another unit of measurement for angles, the radian, is not used in such calculations.
What are degrees, everyone remembers from school curriculum. The aspect ratio of a right 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 the sides (legs) is 1:1. In cases where the ratio does not give a clear idea of the slope, we talk about a percentage. This is the same ratio, but calculated in shares and 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 depicted in the diagram below:
Formulas for calculating the angle of the roof, the length of the rafters and the area covered by roofing material
To easily calculate the dimensions of roof elements and rafter systems, you need to remember how we solved problems with triangles at school, using basic trigonometric functions.
How will this help in roof calculations? We break 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 of a hip roof, which is an isosceles triangle. From the vertex 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 inclination of the hip - α, the angle of inclination of the roof - β and obtain the length of the rafters of the triangular and trapezoidal slope.
Formulas for calculation (length units must be the same - m, cm or mm - in all calculations to avoid confusion):
Attention! Calculating rafter lengths using these formulas does not take into account the amount of overhang.
Example
The roof is hipped and hipped. Ridge height (SM) - 2.25 m, span width (W/2) - 7.0 m, depth of slope of the end part of the roof (MN) - 1.5 m.
Having received the values of sin(α) and tan(β), you can determine the value of the angles using the Bradis table. A complete and accurate table up to the minute is a whole brochure, and for rough calculations, which in in this case are valid, you can use a small table of values.
Table 1
| Roof angle, 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°)
- tan(β) = 0.643, β = 32.6° (obtained by interpolating neighboring values for angles of 30° and 35°)
Let's remember these numbers, they will be useful to us when choosing material.
To calculate the amount of roofing material, you will need to determine the coverage area. Ramp area gable roof- rectangle. Its area is the product of the sides. For our example - a hip roof - this comes down to determining the areas of the triangle and 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 elongation of the roof beyond the walls, we take the overhang length to be 0.5 m):
- S = ((2.704 + 0.5) · (7.5 + 2 x 0.5)) / 2 = 13.62 m2
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 = W - 2 MN = 9 m
We calculate the area taking into account overhangs:
- S = (3.905 + 0.5) · ((12.0 + 2 x 0.5) + 9.0) / 2 = 48.56 m2
Total coverage area of four slopes:
- S Σ = (13.62 + 48.46) 2 = 124.16 m 2
Recommendations for roof slope depending on purpose and material
An unused roof can have a minimum slope angle of 2-7°, which ensures 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 and garages.
If the under-roof space is intended to be used as an attic or attic, the slope of the single- or gable roof must be large enough, otherwise a person will not be able to straighten up, and the usable area will be “eaten up” by the rafter system. Therefore, it is advisable to use in this case broken roof, For example, mansard type. The minimum ceiling height in such a room should be at least 2.0 m, but preferably for a comfortable stay - 2.5 m.
Options for arranging the attic: 1-2. Classic gable roof. 3. Roof with variable angle. 4. Roof with remote consoles
When accepting a particular material as a roofing material, it is necessary to take into account the minimum and maximum slope requirements. Otherwise, there may be problems requiring repair of the roof or the entire house.
table 2
| Roof type | Range of permissible mounting angles, in degrees | Optimal roof slope, in degrees |
| Roofing made of roofing felt with sprinkles | 3-30 | 4-10 |
| Tarpaulin roofing, two-layer | 4-50 | 6-12 |
| Zinc roofing with double standing seams (made of zinc strips) | 3-90 | 5-30 |
| Tarmac roofing, simple | 8-15 | 10-12 |
| Flat roof covered with roofing steel | 12-18 | 15 |
| 4-groove tongue-and-groove tiles | 18-50 | 22-45 |
| Shingle roofing | 18-21 | 19-20 |
| Tongue tiles, normal | 20-33 | 22 |
| Corrugated sheet | 18-35 | 25 |
| Corrugated Asbestos Cement Sheet | 5-90 | 30 |
| Artificial slate | 20-90 | 25-45 |
| Slate roofing, two-layer | 25-90 | 30-50 |
| Slate roofing, normal | 30-90 | 45 |
| Glass roof | 30-45 | 33 |
| Roof tiles, double layer | 35-60 | 45 |
| Grooved Dutch tiles | 40-60 | 45 |
The angles of inclination 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 structure of the house must withstand static and dynamic loads from the roof. Static loads are the weight of the rafter system and roofing materials, as well as roof space equipment. This is a constant value.
Dynamic loads are variable values depending on climate and time of year. 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). This calculation, taking into account all possible factors during a particular construction, cannot be presented in full in this article.
Wind load is calculated taking into account zoning, as well as location features (leeward, windward side) and the angle of inclination of the roof, and the height of the building. The calculation is based on wind pressure, the average values of which depend on the region of the house being built. The remaining data is needed to determine coefficients that correct a relatively constant value for the climatic region. The greater the angle of inclination, the more severe wind loads the roof experiences.
Table 3
Snow load, in contrast to wind load, is related to the angle of inclination of the roof in the opposite way: the smaller the angle, the more snow is retained on the roof, the lower the probability of snow cover melting without the use of additional means, and the greater the load the structure experiences.
Table 4
Take the issue of determining loads seriously. Calculation of sections, design, and therefore reliability and cost of the rafter system depends on the obtained values. If you are not confident in your abilities, it is better to order load calculations from specialists.
The roof of the house must be reliable and beautiful, and this is possible with correct definition its angle of inclination for a given type of roofing material. How to calculate the roof slope angle is in the article.
Purpose of the under-roof space
Before calculating the angle of the roof, you need to decide how it will be used. attic space. If you plan to make it residential, the angle of inclination will have to be large - so that the room is more spacious and the ceilings are higher. The second way out is to make a broken line. Most often, such a roof is made of a gable roof, but it can also have four slopes. It’s just that in the second option the rafter system turns out to be very complicated and you simply cannot do without an experienced designer, and the majority prefer to do everything on their own, with their own hands.
When increasing the roof pitch there are a few things to remember:
This does not mean that low-slope roofs are better. They are cheaper in materials - smaller area roofs, but have their own nuances:
- They require snow retention measures to prevent avalanches.
- Instead of snow retainers, roof heating can be used to gradually melt snow and drain water in a timely manner.
- With a small slope, there is a high probability that moisture will flow into the joints. This entails enhanced waterproofing measures.
So roofs with a low slope are also not a gift. Conclusion: the angle of inclination of the roof must be calculated in such a way as to find a compromise between the aesthetic component (the house should look harmonious), practical (with a living space under the roof) and material (costs must be optimized).
Angle of inclination depending on roofing material
The roof on a house can have almost any shape - it can have low slopes, it can have almost vertical slopes. It is important to correctly calculate its parameters - the cross-section of the rafter legs and the pitch of their installation. If you want to lay a certain type of roofing material on the roof, you need to take into account such an indicator as the maximum and minimum angle of inclination for this material.
The minimum angles are specified in GOST (see table above), but often manufacturers give their recommendations, so it is advisable to decide on a specific brand at the design stage.
More often, the angle of the roof slope is often determined based on how their neighbors are made. WITH practical point From a perspective, this is correct - the conditions of nearby houses are similar, and if the neighboring roofs are in good condition and do not leak, you can take their parameters as a basis. If there are no roofs in the neighborhood with the roofing material that you plan to use, you can start calculations with average values. They are shown in the following table.
| Type of roofing material | Recommended tilt angle minimum/maximum | What slope of the slope is most often done |
|---|---|---|
| Roofing made of roofing felt with sprinkles | 3°/30° | 4°-10° |
| Two-layer tar paper | 4°/50° | 6°-12° |
| Zinc with double standing seams | 3°/90° | 5°-30° |
| 4-groove tongue-and-groove tiles | 18°/50° | 22°-45° |
| Dutch tiles | 40°/60° | 45° |
| Regular ceramic tiles | 20°/33° | 22° |
| Corrugated sheeting and metal tiles | 18°/35° | 25° |
| Asbestos cement slate | 5°/90° | 30° |
| Artificial slate | 20°/90° | 25°-45° |
| Straw or reeds | 45°/80° | 60°-70° |
As you can see, in the “how they do it” column, in most cases there is a significant range. So it is possible to vary the appearance of a building even with the same roof. After all, in addition to its practical role, the roof is also a decoration. And when choosing the angle of its inclination, the aesthetic component plays an important role. This is easier to do in programs that make it possible to display an object in a three-dimensional image. If you use this technique, then calculate the angle of inclination of the roof in this case - select it from a certain range.
Influence of climatic factors
The angle of the roof is affected by the amount of snow that falls during the winter in a particular region. Wind loads are also taken into account during the design.
Everything is more or less simple. According to long-term observations, the entire territory of the Russian Federation is divided into zones with the same snow and wind load. These zones are mapped and shaded different colors, so it's easy to navigate. Using the map, determine the location of the house, find the zone, and use it to determine the value of the wind and snow load.
Calculation of snow loads
There are two numbers on the snow load map. The first is used when calculating the strength of a structure (our case), the second is used when determining the permissible deflection of beams. Once again: when calculating the angle of inclination of the roof, we use the first number.
The main task of calculating snow loads is to take into account the planned roof slope. The steeper the slope, the less snow can be retained on it; accordingly, a smaller cross-section of rafters or a larger pitch for their installation will be required. To take this parameter into account, correction factors are introduced:
- tilt angle less than 25° - coefficient 1;
- from 25° to 60° - 0.7;
- on roofs with a slope of more than 60°, snow loads are not taken into account - snow is not retained on them in sufficient quantities.
As we can see from the list of coefficients, the value changes only on roofs with a slope angle of 25° - 60°. For others, this action makes no sense. So, to determine the actual snow load on the planned roof, we take the value found on the map and multiply it by a coefficient.
For example, we calculate the snow load for a house in Nizhny Novgorod, the roof slope angle is 45°. According to the map, this is zone 4, with an average snow load of 240 kg/m2. A roof with such a slope requires adjustment - we multiply the found value by 0.7. We get 240 kg/m2 * 0.7 = 167 kg/m2. This is only part of calculating the roof angle.
Calculation of wind loads
The effect of snow is easy to calculate - the more snow in the region, the greater the possible loads. Predicting wind behavior is much more difficult. You can only rely on the prevailing winds, the location of the house and its height. These data are taken into account using coefficients when calculating the roof slope angle.
The position of the house relative to the wind rose has great importance. If the house is located between taller buildings, wind loads will be less than if it is located on open area. All houses are divided into three groups according to the type of location:
- Zone "A". Houses located in open areas - in the steppe, desert, tundra, on the banks of rivers, lakes, seas, etc.
- Zone "B". The houses are located in wooded areas, in small towns and villages, with a wind barrier no more than 10 m high.
- Zone "B". Buildings located in densely built areas with a height of at least 25 m.
A house is considered to belong to a given zone if the specified environment is at a distance of at least 30 times the height of the house. For example, the height of the house is 3.3 meters. If at a distance of 99 meters (3.3 m * 30 = 99 m) there are only small one-story houses or trees, it is considered to belong to zone “B” (even if it is geographically located in a large city).
Depending on the zone, coefficients are introduced that take into account the height of the building (shown in the table). Then they are used when calculating the wind load on the roof of a house.
| Building height | Zone "A" | Zone "B" | Zone "B" |
|---|---|---|---|
| less than 5 meters | 0,75 | 0,5 | 0,4 |
| from 5 m to 10 m | 1,0 | 0,65 | 0,4 |
| from 10 m to 20 m | 1,25 | 0,85 | 0,55 |
For example, let’s calculate the wind load for Nizhny Novgorod, cottage located in the private sector - belongs to group “B”. Using the map, we find the wind load zone - 1, the wind load for it is 32 kg/m 2. In the table we find the coefficient (for buildings below 5 meters), it is equal to 0.5. Multiply: 32 kg/m2 * 0.5 = 16 kg/m2.
But that is not all. We must also take into account the aerodynamic components of the wind (under certain conditions it tends to blow off the roof). Depending on the direction of the wind and its impact on the roof, it is divided into zones. Each of them has different loads. In principle, rafters can be installed in each zone different sizes, but they don’t do that - it’s unjustified. To simplify the calculations, it is recommended to take indicators from the most loaded zones G and H (see tables).
The found coefficients are applied to the wind load calculated above. If there are two coefficients - with a negative and a positive component, both values are calculated, and then they are summed.
The found values of wind and snow loads are the basis for calculating the cross-section of the rafter legs and the pitch of their installation, but not only. The total load (weight of the roof structure + snow + wind) should not exceed 300 kg/m2. If, after all the calculations, the amount you get is more, you need to either choose lighter roofing materials or reduce the angle of the roof.
The content of the articleThe roofs of private houses, as a rule, always have slopes - this roof structure is the easiest to operate and maintain. Water and snow drain better and faster from such roofs, which guarantees excellent waterproofing. And the appearance of a private house becomes more attractive.
In addition, an additional room appears in the attic, which can be used for living and installing an attic or for numerous household needs.
Factors influencing the shape of the roof
To make the roof reliable and comfortable, it is necessary to correctly calculate the angle of the roof slope, which depends on many reasons. First of all, these are the climatic conditions of living and the characteristics of the roofing material. Natural conditions affecting the size of the roof slope:
- As the roof slope increases, the wind load on the roof structure increases. For example, if the angle of inclination is increased from 10 degrees to 45 degrees, then the load on the structure due to wind will increase five times. If the angle is made small, less than 10 degrees, then there is a high probability of the covering sheets being torn off due to strong wind that gets under the joints;
- Precipitation in the form of rain and snow also affects the slope of the roof. As the slope increases, precipitation flows off the roof slopes better. The highest snow load in winter time happens on slopes with a roof angle of about 30 degrees. At an angle of 45 degrees the snow will disappear completely.
With a low slope of the roof slopes, as a result of strong gusts of wind, water can get under the joints of the covering.
In the question of what angle of the roof slope should be made, the type of roofing matters:
- When using metal tiles as a roofing material, you need to take into account the considerable weight of this coating. Therefore, the angle of inclination of the roof should not be very large. This is especially important in areas where constant and strong winds prevail, as the mechanical load on the roof structure increases. For this coating, the minimum slope angle is approximately 22 degrees. In this case, moisture will not accumulate, but will be effectively removed from the roof. In addition, the joints of the coating will be reliably protected.
- Corrugated sheeting is currently the most popular roofing covering for private homes. It is lightweight, easy to install and maintain the roof. The minimum roof slope using this material is 12 degrees.
- When using rolled materials, they are also called soft roof, the angle of inclination of the slopes depends on the number of layers of coating. For a coating that consists of two layers, the minimum tilt angle is up to 15 degrees. For three layers this value should be from two to five degrees. If the roof needs to be covered with a membrane covering, the angle of inclination should also be from two to five degrees.
From the above we can conclude that making a decision on the optimal roof slope angle depends on natural conditions, type of roofing material and capabilities of the home owner.
With a large slope, the consumption of materials during roof construction increases.
In addition, the type and pitch of the sheathing depends on the slope of the roof slopes. The smaller the roof slope, the smaller the sheathing pitch should be.. For minimum angles it is approximately 35 to 45 centimeters.
- with a roof slope of up to ten degrees, the roof covering can be made using stone and gravel chips;
- if the roof slope is more than ten degrees, then waterproofing using bituminous materials should be used. For rolled materials, it is necessary to use an additional protective coating;
- When using corrugated board and slate, it is recommended to seal joints and seams; the joints should be double.
- If the amount of precipitation in the area where the residential building is located is high, then it is better to make the tilt angle 45 degrees. With minimal precipitation, the roof slope can be made at 30 degrees. In case of strong and frequent winds, the angle of inclination should be from 15 to 20 degrees. If the wind loads are small, then it is better to make a roof with an inclination angle of 35 to 40 degrees.
When calculating the angle of inclination of the roof, it is necessary to take into account that the higher the average annual temperature and the less precipitation, the more flat the roof can be built.
It is necessary to take into account that the type and design of the drainage system of the entire house depends on the slope of the roof.
Choosing the angle of the roof, depending on various factors
When determining the roof slope there is no perfect solution, which is suitable for all climatic requirements. It is important to find here best option, on which the consumption of materials and costs of funds depends.
How larger area roof, the more expensive it costs.
The recommended roof slope angle is from 20 to 45 degrees. When increasing it, it is necessary to take into account the creation of additional structures to strengthen the entire structure. And reducing the angle will lead to additional costs of materials to ensure normal waterproofing of the roof of the house.
In civil low-rise construction, experienced builders call pitched structures the most common, rational and economically feasible type of roof. They can consist of one, two, three or even four slopes, planes that meet at one point, called the ridge. From flat roofs pitched ones are distinguished by an angle of inclination, which, according to building regulations must exceed 2.5 degrees. The choice of slope is an important stage in creating a project, on which the strength, load-bearing capacity and durability of the structure depend. In this article we will tell you how to choose the right angle of inclination to facilitate snow melting in winter.
The angle of inclination of the roof is a parameter for the engineering calculation of roofing structures, reflecting the ratio of the height of the ridge to the width of the base of the slope. Pitched roofs can have a slope of 2.5-80 degrees, however, the optimal range of slope angles is 20-450. The area of the slopes, wind resistance and snow load depend on this parameter. The following terms are found in the specialized literature:
- Minimum slope. The minimum tilt angle in general is 2.5 degrees, but depending on the type used waterproofing material this parameter may increase. The minimum angle for roll bitumen and membrane coatings is the smallest; it is 2-4 degrees. The minimum permissible value for metal tiles and corrugated sheets is 11-12 0, for ceramic tiles – 22 0 .
- Optimal. Optimal is the most suitable roof slope in given climatic conditions when using a certain waterproofing material. The optimal angle of inclination ensures that snow melts off independently, making roof maintenance easier.
Important! The slope of a roof can be expressed as degrees, as a percentage, or as an aspect ratio. To calculate this parameter of the roof structure, it is necessary to divide half the width of the facade by the height, and then multiply by 100 percent.
Criterias of choice
The choice of slope is based on an engineering calculation that takes into account the climatic conditions of the area where construction is taking place, the characteristics of the roofing and the load-bearing capacity of the rafter frame. To ensure a reliable design, the following criteria must be taken into account:
- Wind load. The steeper the roof, the stronger its sailing ability. Therefore, in regions with strong, gusty winds, flatter roofing structures are preferable. Although, on the other hand, the wind can tear off waterproofing material from low-slope slopes.
- Snow load. The greater the snow load, the more covered the slopes become. A roof inclination angle of 40-45 degrees ensures that snow will melt off the surface of the roofing material on its own.
- Characteristics finishing coating. Each roofing covering has an optimal slope that must be taken into account when designing the structure.
- Bearing capacity of the frame. The smaller the cross-section of the frame elements and the greater the distance between them, the higher the slope must be to withstand the snow load.
Optimal indicator for facilitating snow melting
The limiting factor when choosing the angle of inclination roof slopes V middle lane Russia is characterized by a high snow load, characteristic of this area. Large amounts of snow falling in winter increase the pressure on the rafter system, leading to deformation of the frame and roofing material of the structure. Experienced craftsmen believe that there is a strong correlation between slope and resistance to snow load:
- If it is less than 30 degrees, then snow accumulates on the surface of the slopes. Snow drifts and ice have a significant mass, due to which the load on the rafter frame increases, reaching critical levels. However, some of the snow is blown away from the surface by the wind. If the angle of the roof is in this range, then snow guards are not installed on it, especially if the roofing material has a rough surface.
- At a value of 0 degrees (i.e. for flat roofs), the snow load on the surface reaches its maximum values. Snow on such structures accumulates into large drifts, which lead to the collapse of the frame if the roof is not periodically cleaned.
- If the roof is 45 degrees or higher, then in calculating the load on the rafter frame the weight of the snow can be neglected, since the snow slides off the slopes on its own without stopping on the slope. To ensure safe operation of a roof with a large angle of inclination, snow cutters are installed on it, cutting the layer of snow as it descends into thinner plates that have a lower speed and fall energy.
Please note! According to construction climatology, the territory of Russia is divided into 8 climatic zones, each of which has its own average annual snow load. This reference value is used to calculate the roof slope, the section thickness of the rafter frame elements and the selection of roofing.
Impact on design
It is important that changing the slope to facilitate snow melting greatly affects the roof structure as a whole. An increase in slope has the following consequences:
- Increase in weight of the roofing pie. The weight of 1 square meter of a roofing pie with a slope of 50 degrees is 2-2.5 times higher than that of a roof with a slope of 2 degrees.
- Increasing the area of the slopes. The steeper the roof, the larger the area of its slopes, the greater the consumption, and, consequently, the cost of the roofing material.
- Lightening the rafter frame. In the absence of a snow load, you can lighten the roof frame to save on wood.
- Inability to use roll materials. If the roof slope exceeds 40 degrees, it is not recommended to use bitumen and membrane roll materials, since they are under the influence high temperature they can simply “slide” down.
Experienced craftsmen note that the right choice helps to increase the service life of roofing structures and facilitate the operation and maintenance of the roof in snowy Russian winters. Errors in the design associated with the incorrect choice of the optimal angle lead to deformation of the rafters, collapse of the sheathing, and the pouring of atmospheric moisture into the joint space during slanting rain or during thaws.
Video instruction
