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Optimum roof height / width ratio. Calculation of the height of the ridge of a hipped roof

How to calculate the height of the roof

What is important to know for calculations and what are the risks of errors

  1. Types and forms of modern roofs
  2. Ridge girder and slope angles
  3. Calculations of the height of roofs of different shapes
  4. Roof calculation using online resources
  5. What to consider when starting roof calculations

The final stage in the construction of any house (be it a spacious main dwelling or a small country house) is the arrangement of the roof. It is she who gives the exterior a presentable and complete look. But at the same time it performs a very important function - it retains heat, creates a cozy, most comfortable and pleasant atmosphere inside. It is this element of any structure, without exaggeration, called one of the most important.

What determines the height of the structure and what is taken into account when performing pre-installation calculations

It is especially important to know how to calculate the height of the roof for a house, and to understand exactly how to do it correctly. That is why you need to take some time to study this issue. Inaccuracies in pre-assembly calculations lead to serious problems that are too difficult to deal with later. Often, to eliminate errors, you have to start working on the roof arrangement anew.

For example, if the slopes are made with a small angle of inclination, then such a design will cause serious harm to winter snowfalls (due to the accumulation of snow, there is a risk that the roof will break). It is logical to assume that you can just make a high skate and all problems will be solved. But this is not so, because a roof that is too high is most vulnerable to gusts of wind.

  • general area of ​​the structure;
  • climatic conditions (as you might have guessed, sloping roofs, which are optimal for warm continents, are not recommended in regions with snowy winters);
  • material for arranging the roof, as well as lathing;
  • the selected form;
  • the height of the main building;
  • host's personal preferences and tastes.

The design parameters are largely influenced by a number of other factors, for example, there is a direct dependence on the layer of the installed insulation or the installation of snow protectors. The dimensions of the ridge are associated with the features of the rafter system, but at the same time they can increase the total area of ​​the roof and the amount of materials required for its arrangement.

Everything described above confirms the fact that the strength of the structure, the durability of its operation, aesthetics and harmony of the external appearance of the building depend on the size of the roof.

What are the common types of modern roofing structures

The type of roof has the most direct influence on the calculation and the formulas used for it, as well as on the value and, therefore, on the consumption of material that must be purchased for arranging the roof.

Today, the following structures are most often erected:

  • single-slope (it is preferable to use it for outbuildings);
  • gable (the most popular for residential buildings);
  • hipped. Also an excellent choice for residential buildings. Various options are provided here: spectacular hip-roof (a characteristic feature of which is the same size and shape of all slopes) or complex hip ones (their feature is the participation of two triangular hips and two slopes with a break (trapezoidal shape));
  • attic (consists of two slopes, but always with a break). This break allows you to increase the area of ​​the attic.

The ridge and the definition of rational angles of inclination of the slopes

For calculations of different shapes of the roof, such a value as the size of the ridge is used. This name means the upper, horizontally located rib of the structure, which was formed when two roof slopes (inclined planes) intersect.

There is a ridge on all types of roofs, except for tent and domed ones.

If the design is simple, gable, then it is one, but if it is complex, then two or more skates are formed. During the erection of the roof, the rafter legs rest on the ridge girders, and based on which roofing material is chosen for the final coating, the base of the ridge is also selected.

Knowing how to calculate the height of the roof correctly is also necessary for the construction of a reliable and durable structure, as well as in order to predict the preliminary construction costs and plan a budget. In calculating the rational angle of inclination, the material from which it was decided to lay out the roof is taken into account: some roof coverings can be laid at an angle of up to 90 degrees, while others - only from 15 to 60 degrees.

When choosing which slope of the planes to choose a roof for your house, you need to take into account the functionality, the overall appearance of the resulting structure (after all, you want to get an aesthetic structure) and climatic conditions. As practice shows, for European countries, an angle of 35-40 degrees can be called an ideal solution.

Examples of calculations that are easy to do yourself

In principle, if we are talking about simple roof structures, then it will take quite a bit to calculate the height of the roof: a calculator and several well-known principles from the foundations of geometry, which are taught in the school curriculum.

The basic principle of calculation is taken from the rule that the length of one leg in a right-angled triangle will be equal to the length of the other, if it is multiplied by the tangent of the angle formed with the base.

  • we measure the width of the building (let's say we have a four-meter house);

  • we take the angle value equal to 35 degrees (as the recommended optimal option for European latitudes);

  • we calculate the tangent, it is obtained for a given angle 0.7002;

  • 4 meters * 0.7002 = 2.8 meters.

If a gable design is chosen, then in this case the height of the ridge is also very simple to calculate: the width of the house can be divided by "two" and then multiplied by the tangent of the angle formed by the slope of the slopes. Consider, for clarity, how to calculate the height of a gable roof using the example of a house, whose width will be 10 meters, described above. . So for the calculations:

  • we take the angle equal to 35 degrees;

  • we calculate the tangent, it turns out to be 0.7002;

  • 10 meters / 2 * 0.7002 = 3.5 meters.

The most used today are four-slope structures, and to calculate them, you can use the same principle (formula) as for calculating the height of the ridge of a gable roof, but only the width of the house is divided not by two, but by four. Plus, when doing calculations for a hipped roof, it is important to take into account directly the length of the ridge run, as well as the rafter system.

The most complex calculations are accompanied by the arrangement of the roof of the attic type, a characteristic feature of which can be called the presence of two slopes with a break, which from the side makes its general appearance, as it were, "broken". Arrangement of a sloping roof will increase the functional area of ​​the attic. The calculation of the hip roof is based on the above example of calculating the height of a gable roof, but do not forget that the roof does not have one angle of inclination, but several. Before proceeding to settlement operations, you need to decide on them. Practice shows that it is best to choose the following angles:

  • for the lower one - over 40 degrees;

  • for the rest - less than 40 degrees, but necessarily more than 15.

To simplify calculations, but at the same time to get the most accurate result quickly, experts prefer to use the method “ golden ratio ", For this, the roof contour is inscribed in a circle on the drawing. By resorting to this successful rule, you can easily solve the question of how to correctly calculate the height of the roof, and most importantly, avoid inaccuracies in the calculation, which in practice will lead to the fact that the general appearance of the structure will turn out to be unaesthetic, inharmonious and simply ugly.

Where to go for help: online resource and consultants

If the roof being erected is of a complex shape, then it also requires more voluminous, time-consuming calculations. For calculations, data on the cross-section of the rafters, the step between them, the size of the spans of the rafter structure are used. In addition, the dimensions of the roof windows, chimneys, the presence of parapets and overhangs are taken into account, it is imperative to analyze the possibility of supports and the endurance of the foundation.

Today, anyone who does not know how to calculate the height of the roof can do this by contacting assistants who can be found on the Internet. These can be specialists who are ready to provide you with such services online, or a special Internet resource called a "calculator", in which case the site visitor enters the requested data and the system performs calculations on them.


When choosing whom to turn to for help, remember that a hip roof is not cheap construction, therefore it does not tolerate mistakes and inaccuracies. The correctness of the calculations performed must be guaranteed. For beginners, the calculations of hipped, hip and hip roofs turn out to be quite difficult, so it is better to entrust them to a design specialist with experience in this field. Independently, you can only deal with calculations relating to single-slope structures for outbuildings and garages, or simple gable ones, built to cover a small country house.

Calculating the parameters of the roof is the most important step,

relating to the construction of the roof. It is its result and accuracy that affects how reliable the structure will be, how long it will last, whether it will have an attractive and harmonious appearance. You don't need to spare time and effort to double-check the results and make sure they are accurate. This is a guarantee that you will have the most durable home, designed for many years of use and providing comfort, coziness and warmth.

Accurate and correctly calculated data will help to avoid unnecessary costs for the purchase of materials, and this is a reasonable savings in construction.

When constructing any building, one of the most significant moments is the correct calculation of the height of the roof ridge, as well as its area. With a low ridge height, a large amount of snow can collect on the roof, which will create additional stress on the entire structure. On the other hand, with a sufficiently high ridge and a large coverage area, the windage of the roof increases, which can become a problem in strong winds. Therefore, it is important to know how to calculate the height of the roof ridge, preventing its premature destruction.

Features of roof design

When designing any building, it is important to correctly calculate the parameters of the roof. All possible loads must be taken into account here, as well as the required amount of roofing materials. In this case, one of the main parameters will be the correct slope of the slopes of the structure. In typical gable roofs, the slopes usually have a slope of 12-45 degrees. The direct dependence of this angle of inclination on the loads created by the weight of the roof on the entire structure of the roof of the building is known.

Note! It is necessary to make additional strengthening of the rafter system, which will entail additional construction costs. If you reduce the slope of the slopes, then there will be an increase in the load on all structural elements due to atmospheric precipitation.

It is equally important to correctly calculate the rafter system. This is caused by the transfer of the total load from the rafter legs to the load-bearing walls of the building. In turn, the rafter legs are determined by the size of their section and length. Such structural elements are selected on the basis of what acting loads are on the roof, taking into account the angle of the slopes. To ensure the necessary margin of safety, experts recommend slightly increasing the obtained results of calculating the thickness of the rafter legs.

Since the roof configuration can be different, the calculation of the required parameters will be made depending on some features. To correctly calculate the height of the roof, you should always take into account the number of slopes and its shape. Neglect of such characteristics will lead to calculation errors. Without such data, it will be impossible to determine the roof area, as well as calculate the required amount of materials for the roofing device. The height of the ridge affects the length and configuration of the rafters.

Main settings

When building your own house, each owner will certainly be faced with the calculation of the height of the roof level. Before determining such a parameter, it is necessary to take into account the following nuances:

  • the number of skates;
  • the presence of a residential attic or attic;
  • the angle of inclination of the slopes, taking into account possible atmospheric precipitation;
  • selected roofing material.

In this case, one should take into account the simple dependence of the amount of precipitation and the angle of inclination of the slopes. The amount of material required for roofing can be determined by first calculating the height of the roof. In practice, a 45-degree slope implies a 1.5-fold increase in the cost of the roof compared to a flat slope design.

Building regulations are considered to dictate the proportions and height of the roof ridge. Meanwhile, such a parameter can be calculated knowing the actual dimensions of the walls of the structure. In this case, the calculation of the height of the ridge can be determined using the simplest geometric formulas. To do this, you need to know the width of the structure, as well as the angle that determines the slope of the roof slopes.

Calculations

Parameters such as the height of the roof ridge and the angle of inclination of its slope are directly related. In addition, the selected roofing material also influences the angle of inclination of the roof. For example, soft shingles can be installed on roofs with a slope of 11–90 degrees. Ceramic tiles require a slope limitation of up to 60 degrees.

It is also necessary to take into account the aesthetic component, therefore, it is necessary to provide for the correspondence of the height of the roof ridge to the height of the building. The fact is that an excessively flat or too high roof can adversely affect the appearance of the structure. Taking into account the existing climatic conditions, the most optimal option is considered to be the angle of inclination of the roof, which is 35–45 degrees. A roof with a flatter structure will be subject to increased stress due to precipitation.

If we take the height of the ridge as one of the legs of a right-angled triangle, then the other leg will be half the width of the building. Accordingly, the length of the slope will be considered a hypotenuse. In accordance with the trigonometric formula, the length of the leg in such a triangle will be equal to the length of the second leg, multiplied by the value of the tangent of the angle at the base. For example, let's take a building width of 6 m with a roof slope angle of 40 degrees. Referring to the Bradis trigonometric table, we determine the tangent of an angle of 40 degrees. It will be equal to 0.83. It turns out that half the width of the house - 3 meters - needs to be multiplied by 0.83. As a result, we get the height of the ridge of the roof of such a building, which will be 2.49 m.

Any type of building at the end of construction is clearly emphasized by the roof. But you should know how to calculate the height of the roof correctly, because many factors depend on it. The comfort of a person from living in this room will depend on how correctly the calculations are carried out and the type of material is chosen. Also, this nuance directly affects the significant savings at the time of purchasing lumber.

To determine the calculations, you need to understand what shape of the roof is necessary for the structure of the building. It should not only protect the building from the external environment, but also harmoniously complement the entire building as a whole. The most popular and widely used form of roof is gable. It is simple both in calculations and in installation.

The hip type of roof is significantly different from the classic version, since it includes not two slopes, but four. Triangular slopes, which are located on the sides, are called hips. Also one of the most popular roofs is called a hipped roof, which also contains four slopes. So that they all have straight sides, you should know how to calculate the height of the roof from the slopes to the ridge.

The main parameters of the roof

Carrying out the construction of their own house, each owner asks the question of how to calculate the height of the roof. The answer is actually simple: it is imperative that you pay attention at the time of calculations to some of the nuances. Let's consider them:

  • the number of rays;
  • whether there is an attic room or not;
  • the size of the slopes of the slopes;
  • the type of material used in roofing.

How the roof height is calculated can be influenced by the location of the house. Having decided on the direction of the wind and other climatic factors, the height of the ridge can be calculated using geometric calculations based on the size of the building frame. To do this, you need to know the width of the structure and the angles that determine the slope of the roof slopes.

Roof height with attic room

If you are planning with an attic room, then you should know how to calculate the height of the roof of the house accurately. To do this, the first step is to decide what type of roof will be erected:

  • roof with one or two slopes;
  • to calculate the slopes of the slopes, you need to pay special attention to the strength of the wind, the rate of precipitation of various forms;
  • when choosing roofing elements, it must be remembered that the slope must correspond to the characteristics of the materials.

The type of roof should be planned, as the attic space should have a spacious area. It is important that the room located on the roof is bright. For this it is necessary to install windows on the sunny side. The height of the roof should not be too high, since a lot of building material will be required for its device. In this regard, significant financial costs will have to be incurred. In the case of a hip roof device, the attic room will be spacious, light, and the ridge height will be small.

Moments to consider when calculating the height of the roof

According to experts, the roof is the most important part of a building. If its installation is done correctly, then it will also give an aesthetic look to the whole house. In order to correctly determine how to calculate the height, several factors must be taken into account, such as:

  • the number of slopes, as well as the angles of inclination;
  • shape;
  • the level of the height of the entire structure as a whole;
  • climatic conditions;
  • types of building elements;
  • the desire of the owner.

In addition, the size of the roof can be increased with a ridge, since the number of rafters on the roof depends on it. Therefore, the first thing in the calculation is calculated and then the size and number of rafters in the roofing system are deposited from this size. From these calculations, the total coverage area will be known. This data will help to calculate the amount of materials that will be required for construction.

Roofing materials

Many owners who have no experience in construction work want to do it with their own hands. But many do not know how to do this correctly, and what materials will be required to complete the roofing device. The list of required materials includes:

  • lathing;
  • nails;
  • rafters;
  • rafter;
  • insulation;
  • vapor barrier;
  • roof covering;
  • screws.

If all the calculations are carried out correctly, then the entire structure will not only complement the house, but also protect it from the external environment.

Guidelines for determining the height of the ridge

A ridge is a horizontally located rib on which lateral plane connections are formed. With its help, you can understand how to calculate the height of the ridge of a building. These parameters are the main value in the calculations. If the roof height is calculated incorrectly, then in addition to violations in aesthetics, there will be technical problems during the operation of the building. It often happens that the owner wants to implement such ideas that are prohibited for technical reasons in the construction of the roof.

To make it easier to make the roof structure uniform, it is performed in the form of a triangle. This option is widely used in construction. Also, gable type roofs with asymmetrical sides of the slopes are often erected. The angle of inclination is most often the same for such roofs, because the level of the ridge height is calculated using the standard version.

Hip roof system

In order to carry out the installation, you should know how to calculate the height and what material is required. The main components of this type of roof:

  • Ridge board. It is located at the top of the entire structure and is located in the very center. This element is considered an important part in the rafter system.
  • The rafter guides are the basis on which the lathing is fixed.
  • Slant rafters are designed to accommodate the main part of the structure.
  • Hip rafters are elements in a complex roof system.

Having decided on the elements of the rafter system, you can safely start the hip type.

Calculation of a hipped roof

The four-pitched roofing device can be of two types: hip and hip. Therefore, many people ask themselves the question of how to calculate the height.First of all, such a coating is used in buildings of a square type, that is, all sides of the load-bearing walls must be equal. It is also quite convenient to plan an attic space under such a roof. It will turn out to be quite large and light due to the skylights. They can be positioned on either side of the ramp, since they have almost equal sides.

The only drawback of this type of construction is the complexity of installation. The cost of materials is slightly more expensive than that of the gable version due to the volume of the area. This type of roof is not recommended to be installed in climatic zones with high windiness. Strong gusts can damage the roof by slightly sloping the ramps.

The gable roof has long become an architectural classic. The list of its advantages includes ease of installation, low maintenance costs and practicality in terms of the natural removal of rainwater and snow. To fully experience these advantages, it is necessary to correctly think over the roof project and calculate the dimensions. This is the only way to make the structure durable and maintain an attractive appearance for many years.

The main parameters of the gable roof

Selecting the optimal roof size is a complex process of finding a compromise between the desired appearance of the building and its safety requirements. In a properly designed roof, all proportions are close to ideal. The main parameters of a gable roof include the angle of inclination, the height of the ridge, the width of the roof and its overhangs.

Roof slope is a value that determines the position of the slope relative to the horizon line. The choice of this indicator is carried out at the design stage of the structure. Traditionally, both slopes of a gable roof are made with the same slope angles, but asymmetric varieties are also found.

Most often there are roofs with a slope of 20 ° to 45 °

The unit of measure for slope is degrees. For roofs, the range is 1 0 -45 0. The larger the number, the sharper the structure, and vice versa, as the degree decreases, the roof becomes sloping.
Depending on the slope, there are several types of roofs:

  • flat (less than 5 °), the advantages of which are low material consumption and ease of maintenance, and the disadvantages are the mandatory presence of a good waterproofing system and measures to prevent the accumulation of snow;
  • flat (up to 30 °), allowing the use of all existing materials as a roof covering, but more expensive in cost than flat;
  • steep (more than 30 °), capable of self-cleaning, but not resistant to wind load.

The tool for measuring the angle of the slope is an inclinometer. Modern models are equipped with an electronic display and a bubble level. When the device is oriented horizontally, the scale displays "0".

Manufacturers offer to purchase inclinometers with laser sensors that allow taking measurements at a distance from the object.

Photo Gallery: Roofs with Different Slope Values

The load on a roof with a 45 ° slope is 5 times higher than for a roof with an 11 ° angle
Steep slopes, due to the large slope, are good at removing precipitation
A multi-slope roof is erected if it is necessary to connect walls of different heights or an adjacent extension with the house
The minimum slope angle recommended by builders is 14 °

In a number of normative documents, for example, SNiP II-26–76 "Roofs", the slope is indicated as a percentage. There are no strict recommendations for a single parameter designation. But the value in percentage is very different from the option in degrees. So, 1 0 equals 1.7%, and 30 0 equals 57.7%. For error-free and quick conversion of some units of measurement to others, special tables have been created.

Table: Relationship Between Slope Units

Slope, 0Slope,%Slope, 0Slope,%Slope, 0Slope,%
1 1,7 16 28,7 31 60,0
2 3,5 17 30,5 32 62,4
3 5,2 18 32,5 33 64,9
4 7,0 19 34,4 34 67,4
5 8,7 20 36,4 35 70,0
6 10,5 21 38,4 36 72,6
7 12,3 22 40,4 37 75,4
8 14,1 23 42,4 38 78,9
9 15,8 24 44,5 39 80,9
10 17,6 25 46,6 40 83,9
11 19,3 26 48,7 41 86,0
12 21,1 27 50,9 42 90,0
13 23,0 28 53,1 43 93,0
14 24,9 29 55,4 44 96,5
15 26,8 30 57,7 45 100

Ridge height

Another important roof parameter is the ridge height. The ridge is the upper point of the rafter system, located at the intersection of the slope planes. It serves as a support for the rafters, giving the roof the necessary rigidity, and allows you to evenly distribute the load on the entire structure. Structurally, it is a horizontal rib made of a wooden beam. If you imagine a gable roof in the form of a triangle, then the height of the ridge is the distance from the base to the top of the figure.

According to the rules of geometry, the height of the ridge is equal to the length of the leg of a right-angled triangle

Total roof width and overhang widths

The total width of the roof is determined by the width of its box (the size of the rafter system) and the width of the eaves.

The overhang is the part of the roof protruding from the walls. The width of the overhang is the distance from the intersection of the load-bearing wall with the roof to the bottom of the roofing sheet. Despite its modest dimensions and a small percentage in the total area, the overhang plays a key role in the operation of the house. The cornice protects the outer walls from atmospheric precipitation, keeping their coating intact. It creates a shade in the local area in the summer heat and shelters people during a snowfall. In addition, the overhang facilitates the drainage of rainwater from the roof.

The required size of the eaves overhang B is obtained by lengthening or building the rafter legs

There are 2 types of overhangs, differing in location and width:

  • pediment - small in width section of the roof slope, located on the side of the pediment;
  • cornice - a wider overhang that is located along the roof.

To protect the lower surface, the overhang is sheathed with edged board, siding or soffits

Photo gallery: roofs with different overhang widths

The optimal width of the cornice is in the range of 50-60 cm
The edge of the roof ends at the top line of the gable or wall
Houses built in Mediterranean style have narrow overhangs and a slight slope
A wide cornice gives monumentality to the entire building

Factors affecting roof parameters

The first stage in the construction of a roof is the development and preparation of a technical plan. In it, it is necessary to take into account all the nuances that will affect the life of the roof. The design parameters are determined when considering a group of factors: the climatic characteristics of the region, the presence of an attic and the type of roofing material.

Depending on the area in which the building is located, it can be influenced by various natural forces and loads. Among them are wind, snow pressure and water impact. You can determine their value by contacting a special construction organization that performs such surveys. For those who are not looking for simple ways, there is an option to independently determine the parameters.

Wind load

The wind creates significant pressure on the walls and roof of the building. The air stream, which meets an obstacle in its path, is divided, rushing in opposite directions: to the foundation and the overhang of the roof. Excessive overhang pressure can cause the roof to break. To protect the building from destruction, the aerodynamic coefficient is estimated, which depends on the angle of inclination of the slope.
The steeper the slope and the higher the ridge, the stronger the wind load per 1 m2 of surface. In this case, the wind tends to overturn the roof. The hurricane wind affects the flat roofs differently - the lifting force raises and carries away the crown of the house. Therefore, for areas with low to moderate wind strength, roofs with any ridge height and slope can be designed. And for places with strong gusts of wind, low-slope views from 15 to 25 ° are recommended.

In addition to the horizontal impact, the wind exerts pressure in the vertical plane, pressing the roofing material against the sheathing

Calculating the wind load on a gable roof

The calculated wind load is the product of two components: the standard value of the parameter (W) and the coefficient (k), which takes into account the change in pressure depending on the height (z). The guideline value is determined using a wind load map.

The territory of the country is divided into 8 zones with different nominal wind load values

The height factor is calculated from the table below based on the respective terrain:

  1. A - coastal areas of water bodies (seas, lakes), deserts, steppes and tundra.
  2. B - urban area with obstacles and buildings with a height of 10–25 m.
  3. С - urban area with structures from 25 m in height.

Table: coefficient for calculating wind load

Height z, mCoefficient k for different types of terrain
BUTINWITH
up to 50,75 0,50 0,40
10 1,00 0,65 0,40
20 1,25 0,85 0,55
40 1,50 1,10 0,80
60 1,70 1,30 1,00
80 1,80 1,45 1,15
100 2,00 1,60 1,25
150 2,25 1,90 1,55
200 2,45 2,10 1,80
250 2,65 2,30 2,00
300 2,75 2,50 2,20
350 2,75 2,75 2,35
480 2,75 2,75 2,75

Let's look at an example. It is necessary to determine the design wind load and make a conclusion about the acceptable roof slope. Initial data: the region - the city of Moscow with a terrain view B, the height of the house is 20 m. We find on the map Moscow - zone 1 with a load of 32 kg / m 2. By combining the rows and columns of the table, we find that for a height of 20 m and a type of terrain B, the desired coefficient is 0.85. Multiplying the two numbers, we determine that the wind load will be 27.2 kg / m 2. Since the obtained value is not large, it is possible to use a slope of 35–45 °, otherwise it is necessary to take a slope angle of 15–25 °.

Snow load

Masses of snow accumulating on the roof exert a certain pressure on the roof. The larger the drifts, the greater the load. But not only the pressure of the snow is dangerous, but also its melting when the temperature rises. The average weight of freshly fallen snow per 1 m 3 reaches 100 kg, and in its raw form this figure increases threefold. All this can cause deformation of the roof, a violation of its tightness, and in some cases lead to the collapse of the structure.

The greater the slope of the slope, the easier it is for snow deposits to be removed from the roof. In areas with heavy snowfall, a maximum slope steepness of 60º should be assumed. However, the construction of a roof with a slope of 45º contributes to the natural removal of snow.

Heat from below melts snow, increasing the risk of leaks

Calculation of snow load on a gable roof

The value of the snow load is obtained by multiplying the average load (S), characteristic for a certain type of terrain, and the correction factor (m). The average S value is found from the snow load map of Russia.

The territory of Russia includes 8 snow regions

The correction factor m varies depending on the slope of the roof:

  • with a roof angle of up to 25 0 m is equal to 1;
  • the average value of m for the range 25 0 –60 0 is 0.7;
  • for steep roofs with an angle of more than 60 0, the coefficient m is not involved in the calculations.

Let's look at an example. It is necessary to determine the snow load for a house with a slope angle of 35 0, located in Moscow. From the map we find that the required city is located in zone 3 with a snow load of 180 kg / m 2. The coefficient m is taken equal to 0.7. Consequently, the desired value of 127 kg / m 2 will be obtained by multiplying these two parameters.

The total load, which consists of the weight of the entire roof, snow and wind loads, should not exceed 300 kg / m 2. Otherwise, you should choose a lighter roofing material or change the slope of the slope.

Roof type: attic or non-attic

There are 2 types of gable roofs: attic and attic. Their names speak for themselves. So, an attic (split) roof is equipped with a non-residential attic, and an attic (combined) roof is equipped with an exploited attic. If you intend to use the space under the roof for storing items that are not used in everyday life, then there is no point in increasing the height of the roof ridge. Conversely, when planning in an under-roof living room, the height of the ridge should be increased.

The height of any type of roof must be sufficient for internal repairs.

For non-residential roofs, the height of the ridge is determined by fire safety rules. Building codes state that the attic must contain a through passage 1.6 m high and 1.2 m long. For residential roofs, the height is set based on the convenience of living and the problem-free placement of furniture.

Type of roofing material

Until recently, the construction market offered only a few types of roofing materials. It was traditional slate and galvanized steel sheet. Now the assortment has been significantly replenished with new products. When choosing a material for a roof, there are several rules to consider:

  1. With a decrease in the size of piece roofing materials, the angle of inclination is increased. This is due to the large number of joints that are potential leak points. Therefore, they try to make the descent of precipitation as fast as possible.
  2. For roofs with a low ridge height, it is preferable to use rolled roofing materials or large sheet canvases.
  3. The more the roofing material weighs, the steeper the roof slope should be.

The range of possible slopes is described in the manufacturer's instructions for installing the roof.

Material typeMinimum
slope, 0
Note
Metal tile22 Theoretically, installation on a roof with an angle of 11 0 –12 0 is possible, but for better sealing choose a higher slope
Corrugated board5 When the angle of inclination is changed to a larger side, the overlap of one sheet on another is increased
Asbestos-cement slate25 If the slope is less than recommended, snow will accumulate on the roof, under the weight of which the roofing material will collapse
Soft roll roof
(roofing material, ondulin)
2 The minimum slope angle depends on the number of layers: for one layer 2 0, and for three - 15 0
Seam roof7 For roofs with a slight slope, it is recommended to purchase a double standing seam

Cost of a gable roof

It is logical that with an increase in the slope of the slope, the roof area increases. This leads to an increased consumption of sawing and roofing materials and components (nails, screws) for securing them. The cost of a roof with an angle of 60 ° is 2 times more than creating a flat roof, and a slope of 45 ° will cost 1.5 times more.

The greater the total load on the roof, the larger the cross-section of the timber is used for the rafter system. With a slight slope of the roof, the pitch of the lathing is reduced to 35–40 cm or the frame is made solid.

Calculation of roof dimensions without errors will save the family budget

Video: rafter system and roof parameters

Calculation of roof parameters

An online calculator can be used to quickly calculate roof dimensions. Initial data (dimensions of the base of the building, type of roofing material, lifting height) are entered into the fields of the program, and the result is the required value of the slope of the rafters, roof area, weight and amount of roofing material. A small minus - the stages of the calculation are hidden from the user.

For a better understanding and clarity of the process, you can carry out independent calculations of the parameters of the roof. There is a mathematical and graphical method for calculating the roof. The first is based on trigonometric identities. A gable roof is represented as an isosceles triangle, the dimensions of which are the parameters of the roof.

Trigonometry formulas can be used to calculate roof parameters

Calculation of the slope angle of roof slopes

The initial data for determining the slope angle is the selected roof height and half of its width. As an example, consider a classic gable roof with symmetrical ramps. We have: ridge height 3 m, wall length 12 m.

Dimensions c and d are usually called the laying of the roof.

Slope calculation sequence:

  1. We divide the conditional roof into 2 right-angled triangles, for which we draw a perpendicular from the top to the base of the figure.
  2. Consider one of the right-angled triangles (left or right).
  3. Since the construction is symmetrical, the projections of the slopes c and d will be the same. They are equal to half the length of the wall, i.e. 12/2 = 6 m.
  4. To calculate the slope angle of the slope A, we calculate its tangent. From the school course, we remember that the tangent is the ratio of the opposite leg to the adjacent one. The opposite side is the height of the roof and the adjacent side is half the length of the roof. We get that the tangent is 3/6 = 0.5.
  5. To determine what angle the resulting tangent has, we use the Bradis table. Having found the value 0.5 in it, we find that the slope angle is 26 0.

To convert tangents or sines of an angle to degrees, you can use simplified tables.

Table: determination of the slope of the slope through the tangent of the angle for the range 5-60 0

Tilt angle
roofs, 0
Tangent
angle A
Sinus
angle 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 0,5
35 0,7 0,57
40 0,84 0,64
45 1,0 0,71
50 1,19 0,77
55 1,43 0,82
60 1,73 0,87

Calculation of the rise of the gable roof and the height of the ridge

The height of the roof is closely related to the steepness of the slope. It is determined in the opposite way to the method of obtaining the slope. The calculation is based on the angle of inclination of the roof, which is suitable for a given area, depending on the snow and wind load, the type of roof.

The more the slope, the more free space under the roof

The procedure for calculating the roof lift:

  1. For convenience, we divide our "roof" into two equal parts, the axis of symmetry will be the height of the ridge.
  2. We determine the tangent of the selected angle of inclination of the roof, for which we use Bradis tables or an engineering calculator.
  3. Knowing the width of the house, we calculate the size of its half.
  4. We find the height of the slope by the formula H = (B / 2) * tg (A), where H is the height of the roof, B is the width, and A is the slope angle of the slope.

Let's use the given algorithm. For example, you need to set the height of the gable roof of a house with a width of 8 m and an angle of inclination of 35 0. Using the calculator, we find that the tangent of 35 0 is 0.7. Half the width of the house is 4 m. Substituting the parameters into the trigonometric formula, we find that H = 4 * 0.7 = 2.8 m.

Competently calculated roof height gives the house a harmonious look

The above procedure refers to determining the rise of the roof, that is, the distance from the bottom of the attic floor to the support point of the rafter legs. If the rafters protrude above the ridge beam, then the total height of the ridge is determined as the sum of the roof lift and 2/3 of the thickness of the rafter beam. So, the total length of the ridge for a roof with a rise of 2.8 m and a beam thickness of 0.15 m is 2.9 m.

In places where ledges are cut for assembly with a ridge run, the rafters are reduced by 1/3

Calculation of the length of the rafters and the width of the roof

To calculate the length of the rafters (hypotenuse in a right triangle), you can go in two ways:

  1. Calculate the size using the Pythagorean theorem, which says: the sum of the squares of the legs is equal to the square of the hypotenuse.
  2. Use trigonometric identity: the length of the hypotenuse in a right-angled triangle is the ratio of the opposite leg (roof height) to the sine of the angle (roof slope).

Let's consider both cases. Let's say we have a roof height of 2 m and a span of 3 m.We substitute the values ​​in the Pythagorean theorem and we find that the desired value is equal to the square root of 13, which is 3.6 m.

Knowing the two legs of the triangle, you can easily calculate the hypotenuse or the length of the slope.

The second way to solve the problem is to find the answer through trigonometric identities. We have a roof with a slope angle of 45 0 and a rise height of 2 m.Then the length of the rafters is calculated as the ratio of the number of rise of 2 m to the sine of the slope 45 0, which is 2.83 m.

The width of the roof (in the figure Lbd) is the sum of the length of the rafters (Lc) and the length of the eaves (Lкc). And the length of the roof (Lcd) is the sum of the length of the wall of the house (Ldd) and two gable overhangs (Lfs). For a house with a box width of 6 m and overhangs of 0.5 m, the roof width will be 6.5 m.

Building codes do not regulate a clear value for the length of the slope, it can be selected in a wide range of sizes

Calculation of the roof area

Knowing the length of the slope and the width of the roof, you can easily find its area by multiplying the indicated dimensions. For a gable roof, the total roof area is equal to the sum of the areas of both slope surfaces... Let's dwell on a specific example. Let the roof of the house have a width of 3 m and a length of 4 m. Then the area of ​​one slope is 12m 2, and the total area of ​​the entire roof is 24m 2.

Incorrect calculation of the roof area can lead to additional costs when buying roofing material

Calculation of materials for the roof

To determine the amount of roofing materials, you need to arm yourself with the roof area. All materials are overlapped, so when buying, you should make a small margin of 5-10% of the nominal calculations. The correct calculation of the amount of materials will significantly save the budget of construction work.

General rules for calculating sawn timber:

  1. Dimensions and section of the Mauerlat. The minimum possible cross-section of the bar is 100 × 100 mm. The length corresponds to the perimeter of the box, the margin for connections is set at around 5%. The volume of the bar is obtained by multiplying the dimensions of the section and the length. And if you multiply the resulting value by the density of the wood, then there is the mass of the lumber.
  2. The size and number of rafters. The calculation is based on the total load on the roof (pressure of the roofing cake, snow and wind). Let us assume that the total load is 2400 kg / m 2. The average load per 1 m of rafters is 100 kg. Given this, the footage of the rafters will be equal to 2400/100 = 24 m. For a rafter length of 3 m, we get only 8 rafter legs or 4 pairs. The cross-section of the rafters is taken from 25x100 mm and above.
  3. The amount of material for the lathing. Depends on the type of roofing: for bituminous tiles, a continuous crate is built, and for corrugated board or asbestos-cement slate, thinned.

Let's consider the calculation of roofing materials using the example of metal tiles. It is a sheet material that is installed on the roof in one or more rows.

Calculation sequence:

  1. Determination of the number of sheets. The sheet of metal tile has a full 1180 mm and a working width of 1100 mm. The latter is smaller than the real one and is not taken into account in the calculation, since it is used to overlap the joints. The number of sheets is defined as the ratio of the total width of the roof (including overhangs) to the effective width of the sheet. Moreover, the result of division is rounded up to an integer value. So, for a roof with a slope width of 8 m and a sheet of Monterrey metal tiles with a width of 1.1 m, the number of sheets is calculated according to the formula: 8 / 1.1 = 7.3 pieces, and taking into account rounding 8 pieces. If the canvas is laid in several vertical rows, then the length of the slope is divided by the length of the roofing sheet, taking into account the overlap between the sheets of up to 15 cm.Considering that the roof is gable, the value is doubled, i.e. 16 sheets in total will be required.
  2. Determination of the total area. To determine the total area of ​​the roofing material, the number of canvases is multiplied by the total area (product of the full width and length) of one sheet. In our case, 8 * (1.18 m * 5 m) = 47.2 m 2. For gable structures, the result is multiplied by two. We get that the entire roof area is 94.4 m 2.
  3. Determination of the amount of waterproofing. A standard roll of waterproofing material has an area of ​​65m 2 without overlap. The number of rolls is obtained by dividing the total roof area by the area of ​​the foil, ie 94.4 m 2/65 m 2 = 1.45 or 2 full rolls.
  4. Determination of the number of fasteners. There are 6-7 self-tapping screws per 1 m 2 of the roof. Then, for our situation: 94.4 m 2 * 7 = 661 self-tapping screws.
  5. Determination of the number of extensions (skates, wind bars). The total footage of the planks is 2 m, and the working area is 1.9 m due to partial overlap. Dividing the length of the slope by the working length of the slats, we get the required number of extensions.

Video: calculating materials for a gable roof using an online calculator

The graphic method for determining the parameters of the roof is to draw it on a reduced scale. For him you will need a piece of paper (plain or millimeter), a protractor, a ruler and a pencil. Procedure:

  1. The scale is being matched. Its optimal value is 1: 100, that is, for every 1 cm of paper sheet there is 1 m of the structure.
  2. A horizontal line is drawn, the length of which corresponds to the base of the roof.
  3. The middle of the segment is located, from the point of which a perpendicular is drawn upward (vertical line at an angle of 90 0).
  4. With the help of a protractor, the required roof angle is laid from the border of the roof base and an inclined line is drawn.
  5. The intersection of the inclined line with the perpendicular gives the height of the roof rise.

Video: manual calculation of materials for a gable roof

The first thing that pays attention to is the visual appearance of the roof. Architects make sure that the roof is in harmony with the facade of the building. But beauty alone is not enough. It is important to correctly calculate the parameters so that the structure is durable and functional. Neglecting snow and wind loads, installing rafters at the wrong angle can cause the roof to collapse. And an incorrect determination of the roof area will lead to additional costs for the purchase of missing materials. Therefore, you should take a responsible approach to calculations, paying attention to all the nuances.

Aesthetic indicators, architectural specifics and technical characteristics of the house depend on the height of the roof ridge. It is extremely important when developing a project to correctly determine the correct size of the structure.

To obtain the ideal result, we suggest that today you figure out how to calculate the height of the ridge of a gable roof, and which method is best to use in independent calculations.

A ridge is the horizontal edge of a gable roof, formed at the junction of the tops of its inclined planes. The height of the ridge, without the slightest doubt, will be attributed to the most significant parameters that determine the proportions of the roof.

Both underestimation and overestimation of it can lead not only to a violation of the architectural picture, but also to problems in operation. The ardent desire of the owner of the house to embody his own ideas often goes against the technical prescriptions, familiarization with which will help to avoid serious mistakes.

In order to make the process of studying the studied value simpler and clearer, let's imagine the future roof in the form of an equilateral triangle. This is the most common option. In addition to it, there are asymmetric gable roofs with slopes differing in area.

However, the angle of inclination of both structural components is most often equal, because the ridge height is calculated according to the standard scheme.

For convenience, we divide the equilateral triangle into two symmetrical parts. The line running from the apex of the triangle to its base is the axis of symmetry of the figure presented by us, it is also the leg of a right-angled triangle and the height of the ridge.

Landmark number 1: Atmospheric phenomena

It is pointless to argue with the climatic reality; it is necessary to adapt to its adamant dictation and adapt. The atmospheric phenomena that influence the choice of the height of the ridge include:

... In areas where weather conditions are characterized by frequent gusty winds, it is customary to construct flat and low-pitched roof structures with an angle of inclination of up to 10º. In regions with weak and moderate winds, the height of the ridge can be anything.
  • Precipitation... Precipitation is a potential threat of leaks, due to which they become damp, then gradually become unusable elements of the rafter system and the roofing pie. Precipitation is removed from roofs with a steepness of more than 45º much faster than from shallow structures.
  • Snow cover mass... In areas with heavy winter precipitation, it is recommended to erect roofs with a slope of more than 45º in order to optimize the rate of descent of snow deposits. Lower and flatter roofs will need to be brushed off more frequently.
  • The indicated characteristics will be prompted by the local meteorological service. You can independently find them in the collection of rules and tables on building climatology SNiP 23-01-99 or according to the zoning maps given in SP 20.13330.2011.

    Landmark number 2: The presence of an attic

    In the family of gable roofs, there are attic and non-attic representatives. In the first case, the attic space is separated from the box of the house by a ceiling. They are also called "separate", which confirms the architectural independence of the premises between the roof structure and the floor.

    Attic representatives are residential and non-residential. The height of the ridge of residential roofs is determined by the ease of movement. Structures with an exploited attic are built mainly according to, involving the construction of a rafter system of two tiers.

    The height of the ridge of an exploited attic roof consists of two values: the height of the lower part of the roof and the height of the top of the roof, erected on the lower tier. The height dimension of the lower tier is usually taken from 2.0 to 2.3 m.

    It is calculated by adding the height of the tallest of the future owners and a stock of 30 - 40 cm, necessary for the convenience and safety of movement. The size of the top of the sloping roof is arbitrary, depending on the taste preferences of the owners.

    The height of the ridge of non-residential attics is determined by fire regulations. In addition, the size of the attic space should not create an obstacle to maintenance. The building code regulations indicate that the attic must have a through passage along the entire roof of at least 1.6 m in height and 1.2 m in length. On short sections of complex construction, the width and height of the walk-through can be reduced by 40 cm in both directions.

    In the second "unattended" case, the space under the roof is not separated from the box by an overlap. Usually it is located below: at the level of the ceiling system of the previous floor. Roofs without roofs are called "combined", which just speaks about the connection of the space under the roof with a part of the foot space.

    Bright representatives of designs without an attic belong to. They are erected according to the usual gable pattern, but the Mauerlat is laid on walls at least 1.4 m high. The height of the ridge of a half attic is measured from the lower edge of the Mauerlat.

    The practicality of constructing a semi-attic roof in regions with a high wind load can hardly be overestimated. Thanks to its erection, a minimum lateral load acts on the roof, and the owners receive a comfortable and very spacious additional floor.

    Without an attic and an attic floor, they construct low, small household buildings, warehouses. The overlapping device in such situations is not economical and unreasonable from the point of view of access for maintenance.

    Landmark number 3: Type of roofing

    We have already presented a gable roof with an equilateral triangle. And the height of the ridge was represented by the leg of its rectangular counterpart, obtained by dividing the structure into two symmetrical parts. In the geometric shape we created, all the components are interconnected, including the angles and side lengths.

    As roof designers, we are interested in the angle of its slope. it is directly dependent on the type and technical characteristics of the roofing. It is he who will help determine the optimal height of the designed structure.


    There are several rules for the selection of roofing material, taking into account the height of the ridge and the steepness of the roof, these are:

    • The smaller the piece elements of the roof, the greater the angle of inclination of the pitched planes must be. Numerous joints of piece coatings create the prerequisites for moisture penetration under the roof, therefore precipitation must be accelerated.
    • The lower the roof, the fewer joints and seams there should be on the covering. The priority for the arrangement is large-sheet and roll roofs.
    • The heavier the roof, the steeper the roof should be built. The weight of massive elements will be distributed in projection per unit area of ​​the base. As a result, the higher the ridge, the less weight presses on the rafter system and overlap.

    True, arranging a steep roof with a high ridge will cost more. It will take 1.5 times more material to erect a structure with a slope of 45º than to cover a flat roof with a steepness of up to 7 - 10º. And if the slopes are tilted at an angle of 60º, the costs will double.


    Usually, the range of suitable slope angles by roofing manufacturers is indicated in the instructions. The manufacturer's recommendation should be followed in the name of the long term service of the structure.

    Knowing the recommended angle of inclination, the width of the eaves and the dimensions of the house box, you can find the height of the ridge in the course of simple geometric constructions. However, in designing roofs, it is not only the graphical method that is used.

    The slope of the slopes is indicated by degrees, percentages or decimal fractions, in the numerator of which the height of the ridge is indicated, in the denominator - half of the span to be overlapped. All three slope expressions are interrelated, but the latter is more convenient on site.

    There are few people who want to postpone the angle of inclination of the slope with a construction protractor at the facility. Moreover, the process of installing layered rafters, for example, is carried out on an already installed ridge girder. Those. you need to know the height of the ridge run in advance. This is another compelling reason for the interest in calculating skate height.

    There is a general attitude towards the percentage of roof slope both among craftsmen and among domestic craftsmen. Interest will only help you get confused. The most acceptable method of displaying the slope is the ratio of the height of the ridge to the half of the span to be covered. It is most commonly used on the construction site.


    Knowing the height of the ridge, you don't have to peep into the design documentation every minute. Simply by measuring, the middle of the gable wall is determined. At the point obtained, a bar or pole is nailed strictly vertically. From the top edge of the Mauerlat pre-installed on the wall, the size we are examining is laid up. They are guided by it during the construction of the rafter system.

    Methods for determining the height of the ridge

    To calculate the height of the ridge of a gable roof, the area of ​​planes and other dimensions of the designed structure, there are a significant number of calculator programs in the network. All calculations are carried out automatically, the speed and simplicity of the procedure are pleasing. True, it is difficult to check the results of the calculations without a visual representation of the planned roof configuration. And even if you accidentally enter the wrong number, you will only be able to find "amazing" dimensions on the construction site. Therefore, it is better to understand in advance the peculiarities of construction and calculations, so that a banal flaw does not cause ultra-high costs.

    Independent designers will need memories of the school trigonometry course and the desire to build diagrams to scale using a monitor or an ordinary piece of paper.

    Mathematical and graphic methods

    The following methods are used to determine the height of the roof ridge:

    • Mathematical... It consists in calculating the size according to the formula for calculating the length of one of the sides of a right-angled triangle.
    • Graphic... It consists in building a scaled roof scheme to obtain the height of the ridge.

    For the production of mathematical calculations, the formula a = b × tgα is used, where a is the required ridge height; b - half of the span width; tgα is the slope angle chosen by the owner of the house on the basis of technical regulations and recommendations of the roofing manufacturer.

    Graphically, the height of the ridge is determined at the intersection of the axis of symmetry of the roof and the slope line, set at a given angle from the extreme point of the eaves. Let's look at one of the illustrative examples of graphical construction to get an idea of ​​the process.

    Let's note an important nuance. In the described methods, the roof lift is calculated, and not the total height of the ridge. The real value depends on the technology for attaching the top of the rafters. In hanging systems, the ridge height remains unchanged. Similarly, in layered versions, if the top of the rafter does not protrude above the ridge line.

    If the tops of the rafter legs rise above the girder, then 2/3 of the thickness of the board or timber used in the construction of the rafter system should be added to the rise of the roof. It is believed that the depth of the cut reduces the thickness of the material by a third.

    The lathing and the thickness of the roof covering erected on top of the rafters are usually neglected in the calculations. It is almost impossible to avoid slight deviations during the construction of the roof, in fact, 5-7 cm of a roof with a crate has almost nothing to do with it.

    Practical calculation example

    Let us analyze the procedure for calculating the height of the skate using a specific example. This is how the dimensions of a gable roof are calculated by North American carpenters who specialize in the construction of low-rise frame houses. In principle, the process is no different from the actions of craftsmen in other countries.

    In the example, there is a purely technological specificity: the attachment point for the lower heels of the rafter legs to the base is attached with a cut. The rafters rest on the ridge board. If this is not taken into account when drawing up a diagram and performing calculations, the slope will change, which is highly undesirable when choosing the boundary value of the slope angle recommended by the coating manufacturer.

    The independent constructions are based on the same equilateral triangle, divided into two symmetrical halves. We know the width of the span of the house box and the angle of inclination. it is selected according to the type of roofing.

    The algorithm for calculating the height of the skate comes down to a number of the following actions:

    • Let's build a scaled diagram and plot the exact dimensions of the box to be equipped on it. The most convenient and understandable scale is 1: 100, according to which 1 cm displays at a scale of 1 m.If it is uncomfortable to work with such a reduction, you can choose a smaller or larger scale.
    • Find the middle of the span and draw the axis of symmetry of the roof upward from the resulting point.
    • From the corner of the box, we postpone the slope of the projected roof with a protractor. Draw the slope line according to the marked angle.
    • The intersection of the axis of symmetry of the roof and the slope line of the slopes, i.e. diagonals, will give us the opportunity to estimate at what height the ridge board will be located.
    • We outline schematically the outline of the ridge girder and the support post on which the girder will fit. Their axis of symmetry must coincide with the axis of symmetry of the roof. You just need to set aside half the thickness of the ridge board on both sides of the axis and draw arbitrary lines.
    • The line of the base of the triangle, the diagonal and the nearby side face of the ridge girder, together with the rack, define the desired triangle, the vertical leg of which is the rise of the roof.
    • The rise is reduced by 1/3 of the thickness of the board, i.e. to the depth of the cut of the lower rafter assembly.
    • From the obtained height, we put the width of the ridge board upwards and draw a ridge run, then a ridge rack.
    • On a scale we draw a rafter leg, not forgetting that it will sag by 1/3 of the width due to the cut. To simplify the work parallel to the diagonal, draw a straight line at a distance of 2/3 of the thickness of the rafter board.

    Simply put, the height of the ridge is the sum of the roof lift and 2/3 of the thickness of the rafter board. In practice, there will be no impeccable accuracy, but the error can be considered insignificant and quite acceptable according to the building codes for the construction of wooden structures, prescribed in the collection of SP 64.13330.2011. Ideally, the compression and crushing processes of the timber parts of the system should be considered.

    Video example of a skate device

    The video will introduce you to the variant of constructing the ridge of a gable roof, similar to that described in the example of the structure:

    A well-designed roof with the correct ridge height will look great. Its components will not create conditions for leaks and premature wear of the structure. It is not difficult to master the calculation methods we have proposed.