Calculation of metal tile semi-hipped roof online calculator. How to calculate the area of ​​\u200b\u200ba hipped roof? Roof elements with four slopes

Planning the future appearance of the roof of a house almost always runs into the problem of checking the designed truss system for strength, rigidity and stability. Very beautiful and elegant on paper, four-pitched, hipped, broken, hip and half-hip structures in practice require the developer to have knowledge and understanding of how to calculate a hip roof in the most understandable and accessible way. The more complex and intricate the roof structure is, the more difficult it is to calculate its characteristics and obtain a reliable result.

What does it mean to correctly calculate the roof

There are several basic methods that allow you to calculate the hip roof of a house with a relatively small error. All of them are widely used in everyday design and have been repeatedly tested in practice. For a private non-professional developer, you can use three methods that allow you to calculate the parameters of the roof, having knowledge within the school mathematics course:

• The tabular calculation method, the most beloved and widely used in the design of hip and any other standard roofing schemes. It allows you to calculate the main parameters of the roof structure using tabular data summarized in reference books and manuals;
• Calculate the parameters based on trigonometric formulas and the simplest hip roof model. By graphical construction and drawing of the future hip structure on an enlarged scale, you can get all the necessary information about the parameters of the roof by a simple measurement;
• Using ready-made programs and online calculators. It is practically impossible to do such a volume of work manually, to calculate the strength and geometry of the roof without basic education and preparation in any other way.

There are a great many specialized programs, and it is often much more difficult to choose the right software package today than to calculate the hip roof geometry with its help.

Note! Full-fledged software systems have high customization flexibility and allow you to calculate the most complex options, for example, to calculate a hip roof with a bay window.

As with any other program, when working with ASPSK, you need to understand the essence of the calculations, if necessary, be able to perform a verification calculation of the hip roof angle using school trigonometric formulas. To date, almost all more or less complex calculations are performed using only three main methods. Even experienced and self-confident design engineers and architects prefer to carry out the calculation of a four-pitched hip roof with a mandatory recheck, as they say, “on paper”.

What is a hip roof, and why you need to calculate it

The hip scheme is currently used in 90 cases out of 100 in the construction of new and repair of old houses. A four-pitched roof, hip or half-hip scheme, has a number of advantages:

• The design turns out to be quite compact, with good resistance to horizontal wind load, pressure of rainwater and snow layers;
• The hip roofing scheme allows you to minimize heat loss through the roofing and eliminate water leakage through the gables, which often suffer from gable roofing schemes;
• The weight of the truss frame and roofing material of the hip roof is less than that of traditional gable structures, but the cost of assembly and arrangement is much higher.

If you calculate the roof according to all the rules, the cost of arranging the roof will only slightly exceed the traditional single-pitched and double-pitched structures. As a result, having spent some resources to calculate the optimal parameters of the hip roof, you can optimize costs as much as possible, and at the same time get the most durable, warm and durable roof structure.

Features of the application of various methods for calculating the hip roof

In addition to the strength and stability of the structure, important information is the consumption of materials, especially expensive ones, long timber and logs, insulation and roofing. Before calculating the selected option for stiffness and deflection of the rafters, a preliminary selection and calculation of the angle of the hip roof is performed. This parameter depends on:

• Selection of the height of the ridge and the nature of the roofing material planned for use in the design of the hip roof;
• Based on the value of the angle and the roofing material, it is possible to calculate the area of ​​the hip roof and the size of the strength elements.

Knowing the parameters of the roof, the elements of the truss frame, it will not be difficult to calculate the total weight of the hip structure and the cost of materials. You can calculate the cost of building a roof and the amount of pressure on the walls and foundation of the building.

The simplest calculation of the hip roof geometry

For a preliminary calculation of the hip roof frame, you can use the simplified model shown in the figure below.

As the initial parameters, we take the dimensions of the base of the roof or the box of the building. Before calculating the area of ​​\u200b\u200bthe hip roof, it is necessary to resolve the issue of the angle of inclination. Usually the customer offers several options for roofing, each of which has its own optimal angle of inclination. The second factor that you need to know in order to correctly calculate the bearing capacity of the roof is the maximum thickness and weight of the snow cover. For higher latitudes, the angle of the hip roof is chosen at least 30 ° and even 45 °, which makes it possible not to take into account the pressure of the snow mass on the rafters.

Important! A simplified hipped roof model can be used to calculate any hip structure. For example, to calculate the area of ​​the classic version of the roof with two short hips and two elongated hip slopes, it is enough to add to the hipped roof area the surface area of ​​the slope rectangles formed by the ridge beam and the long ordinary rafter leg.

After choosing the angle, it is necessary to calculate the ridge of the hip roof, it is not difficult to do this, according to the formula of the sine or tangent of the angle of a right triangle. Using trigonometric formulas, it is possible to calculate the length of ordinary and corner rafters, but in practice, most often the dimensions of individual elements of the truss frame are simply recalculated using coefficients from the tables. Knowing the angle of inclination and the length of an ordinary rafter, it is possible to calculate the angular and intermediate values.

After the preliminary values ​​\u200b\u200bof the dimensions of the ridge, layered and ordinary rafters have become known, it is necessary to draw up an accurate drawing of the hip roof, on which you can graphically calculate and more accurately measure the resulting details of additional power elements. In this way, the calculation of the wooden skeletons of ships, bridges, complex structures of buildings made of stone and wood was carried out for several centuries, until modern mathematical methods appeared.

When using a sufficiently small scale, approximately 1:7 or 1:10, it is possible to graphically calculate absolutely all the details of a hip roof on the finished drawing. Oddly enough, but the accuracy of such a calculation is only slightly higher than the standard value adopted for ordinary engineering calculations. Moreover, when drawing up detailing and calculating the dimensions of blanks for specific parts, for example, under rafter beams or struts, the length and section are chosen with the required allowance for trimming or grinding the surface of the beam.

Only after drawing a draft design drawing, you can proceed to the most critical stage - the calculation of strength and stiffness, or most often - the maximum deflection of the rafters, ridge beams, overhangs and other structural elements. The easiest way is to calculate the roof parameters using a ready-made program.

Method for calculating the hip roof using programs

In the simplest case, you can check and calculate the preliminary information and characteristics of the hip roof using an online calculator. Companies that provide online software systems use ready-made modules that contain the basic requirements of building codes and rules “Loads and Impacts”, as well as the defining provisions of TCP 45-5.05-146-2009. True, only the simplest version of a hip roof can calculate such a calculator.

For the calculation, you will need to enter only a limited set of basic information about the roof structure:

• Dimensions of the base or Mauerlat of the roof;
• slope angle;
• The length of the end and side overhangs;
• Materials for the manufacture of load-bearing elements and roofing;
• Step of rafter legs and lathing;
• Wind and snow load data for a specific region.

At the output of the calculator, the program produces a fairly large amount of information. First of all, the compliance of the laid angle of inclination of the rafters with the selected material for roofing is checked. In the second paragraph, the program will try to calculate the roof area, taking into account the overhangs and the total load on the truss system at the given angles of inclination of the hip and side slopes, separately for clean roofing material and separately under the maximum layer of snow.

At the second stage, the parameters of the truss system are issued:

• The length of the hip, corner and ordinary rafters;
• The number of rafter legs on each part of the hip roof;
• The total weight of the truss frame and the recommended section for each of the rafters.

As a result of the program, you can additionally find out the volume of lumber and the area of ​​​​roofing. The data obtained allow us to calculate the costs and cost of materials for the manufacture of the roof. In some calculators, you can get several calculation options, but most often you have to calculate the cheapest and most durable option yourself. On average, to obtain the most optimal slope scheme and rafter sizes, you have to work out at least 30-35 different options. Usually, 10-12% is added to the cost for the costs associated with preparing for construction and delivery to the construction site.

Conclusion

A significant drawback of such calculators is a simplified scheme, according to which it is necessary to calculate the parameters of a hip roof. A simple online program does not answer the main question - how stable and rigid the frame will be, and what will be the maximum deflection of the rafters and battens under the most unfavorable loading conditions. Therefore, complex variants of roofing structures are best calculated using specialized ASPSK software systems.

A fairly popular type of roof is. This variety is referred to as four-slope structures.

For slate, the calculation example is as follows:

1. Usually, seven sheets of wave slate are used for covering, the useful area of ​​\u200b\u200bwhich is 1.335 m 2.
2. If 8 sheets of such material are used, then the value of the usable area is 1.56 m 2.
3. Further, the value of the total roof area is divided by the value of the usable area of ​​the material. If the roof area, for example, is 26.7 m 2, then the number of slate sheets required for roofing equipment is 20 pieces.

Calculation example for metal tiles:

1. When choosing a similar material for coating, it is worth knowing that the smaller the size of the material, the larger the size of the joints must be used.
2. Initially, the value of the total area is multiplied by a correction factor equal to 1.1.
3. After that, the resulting area value is divided by the useful area of ​​​​the tile, depending on its size and, accordingly, the size of the overlaps.

If the structure of the roof covering is combined and complex, then the value of overspending can reach 60%.

Roof Calculator

Rafter step

The value of the distance that is formed between the two rafters is called a step. Most of the structures are made in such a way that the step is 1 m. The minimum allowable value of such a parameter, equal to 60 cm, has also been established.

The process for calculating the distance between the rafters is as follows:

1. Initially, you need to choose the approximate estimated step of the truss system. You can build on the above values, i.e. the distance is 1 m.
2. The next value you need is the length of the skate (ramp).
3. After that, the length of the rafter is divided by the approximately selected step value. The result is rounded up to a higher value, after which it is increased by 1.
4. The last one in the calculation is the division of the total length of the slope by the value from the previous paragraph. This will be the required distance that must be observed during the installation process.

As an example, consider the construction, whose slope length is 12 m, and the approximately chosen step distance is 0.8 m:

1. 12 / 0.8 = 15. If the number in the calculation turned out to be non-integer, then it should be rounded up to the nearest integer value.
2. 15 + 1 = 16. An increase per unit for more accurate calculations of the number of legs in the structure.
3. 12/16 \u003d 0.75 m. This value will be the optimal step distance for the rafter structure.

Rafter step

Choosing the angle of the roof slope and determining the height of the ridge

As in previous calculations, the process of determining the height of the ridge depends on the selected slope angle. Despite the fact that the hip roof structure allows you to build slopes with different angles, it is best to make a structure with the same angles.

This will allow the load to be distributed evenly and the roof to have an aesthetic appearance.

ATTENTION!

The value of the angle of inclination relative to the hip version of the design varies between 20 and 45 degrees.

A more specific definition of such a parameter is influenced by:

1. The increased load factor from snow implies the construction of a structure with a steeper slope.
2. If the wind in the area where the house is located is strong and gusty, then it is recommended that the slope be no more than 30 degrees.
3. The intention is to use the attic space for living quarters. In this case, the ease of movement in the attic and the ability to provide all communication structures in such a way that they have free access if necessary are taken into account.
4. The coating chosen for the roof also plays an important role. When choosing a specific material, you need to take an interest in the minimum permitted characteristics in relation to the slope angle.

Regarding the height of the ridge, it is very simple to determine it, knowing the value of the slope angle. In the design, it is necessary to conditionally select a right-angled triangle, in which one of the sides will be the desired height.

Formula: h = b / 2 * tanA.

Roof slope

Conclusion

The stage of designing a house and all elements of its construction is quite complex and painstaking. It is very important to carefully carry out all calculations and double-check them every time. This task can be facilitated by a visual representation on a smaller scale of the entire future design.

In contact with

• During the construction of a house, questions arise, such as, for example, the calculation of the material for the roof, which are directly related to its architectural form - the number of slopes, the presence of an attic, etc. When drafting a structure, all its parameters must be carefully verified to ensure its reliability and security.

  A four-pitched roof is characterized by two triangular slopes (hips) from the end sides. It is classified mainly as a hip, or as a tent. The hip consists of two triangles and two trapezoids (the side slopes are isosceles triangles, and the front ones are regular trapezoids). If its slopes do not reach the eaves at the lowest point, then it is called half-hip. The box of the building in this case has the shape of a rectangle. If it is presented in the form of a square, a hipped roof is made, the four triangular slopes of which converge at a single vertex.

  How to calculate a hipped roof: dimensions of the base, slope

  Knowing the linear dimensions of the base and the angle of inclination of its slopes, it is possible to calculate a hipped roof. As a rule, it is carried out according to the following principle: the slopes are divided into several elements, each of which is calculated separately, after which the results are summarized. Thus, you can calculate the total area of ​​\u200b\u200ba hipped roof.
  The supporting structure of the hipped roof has a complex frame. The central rafters included in it create an extra load. In addition, the rafters must withstand the load of the roof covering, as well as snow and wind. Therefore, it is required to additionally calculate the parameters of the four-slope structure, for example, the weight of roofing and finishing materials, the climatic features of the region.

  Obviously, any inaccuracy in the calculations can have serious consequences, so they are carried out with great care and taking into account all possible options.

  In this case, the following indicators should also be taken into account:

  A competent calculation of a hipped roof requires taking into account the data of meteorological services of the area of ​​​​residence. To accurately determine the required roof height and slope angles of all four slopes, the following data are required: indicators

  • wind strength and speed in the area of ​​the house under construction;
  • rainfall intensity;
  • roofing material used.

  Design and calculations: we make a project using a drawing

  Before starting work on the arrangement of the roof, it is necessary to design, calculate and execute a drawing of the future four-pitched structure.

  The slope of the slope of the slopes, depending on the purpose of the attic, atmospheric loads and the type of material for the roof, ranges from 5º–60º.

  In regions with frequent strong winds or low rainfall, the slope of the slopes is small, and in areas with significant snow loads and frequent rains, it is much larger, 48–60º.

  In turn, based on the angle of inclination, the material for the roof is chosen:

  • 5º–18º - roll coating,
  • 14º–60º - roofing metal, asbestos-cement sheets;
  • 30º–60º - tiled.

  The height of the hipped roof ridge for a given slope of the slopes is calculated using trigonometric formulas for right triangles.

  The project of a house with a hipped roof begins with the calculation of rafters. Their cross section depends on the angle of inclination of the slopes and the total value of the expected total loads: the weight of the rafter structure, roofing cake, snow and wind loads. The minimum margin of safety for rafters should be 1.4.

  Calculations also determine:

  • rafter pitch and their bearing capacity,
  • which rafters to use - layered or hanging,
  • the need for additional elements: braces that help reduce the load on the rafters, or puffs that protect the structure from loosening,
  • the need to increase the length of the rafters or doubling the beam to strengthen them, etc.

  When designing a truss system, they calculate:

  • for strength - the rafters should not break;
  • on the degree of deformation under certain parameters, for example, the deflection of rafters for mansard roofs should not exceed 0.4% of their length.

  Features of calculating the load on the truss system

  The truss system is under the influence of permanent and temporary loads.
  The first include the mass of the roof, lathing and counter-lattices, runs and the rafters themselves, and the second - wind, snow and useful - this is the load from ceilings, hot water tanks, ventilation chambers and other things suspended from trusses.

  The parameter for calculating snow loads for the middle latitudes of the country according to the standard is 180 kg / m² per horizontal projection of the roof. Having accumulated, a snow bag can increase this value to 400-450 kg / m². For the same regions, the design parameter for wind loads is 35 kg/m².

  When the slope is more than 60°, the snow load is not taken into account, and when the slope is less than 30°, the wind load is not taken into account. The parameters of these loads can be adjusted using the available correction factors, which take into account local climatic conditions. The total mass of the roof is calculated based on the area of ​​\u200b\u200bthe structure and the materials used.

Building a house is a very responsible and expensive project, and one of the most difficult and costly stages is the construction of a roof. Correct calculation of its area can significantly reduce the cost of its construction. In this regard, it is necessary to clearly understand the procedure and methodology for calculating the area of ​​\u200b\u200bthe roof. The first step is to determine the type of roof for which the calculation will be performed. Anyone who is looking for an answer to the question of how to calculate a hipped roof will benefit from our article.

Today, the following types of roofs are distinguished, which differ in their design:

• lean-to;
• gable;
• four-slope;
• half hip;
• attic type;
• hipped roof;
• 4-pitched spire-shaped.

Regardless of the type of roof, when purchasing building materials, the correctness of the calculations made is crucial. Given the trend towards ever-increasing prices for all building materials, accurately determining the area of ​​​​the roof will be an effective way to save money. And the calculation method itself is not so complicated, it requires attentiveness, knowledge of the school geometry course, knowledge of the geometric parameters of the building and the ridge, as well as the correct names of the roof construction elements.

Hip roof area

The most popular roof option today is a four-slope, which involves the presence of 4 slopes located at an angle to the base. To calculate the area of ​​\u200b\u200ba hipped roof, we need:

• calculate this value for each slope;
• add together the resulting values.

It is very important to check the results of your calculations several times, otherwise you may end up with a surplus or shortage of building material.

In most cases, all construction and design companies have as their input the projection of the roof, that is, the area of ​​\u200b\u200bthe base under it. Before starting the calculation work, we will divide the projection zone into simple constituent figures: trapezoids, triangles, rectangles and squares. The formula for calculating the area of ​​each of these figures is well known to every student, so it will take a little time to get the result using a calculator. Taking into account that each projection element is at an angle, its area should be multiplied by the accepted cosine of the slope angle. After adding up all the results obtained, we get the area of ​​\u200b\u200ba hipped roof. As can be seen from the description, calculating this value will not cause any particular difficulties for people with an average level of knowledge of the school geometry course. For this reason, many builders assign the functions of performing such important tasks to their production workers: foremen, technical supervision workers and other engineering and technical workers.

One of the important conditions is the calculation of the cornice overhang, and not the edge of the building, otherwise the result will be incorrect.

The area of ​​\u200b\u200ba hipped roof is calculated in compliance with the following rules:

• it is necessary to take into account the area of ​​the following elements: ventilation ducts, chimneys, attic and its windows;
• the length of the slope is measured from the bottom of the ridge to the top of the eaves;
• for parapets, overhangs and firewalls, add 5% of the length;
• in order to calculate the required consumption of building material, you need to know the type of roofing, since each of them has its own consumption rates;
• when covered with shingles or rolled materials, the length of the slopes will decrease by at least seventy centimeters.

You should be aware that roll materials are the most economical option for covering a roof with a complex shape. They fit perfectly on almost any surface, their installation does not cause difficulties and takes place in the shortest possible time.

Calculation of roofing materials

The purchase of roofing materials is accompanied by significant financial expenses, the optimization of which can save huge amounts of money. For this reason, when calculating the area of ​​​​a 4-pitched roof for the purchase of roofing material, the following features must be taken into account:

Using a simple method of carrying out calculations according to the above formulas, you can get a reliable result, which, with a competent approach, is converted into money saved on the purchase of building and roofing materials.

How to calculate the area of ​​\u200b\u200ba hipped roof. Calculation of the amount of material for a hipped roof. Required formulas for calculating the area

How to calculate roof area? Calculation of the roof area of ​​a hipped roof

Before proceeding with the construction of the roof, be sure to draw up an appropriate project. This will save you money and avoid unnecessary rework. To calculate the required amount of material, the roof should be conditionally divided into simple geometric shapes. Next is the area of ​​each element. The results obtained are added up. Let's look at how to calculate the area of ​​\u200b\u200ba roof of one kind or another, in more detail.

Roof measurement rules

First of all, you need to determine the angle of inclination of the slope. It is its value, as well as the width of the pediment and the length of the slope, in most cases that are the main values ​​​​used in the formulas for calculating the required amount of roofing material and elements of the truss system. If the latter has already been erected, additional measurements should be taken. This will allow you to more accurately determine the amount of the required roofing material, vapor and waterproofing film, as well as insulation.

First, let's figure out how to take measurements of the roof. The rules for the work in this case are as follows:

• The length of the slope is measured from the highest point on the ridge to the lowest point on the overhang of the eaves.
• Horizontal measurements are taken not along the facade, but along the eaves of the roof itself.
• The correctness of the measurement of the slopes is checked by making a measurement diagonally.
• Record the results on paper with a roofing scheme drawn on it in advance.

How to find out the area of ​​\u200b\u200ba shed roof

• K \u003d √A 2 + B 2, where A is the width of the span, B is the height of the rack under the rafters. To the result K, add the length of the overhang and get the length of the rafter T.
• C \u003d T x M, where C is the roof area, M is the length of the slope eaves.

If the height of the rack is not known, the length of the rafter is often found a little differently: the width of the span is multiplied by the cosine of the angle and the length of the overhang is added.

Gable roof area

The question of how to calculate the area of ​​\u200b\u200ba gable roof is also not particularly difficult. The area of ​​\u200b\u200ba gable roof is exactly the same as that of a shed roof. The formulas used are the same. The only difference is that the area of ​​\u200b\u200bthe slope must be multiplied by 2. Sometimes the gables of such a roof are also sheathed with roofing material. In this case, the calculation is carried out according to the formula for finding the area of ​​a triangle:

• C \u003d 1/2 H x A, where H is the height of the roof, A is the width of the span.

There is another answer to the question of how to calculate the area of ​​\u200b\u200ba gable roof. If the height of the roof is not initially known, calculations can be made from the slope of the slope. In this case, the formula for the area of ​​a triangle will look like this:

• C \u003d 1/2 A x B x sine a, where A is the span width, B is the length of the rafter, and is the angle of inclination of the slope.

The area of ​​the broken gable roof

The gable broken roof consists of four planes. First you need to calculate their area. To do this, we first find the length of the layered or hanging rafters (K = √A 2 + B 2). Next, the rectangle area formula is used, that is, the result obtained is multiplied by the length of the cornice or run, respectively. At the final stage, we add up all the received numbers.

How to find the area of ​​\u200b\u200ba hipped roof

The most difficult thing is to calculate the area of ​​\u200b\u200bthe roof of a hipped roof. The calculation method primarily depends on the design features of the truss system. First, let's deal with the calculations of the hipped roof. It consists of four triangles of the same area. It is this design that is used most often. Therefore, in this case, we use the same formulas that we used to calculate the area of ​​\u200b\u200bthe pediment of a gable roof.

The calculation of the roof area of ​​a four-pitched hip roof is carried out taking into account the fact that it consists of two triangles and two trapezoids. The area of ​​triangles is found by the formula:

• C \u003d 1 / 2 H x A, where H is the height of the triangle, A is the length of the crossbar. The result is multiplied by 2.

• C \u003d (A + B) x H: 2, where A is the length of the upper run, B is the length of the lower run, H is the height of the roof.

Thus, we multiply the result by 2 and add the area of ​​\u200b\u200btwo triangles to it.

The nuances of calculating sheet roofing material

How to calculate the area of ​​\u200b\u200bthe roof, we found out. Next, we will figure out how to find out the amount of roofing material you need. Of course, in order to find out the number of sheets needed to cover the roof, you need to know their length and width. In addition, the calculation should take into account the length of the overhangs of the cornices, as well as the width of the horizontal and vertical overlaps. Usually they are 15-25 cm. The area of ​​​​the pipe and ventilation outlets in the case of using sheet materials is not deducted from the total area. In addition to the roof area, in this case it will be necessary to find out the required number of ridge elements and valleys. The calculation of rolled soft material is carried out according to the same rules. The only thing in this case is to take into account the width of the overlap on the ridge and in the valleys.

How to correctly calculate the required amount of piece roofing material

When calculating the amount of ceramic tiles required to cover the roof, its length and width should be taken into account. Useful width is specified by the manufacturer. The useful length is calculated taking into account the overlap, which can be different at different angles of the roof. First you will need to calculate how many tiles will be needed to cover 1 m 2 of the roof. The result is multiplied by the area of ​​the roof.

Sometimes roofs are covered with such interesting material as wooden tiles. The calculation in this case is carried out in the same way as for the usual one. However, the elements of this roofing material are most often stacked in three layers. Thus, the result obtained should be additionally multiplied by 3.

Calculation of waterproofing material

The waterproofing film is mounted on the roof in strips with an overlap of 10 cm. This must be taken into account when calculating. The overlaps on the eaves and gable overhangs will have to be 15 cm. It should also be borne in mind that the film is almost always laid with an indent of 30 cm from the ridge. This place is closed with a special insulating tape. Among other things, the waterproofing film must be applied in the area of ​​the valleys and pipes.

Finally, we will give a couple of useful tips on how to calculate the roof area and the amount of material. After completing all the necessary calculations, be sure to add 10% to the result. The fact is that losses during roof sheathing work are inevitable. Almost all roofing materials are sold in batches. And this means that it will be impossible to pick up additional sheets of exactly the same shade as those already used for coating. If the roof has a complex configuration, the margin should be increased to at least 13%, since the number of trimmings in this case increases. Especially a lot of waste remains when sheathing gables and triangular slopes. In the event that there are many such elements in the roof structure, more than 13% of the material should be purchased additionally.

Thus, you now know how to calculate the roof area correctly. The work is quite complex and requires precision. However, it is quite possible to do it yourself. Especially if the roof has a not too complicated design. The same applies to the calculation of roofing material.

In order to determine the amount of roofing material needed, you should know how to calculate the area of ​​\u200b\u200bthe roof. This procedure is rather complicated and requires precision. The calculations use formulas for finding the area of ​​simple geometric shapes.

How to calculate the area of ​​\u200b\u200ba hipped roof - rules and sequence

Four-pitched roof of the house

Four-pitched roofs are the most popular option in modern private construction. Often, developers have a question: how to calculate the area of ​​\u200b\u200ba hipped roof. This is necessary to determine the amount of roofing material, waterproofing and insulation.

Today, you can make a calculation using computer programs designed for any type of roof. This has its advantages: high accuracy, the possibility of choosing various design options, and convenience. However, some builders prefer to rely on their own wits rather than spending money on something they can do themselves.

Before proceeding with the calculation of the roof area, a detailed plan should be drawn up, where all dimensions will be applied. Not a single element of the roof should be overlooked. In addition, already at the stage of designing a house, one should decide on the choice of roofing material, since the slope of the roof depends on this. The sharper the angle of inclination, the longer the roof slope. And that means more material consumption. In addition, each roofing material is individual. For example, profiled metal sheets require much more overlap during installation than, say, natural shingles.

Having an accurate calculation of the roof area of ​​​​the house, you can choose the most profitable roofing material, as well as insulation, steam and waterproofing.

Four-pitched roofs may differ in shape:

• directly four-sided;
• half hip;
• hip;
• four-slope gable.

The roof areas are most simply calculated, the slopes of which are regular trapezoids and triangles and do not have any breaks on the slopes.

However, in modern construction, hip roofs are increasingly being erected, with many slopes, the surface of which can consist not only of triangles and trapezoids, but also rhombuses, rectangles and other geometric shapes.

That is why, before you start calculating a four-pitched roof, it is advisable to refresh your knowledge in the course of school geometry.

Self-calculation of the area of ​​\u200b\u200ba hipped roof

As mentioned earlier, first of all, a complete roof plan is drawn up. If there is no house project or the rafter system has already been installed, then the roof plan will have to be drawn up according to the existing frame. All you need is a tape measure and a corner. With this tool, all roof lines are measured, from the ridge to the floors. If the roof is multi-level and consists of different heights, then the drawing must reflect where what height is. It is also desirable to draw up a roof plan in projection. This will help to present the picture most clearly. However, it is only necessary to make a roof projection if you have drawing skills.

Having drawn up a detailed drawing, it will not be difficult to decompose the roof into separate geometric constituent elements. This is necessary for more accurate calculations.

Remember that the dimensions of the roof cannot be limited only to its perimeter. It is also necessary to add the length of the roof overhangs where it is supposed.

Rules to be followed when calculating a four-pitched roof:

1. It is necessary to break the drawing into separate geometric shapes. Put each of them on a separate drawing. Transfer all dimensions.

The simpler the figures are, and the more parameters you know, the easier it will be to calculate.

• The length of one slope is determined by measuring the distance from the extreme line of the eaves to the ridge.
• Each roof slope is calculated as follows: the area of ​​\u200b\u200bthe figure is multiplied by the cosine of the angle at which this roofing element is located.
• If any slope is an irregular rectangle, it must be divided into regular geometric shapes. And also to calculate each separately.
• After the calculations of each element separately, the obtained digital values ​​are summed up.

Calculation of the hip roof area

For example, let's take a calculation of the roof of a four-pitched roof.

Suppose that our four-pitched roof consists of the following elements: two regular trapezoids and two isosceles triangles. The roof slopes are at an angle of 30°. The cosine of this angle is 0.87.

Trapezoidal slopes have the following parameters: one side is 10 m, the other is 7 m, the height is 3 m.

Triangular slopes: two sides of 3.34 m, one side of 7 m. The height of the triangle is 4.8 m.

Let's start with the calculations.

The area of ​​a trapezoid is found as follows: sum the length of the horizontal sides, divide by 2, multiply by the height. That is, in our case: S \u003d (10 + 7) / 2 x 3 \u003d 25.5.

Do not forget that the resulting number must be multiplied by the cosine of the angle, in our case by 0.87. As a result, the area of ​​\u200b\u200bthe trapezoid slope is 22.185. We round up, up to 22.5 meters.

The final step is the summation of all areas: S = 22.5 × 2 + 14.7 × 2 = 74.4. Round up to 75.

Thus, the area of ​​\u200b\u200ba hipped roof, in our case, will be equal to 75 m².

During the calculation, various small elements, such as dormer windows, ventilation ducts, chimneys, parapets or skylights, are not subtracted from the total area. Since their area is small, they do not entail special financial costs. In addition, it is quite possible to make a mistake in the calculation.

Calculation of roofing and other materials

After the calculation of the four-pitched roof has been carried out, and the total area has been calculated, you can begin to calculate the required footage of roofing material. It is an erroneous opinion that the area of ​​​​the drawing of the roof and the area of ​​\u200b\u200bthe required material are the same. The bottom line is that all elements of the roofing material must be laid in an overlap. In addition, each roofing material has its own technical indicators of the amount of overlap. Accordingly, the cost of materials increases significantly.

When calculating the required amount of roofing material for a multi-level roof, it is advisable to seek help from a computer program. It will make calculations faster and more reliable.

But you can do the calculation of the required material for a simple roof yourself. This does not pose any particular difficulty.

Let's give an example of calculating the amount of slate for our hipped roof, the area of ​​which we calculated earlier.

To do this, we need to make a proportion:

X - 15%, where S - roof area, X - margin equal to 15%.

After X is calculated, the resulting number must be added to the area S. As a result, the area of ​​\u200b\u200bthe required amount of material will be obtained.

Thus, in our case, the proportion will look like this:

X = 15 x 75 / 100 = 11.25. round up to 11.5.

11.5 + 75 = 86.25 (m?) - the area of ​​\u200b\u200bthe required roofing material.

Calculation of roofing materials

In addition, when calculating the required material, it should be remembered that there will always be waste, they may need up to 20% of the material. That is, again, you should make a proportion, where X is now the expense. The result obtained is added to the area.

When erecting a complex roof, a stock of material should be taken not 15%, but not less than 20%.

The calculation of soft roofs is carried out according to the same formulas as the calculation of slate. Consumption depends on the type of roofing material and the technology of its installation. The areas of valleys and ridges are considered and ordered separately, since they are measured not in square meters, but in running meters.

The length of the roofing sheets, determined by the height of the slope, is calculated by the size of the roof of the house. As a rule, metal tiles are produced up to 8 meters long. In this case, the thickness of the sheets is from 0.2 to 0.4 cm. As a result, long metal sheets bend very strongly. This can complicate the transportation process, as the sheets may break on the way. Therefore, when ordering a metal tile, take into account the area of ​​the roof, roofing sheets, choose the most appropriate size. Also follow to take into account the qualifications of workers who will be engaged in laying the roof. Thus, with a roof area of ​​up to 150 m? it is recommended to purchase roofing sheets up to 2 m long. with a roof area of ​​up to 250 m? roofing sheets up to 4 m long are preferred, with a roof area of ​​​​more than 250 m? get sheets with a length of more than 6 m. Metal sheets with a length of more than 6 meters are difficult to lay, as they bend very strongly. For their installation, you need to hire experienced roofers.

When transporting long roofing sheets, the process of loading, transporting and storing the material should be controlled.

Since on complex roofs material consumption is high. It is preferable to purchase piece material. Piece material is soft roofing, for example, flexible bituminous tiles. Thus, waste is minimized due to the small size of the elements. But with a competent calculation and a responsible approach, the installation of the roof can be carried out in such a way that high costs can be avoided.

Please note that soft roofs require the organization of a continuous sheathing, as well as additional installation costs. At the same time, the prices for these types of coatings are much higher.

Thus, the calculation of a hipped roof allows you to timely calculate the upcoming costs for the purchase of roofing material, insulation and waterproofing.

How to calculate the area of ​​\u200b\u200ba hipped roof without the involvement of third-party specialists? What are the main parameters you need to know in order to calculate the roof of a hipped roof, gable? An example of the calculation is in our article.

Four-pitched roof structures have not only a spectacular and attractive appearance, but also have many other advantages. However, the calculation of four-pitched roofs and their elements, as well as their installation, is a technically complex matter, and cannot be carried out without a thorough acquaintance with the features of this process.

Varieties of hipped roofs

Roofs with four roof slopes have quite a few varieties, the most common of which are as follows:

• hip;
• tent;
• half hip;
• broken lines.

There are other options for four-pitched roofs, but they are much less common.

Hip roofs have two triangular end and two trapezoidal slopes. The end slopes are called hips and extend from the ridge at the top to the cornice at the bottom. This design makes such a roof the best option for the rapid convergence of precipitation from it. At the same time, due to the technological features of the structure, the calculation of a four-pitched hip roof and installation work for its installation are the most difficult to perform.

The slopes of hipped roofs are four triangles with equal sides. The bases of these triangular slopes form a square. Calculating the area of ​​a hipped roof of this type is also technically quite complicated, although somewhat simpler compared to the previous version. Such roofs are often made on gazebos. Before you make a hipped roof for a gazebo, you need to perform careful calculations.

Quite widespread is also another type of four-pitched roofs - half-hipped. They are a cross between a hip and a conventional gable roof. You need to know how to calculate the half-hip roof correctly. A feature of the design of such roofs is the absence of sharp corners, and their gable is made in the form of a trapezoid. Knowing how to calculate the gable area, you can immediately order material for gable sheathing. The functional advantage of semi-hip roofs is their high resistance to strong wind loads. Design and installation work here may have some features, and if we talk about how to correctly calculate this type of hipped roof, then the weather conditions of the area should be taken into account. Where snowfalls are frequent, steeper slopes and small canopies are built, and in less snowy regions, the opposite is true.

Broken hipped roofs are also quite common. Their peculiarity lies in the fact that geometrically their end sections are a broken line, from where such a name came from. The advantage of broken hipped roofs is that they have an attractive appearance and make it possible to use the living space as efficiently as possible. Equally important is the fact that such roofs have a relatively simple truss system. At the same time, the question of how to calculate the area of ​​a hipped roof of a broken type is quite complicated, and is usually done by professionals in the construction business.

In general, the calculation of four-pitched roofs of any kind, and, accordingly, their installation is not an easy task, requiring a certain skill and experience in the field of construction work.

Design features

Due to the inclined position of the pitched surfaces, the shape of the four-pitched roof differs significantly from the rectangular one. It is the non-standard form that primarily determines the main difficulties in the calculations and during the installation process, in particular, how to calculate the area of ​​\u200b\u200ba hipped roof of a house, calculate the required number of certain elements, how to connect the structural parts of the roof together, how to calculate the volume of a hipped roof roofs, etc.

Roofs with four slopes, depending on the variety, may have a different structure and constituent elements. However, the general principles of their device are largely identical, and they can be considered on the example of hip roofs - as the most typical version of hipped roofs.

When considering the arrangement of the central part of the hip roof, one can notice a resemblance to a conventional gable roof. The process of arranging the central part of such roofs also has much in common. Most often, rafter systems of a layered type are used here, hanging truss structures are used somewhat less frequently. When arranging a layered variety of rafters, they are supported on a ridge run located at the top of the roof, which, in turn, is installed on a running frame. The frame for installing the ridge run consists of racks and a horizontally located bed. A very important point is its support on a solid foundation, which can be a load-bearing wall in the center of the structure being built. Sometimes in the truss systems of complex hip roofs, not one central run is arranged, but two parallel beams.

If the location of the load-bearing walls does not allow them to be used as a support for the purlin frame, then for this purpose a powerful ceiling is equipped, for example, from concrete slabs. The strength of the ceiling must be sufficient to withstand the weight of the truss system, all roofing components and the resulting external loads.

Reliability of concrete slabs is usually great enough to withstand the load of any type of roofing system and weight. Therefore, the question of how to calculate a hipped roof in terms of weight indicators is not of great importance in this case. It is only important to correctly make all other measurements, and then, in accordance with them, carry out the installation process.

Sometimes, instead of concrete slabs, wooden beams are used to equip the supporting structures. Naturally, in terms of strength, this method is noticeably inferior to the previous version. At the same time, the running frame is installed on a thick beam with dimensions of 100-150 by 200 millimeters. The ridge run itself is made of a similar material, as well as the bed, if there is a need to use it. Laying of supports under the racks of the running frame is carried out crosswise with the floor beams. Stands, struts and wind ties are made from a bar measuring 100 by 150 millimeters.

The complexity of the design of a hipped roof makes it difficult to arrange supports for pitched surfaces. To this end, the corner zones are connected to the ridge run by means of diagonal rafters (sloping rafter legs). These bars are longer than usual and should have greater strength, since the shortened rafters of pitched structures rest against them.

Installation work is even more complicated if a hip roof with additional extensions is equipped. In this case, the question of how to calculate the quadrature of a hipped roof and its other parameters is a difficult task, for which the complex roof structure is conditionally divided into several simple sections, and then calculations are made for each of them separately.

The main stages of installation of the truss system of a four-pitched hip roof

The process of building a truss system of a four-pitched hip roof consists of the following successive stages:

1. Installation of the frame for the ridge run.
2. Installing first the layered, and then the central parts of the truss structure.
3. Marking by means of a cord or rope of the directions for mounting the diagonal bars.
4. Installation of diagonal rafter legs in accordance with the markings made.
5. Installation of shortened rafter legs - sprigs - resting against diagonal rafters.
6. Sheathing with a wind board around the perimeter of the roof.

Shortened rafter legs, called sprigs, form a plane for the location of the hip roof slopes. Diagonal rafters, which abut the sprigs, are most often made of double stitched boards, which helps to increase their bearing capacity. This is important, since the load on them exceeds the load on ordinary rafters by about one and a half times. If the diagonal rafters cover a large area, then to give them additional strength, additional supports are installed: struts, trusses or racks made of timber.

As you can see, the process of arranging the hip roof truss system has a large number of nuances that must be carefully taken into account when carrying out calculations and installation work.

Arrangement of the attic

A four-pitched roofing can be installed over a finished attic space or over an outbuilding, over which it makes no sense to equip a separate attic. If such a roof is installed over a residential building without an attic, then the need for arranging an attic is usually present. Attic hipped roofs are widely used in residential construction.

At the same time, it should be noted that attic spaces of hipped roofs are usually not intended for active and frequent use, since the sloping of various roof surfaces leads to significant inconvenience in this regard. In order for the attic to be suitable for use as a separate utility room, its height and dimensions will have to be significantly increased. In this case, the consumption of materials will also be significantly higher. All these nuances should be taken into account before calculating the height of the hipped roof so that the attic space meets the requirements and requests of the owners of the dwelling.

A few words should also be said about how to calculate the height of the hipped roof ridge. The ridge structure, as a rule, is the central and most elevated part of the roof structure. The question at what height to install it, in general, also depends on the intended use of the under-roof space, as well as on the personal preferences of the owners of the house. A higher roof will provide more efficient use of the attic or attic. At the same time, a low-height roof is the best option in terms of economy, minimal material consumption and labor costs.

Parameters that should be calculated when arranging a hipped roof

If we talk about the necessary calculations before carrying out installation work, first of all, we should mention how to calculate the roof area of ​​\u200b\u200ba hipped roof. The correct option here is to calculate for each of the roof slopes separately, with the subsequent addition of the results. In this case, standard mathematical formulas are used to calculate the area of ​​certain geometric shapes.

So, for example, if the slope has a triangular shape, then a perpendicular line to the base, called the height, is drawn from its top by means of a rope or cord. Further, this very height of the triangular slope is multiplied by the length of the base, and the resulting amount is divided in half. The result will be the area of ​​a triangular roof slope.

For trapezoidal slopes, the formula is somewhat different: first, the length of the upper and lower bases of the trapezoid is added, then their sum is divided in half and multiplied by the height of the slope.

Another important point in calculating a hipped roof is to determine the required distance between the rafters. The size of the gaps depends mainly on the material of the roofing. So, for example, for metal tiles and corrugated board, it is 60-90 centimeters, and for bituminous tiles - 100-120 centimeters, since in the latter case the roof is laid on a continuous crate of plywood.

Calculation - what and how to calculate

Of no small importance is the correct choice of the angle of inclination of the roof slopes, where a number of factors must be taken into account:

• The weight of the roofing - the larger it is, the steeper the roof should be equipped.
• The dimensions of the elements of the coating. If they are small and there are many butt sections between them, then the probability of water penetration between them increases, and therefore the slopes should be located at a higher angle.
• The climate of the area. In areas where frequent snowfalls occur, roof slopes should be placed more steeply, which ensures rapid convergence of precipitation.
• Fire safety rules for attic roofs. In accordance with them, with large attic sizes, there should be a through passage through it 160 centimeters high and 120 centimeters wide. If the attic is small (up to 2 meters in length), then the minimum dimensions of the passage should be 120 and 90 centimeters, respectively.
• The height of the chimney for fireplace and stove structures. The total height, together with the outer part extending beyond the roof, must be at least 5 meters. Of course, this heating option is not suitable for small buildings with sloping roofs.

The size of the section of the rafter beams can also be different, and depends on the total load falling on the truss system. The total load is determined by the weight of the roofing cake and the pressure of external factors such as wind and snow. Accordingly, the roofing material and the climate of the area also matter here. It is clear that the greater the load on the truss structure, the greater the cross section of the rafters should be.

In addition to the above nuances, there are some other features that should be considered when choosing a hipped roof for a house:

• The design of the four-pitched roof allows you to equip large overhangs on all four sides, providing protection for the facade and walls from precipitation.
• Although, in general, a four-slope roof structure is more expensive than a two-slope one, however, due to the lack of need for arranging gables, this difference is not so great.
• If a hipped roof is intended for an attic structure, then visually it will look lower, which should be taken into account when designing.
• Installation of any kind of hipped roof should begin with a ridge structure. Mauerlat must be securely fixed and connected at the corner sections, and the racks of the running frame must have a solid foundation.
• To fix various roofing elements, it is recommended to use modern metal fasteners.
• At the end of all work, before the hipped roof of the house is considered completely ready for operation, it is necessary to revise all structures, elements and butt joints again.
• Since the construction of a hipped roof is not an easy task, it is possible to take on it only if you have sufficient self-confidence. Otherwise, the most correct decision would be to entrust the installation work to specialists.