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During the construction of a house, questions arise, such as calculating the material for the roof, which are directly related to its architectural form - the number of slopes, the presence of an attic, etc. When drawing up a design for a structure, all its parameters must be carefully verified to ensure its reliability and safety.
A hipped roof is characterized by two triangular slopes (hips) on the end sides. It is classified mainly as hip or tent. The hip consists of two triangles and two trapezoids (the side slopes are isosceles triangles, and the front slopes are regular trapezoids). If its slopes do not reach the eaves at the lowest point, then it is called half-hip. The building box in this case has the shape of a rectangle. If it is presented in the form of a square, a hip roof is made, the four triangular slopes of which converge at a single peak.
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, you can perform a calculation 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 summed up. In this way, you can calculate the total area of the hipped roof.
The supporting structure of the hipped roof has a complex frame. The central rafters included in it create unnecessary load. In addition, the rafters must withstand the load of the roof covering, as well as snow and wind. Therefore, it is necessary to additionally calculate the parameters of the hipped structure, for example, the weight of roofing and finishing materials, 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.
The following indicators should also be taken into account:
Competent calculation of a hipped roof requires taking into account data from meteorological services of the area of residence. To accurately determine the required roof height and inclination angles of all four slopes, the following data is required: indicators
- wind strength and speed in the area of the house under construction;
- precipitation intensity;
- used roofing material.
Design and calculations: we make a project using a drawing
Before starting work on arranging the roof, it is necessary to design, calculate and draw a drawing of the future hipped structure.
The slope of the slopes, depending on the purpose of the attic, atmospheric loads and the type of roofing material, ranges from 5º–60º.
In regions with frequent strong winds or low precipitation, the slope of the slopes is small, and in areas with significant snow loads and frequent rains, it is significantly greater, 48–60º.
In turn, based on the angle of inclination, the roofing material is selected:
- 5º–18º – roll coating,
- 14º–60º – roofing metal, asbestos cement sheets;
- 30º–60º – tiled.
The height of the ridge of a hipped roof for a given slope of the slopes is calculated using trigonometric formulas for right triangles.
The design of a house with a hipped roof begins with the calculation of the 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 pie, snow and wind loads. The minimum safety margin of the rafters should be 1.4.Using calculations, we also determine:
- pitch of rafters and their load-bearing capacity,
- which rafters to use - layered or hanging,
- necessity additional elements: braces that help reduce the load on the rafters, or ties that protect the structure from loosening,
- the need to increase the length of the rafters or double the beams to strengthen them, etc.
When designing, the rafter system is calculated:
- for strength - the rafters should not break;
- on the degree of deformation under certain parameters, for example, the deflection of rafters for attic roofs should not exceed 0.4% of their length.
Features of calculating the load on the rafter system
The rafter system is under the influence of permanent and temporary loads.
The first includes the mass of the roof, sheathing and counter-lattice, purlins and the rafters themselves, and the second includes wind, snow and useful loads from ceilings, water-heating tanks, ventilation chambers and other things suspended from trusses.The standard parameter for calculating snow loads for the middle latitudes of the country is 180 kg/m² per horizontal projection of the roof. Having accumulated 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 slopes are inclined 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 available correction factors that take into account local climatic conditions. The total mass of the roof is calculated based on the area of the structure and the materials used.
The construction of a hip roof structure with four slopes is considered one of the most complex options construction and arrangement due to the presence in the frame of numerous rather complex interface nodes. Before the construction of the rafter system begins, it is necessary to make a general calculation with the drawing, and only after that the situation will become clear how massive and heavy the rafter structure will be.
What does the calculation of a hipped roof consist of?
In any hip roof design, from the simplest hip roof to a complex hip roof broken type, the calculation is performed according to the same scheme:
- A preliminary design of a hip roof is carried out with your own hands in accordance with the construction plan and design specifications;
- The basic drawing of the hip roof is being developed;
- The calculation of the hip roof, the most loaded parts of the frame of the hipped hip roof, is carried out;
- The dimensions of the main parts of the rafter system are specified, and detailed drawings of individual components are made.
For your information! Only after completing the calculations and details can you draw up an estimate and calculate the cost of building a beautiful hipped hip roof.
In this case, the manual calculation method is given wooden frame and roof truss system. The method and main stages of calculation are not particularly difficult; even schoolchildren can carry out the design and understand the calculations. If a person knows the calculation method, then he has a clear understanding of how the rafter, ridge and support beams work, where the most weak links hipped roof.
To determine dimensions, you can use any online program or computer-aided design system, but sometimes you have to do what is called “on the fly” to assess strength and stability.
Hip roof device
Structurally, the classic hip roof consists of two main slopes and two side hips. To calculate the lengths and sections of the beam, it is necessary to draw up the most accurate sketch, or better yet -. Using diagrams with different roof inclination angles and heights, you can draw and calculate various options roof layout, and most importantly - to determine the geometric dimensions of the most loaded frame parts.
The main structural elements of a hipped roof are:
- Ordinary rafter beams forming two main slopes. The rafters are exactly the same in shape and design as in a regular gable roof. The slopes have the shape of an isosceles trapezoid;
- Hip corner rafters, also called slanted or diagonal rafters, are located in the corners of the roof frame and form the so-called hip slopes in the form of symmetrical isosceles triangles;
- External rafters, from which the plane of the hip slopes is formed;
- Vertical posts on which the ridge beam and all four slopes rest.
In addition, the design uses a large number of auxiliary elements, designed to increase the rigidity of the entire hip frame. These are all kinds of struts, spacers, trusses installed as supporting elements of the rafters, photo.
The longest rafters are called corner rafters, the shortest are called external rafters.
Calculation of roof frame parameters
According to the conditions of the task, it will be necessary, using the drawings, to perform an assessment calculation of the most loaded elements of the rafter system - the vertical support post and the rafter beam of the hip roof. In addition, it is necessary to calculate their sizes and the position of the cutting lines under the supporting surfaces on the mauerlat and ridge girder.
Typically, schemes with a single ridge girder are used, as in the drawing, but if the under-roof space is planned to be used as an attic or attic room, in this case, the hipped roof is built according to a two-girder scheme. This option is much more expensive, but allows you to get a more stable and rigid hip structure in the case of building a roof with a large slope surface.
Both versions of the hipped roof use layered rafters with fixation of the rafter beams on the mauerlat and support on the ridge girder. The calculation of both hip roofs is performed using the same method.
To perform the calculation we need:
- Determine the loads acting on the hip roof frame;
- Check the strength and stability of the vertical support post;
- Calculate the deflection and strength of a row and diagonal rafter beam.
To perform the calculation, use the simplified diagram of a hipped hip roof shown below.
All elements of the frame of a hipped hip roof can be conditionally divided into two groups - beams, including racks. The former operate under deflection conditions or under the influence of a bending moment. The second group of power elements refers to simpler cases; they operate under conditions of linear compression or tension. In this case, the calculation of the load-bearing capacity of a compressed rack is determined from the conditions of static stability under a compressive load.
Methodology for calculating the stability and strength of vertical supports and struts
At the first stage, you need to determine the strength of the vertical post based on the known value of the vertical load. The force of pressure on the vertical posts is calculated as the sum of three components - the mass of the roof with roofing and the weight of the maximum snow cover. Since the slopes are located at an angle, the final vertical pressure perceived by the roof can be roughly taken as half the weight of the wooden structures of the hipped structure and the mass of snow, calculated based on the area roofing, multiplied by Weight Limit 1 m 2 of roof snow cover for a given region. 
The strength of the vertical support is determined from the following ratio:
σ = P/S ≤ M s, where M s is the specific compressive strength of a particular type of wood, P is the vertical load under the influence of the weight of the hipped frame and the mass of snow, in kilograms, S is the total cross-sectional area of all vertical supports in this structure. The value obtained from division should not be greater than M s, a reference value that can be taken from a reference book or SNiP No. II-25-80. For example, a stand made of dry pine, with a cross-section of 120 cm2, can withstand a huge vertical load of almost 16 tons, so strength calculations are not of decisive importance.
Almost always calculations vertical racks performed according to the stability margin or the ability of the support to absorb force without deformation or bending.
To classify the flexibility of a support, the concept of flexibility coefficient λ is introduced; for a cube it is equal to 0, for most real wooden supports its value can be from 40 to 100 units.
The formula for calculating the stability of a long wooden rod, which is the support of a hipped roof, looks like this: σ = P/ φS ≤ M s, where φ is the longitudinal bending coefficient, determined in accordance with the provisions of SNiP No. II-25-80 according to the formula:
- For values of λ less than 70 units, φ is calculated using the formula: φ = 1 - 0.8(λ/100) 2 ;
- For values of λ greater than 70 units, φ is obtained: φ=3000/ λ 2 .
The practical value of φ ranges from 0.3 to 0.7.
The easiest way is to use a graph that allows you to obtain the exact value of φ from the dependence λ - φ and the ratio of length to diameter of the support and perform a stability check calculation.
Strength of the rafter beam
The calculation of load-bearing vertical supports, as a rule, is a test, since in reality the margin of strength and stability of racks made from standard 100x150 mm timber for most hip roofs is always greater than what is required in reality. It is much more important to check the strength of the diagonal rafter beams, which often break under the weight of snow due to an insufficient reserve of rigidity.
To check the strength of a rafter beam under load, the standard formula is used - (Р/φS) + (M z /W z) ≤ M y , Where :
- P is the total load from the weight of the hip roof structure, snow cover and the vertical component of pressure from the wind flow in kg;
- S - cross-sectional size in cm 2;
- W z and M z are the moment of resistance and the value of the bending moment of the rafter beam, respectively;
- M y is a reference value for the resistance of a specific wood species of a beam to bending force.
For your information! When the angle of inclination is less than 27 o, the magnitude of the wind load on the frame of a hip hip roof can be neglected, but at the same time the component from snow and the additional weight of the sheathing increases.
All strength calculations are performed on the assumption that the wood of the beam used for the hip roof rafters has no defects or damage, which in practice is not always true. In addition, boards from different parts tree trunks have different strengths, so the rafters for a hipped hip roof are made as composites, in the form of a package of two or three 50x150 mm boards knocked together. Calculations of such a rafter according to the standard scheme.
Calculation of the geometry of the elements of a hip hip roof
The design of a hip hip roof can be represented as a spatial set of rectangles and trapezoids.
The initial values are the dimensions of the Mauerlat rectangle, which will be used to calculate all elements of the hipped roof frame.
First you need to calculate the height of the vertical support posts. For this, a value equal to half the length of the side wall is used, minus ½ the thickness of the house wall S. Knowing the angle of inclination of the overhang A, we can easily determine the height of the vertical support of the ridge beam using the formula: H k = 0.5(L bc - 0.5S)*tgA.
Having accepted the fact that L oq =L do, we can determine:
- The length of the horizontal projection of the corner rafter beam according to the planimetry formula L oc = 1.22*L do and, accordingly, the size of the diagonal rafter itself L ac, using the Pythagorean theorem and legs L oc and H k;
- The length of the ridge girder, as the longitudinal dimension of the building box, minus the doubled length L do, L ak = L cm -2L do.
In addition to the actual dimensions of the frame, it is necessary to calculate the places where the row and diagonal rafter beams are cut.
To do this, along the lower edge of the board of an ordinary rafter, the calculated dimension H ad is laid off, after which the width of the Mauerlat is laid off at the angle of inclination of the slope and a wedge-shaped cut is made, as in the figure.
Conclusion
Competent operation requires certain knowledge in structural mechanics and strength materials, especially in matters of strength and stability of structures. However, for simple circuits, for example, for a gazebo or shed, strength problems are not so critical. It is enough to know the rules of geometric calculation of a hip-type hip roof, and for the most important supporting and rafter elements use timber with an increased safety margin.
Hip roof - This is a type of attic roof. It is often installed in houses where it is planned to arrange additional residential or non-residential space. Hip roof design hipped. The two side parts – the slopes – have a trapezoidal shape, the two end parts – the hips – are triangular.
Advantages of a hip roof:
- Ability to withstand even strong gusts of wind;
- Rigid construction minimizes roof deformation;
- Aesthetic appearance, the ability to visually make the building more compact;
- The ability to equip large side eaves overhangs, providing this additional protection walls of the building from the effects of precipitation.
The disadvantages of hip roofs include the complexity of design and installation, and high cost.
- This is the basis of the roof. Rafters are most often made from coniferous tree, treated with a special compound to prevent rotting and insects from settling in it.
To support the rafters on the hip roof, a mauerlat is installed - a beam, which is also intended to distribute the load on the walls of the building. The central element is the ridge of the hip roof, to which it is attached most of rafters
There are three types:
- Central (ordinary) - attached to the ridge beam at the same distance from each other;
- Diagonal - join with corner rafters;
- Corner - attached to the ridge beam and connected to diagonal rafters at different heights so that the structure gains additional strength.
After installing the rafter system, the sheathing is installed and the insulating materials and coating. At the same time, chimneys, drainage and ventilation systems are being installed.
Rafter hip roof– the design is complex, requiring careful calculations before the installation process. One of the important parameters is hip roof angle. It depends on the expected load on the roof, the strength of the influence of external factors, for example, wind, snow. Roofing materials also affect the angle of the roof. The maximum recommended for slate is 22°, the minimum is for multi-layer roll material— 5°. The material that can be used to cover a hip roof at any angle of inclination is membrane roofing.
Accurate preliminary hip roof calculation will avoid extra costs and unpleasant moments during installation. There are several calculation methods, as well as many online calculators for determining hip roof area, hip roof height and other design parameters. But top scores demonstrates the use of special software. In just a few minutes, after entering basic data, the user will receive accurate, reliable calculations, based on which you can safely begin construction. The programs are good because they provide all the parameters for the most objective calculation.
Fill in the dimensions in millimeters:
Y– roof height, this is the distance from the attic floor to the ridge unit (top of the “tent”). Meaning Y affects the angle of inclination of the roof (for a hipped roof from 5 to 60 degrees). The angle of inclination of the roof slope is determined taking into account the type of building, the purpose of the attic space, snow load and type of roofing material (for example, for roofing felt - 8-18°, slate or metal sheets–14-60°, tiles – 30-60°). If the attic is non-residential, you should choose a small height (saving material for rafters, waterproofing and roofing), but sufficient for inspection, maintenance and repair (approximately 1500 mm). It is imperative to take into account the requirements of SP 20.13330.2011 “Loads and impacts” (updated edition of SNiP 2.01.07-85*). It should be remembered that on a roof of low height (tilt angle up to 30 degrees) snow can accumulate, which increases the load on the roof truss system and negatively affects its tightness and durability. The high roof (tilt angle 45-60°) makes it possible to equip a living space under its arch and does not allow precipitation to linger, but is vulnerable to strong gusts of wind. The optimal angle of inclination of a hipped roof is often in the range of 30-45 degrees.
X– Roof length (excluding overhangs), in fact this is the length value façade wall Your house.
Z– The width of the roof is determined by the width of the building.
C– the size of the eaves overhang (necessary to protect the walls and foundation from precipitation) is determined taking into account the climatic characteristics of your region (SP 20.13330.2011) and the general architectural design.
For one and two-story houses with drainage system minimum size C– 400 mm (according to SNiP II-26-76*), without organizing external water drainage, not less than 600 mm. The optimal overhang is approximately 500 mm.
U– Width of the rafters.
W– Thickness of the rafters.
S– The pitch of the rafters, i.e. distance between adjacent rafters.
U And W– important parameters that determine the reliability of the entire rafter system. The required rafter section ( U X W) depends on: loads (constant - the weight of the rafter system, sheathing, roofing pie; temporary - snow, wind; special - seismic impacts, dynamic loads from industrial explosions), the quality and type of material used (boards, timber, laminated veneer lumber), length rafter leg, distances between rafters. Approximate section of timber and step ( S) for rafters of different lengths is given in the table.
| Rafter length, mm | Rafter pitch, mm | Rafter section, mm |
| Up to 3000 | 1200 | 80x100 |
| Up to 3000 | 1800 | 90x100 |
| Up to 4000 | 1000 | 80x160 |
| Up to 4000 | 1400 | 80x180 |
| Up to 4000 | 1800 | 90x180 |
| Up to 6000 | 1000 | 80x200 |
| Up to 6000 | 1400 | 100x200 |
When choosing a rafter section, be sure to follow the recommendations given in SP 64.13330.2011 “ Wooden structures"", SNiP II-26-76* "Roofs" taking into account SP 20.13330.2011 "Loads and impacts".
O1– Width of sheathing boards.
O2– Thickness of sheathing boards.
R– Sheathing pitch (i.e. the distance between adjacent boards).
Lathing rafter frame roof performs supporting functions, its cross-section (width O1 and thickness O2) is determined by the weight, rigidity of the roofing material and the angle of the roof. The lathing should provide sufficient support, but at the same time not weigh down the structure. Determine approximate width values ( O1), thickness ( O2) boards for sheathing and step ( R) is possible using table data.
Filling out the fields online calculator and a palm roof, you need to choose the optimal cross-section of the sheathing and its pitch in a particular case, the recommendations given in SP 64.13330.2011 “Wooden Structures”, SNiP II-26-76* “Roofs” and SP 20.13330.2011 “Loads and Impacts” will help.
If you need a drawing close to GOST requirements, check the “Black and white drawing” box; this will save color ink or toner when printing.
Hip roof calculation results:
Our online calculator with drawings will help you calculate the materials for arranging a hip or hip roof and create detailed drawings (with exact dimensions of all parts of the rafter system). You can find out for free the area, width, height of the roof, the length of lumber for eaves, ridges, rafters, sheathing for each side of the roof and the required volume of wood for each item. Such data will allow you to form an idea of the cost of a hipped roof (make an estimate) and purchase the required amount of lumber for the rafter system. It is also recommended to obtain advice from a qualified specialist (roofer builder with experience in implementing successful projects) on roof installation, since the comfort and coziness of your home largely depends on its quality and reliability.
For small outbuildings, simple pitched roof. For a private house, it is worth choosing something more efficient and beautiful, for example, a roof with four slopes. This option is used quite often, especially if the “box” of the house is square in shape. But such a design can be quite complex. How to correctly calculate a hipped roof? Let's figure it out.
Calculation of a hipped roof - general concepts
First of all, it is worth understanding the design of the hipped roof itself and its varieties. General ideas can be obtained from the name. In such a roof, four slopes are used at once. The following types are distinguished:
- Tent. This option can be called a classic hipped roof. This design has triangular slopes converging at one point at the top of the roof. Hip roofing is used mainly in the construction of square buildings.
- Hip. In this case, two sides are triangular in shape, and the other two are made in the form of a trapezoid. This roof structure is more common than a hip roof. This option is most often used if they want to make an attic.
Each type of hipped roof has its own subtypes. There are complex and more simple designs. But in any case, it is very important to make the correct calculation of the hipped roof; its durability and reliability will depend on this.
A roof with four slopes has its advantages. For example, under such a roof there is a lot of space left, which will be reliably protected from weather conditions and cold. As a result, you will have a free space that can be used for storing things or for living. Moreover, she herself rafter system Quite durable, such a roof can withstand heavy loads.
If we talk about the disadvantages, then first of all it is worth mentioning the complexity of the design. If you compare it with a pitched or gable roof, then when constructing it you need to have certain skills and abilities. Therefore, most often, when constructing a hipped roof, they resort to the help of professionals.
When building a house, the “box” of which is made in the form of a square, very often they choose a roof consisting of four slopes. But even with a different form of structure, this roof option is quite acceptable. Hip roof durable and reliable, in addition, it can decorate your home. But, as with any construction, it is very important to make the correct calculation, this is what will be discussed in the next part.
We carry out calculations
Before starting any construction, it is necessary to make a design for the future structure, calculate all the parameters and the amount of materials used. When it comes to a roof, the following characteristics are important:
- roofing materials used;
- slope slope;
- parameters and design of the rafter system.
The maximum and minimum slope stingray This is where the calculation of a hipped roof begins. For example, for slate this value ranges from 15 to 60 degrees. If you use the metal tiles that are popular today, the slope angle can be from 30 to 60 degrees. For soft roof this parameter should not exceed 15-20 degrees.
In addition, when choosing the slope of the slope, it may depend on the amount of winter precipitation and architectural features. If there is a lot of snow, the slope becomes larger. In this case, you will not have to remove snow from the roof.
But it is worth remembering that the greater the slope, the higher the roof will be. Therefore it is necessary to do correct calculations so that snow does not accumulate and spoil appearance the house itself.
