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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, you can calculate 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 a four-pitched 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.
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;
- used roofing material.
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,
- necessity 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, battens and counter battens, 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 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 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.
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 turn out to be.
What is the calculation of a hipped roof
In any design of a hipped roof, from the simplest hip roof to a complex hip roof broken type, the calculation is performed according to the same scheme:
- Do-it-yourself sketch design of a hip roof is carried out according to the design plan and design assignment;
- The main drawing of the hip roof is being developed;
- The calculation of the hip roof, the most loaded parts of the frame of the four-slope hip roof is carried out;
- Clarify the dimensions of the main parts of the truss system, perform detailed drawings of individual nodes.
For your information! Only after performing the calculations and detailing, it is possible to draw up an estimate and calculate the cost of building a beautiful four-pitched hip roof.
In this case, the method of manual calculation is given. wooden frame and roof truss system. The method and main stages of the calculation are not particularly difficult; even schoolchildren are quite capable of designing and understanding the calculations. If a person owns the calculation method, then he has a clear understanding of how the rafter, ridge and support beam work, where the most weak links hipped roof.
You can use any online program or computer-aided design system to determine the dimensions, but sometimes you have to do the assessment of strength and stability, as they say, “on the go”.
Hip roof device
Structurally, the classic four-pitched hip roof consists of two main slopes and two side hips. To calculate the lengths and sections of the timber, it is necessary to draw up the most accurate sketch, or better -. Using diagrams with different versions of the angles of inclination and height of the roof, you can draw and calculate various options roof layout, and most importantly - to determine the geometric dimensions of the most loaded parts of the frame.
The main structural elements of a hipped roof are:
- Ordinary truss beams that form two main slopes. The rafters are exactly the same in form and execution as in the usual gable roof. The slopes have the shape of an isosceles trapezoid;
- Hip corner, also called oblique 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;
- Outdoor rafters, from which the plane of the hip slopes is formed;
- Vertical racks 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 four-pitched frame. These are all kinds of struts, struts, trusses installed as supporting elements of rafters, photo.
The longest rafters are called corner, the shortest - outdoor.
Calculation of roof frame parameters
According to the terms of the task, it will be necessary, using the drawings, to perform an estimated calculation of the most loaded elements of the truss system - a vertical support post and a truss beam of a four-pitched hip roof. In addition, it is necessary to calculate their dimensions and the position of the lines washed down under the supporting surfaces on the Mauerlat and the ridge run.
Typically, schemes with a single ridge run are used, as in the drawing, but if they plan to use the under-roof space as an attic or attic room, in this case, a hipped roof is built according to a two-run scheme. This option is much more expensive, but allows you to get a more stable and rigid hip design in the case of building a roof with a large slope surface.
Both versions of the hipped roof use layered rafters with the rafter beams fixed on the Mauerlat and supported on the ridge run. The calculation of both hip roofs is performed using the same method.
To perform the calculation, we need:
- Determine the loads acting on the frame of the hip roof;
- Check the strength and stability of the vertical support post;
- Calculate the deflection and strength of an ordinary and diagonal rafter.
To perform the calculation, a simplified diagram of a four-pitched hip roof is used, shown below.
All elements of the frame of a four-pitched hip roof can be conditionally divided into two groups - beams, including racks. The former work under deflection or under the action 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 bearing capacity of the compressed rack is determined from the conditions of static stability under compressive load.
Method for calculating the stability and strength of vertical supports and struts
At the first stage, it is necessary to determine the strength of the vertical rack, based on the known value of the vertical load. The pressure force on the vertical racks is calculated as the sum of three components - the mass of the roof with roofing and the weight from the maximum snow cover. Since the slopes are at an angle, the resulting vertical pressure perceived by the roof can be roughly taken as half the weight of the wooden structures of the four-slope 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 \u003d 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 weight of the four-slope frame and the mass of snow, in kilograms, S is the total cross-sectional area of \u200b\u200ball vertical supports in this structure. The value obtained from division should not be more than M s, a reference value that can be taken from the reference book or SNiP No. II-25-80. For example, a rack made of dry pine, with a cross section of 120 cm 2, can withstand a huge vertical load of almost 16 tons, so the strength calculation is not of decisive importance.
Almost always calculations uprights perform according to the margin of stability or the ability of the support to perceive force without deformation and bending.
To classify the flexibility of the supports, the concept of the flexibility coefficient λ is introduced, for a cube it is 0, for most real wooden poles its value can be from 40 to 100 units.
The formula for calculating the stability of a long wooden rod, which is a hipped roof support, looks like this:
- For values of λ less than 70 units, φ is calculated by the formula: φ = 1 - 0.8(λ/100) 2 ;
- For values of λ greater than 70 units φ get: 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 the length to the diameter of the support and perform a verification calculation for stability.
Rafter beam strength
The calculation of load-bearing vertical supports, as a rule, is a test, since in reality the margin of safety and stability of racks made from a standard beam of 100x150 mm for most hip roofs is always greater than required in reality. It is much more important to check the strength of the diagonal truss beam, which often break under the weight of snow due to insufficient rigidity.
To check the strength of the rafter beam to the 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 pressure component from the wind flow in kg;
- S is the size of the cross section in cm 2;
- W z and M z - 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 particular type of wood beam to a bending force.
For your information! At an angle of inclination of less than 27 °, the magnitude of the wind load on the frame of a hip hipped roof can be neglected, but the component from snow and the additional weight of the crate increases.
All strength calculations are based on the assumption that the wood of the beam used for hip roof rafters is free of defects and damage, which in practice is not always true. In addition, boards different parts tree trunks have different strengths, so the rafters for a four-pitched hip roof are made composite, in the form of a package of two or three 50x150 mm boards knocked down. Calculations of such a rafter according to the standard scheme.
Calculation of the geometry of the hip hip roof elements
The design of a hip hipped 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 the elements of the four-pitched roof frame.
Initially, 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 of the wall thickness of the house S. Knowing the angle of inclination of the overhang A, we easily determine the height of the vertical support of the ridge beam according to the formula: H k \u003d 0.5 (L bc - 0.5S) * tgA.
Accepting the fact that L oq =L do , we can determine:
- The length of the horizontal projection of the corner rafter 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 the legs L oc and H k ;
- The length of the ridge run, as the longitudinal size 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 for washing down ordinary and diagonal rafters.
To do this, along the lower edge of the board of an ordinary rafter, the size obtained by calculation is set aside Had, after which the width of the Mauerlat is laid off at the slope of the slope and a wedge-shaped gash is made, as in the figure.
Conclusion
Competent operation requires certain knowledge in structural mechanics and strength of materials, especially in matters of strength and stability of structures. However, for simple circuits, for example, for a gazebo or a barn, strength problems are not so critical. It is enough to know the rules for the geometric calculation of a four-pitched hip roof, and for the most important supporting and rafter elements, use a beam with an increased margin of safety.
hip roof - This is a type of attic roof. It is often installed in houses where it is planned to equip additional residential or non-residential space. hip roof construction four-slope. Two side parts - slopes, have a trapezoidal shape, two end - hips - triangular.
Benefits of a hip roof:
- The 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 atmospheric precipitation.
The disadvantages of hip roofs include the complexity of design and installation, high cost.
- this is the basis of the roof. Rafters are most often made of coniferous tree, treated with a special compound to prevent decay and insect settlement in it.
To support the rafters on the hip roof, a Mauerlat is installed - a bar designed also 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 of them:
- Central (ordinary) - attached to the ridge beam at the same distance from each other;
- Diagonal - are joined with corner rafters;
- Corner - attached to the ridge beam and connected to diagonal rafters at different heights in order for the structure to acquire additional strength.
After installing the truss system, the crate is mounted, insulating materials and coverage. At the same time, chimneys, drainage systems, and ventilation systems are being equipped.
Rafter hip roof- the design is complex, requiring careful calculations before the installation process. One of the important parameters is hip roof pitch. It depends on the expected load on the roof, the force of external factors, such as wind, snow. Roofing materials also affect the angle of the roof. The maximum recommended for slate is 22°, the minimum is for multilayer roll material— 5°. The material that can be used to cover a hip roof at any angle of inclination is a membrane roof.
Precise Preliminary hip roof calculation avoid extra costs and unpleasant moments during installation. There are several calculation methods, as well as many online calculators to determine hip roof area, hip roof height and other design parameters. But top scores demonstrates the use of a special software. In a few minutes, by entering the basic data, the user will receive accurate, reliable calculations, based on which you can safely start construction. Programs are good because they provide all the parameters for the most objective calculation.
Fill in the dimensions in millimeters:
Y- the height of the roof, this is the distance from the attic floor to the ridge knot (the 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, snow load and type of roofing material (for example, for roofing material - 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 revision, maintenance and repair (approximately 1500 mm). Be sure to take into account the requirements of SP 20.13330.2011 "Loads and Impacts" (updated version of SNiP 2.01.07-85*). It should be remembered that snow can accumulate on a roof of low height (angle of inclination up to 30 degrees), which increases the load on the roof truss system and negatively affects its tightness and durability. A high roof (angle of inclination 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- The length of the roof (excluding overhangs), in fact, this is the value of the length facade wall Your house.
Z- The width of the roof is determined by the width of the building.
C- the size of the cornice overhang (necessary to protect the walls and foundation from precipitation) is determined taking into account the climatic features of your region (SP 20.13330.2011) and the general architectural idea.
For one and two-storey houses with drainage system minimum size C- 400 mm (according to SNiP II-26-76 *), without the organization of external water flow, not less than 600 mm. The optimal overhang is approximately 500 mm.
U- Rafter width.
W- Rafter thickness.
S- Rafter pitch, i.e. distance between adjacent rafters.
U And W- important parameters that determine the reliability of the entire truss system. The desired section of the rafter ( U X W) depends on: loads (permanent - the weight of the rafter system, lathing, roofing cake; temporary - snow, wind; special - seismic effects, dynamic loads from industrial explosions), the quality and type of material used (board, timber, glued laminated timber), length rafter leg, the distance between the rafters. Approximate section of the beam 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 section of rafters, be sure to follow the recommendations induced in SP 64.13330.2011 " wooden structures» », SNiP II-26-76* «Roofs» taking into account SP 20.13330.2011 «Loads and impacts».
O1- The width of the boards of the crate.
O2- The thickness of the boards of the crate.
R- Lathing pitch (i.e. the distance between adjacent boards).
crate roof frame roof performs supporting functions, its cross section (width O1 and thickness O2) is determined by the weight, stiffness of the roofing material and the angle of the roof. The crate should provide sufficient support, but at the same time not weigh down the structure. Determine approximate width values ( O1), thickness ( O2) boards for battens and step ( R) can be done using the table data.
Filling in the fields online calculator and palm roof, you need to choose the optimal section of the crate and its step 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 that is close to the requirements of GOST, check the box "Black and white drawing", 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 the exact dimensions of all parts of the truss system). You can find out for free the area, width, height of the roof, the length of lumber for cornices, ridges, rafters, battens for each side of the roof and the required amount of wood for each item. Such data will allow you to form an idea of \u200b\u200bthe cost of a hipped roof (make an estimate) and purchase the right amount of lumber for the truss system. It is also recommended to get advice from a qualified specialist (roof builder with experience in implementing successful projects) on the arrangement of the roof, since the comfort and coziness of your home largely depends on its quality and reliability.
For small outbuildings often use a simple pitched roof. For a private house, you should choose 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 has a square shape. But such a design can be quite complex. And 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 dealing with the very design of the hipped roof and its varieties. General ideas can be obtained already based on the name. In such a roof, four slopes are used at once. In this case, the following varieties are distinguished:
- Shatrovaya. It is this option that can be called a classic hipped roof. This design has triangular slopes converging at one point at the top of the roof. Hipped roofing is mainly used in the construction of square buildings.
- Hip. In this case, two sides have a triangular shape, and the other two are made in the form of a trapezoid. This roof design is more common than hipped roof. It is this option that is most often used if they want to make an attic.
Each type of hipped roof has its own subspecies. 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.
Roofing with four slopes has its advantages. For example, under such a roof there is a lot of space that will be reliably protected from atmospheric phenomena and cold. As a result, you will have a free space that can be used for storage or for living. In addition, herself rafter system quite strong, such a roof is able to withstand heavy loads.
If we talk about the shortcomings, then first of all it is worth mentioning the complexity of the design. If you compare it with a shed or gable roof, then during the construction you need to have certain skills and abilities. Therefore, most often, when erecting 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 version of the roof is quite acceptable. Four-pitched roof durable and reliable, besides this, it can decorate your home. But, as with any construction, it is very important to make the right calculation, which is what will be discussed in the next part.
We carry out calculations
Before starting any construction, it is necessary to make a project of the future structure, calculate all the parameters and the amount of materials used. When it comes to the roof, then the following characteristics are important:
- used roofing materials;
- slope slope;
- parameters and design of the truss system.
The maximum and minimum slope stingray. This is where the calculation of the hipped roof begins. For example, for slate, this value ranges from 15 to 60 degrees. If you use metal tiles that are popular today, then the slope angle of the slope 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, then the slope is greater. In this case, you do not have to carry out snow removal from the roof.
But it is worth remembering that the greater the angle of inclination, the higher the roof will be. Therefore, it is necessary to do correct calculations so that the snow does not accumulate, and do not spoil appearance the house itself.
