How to calculate the area of a gable roof calculator. Calculation of a gable roof: area, rafters, height
The roof is very important functional element Houses. To ensure the required strength of its structure, special calculations are made, including determining the amount of lumber required. This is very important for determining the scope of upcoming work due to the significant cost of building materials.
Where to start calculating?
The amount of lumber needed directly depends on several factors. When making calculations, you must take into account:
- area of the structure covered by the roof;
- roof type;
- coating material;
- climatic conditions;
- size and cross-section of wooden beams;
- approximate weight of the entire structure.
The easiest way is to perform the calculation yourself for relatively simple roofs, single and double slope.
Tent, hip or broken structures roofs are more complex and require certain knowledge for high-quality calculations necessary materials. The number of slopes in each specific case will depend on the shape of the house and the personal preferences of the owners. Determining the amount of lumber largely depends on this indicator. The frame for the roof is the rafter system.
It should easily withstand strong gusts of wind, significant thickness of snow cover and other impacts, while maintaining the roof itself in working condition. The rafter system is a structure constructed from timber with different sections, boards, logs, other materials and fasteners. The main elements that will be calculated are the mauerlats, rafters, sheathing and counter-lattice. Calculation of the maximum load per 1 m of rafters is carried out using special tables.
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Calculation of the rafter system
Determining the amount of lumber required to construct a roof is carried out in the following order:
- Mauerlats are laid around the perimeter brick house, therefore in in this case comes down to calculating the perimeter of the building. For mauerlats, high-quality logs or timber with a minimum thickness of 100 mm are used.
- To calculate lumber for rafters, you need to determine their length. For example, let's take a gable roof 4 meters high for a house measuring 8 by 10 meters. The rafters are installed across the 10-meter side. Using the Pythagorean theorem, the calculation is made:
- a = √(b2 + (c/2)2), where;
- a – rafter length;
- c – roof height;
- с – building width + 0.5 m eaves outlets;
- a = √(42 + (9/2)2) = 6.02 m.
- The cross-section of the rafter beam is calculated based on many factors. For simple designs use recommendation tables. For example, with a rafter length of 6 m and a pitch of 0.6 m, their cross-section should be at least 50 by 200 mm, with a pitch of 1.1 m - 100 by 200 mm, and with a pitch of 1.75 m - 100 by 250 mm.
- Next, determine total quantity timber for rafters. For example, if a beam with a section of 50 by 200 mm is used, then with a roof length of 10 m, 17 pairs of rafters are needed (10 / 0.6 = 16.66), which, with a length of one rafter leg of 6.02, will be:
17 x 2 x 6.02 = 205 m
With a step of 1.1 m, 9 pairs of beams are needed, or:
9 x 2 x 6.02 = 109 m
The rafters are the main load-bearing elements structures that experience significant loads, so for them you should purchase high-quality lumber from coniferous species with a minimum number of knots, without cracks.
- In addition to the rafters, calculations are made of lumber for the counter-lattice (in the case of waterproofing). It is fixed to the rafters to create a gap between the sheathing and the waterproofing membrane. To install the counter-lattice, use bars 2-5 cm thick, the total footage of which corresponds to total length the required rafter beams.
- The amount of lumber for sheathing depends on the choice roofing material. For example, for bitumen shingles or galvanized steel sheets, a continuous sheathing is arranged, for polymer and ceramic tiles - frequent, and for metal tiles and ondulin - sparse. For continuous sheathing, boards are used, and for sheathing with a certain step, bars with a thickness of at least 5 cm are used. The determination of the step size should be approached with special attention. Too much long distance can lead to deformation of the roof covering, and too small - to an unreasonable increase in the total weight of the structure.
- In addition to the indicated elements, the roof structure uses racks made of timber with a thickness of 100-150 mm to strengthen the structure, tightening, fillets, hemming and front boards.
No house can be built without a roof, and no roof can be built without a supporting structure. Any construction begins with design and calculations. Let's look at how rafters are calculated.
Carrying out such calculations is extremely important. It is unacceptable to build rafter systems “by eye” or “approximately”. It is necessary to take into account all the loads that will affect the roof. They are divided into:
- Permanent. This is the own weight of the coating, waterproofing, sheathing and other components"pirogue". If you plan to install any equipment on the roof, then it is necessary to take into account its weight.
- Variables. This type of load includes the mass of precipitation falling on the roof and other impacts that do not constantly act on the roof.
- Special. In seismically hazardous areas or in areas where hurricane winds regularly occur, it is necessary to provide an additional safety margin.
This is a necessary calculation - the rafters must withstand this constant load for a long time.
Calculation example. Let's take as an example a roof covered with ondulin. The roof consists of the following layers:
- , assembled from planks 2.5 cm thick. The weight of a square meter of this layer is 15 kg.
- Insulation (mineral wool) thickness 10 cm, weight per square meter of insulation 10 kg.
- Waterproofing – polymer-bitumen material. The weight of the waterproofing layer is 5 kg.
- Ondulin. The weight per square meter of this roofing material is 3 kg.
We add up the resulting values – 15+10+5+3 =33 kg.
Multiply by the correction factor 33×1.1=34.1 kg. This value is the weight of the roof pie.
In most cases, during the construction of residential buildings, the load does not reach 50 kg per square meter.
Advice! Experienced builders recommend relying on this figure, although it is clearly overestimated for the majority roofing coverings. But, if after a few decades the owners of the house want to change the roof, then they will not have to change all the rafters - the calculation was made with a substantial margin.
Thus, the load from the weight of the roofing “pie” is 50 × 1.1 = 55 kg/sq. meter
How to calculate snow loads?
Snow load is a fairly serious impact on roof structures, since quite a lot of snow can accumulate on the roof.
In this formula:
Calculation example. For example, it is necessary to calculate the snow load for the roof of a house being built in the Moscow region, and the slope angle is 30 degrees.
The Moscow region is located in the III snow region, for which calculated value the mass of snow per square meter of horizontal surface is 180 kgf/sq. m.
180 x 0.7 = 126 kgf/sq. m.
How to calculate wind loads?
To calculate the load on the rafters, the formula is used:
- Wo is a standard indicator, which is determined from tables, depending on the region of the country.
- k is a correction factor that will allow you to determine the change in wind load depending on the type of terrain and the height of the building.
| Height of the house, measured in meters | A | B |
| 20 | 1,25 | 0,85 |
| 10 | 1 | 0,65 |
| 5 | 0,75 | 0,85 |
A – these are open areas: steppes, sea or lake coasts;
B – areas evenly covered with obstacles, for example, urban areas or forests.
The Moscow region is located in wind region I, the standard value of wind load in this area is 23 kgf/sq.m. m.
The correction factor in our example will be 0.5
23 x 0.5 = 11.5 kgf/sq. m.
This is the wind load value.
How to calculate the cross-sections of rafters and other roofing elements?
To calculate the length of the rafters, you need to know what roofing material you plan to use, as well as what they are made of attic floors (wooden beams or reinforced concrete slabs).
Standard rafters that go on sale have a length of 4.5 and 6 meters. But, if necessary, the length of the rafters can be changed.
The cross-section of the timber used to make rafters depends on the following factors:
- Rafter length;
- Rafter installation step;
- Design values of loads.
The data in the presented table are advisory; they cannot be called a full replacement for calculations. Therefore, calculating the truss is necessary to determine the load-bearing capacity of the roof.
These tables are presented in accordance with atmospheric loads characteristic of the Moscow region.
| The step with which are installed rafters (cm) |
Rafter length (meters) | ||||||
| 3,0 | 3,5 | 4,0 | 4,5 | 5,0 | 5,5 | 6,0 | |
| 215 | 100x150 | 100x175 | 100x200 | 100x200 | 100x250 | 100x250 | — |
| 175 | 75x150 | 75x200 | 75x200 | 100x200 | 100x200 | 100x200 | 100x250 |
| 140 | 75x125 | 75x175 | 75x200 | 75x200 | 75x200 | 100x200 | 100x200 |
| 110 | 75x150 | 75x150 | 75x175 | 75x175 | 75x200 | 75x200 | 100x200 |
| 90 | 50x150 | 50x175 | 50x200 | 75x175 | 75x175 | 75x250 | 75x200 |
| 60 | 40x150 | 40x175 | 50x150 | 50x150 | 50x175 | 50x200 | 50x200 |
Sections of timber for the manufacture of other roofing elements:
- Mauerlat – 100x100, 100x150, 150x150;
- For valleys and making diagonal legs - 100x200;
- Runs – 100x100, 100x150, 100x200;
- Puffs - 50x150;
- Crossbars – 100x150, 100x200;
- Struts – 100x100, 150x150;
- Hemming boards – 25x100.
Having decided on the cross-section and length, as well as the spacing of the rafters, it is easy to calculate the number of rafters, focusing on the length of the walls of the house.
When designing, in addition to strength calculations, the designer must perform deflection calculations.
That is, you need to not only ensure that the rafters do not break under the applied load, but also find out how much the beams can bend.
For example, the calculation of wooden roof truss for the construction of an attic roof, it must be made so that the deflection does not exceed 1/250 of the length of the section on which pressure is applied.
Thus, if rafters with a length of 5 meters are used, then the maximum permissible deflection can reach 20 mm. This value seems quite insignificant, but if it is exceeded, the deformation of the roof will be visually noticeable.
Material quality requirements
If wooden rafters are being calculated, then in addition to parameters such as length and cross-section, the quality of the building material must also be taken into account.
Made from deciduous and coniferous wood.
The basic requirements for the material are set out in GOST 2695-83 and GOST 8486-86. Among them:
- Allows the presence of knots in an amount of no more than three per meter area, the size of the knots should not exceed 30 mm.
- Non-through cracks not exceeding ½ length are allowed;
- The moisture content of lumber should not be higher than 18% when measured with a moisture meter.
When purchasing the material from which it is planned to install rafter systems, the snip prescribes checking the quality document, which indicates:
- Manufacturer information;
- Standard number and product name;
- Product size, humidity and type of wood used;
- Quantity individual elements in packaging;
- Release date of this batch.
Since wood is a natural material, it requires pre-installation preparation. This preparation is planned at the stage when the rafter system is being designed - the construction specification provides for the implementation of protective and constructive measures.
Protective measures include:
- Treating wood with antiseptics to prevent premature decay;
- Treatment of wood with fire retardant impregnations to protect against fire;
- Treatment with bioprotective compounds to protect against insect pests
Constructive measures include:
- Installation of waterproofing gaskets at the point of contact between brick and wooden structures;
- Creation of a waterproofing layer under the roofing material and a vapor barrier layer on the side of the premises in front of the insulation layer;
- Ventilation equipment for under-roof space.
Subject to all technology requirements, the rafter system wooden house will acquire higher strength qualities, and the roof structure will last a long time without requiring repairs.
Programs for design and calculation of truss systems
As can be seen from the above, the calculation is quite difficult. You need to have a sufficient supply of theoretical knowledge, drawing and sketching skills. Naturally, not every person has such professional skills.
Fortunately, today the design task is greatly simplified, since there are very convenient computer programs allowing you to develop designs for various building elements.
Of course, some programs are designed for professionals (for example, AutoCAD, 3D Max, etc.). It is quite difficult for an inexperienced person to understand this software.
But there are more simple options. For example, in the Arkon program you can very easily create various sketch designs to visually see what a particular roof will look like.
There is also a convenient calculator for calculating rafters, which allows you to make calculations efficiently and quickly. The Arkon program is perfect for professionals, but can also be used by private users.
You can also find an online rafter calculation calculator online. However, the calculations made on it are purely advisory values and cannot replace the development of a full-fledged project.
Conclusions
Performing design calculations – important stage creating a roof. Its implementation must be entrusted to professionals. But preliminary calculations You can do it yourself, this will help you better understand the finished project.
The roof of a building is designed to hold external loads and redistribute them to load-bearing walls or supporting structures. These loads include weight roofing pie, the mass of the structure itself, the weight of the snow cover, and so on.
The roof is located on the rafter system. This is the name of the frame structure on which the roof is fixed. It accepts all external loads, distributing them across supporting structures.
The rafter system of a gable roof includes the following elements:
- Mauerlat;
- Struts and braces;
- Side and ridge purlins;
- Rafter legs.
A rafter truss is a structure that includes all of the listed elements with the exception of the Mauerlat.
Calculation of gable roof loads
Constant loads
The first type refers to those loads that always act on the roof (in any season, time of day, and so on). These include the weight of the roofing pie and various equipment installed on the roof. For example, the weight of a satellite dish or aerator. It is necessary to calculate the weight of all truss structure along with fasteners and various elements. Professionals use computer programs as well as special calculators to perform this task.
Calculation gable roof is based on calculating the loads on the rafter legs. First of all, you need to determine the weight of the roofing cake. The task is quite simple, you just need to know the materials used, as well as the dimensions of the roof.
As an example, let’s calculate the weight of a roofing cake with ondulin material. All values are taken approximately; high accuracy is not required here. Usually builders perform calculations of the weight per square meter of roofing. And then this indicator is multiplied by total area roofs.
The roofing pie consists of ondulin, a layer of waterproofing (in this case - insulation on a polymer-bitumen basis), a layer of thermal insulation (weight calculation will be carried out basalt wool) and lathing (the thickness of the boards is 25 mm). Let's calculate the weight of each element separately, and then add up all the values.
Roof calculation gable roof:
- A square meter of roofing material weighs 3.5 kg.
- A square meter of waterproofing layer weighs 5 kg.
- A square meter of insulation weighs 10 kg.
- A square meter of sheathing weighs 14 kg.
Now let's calculate the total weight:
3.5 + 5 + 10 + 14 = 32.5
The resulting value must be multiplied by the correction factor (in this case it is equal to 1.1).
32.5 * 1.1 = 35.75 kg
It turns out that a square meter of roofing cake weighs 35.75 kg. It remains to multiply this parameter by the roof area, then you can calculate a gable roof.
Variable roof loads
Variable loads are those that act on the roof not constantly, but seasonally. A striking example is the snow in winter time. Snow masses settle on the roof, creating additional impact. But in the spring they melt, and accordingly, the pressure decreases.
Variable loads also include wind. This is also a weather phenomenon that does not always work. And there are many such examples. Therefore, it is important to take into account variable loads when calculating the length of the rafters gable roof. When calculating, you need to take into account many different factors affecting the roof of a building.
Now let's take a closer look at snow loads. When calculating this parameter, you need to use a special map. The amount of snow cover in different regions of the country is marked there.
To calculate this type of load, the following formula is used:
Where Sg is the terrain indicator taken from the map, and µ is the correction factor. It depends on the roof slope: the stronger the slope, the lower the correction factor. And here there is important nuance- for roofs with a slope of 60 o or more it is not taken into account at all. After all, the snow will simply roll off them and not accumulate.
The whole country is divided into regions not only by the mass of snow, but also by the strength of the winds. There is a special map on which you can find out this indicator in a certain area.
When calculating roof rafters, wind loads are determined using the following formula:
Where x is the correction factor. It depends on the location of the building and its height. And W o is the parameter selected from the map.
Calculation of the dimensions of the rafter system
When the calculation of all types of loads is finished, you can proceed to the calculation of dimensions rafter system. The work performed will differ depending on what kind of roof structure is planned.
In this case, a gable one is considered.
Section of the rafter leg
The calculation of the rafter leg is based on 3 criteria:
- Loads from the previous section;
- Remoteness of the railings;
- Rafter length.
There is a special table of sections rafter legs, in which you can find out this indicator based on the criteria described above.
Length of rafters in a gable roof
For manual calculations you will need basic knowledge geometry, in particular the Pythagorean theorem. Rafter - hypotenuse right triangle. Its length can be found by dividing the length of the leg by the cosine of the opposite angle.
Let's look at a specific example:
It is required to calculate the length of the rafters of a gable roof for a house with a width of 6 m, in which the slope of the slopes is 45 o. Let L be the length of the rafters. Let's substitute all the data into the formula.
L = 6 / 2 / cos 45 ≈ 6 / 2 / 0.707 ≈ 4.24 meters.
You need to add the length of the visor to the resulting value. It is approximately 0.5 m.
4.24 + 0.5 = 4.74 meters.
This completes the calculation of the length of the rafters for a gable roof. It was manual method completing the task. There are special computer programs designed to automate this process. The easiest way is to use Arkon. This is completely free program, which even a person with little computer knowledge can easily understand.
It is enough to simply specify the input parameters based on the size of the house. The program will independently perform calculations and show the required cross-section, as well as the length of the gable roof rafters.
The strength of a building's roof depends on how correctly the rafters are calculated. In this design, all parameters are important: length, roof angle, beam cross-section.
Factors to consider when calculating
The calculation of the cross-section of the rafters and their length is carried out in several stages. At the first stage, the snow and wind loads are calculated for the selected roof configuration, taking into account correction factors for the height of the building and the angle of inclination of the slope.
Then the load from the weight of the roofing material, insulation and sheathing is added. 10% is added to the resulting total load for a safety margin. The final value is used to calculate the rafters.
It is quite difficult to perform a competent calculation if you do not take into account the strength and frequency of the loads exerted on them.
Factors influencing the roof are divided into three groups:
- constant loads;
- variable loads;
- special loads.
Constant loads act on structural elements without ceasing, regardless of the seasons.
These include the mass of the roof, waterproofing, sheathing, vapor barrier, thermal insulation and all individual parts of the roof that have a constant weight and exert pressure on the rafter system.
The weight of a single-pitch or gable roof increases when massive devices and apparatus are installed on it - antennas, ventilation, snow guards, etc.
Strong influence on the strength of single-pitch rafters and gable roof exerted by the weight of the snow layer, the blowing wind and workers climbing onto the roof.
Such loads are called variable, since they are periodic in nature - strong pressure is replaced by its absence.
A special type includes loads that occur in regions where hurricanes or earthquakes occur frequently.
With this type of load, an additional margin of safety is taken into account during the design and construction of buildings.
Calculating roof rafters is a rather difficult task; a non-specialist may not be able to cope with it.
Calculation of the load on the rafters
Wind load is calculated in a simplified manner as follows: we multiply the regional wind load indicator by a correction factor. The regional indicator is taken from SNiP based on the wind load map.
Correction factor for buildings by height:
- below five meters is taken in the range of 0.5 - 0.75;
- from five to ten meters – 0.65 – 1.0;
- from ten to twenty meters – 0.85 – 1.25.
A lower value of the coefficient is used for built-up or wooded areas, where the wind force is moderated by obstacles, a higher value is taken for open areas.
If the building is located on an area that is open on at least one side, a larger range value also applies.
Snow load is calculated in a similar way - indicator snow load multiply by the correction factor.
The coefficient depends on the angle of the roof:
- a gentle slope with a slope of up to 25 degrees has a coefficient of 1.0;
- for a slope with an angle of inclination from 25 to 60 degrees, the coefficient is 0.7;
- if the slope angle exceeds 60 degrees, then the snow load is not taken into account.
The snow load indicator is indicated on the corresponding SNiP map similar to the wind load map.
If the building is located close to the border of two regions, then the value for the region with the highest indicator is used.
The obtained values of wind and snow load are summed up. The final value obtained at this stage of calculations is called the variable load indicator.
The calculation of permanent loads acting on the rafter system depends on the selected type of roof.
Constant loads are calculated for a roofing “pie” by adding the weight of its components - sheathing, insulation, waterproofing, roofing material.
Weight of the most common roofing materials:
- cement-sand tiles: 20 - 30 kg per square meter;
- slate: 10 - 14 kg per square meter;
- bitumen shingles: 6 - 8 kg per square meter;
- metal tiles: 3.5 - 4.5 kg per square meter;
- ondulin: 3 kg per square meter.
From the given data it follows that the static load may vary depending on the selected type of roofing material used.
By adding the values of static and variable loads and adding 10% for the safety margin, we get the final value that will be used for further calculations of the rafters.
Calculation of the size and pitch of rafters for single-pitch and gable roofs
To accurately calculate the rafter system, there are specialized programs and online calculators.
However, for a simple pitched and gable roof, the necessary parameters can be calculated independently without their help.
It should be noted that the rafter must protrude outward beyond the edge of the wall by at least 60 cm. Standard length the rafters are 6 m. If necessary, by calculating the length, it can be increased.
Calculation of the pitch for the rafters should take into account the distance between them in the range of 60 - 100 cm. The greater the load, the more often it is necessary to install the rafters.
The total number of rafters per roof slope is equal to the length of the slope divided by the pitch of the rafters, plus one rafter. Accordingly, for a gable roof this number must be doubled.
The smaller the calculated rafter spacing, the wider the rafter beam. For load-bearing structures of gable or pitched roof this size should be at least 15 cm for large buildings, and for country houses(barns, gazebos and baths) - 10 cm.
Then the number of rafters per slope is set. To do this, its length should be divided by the installation step. If the house is gabled, then the resulting value should be doubled.
The choice of a suitable rafter section depends on the pitch of the rafters and their length:
| Rafter length, cm | Rafter pitch, cm | Rafter section, cm |
| Up to 600 | 140 | 10x20 |
| 100 | 8x20 | |
| Up to 400 | 180 | 9x18 |
| 140 | 8x18 | |
| 100 | 8x16 | |
| Up to 300 | 180 | 9x10 |
| 120 | 8x10 |
To reduce deformation of rafters and beams during operation, it is best to use dry lumber for the rafter system.
When choosing beams for rafters, you need to pay attention to the absence of cracks and knots.
In the most common case, for a gable roof of a one-story building covered with slate, it is advisable to use wooden rafters cross section 5x15 cm.
Types of rafter structures
Before we start roofing works need to pick up best option rafter structure. Each of them has its pros and cons.
Classification of rafter systems:
- hanging;
- layered;
- hybrid.
If the roof standard width 6 m (correspondingly, this is the length of the rafter leg), then suitable hanging systems. By fixing the ends to the roof ridge and load-bearing wall fastening is done.
In addition, a tightening is installed that prevents deformation of the pressure and stress of the truss structure. In addition, they take on the role of load-bearing beams.
Sloping systems are suitable for roofs of any width. Fixing the bed in relation to the Mauerlat ensures the stability and reliability of the entire structure.
As a result, the pressure is smoothed out by the stand and the tension is reduced. The advantages of a layered rafter system are quite easy installation, but the work will require large expenses, since additional lumber will be required to arrange the beds.
Hybrid structures are most suitable for multi-pitched roofs, in which transitions are accompanied by repeated numerous beams, reinforcements, beams, posts, bevels and other elements that ensure the stability of the system.
The construction of a hybrid structure is expensive and quite complex, so the project development and construction should be carried out by qualified specialists.
The question of calculating rafters (their cross-section, length, pitch and other parameters), which seems simple at first glance, actually requires a thorough and responsible approach.
It is not enough to just estimate the distance from the top external wall buildings to buy the right quantity roofing lumber, because with such a calculation you will have to constantly adjust the work.
To avoid problems during construction, it is necessary to take into account many important parameters: from the thickness and length of the beams to the area of the future roof.
Besides, great value has the terrain and climate of the region in which construction is taking place.
A simple online calculator for calculating a gable roof of a house will calculate the rafters, calculate the rafter system of a gable roof, calculate the roof area, calculate the sheathing, calculate the roofing sheet, calculate the material for the roof.
House with a gable roof. Installation of a gable roof of a house
The most economical in financially among pitched roofs A gable roof is considered to be a gable roof; a builder who does not have special education or skills can make a gable roof with his own hands. The design of the roof of the house will depend on the purpose of using the area of the second floor, as an attic or as a living space - an attic. Miscellaneous purposes – different section rafters, their treatment and roof insulation.
Gable mansard roof requires the presence of chimneys in attic rooms, toilet bathrooms must be located above non-residential areas, excluding the kitchen area. Also needs to be processed wooden beams antiseptic and fire retardant solutions, protecting against mold and fire. Consequently, the cost of a gable roof increases if the second floor of the house is made residential.
Drawing of a gable roof
The roof calculation program will draw a drawing of a gable roof of a house
will calculate the exact quantity building materials for rafter system and roofing. Start roof calculation now!