Gable roof rafter system calculation of materials. Gable roof calculator and rafter system calculation online
A properly selected and installed roof will withstand any weather conditions and will last for decades. What will the roof be like? country house, and what materials it will consist of is determined at the design stage. It is better to entrust the technical nuances of design to professionals. Before making the final choice, the future owner needs to get an idea of the features various types roofs and (which is important) about the amount that the chosen structure and roofing material will cost. At this stage, a roofing calculator will help you calculate the material for a gable roof, or any other - this is a quick way to get a detailed answer.
The calculator will help you estimate the cost of a roof in the early planning stages Source colourbox.com
Online roofing calculator
To find out the approximate cost of roofing of various types, use the following calculator:
Parameters for calculating roofs and roofing materials
Before calculating the roof of a house, the calculator will ask for certain data. One of them is the type of roof. There are two criteria by which you can determine the type of roof: the angle of the roof and the number of slopes (planes). If the angle of inclination of the roof is zero, the roof is called flat; if it is greater than zero, it is called pitched. Pitched structures, in turn, are divided into types, depending on the number of slopes. In private low-rise construction, several types of roofs are common, including:
Single-pitch. It looks rather modest, but it is the simplest in design and the least expensive to build. It is a plane supported by walls of different heights. A shed roof can be seen on a garage, shed or modern project in high-tech style. Such designs are described by a small number of parameters and are calculated on all online calculators.
Common forms pitched structures Source remokna.in.ua
Gable (gable). The most common classic version with two rectangular inclined planes connected by a ridge, and a centuries-old history. The vertical triangular planes between the slopes are called pediments (gables). In modern private construction, the symmetry of the slopes is an optional condition. They can have different slopes and vary in size (broken), which opens up great design possibilities roofing structures. Gable roof - perfect option for the installation of an attic. For calculations on the online calculator, parameters such as the length and width of the slopes, the length of the overhangs and the height of the structure are used.
Hip (hatched). The main slopes are called hips and have the form of trapezoids, and the pediments are not located vertically, but at an angle, turning into slopes. The hip system is much more difficult to develop and install than the previous ones, but this is compensated by the increased stability of the structure. In addition, the hip roof allows you to raise the ceiling for the attic, making it much more comfortable. Calculation hip roof on the online calculator has certain subtleties (the base can be square or rectangular) and includes the angle of inclination of the slopes.
Multi-forceps. A complex structure consisting of several tongs (gable elements). Calculating such a roof is a job for an experienced architect. There are online calculators that calculate the roof area of a three-gable roof, but the calculation results they give are very approximate.
Complexity rafter system multi-gable roofing eliminates independent planning Source yandex.ru
Attic. The slope consists of two elements: the lower, steeper one, and the upper, flatter one. This design allows you to increase usable area premises, but to calculate it using an online calculator, you will need at least a preliminary drawing and understanding of the structure of the rafter system.
Types of roofing materials
The issue of roofing material is also decided at the design stage. His choice is influenced not only by the designer’s preferences, but also by more real factors, including the amount of precipitation and wind strength in the region. The online calculator makes it possible to find out not only the quantity, but also the cost of the selected material. Typically a roof calculator is configured to calculate the following materials:
Corrugated sheet.
Metal tiles.
Soft (roll) roofing.
Seam covering(steel, aluminum or copper).
Roof tiles. Ceramic (piece), flexible (soft), cement-sand, composite.
Slate(mainly for outbuildings).
Calculator for calculating metal tiles (works with several types of roofs) Source amvita.ru
Basic elements of roofing structure
The roof of a country cottage is not only a decorative detail and business card buildings, but also a complex engineering system. It consists of a variety of building parts, the main ones of which are the following:
Mauerlat. A beam that is laid on top of load-bearing walls. It supports the rafter system and transfers the load from the roof to the building.
Rafters. Beams or boards located at an angle are the basis of the system. The online calculator allows you to calculate some parameters of the rafter system.
Auxiliary elements. Racks, beams, purlins and tie-downs serve to secure the rafters and strengthen the structure.
Horse. The top edge of the roof, the intersection of the slopes.
Lathing. A lattice structure onto which the roofing material is attached. Some types of roofing require a continuous deck. The sheathing parameters on the online calculator are calculated quite well, especially for roofs of simple construction.
Main structural elements of the rafter system Source kafmt.ru
On our website you can find contacts of construction companies that offer country house design services. You can communicate directly with representatives by visiting the “Low-Rise Country” exhibition of houses.
What is calculated on an online calculator: types and possibilities
Even with ready-made drawings in hand, the future owner will not always find time to carefully study them and painstaking calculations on paper. Among all the ways to solve the question of how to calculate the roof of a house, an online calculator will be the best option. There are two types of calculators that perform a certain type of calculation:
Standard roof calculator
The most common type, which allows you to obtain the basic parameters, from the angle of inclination of the rafters to permissible load on the roof. In counting roofing material As a rule, all popular options are available (all kinds of tiles, slate, ondulin and other materials). There are a wide range of calculators for calculating single-, gable- and hip roofs; there are settlement services hip roof or attic. The online gable or shed roof calculator is designed for simple tasks; more advanced calculation programs must be downloaded and installed on your computer.
Fragment of an online calculator for calculating a hip roof Source citymang.ru
Construction calculator
Complex calculation algorithms are used for calculations; as a result, you can get not only tables of numbers, but also a set of detailed drawings, as well as 3D visualization. IN construction calculator As a rule, any type of roof can be calculated. In addition to the basic parameters, you can find out how much lumber you will need, select optimal insulation and vapor barrier. The drawings will show the layout of the rafter system and sheathing and will allow you to check the correct angle of inclination and location of the rafters.
Online calculator device for calculating a gable roof
Rafter system calculation calculator gable roof is an easy-to-use mechanism that allows you to perform basic structural calculations. The interface of any service has a convenient and intuitive appearance and looks like a set of empty fields with an explanation. For the convenience of visitors, schematic images are placed nearby on the page. various types roofs with parameters marked on them.
Before starting calculations, you should familiarize yourself with the designation of the fields Source stankotec.ru
The user just has to enter the required value (size) in each field or select an option from the available ones. When filling out, pay attention to the dimensions - parameters can be entered in cm or mm. After filling in the fields, you press the calculation button and get the desired result in the form of the following data:
Number of roofing materials. The calculator will allow you to calculate the amount of metal tiles (or other material) for a country house with a gable, hip or other roof.
Calculation of the rafter system and roof gable. Based on the specified wall width and height to the ridge, the service will help determine the length of the rafters and the area of the roof gable.
To calculate the material for the roof of a house, the “gable” program will require you to enter the following values:
Roof dimensions. There are separate fields for entering height, width (on each side) and overhang.
Rafter dimensions. The width and thickness are set, as well as the distance between the rafters and the distance to the edge of the roof.
Video description
About calculating the roof using a construction calculator in the following video:
Sheathing parameters. Enter the width and thickness of the boards, the distance between them.
Roofing material parameters. If a roofing sheet is selected, specify the height, width and overlap of the sheet.
The result of the calculation will be the following parameters:
Roof size. Height and width of the canvas, total area.
Rafters. Number and length of rafters. The volume is also calculated required material(in cubic meters).
Lathing. The calculation shows the number of rows of boards, the length of each part and the volume of the sheathing boards.
Roofing material. The area of hydro- and vapor barrier is calculated. So, if roofing felt or glassine is selected as the under-roofing material, the calculator shows required amount rolls (based on the roll size), taking into account overlap.
Roofing material. The calculator determines not only the coverage area, but also the weight and required amount of the selected material.
Calculator for calculating basic elements gable roof Source stankotec.ru
Calculation of additional parameters
Many online services calculate additional, no less useful quantities:
Roof angle. The calculator will determine not only the optimal angle, but also tell you whether it is suitable for the selected roofing material. By changing the height of the rise or the width of the base, you can achieve full compliance of the angle with the material.
Calculation of wind and snow load . For some areas, this load may be a determining factor in choosing a roof type. You will need to enter into the calculator Additional information: region of construction, type of terrain, height to the ridge of the building, type of wood for the rafters.
Chimney calculation. For safe operation, it is necessary to determine the height of the chimney relative to the roof ridge. Incorrect design can affect the stable operation of heating devices and lead to unplanned financial expenses (if rework is required).
When calculating the chimney, the presence of obstacles near the home is taken into account Source stroim-dom.radiomoon.ru
Limitations in using the online calculator
Roofing calculators offered by online resources are an affordable and very fast way to get the necessary information. But like any mechanisms designed for the mass user, such calculators tend to use generalized calculation techniques. The worst thing is that the calculation process is hidden from the person using the calculator; It is very difficult to double-check the output information.
The calculator for calculating the roof of a house may contain certain (acceptable) variations in parameters, which, nevertheless, will affect the final result. Possible results that may contain inaccurate (approximate) values include:
Determining the total amount of roofing material
Building materials are never laid joint-to-joint, so the roof surface area and roofing area will always be different. When calculating, the roof area is usually increased by 15% - this provides a margin when forming an overlap.
Video description
How to calculate a gable roof using a free calculator in the following video:
If the roof has complex design, the calculation also becomes more complicated, since an experienced designer simultaneously solves the additional problem of waste minimization. For such purposes, different algorithms are used (with different accumulating errors and with different results), which of them is included in the calculator is known only to its developers.
It is believed that the calculator helps you save on the purchase of building materials. But when installing a complex-shaped roof, it often turns out that unnecessary (often expensive) materials were purchased. The opposite situation, when there is not enough material and you have to pay for an unplanned purchase and delivery, is no less annoying.
Determining the slope for a roof
Building codes require minimum slope values for each roofing material. They are calculated taking into account the slope of the roof and additional indicators (wind and snow load). Specialists perform calculations according to SNiP “Loads and Impacts” standards and additional design standards. It is not possible to check what indicators the roofing calculator uses in its work.
Some calculators take into account additional parameters (the presence of roof windows and drainage systems) Source stankotec.ru
Roof calculation: how to avoid mistakes
In calculations you can go one of the following ways:
Calculate the roof manually. If you have basic knowledge of geometry, you can make preliminary calculations manually. To do this, just stock up on paper, a pencil, a regular calculator, and remember that any roof is a set of simple shapes (rectangles and triangles), the calculation of the area of which is described by the simplest formulas from school course. The method does not work well if the calculations become more complicated. They take a lot of time and increase the risk of error.
Roof calculations should be carried out in online service . It should be taken into account that the values are always averaged; Your planned home may require a custom solution.
Check the roof calculation manually using a calculator. Roofing online calculators are in a convenient way simulate the roof structure and find out the required amount of building materials. Calculation simple designs It’s quite easy to check, but if you don’t have a specialized education, confusion with coefficients and percentages is inevitable. Differing results will cause lengthy double-checks and searches for errors, as well as mistrust in the abilities of the calculator (or your own).
Checking the calculation results will require time and care Source transsib6.ru
Professional roof calculation. For preliminary calculations in order to determine the materials and design of the roof, this method is clearly not suitable. But when ordering a turnkey house, construction company will prepare a full-fledged project, which will indicate all calculations and estimates. In addition, specialists can make preliminary calculations for you even at the stage of discussing the project.
Conclusion
An online roofing calculator is considered to be a good tool for determining the basic parameters of a future roof. But professional builders It is recommended to use it only for a rough estimate of the quantity and cost of building materials. The calculator can also become an indispensable tool for comparing the costs of different technologies.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, lathing, 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 retainers, etc.
The strength of the rafters of a pitched and gable roof is strongly influenced 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 coefficient value is used for built-up or wooded areas where the wind force is moderated by obstacles, higher value 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 - we multiply the snow load indicator by a 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 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 the beginning 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 the load-bearing wall, fastening is achieved.
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 that it is quite simple to install, 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 in order to buy the appropriate amount of 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.
In addition, the terrain and climate of the region in which construction is taking place are of great importance.
Specify the parameters of wooden rafters:
B– rafter width, an important parameter that determines the reliability of the rafter system. The required rafter section (in particular width) depends on: loads (constant - the weight of the sheathing and roofing pie, as well as temporary - snow, wind), the material used (quality and its type: board, timber, laminated veneer lumber), length rafter leg, distances between rafters. You can determine the approximate cross-section of the beam for the rafters using the table data (the width value is the larger value from column 3, for example, with a rafter length of up to 3000 mm and a pitch of 1200 mm, the desired width value is 100 mm). When choosing the width of the rafters, be sure to take into account the recommendations given in SP 64.13330.2011 “ Wooden structures"and SP 20.13330.2011 "Loads and impacts".
| Rafter length, mm | Rafter pitch, mm | Rafter section, mm |
| Up to 3000 mm | 1200 | 80x100 |
| Up to 3000 mm | 1800 | 90x100 |
| Up to 4000 mm | 1000 | 80x160 |
| Up to 4000 mm | 1400 | 80x180 |
| Up to 4000 mm | 1800 | 90x180 |
| Up to 6000 mm | 1000 | 80x200 |
| Up to 6000 mm | 1400 | 100x200 |
Y– roof height, distance from the ridge to the attic floor. Affects the angle of inclination of the roof. If you plan to arrange non-residential attic, you should choose a small height (less material will be required for rafters, waterproofing and roofing), but sufficient for inspection and maintenance (at least 1500 mm). If it is necessary to equip a living space under the roof arch, to determine its height, you must focus on the height of the tallest family member plus 400-500 mm (approximately 1900-2500 mm). In any case, you must also take into account the requirements of SP 20.13330.2011 (updated edition of SNiP 2.01.07-85*). It should be remembered that on a roof with a small angle of inclination (small height) precipitation can be retained, which negatively affects its tightness and durability. However, a high roof becomes more vulnerable to strong wind gusts. Optimal angle the inclination is within 30-45 degrees.
X– The width of the roof (without overhangs) is determined by the width of the outer perimeter of your house.
C– the size of the overhang, an important structural element of the roof that protects the walls and foundation from precipitation, is determined taking into account the climatic conditions of your region (SP 20.13330.2011) and the general architectural idea. For one and two-story houses without organizing external water flow of at least 600 mm. If you arrange a drainage system, you can reduce it to 400 mm (SNB 3.02.04-03). According to the requirements of IRC-2012, paragraph R802.7.1.1 (International Building Code for 1-2 apartment individual residential buildings), the maximum length of the free overhang of rafters, which does not require the installation of additional support struts, is 610 mm. The optimal overhang size is considered to be 500 mm.
Z– this is the distance from the top edge of the rafter to the cut. Size Z is related to the width of the rafter by a simple ratio - no more than 2/3 of its width (neglecting this rule significantly reduces bearing capacity rafters). The cut is necessary to attach the rafters to the mauerlat - a support that takes the load from the roof and redistributes it to the load-bearing walls.
By checking the “Black and white drawing” option, you will receive a drawing that is close to GOST requirements and will be able to print it without wasting color paint or toner.
Calculation results:
Length to rafter overhang– this size should be used to mark the cut of the rafters to the mauerlat.
Overhang length will show how far it is necessary to extend the rafter beyond the perimeter of the house to obtain a given roof overhang ( WITH) protecting from bad weather.
Having calculated total length of rafters and overhang It’s not difficult to find out the required amount of lumber of the required length and estimate how much reagents are needed to treat wood from rotting.
Calculation of the angle and section of the rafters: The cut angle is the angle at which the ends of the rafters must be cut to connect to each other. The beginning of the cut should be measured at the same angle to the edge of the rafter. To maintain the same cutting angle on all rafters, it is advisable to use a template.
A gable roof is formed on the basis of a frame that combines the simplicity of the device and unsurpassed reliability. But the roof skeleton of two rectangular slopes can boast of these advantages only if the rafter legs are carefully selected.
Parameters of the gable roof rafter system
It’s worth starting the calculations if you understand that the rafter system of a gable roof is a complex of triangles, the most rigid elements of the frame. They are assembled from boards, the size of which plays a special role.
Rafter length
The formula will help determine the length of durable boards for the rafter systema²+b²=c², derived by Pythagoras.
The length of the rafter can be found by knowing the width of the house and the height of the roof
The parameter “a” indicates the height and is independently selected. It depends on whether the under-roof space will be residential, and also has certain recommendations if an attic is planned.
Behind the letter "b" is the width of the building, divided in two. And “c” represents the hypotenuse of the triangle, that is, the length of the rafter legs.
Let’s assume that the width of half the house is three meters, and it was decided to make the roof two meters high. In this case, the length of the rafter legs will reach 3.6 m (c=√a²+b²=4+√9=√13≈3.6).
You should add 60–70 cm to the figure obtained from the Pythagorean formula. The extra centimeters will be needed to carry the rafter leg beyond the wall and make the necessary cuts.
The six-meter rafter is the longest, so it is suitable as a rafter leg
The maximum length of timber used as a rafter leg is 6 m. If a strong board is required longer length, then they resort to the method of fusion - nailing a section from another beam to the rafter leg.
Section of rafter legs
For various elements of the rafter system, there are standard sizes:
- 10x10 or 15x15 cm - for mauerlat timber;
- 10x15 or 10x20 cm - for the rafter leg;
- 5x15 or 5x20 cm - for purlin and bracing;
- 10x10 or 10x15 cm - for a stand;
- 5x10 or 5x15 cm - for a bed;
- 2x10, 2.5x15 cm - for laths.
Thickness of each part load-bearing structure roofing is determined by the load that it will experience.
A beam with a section of 10x20 cm is ideal for creating a rafter leg
The cross-section of the rafter legs of a gable roof is affected by:
The most significant effect on the cross-section of the rafter legs is the pitch of the rafters. An increase in the distance between the beams entails increased pressure on the supporting structure of the roof, and this obliges the builder to use thick rafter legs.
Table: rafter cross-section depending on length and pitch
Variable impact on the rafter system
The pressure on the rafter legs can be constant or variable.
From time to time and with varying intensity, the supporting structure of the roof is affected by wind, snow and precipitation. In general, the roof slope is comparable to a sail, which can break under the pressure of natural phenomena.
The wind tends to overturn or lift the roof, so it is important to make all the calculations correctly
The variable wind load on the rafters is determined by the formula W = Wo × k x c, where W is the wind load indicator, Wo is the value of the wind load characteristic of a certain area of Russia, k is a correction factor determined by the height of the structure and the nature of the terrain, and c is the aerodynamic factor coefficient.
The aerodynamic coefficient can vary from -1.8 to +0.8. A negative value is typical for a rising roof, while a positive value is typical for a roof on which the wind presses. At simplified calculation with a focus on improving strength, the aerodynamic coefficient is considered equal to 0.8.
Calculation of wind pressure on the roof is based on the location of the house
The standard value of wind pressure is determined from map 3 of Appendix 5 in SNiP 2.01.07–85 and a special table. The coefficient taking into account the change in wind pressure with height is also standardized.
Table: standard value of wind pressure
Table: k coefficient value
It's not just the terrain that affects wind loads. Great importance has a residential area. Behind the wall of tall buildings the house is in almost no danger, but in an open space the wind can become a serious enemy for it.
The snow load on the rafter system is calculated using the formula S = Sg × µ, that is, the weight of the snow mass per 1 m² is multiplied by a correction factor, the value of which reflects the degree of roof slope.
The weight of the snow layer is indicated in SNiP “Rafter Systems” and is determined by the type of terrain where the building is built.
The snow load on the roof depends on where the house is located
The correction factor, if the roof slopes tilt less than 25°, is equal to one. And in the case of a roof slope of 25–60°, this figure decreases to 0.7.
When the roof is sloped more than 60 degrees, the snow load is discounted. Still, snow rolls off a steep roof quickly, without having time to negative influence to the rafters.
Constant loads
Loads acting continuously are considered to be the weight of the roofing pie, including sheathing, insulation, films and Decoration Materials for arranging an attic.
The roofing pie creates constant pressure on the rafters
The weight of the roof is the sum of the weight of all materials used in the construction of the roof. On average it is 40–45 kg/sq.m. According to the rules, per 1 m² of rafter system there should not be more than 50 kg of roofing material weight.
To ensure that there is no doubt about the strength of the rafter system, it is worth adding 10% to the calculation of the load on the rafter legs.
Table: weight of roofing materials per 1 m²
| Type of roofing finish | Weight in kg per 1 m² |
| Rolled bitumen-polymer sheet | 4–8 |
| Bitumen-polymer soft tiles | 7–8 |
| Ondulin | 3–4 |
| Metal tiles | 4–6 |
| Corrugated sheeting, seam roofing, galvanized metal sheets | 4–6 |
| Cement-sand tiles | 40–50 |
| Ceramic tiles | 35–40 |
| Slate | 10–14 |
| Slate roofing | 40–50 |
| Copper | 8 |
| Green roof | 80–150 |
| Rough flooring | 18–20 |
| Lathing | 8–10 |
| The rafter system itself | 15–20 |
Number of beams
How many rafters will be needed to arrange the frame of a gable roof is determined by dividing the width of the roof by the pitch between the beams and adding one to the resulting value. It indicates an additional rafter that will need to be placed on the edge of the roof.
Let's say it was decided to leave 60 cm between the rafters, and the length of the roof is 6 m (600 cm). It turns out that 11 rafters are needed (including the additional timber).
The rafter system of a gable roof is a structure made from a certain number of rafters
The pitch of the beams of the supporting roof structure
To determine the distance between the beams of the supporting roof structure, you should pay close attention to such points as:
- weight of roofing materials;
- the length and thickness of the beam - the future rafter leg;
- degree of roof slope;
- level of wind and snow loads.
It is customary to place rafters at 90–100 cm intervals when choosing a lightweight roofing material
A normal step for rafter legs is 60–120 cm. The choice in favor of 60 or 80 cm is made in the case of constructing a roof inclined at 45˚. The same small step should be taken if you want to cover wooden frame roofs heavy materials like ceramic tiles, asbestos-cement slate and cement-sand tiles.
Table: rafter pitch depending on length and cross-section
Formulas for calculating the rafter system of a gable roof
Calculation of the rafter system comes down to establishing the pressure on each beam and determining the optimal cross-section.
When calculating the rafter system of a gable roof, proceed as follows:
- Using the formula Qr=AxQ they find out what the load on linear meter each rafter leg. Qr is the distributed load per linear meter of a rafter leg, expressed in kg/m, A is the distance between the rafters in meters, and Q is the total load in kg/m².
- Proceed to determining the minimum cross-section of the rafter beam. To do this, study the data from the table included in GOST 24454–80 “Softwood lumber. Dimensions".
- Based on standard parameters, choose the section width. And the section height is calculated using the formula H ≥ 8.6 Lmax sqrt(Qr/(BRbend)), if the roof slope is α< 30°, или формулу H ≥ 9,5·Lmax·sqrt(Qr/(B·Rизг)), когда уклон крыши α >30°. H is the section height in cm, Lmax is the working section of the rafter leg maximum length in meters, Qr - distributed load per linear meter of rafter leg in kg/m, B - section width cm, Rbend - bending resistance of wood, kg/cm². If the material is made from pine or spruce, then Ri can be equal to 140 kg/cm² (grade 1 wood), 130 kg/cm² (grade 2) or 85 kg/cm² (grade 3). Sqrt is the square root.
- Check whether the deflection value complies with the standards. It should not be greater than the figure obtained by dividing L by 200. L refers to the length of the working section. Correspondence of the deflection value to the ratio L/200 is feasible only if the inequality 3.125·Qr·(Lmax)³/(B·H³) ≤ 1 is true. Qr denotes the distributed load per linear meter of the rafter leg (kg/m), Lmax is the working section of the rafter leg maximum length (m), B is the section width (cm), and H is the section height (cm).
- When the above inequality is violated, the indicators B and H increase.
Table: nominal dimensions of thickness and width of lumber (mm)
| Board thickness - section width (B) | Board width - section height (H) | ||||||||
| 16 | 75 | 100 | 125 | 150 | - | - | - | - | - |
| 19 | 75 | 100 | 125 | 150 | 175 | - | - | - | - |
| 22 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | - | - |
| 25 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 32 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 40 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 44 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 60 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 75 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 100 | - | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 125 | - | - | 125 | 150 | 175 | 200 | 225 | 250 | - |
| 150 | - | - | - | 150 | 175 | 200 | 225 | 250 | - |
| 175 | - | - | - | - | 175 | 200 | 225 | 250 | - |
| 200 | - | - | - | - | - | 200 | 225 | 250 | - |
| 250 | - | - | - | - | - | - | - | 250 | - |
Example of load-bearing structure calculation
Let us assume that α (roof inclination angle) = 36°, A (distance between rafters) = 0.8 m, and Lmax (working section of the rafter leg of maximum length) = 2.8 m. First grade pine material is used as beams , which means that Rben = 140 kg/cm².
Cement-sand tiles were chosen to cover the roof, and therefore the weight of the roof is 50 kg/m². Total load (Q) experienced by each square meter, equal to 303 kg/m². And for the construction of the rafter system, beams 5 cm thick are used.
The following computational steps follow from this:
- Qr=A·Q= 0.8·303=242 kg/m - distributed load per linear meter of rafter beam.
- H ≥ 9.5·Lmax·sqrt(Qr/B·Rben).
- H ≥ 9.5 2.8 sqrt(242/5 140).
- 3.125·Qr·(Lmax)³/B·H³ ≤ 1.
- 3.125·242·(2.8)³ / 5·(17.5)³= 0.61.
- H ≥ (approximate height of the rafter section).
In the table standard sizes you need to find a cross-sectional height of the rafters that is close to 15.6 cm. A suitable parameter is 17.5 cm (with a section width of 5 cm).
This value is quite consistent with the deflection in regulatory documents, and this is proven by the inequality 3.125·Qr·(Lmax)³/B·H³ ≤ 1. Substituting the values (3.125·242·(2.8)³ / 5·(17.5)³) into it, we find that 0.61< 1. Можно сделать вывод: сечение пиломатериала выбрано верно.
Video: detailed calculation of the rafter system
Calculating the rafter system of a gable roof is a whole complex of calculations. In order for the beams to cope with the task assigned to them, the builder needs to accurately determine the length, quantity and cross-section of the material, find out the load on it and find out what the pitch between the rafters should be.
Do you want to calculate the rafter system quickly, without studying theory and with reliable results? Take advantage online calculator Online!
Can you imagine a person without bones? In the same way, a pitched roof without a rafter system is more like a structure from a fairy tale about the three little pigs, which can easily be swept away by natural elements. A strong and reliable rafter system is the key to the durability of the roof structure. In order to design a high-quality rafter system, it is necessary to take into account and predict the main factors affecting the strength of the structure.
Take into account all the bends of the roof, correction factors for uneven distribution of snow over the surface, snow drift by the wind, the slope of the slopes, all aerodynamic coefficients, forces of influence on the structural elements of the roof, and so on - calculate all this as close as possible to the real situation, and also take into account everything loads and skillfully assembling their combinations is not an easy task.
If you want to understand it thoroughly - list useful literature is given at the end of the article. Of course, a strength of strength course for a complete understanding of the principles and impeccable calculation of the rafter system cannot be fit into one article, so we will present the main points for simplified versioncalculation.
Load classification
Loads on the rafter system are classified into:
1) Basic:
- permanent loads: the weight of themselves truss structures and roofs,
- long-term loads- snow and temperature loads with a reduced design value (used when it is necessary to take into account the influence of load duration when testing endurance),
- variable short-term influence- snow and temperature effects at the full calculated value.
2) Additional- wind pressure, weight of builders, ice loads.
3) Force majeure- explosions, seismic activity, fire, accidents.
To carry out the calculation of the rafter system, it is customary to calculate the maximum loads in order to then, based on the calculated values, determine the parameters of the elements of the rafter system that can withstand these loads.
Calculation of the rafter system pitched roofs produced according to two limit states:
a) The limit at which structural failure occurs. The maximum possible loads on the structural strength of the rafters should be less than the maximum permissible.
b) Limit state at which deflections and deformations occur. The resulting deflection of the system under load should be less than the maximum possible.
For a simpler calculation, only the first method is used.
Calculation of snow loads on the roof
To count snow load use the following formula: Ms = Q x Ks x Kc
Q- the weight of snow cover covering 1 m2 of a flat horizontal roof surface. Depends on the territory and is determined from the map in Figure No. X for the second limit state - calculation of deflection (when the house is located at the junction of two zones, a snow load with a large value is selected).
For strength calculations according to the first type, the load value is selected according to the area of residence on the map (the first digit in the indicated fraction is the numerator), or is taken from table No. 1:
The first value in the table is measured in kPa, in parentheses the desired converted value is in kg/m2.
Ks- correction factor for the roof slope angle.
- For roofs with steep slopes with an angle of more than 60 degrees, snow loads are not taken into account, Ks=0 (snow does not accumulate on steeply pitched roofs).
- For roofs with an angle from 25 to 60, the coefficient is taken 0.7.
- For others it is equal to 1.
The angle of the roof can be determined online roof calculator the appropriate type.
Kc- coefficient of wind removal of snow from roofs. Assuming a flat roof with a slope angle of 7-12 degrees in areas on the map with a wind speed of 4 m/s, Kc is taken = 0.85. The map shows zoning based on wind speed.
Drift factor Kc is not taken into account in areas with January temperatures warmer than -5 degrees, since an ice crust forms on the roof and snow does not blow off. The coefficient is not taken into account if the building is blocked from the wind by a taller neighboring building.
The snow falls unevenly. Often, a so-called snow bag is formed on the leeward side, especially at joints and kinks (valley). Therefore, if you want a strong roof, keep the rafter spacing to a minimum in this place, and also pay close attention to the recommendations of roofing material manufacturers - snow can break off the overhang if it is of the wrong size.
We remind you that the calculation given above is presented to your attention in a simplified form. For a more reliable calculation, we recommend multiplying the result by the load safety factor (for snow load = 1.4).
Calculation of wind loads on the rafter system
We've sorted out the snow pressure, now let's move on to calculating the wind influence.
Regardless of the angle of the slope, the wind has a strong impact on the roof: it tries to throw off a steeply pitched roof, more flat roof- lift from the leeward side.
To calculate the wind load, its horizontal direction is taken into account, while it blows bidirectionally: on the facade and on the roof slope. In the first case, the flow is divided into several - part goes down to the foundation, part of the flow tangentially from below vertically presses on the roof overhang, trying to lift it.
In the second case, acting on the roof slopes, the wind presses perpendicular to the slope, pressing it in; a vortex is also formed tangentially on the windward side, going around the ridge and turning into a lifting force on the leeward side, due to the difference in wind pressure on both sides.
To calculate the average wind load use the formula
Mv = Wo x Kv x Kc x strength factor,
Where Wo- wind pressure load determined from the map
Kv- wind pressure correction factor, depending on the height of the building and the terrain.
Kc- aerodynamic coefficient, depends on the geometry of the roof structure and wind direction. Values are negative for the leeward side, positive for the windward side
For a pitched roof, you need to take the coefficient from the table for Ce1.
To simplify the calculation, it is easier to take the maximum value of C, equal to 0.8.
Calculation of own weight, roofing pie
To calculate permanent load you need to calculate the weight of the roof (roofing pie - see Figure X below) per 1 m2, the resulting weight must be multiplied by a correction factor of 1.1 - the rafter system must withstand this load throughout its entire service life.
The weight of the roof consists of:
- the volume of wood (m3) used as sheathing is multiplied by the density of the wood (500 kg/m3)
- weight of the rafter system
- weight of 1m2 roofing material
- weight 1m2 of insulation weight
- weight of 1m2 of finishing material
- weight 1m2 of waterproofing.
All these parameters can be easily obtained by checking this data with the seller, or looking at the main characteristics on the label: m3, m2, density, thickness - perform simple arithmetic operations.
Example: for insulation with a density of 35 kg/m3, packed in a roll 10 cm or 0.1 m thick, 10 m long and 1.2 m wide, weight 1 m2 will be equal to (0.1 x 1.2 x 10) x 35 / (0.1 x 1.2) = 3.5 kg/m2. The weight of other materials can be calculated using the same principle, just do not forget to convert centimeters to meters.
More often the roof load per 1 m2 does not exceed 50 kg, therefore, when making calculations, this value is used, multiplied by 1.1, i.e. use 55 kg/m2, which itself is taken as a reserve.
More data can be taken from the table below:
10 - 15 kg/m² |
|
Ceramic tiles | 35 - 50kg/m² |
Cement-sand tiles | 40 - 50 kg/m² |
Bituminous shingles | 8 - 12 kg/m² |
Metal tiles | |
Corrugated sheet | |
Subfloor weight | 18 - 20 kg/m² |
Sheathing weight | 8 - 12 kg/m² |
Rafter system weight | 15 - 20 kg/m² |
Collecting loads
According to the simplified version, now it is necessary to add up all the loads found above by simple summation, we will get the final load in kilograms per 1 m2 of roof.
Calculation of the rafter system
After collecting the main loads, you can already determine the main parameters of the rafters.
falls on each rafter leg separately, convert kg/m2 to kg/m.We calculate using the formula: N = rafter spacing x Q, Where
N - uniform load on the rafter leg, kg/m
rafter pitch - distance between rafters, m
Q - final roof load calculated above, kg/m²
It is clear from the formula that by changing the distance between the rafters, you can regulate the uniform load on each rafter leg. Typically, the pitch of the rafters is in the range from 0.6 to 1.2 m. For a roof with insulation, when choosing a pitch, it is reasonable to focus on the parameters of the insulation sheet.
In general, when determining the installation pitch of the rafters, it is better to proceed from economic considerations: calculate all the options for the location of the rafters and choose the cheapest and optimal in terms of quantitative consumption of materials for the rafter structure.
- Calculation of the cross-section and thickness of the rafter leg
In the construction of private houses and cottages, when choosing the section and thickness of the rafters, they are guided by the table below (the cross section of the rafters is indicated in mm). The table contains average values for the territory of Russia, and also takes into account the sizes building materials presented on the market. In general, this table is enough to determine what cross-section of timber you need to purchase.
However, we should not forget that the dimensions of the rafter leg depend on the design of the rafter system, the quality of the material used, constant and variable loads exerted on the roof.
In practice, when building a private residential building, boards with a cross section of 50x150 mm (thickness x width) are most often used for rafters.
Independent calculation of rafter cross-section
As mentioned above, rafters are calculated based on maximum load and deflection. In the first case, take into account maximum torque bending, in the second - the section of the rafter leg is checked for resistance to deflection over the longest section of the span. The formulas are quite complex, so we have chosen for you simplified version.
The section thickness (or height) is calculated using the formula:
a) If the roof angle< 30°, стропила рассматриваются как изгибаемые
H ≥ 8.6 x Lm x √(N / (B x Rben))
b) If the roof slope is > 30°, the rafters are flexurally compressed
H ≥ 9.5 x Lm x √(N / (B x Rben))
Designations:
H, cm- rafter height
Lm, m- working section of the longest rafter leg
N,
kg/m- distributed load on the rafter leg
B, cm- rafter width
Rizg, kg/cm²- bending resistance of wood
For pine and spruce Rizg depending on the type of wood is equal to:
It is important to check that the deflection does not exceed the permitted value.
The deflection of the rafters should be less L/200- length of the largest span being tested between supports in centimeters divided by 200.
This condition is true if the following inequality is satisfied:
3,125 xNx(Lm)³ / (BxH³) ≤ 1
N (kg/m) - distributed load per linear meter of rafter leg
Lm (m) - working section of the rafter leg of maximum length
B (cm) - section width
H (cm) - section height
If the value is greater than one, it is necessary to increase the rafter parameters B or H.
Sources used:
- SNiP 2.01.07-85 Loads and impacts with latest changes 2008
- SNiP II-26-76 “Roofs”
- SNiP II-25-80 “Wooden structures”
- SNiP 3.04.01-87 “Insulating and finishing coatings”
- A.A. Savelyev “Rafter systems” 2000
- K-G. Götz, Dieter Hoor, Karl Möhler, Julius Natterer “Atlas of wooden structures”