The rafter system is the main part of the blood, which perceives all the loads acting on the roof and resists them. To ensure the high-quality functioning of the rafters, the correct calculation of the parameters is required.
How to calculate the truss system
To make the calculation of the materials used in the truss system on our own, simplified calculation formulas are presented in order to increase the strength of the system elements. This simplification increases the amount of materials used, but if the roof has small dimensions, then such an increase will not be noticeable. Formulas allow you to calculate the following types of roofs:
- lean-to;
- gable;
- attic.
Video: calculation of the truss system
Calculation of the load on the rafters of a gable roof
For the construction of a sloping roof, a supporting strong frame is required, to which all other elements will be attached. When developing a project, the required length and cross-sectional area of the rafter beam and other parts are calculated truss system, which will be affected by variable and constant loads.
To calculate the system, it is necessary to take into account the peculiarities of the local climate Loads that act constantly:
- the mass of all elements of the roof structure, such as roofing material, lathing, waterproofing, thermal insulation, inner lining attic or attic;
- weight of equipment and various items, which are attached to the rafters inside the attic or attic.
Variable loads:
- load created by wind and precipitation;
- the mass of the worker who performs repairs or cleaning.
Variable loads also include seismic loads and other types of special loads that impose additional requirements on the roof structure.
The angle of inclination of the slope depends on the wind load In most areas Russian Federation the problem of snow load is acute - the rafter system must perceive the fallen mass of snow without deforming the structure (the requirement is most relevant for shed roofs). With a decrease in the angle of inclination of the roof, the snow load increases. Arrangement shed roof with a slope angle close to zero requires the installation of rafters with a large cross-sectional area, with a small step. You will also need to constantly clean it. This also applies to roofs with an angle of inclination up to 25 o.
The snow load is calculated using the formula: S = Sg × µ, where:
- Sg is the mass of snow cover on a flat horizontal surface 1 m 2 in size. The value is determined according to the tables in SNiP "Truss systems" based on the required area in which construction is underway;
- µ - coefficient taking into account the angle of inclination of the roof slope.
At an angle of inclination up to 25 0, the value of the coefficient is 1.0, from 25 o to 60 o - 0.7, over 60 o - the value of snow loads is not involved in the calculations.
The amount of precipitation affects the calculation of the roof The wind load is calculated using the formula: W = Wo × k, where:
- Wo - the magnitude of the wind load, determined according to the tabular values, taking into account the nature of the area where the construction is being carried out;
- k is a coefficient that takes into account the height of the building and the nature of the terrain.
With a building height of 5 m, the value of the coefficients is kA=0.75 and kB=0.85, 10 m - kA=1 and kB=0.65, 20 m - kA=1.25 and kB=0.85 .
Roof rafter section
Calculating the size of the rafter is not difficult, given the following point - the roof is a system of triangles (applies to all types of roofs). Having the overall dimensions of the building, the value of the angle of inclination of the roof or the height of the ridge, and using the Pythagorean theorem, the size of the length of the rafters from the ridge beam to the outer edge of the wall is determined. The length of the cornice is added to this size (in the case when the rafters protrude beyond the wall). Sometimes the cornice is made by mounting fillies. When calculating the roof area, the lengths of the filly and rafters are summed up, which allows you to calculate the required number roofing material.
The cross section of the beam for rafters depends on many parameters. To determine the cross section of the timber used in the construction of any type of roof, in accordance with the required length of the rafter, its installation step and other parameters, it is best to use reference books.
The range of dimensions of the rafter beam lies in the range from 40x150 to 100x250 mm. The length of the rafter is determined by the angle of inclination and the distance between the walls.
An increase in the slope of the roof entails an increase in the length of the rafter, and, accordingly, an increase in the cross-sectional area of \u200b\u200bthe beam. This is necessary in order to provide the necessary structural strength. At the same time, the level of snow load is reduced, which means that the rafters can be installed in large increments. But by increasing the step, you increase the total load that will affect the rafter.
When making a calculation, be sure to take into account all the nuances, such as humidity, density and quality of lumber, if the roof is made of wood, the thickness of the rolled metal used - if the roof is made of metal.
The basic principle of calculations is as follows - the magnitude of the load acting on the roof determines the size of the beam section. The larger the cross section, the stronger the structure, but the greater its total mass, and, accordingly, the greater the load on the walls and foundation of the building.
How to calculate the length of the gable roof rafters
The rigidity of the structure of the truss system is a mandatory requirement, and its provision eliminates deflection when exposed to loads. The rafters bend in case of errors in the calculations of the structure and the size of the step with which the rafter is installed. In the case when this defect is detected after the completion of work, it is necessary to strengthen the structure with struts, thereby increasing its rigidity. With a rafter beam length of more than 4.5 m, the use of struts is mandatory, since the deflection will be formed in any case under the influence of the own weight of the beam. This factor must be taken into account when performing calculations.
The length of the rafters depends on their location in the system. Determination of the distance between the rafters
The standard step with which the installation of rafters in a residential building is carried out is about 600–1000 millimeters. Its value is affected by:
It is not recommended to artificially reduce or increase the pitch of the rafters. The required number of rafters is determined taking into account the step with which they will be installed. For this:
- The optimal installation step is selected.
- The length of the wall is divided by the selected step and one is added to the resulting value.
- The resulting number is rounded up to an integer.
- The length of the wall is re-divided by the resulting number, thereby determining the desired installation step for the rafters.
The area of the truss system
When calculating the area gable roof the following factors need to be taken into account:
- The total area, which consists of the area of two slopes. Based on this, the area of \u200b\u200bone slope is determined and the resulting value is multiplied by the number 2.
- In the case when the sizes of the slopes differ from each other, the area of each slope is found individually. The total area is calculated by adding the obtained values for each slope.
- In the case when one of the angles of the slope is more or less than 90 °, in order to determine the area of \u200b\u200bthe slope, it is “broken” into simple figures and their area is calculated separately, and then the results are added.
- When calculating the area, the area of chimneys, windows and ventilation ducts.
- The area of gable and cornice overhangs, parapets and firewall walls is taken into account.
The calculation of the truss system depends on the type of roof For example, a house has a length of 9 m and a width of 7 m, a rafter beam has a length of 4 m, a cornice overhang is 0.4 m, a gable overhang is 0.6 m.
The value of the slope area is found by the formula S \u003d (L dd + 2 × L fs) × (L c + L ks), where:
- L dd - wall length;
- L fs - the length of the overhang of the gable;
- L c - the length of the rafter beam;
- L ks - the length of the overhang of the cornice.
It turns out that the area of the slope is S \u003d (9 + 2 × 0.6) × (4 + 0.4) \u003d 10.2 × 4.4 \u003d 44.9 m 2.
The total roof area is S = 2 × 44.9 = 89.8 m 2.
If tiles or soft covering in rolls are used as roofing material, then the length of the slopes will be 0.6–0.8 m less.
The size of a gable roof is calculated in order to determine the required amount of roofing material. With an increase in the angle of inclination of the roof, the consumption of material also increases. The stock should be about 10-15%. It is due to overlapping. To determine the exact amount of material, taking into account the slope of the slopes, it is best to use reference books.
Video: gable roof truss system
How to calculate the length of hip roof rafters
Despite the variety of types of roofs, their design consists of the same elements of the truss system. For hip roofs:
Video: hip roof truss system
What affects the angle of the rafters
For example, the slope of a shed roof is about 9–20 o, and depends on:
- type of roofing material;
- climate in the region;
- functional properties of the building.
In the case when the roof has two, three or four slopes, then in addition to the geography of construction, the purpose of the attic space will also have an impact. When the purpose of the attic is to store various property, then a large height is not required, and in the case of use as a living space, high roof equipment with a large angle of inclination will be required. Hence it follows:
- appearance of the facade of the house;
- roofing material used;
- influence of weather conditions.
Naturally, for areas with strong winds the best choice there will be a roof with a small angle of inclination - to reduce the wind load on the structure. This also applies to regions with a hot climate, where often the amount of precipitation is minimal. In areas with high precipitation (snow, hail, rain), a maximum roof slope is required, which can be up to 60 degrees. This angle of inclination minimizes the snow load.
The angle of inclination of the slope of any roof largely depends on the climate. As a result, for the correct calculation of the angle of inclination of the roof, it is necessary to take into account all the above factors, so the calculation will be carried out in the range of values from 9 ° to 60 °. Very often, the result of calculations shows that the ideal angle of inclination lies in the range from 20 ° to 40 °. With these values, it is allowed to use almost all types of roofing materials - corrugated board, metal tiles, slate and others. But it should be noted that each roofing material also has its own requirements for roof construction.
Without the dimensions of the rafters, it is impossible to start the construction of the roof. Take this matter seriously. Do not limit yourself only to the calculations of the truss system, the choice of its design and the determination of the existing loads. Building a house is an integral project in which everything is interconnected. In no case should such elements as the foundation, the supporting structure of the walls, the rafters, the roof, be considered separately. A high-quality project necessarily takes into account all factors in a comprehensive manner. And if you plan to build housing for your own needs, then best solution there will be an appeal to specialists who will solve pressing issues and perform design and construction without errors.
Introducing a free calculator for gable roof calculations. Online calculation of the crate, the angle of the rafters and the required amount of materials.
Specify roofing material:
Select a material from the list -- Slate (corrugated asbestos-cement sheets): Medium profile (11 kg/m2) Slate (corrugated asbestos-cement sheets): Reinforced profile (13 kg/m2) Corrugated cellulose-bitumen sheets (6 kg/m2) Bituminous (soft , flexible) tiles (15 kg/m2) Galvanized sheet metal (6.5 kg/m2) Sheet steel (8 kg/m2) Ceramic tiles (50 kg/m2) Cement-sand tiles (70 kg/m2) Metal tiles, corrugated board (5 kg/m2) Keramoplast (5.5 kg/m2) Seam roof (6 kg/m2) Polymer-sand tile (25 kg/m2) Ondulin (Euro slate) (4 kg/m2) Composite tile (7 kg/m2) ) Natural slate (40 kg/m2) Specify the weight of 1 square meter of coating (? kg/m2)
kg/m2
Enter roof parameters:
Base Width A (cm)
Base length D (cm)
Lift height B (cm)
Length of side overhangs C (cm)
Front and rear overhang length E (cm)
Rafter:
Rafter pitch (cm)
Type of wood for rafters (cm)
Working section of the side rafter (optional) (cm) ">
Lathing calculation:
Purlin board width (cm)
Lathing board thickness (cm)
Distance between decking boards
F(cm)
Snow load calculation:
Select your region using the map below
1 (80/56 kg/m2) 2 (120/84 kg/m2) 3 (180/126 kg/m2) 4 (240/168 kg/m2) 5 (320/224 kg/m2) 6 (400/280 kg/m2) 7 (480/336 kg/m2) 8 (560/392 kg/m2)
Wind load calculation:
Ia I II III IV V VI VII
Height to building ridge
5 m from 5 m to 10 m from 10 m
Terrain type
Open area Closed area Urban areas
Calculation results
Roof pitch: 0 degrees.
The angle of inclination is suitable for this material.
The angle of inclination for this material is desirable to increase!
It is desirable to reduce the angle of inclination for this material!
Roof surface area: 0 m2.
Approximate weight of roofing material: 0 kg.
Number of rolls of insulation material with 10% overlap (1x15 m): 0 rolls.
Rafter:
Load on the truss system: 0 kg/m2.
Rafter length: 0 cm
Number of rafters: 0 pcs
Lathing:
Number of rows of lathing (for the entire roof): 0 rows.
Uniform distance between the boards of the crate: 0 cm
The number of boards of the crate with a standard length of 6 meters: 0 pcs
Volume of boards of an obreshetka: 0 m 3 .
Approximate weight of the boards of the crate: 0 kg.
More information about the calculator
The online gable (gable) roof calculator will help you calculate the angle of the slope, the size and number of rafters, the number of sheathing, as well as the amount of materials needed online. Such common roofing materials as metal tile, slate, ondulin, tiles made of ceramics, bitumen, cement and other materials have been entered into the calculation base in advance.
Note! Calculations are made on the basis of SNiP "Loads and Impacts" and TCP 45-5.05-146-2009, taking into account the standards contained in these documents.
Gable roof (there are also spellings "gable roof", "gable roof") - a variant of the roof with two slopes going from the ridge to the outer walls of the building. Today it is the most common type of roofs, due to the ease of execution, low cost and attractive appearance.
The rafters in the construction of such a roof in pairs lean against each other and are connected by a crate. The end sides of a structure with such a roof are triangular in shape and are called pediments (sometimes tongs). Usually, an attic is arranged under a gable roof, and small attic windows are made on the gables for lighting.
When filling out the fields of the calculator, pay attention to the icon "Additional Information", under which explanations are hidden for each item.
The calculation results are also accompanied by explanations, which you can find below.
Explanations for the calculation results
Roof slope
This is the name of the angle at which the slope and rafters are inclined to the plane of the ceiling. The calculations are made taking into account the fact that it is planned to build a symmetrical gable roof. By entering an angle, you can not only calculate right amount materials for a given angle, but also to check if it is possible to build a roof at this angle from the materials you have chosen. You can reduce or increase the angle by changing the width of the base or the height of the lift: these parameters are tightly interconnected.
Roof surface area
The total area of the roof slopes, including the area of overhangs of a given length. Determines the amount of roofing and subroofing material required in the construction of the roof.
Approximate weight of roofing material
The estimated total weight of the roofing material.
Number of rolls of insulating material
The required amount of roofing material, taking into account the required overlap of 10%. In calculations, we proceed from rolls 15 meters long and 1 meter wide.
Load on the truss system
The maximum possible load, taking into account wind and snow loads, attributable to the rafters.
Rafter length
Rafters are measured from the base of the slope to the ridge of the roof.
Number of rafters
The total number of rafters required for a roof truss system at a given pitch.
Minimum section of rafters
To provide the roof with sufficient strength, it is necessary to choose rafters with the section options proposed here.
Number of rows of battens
With the parameters you set, this number of rows of crates will be required. If you need to determine the number of rows for one slope, then this value must be divided by 2.
Uniform spacing between boards
To eliminate the overspending of materials and save yourself from unnecessary trimming work, you need to choose a given distance between the boards of the crate.
The volume of boards of the crate
The number of boards required for the sheathing of the entire roof (in cubic meters).
The gable roof is formed on the basis of a frame that combines the elementary nature of the device and unsurpassed reliability. But the backbone of the roof in two rectangular slopes can boast of these advantages only in the case of a careful selection of rafter legs.
Parameters of the gable roof truss system
It is worth starting the calculations if you understand that the truss 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 truss 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" denotes the height and is self-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 say that the width of half of 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).
To the figure obtained from the Pythagorean formula, 60–70 cm should be added. Extra centimeters will be needed to take the rafter leg out of the wall and make the necessary cuts.
The six-meter rafter is the longest, therefore it is suitable as a rafter leg
The maximum length of a beam used as a rafter leg is 6 m. If a strong board of greater length is required, then they resort to the method of fusion - nailing a segment from another beam to the rafter leg.
Section of rafter legs
For various elements truss system has its own standard sizes:
- 10x10 or 15x15 cm - for Mauerlat timber;
- 10x15 or 10x20 cm - for the rafter leg;
- 5x15 or 5x20 cm - for running and brace;
- 10x10 or 10x15 cm - for the rack;
- 5x10 or 5x15 cm - for lying down;
- 2x10, 2.5x15 cm - for purlins.
The thickness of each part of the supporting structure of the roof 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 section of the rafter legs of a gable roof is affected by:
The pitch of the rafters affects the cross section of the rafter legs most significantly. An increase in the distance between the bars entails an increase in pressure on the supporting structure of the roof, and this obliges the builder to use thick rafter legs.
Table: cross-section of rafters depending on length and pitch
Variable impact on the truss system
The pressure on the rafter legs is constant and variable.
From time to time and with varying intensity, wind, snow and precipitation affect the supporting structure of the roof. In general, the roof slope is comparable to a sail, which is under pressure natural phenomena may break.
The wind tends to overturn or raise 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 \u003d Wo × kxc, where W is the wind load indicator, Wo is the value of the wind load characteristic of a certain area of \u200b\u200bRussia, k is a correction factor determined by the height of the structure and the nature of the terrain, and c is the aerodynamic coefficient.
The aerodynamic coefficient can range from -1.8 to +0.8. A minus value is typical for a rising roof, and a positive value is for a roof that is being pressed by the wind. In a 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 recognized from map 3 of Appendix 5 in SNiP 2.01.07–85 and a special table. The coefficient that takes into account the change in wind pressure with height is also standardized.
Table: standard value of wind pressure
Table: value of coefficient k
The wind load is not only affected by the terrain. Great importance has a housing area. Behind the wall of tall buildings, the house is almost in no danger, but in open space the wind can become a serious enemy for it.
The snow load on the rafter system is calculated by the formula S = Sg × µ, that is, the weight snow mass per 1 m² is multiplied by a correction factor, the value of which reflects the degree of slope of the roof.
The weight of the snow layer is indicated in the SNiP "Truss Systems" and is determined by the type of area where the building was built.
Snow load on the roof depends on where the house is located
The correction factor, if the roof slopes heel 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 tilted more than 60 degrees, the snow load is discounted. Still, snow rolls off a steep roof quickly, without having time to have a negative impact on the rafters.
Permanent loads
Continuous loads are considered to be the weight of the roofing pie, including the lathing, insulation, films and Decoration Materials for the attic.
Roofing cake creates constant pressure on the rafters
The weight of a roof is the sum of the weights of all the materials used in the construction of the roof. On average, it is 40–45 kg / sq.m. According to the rules, 1 m² of the truss system should not account for more than 50 kg of the weight of roofing materials.
So that there is no doubt about the strength of the rafter system, 10% should be added to the calculation of the load on the rafter legs.
Table: weight of roofing materials per 1 m²
| Type of roof finish | Weight in kg per 1 m² |
| Rolled bitumen-polymer sheet | 4–8 |
| Bitumen-polymer soft tile | 7–8 |
| Ondulin | 3–4 |
| metal tile | 4–6 |
| Decking, seam roofing, galvanized metal sheets | 4–6 |
| Cement-sand tiles | 40–50 |
| Ceramic tiles | 35–40 |
| Slate | 10–14 |
| slate roof | 40–50 |
| Copper | 8 |
| green roof | 80–150 |
| Draft flooring | 18–20 |
| crate | 8–10 |
| The truss system itself | 15–20 |
Number of bars
How many rafters will be needed to equip the frame of a gable roof is set by dividing the width of the roof by a step between the bars and adding one to the resulting value. It indicates an additional rafter that will need to be placed on the edge of the roof.
Suppose it is 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 (taking into account the additional timber).
The gable roof truss system is a construction of a certain number of rafters
The step of the beams of the supporting structure of the roof
To determine the distance between the beams of the supporting structure of the roof, 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 slope of the roof;
- level of wind and snow loads.
After 90-100 cm, it is customary to place the rafters in the case of choosing a light roofing material
A step of 60–120 cm is considered normal for rafter legs. The choice in favor of 60 or 80 cm is made in the case of the construction of a roof inclined by 45˚. The same small step should be, if desired, to cover wooden frame roofs with heavy materials such as ceramic tiles, asbestos-cement slates and cement-sand tiles.
Table: rafter pitch depending on length and section
Formulas for calculating the truss system of a gable roof
The calculation of the truss system comes down to setting the pressure on each beam and determining the optimal section.
When calculating the truss system of a gable roof, they act as follows:
- According to the formula Qr \u003d AxQ, they find out what is the load on running meter each rafter leg. Qr is the distributed load per linear meter of the rafter leg, expressed in kg/m, A is the distance between the rafters in meters, and Q is the total load in kg/m².
- They proceed to the determination of the minimum cross-section of the beam-rafter. To do this, study the data of the table listed in GOST 24454–80 “Softwood lumber. Dimensions".
- Focusing on standard parameters, choose the width of the section. And the height of the section is calculated using the formula H ≥ 8.6 Lmax sqrt (Qr / (B Rbend)) if the roof slope α< 30°, или формулу H ≥ 9,5·Lmax·sqrt(Qr/(B·Rизг)), когда уклон крыши α >30°. H is the height of the section in cm, Lmax is the working section of the rafter leg of maximum length in meters, Qr is the distributed load per linear meter of the rafter leg in kg / m, B is the section width cm, Rbend is the resistance of wood to bending, kg / cm². If the material is made from pine or spruce, then Rizg can be equal to 140 kg / cm² (wood grade 1), 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 more than the figure that results from dividing L by 200. L is the length of the working area. The compliance of the deflection value with the L / 200 ratio is feasible only if the inequality 3.125 Qr (Lmax)³ / (B H³) ≤ 1 is true. Qr indicates 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 width of the section (cm), and H is the height of the section (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 | - |
An example of the calculation of the supporting structure
Assume that α (roof pitch) = 36°, A (rafter spacing) = 0.8 m, and Lmax (maximum rafter length) = 2.8 m. , which means that Rizg \u003d 140 kg / cm².
Cement-sand tiles were chosen for the roof covering, and therefore the weight of the roof is 50 kg/m². The total load (Q) experienced by each square meter, is equal to 303 kg / m². And for the construction of the truss system, bars 5 cm thick are used.
From this follow the following computational steps:
- Qr=A·Q= 0.8·303=242 kg/m - distributed load per linear meter of rafter beam.
- H ≥ 9.5 Lmax sqrt(Qr/B Rbend).
- 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).
Table standard sizes you need to find the height of the rafter section, 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 index in the regulatory documents, and this is proved by the inequality 3.125 Qr (Lmax)³ / B H³ ≤ 1. Substituting into it the values (3.125 242 (2.8)³ / 5 (17, 5)³), it turns out that 0.61< 1. Можно сделать вывод: сечение пиломатериала выбрано верно.
Video: detailed calculation of the truss system
The calculation of the gable roof truss system is a whole complex of calculations. In order for the bars 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 step between the rafters should be.
When designing the roof rafters of a private house, you need to be able to correctly calculate the angle of the roof. How to navigate in various units of measurement, what formulas to calculate and how the angle of inclination affects the wind and snow load of the roof, we will talk in this article.
The roof of a private house built according to individual project, can be very simple or surprisingly whimsical. The slope angle of each slope depends on architectural solution the whole house, the presence of an attic or attic, the roofing material used, the climatic zone in which it is located household plot. In a compromise of these parameters, it is necessary to find the optimal solution that combines the strength of the roof with beneficial use roof space and appearance house or building complex.
Roof angle units
The angle of inclination is the value between the horizontal part of the structure, slabs or floor beams, and the roof surface or rafters.
In reference books, SNiP, technical literature, there are various units for measuring angles:
- degrees;
- aspect ratio;
- interest.
Another unit for measuring angles - radians - is not used in such calculations.
What are degrees, everyone remembers from the school curriculum. The ratio of the sides of a right-angled triangle, which is formed by the base - L, height - H (see the figure above) and the roof deck is expressed as H: L. If α = 45°, the triangle is equilateral and the ratio of sides (legs) is 1:1. In the case when the ratio does not give a clear idea of the slope, they speak of a percentage. This is the same ratio, but calculated in shares converted to percentages. For example, with H = 2.25 m and L = 5.60 m:
- 2.25 m / 5.60 m 100% = 40%
The digital expression of some units through others is clearly shown in the diagram below:
Formulas for calculating the angle of inclination of the roof, the length of the rafters and the area covered by the roofing material
To easily calculate the dimensions of the elements of the roof and truss system, you need to remember how we solved problems with triangles at school, using basic trigonometric functions.
How does this help in calculating the roof? We break complex elements into simple right-angled triangles and find a solution for each case using trigonometric functions and the Pythagorean theorem.
More complex configurations are more common.
For example, you need to calculate the length of the rafters of the end part of the hip roof, which is an isosceles triangle. From the vertex of the triangle we lower the perpendicular to the base and get right triangle, whose hypotenuse is the midline of the end of the roof. Knowing the width of the span and the height of the ridge, from a structure divided into elementary triangles, you can find the angle of the hip - α, the angle of the roof - β and get the length of the rafters of a triangular and trapezoidal slope.
Calculation formulas (length units must be the same - m, cm or mm - in all calculations to avoid confusion):
Attention! The calculation of the lengths of the rafters according to these formulas does not take into account the size of the overhang.
Example
The roof is hipped, hipped. Ridge height (CM) - 2.25 m, span width (W / 2) - 7.0 m, depth of inclination of the end part of the roof (MN) - 1.5 m.
Having obtained the values of sin(α) and tg(β), you can determine the value of the angles using the Bradis table. A complete and accurate table with an accuracy of up to a minute is a whole brochure, and for rough calculations, which are acceptable in this case, you can use a small table of values.
Table 1
| Roof pitch, in degrees | tg(a) | sin(a) |
| 5 | 0,09 | 0,09 |
| 10 | 0,18 | 0,17 |
| 15 | 0,27 | 0,26 |
| 20 | 0,36 | 0,34 |
| 25 | 0,47 | 0,42 |
| 30 | 0,58 | 0,50 |
| 35 | 0,70 | 0,57 |
| 40 | 0,84 | 0,64 |
| 45 | 1,00 | 0,71 |
| 50 | 1,19 | 0,77 |
| 55 | 1,43 | 0,82 |
| 60 | 1,73 | 0,87 |
| 65 | 2,14 | 0,91 |
| 70 | 2,75 | 0,94 |
| 75 | 3,73 | 0,96 |
| 80 | 5,67 | 0,98 |
| 85 | 11,43 | 0,99 |
| 90 | ∞ | 1 |
For our example:
- sin(α) = 0.832, α = 56.2° (obtained by interpolating neighboring values for angles of 55° and 60°)
- tg(β) = 0.643, β = 32.6° (obtained by interpolation of neighboring values for angles of 30° and 35°)
Remember these numbers, they will be useful to us when choosing a material.
To calculate the amount of roofing material, you will need to determine the area of \u200b\u200bcoverage. The area of the slope of a gable roof is a rectangle. Its area is the product of the sides. For our example - a hip roof - this comes down to determining the areas of a triangle and a trapezoid.
For our example, the area of one end triangular slope with CN = 2.704 m and W / 2 = 7.0 m (the calculation must be performed taking into account the extension of the roof beyond the walls, we take the length of the overhang - 0.5 m):
- S \u003d ((2.704 + 0.5) (7.5 + 2 x 0.5)) / 2 \u003d 13.62 m 2
The area of one side trapezoidal slope at W = 12.0 m, H c = 3.905 m (trapezoid height) and MN = 1.5 m:
- L k \u003d W - 2 MN \u003d 9 m
We calculate the area, taking into account overhangs:
- S \u003d (3.905 + 0.5) ((12.0 + 2 x 0.5) + 9.0) / 2 \u003d 48.56 m 2
The total area covered by four slopes:
- S Σ \u003d (13.62 + 48.46) 2 \u003d 124.16 m 2
Roof slope recommendations depending on the purpose and material
An unused roof may have minimum angle tilt 2-7°, which provides immunity to wind loads. For normal snow melting, it is better to increase the angle to 10 °. Such roofs are common in the construction of outbuildings, garages.
If the roof space is supposed to be used as an attic or attic, the slope of a single or gable roof must be large enough, otherwise the person will not be able to straighten up, and the usable area will be “eaten up” by the truss system. Therefore, it is advisable to use in this case a sloping roof, for example, a mansard type. The minimum ceiling height in such a room should be at least 2.0 m, but it is desirable for a comfortable stay - 2.5 m.
Options for arranging the attic: 1-2. Double pitched roof classic. 3. Roof with a variable angle of inclination. 4. Roof with remote consoles
Taking this or that material as roofing, it is necessary to take into account the requirements for the minimum and maximum slope. Otherwise, there may be problems that require repair of the roof or the entire house.
table 2
| roof type | Range of permissible mounting angles, in degrees | Optimum roof slope, in degrees |
| Roofing with roofing | 3-30 | 4-10 |
| Tole roof, two-layer | 4-50 | 6-12 |
| Zinc roofing with double standing seams (zinc strips) | 3-90 | 5-30 |
| Tole roof, simple | 8-15 | 10-12 |
| Sloping roof covered with roofing steel | 12-18 | 15 |
| Groove tile with 4 grooves | 18-50 | 22-45 |
| shingle roof | 18-21 | 19-20 |
| Grooved tiles, normal | 20-33 | 22 |
| Decking | 18-35 | 25 |
| Corrugated Asbestos Cement Sheet | 5-90 | 30 |
| artificial slate | 20-90 | 25-45 |
| Slate roof, double layer | 25-90 | 30-50 |
| Slate roof, normal | 30-90 | 45 |
| glass roof | 30-45 | 33 |
| Roof tiles, two-layer | 35-60 | 45 |
| Grooved Dutch tile | 40-60 | 45 |
The tilt angles obtained in our example are in the range of 32-56°, which corresponds to slate roof, but does not exclude some other materials.
Determination of dynamic loads depending on the angle of inclination
The design of the house must withstand static and dynamic loads from the roof. Static loads are the weight of the truss system and roofing materials, as well as the equipment of the under-roof space. This is a constant value.
Dynamic loads are variable values depending on the climate and season. In order to correctly calculate the loads, taking into account their possible compatibility (simultaneity), we recommend studying SP 20.13330.2011 (sections 10, 11 and Appendix G). In full, this calculation, taking into account all possible factors in a particular construction, cannot be presented in this article.
The wind load is calculated taking into account the zoning, as well as the location features (leeward, windward side) and the angle of the roof, the height of the building. The calculation is based on wind pressure, the average values of which depend on the region of the house under construction. The remaining data are needed to determine the coefficients that correct a relatively constant value for the climatic region. The larger the angle of inclination, the more serious wind loads the roof experiences.
Table 3
Snow load, unlike wind load, is related to the angle of the roof in the opposite way: the smaller the angle, the more snow lingers on the roof, the lower the probability of snow cover convergence without the use of additional means, and the greater the load the structure experiences.
Table 4
Approach the issue of determining loads seriously. The calculation of sections, designs, and hence the reliability and cost of the truss system depends on the values obtained. If you are not confident in your abilities, it is better to order a load calculation from specialists.
The roof is one of the main elements of the roof, which takes on all the impacts coming from the atmosphere.
The main function is to drain water and disperse the load on the top of the building after snow falls.
Quality roofing is valued for long-term operation and nice appearance.
Roof calculation online (calculator with drawings) - will help you make a reliable calculation of the amount of roofing, rafters and battens.
In construction, there are several types of coatings, which in turn are further divided into subspecies. The most common building surfaces are flat(sometimes operated and non-operated) and attic(this includes a whole group of roofs:, conical and others). Without a doubt, when it comes to choosing the type of roof, a further definition of the surface material becomes relevant.
The most popular types include:
- , aluminum seam and other metal roofs;
- slate coating;
- roof made from natural materials.
Roofing materials
As part of the truss system includes many construction "spare parts", but the main ones in this wide list are:
- slopes (inclined planes),
- crate,
- rafters,
- mauerlat bar.
In addition, a gutter, aerator, drainage pipe and others take a certain role in the process of shelter and further functioning of the shelter.
The truss system is represented as a carrier system, which is based on inclined rafter legs, vertical racks, as well as inclined struts. In some cases, it becomes necessary to use rafter beams, which will “tie” the rafter legs. There are hanging and layered rafters. In the first group, trusses with sleepers are separately distinguished.
Roof device
The next layer in the design mansard roof serves as crate, which is laid over the legs of the truss system. Thus, a certain foundation for the roofing deck appears, and the spatial component of the eaves also expands significantly. Most often, this element is made of either wood or metal.
Mauerlat also adheres to its niche of responsibility. It acts as a support for the rafters along the edges., and put it on outer wall along the perimeter. The beam is usually lumber (tobish made of wood), but it is quite reasonable if, in the case of a special metal frame, similar contents will be used to prepare the Mauerlat.
Roof calculation online calculator
How to calculate the roof of a house and how to calculate the material for the roof quickly and without errors? In this you can specially designed service - construction calculator for calculating the roof of a private house. The calculator calculates the amount, weight, and more.
Calculator field designations
Specify roofing material:
Select a material from the list -- Slate (corrugated asbestos-cement sheets): Medium profile (11 kg/m2) Slate (corrugated asbestos-cement sheets): Reinforced profile (13 kg/m2) Corrugated cellulose-bitumen sheets (6 kg/m2) Bituminous (soft , flexible) tiles (15 kg/m2) Galvanized sheet metal (6.5 kg/m2) Sheet steel (8 kg/m2) Ceramic tiles (50 kg/m2) Cement-sand tiles (70 kg/m2) Metal tiles, corrugated board (5 kg/m2) Keramoplast (5.5 kg/m2) Seam roof (6 kg/m2) Polymer-sand tile (25 kg/m2) Ondulin (Euro slate) (4 kg/m2) Composite tile (7 kg/m2) ) Natural slate (40 kg/m2) Specify the weight of 1 square meter of coating (? kg/m2)
kg/m2
Enter the roof parameters (photo above):
Base Width A (cm)
Base length D (cm)
Lift height B (cm)
Length of side overhangs C (cm)
Front and rear overhang length E (cm)
Rafter:
Rafter pitch (cm)
Type of wood for rafters (cm)
Working section of the side rafter (optional) (cm)
Lathing calculation:
Purlin board width (cm)
Lathing board thickness (cm)
Distance between decking boards
F(cm)
Snow load calculation (pictured below):
Choose your region
1 (80/56 kg/m2) 2 (120/84 kg/m2) 3 (180/126 kg/m2) 4 (240/168 kg/m2) 5 (320/224 kg/m2) 6 (400/280 kg/m2) 7 (480/336 kg/m2) 8 (560/392 kg/m2)
Wind load calculation:
Ia I II III IV V VI VII
Height to building ridge
5 m from 5 m to 10 m from 10 m
Terrain type
Open area Closed area Urban areas
Calculation results
Roof pitch: 0 degrees.
The angle of inclination is suitable for this material.
The angle of inclination for this material is desirable to increase!
It is desirable to reduce the angle of inclination for this material!
Roof surface area: 0 m2.
Approximate weight of roofing material: 0 kg.
Number of rolls of insulation material with 10% overlap (1x15 m): 0 rolls.
Rafter:
Load on the truss system: 0 kg/m2.
Rafter length: 0 cm
Number of rafters: 0 pcs
Lathing:
Number of rows of lathing (for the entire roof): 0 rows.
Uniform distance between the boards of the crate: 0 cm
The number of boards of the crate with a standard length of 6 meters: 0 pcs
Volume of boards of an obreshetka: 0 m 3 .
Approximate weight of the boards of the crate: 0 kg.
Snow load region
Explanation of calculator fields
Loads acting on the roof
It is likely that when it comes to choosing the type of roof and roofing, one should be guided by more than just visual requirements. First of all, it is necessary to pay attention to studying the issue of the load on the hip.
NOTE!
The roof is affected not only by precipitation and their volumes- temperature instability and various causes of physical and mechanical origin also exert serious pressure on the surface.
There are many reasons and sources of influence, but the leading ones are snow and wind. What can we say if building codes require without fail calculations for the future canopy. The calculation has a pronounced individuality in view of the differences in the volume of snow cover that falls in a particular region.
The wind load is not as harmless as it might seem at first glance. In some cases, we have to talk about the load due to the weight of one of the elements of the hip. Most often, the crate or roof acts as a weighting agent.
The topical issue of load is faced by those who is going to use the attic space all year round. In this case, large-scale insulation is necessary (slopes, side walls, etc.), which leads to a significant increase in the pressure force on the surface of the walls. When the attic is not planned to be transferred to a living space, then only one floor needs to be insulated.
The load-bearing structure of the eaves can also exert a noticeable load due to its own weight. In this situation, the load indicators are determined taking into account the average density of materials and the design values of the parameters of a constructive and geometric nature.
All of the above factors of influence are not so easy to analyze, but fortunately, all the necessary SNiPs have long been developed, the norms of which can be consulted at any time.
Cover area calculation
Inevitable in any canopy design. If the surface of the house will be displayed in a shed plane, then you are very lucky with the calculations.
In such conditions, measure the length and width of the structure, add up the indicators of conditional overhangs and then multiply the two results one by the other.
When it comes to the roof, then several more positions should be used in the calculation, including the angle of inclination of one or another element. First of all, we recommend dividing all capacious parts of the coating into certain parts (for example, into triangles).
In the case of a gable surface, the area of each inclination should be multiplied individually by the cosine of the oblique angle. The slope angle is a figure taken from the intersection of the slope and the floor. As for measuring the length of one inclined, the mentioned parameter should be fixed at the available distance from the ridge to the edge of the eaves.
Roof area calculation
Therefore, the solution algorithm in all projects that use pitched eaves is similar. Upon completion of the marked actions, in order to find out the area of \u200b\u200bthe house dome, you will need to sum up the results obtained.
At construction warehouses and in related stores, slopes with the shape of an irregular polygon can be sold. In this case, remember the advice that has already sounded in the material - divide the plane into identical geometric shapes and, after completing the calculations, simply add them together.
Calculation of the amount of materials for the roof on the example of metal tiles
The metal tile should begin to be considered from the angle of inclination, which was already mentioned in the previous paragraph. If we talk about extremes, then there are all theoretical grounds for saying about 11-70 degree interval. That's just practice, as you know, makes its own adjustments and they do not always coincide with theory.
Experts claim that 45 degrees is the optimal angle of inclination.
Especially when it comes to the roof of the house, which is located in an area with minimal rainfall, which does not require significant slopes. If snow is a fairly frequent guest, then 45 degrees will be the most the best options, that's just because of the increase in wind pressure, it will be necessary to strengthen the crate and truss system. In addition, the greater the slope, the more material will go to the eaves.
Consider the calculation algorithm using the example of a gable roof:
- Let the oblique angle be expressed by the letter A, and ½ of the covered span - B, the height will be H.
- We introduce an action to find the tangent, which is solved by dividing H by B. We know the mentioned values, therefore, using the Bradis table, we find the value of the angle of inclination A through the arc tangent (H / B).
- It is better to use a calculator that can calculate inverse trigonometric functions to solve such serious actions. Then, multiplying B by the length of the cover, we find the area of \u200b\u200beach inclination.
Regarding material costs, such calculations are already addressed at the final design stage. First you need to calculate the surface area that will be laid and directly the dimensions of the roofing material. Let's take a metal tile as an example.
roof area
So, the parameter of the real width is 1180 mm, the effective one is 1100 mm. Now we turn to calculating the length of the coverage of the house, which we have already talked about. Since we are analyzing a fictitious calculation as an example, let the mentioned indicator be equal to 6 meters.
We divide this number by the effective width and get 5.45. The solution of the action displays the number of sheets needed, and since the number did not turn out to be an integer, for obvious reasons we round it up.
Thus, we need 6 sheets of metal tiles for flooring one row along the length of the eaves. We proceed to the calculation of the number of sheets vertically.
For measuring vertical row the size of the overlap should be taken into account (usually taken at a value of 140-150 mm), the distance between the ridge and the cornice, as well as the length of the cornice overhang.
Let the distance be 4 meters, and the overhang - 30 cm. Having made a simple addition, we get a size of 4.3 meters. Let's take the conditional length of a metal tile sheet as 1 meter. Taking into account the overlap, the effective length of one roofing unit will be 0.85 m.
After that, we divide the result of 4.3 m by the effective length and at the end we get 5.05 sheets. In such a small deviation from a whole number, we advise you to round down.
Calculation of steam and waterproofing
- and it is considered very simple. To do this, you just need to divide the covered area by the same parameter of the roofing deck. For example, we are talking about a gable canopy.
Conventionally, we take a slope length of 5 meters and a width of 4 m. Therefore, the area of \u200b\u200bone unit is 20 square meters. m, and the total figure for two slopes will be 40 square meters. m. Steam and waterproofing material is considered to be in rolls.
Useful video
Video instruction for calculating the roof:
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