How to calculate the truss system. Do-it-yourself calculation of the truss system
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When planning the construction of low-rise residential, utility or commercial buildings, most designers choose a gable roof structure. This is due to the relatively simple installation technology, increased reliability of the design, effective removal of precipitation from the roof and unpretentiousness to operating conditions. However, to achieve all the benefits, you need to correctly design and install the rafters for a gable roof with your own hands.
Exterior of a house with a gable roof
Gable roofs are two inclined rectangular planes (slopes), which are supported by a rafter system. The side parts are made deaf or windows and sheathing are installed on them. The main parameters of such a roof are: the angle of inclination and the location of the ridge relative to the center line passing through the walls perpendicular to the slopes. That is, a gable structure does not have to have the same slope of the slopes or have a symmetrical appearance.
Many original designs use asymmetrical sloping designs to accommodate certain climate conditions or to improve façade design. It is worth noting that such solutions are very original, but in practice they are quite difficult to implement. This is due to the following reasons:
- The load on the walls and foundation increases at the place where the roof ridge is displaced. As a result, calculations can be significantly more complicated, especially when heavy roofing materials such as slate or ceramic tiles are used.
- It is required to produce separate structural elements for each slope, which can significantly increase the construction time.
- The roof at large angles of inclination of the slopes can be significantly affected by the pressure of wind flows. Therefore, it will be necessary to take into account the predominant direction of the winds in the calculations.
The main elements of the pitched roof system
Before you make rafters on a gable roof, you need to create a project, as well as study all the structural elements. You will need to design the following main nodes:
- Mauerlat. It ensures the transfer of the load of the roof structure to the load-bearing walls of the object, creating its uniform distribution. The beam is made from hardwoods such as larch, oak, ash. The minimum allowable cross section is 100x100 mm. It is allowed to use not only solid timber, but also glued, but with a section of 100x150 mm.
- rafters. The main structural element, which is designed to form a supporting frame, perceive the load of the roofing material through the crate and transfer the load to the Mauerlat. The distance between the rafters of a gable roof is from 0.6 to 1.2 m, depending on the weight of the roofing material and the amount of precipitation in a particular area.
- puff. A special design used to fix two inclined beams of slopes at a given angle of inclination, which is mounted at a level just above the beams or slightly below the ridge. It is used in layered types of roofs.
- Rack. It is a vertically installed and firmly fixed element that performs the load-bearing functions of the roof. It is usually installed on the walls of the building to partially transfer the load of the roof. Gives additional rigidity to the structure.
- Run. There are two types: side and ridge. The side beam is a bar supported on racks and located parallel to the ridge beam. Helps prevent bending of the ramp under significant loads. The ridge run is installed along the line of junction of one slope to another and serves as a support for the ridge.
- Strut. Represents auxiliary supports for racks, which are located at an angle of 45 0 to the load-bearing beams of the ramps in order to increase the contact area with the racks and reduce the risk of ramp deformation.
- Sill. Serves as a fulcrum for the strut and strut.
- crate. It is used to fix the truss system in the transverse direction, transfer the load of the roofing material and its fastening, as well as ensure resistance to loads in the runs between the supporting beams.
Helpful information! Struts for the northern regions due to increased snow and ice loads on the roofs can be installed not only longitudinally, but also diagonally. Thus, a significant part of the load is perceived by the racks, and not by the walls of the building.
Calculation of the length and pitch of the rafters
When installing rafters for a gable roof with your own hands, you need to observe the fixing step of 0.6-1 m. The choice depends on the calculated loads, taking into account the margin of safety. The smaller the step, the stronger the structure and the greater the consumption of building materials. A large interval of 0.8-1 m is allowed to be used only when laying light roofing sheets and slope angles of 15 0 -20 0. It is recommended to choose a step within 0.6-0.8 m.
The length of the beams, knowing the angle of inclination of the slopes and the distance between the two walls of the object, is quite simple to calculate using the Pythagorean theorem. However, the actual length must be increased by 60-70 cm, which will go to their docking, as well as to the overhang of the slopes of about 0.5-0.6 m.
Rafters are the backbone of any roof. They bear the main load associated with the weight of the roof, wind and snow pressure. For long-term and trouble-free operation of the roof, it is important to make accurate calculations of these loads, determine the strength characteristics of the rafters, their cross section, length, quantity, as well as the amount of material required for the arrangement of the roof frame. All these calculations can be done independently.
Calculation of rafters using online programs
It is easiest to calculate the rafters using an online calculator. You set the initial data, and the program calculates the necessary parameters. Existing programs are different in their functionality. A number of them are complex in nature and calculate many parameters of the truss system, others are much simpler and involve the calculation of one or two indicators. Among the complex services, it is worth highlighting the Stroy-calc series of construction calculators for calculating the parameters of roof rafters with one, two slopes, an attic and hips.
The Stroy-calc calculator is used to calculate the parameters of roof rafters with one, two slopes, an attic and hips
The program also takes into account the roofing material, i.e., together with the calculation of the truss system, you can obtain data on the required amount of finishing coating from:
- ceramic tiles;
- cement-sand tiles;
- bituminous tiles;
- metal tiles;
- slate (asbestos-cement slabs);
- steel seam roof;
- bituminous slate.
In order to obtain the desired result, the following information is entered:
- roof characteristics: roofing material, base width, base length, rise height, overhang length;
- rafter characteristics: rafter pitch, type of wood for rafters;
- lathing characteristics: width, board thickness, distance between rows;
- snow load on the rafters: selection of the snow load region on the map.
The program contains drawings of types of roofs, which graphically show the data entry parameters. As a result, information is displayed on:
- roof - slope angle, surface area, approximate weight of the roofing material;
- rafters - length, minimum section, quantity, volume of timber for rafters, their approximate weight, layout (drawing);
- crate - the number of rows, the distance between the boards, the number of boards, their volume, approximate weight.
Online calculators, of course, cannot take into account the design features of rafters in all situations. To obtain accurate data for a specific roof option, all calculations must be done manually. We offer you methods for calculating the loads on the rafters (snow, wind, roofing cake), as well as determining the parameters of the rafters (section, length, quantity, pitch). Based on these data, it will also be possible to calculate the amount of wood needed to equip the truss system.
Calculation of the load on the rafters
The rafters hold up the roof. Therefore, loads are transferred to them both from external natural factors and from the weight of the roofing cake (battens, insulation, hydro and vapor barriers). The main external loads are associated with the effects of snow and wind.
Snow load
Snow load is determined by the formula: S =μ ∙ S g , where:
- S - the desired value of the load;
- μ - coefficient determined by the slope of the roof (the greater the slope, the lower this coefficient, since the snow will melt, so its pressure will be less);
- S g - the norm of snow pressure in a particular region of the country (kg / m 2), calculated from the results of long-term observations.
The angle of the roof is calculated from its main triangle
To determine the coefficient μ, it is necessary to know the angle of inclination of the slope. It often happens that the width and height of the roof are given, but the angle of inclination is unknown. In this case, it must be calculated by the formula tg α \u003d H / L, where H is the height of the ridge, L is half the width of the building (along the gable side), tg α is the tangent of the desired angle. Further, the value of the angle itself is taken from special tables.
Table: slope angle value according to its tangent
| tgα | α, deg |
| 0,27 | 15 |
| 0,36 | 20 |
| 0,47 | 25 |
| 0,58 | 30 |
| 0,70 | 35 |
| 0,84 | 40 |
| 1,0 | 45 |
| 1,2 | 50 |
| 1,4 | 55 |
| 1,73 | 60 |
| 2,14 | 65 |
Suppose the house is 8 m wide and 2.32 m high at the ridge. Then tg α = 2.32/4 = 0.58. According to the table, we find that α \u003d 30 o.
The coefficient μ is determined by the following method:
- at slope angles up to 25 о μ = 1;
- for angles from 25 to 60 about μ = 0.7;
- for steeper slopes μ = 0, i.e. the snow load is not taken into account.
Thus, for the considered structure μ = 0.7. The value of S g is selected based on the location of the region in which construction is being carried out on the map of snow loads.
The snow load map allows you to determine the pressure of snow on the roof in various regions of Russia
Having determined the number of the region on the map, the value of the standard snow load can be found from the corresponding table.
Table: normative snow load by region
| region number | I | II | III | IV | V | VI | VII | VIII |
| S g, kg / m 2 | 80 | 120 | 180 | 240 | 320 | 400 | 480 | 560 |
Let's assume that our house is located in the Moscow region. This is the third region in terms of snow load. S g here is 180 kg/m 2 . Then the total snow load on the roof of the house will be S = 0.7 ∙ 180 = 126 kg / m 2.
wind load
The wind load depends on the region of the country where the house is built, the height of the house, the characteristics of the terrain and the slope of the roof. It is calculated according to the formula: W m \u003d W about ∙ K ∙ C, where:
- W about - standard value of wind pressure;
- K - coefficient taking into account the change in wind pressure at altitude;
- C - aerodynamic coefficient, taking into account the shape of the roof (with gentle or steep slopes).
The normative value of wind pressure is determined from the map of wind loads.
The wind load map allows you to determine the wind pressure on the roof in various regions of Russia
Table: standard wind load by region
| region number | 1a | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| W o , kgf / m 2 | 24 | 32 | 42 | 53 | 67 | 84 | 100 | 120 |
According to the level of wind loads, the Moscow Region is in the first zone. Therefore, the standard value of wind pressure W about for our case is 32 kg/m 2 .
The value of K is determined from a special table. The higher the house and the more open area it is built, the greater the value of K.
Table: coefficient taking into account wind pressure at altitude
Let's take the average height of the house - from 5 to 10 m, and we will consider the area closed (this type corresponds to most areas where suburban construction is carried out). Hence, the coefficient K in our case will be equal to 0.65.
The aerodynamic coefficient can range from -1.8 to 0.8. A negative coefficient means that the wind is trying to raise the roof (usually with gentle slopes), a positive coefficient means that it is tilting (with steep slopes). For reliability, we take the maximum value of this coefficient equal to 0.8.
The wind affects the roofs with steep and gentle slopes in different ways.
Thus, the total wind load on the house we are considering will be equal to W m = 32 ∙ 0.65 ∙ 0.8 = 16.6 kg / m 2.
Roofing cake weight
The total weight per square meter of the roofing cake will be equal to the sum of the specific gravity of all its constituent elements:
- crates made of coniferous wood (8 - 12 kg);
- roofing (for example, we take corrugated board - 5 kg);
- waterproofing from a polymer membrane (1.4 - 2.0 kg);
- vapor barrier made of reinforced film (0.9 - 1.2 kg);
- insulation (mineral wool - 10 kg).
The weight of other types of roofing can be determined from a special table.
Table: weight of various types of roofing
For greater reliability, we take the maximum values of the weight of the components of the roofing cake: P \u003d 12 + 5 + 2 + 1.2 + 10 \u003d 30.2 kg / m 2. We add a margin of 10% in case of any additional structures or non-standard types of coating: P = 30.2 ∙ 1.1 = 33.2 kg / m 2.
Total load on the rafters
The total load on the rafters is calculated by the formula: Q \u003d S + W m + P, where:
Recall that the calculation is carried out for the Moscow region, the roofing is corrugated board, the angle of inclination of the roof is 30 °: Q = 126 + 16.6 + 33.2 = 175.8 kg / m 2. Thus, the total load per square meter of rafters is 175.8 kg. If the roof area is 100 m 2, then the total load is 17580 kg.
It is erroneous to believe that reducing the weight of the roofing significantly reduces the load on the rafters. Let's take cement-sand tiles (50 kg / m 2) as a coating. Then the weight of the roof will increase by 45 kg / m 2 and will not be 33.2, but 76.4 kg / m 2. In this case, Q \u003d 126 + 16.6 + 76.4 \u003d 219 kg / m 2. It turns out that with an increase in the mass of the roofing by 10 times (from 5 to 50 kg / m 2), the total load increased by only 25%, which can be considered a not so significant increase.
Calculation of rafter parameters
Knowing the magnitude of the loads on the roof, we can calculate the specific parameters of the material required for the installation of the truss system: section, length, quantity and pitch.
Selection of the cross section of the rafters
The cross section of the rafters is calculated by the formula: H \u003d K c ∙ L max ∙ √Q r / (B ∙ R izg), where:
- K c - coefficient equal to 8.6 at an angle of inclination less than 30 about, and 9.5 at a greater slope;
- L max - the largest span of the rafter;
- B is the thickness of the rafter section in meters;
- R bend - bending resistance of the material (kg / cm 2).
The meaning of the formula is that the required section size increases along with an increase in the largest span of the rafter and the load on its linear meter and decreases with an increase in the thickness of the rafter and the resistance of wood to bending.
Let's calculate all the elements of this formula. First of all, we determine the load per linear meter of the rafter. This is done according to the formula: Q r \u003d A ∙ Q, where:
- Q r - calculated value;
- A - the distance between the rafters in meters;
The logic of the calculation is quite simple: the less often the rafters are located and the smaller they are, the greater the load per linear meter will be.
We have already calculated the total load per 1 square meter of rafters. It is equal to 175.8 kg / m 2 for our example. Let us assume that A = 0.6 m. Then Q r = 0.6 ∙ 175.8 = 105.5 kg/m. This value will be required for further calculations.
Now let's determine the width of the sawn timber section according to GOST 24454–80 "Softwood lumber". We look at what sections the wood is sawn - these are standard values.
Table: determination of standard board width values depending on its thickness
| Board thickness - section width, mm | Board width - section height, mm | ||||||||
| 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 | ||||||||
Decide on the thickness of the board (B). Let it correspond to the most commonly used edged lumber - 50 mm or 0.05 m.
Next, we need to know the largest span of the rafter (L max). To do this, you need to turn to the project and find a drawing of a truss truss, where all its dimensions will be indicated. Let us take in our case L max equal to 2.7 m.
The value of the largest rafter span (Lmax) is an important component for calculating its cross section and is determined from the drawing of the truss truss
The value of the resistance of the material to bending (R bend) depends on the type of wood. For the first grade, it is 140 kg / cm 2, the second - 130 kg / cm 2, the third - 85 kg / cm 2. Let's take the value for the second grade: it is not very different from the first, but the second grade of wood is cheaper.
We substitute all the obtained values \u200b\u200bin the above formula and get H \u003d 9.5 ∙ 2.7 ∙ √ (105.5) / (0.05x130) \u003d 103.4 mm. With a rafter thickness of 50 mm, there is no standard width value of 103.4 mm, so we take the nearest larger value from the table above. It will be 125 mm. Thus, a sufficient cross-section of lumber with a rafter pitch of 0.6 m, a maximum span of 2.7 m and a roof load of 175.8 kg / m 2 is 50x125 mm.
- mauerlat - 100x100, 100x150, 150x150;
- rafter legs and valleys - 100x200;
- crossbars - 100x150, 100x200;
- racks - 100x100, 150x150.
These are sections with a margin. If you want to save material, you can use the above method.
Video: calculation of loads on rafters and their cross section
Rafter length
In the manufacture of rafters, in addition to the section, their length is also important. It depends, in particular, on the slope with which the roof will be built. The pitch of the roof usually varies between 20 and 45 degrees, but varies depending on the roofing material used, since not every roofing material can be used with any roof pitch.
Influence of the type of roofing material on the angle of the roof slope
Permissible roof slope angles for roofing materials:
- roll coatings - flat and low-slope roofs (up to 22 o);
- bituminous roofing and folded metal sheets - any slope;
- fiber cement sheets, corrugated board - from 4.5 o;
- metal tile, bituminous, ceramic tile, slate - from 22 o;
- high-profile piece tile, slate - from 25 about.
Permissible roof slope angles are determined by the roofing material used.
Despite the fact that the permissible roof slope angles can be very small, we still recommend making them large to reduce the snow load. For corrugated board, they can range from 20 o, metal tiles - 25 o, slate - 35 o, seam roof - 18 - 35 o.
The length of the rafters of different types of roofs is considered differently. We will show how this is done for a single-pitched and gable roof.
Calculation of the length of the rafters of shed roofs
The length of the rafter leg is calculated according to the formula L c \u003d L bc / sin A, where L bc is the amount by which the wall must be raised, and A is the angle of the roof slope. To understand the meaning of the formula for calculating L c, recall that the sine of the angle of a right triangle is equal to the ratio of the opposite leg to the hypotenuse. Thus, sin A \u003d L bc / L c. The value of L bc can be calculated by applying the formula: L bc \u003d L cd ∙ tg A, where L cd is the length of the wall of the house.
All formulas for calculating the truss system of a shed roof are taken from a right triangle, which is the projection of the under-roof space onto the gable
It is easiest to find the values \u200b\u200bof tg A and sin A using the table.
Table: determination of the values of trigonometric functions by the angle of the roof slope
| Roof slope angle, degrees | tg A | sin A | cos A |
| 5 | 0,09 | 0,09 | 1,00 |
| 10 | 0,18 | 0,17 | 0,98 |
| 15 | 0,27 | 0,26 | 0,97 |
| 20 | 0,36 | 0,34 | 0,94 |
| 25 | 0,47 | 0,42 | 0,91 |
| 30 | 0,58 | 0,50 | 0,87 |
| 35 | 0,70 | 0,57 | 0,82 |
| 40 | 0,84 | 0,64 | 0,77 |
| 45 | 1,00 | 0,71 | 0,71 |
| 50 | 1,19 | 0,77 | 0,64 |
| 55 | 1,43 | 0,82 | 0,57 |
| 60 | 1,73 | 0,87 | 0,50 |
Consider an example.
- Let's take the length of the wall of the house, equal to 6 m, and the angle of inclination of the roof of 30 o.
- Then the height of the wall rise L bc = 6 ∙ tg 30 o = 6 ∙ 0.58 = 3.48 m.
- The length of the rafter leg L c \u003d 3.48 / sin 30 o \u003d 3.48 / 0.5 \u003d 6.96 m.
Calculation of the length of the gable roof rafters
A gable roof can be represented as an isosceles triangle formed by two slopes and a transverse ceiling beam.
The graphical representation of a gable roof in the form of an isosceles triangle allows you to determine the length of the rafter leg in two different ways
The length of the rafter leg (a) can be determined in two different ways.
- If the width of the house b and the angle of inclination of the roof A are known. Then a \u003d b / (2 ∙ cos A). Let's say that the width of the house is 8 m, and the angle A is 35 o. Then a \u003d 8 / (2 ∙ cos 35 o) \u003d 8 / (2 ∙ 0.82) \u003d 4.88. We add 0.5 m to the overhangs and get the length of the rafter leg equal to 5.38 m.
- If the width of the roof b and its height in the ridge h are known. In this case a = √b 2 + h 2 . Let us assume that the height of the ridge is 2.79 m. Then a = √4 2 +2.79 2 = √16 + 7.78 = √23.78 = 4.88. We add 0.5 m to the overhang and as a result we have the same 5.38 m.
It must be borne in mind that the standard length of sawn wood is 6 meters. With a longer length, they will either need to be spliced or made to order, which, of course, will be more expensive.
Video: rafter calculation
Rafter step calculation
Pitch is the distance between adjacent rafters. It determines how many rafters we need for the roof. The step size is usually set equal to from 60 cm to 1 m. To calculate a specific step size, you must:
- Select an approximate step.
- Determine the length of the slope. Usually this value is set by the project.
- Divide the length of the slope by the approximately selected step size. If a fractional number is obtained, then the result is rounded up and 1 is added (this adjustment is necessary because there must be rafters along both slope boundaries).
- Divide the slope length by the number obtained in the previous paragraph.
For clarity, we will show the calculation process using a specific example.
Suppose that the approximate step is 1 m, and the length of the ramp is 12 m.
- We divide the length of the slope by the approximately selected step size: 12 / 1 \u003d 12.
- We add 1 to the resulting number, we get 13.
- We divide the length of the slope by the resulting number: 12/13 \u003d 0.92 m.
It must be understood that the value obtained is the distance between the centers of the rafter logs.
The step between the rafters can also be determined from the table for a given cross section and the length of the rafter leg.
Table: calculation of the pitch of the rafters depending on the length of the rafter leg and the section of the beam
| Rafter pitch, m | Rafter leg length in meters | ||||||
| 3,0 | 3,5 | 4,0 | 4,5 | 5,0 | 5,5 | 6,0 | |
| 0,6 | 40x150 | 40x175 | 50x150 | 50x150 | 50x175 | 50x200 | 50x200 |
| 0,9 | 50x150 | 50x175 | 50x200 | 75x175 | 75x175 | 75x200 | 75x200 |
| 1,1 | 75x125 | 75x150 | 75x175 | 75x175 | 75x200 | 75x200 | 75x200 |
| 1,4 | 75x150 | 75x175 | 75x200 | 75x200 | 75x200 | 100x200 | 100x200 |
| 1,75 | 75x150 | 75x200 | 75x200 | 100x200 | 100x200 | 100x250 | 100x250 |
| 2,15 | 100x150 | 100x175 | 100x200 | 100x200 | 100x250 | 100x250 | - |
According to the same table, you can determine the permissible cross-section of the rafter, knowing the size of the step and its length. So, with a step of 0.9 m and a length of 5 m, we get a section of 75x175 mm.
With the thickness of the beam of the rafter legs more than usual, the distance between the rafters can also be made larger.
Table: calculation of the pitch of rafters from thick beams and logs
| Distance between the rafters m | The greatest length of the rafter leg, m | ||||||
| 3,2 | 3,7 | 4,4 | 5,2 | 5,9 | 6,6 | ||
| 1,2 | beam | 9x11 | 9x14 | 9x17 | 9x19 | 9x20 | 9x20 |
| log | 11 | 14 | 17 | 19 | 20 | 20 | |
| 1,6 | beam | 9x11 | 9x17 | 9x19 | 9x20 | 11x21 | 13x24 |
| log | 11 | 17 | 19 | 20 | 21 | 24 | |
| 1,8 | beam | 10x15 | 10x18 | 10x19 | 12x22 | - | - |
| log | 15 | 18 | 19 | 22 | - | - | |
| 2,2 | beam | 10x17 | 10x19 | 12x22 | - | - | - |
| log | 17 | 19 | 22 | - | - | - | |
Calculation of the number of rafters
- Depending on the load on the rafter system, we select the section of the rafter leg.
- We calculate the length of the rafter.
- According to the table, we select the step of the rafters.
- We divide the width of the roof by the pitch of the rafters and get their number.
For example, we calculate the number of rafters for a gable roof 10 m wide with a rafter leg length of 4 m and its cross section of 50x150 mm.
- We set the step equal to 0.6 m.
- We divide 10 m by 0.6 m, we get 16.6.
- Add one rafter to the edge of the roof and round up. We get 18 rafters per slope.
Calculation of the amount of wood required for the manufacture of rafters
For the construction of rafters, coniferous wood is most often used. Knowing how many rafters are required for the roof and how much wood is contained in one bar, we calculate the required amount of wood. Suppose that we have made a complete calculation of the truss system and received that 18 units of timber with a size of 150x150 mm are needed. Let's look at the table below.
Table: the amount of timber in a cubic meter of lumber
| The size timber, mm | Number of beams 6 m long 1 m 3 lumber, pcs. | The volume of one bar 6 m long, m 3 |
| 100x100 | 16,6 | 0,06 |
| 100x150 | 11,1 | 0,09 |
| 100x200 | 8,3 | 0,12 |
| 150x150 | 7,4 | 0,135 |
| 150x200 | 5,5 | 0,18 |
| 150x300 | 3,7 | 0,27 |
| 200x200 | 4,1 | 0,24 |
The volume of one bar 150 x 150 mm is 0.135 m 3. This means that the volume of lumber for 18 rafters will be 0.135 m 3 ∙ 18 = 2.43 m 3.
Video: material calculation for gable roof rafters
The correct calculation of the main parameters allows you to make the truss system safe, reliable and durable. Knowing the required volume of wood allows you to save money on arranging rafters. Online calculators greatly facilitate the calculation of all the technical characteristics of the roof frame, save time on calculations and increase their accuracy.
How to calculate the parameters of the gable roof of a private house? You can use an online calculator. But what if there is no way to use the rafter calculator? If you wish, you can calculate on paper the main parameters of the construction of the roof. I will tell you how to perform calculations in accordance with the loads acting on the truss system.
| Illustrations | Calculation options |
| The weight of the snow. Despite the slope of the slopes, a large amount of snow accumulates on the roof surface, as shown in the photo. The mass of snow cover affects the roof pie, the rafters and the load-bearing walls. | |
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wind pressure. Depending on the angle of inclination, the wind affects the roof.
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Roofing material weight. A pie is a multilayer structure, which, depending on the number of structural elements, has one or another mass. This means that when doing calculations with your own hands, you need to find the optimal ratio of the parameters of the pie and the material from which the load-bearing walls are built. |
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Rafter weight. The stronger the rafters, the heavier they are and their price is higher, and vice versa, reducing the strength of the rafters will lead to the fact that the system will be lighter. Our task, in the calculations, is to choose those parameters of the rafters that will correspond to the mechanical load from the roofing material. |
Calculation of the maximum weight of snow
The value of the maximum snow severity can be calculated by the formula S=µ·Sg, where:
- S is the amount of snow load (in kg / m 2);
- µ - coefficient of slope of the roof (depends on the angle of inclination of the rafters α);
- Sg - standard weight of snow (in kg / m 2).
In order to make calculations according to the proposed formula, we will determine the dependence of the conditional value µ on the angle of inclination α.
In the diagram you can see the ratio of the angle of inclination of the slope and the geometric parameters of the truss truss, which is formed by diagonal and horizontal beams.
Table 1 offers the already calculated results of dividing such quantities as the height of the roof to the ridge and half the puff - the beam forming the ceiling.
An angle of inclination (α) of 30° or less corresponds to a factor (µ) of 1. If the angle is equal to or greater than 60°, then µ is 0. If 60°>α>30°, then the value of µ can be calculated using the formula: µ = 0.033 (60-α).
Parameters of standard snow load in kg/m²:
After the slope coefficient of the rafters and the parameters of the normative snow severity are known, we return to the formula S = µ·Sg, insert the available parameters and calculate the rafters taking into account the impact of the precipitation layer.
Calculation of the maximum allowable wind pressure
The importance of calculating the effects of wind is due to the following points:
- If the angle of inclination α is greater than 30°, the windage of the structure increases. Because of this, one of the slopes or the gable has additional pressure, which negatively affects the state of the structure.
- If the angle of inclination α is less than 30°, when the air flow goes around the roof, an aerodynamic lifting force and a turbulence zone under the overhangs are formed.
The calculation of the permissible load of the air flow is carried out according to the formula Wo K C = Wm, where:
- Wm - the maximum allowable impact of the air flow;
- Wo - conditional impact of the air flow (determined from Table 2 and from the wind pressure map);
- K is the coefficient of change in the impact of the air flow with height (shown in Table 3 in relation to the height of the building);
- C is the drag coefficient.
Drag coefficient C according to the configuration of the roof and building can be important<1,8 (ветер поднимает крышу), >0.8 (wind presses on one of the slopes). Let's simplify the calculation in the direction of increasing strength and assume that the value of the coefficient C is 0.8.
Now that all the coefficients are known, it remains to insert them into the formula Wo·K·C = Wm and calculate the maximum allowable value of the impact of the air flow Wm.
Calculation of the mass of the roof
When buying roof coverings, you can find out the weight from the seller or on the packaging. But in order to calculate in advance which material is suitable, you can use the table. To calculate, you need to calculate the area of \u200b\u200bthe roof slopes and multiply by the proposed values.
In addition to the mass of the coating, the load-bearing walls bear the weight of the rafters themselves, the boards of the lathing, counter-lattices, etc. The average values of the severity of the elements of the truss system can be found in the proposed table.
The weight values are given on the basis of kilograms per square meter, on the basis that the distance between the boards of the crate is standard 50-60 cm. To calculate the mass of the structure, we find out the area of \u200b\u200bthe slopes and multiply by the proposed values.
It is desirable to round up the results of calculations so that the resulting value provides the greatest strength of the truss system.
Summing up
Now you know what factors take into account the calculation of the roof truss system, and therefore you can calculate the necessary values on your own, without using the online calculation calculator. More useful information can be found by watching the video in this article. Ask questions of interest in the comments.
-> Calculation of the truss systemThe main element of the roof, perceiving and resisting all types of loads, is rafter system. Therefore, in order for your roof to reliably withstand all environmental influences, it is very important to make the correct calculation of the truss system.
For self-calculation of the characteristics of the materials necessary for the installation of the truss system, I give simplified calculation formulas. Simplifications are made in the direction of increasing the strength of the structure. This will cause some increase in the consumption of lumber, but on small roofs of individual buildings it will not be significant. These formulas can be used when calculating gable attic and mansard, as well as shed roofs.
Based on the calculation methodology below, programmer Andrey Mutovkin (Andrey's business card - Mutovkin.rf) developed a truss system calculation program for his own needs. At my request, he generously allowed me to post it on the site. You can download the program.
The calculation methodology was compiled on the basis of SNiP 2.01.07-85 "Loads and impacts", taking into account the "Changes ..." of 2008, as well as on the basis of formulas given in other sources. I developed this technique many years ago, and time has confirmed its correctness.
To calculate the rafter system, first of all, it is necessary to calculate all the loads acting on the roof.
I. Loads acting on the roof.
1. Snow loads.
2. Wind loads.
On the truss system, in addition to the above, the load from the roof elements also acts:
3. Roof weight.
4. The weight of the rough flooring and lathing.
5. The weight of the insulation (in the case of an insulated attic).
6. The weight of the rafter system itself.
Let's consider all these loads in more detail.
1. Snow loads.
To calculate the snow load, we use the formula:
Where,
S - the desired value of the snow load, kg / m²
µ is a coefficient depending on the slope of the roof.
Sg - normative snow load, kg/m².
µ - coefficient depending on the slope of the roof α. Dimensionless value.
You can approximately determine the angle of the roof slope α by the result of dividing the height H by half the span - L.
The results are summarized in the table:
Then if α is less than or equal to 30°, µ = 1 ;
if α is greater than or equal to 60°, µ = 0 ;
if 30° is calculated by the formula:
µ = 0.033 (60-α);
Sg - normative snow load, kg/m².
For Russia, it is accepted according to map 1 of mandatory annex 5 of SNiP 2.01.07-85 "Loads and impacts"
For Belarus, the normative snow load Sg is determined
Technical code of GOOD PRACTICE Eurocode 1. EFFECTS ON STRUCTURES Part 1-3. General impacts. Snow loads. TCH EN1991-1-3-2009 (02250).
For instance,
Brest (I) - 120 kg/m²,
Grodno (II) - 140 kg/m²,
Minsk (III) - 160 kg/m²,
Vitebsk (IV) - 180 kg/m².
Find the maximum possible snow load on a roof with a height of 2.5 m and a span of 7 m.
The building is located in the village. Babenki, Ivanovo region RF.
According to map 1 of the mandatory annex 5 of SNiP 2.01.07-85 "Loads and impacts", we determine Sg - the standard snow load for the city of Ivanovo (IV district):
Sg=240 kg/m²
We determine the angle of the roof slope α.
To do this, we divide the height of the roof (H) by half the span (L): 2.5 / 3.5 \u003d 0.714
and according to the table we find the slope angle α=36°.
Since 30° , calculation µ will be produced according to the formula µ = 0.033 (60-α) .
Substituting the value α=36° , we find: µ = 0.033 (60-36)= 0.79
Then S \u003d Sg µ \u003d 240 0.79 \u003d 189 kg / m²;
the maximum possible snow load on our roof will be 189kg/m².
2. Wind loads.
If the roof is steep (α > 30°), then because of its windage, the wind presses on one of the slopes and tends to overturn it.
If the roof is flat (α , then the lifting aerodynamic force that occurs when the wind bends around it, as well as turbulence under the overhangs, tend to raise this roof.
According to SNiP 2.01.07-85 "Loads and actions" (in Belarus - Eurocode 1 IMPACTS ON STRUCTURES Part 1-4. General actions. Wind actions), the standard value of the average component of the wind load Wm at a height Z above the ground should be determined by the formula :
Where,
Wo - normative value of wind pressure.
K is a coefficient that takes into account the change in wind pressure along the height.
C - aerodynamic coefficient.
K is a coefficient that takes into account the change in wind pressure along the height. Its values, depending on the height of the building and the nature of the terrain, are summarized in Table 3.
C - aerodynamic coefficient,
which, depending on the configuration of the building and the roof, can take values from minus 1.8 (the roof rises) to plus 0.8 (the wind presses on the roof). Since our calculation is simplified in the direction of increasing strength, we take the value of C equal to 0.8.
When building a roof, it must be remembered that wind forces tending to lift or tear off the roof can reach significant values, and therefore the bottom of each rafter leg must be properly attached to the walls or to the mats.
This is done by any means, for example, using annealed (for softness) steel wire with a diameter of 5 - 6 mm. With this wire, each rafter leg is screwed to the mats or to the ears of the floor slabs. It's obvious that the heavier the roof, the better!
Determine the average wind load on the roof of a one-story house with a ridge height from the ground - 6m. , slope angle α=36° in the village of Babenki, Ivanovo Region. RF.
According to map 3 of Appendix 5 in "SNiP 2.01.07-85" we find that the Ivanovo region belongs to the second wind region Wo = 30 kg / m²
Since all buildings in the village are below 10m, coefficient K= 1.0
The value of the aerodynamic coefficient C is taken equal to 0.8
standard value of the average component of the wind load Wm = 30 1.0 0.8 = 24 kg / m².
For information: if the wind blows at the end of this roof, then a lifting (tearing) force of up to 33.6 kg / m² acts on its edge
3. Roof weight.
Different types of roofing have the following weight:
1. Slate 10 - 15 kg/m²;
2. Ondulin (bituminous slate) 4 - 6 kg/m²;
3. Ceramic tiles 35 - 50kg/m²;
4. Cement-sand tiles 40 - 50 kg/m²;
5. Bituminous tiles 8 - 12 kg/m²;
6. Metal tile 4 - 5 kg/m²;
7. Decking 4 - 5 kg/m²;
4. The weight of the rough flooring, lathing and truss system.
Draft flooring weight 18 - 20 kg/m²;
Lathing weight 8 - 10 kg/m²;
The weight of the rafter system itself is 15 - 20 kg / m²;
When calculating the final load on the truss system, all of the above loads are summed up.
And now I will tell you a little secret. Sellers of some types of roofing materials note their lightness as one of the positive properties, which, according to them, will lead to significant savings in lumber in the manufacture of the truss system.
As a refutation of this statement, I will give the following example.
Calculation of the load on the truss system when using various roofing materials.
Let's calculate the load on the truss system when using the heaviest (Cement-sand tile
50 kg / m²) and the lightest (Metal tile 5 kg / m²) roofing material for our house in the village of Babenki, Ivanovo region. RF.
Cement-sand tiles:
Wind loads - 24kg/m²
Roof weight - 50 kg/m²
Lathing weight - 20 kg/m²
Total - 303 kg/m²
Metal tile:
Snow loads - 189kg/m²
Wind loads - 24kg/m²
Roof weight - 5 kg/m²
Lathing weight - 20 kg/m²
The weight of the truss system itself is 20 kg / m²
Total - 258 kg/m²
Obviously, the existing difference in design loads (only about 15%) cannot lead to any tangible savings in lumber.
So, with the calculation of the total load Q, acting on a square meter of the roof, we figured it out!
I especially draw your attention: when calculating, carefully follow the dimension !!!
II. Calculation of the truss system.
truss system consists of separate rafters (rafter legs), so the calculation is reduced to determining the load on each rafter leg separately and calculating the section of a separate rafter leg.
1. We find the distributed load per linear meter of each rafter leg.
Where
Qr - distributed load per linear meter of the rafter leg - kg / m,
A - distance between rafters (rafter pitch) - m,
Q - total load acting on a square meter of roof - kg / m².
2. We determine in the rafter leg the working section of the maximum length Lmax.
3. We calculate the minimum cross section of the material of the rafter leg.
When choosing a material for rafters, we are guided by a table of standard sizes of lumber (GOST 24454-80 Softwood lumber. Dimensions), which are summarized in Table 4.
| 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 |
A. We calculate the cross section of the rafter leg.
We set the width of the section arbitrarily in accordance with the standard dimensions, and the height of the section is determined by the formula:
H ≥ 8.6 Lmax sqrt(Qr/(B Rbend)), if the slope of the roof α
H ≥ 9.5 Lmax sqrt(Qr/(B Rbend)), if the roof pitch α > 30°.
H - section height cm,
B - section width cm,
Rizg - resistance of wood to bending, kg / cm².
For pine and spruce Rizg is equal to:
Grade 1 - 140 kg / cm²;
Grade 2 - 130 kg / cm²;
Grade 3 - 85 kg / cm²;
sqrt - square root
B. We check whether the deflection value fits into the standard.
The normalized deflection of the material under load for all roof elements should not exceed the value L / 200. Where, L is the length of the working area.
This condition is satisfied if the following inequality is true:
3.125 Qr (Lmax)³/(B H³) ≤ 1
Where,
Qr - distributed load per linear meter of the rafter leg - kg / m,
Lmax - working section of the rafter leg of maximum length m,
B - section width cm,
H - section height cm,
If the inequality is not met, then increase B or H .
Condition:
Roof slope angle α = 36°;
Rafter pitch A = 0.8 m;
The working section of the rafter leg is maximum length Lmax = 2.8 m;
Material - pine 1 grade (Rizg = 140 kg / cm²);
Roof - cement-sand tiles (Roof weight - 50 kg / m²).
As it was calculated, the total load acting on a square meter of the roof is Q \u003d 303 kg / m².
1. We find the distributed load per linear meter of each rafter leg Qr=A·Q;
Qr=0.8 303=242 kg/m;
2. Let's choose the thickness of the board for the rafters - 5cm.
We calculate the cross section of the rafter leg with a section width of 5 cm.
Then, H ≥ 9.5 Lmax sqrt(Qr/B Rbend), since the slope of the roof α > 30°:
H ≥ 9.5 2.8 sqrt(242/5 140)
H ≥15.6 cm;
From the table of standard lumber sizes, select a board with the nearest section:
width - 5 cm, height - 17.5 cm.
3. We check whether the deflection value is within the standard. For this, the inequality must be observed:
3.125 Qr (Lmax)³/B H³ ≤ 1
Substituting the values, we have: 3.125 242 (2.8)³ / 5 (17.5)³ = 0.61
Meaning 0.61, then the cross section of the material of the rafters is chosen correctly.
The cross section of the rafters, installed in increments of 0.8 m, for the roof of our house will be: width - 5 cm, height - 17.5 cm.
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The strength of the roof directly depends on how accurately the calculation of the truss system is made, in which both the angle of inclination of the slopes and the length, as well as the cross section of the beams, matter.
Choosing a truss structure
The strength of the roof is determined not only by the material from which the rafter legs are made, but also by the scheme of their assembly. For example, someone might decide that metal trusses would be the most reliable roofing solution, but be aware that this will create additional stress on the walls and foundation, which will have to be reinforced. Therefore, lumber is often used for rafters, among which one can distinguish timber, boards, as well as planks of different sections for lathing. Rarely used round.
Wood is strong enough, but it is very important to measure the area of the roof with the length and cross section of the supporting elements. That is why the mauerlat (supporting horizontal beams along the upper edge of the walls along the entire perimeter of the house) is selected with a large margin of safety. In addition, all parts are sized to support their own total weight together with the roof and additional live loads (long or short). All this should be taken into account directly in the design of the house.
Regardless of the design, only certain elements are used in it, namely: rafter legs, racks, angled struts, ridge beam. Crossbars and girders are also needed, which provide rigidity to the roof frame. But since the fundamental factor is the area of \u200b\u200bthe roof and its slope, calculations are carried out only with respect to the rafters: their length, section and angle to the horizon, as well as the distance between them. It is known that the triangle resists loads best of all, therefore it is this figure that is formed with the help of crossbars installed as crossbars between the rafters of a gable roof.