The construction of a house always ends with the construction of a roof, which involves the obligatory installation of a truss system. This design includes rafter legs, Mauerlat, puffs, struts, sprigs, sprengels, racks, crates and other elements that ensure the strength and rigidity of the entire system.
In different roof structures, the rafter leg can be called an ordinary rafter or a diagonal (sloping) rafter leg and requires a strength calculation. The calculation of the truss system is based on the collection of permanent and temporary loads that will act on the roof.
Permanent loads:
- the weight of all elements of the roof structure;
- weight of steam and waterproofing materials;
- weight of roofing material;
- the weight of the finishing materials of the ceiling, in the presence of attic rooms.
Live loads:
Characteristics of rafter legs
Based on the obtained load value, the rafter leg is calculated, its length and cross section, depending on the selected material, the type of roof and the type of rafters - layered or hanging. Some types of complex roofs may contain both.
And in hip roofs, in addition to rafter legs, shortened rafters are also used, which are called sprigs and also require their own calculation. In addition, all additional elements of the truss system, such as puffs, struts, racks and crossbars, need to be calculated, since they have a certain load transmitted from the rafters.
The length of the rafter leg depends, first of all, on the size of the building, as well as on the slope of the roof slopes, which is obtained from the chosen roof shape. Usually, they try to make the length of the rafter no more than 6 m, so all lumber that goes on sale has exactly this maximum length. But it happens that the dimensions of the house require rafters of greater length, in which case they are increased. Basically, long rafter legs are found at sloping (diagonal) rafters, during the construction of hip or semi-hip roofs.
The choice of section of the rafter leg is influenced by multiple factors:
- permanent and temporary loads;
- type of roofing material;
- the slope of the slopes;
- roof type;
- the size of the house;
- climatic conditions;
- the quality of the material for the manufacture of rafter legs.
Coniferous wood is used for the roof construction. But, when choosing, you need to make sure that you do not come across boards or bars with blue, a lot of large knots.
The moisture content of wood should be no more than 20-22%, since a tree that is too wet will change in size as it dries, and this, in turn, can lead to a violation of the tightness of the roof and other negative consequences.
It is best if the calculation of the truss system is carried out by a specialist. Currently, there are enough companies that offer such services.
You can independently calculate the rafter legs, dimensions and length, if you use ready-made calculators on the Internet. One has only to enter the required dimensions into the program, and the program itself will already give the finished result of the section, length and pitch of the rafters.
In the construction of private residential buildings, as a rule, boards with a section of 50x150 mm are used in the manufacture of roof rafters of any configuration. The pitch of the rafter legs is approximately 1 meter, depending on the type of roofing material chosen, the amount of snow in winter and the slope of the roof.
So, for roofs with a slope of more than 45 degrees, the pitch of the rafters is selected within 1.2-1.4 m, and for regions with large snow loads, this distance will be 0.6-0.8 m.
You should also pay attention to the type of roofing material. The heaviest is considered natural tiles. The cross section of the rafter legs will increase accordingly if there is a large length of the rafter legs and their step.
Features of mounting rafter legs
Fastening the rafter legs to the Mauerlat is the most crucial moment in the entire roof construction. The strength of the entire roof structure depends on the correct connection of the rafters and the Mauerlat.
There are two ways of fastening - sliding and rigid., each of which fits a certain type of rafters - hanging or layered.
Rigid fastening excludes any shifts, turns or bends of rafters. This is achieved by making cuts on the rafter itself and then fixing the rafter leg with the mauerlat using metal staples, wire or long nails, as well as using metal corners.
A sliding joint, or as it is often called a "swivel", can have two degrees of freedom. Such a connection is often used in the construction of wooden houses to give the roof the freedom to gradually settle on the frame, which can shrink over several years. In this case, the connection of the rafter legs on the ridge is not made rigid. The rafter leg itself, when sliding, is connected to the Mauerlat with the help of a gash and reinforcement from the sides with two nails hammered obliquely in relation to each other or by driving one nail from top to bottom into the rafter leg with penetration into the Mauerlat.
Other methods are the use of metal plates that have holes for nails or the connection of rafters and Mauerlat with metal brackets.
When building a hip roof, the diagonal rafter leg often turns out to be more than 6 meters in length, and therefore requires building up.
This is achieved by pairing two boards, which are used in the construction of conventional rafters. Diagonal rafters are always longer than ordinary rafters, moreover, they experience a load one and a half times higher than that of ordinary rafters, since slanting legs also rely on them.
In order to calculate the roof truss system, a person who is not familiar with all the nuances of complex design calculations in accordance with SNIP and other standards can use our roof construction calculators.
As initial parameters, it is necessary to enter the data of some elements of the truss system:
- specify the step of the rafters (the distance between them - the step regulates the load on the rafter system),
- rafter dimensions - the so-called section = thickness x width of a board or beam
Here it is worth saying that the board is a more affordable option for installing a roofing system, since it can withstand loads, and, importantly, it costs several times more budget.
In the two tables below we have collected commonly used in construction sizes of rafters and battens broken down by type of roofing. The minimum angle of inclination of the roof is also given as optimal, depending on its type, in some places the angle is indicated as minimal, but all according to SNIP.
The main most commonly used parameters of the elements of the truss system are the pitch and cross section of the rafters, the angle of inclination of the roof, depending on the type of roofing material:
roof type | Optimum roof slope, degrees | rafter step, | rafter section, |
Decking | (optimum - 20-30) | board 5 x 15 |
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board 5 x 20 |
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Cement-sand tiles | ≤ 75; ≤ 90; ≤ 110 | board 5 x 15 |
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ceramic tiles | board 5 x 15; 6x18 |
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soft roof (roll; bituminous tiles) | board 5 x 15 |
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metal tile | board 5 x 15; 5 x 20 (for insulation) |
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board 5 x 15; 5x15 |
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asbestos-cement sheets of ordinary profile |
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asbestos-cement sheets of a unified profile |
To calculate the rafters of a gable roof in automatic mode, the rafter calculator on our website will help you.
The following table contains data on crate, counter-crate and according to the roofing material:
| roof type | Shelter. material Length x width x thickness, mm | Roof slope, degrees | Lathing pitch, cm | Lathing section, cm | Counter-batten, cm (pitch = rafter pitch) | An overlap of blood. sheets, cm |
| Decking: | Min 12 (optimum - 20-30) | according to the angle of inclination | board 3 x 10 | the width of the beam is slightly less than the rafters with a thickness of 2.5 - 4 | horizon. overlap:roof angle less than 15° - 20 cm; 15-30° - 15 -20; from 30° - 10 -15 |
|
| NS-20 | thickness 0.55 | 30; 45 | 40; 60 | |||
| 0,75 | 30; 45 | 50; 70 | ||||
| NS-35 | 0,55 | 30; 45 | 100; 100 | |||
| 0,75 | 30; 45 | 120; 130 | ||||
| S-44 | 0,55 | 30; 45 | 90; 150 | |||
| 0,75 | 30; 45 | 110; 140 | ||||
| Cement-sand tiles and ceramic tiles | from manufacturer and type | 22 - 30 | 31,2 - 33,5 | timber from the pitch of the rafters:3x5; 4x5; 4x6 or 5x5 | from 3 x 5 | 8,5 - 10,8 |
| 30 - 90 | 32,1 - 34,5 | board 5 x 15; 6x18 | 7,5 - 10,8 | |||
| soft roof (roll; bituminous tiles) | from the manufacturer | from 7 | 1. rolled - on a continuous crate 3 - 5 mm gap;2. soft tiles - 30 cm step of the boards of the sheathing under the OSB | 1.solid 2. lathing from a board 2.5 x 10-15 + OSB 9mm | from 3 x 5 | for rolled - 15-30; for soft tiles - from 15 |
| Metal tiles | opt. 4500 x 1160 - 1190 x 0.5 profile height 1.8 - 2.5 cm wave pitch 35-40 cm | from 20 | 80 - 100 (from wave) | board 5 x 20; timber 4 x 6 | from 3 x 5 | depending on brand 6 - 9 |
| Slate | 3600 x 1500 x 8-10 3000 x 1500 x 8-10 2500 x 1200 x 6-8-10 | 14 - 60; opt. 25-45 | the sheet should rest on 2 beams of the crate | from 3 x 5 | from 12 to 30 | |
| asbestos-cement sheets are common. profile | 50 - 54 | board 5-6 x 10; timber from 5 x 5 | should cover the wave | |||
| asbestos-cement sheets unified. profile | 60 - 75 | board 5-6 x 10; timber from 7.5 x 7.5 | ||||
| bitumen corrugated sheet (euroslate)- For example ondulin | 2000 x 950 x 3 wave height 36 | 5 - 10 | 5 | solid (gap up to 5 cm) | from 3 x 5 | 3; lateral - 2 waves |
| 10 - 15 | 45 | 2; lateral - 1 wave | ||||
| from 15 | 60 | board 5 x 20; timber 4 x 5; 5x5 | 1.7; lateral - 1 wave | |||
In order to independently determine the dimension of the entire rafter system, it is necessary to calculate the main influence of wind, snow masses, as well as the weight of roofing materials and structural load-bearing roof elements in the aggregate.
Again, we remind you that the calculation is given for review in a much simplified format, since for an accurate calculation it is necessary to take into account the vertical and horizontal loads on the rafter legs, additionally calculate the resistance of the rafters to bending, compression and tension, check the structures for their ability to resist chipping and crushing.
If you do not have a complex architectural structure, you can easily build a roof yourself, based on the optimal dimensions of a beam or board, on standardized roof design parameters.
The figure and table below show standard sections of elements roof structure:
Span (m) | ||||||||||
Installation step (m) |
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We repeat once again that in a simplified format, everyone is able to calculate the ability of a roofing system to withstand loads.
O online roof calculators will help you calculate the amount of timber, roofing and under-roofing materials for the construction of the roof and truss system, as well as the parameters of the roof, battens and rafter legs.
Thus, you can roughly estimate how much building materials you need to purchase, how and in what quantity the crate and rafters will be located.
The design and competent calculations of the elements of the truss structure are the key to success in the construction and subsequent operation of the roof. It is obliged to steadfastly resist the totality of temporary and permanent loads, while at the same time weighing the building to a minimum.
To perform calculations, you can use one of the many programs posted on the network, or do everything manually. However, in both cases, you need to clearly know how to calculate the rafters for the roof in order to thoroughly prepare for construction.
The truss system determines the configuration and strength characteristics of a pitched roof, which performs a number of significant functions. This is a responsible enclosing structure and an important component of the architectural ensemble. Therefore, in the design and calculations of the rafter legs, flaws should be avoided and try to eliminate shortcomings.
As a rule, in design development, several options are considered, from which the optimal solution is selected. Choosing the best option does not mean that you need to make a certain number of projects, perform exact calculations for each, and ultimately prefer the only one.
The very course of determining the length, mounting slope, section of the rafters consists in a scrupulous selection of the shape of the structure and the dimensions of the material for its construction.
For example, in the formula for calculating the bearing capacity of the rafter leg, the parameters of the section of the most suitable material for the price are initially entered. And if the result does not meet technical standards, then increase or decrease the size of the lumber until they achieve maximum compliance.
Tilt angle search method
Determining the slope angle of a pitched structure has architectural and technical aspects. In addition to a proportional configuration that is most suitable for the style of the building, an impeccable solution should take into account:
- Snow load indicators. In areas with heavy rainfall, roofs are erected with a slope of 45º or more. On slopes of such steepness, snow deposits do not linger, due to which the total load on the roof, stops and the building as a whole is significantly reduced.
- Characteristics of the wind load. In areas with gusty strong winds, coastal, steppe and mountainous areas, low-pitched, streamlined structures are being built. The steepness of the slopes there usually does not exceed 30º. In addition, winds prevent the formation of snow deposits on the roofs.
- Weight and type of roofing. The greater the weight and the smaller the elements of the roof, the steeper the truss frame needs to be built. This is necessary in order to reduce the likelihood of leaks through the joints and reduce the specific gravity of the coating per unit of horizontal projection of the roof.
In order to choose the optimal angle of inclination of the rafters, the project must take into account all of the listed requirements. The steepness of the future roof must correspond to the climatic conditions of the area chosen for the construction and the technical data of the roofing.
True, property owners in the northern windless areas should remember that with an increase in the angle of inclination of the rafter legs, the consumption of materials increases. The construction and arrangement of a roof with a slope of 60 - 65º will cost approximately one and a half times more than the construction of a structure with an angle of 45º.
In areas with frequent and strong winds, do not reduce the slope too much in order to save money. Unnecessarily sloping roofs lose architecturally and do not always help reduce costs. In such cases, it is most often necessary to strengthen the insulating layers, which, contrary to the expectations of the economy, leads to an increase in the cost of construction.
The slope of the rafters is expressed in degrees, as a percentage, or in the format of dimensionless units, displaying the ratio of half the span footage to the installation height of the ridge run. It is clear that the angle between the ceiling line and the slope line is outlined in degrees. Percentages are rarely used due to the complexity of their perception.
The most common method of designating the angle of inclination of the rafter legs, used by both designers of low-rise buildings and builders, is dimensionless units. They in shares convey the ratio of the length of the overlapped span to the height of the roof. On the object, it is easiest to find the center of the future gable wall and install a vertical rail in it with a mark for the height of the ridge than to lay off the corners from the edge of the slope.
Calculation of the length of the rafter leg
The length of the rafter is determined after the angle of inclination of the system is selected. Both of these values cannot be attributed to the number of exact values, because in the process of calculating the load, both the steepness and, following it, the length of the rafter leg may vary somewhat.
The main parameters that affect the calculation of the length of the rafters include the type of cornice overhang, according to which:
- The outer edge of the rafter legs is cut flush with the outer surface of the wall. The rafters in this situation do not form a cornice overhang that protects the structure from precipitation. To protect the walls, a drain is installed, fixed on a cornice board nailed to the end edge of the rafters.
- The rafters cut flush with the wall are built up with fillies to form a cornice overhang. Fillies are attached to the rafters with nails after the construction of the truss frame.
- The rafters are initially cut out taking into account the length of the cornice overhang. In the lower segment of the rafter legs, cuts in the form of an angle are chosen. To form cuts, they retreat from the lower edge of the rafters to the width of the eaves extension. Cuttings are needed to increase the bearing area of the rafter legs and to arrange support nodes.
At the stage of calculating the length of the rafter legs, it is necessary to consider options for attaching the roof frame to the Mauerlat, to bypasses or to the upper crown of the log house. If it is planned to install the rafters flush with the outer contour of the house, then the calculation is carried out along the length of the upper edge of the rafter, taking into account the size of the tooth, if it is used to form the lower connecting node.
If the rafter legs are cut taking into account the eaves extension, then the length is calculated from the upper edge of the rafter along with the overhang. Note that the use of triangular cuts significantly accelerates the pace of construction of the truss frame, but weakens the elements of the system. Therefore, when calculating the bearing capacity of rafters with selected cutting angles, a coefficient of 0.8 is applied.
The traditional 55 cm are recognized as the average width of the eaves. However, the spread can be from 10 to 70 or more. The calculations use the projection of the eaves on a horizontal plane.
There is a dependence on the strength characteristics of the material, on the basis of which the manufacturer recommends limit values. For example, slate manufacturers do not recommend moving the roof beyond the wall contour to a distance of more than 10 cm, so that the snow mass accumulating along the roof overhang cannot damage the edge of the eaves.
It is not customary to equip steep roofs with wide overhangs, regardless of the material, cornices are not made wider than 35 - 45 cm. But structures with a slope of up to 30º can perfectly complement a wide cornice, which will serve as a kind of canopy in areas with excessive sunlight. In the case of designing roofs with eaves of 70 cm or more, they are reinforced with additional support posts.
How to calculate the bearing capacity
In the construction of truss frames, lumber made from coniferous wood is used. The harvested timber or board must be at least second grade.
The rafter legs of pitched roofs work on the principle of compressed, curved and compressed-curved elements. With the tasks of resistance to compression and bending, second-rate wood does an excellent job. Only if the structural element will work in tension, the first grade is required.
Rafter systems are arranged from a board or a bar, they are selected with a margin of safety, focusing on the standard dimensions of the lumber produced in-line.
Calculations of the bearing capacity of the rafter legs are carried out in two states, these are:
- Estimated. A condition in which, as a result of an applied load, a structure collapses. Calculations are carried out for the total load, which includes the weight of the roofing pie, the wind load, taking into account the number of storeys of the building, and the mass of snow, taking into account the slope of the roof.
- Regulatory. A condition in which the truss system sags, but the destruction of the system does not occur. It is usually impossible to operate the roof in this condition, but after repair operations it is quite suitable for further use.
In the simplified calculation variant, the second state is 70% of the first value. Those. to obtain standard indicators, the calculated values \u200b\u200bmust be tritely multiplied by a factor of 0.7.
Loads depending on the climatic data of the construction region are determined according to the maps attached to SP 20.13330.2011. The search for standard values on maps is extremely simple - you need to find the place where your city, cottage village or other nearest settlement is located, and take readings about the calculated and standard values from the map.
The average information about snow and wind load should be adjusted according to the architectural specifics of the house. For example, the value taken from the map must be distributed among the slopes in accordance with the wind rose compiled for the area. You can get a printout with it from your local weather service.
On the windward side of the building, the mass of snow will be much less, so the calculated indicator is multiplied by 0.75. On the leeward side, snow deposits will accumulate, so multiply here by 1.25. Most often, in order to unify the material for building a roof, the leeward part of the structure is constructed from a paired board, and the windward part is arranged with the rafters of their single board.
If it is not clear which of the slopes will be on the leeward side, and which vice versa, then it is better to multiply both by 1.25. The margin of safety does not hurt at all, if it does not increase the cost of lumber too much.
The calculated snow weight indicated by the map is still adjusted depending on the steepness of the roof. From the slopes, set at an angle of 60º, the snow will immediately slide off without the slightest delay. In calculations for such steep roofs, the correction factor is not applied. However, at a lower slope, the snow will already be able to linger, therefore, for slopes of 50º, an additive in the form of a coefficient of 0.33 is applied, and for 40º it is the same, but already 0.66.
The wind load is determined in the same way on the corresponding map. The value is adjusted depending on the climatic specifics of the area and on the height of the house.
To calculate the bearing capacity of the main elements of the designed truss system, it is required to find the maximum load on them, summing up the temporary and permanent values. No one will reinforce roofs before a snowy winter, although in the country it would be better to put safety vertical struts in the attic.
In addition to the mass of snow and the pressing force of the winds, it is necessary to take into account the weight of all elements of the roofing pie in the calculations: the lathing installed over the rafters, the roof itself, insulation, internal filing, if it was used. The weight of vapor and waterproofing films with membranes is usually neglected.
Information about the weight of materials is indicated by the manufacturer in the technical data sheets. Data on the mass of the bar and board are taken as an approximation. Although the mass of the crate per meter of projection can be calculated based on the fact that a cubic meter of lumber weighs an average of 500 - 550 kg / m 3, and a similar volume of OSB or plywood is from 600 to 650 kg / m 3.
The load values \u200b\u200bgiven in SNiPs are indicated in kg / m 2. However, the rafter perceives and holds only the load that directly presses on this linear element. In order to calculate the load specifically on the rafters, the totality of the natural tabular values of the loads and the mass of the roofing pie is multiplied by the installation step of the rafter legs.
The load value reduced to linear parameters can be reduced or increased by changing the step - the distance between the rafters. By adjusting the load collection area, its optimal values \u200b\u200bare achieved in the name of the long service life of the pitched roof frame.
Determination of the section of the rafters
Rafter legs of roofs of various steepness perform an ambiguous job. The bending moment acts on the rafters of gently sloping structures, and a compressive force is added to the analogues of steep systems. Therefore, in the calculations of the section of the rafters, the slope of the slopes is necessarily taken into account.
Calculations for structures with a slope up to 30º
Only bending stress acts on the rafter legs of the roofs of the specified steepness. They are calculated for the maximum bending moment with the application of all types of load. Moreover, temporary, i.e. climatic loads are used in the calculations for maximum performance.
For rafters that have only supports under both of their own edges, the point of maximum bending will be in the very center of the rafter leg. If the rafter is laid on three supports and is made up of two simple beams, then the moments of maximum bending will fall on the middle of both spans.
For a solid rafter on three supports, the maximum bend will be in the area of \u200b\u200bthe central support, but since there is a support under the bending section, then it will be directed upwards, and not, as in the previous cases, downwards.
For the normal operation of the rafter legs in the system, two rules must be followed:
- The internal stress formed in the rafter during bending as a result of the load applied to it must be less than the calculated value of the bending resistance of the lumber.
- The deflection of the rafter leg must be less than the normalized deflection value, which is determined by the ratio L / 200, i.e. the element is allowed to bend only by one two-hundredth of its real length.
Further calculations consist in the sequential selection of the dimensions of the rafter leg, which as a result will satisfy the specified conditions. There are two formulas for calculating the cross section. One of them is used to determine the height of a board or beam by an arbitrarily given thickness. The second formula is used to calculate the thickness at an arbitrary height.
In calculations, it is not necessary to use both formulas, it is enough to apply only one. The result obtained as a result of calculations is checked for the first and second limit states. If the calculated value turned out with an impressive margin of safety, an arbitrary indicator entered into the formula can be reduced so as not to overpay for the material.
If the calculated value of the bending moment is greater than L / 200, then an arbitrary value is increased. The selection is carried out in accordance with the standard sizes of commercially available lumber. So the section is selected until the moment when the optimal variant is calculated and obtained.
Consider a simple example of calculations using the formula b = 6Wh². Assume h = 15 cm and W is the M/R ratio of the bend. The value of M is calculated by the formula g × L 2 / 8, where g is the total load vertically directed to the rafter leg, and L is the span length equal to 4 m.
R izg for softwood lumber is taken in accordance with technical standards 130 kg / cm 2. Suppose we calculated the total load in advance, and we got it equal to 345 kg / m. Then:
M = 345 kg/m × 16m 2 /8 = 690 kg/m
To convert to kg / cm, divide the result by 100, we get 0.690 kg / cm.
W \u003d 0.690 kg / cm / 130 kg / cm 2 \u003d 0.00531 cm
B = 6 × 0.00531 cm × 15 2 cm = 7.16 cm
We round the result as it should be up and we get that for the installation of rafters, taking into account the load given in the example, a beam of 150 × 75 mm is required.
We check the result for both states and make sure that the material with the now calculated cross section is suitable for us. σ = 0.0036; f = 1.39
For truss systems with a slope over 30º
Roof rafters with a steepness of more than 30º are forced to resist not only bending, but also the force compressing them along their own axis. In this case, in addition to checking the bending resistance described above and the magnitude of the bend, it is necessary to calculate the rafters by internal stress.
Those. actions are performed in a similar order, but there are several more verification calculations. In the same way, an arbitrary height or arbitrary thickness of lumber is set, with its help the second section parameter is calculated, and then it is checked for compliance with the above three specifications, including compressive strength.
If necessary, to increase the bearing capacity of the rafters, arbitrary values \u200b\u200bentered into the formulas are increased. If the margin of safety is large enough and the standard deflection significantly exceeds the calculated value, then it makes sense to perform the calculations again, reducing the height or thickness of the material.
To select the initial data for the production of calculations, a table will help, which summarizes the generally accepted sizes of lumber produced by us. It will help you choose the cross section and length of the rafter legs for the initial calculations.
Video about rafter calculations
The video clearly demonstrates the principle of performing calculations for the elements of the truss system:
Performing load bearing and rafter angle calculations is an important part of roof framing design. The process is not easy, but it is necessary to understand it both for those who make calculations manually and for those who use the calculation program. You need to know where to take tabular values and what the calculated values \u200b\u200bare given.
truss system, undoubtedly, is the most important structural element of any pitched roof. The consequence of its improper installation can be not only the deformation of the roof, requiring expensive repairs, but also the complete collapse of the roof on the head of an insolvent builder.
The following four main factors influence the stability of the truss system to various loads:
- fastening strength rafters to the ridge and Mauerlat;
- correct calculation of the supporting structure for rafters, depending on the length of the span;
- choice roofing material;
- step between the rafters.
The topic of this article is the choice of material and pitch between the rafters, taking into account the intended type of roof.
What are the calculations based on?
When making calculations, four main indicators are taken into account:
The most important is the calculation of the maximum roof load, consisting of:
- rafter weights,
- crate weight,
- weight of roofing material and insulation,
- snow load (reference information unique to each region),
- wind load (also reference information),
- person's weight (if repair or cleaning is necessary, 175 kg/sq.m).
To carry out accurate calculations, experts use special formulas from sopromat, but when building a private one, you can use approximate recommendations.
Method for calculating the distance between the rafters
Accurate Distance Calculation between rafters is based on the results of a preliminary calculation of the maximum allowable step. To make this calculation, the total load, the roof structure and the material used on the rafter legs are taken into account.
Method for calculating the step of the roof frame:
- Measure the length of the roof from end to end.
- Received distance divided by the maximum step size.
- The resulting value is rounded up to a larger integer.. This is the number of inter-rafter spans.
- Divide the total length of the roof by the number of spans. This is the required rafter step size.
- Add one to the number of spans.This is the required number of rafters.
For some types of roofing material it is desirable to use fixed distances between the rafters, in which case an additional rafter with a non-standard pitch is installed on one of the ends of the roof.
Rafter leg step depending on the material
Can be increased as the strength of the material from which they are made increases. Most often, for each roofing material, the step of the rafters required for it and the permissible sections of the rafter legs, taking into account the load, are indicated.
These recommendations are regional character and are applicable to the central strip of Russia and more southern regions. Before developing a drawing, you should definitely check the level of wind pressure and snow cover in your region, and adjust the pitch and / or cross section of the rafters.
In those regions where the snow load significantly exceeds the wind load, the use of roofs with a slope is recommended. 35 – 45 degrees.
truss system in private houses, it is most often made of logs with a diameter 12 - 22 cm, beam/board thickness 40 – 100 mm and width 150 - 220 mm. When calculating, it is possible to allow the use instead of logs of a certain diameter of bars of the same width, thickness 100 mm.
Rafter structure for corrugated board
Roof structure for ceramic tiles
Ceramic tiles has significant differences from other types of roofing materials, which must be taken into account when designing a truss systems for it:
- 5 to 10 times the weight resulting in doubling the weight of the entire roof. This leads to the need to use the frequent step ( 0.6-0.8 meters) and increased by 25% cross-sectional area of the rafters.
- Fine-grained nature of the material. Increases the requirements for the accuracy of the installation of the transverse battens. The step of the sheathing beam, the permissible sections and installation angles are always indicated in the instructions for each specific tile model.
There are models of tiles designed for installation at an angle. 12 - 60 degrees, ordinary models are recommended to be mounted at an angle 20 - 45 degrees. For crates most often use timber 50x50 mm.
Roof structure for metal roofing
metal tile in fact, it is a less rigid and lighter decorative version of corrugated board, therefore the requirements for the rafter system, in particular for the recommended sections of the rafter legs, are largely the same.
A feature of the truss structure under the metal tile can be called a significant reduction in the pitch of the crate, which should be equal to the length of the longitudinal wave (30 cm for most species). This leads to the need to reduce the distance between the rafters. up to 0.6 - 1 m, to reduce the cost of lumber for the crate. The angle of the roof slope is selected from 22 to 45 degrees.
Rafter structure for ondulin
Ondulin- slate based on fiberglass and bitumen, produced by only one manufacturer and has unified technological installation standards:
- permissible mounting angle - 5 - 45 degrees;
- distance between rafters - 60 cm at a slope angle of up to 15 degrees, up to 90 cm - at an angle of more than 15 degrees;
- crate - solid plywood on a slope up to 10 degrees, board 30x100 mm step by step 45 cm on the slope 10 - 15 degrees, bar 40x50 mm step by step 60 cm on the slope above 15 degrees.
Given the low weight of the material, the cross section of the rafter legs is selected based on the same recommendations as for corrugated board.
Rafter construction under a covering from slate
Slate- traditional, rather rigid and heavy roofing material, fragile, but resistant to constant loads. Such properties change the recommendations for the optimal design of the truss system towards the use of more durable elements and increasing the step between them:
- Due to low tightness, it is undesirable to use slate roofs with a slope angle of less than 22 degrees. If it is necessary to install such a roof, you can use the recommendations for installing an ondulin as an instruction, adjusted for the universal batten pitch - 55 cm.
- Permissible angle for installing rafters under slate - up to 60 degrees.
- The installation step is selected from 0.8 to 1.5 m, depending on the section of the rafter leg, the load and the presence of the crate material.
- The material for the rafters is selected with a slightly larger section than for light roofs. For the most popular move 1.2 m a bar is taken with a section from 75x150 to 100x200 mm, depending on the length of the span between the supports.
- Material for the crate selected in accordance with the distance between the rafters - timber 50x50 mm up to 1.2 m, beam 60x60 mm - 1.2 m and more.
- Lathing step is selected in such a way that each sheet lies on three bars, and has an overlap on 15 cm with neighboring. Considering the standard sheet length 1.75 m, step is used 80 cm.
Rafters for single-pitched and double-pitched roofs
What is the distance of the rafters for a pitched roof? shed roof does not require a complex truss structure. The rafters are laid from wall to wall, most often without the use of a Mauerlat, directly on the crown.
No extra ribs stiffness sets the maximum slope angle - 30 degrees and allowable span length - less than 6 m(for wooden rafters). The optimal angle 15 - 20 degrees.
Such roofs usually not subject to wind loads, but require protection from precipitation. In regions where wind pressure is comparable to snow load, the correct installation of a shed roof "in the wind" can lead to self-cleaning of the roof.
gable roof is a system of parallel triangles interconnected by a Mauerlat and a ridge. There are many elements for firmly fastening the sides of the triangle to each other and transferring loads from the rafter legs to the walls - racks, ties, jibs, support beams, and so on.
The step between the rafters of a gable roof is made taking into account the size of the heat insulator that is laid between them. Approximate step between rafter legs 1-1.2 meters
Rigid Triangle Strength increases as its shape approaches isosceles, therefore, with an increase in the slope angle up to 60 degrees you can expand the step between the rafters.
However, this will also lead to an increase in material consumption and to a multiple increase in the windage of the roof. The optimal slope angle for snowy regions is 45 degrees, for windy - 20 degrees.
Distance between rafters roofs attic type determines how much of the load falls on each element. When designing hip roofing step rafters should be between 60 cm and 1 m.
- The correct fastening of the rafters is no less important than the correct calculation of the structure. Before installing the roof yourself, you should take a lesson from an experienced carpenter and read educational literature.
- When choosing a rafter pitch, do not forget about thermal insulation. All types of insulation can shrink a little, so you can buy them by approximate size. The most commonly produced sizes are 60, 80, 100, 120 cm.
- For roofs with a slope of 45 degrees or more, the weight of a person on the roof can be ignored. This removes 175 kilograms of design load per square meter and allows you to put rafters on average 20% less often.
- Snow and wind load in Russian regions can be found by regulatory documents - maps in the application AND to .
- There are many online roof calculators on the web., capable of, if not correctly calculating all the nuances, then at least advise on the selection of the correct section for the rafters.
To draw up a technical project for a house, it is necessary to calculate the rafters. There are several options for roof structures.
Rafter legs that rest on two supports, while not having any additional stops, are called rafters without struts. They are used for shed roofs, the span of which is about 4.5 meters, or for gable roofs, the span of which is about 9 meters. The rafter system is used either with the transfer of the thrust load to the Mauerlat, or without transfer.
The bending rafter, which does not transfer the load to the walls, has one support firmly fixed and freely rotating. The other support is movable and rotates freely. Three options for attaching rafters can meet these conditions. Let's consider each in detail.
The hemming of the top of the rafter leg or the upper support cut is installed in a horizontal position. It is enough just to change the method of supporting the run, and the rafter leg will immediately show the thrust. This calculation of the rafter leg, due to the rigidity of the conditions for creating the upper node, is usually not used for gable roofs. Most often it is used in the construction of shed roofs, since the slightest inaccuracy in the manufacture of the assembly will turn the non-expansion scheme into a spacer. In addition, in gable types of roofs, if there is no thrust on the Mauerlat, due to the deflection of the rafters under the action of the load, the destruction of the roof ridge assembly may occur.
At first glance, this system may seem unrealistic in execution. Since an emphasis on the Mauerlat is created on the lower part of the rafter, in fact, the system must exert pressure on it, that is, a horizontal force. However, it does not show the expansion load.
Thus, in all three options, the following rule is observed: one edge of the rafter is installed on a sliding support, which allows you to turn. The other is on a hinge that only allows rotation. Fastening rafter legs on sliders are installed using a variety of designs. Most often they are performed using mounting plates. It is also possible to fasten with nails, self-tapping screws, using overhead bars and boards. It is only necessary to choose the right type of fastener that will prevent the rafter leg from sliding in the support.
How to calculate rafters
In the process of calculating the truss structure, as a rule, an “idealized” calculation scheme is adopted. Based on the fact that a certain uniform load will press on the roof, that is, an equal and identical force that acts evenly along the planes of the slopes. In reality, there is no uniform load on all roof slopes. So, the wind sweeps snow on some slopes and blows off from others, the sun melts from some slopes and does not reach the rest, the same situation with landslides. All this makes the load on the slopes completely uneven, although outwardly it may not be noticeable. However, even with an unevenly distributed load, all three of the above options for truss mounts will remain statically stable, but only under one condition - a rigid connection of the ridge run. In this case, the run is either supported by slanting rafter legs, or inserted into the gables of the wall panels of the hip roofs. That is, the truss structure will remain stable only if the ridge run is firmly fixed from possible horizontal displacement.
In the case of manufacturing a gable roof and supporting the purlin only on posts, without relying on the walls of the fronts, the situation worsens. In options numbered 2 and 3, with a decrease in the load on any slope, opposite the calculation on the opposite slope, the roof may move in the direction where the load is greater. The very first option, when the very bottom of the rafter leg is made with a notch with teeth or with a hemming of a support bar, while the top of the horizontal notch is laid on a run, will hold an uneven load well, but only if the uprights that hold the ridge run are perfectly vertical.
In order to give stability to the rafters, a horizontal scrum is included in the system. It is slightly, but still increases stability. That is why in those places where the fight intersects with the racks, it is fixed with a nail fight. The statement that the fight always works only on stretching is fundamentally not true. The fight is a multifunctional element. So, in a non-thrust truss structure, it does not work in the absence of snow on the roof, or it only works in compression when a slight uniform load appears on the slopes. The structure works in tension only during subsidence or deflection of the skate run under the influence of the maximum load. Thus, the fight is an emergency element of the truss structure, which comes into operation when the roof is littered with a large amount of snow, the ridge run turns out to be bent to the maximum calculated value, or uneven unforeseen subsidence of the foundation occurs. The consequence may be uneven subsidence of the ridge run and walls. Thus, the lower the contractions are set, the better. As a rule, they are installed at such a height that they would not create obstacles when walking in the attic, that is, at a height of about 2 meters.
If in options 2 and 3 the lower rafter support unit is replaced with a slider with the edge of the rafter leg extended beyond the wall, then this will strengthen the structure and make it statically stable with completely different combinations of the structure.
Also, one good way to increase the stability of the structure is to fix the bottom of the racks quite rigidly, which will support the run. They are installed by cutting into the bed and fixed with ceilings by any available means. Thus, the lower strut support assembly is converted from a hinged assembly to a rigid pinch assembly.
How to calculate the length of the rafters does not depend on the method of attaching the rafter legs.
The cross section of contractions, due to the development of rather small stresses in them, does not take into account the rafters, but is taken quite constructively. In order to reduce the size of the elements that are used in the construction of the truss structure, the cross section of the scrum is taken to be the same size as the rafter leg, while thinner disks can be used. Contractions are installed either on one or both sides of the rafters and fastened with bolts or nails. When calculating the section of the truss structure, contractions are not taken into account at all, as if they do not exist at all. The only exception is the bolting of the contractions to the rafter legs. In this case, the load-bearing capacity of the wood, due to the weakening of the bolt hole, is reduced by using a factor of 0.8. Simply put, if holes are drilled in the rafter legs for the installation of bolt fights, then the calculated resistance must be taken in the amount of 0.8. When fixing the fights on the rafters only with a nail fight, the weakening of the resistance of the rafter tree does not occur.
But it is necessary to calculate the number of nails. The calculation is made on the cut, that is, the bending of the nails. For the calculated force, they take the spacer, which occurs in the emergency position of the truss structure. Simply put, in the calculation of the connection with nails of the scrum and the rafter leg, a spacer is introduced, which is absent in the standard operation of the rafter system.
The static instability of the trussless system manifests itself only on those roofs where it is not possible to install a ridge run that protects against horizontal displacement.
In buildings with hipped roofs and gables made of stone or brick, non-bracing rafter systems are quite stable and there is no need to take measures to ensure greater stability. However, to prevent accidents of structures, contractions should still be installed. When installing bolts or studs as fasteners, you should pay attention to the diameter of the holes for them. It should be the same as the diameter of the bolts or slightly smaller. In the event of an emergency, the wrench will not work until the gap between the wall of the hole and the stud is selected.
Please note that in this process the bottoms of the rafter legs will move apart at a distance of several millimeters to several centimeters. This can lead to shifting and scrolling of the Mauerlat and to the destruction of the wall cornice. In the case of spacer truss systems, when the mauerlat is firmly fixed, this process can cause the walls to move apart.
Expanded rafters
The rafter that performs bending work and transfers the thrust load to the wall panels must have at least two fixed supports.
To calculate this type of truss systems, we replace the lower supports with different degrees of freedom in the previous schemes with supports with a single degree of freedom - hinged. To do this, where they are not, bars for support are nailed to the edges of the rafter legs. As a rule, a bar is used, the length of which is at least a meter, and the cross section is about 5 by 5 cm, given the nail connection. In another embodiment, it is possible to arrange a support in the form of a tooth. In the first version of the calculation scheme, when the rafters abut horizontally against the run, the upper ends of the rafters are sewn either with nails or with a bolt. Thus, a hinged support is obtained.
As a result, the calculation schemes practically do not change. Internal bending and compression stresses remain unchanged. However, a spacer force appears in the former supports. In the upper nodes of each rafter leg, the oppositely directed spacer, originating from the end of the other rafter leg, disappears. Thus, it does not cause much trouble.
The edges of the rafters, which abut against each other or through the run, may be checked for material collapse.
In rafter spacer systems, the purpose of the fight is different - in emergency situations, it works in compression. In the process of work, it reduces the thrust on the walls of the edge of the rafters, but does not completely exclude it. She will be able to remove it completely if she fixes herself at the very bottom, between the edges of the rafter legs.
Please note that the use of spacer layered truss structures requires careful consideration of the effect of the spacer force on the walls. It is possible to reduce this thrust by installing rigid and durable ridge runs. It is necessary to try to increase the rigidity of the run by installing racks, cantilever beams or struts, or to build a construction lift. This is especially true for houses made of timber, chopped logs, lightweight concrete. Concrete, brick and panel houses are much easier to bear the force of thrust on the walls.
Thus, the truss structure, erected according to the spacer option, is statically stable under various combinations of loads, it does not require a rigid attachment of the Mauerlat to the wall. In order to keep the thrust, the walls of the building must be massive, equipped with a monolithic reinforced concrete belt around the perimeter of the house. In the event of an emergency, inside the spacer system, which works in compression, the fight will not save the situation, but will only partially reduce the spacer, which is transmitted to the walls. It is precisely in order that an emergency would not occur, it is necessary to take into account all the loads that can act on the roof.
Thus, no matter what shape the roof of the house is chosen, the entire truss system must be calculated in such a way as to satisfy the provisions of reliability and strength. To make a complete analysis of the truss structure is not an easy task. A large number of different parameters must be included in the calculation of wooden rafters, including thrust, bending, and possible weight loads. For a more reliable arrangement of the truss system, it is possible to install more suitable fastening methods. At the same time, one should not take the dimensions of the rafters without making a full analysis of their technical and functional abilities.
Calculation of the section of the rafters
The cross section of the truss beams is selected taking into account their lengths and the load received.
So, a beam up to 3 meters long is selected with a section diameter of 10 cm.
A beam, up to 5 meters long, with a section diameter of 20 cm.
A beam, up to 7 meters long - with a cross-sectional diameter of up to 24 cm.
How to calculate rafters - an example
Given a two-story house measuring 8 by 10 meters, the height of each floor is 3 meters. Corrugated asbestos-cement sheets were chosen for the roof. The roof is gable, the supporting posts of which are located along the central load-bearing wall. The pitch of the rafters is 100 cm. It is required to choose the length of the rafters.
How to calculate the length of the rafters? As follows: the length of the rafter legs can be chosen so that three rows of slate sheets can be laid on them. Then the required length: 1.65 x3 \u003d 4.95 m. The roof slope in this case will be 27.3 °, the height of the triangle formed, that is, the attic space, is 2.26 meters.
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