We present a free calculator for gable roof calculations. Online calculation of the sheathing, the angle of the rafters and the required amount of materials.
Specify roofing material:
Select a material from the list -- Slate (corrugated asbestos cement sheets): Medium profile (11 kg/m2) Slate (corrugated asbestos cement sheets): Reinforced profile (13 kg/m2) Corrugated cellulose-bitumen sheets (6 kg/m2) Bitumen (soft , flexible) tiles (15 kg/m2) Galvanized sheet (6.5 kg/m2) Sheet steel (8 kg/m2) Ceramic tiles(50 kg/m2) Cement-sand tiles (70 kg/m2) Metal tiles, corrugated sheets (5 kg/m2) Keramoplast (5.5 kg/m2) Seam roofing (6 kg/m2) Polymer-sand tiles (25 kg/m2) m2) Ondulin (Euro slate) (4 kg/m2) Composite tiles(7 kg/m2) Natural slate (40 kg/m2) Specify the weight of 1 square meter of coating (? kg/m2)
kg/m2
Enter roof parameters:
Base width A (cm)
Base length D (cm)
Lifting height B (cm)
Length of side overhangs C (cm)
Front and rear overhang length E (cm)
Rafters:
Rafter pitch (cm)
Type of wood for rafters (cm)
Working area of the side rafter (optional) (cm) ">
Lathing calculation:
Sheathing board width (cm)
Sheathing board thickness (cm)
Distance between sheathing boards
F (cm)
Snow load calculation:
Select your region using the map below
1 (80/56 kg/m2) 2 (120/84 kg/m2) 3 (180/126 kg/m2) 4 (240/168 kg/m2) 5 (320/224 kg/m2) 6 (400/280 kg/m2) 7 (480/336 kg/m2) 8 (560/392 kg/m2)
Wind load calculation:
Ia I II III IV V VI VII
Height to the ridge of the building
5 m from 5 m to 10 m from 10 m
Terrain type
Open area Closed area Urban areas
Calculation results
Roof angle: 0 degrees.
The angle of inclination is suitable for this material.
It is advisable to increase the angle of inclination for this material!
It is advisable to reduce the angle of inclination for this material!
Roof surface area: 0 m2.
Approximate weight roofing material: 0 kg.
Number of rolls of insulating material with 10% overlap (1x15 m): 0 rolls.
Rafters:
Load on the rafter system: 0 kg/m2.
Rafter length: 0 cm
Number of rafters: 0 pcs.
Lathing:
Number of rows of sheathing (for the entire roof): 0 rows.
Uniform distance between sheathing boards: 0 cm
Number of sheathing boards with a standard length of 6 meters: 0 pcs.
Volume of sheathing boards: 0 m3.
Approximate weight of sheathing boards: 0 kg.
Additional information about the calculator
An online calculator for a gable (gable) roof will help you calculate the angle of the slope, the size and number of rafters, the amount of sheathing, and the volume necessary materials in online mode. The calculation base includes in advance such common roofing materials as metal tiles, slate, ondulin, tiles made of ceramics, bitumen, cement and other materials.
Note! Calculations are made based on SNiP “Loads and Impacts” and TKP 45-5.05-146-2009, taking into account the standards contained in these documents.
A gable roof (also spelled “gable roof”, “gable roof”) is a variant of a roof with two slopes running from the ridge to the outer walls of the building. Today this is the most common type of roof, due to its ease of execution, low cost and attractive appearance.
The rafters in the construction of such a roof rest on each other in pairs and are connected by sheathing. End sides structures with such a roof have the shape of a triangle and are called pediments (sometimes gables). Usually, an attic is installed under a gable roof, and small attic windows are made on the gables for lighting.
When filling out the fields of the calculator, pay attention to the “Additional information” icon, which hides explanations for each item.
The calculation results are also accompanied by explanations, which you can read below.
Explanations for the calculation results
Roof angle
This is the name of the angle at which the slope and rafters are inclined to the plane of the ceiling. The calculations were made taking into account the fact that it is planned to build a symmetrical gable roof. By entering an angle, you can not only calculate the required amount of materials for a given angle, but also check whether it is possible to build a roof at this angle from the materials you have chosen. You can decrease or increase the angle by changing the width of the base or the height of the rise: these parameters are strictly interconnected.
Roof surface area
The total area of the roof slopes, including the area of overhangs of a given length. Determines the amount of roofing and under-roofing material required during roof construction.
Approximate weight of roofing material
Estimated total weight of roofing material.
Number of rolls of insulation material
The required amount of under-roofing material, taking into account the required overlap of 10%. In our calculations, we assume rolls 15 meters long and 1 meter wide.
Load on the rafter system
The maximum possible load, taking into account wind and snow loads, on the rafters.
Rafter length
Rafters are measured from the base of the slope to the ridge of the roof.
Number of rafters
The total number of rafters required for rafter system roofs at a given pitch.
Minimum rafter section
To ensure the roof has sufficient strength, it is necessary to select rafters with the section options suggested here.
Number of rows of sheathing
With the parameters you specify, this number of rows of sheathing will be required. If you need to determine the number of rows for one slope, then this value must be divided by 2.
Uniform distance between sheathing boards
To eliminate waste of materials and save yourself from unnecessary trimming work, you need to choose a given distance between the sheathing boards.
Volume of sheathing boards
The number of boards required to sheath the entire roof (in cubic meters).
Design and competent calculations of elements truss structure– the key to success in the construction and subsequent operation of the roof. It must firmly resist a combination of temporary and permanent loads, while adding minimal weight to the structure.
To perform calculations, you can use one of the many programs available on the Internet, 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 rafter 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 rafter legs, one should avoid flaws and try to eliminate shortcomings.
As a rule, in design developments several options are considered from which to choose optimal solution. Choice the best option does not mean at all that you need to create a certain number of projects, perform accurate calculations for each and ultimately choose the only one.
The very process of determining the length, installation slope, and cross-section of the rafters lies in the 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 rafter leg Initially, the cross-section parameters of the material most suitable for the price are entered. And if the result does not meet technical standards, then increase or decrease the size of the lumber until maximum compliance is achieved.
Inclination angle search method
Determining the slope angle pitched design there are architectural and technical aspects. In addition to the proportional configuration that best suits the style of the building, an impeccable solution should take into account:
- Snow load indicators. In areas with heavy rainfall, roofs with a slope of 45º or more are erected. Snow deposits do not linger on slopes of such steepness, due to which the total load on the roof, footings and the building as a whole is significantly reduced.
- Wind load characteristics. In areas with gusty strong winds, coastal, steppe and mountain areas, low-slope structures of a streamlined shape are built. The steepness of the slopes there usually does not exceed 30º. In addition, winds prevent the formation of snow deposits on roofs.
- Weight and type of roofing covering. The greater the weight and the smaller the roof elements, the steeper the rafter frame needs to be constructed. This is necessary to reduce the likelihood of leaks through connections and reduce specific gravity coverage per unit horizontal projection of the roof.
To choose optimal angle the slope of the rafters, the project must take into account all the listed requirements. The steepness of the future roof must correspond climatic conditions the area chosen for construction and the technical data of the roofing covering.
True, property owners in northern windless areas should remember that as the angle of inclination of the rafter legs increases, 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, you should not reduce the slope too much in order to save money. Excessively sloping roofs are disadvantageous in architectural terms and do not always help reduce costs. In such cases, strengthening of the insulating layers is most often required, which, contrary to the expectations of the economist, leads to higher construction costs.
The slope of the rafters is expressed in degrees, as a percentage, or in the format of dimensionless units that reflect the ratio of half the meter of the span to the installation height of the ridge run. It is clear that the angle between the ceiling line and the slope line is delineated in degrees. Percentages are rarely used because they are difficult to perceive.
The most common method of indicating the angle of inclination of rafter legs, used by both designers of low-rise buildings and builders, is dimensionless units. They convey in fractions the ratio of the length of the covered span to the height of the roof. On site, the easiest way is 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, rather than putting corners away from the edge of the slope.
Calculation of the length of the rafter leg
The length of the rafters is determined after the angle of inclination of the system is selected. Both of these values cannot be considered exact values, because in the process of calculating the load, both the steepness and the subsequent length of the rafter leg may change slightly.
The main parameters that influence the calculation of the length of the rafters include the type of eaves overhang of the roof, according to which:
- The outer edge of the rafter legs is cut flush with the outer surface of the wall. In this situation, the rafters do not form a cornice overhang that protects the structure from precipitation. To protect the walls, a drain is installed, secured to a cornice board nailed to the end edge of the rafters.
- The rafters, cut flush with the wall, are extended with fillets to form a cornice overhang. The fillies are attached to the rafters with nails after the construction of the rafter frame.
- The rafters are initially cut taking into account the length of the eaves overhang. In the lower segment of the rafter legs, notches in the form of an angle are chosen. To form notches, step back from the lower edge of the rafters to the width of the eaves extension. Notches are needed to increase the supporting area of the rafter legs and to install support units.
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 the bypasses or to the upper crown of the log house. If it is planned to install the rafters flush with the external contour of the house, then the calculation is carried out according to 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 along the upper edge of the rafter along with the overhang. Note that the use of triangular notches significantly speeds up the pace of construction of the rafter frame, but weakens the elements of the system. Therefore, when calculating the load-bearing capacity of rafters with selected cutting angles, a coefficient of 0.8 is used.
The average width of the cornice extension is considered to be traditional 55 cm. However, the spread can be from 10 to 70 or more. The calculations use the projection of the cornice extension onto the 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 advise extending the roof beyond the contour of the walls to a distance of more than 10 cm, so that the snow mass accumulating along the eaves of the roof cannot damage the edge of the cornice.
It is not customary to equip steep roofs with wide overhangs; regardless of the material, the eaves are not made wider than 35 - 45 cm. But structures with a slope of up to 30º can be perfectly complemented by a wide eaves, which will serve as a kind of canopy in areas with excess sunlight. In the case of designing roofs with eaves extensions of 70 cm or more, they are strengthened with additional support posts.
How to calculate load-bearing capacity
In construction rafter frames Lumber made from softwood is used. The prepared timber or board must be at least second grade.
Rafter legs pitched roofs work on the principle of compressed, curved and compressed-curved elements. Second-grade wood copes excellently with the tasks of resisting compression and bending. Only if the structural element will work in tension is the first grade required.
Rafter systems are made from boards or timber, they are selected with a margin of safety, focusing on the standard sizes of lumber produced in-line.
Calculations of the load-bearing capacity of rafter legs are carried out in two states, these are:
- Estimated. A condition in which a structure collapses as a result of an applied load. Calculations are carried out for the total load, which includes the weight of the roofing pie, wind load taking into account the number of floors of the building, and the mass of snow taking into account the roof slope.
- Regulatory. A condition in which the rafter system bends, but the system does not collapse. It is usually impossible to operate a roof in this condition, but after repair operations it is quite suitable for further use.
In a simplified calculation version, the second state is 70% of the first value. Those. to obtain standard indicators calculated values you just need to multiply it by a factor of 0.7.
Loads depending on the climatic data of the construction region are determined from the maps attached to SP 20.13330.2011. Searching for standard values on maps is extremely simple - you need to find the place where your city, cottage community or other nearby locality, and take readings about the calculated and standard value from the card.
Average information about snow and wind loads 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 of it from your local weather service.
On the windward side of the building, the mass of snow will be much less, so the calculated figure is multiplied by 0.75. On the leeward side, snow deposits will accumulate, so they multiply here by 1.25. Most often, in order to unify the material for roof construction, the leeward part of the structure is constructed from a paired board, and the windward part is constructed with rafters from a single board.
If it is unclear which of the slopes will be on the leeward side and which on the contrary, then it is better to multiply both by 1.25. The margin of safety will not hurt at all, if it does not increase the cost of lumber too much.
The estimated snow weight indicated by the map is also adjusted depending on the steepness of the roof. From the slopes, installed at an angle of 60º, the snow will immediately slide off without the slightest delay. In calculations for such steep roofs, a correction factor is not used. However, at a lower slope, snow can already be retained, so for slopes of 50º an additive is used in the form of a coefficient of 0.33, and for 40º it is the same, but already 0.66.
Wind load is determined in a similar way by corresponding map. The value is adjusted depending on the climatic specifics of the area and the height of the house.
To calculate the load-bearing capacity of the main elements of the designed rafter system, it is necessary to find the maximum load on them, summing up the temporary and permanent values. Nobody will strengthen the roofs before a snowy winter, although at the dacha it would be better to install vertical safety struts in the attic.
In addition to the mass of snow and the pressing force of the winds, calculations must take into account the weight of all elements of the roofing pie: the sheathing installed on top of the rafters, the roof itself, insulation, and inner sheathing, if used. The weight of vapor and waterproofing films with membranes is usually neglected.
Information on the weight of materials is indicated by the manufacturer in technical passports. Data on the mass of the block and board are taken as an approximation. Although the mass of the sheathing per meter of projection can be calculated, taking as a basis the fact that a cubic meter of lumber weighs on average 500 - 550 kg/m3, and a similar volume of OSB or plywood from 600 to 650 kg/m3.
The load values given in SNiPs are indicated in kg/m2. 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 are multiplied by the installation step of the rafter legs.
The load value reduced to linear parameters can be reduced or increased by changing the pitch - the distance between the rafters. By adjusting the load collection area, we achieve its optimal values in the name of long service pitched roof frame.
Determining the cross section of rafters
The rafters of roofs of varying steepness perform ambiguous work. The rafters of flat structures are affected mainly by a bending moment; on analogues of steep systems, a compressive force is added to it. Therefore, when calculating the cross-section of rafters, the slope of the slopes must be taken into account.
Calculations for structures with a slope of up to 30º
Only bending stress acts on the rafters of 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 calculations based on maximum values.
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 made up of two simple beams, then the moments of maximum bending will occur in the middle of both spans.
For a solid rafter on three supports, the maximum bend will be in the area of the central support, but since... there is a support under the bending section, then it will be directed upward, and not downward as in the previous cases.
For 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 one two-hundredth of its actual length.
Further calculations consist of sequential selection of the dimensions of the rafter leg, which will ultimately 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 based on an arbitrarily specified thickness. The second formula is used to calculate the thickness at an arbitrarily specified height.
It is not necessary to use both formulas in calculations; it is enough to use only one. The result obtained as a result of the calculations is checked by the first and second limit state. If the calculated value is obtained with an impressive margin of safety, the 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 turns out to be greater than L/200, then the arbitrary value is increased. The selection is carried out in accordance with the standard sizes of commercially available lumber. This is how the cross section is selected until the optimal option is calculated and obtained.
Let's consider a simple example of calculations using the formula b = 6Wh². Suppose h = 15 cm, and W is the ratio M/R bend. We calculate the value of M using the formula g×L 2 /8, where g is the total load vertically directed on the rafter leg, and L is the span length equal to 4 m.
R bend for softwood lumber is accepted in accordance with technical standards as 130 kg/cm 2. Let's say we calculated the total load in advance, and it turned out to be 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 = 0.690 kg/cm/130 kg/cm 2 = 0.00531 cm
B = 6 × 0.00531 cm × 15 2 cm = 7.16 cm
We round the result up as expected and find that to install the rafters, taking into account the load given in the example, you will need a beam of 150x75 mm.
We check the result for both conditions and make sure that the material with the currently calculated cross-section is suitable for us. σ = 0.0036; f = 1.39
For rafter systems with a slope over 30º
Roof rafters with a slope 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 bending value, it is necessary to calculate the rafters based on internal stress.
Those. the actions are performed in a similar order, but there are slightly 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 a check is carried out for compliance with the above three technical specifications, including compression resistance.
If it is necessary to increase the load-bearing capacity of the rafters, the arbitrary values entered into the formulas are increased. If the safety factor 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.
A table that summarizes the generally accepted sizes of lumber produced by us will help you select the initial data for making calculations. It will help you select the cross-section and length of the rafter legs for initial calculations.
Video about rafter calculations
The video clearly demonstrates the principle of performing calculations for the elements of the rafter system:
Carrying out load-bearing capacity and rafter angle calculations is an important part of roof frame 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 a calculation program. You need to know where to get tabular values and what the calculated values give.
Take advantage online calculator gable roof to calculate the amount of sheathing, the angle of inclination of the rafter system, and the load (wind and snow) on the roof. Our free calculator will help you calculate required amount material for this type of roof.
Specify roofing material:
Select a material from the list -- Slate (corrugated asbestos cement sheets): Medium profile (11 kg/m2) Slate (corrugated asbestos cement sheets): Reinforced profile (13 kg/m2) Corrugated cellulose-bitumen sheets (6 kg/m2) Bitumen (soft , flexible) tiles (15 kg/m2) Galvanized sheet metal (6.5 kg/m2) Sheet steel (8 kg/m2) Ceramic tiles (50 kg/m2) Cement-sand tiles (70 kg/m2) Metal tiles, corrugated sheets (5 kg/m2) Keramoplast (5.5 kg/m2) Seam roofing (6 kg/m2) Polymer-sand tiles (25 kg/m2) Ondulin (Euro slate) (4 kg/m2) Composite tiles (7 kg/m2) ) Natural slate (40 kg/m2) Specify the weight of 1 square meter of coating (? kg/m2)
kg/m2
Enter roof parameters:
Base width A (cm)
Base length D (cm)
Lifting height B (cm)
Length of side overhangs C (cm)
Front and rear overhang length E (cm)
Rafters:
Rafter pitch (cm)
Type of wood for rafters (cm)
Working area of the side rafter (optional) (cm)
Lathing calculation:
Sheathing board width (cm)
Sheathing board thickness (cm)
Distance between sheathing boards
F (cm)
Snow load calculation:
Select your region using the map below
1 (80/56 kg/m2) 2 (120/84 kg/m2) 3 (180/126 kg/m2) 4 (240/168 kg/m2) 5 (320/224 kg/m2) 6 (400/280 kg/m2) 7 (480/336 kg/m2) 8 (560/392 kg/m2)
Wind load calculation:
Ia I II III IV V VI VII
Height to the ridge of the building
5 m from 5 m to 10 m from 10 m
Terrain type
Open area Closed area Urban areas
Calculation results
Roof angle: 0 degrees.
The angle of inclination is suitable for this material.
It is advisable to increase the angle of inclination for this material!
It is advisable to reduce the angle of inclination for this material!
Roof surface area: 0 m2.
Approximate weight of roofing material: 0 kg.
Number of rolls of insulating material with 10% overlap (1×15 m): 0 rolls.
Rafters:
Load on the rafter system: 0 kg/m2.
Rafter length: 0 cm
Number of rafters: 0 pcs.
Lathing:
Number of rows of sheathing (for the entire roof): 0 rows.
Uniform distance between sheathing boards: 0 cm
Number of sheathing boards with a standard length of 6 meters: 0 pcs.
Volume of sheathing boards: 0 m3.
Approximate weight of sheathing boards: 0 kg.
About the calculator
An online calculator for a gable roof, also called a gable roof, will help you calculate the required angle of inclination of the slopes, determine the cross-section and number of rafters, the volume of materials for the sheathing, the consumption of insulating materials, and at the same time take into account existing standards for wind and snow loads. You will not have to perform unnecessary additional calculations, because this calculator contains most of the existing roofing materials. You can easily calculate the consumption and weight of such common materials as bitumen shingles, cement-sand and ceramic tiles, metal tiles, bitumen and asbestos-cement slate, ondulin and others. If you use non-standard material, or want to get more accurate calculations, you can specify the weight of your own roofing material by selecting the appropriate item in the drop-down list of materials.
Note!
The calculator makes calculations in accordance with the current SNiP “Loads and Impacts” and TKP 45-5.05-146-2009.
A gable roof (there are variants of the name “gable roof” and “gable roof”) is the most common type of roof, in which there are two inclined slopes from the ridge to the outer walls of the structure. The popularity of this type of roof is explained by their moderate cost, ease of construction, good performance qualities and attractive appearance.
In this design, the rafters of different slopes rest on each other in pairs and are sheathed with sheathing boards. The end of a building with a gable roof has a triangular shape and is called a pediment (the name “gable” is also found). Typically, under the roof slopes there is an attic space, naturally illuminated by small window openings located in the upper part of the gables.
When filling out the fields of the calculator, you can find out additional information located under the sign.
If you have any questions or ideas regarding this calculator, you can write to us using the form at the bottom of the page. We'd love to hear your opinion.
Additional information about the calculation results
Roof angle
The slope and rafters are inclined at this angle to the base of the roof. Roofing materials have individual maximum roof slope angles, so for some materials the angle may be outside the limits acceptable standards. Whether your angle suits the selected material or not - you will find out in the calculation results. In any case, it is always possible to adjust the height of the roof (B) or the width of the base (A), or choose a different roofing material.
Roof surface area
The area of the entire roof surface, including overhangs. To determine the area of one slope, it is enough to divide the resulting value by two.
Approximate weight of roofing material
Weight of the selected roofing material based on total area roofs (including overhangs).
Number of rolls of insulation material
The amount of insulating material required to build a roof. The quantity in rolls required for the entire roof area is indicated. The roll standard is taken as a basis - 15 meters long, 1 meter wide. The calculation also took into account an overlap of 10% at the joints.
Load on the rafter system
Maximum weight per rafter system. Wind and snow loads, the angle of the roof, as well as the weight of the entire structure are taken into account.
Rafter length
The full length of the rafters from the ridge of the roof to the edge of the slope.
Number of rafters
The total number of rafters required for a rafter system at a given pitch.
Minimum section of rafters / Weight of rafters / Volume of beams
- The first column shows the cross-sections of the rafters according to GOST 24454-80 Softwood lumber. Here are the sections that can be used to build a given structure. The calculator proceeds from the total loads that can affect the structure of a given roof and selects section options that satisfy them.
- The second column indicates the total weight of all rafters with the specified cross-section, if they are used to build a given roof.
- The third column indicates the total volume of this timber in cubic meters. This volume will be useful to you when calculating the cost.
Number of rows of sheathing
The number of rows of sheathing that will be needed for the entire roof with the given parameters. To calculate the number of rows of sheathing for one slope, you need to divide the resulting value by two.
Uniform distance between sheathing boards
Volume of sheathing boards
The total volume of sheathing for a given roof. This value will help you calculate lumber costs.
A gable roof or gable roof is a roof with two slopes, i.e. having 2 inclined surfaces (slopes) of a rectangular shape.
Frame gable roof by virtue of design features ideally combines simplicity of design and maintenance with reliability and durability. These and many other parameters make the construction of a gable roof practical and rational decision for private and commercial housing construction.
In this article, we will look at how to make a rafter system for a gable roof with your own hands. For effective perception of the material, it is presented in the form of step-by-step instructions from A to Z, from selection and calculations, to installation of the Mauerlat and sheathing under the roof. Each stage is accompanied by tables, diagrams, drawings, drawings and photos.
The popularity of the house roof is due to a number of advantages:
- design variability;
- simplicity in calculations;
- naturalness of water flow;
- integrity of the structure reduces the likelihood of leaks;
- efficiency;
- preservation usable area attic or the possibility of arranging an attic;
- high maintainability;
- strength and wear resistance.
Types of gable roof
The installation of a gable roof truss system depends, first of all, on its design.
There are several options for gable roofs (types, types):
The most common roof installation option due to its simplicity and reliability. Thanks to symmetry, a uniform distribution of loads on the load-bearing walls and mauerlat is achieved. The type and thickness of the insulation does not affect the choice of material.
The cross-section of the beam makes it possible to provide a reserve of bearing capacity. There is no possibility of rafters bending. Supports and struts can be placed almost anywhere.
An obvious drawback is the impossibility of arranging a full attic floor. Due to sharp corners, “dead” zones appear that are unsuitable for use.
The arrangement of one angle of more than 45° leads to a reduction in the amount of unused area. There is an opportunity to do living rooms under the roof. At the same time, the requirements for calculations increase, because the load on the walls and foundation will be distributed unevenly.
This roof design allows you to equip a full second floor under the roof.
Naturally, a simple gable rafter roof differs from a broken line, not only visually. The main difficulty lies in the complexity of the calculations.
Design of a gable roof truss system
Building a roof of any complexity with your own hands requires knowledge of the purpose of the basic structural elements.
The locations of the elements are shown in the photo.
- Mauerlat. Designed to distribute the load from the rafter system onto the load-bearing walls of the building. To arrange the Mauerlat, a timber made of durable wood is selected. Preferably larch, pine, oak. The cross-section of the timber depends on its type - solid or glued, as well as on the expected age of the structure. The most popular sizes are 100x100, 150x150 mm.
Advice. For a metal rafter system, the Mauerlat must also be metal. For example, a channel or an I-profile.
- Rafter leg. The main element of the system. To make rafter legs, a strong beam or log is used. The legs connected at the top form a truss.
Silhouette roof truss defines appearance buildings. Examples of farms in the photo.
The parameters of the rafters are important. They will be discussed below.
- Puff- connects the rafter legs and gives them rigidity.
- Run:
- Ridge run, is mounted at the junction of one rafter to another. In the future, the roof ridge will be installed on it.
- Side purlins, they provide the truss with additional rigidity. Their number and size depend on the load on the system.
- Rafter stand- vertically located beam. It also takes on part of the load from the weight of the roof. In a simple gable roof it is usually located in the center. With a significant span width - in the center and on the sides. In an asymmetrical gable roof, the installation location depends on the length of the rafters. With a broken roof and the arrangement of one room in the attic attic, the racks are located on the sides, leaving free space for moving. If there are supposed to be two rooms, the racks are located in the center and on the sides.
The location of the rack depending on the length of the roof is shown in the figure.
- Strut. Serves as a support for the stand.
Advice. Installing the brace at an angle of 45° significantly reduces the risk of deformation from wind and snow loads.
In regions with significant wind and snow loads, not only longitudinal struts are installed (located in the same plane as the rafter pair), but also diagonal ones.
- Sill. Its purpose is to serve as a support for the rack and a place for attaching the strut.
- Lathing. Designed for movement during construction work and fixing roofing material. Installed perpendicular to the rafter legs.
Advice. An important purpose of the sheathing is to redistribute the load from the roofing material to the rafter system.
Having a drawing and diagram indicating the location of all the listed structural elements will help in the work.
Advice. Be sure to add information about the passage of the ventilation shaft and chimney to the gable roof rafter system diagram.
The technology of their installation is determined by the type of roof.
Selection of material for rafters
When calculating the material for a gable roof, you need to choose quality wood without damage or wormholes. The presence of knots for beams, mauerlat and rafters is not allowed.
For sheathing boards, there should be a minimum of knots, and they should not fall out. The wood must be durable and treated with the necessary preparations that will increase its properties.
Advice. The length of the knot should not exceed 1/3 of the thickness of the timber.
Calculation of the rafter system of a gable roof
Calculating the material parameters is an important step, so we present the calculation algorithm step by step.
It is important to know: the entire rafter system consists of many triangles, as the most rigid element. In turn, if the stingrays have different shape, i.e. are an irregular rectangle, then you need to divide it into separate components and calculate the load and amount of materials for each. After calculations, summarize the data.
1. Calculation of the load on the rafter system
The load on the rafters can be of three types:
- Constant loads. Their action will always be felt by the rafter system. Such loads include the weight of the roof, sheathing, insulation, films, additional roofing elements, finishing materials For . The weight of the roof is the sum of the weight of all its constituent elements; such a load is easier to take into account. On average, the constant load on the rafters is 40-45 kg/sq.m.
Advice. To make a safety margin for the rafter system, it is better to add 10% to the calculation.
For reference: The weight of some roofing materials per 1 sq.m. presented in the table
Advice. It is desirable that the weight of roofing material per 1 sq.m. roof area did not exceed 50 kg.
- Variable loads. They act at different times and with different strengths. Such loads include: wind load and its strength, snow load, precipitation intensity.
In essence, the roof slope is like a sail and, if you take into account the wind load, the entire roof structure can be destroyed.
The calculation is carried out according to the formula: wind load is equal to the regional indicator multiplied by the correction factor. These indicators are contained in SNiP “Loads and Impacts” and are determined not only by the region, but also by the location of the house. For example, on a private house surrounded by multi-story buildings, there is less load. Standing separately Vacation home or the cottage experiences increased wind loads.
2. Calculation of snow load on the roof
The roof calculation for snow load is carried out according to the formula:
The total snow load is equal to the weight of the snow multiplied by the correction factor. The coefficient takes into account wind pressure and aerodynamic influence.
The weight of snow that falls on 1 square meter. roof area (according to SNiP 2.01.07-85) is in the range of 80-320 kg/sq.m.
Coefficients showing the dependence on the slope angle are shown in the photo.
Nuance. When the slope angle is over 60 ° the snow load does not affect the calculation. Because the snow will quickly slide down and will not affect the strength of the beam.
- Special loads. Accounting for such loads is carried out in places with high seismic activity, tornadoes, and storm winds. For our latitudes, it is enough to make a safety margin.
Nuance. The simultaneous action of many factors causes a synergy effect. This is worth considering (see photo).
Assessment of the condition and load-bearing capacity of walls and foundations
It should be borne in mind that the roof has significant weight, which can cause damage to the rest of the building.
Determining the roof configuration:
- simple symmetrical;
- simple asymmetrical;
- broken line
How more complex form roof, the greater the number of trusses and sub-rafter elements needed to create the necessary safety margin.
The angle of inclination of a gable roof is determined primarily by the roofing material. After all, each of them puts forward their own demands.
- soft roof - 5-20°;
- metal tiles, slate, corrugated sheets, ondulin - 20-45°.
It should be noted that increasing the angle increases the area of space under the roof, but also the amount of material. What affects total cost works
Nuance. Minimum angle The slope of the gable roof should be at least 5°.
5. Calculation of rafter pitch
The pitch of the gable roof rafters for residential buildings can be from 60 to 100 cm. The choice depends on the roofing material and the weight of the roof structure. Then the number of rafter legs is calculated by dividing the length of the slope by the distance between the rafter pairs plus 1. The resulting number determines the number of legs per slope. For the second, the number must be multiplied by 2.
Rafter length for attic roof calculated using the Pythagorean theorem.
Parameter "a"(roof height) is set independently. Its value determines the possibility of arranging a living space under the roof, the convenience of being in the attic, and the consumption of material for the construction of the roof.
Parameter "b" equal to half the width of the building.
Parameter "c" represents the hypotenuse of the triangle.
Advice. To the obtained value you need to add 60-70 cm for cutting and moving the rafter leg beyond the wall.
It is worth noting that the maximum length of the beam is 6 m.p. Therefore, if necessary, the timber for the rafters can be spliced (extension, joining, joining).
The method of splicing rafters along the length is shown in the photo.
The width of the roof rafters depends on the distance between opposite load-bearing walls.
7. Calculation of the rafter cross-section
The cross-section of the rafters of a gable roof depends on several factors:
- loads, we have already written about it;
- type of material used. For example, a log can withstand one load, timber - another, laminated timber - a third;
- rafter leg lengths;
- the type of wood used in construction;
- distances between rafters (rafter pitch).
You can determine the cross-section of the beam for the rafters, knowing the distance between the rafters and the length of the rafters using the data below.
Rafter cross-section - table
Advice. The larger the installation pitch of the rafters, the greater the load on one rafter pair. This means that the cross-section of the rafters needs to be increased.
Dimensions of lumber (timbers and boards) for a gable rafter system:
- thickness (section) of the Mauerlat - 10x10 or 15x15 cm;
- the thickness of the rafter leg and tie is 10x15 or 10x20 cm. Sometimes a beam of 5x15 or 5x20 cm is used;
- run and strut - 5x15 or 5x20. Depending on the width of the foot;
- stand - 10x10 or 10x15;
- bench - 5x10 or 5x15 (depending on the width of the rack);
- thickness (section) of the roof sheathing - 2x10, 2.5x15 (depending on the roofing material).
Types of gable roof rafter system
For the roof structure under consideration, there are 2 options: layered and hanging rafters.
Let's consider each type in detail in order to make an informed choice.
Hanging rafters
They are used for roof widths of no more than 6 lm. Installation of hanging rafters is carried out by attaching the legs to the load-bearing wall and ridge run. The design of hanging rafters is special in that the rafter legs are under the influence of a bursting force. Hanging rafters with a tightening installed between the legs, reduce its influence. The tie in the rafter system can be wooden or metal. Often the ties are placed at the bottom, then they play the role of load-bearing beams. It is important to ensure that the tie is securely attached to the rafter leg. Because a bursting force is also transmitted to it.
Advice.
The higher the tightening is located, the greater strength it should have.
If the tightening is not installed, the load-bearing walls may simply “move apart” from the pressure created by the rafter system.
Layered rafters
They are used for arranging roofs of any size. The design of layered rafters provides for the presence of a beam and a stand. The bench lying parallel to the Mauerlat takes on part of the load. Thus, the rafter legs are, as it were, inclined towards each other and supported by a stand. The rafter legs of the layered system work only in bending. And the ease of installation also tips the scales in their favor. The only drawback is the presence of a stand.
Combined
Due to the fact that modern roofs They are distinguished by a wide variety of shapes and complexity of configurations; a combined type of rafter system is used.
After choosing the type of rafter system, you can accurately calculate the amount of materials. Write down the calculation results. At the same time, professionals recommend drawing up drawings for each roof element.
Installation of a gable roof rafter system
After the gable roof rafters have been calculated, installation can begin. We will divide the process into stages and give a description of each of them. It will turn out to be unique step-by-step instruction, containing additional information for each stage.
1. Attaching the Mauerlat to the wall
The beam is installed along the length of the wall on which the rafters will rest.
In log houses, the role of the mauerlat is played by the upper crown. In buildings built from porous material (aerated concrete, foam concrete) or brick, the Mauerlat is installed along the entire length of the load-bearing wall. In other cases, it can be installed between the rafter legs.
Material prepared for the website www.site
Since the length of the Mauerlat exceeds the standard dimensions of lumber, it has to be spliced.
The connection of the Mauerlat to each other is done as shown in the figure.
How to connect the Mauerlat?
The beams are cut only at an angle of 90°. Connections are made using bolts. Nails, wire, wooden dowels are not used.
How to attach the Mauerlat?
The Mauerlat is installed at the top of the wall. The installation technology provides several ways to attach the Mauerlat:
- strictly in the center of the load-bearing wall;
- with a shift to one side.
Advice.
The Mauerlat cannot be placed closer than 5 cm to the outer edge of the wall.
To protect the timber for the Mauerlat from damage, it is laid on a layer of waterproofing material, which most often is ordinary roofing felt.
Reliability of Mauerlat fastening important aspect construction. This is due to the fact that the roof slope is like a sail. That is, it experiences strong wind load. Therefore, the Mauerlat must be firmly fixed to the wall.
Methods for attaching the Mauerlat to the wall and rafters
Anchor bolts. Ideal for monolithic structures.
Wooden dowels. Used for log houses and beams. But, they are always used with additional fasteners.
Staples.
Stud or fittings. It is used if the cottage is built from porous materials (aerated concrete, foam concrete).
Sliding mount (hinge). Tying in this way allows for the displacement of the rafter legs when the house shrinks.
Annealed wire (knitting, steel). Used as an additional mount in most cases.
2. Manufacturing of trusses or pairs
Installation is carried out in two ways:
- installation of beams directly on the roof. It is not used often, since it is problematic to carry out all the work, measurements, and trimming at height. But it allows you to completely do the installation yourself;
- assembly on the ground. Those., individual elements(triangles or pairs) for the rafter system can be assembled at the bottom and then raised to the roof. The advantage of such a system is faster performance of high-altitude work. The disadvantage is that the weight assembled structure roof truss can be significant. To lift it you will need special equipment.
Advice. Before assembling the rafter legs, you need to apply markings. It is very convenient to use templates for these purposes. The rafter pairs assembled according to the template will be absolutely identical. To make a template, you need to take two boards, the length of each of which is equal to the length of one rafter, and connect them together.
3. Installation of rafter legs
The assembled pairs rise to the top and are installed on the Mauerlat. To do this, you need to make a gash at the bottom of the rafter legs.
Advice. Since the slots on the Mauerlat will weaken it, you can only make cuts on the rafter leg. To ensure that the cut is uniform and fits tightly to the base, you need to use a template. It is cut out of plywood.
Methods of fastening the rafter leg are shown in the figure.
Start installation rafter pairs needed from opposite ends of the roof.
Advice. To correctly install the rafter legs, it is better to use temporary struts and spacers.
A string is stretched between the fixed pairs. It will simplify the installation of subsequent rafter pairs. It will also indicate the level of the ridge.
If the rafter system is mounted directly on the roof of the house, then after installing the two outer rafter legs, the ridge support is installed. Next, the halves of the rafter pair are attached to it.
It is worth noting that the opinions of professionals differ on this issue. Some advise using a staggered fastening pattern, which will allow the increasing load to be distributed more evenly on the walls and foundation. This order involves installing one rafter in a checkerboard pattern. After part of the rafter legs is installed, the missing parts of the pair are mounted. Others insist that it is necessary to mount each pair in a sequential manner. Depending on the size of the structure and the configuration of the truss, the rafter legs are reinforced with supports and racks.
Nuance. Connect additional elements structures using cutting. It is preferable to fix them with construction staples.
If necessary, you can lengthen the rafter leg.
Methods for splicing rafter legs are shown in the photo.
Advice. The method by which the mauerlat is lengthened (cut at 90°) cannot be used in this case. This will weaken the rafter.
4. Installing the ridge of a gable roof
The roof ridge unit is made by connecting the rafter legs at the top.
Roof ridge structure:
- Method without using a support beam (see figure).
- Method using rafter beams. The beam is needed for large roofs. In the future, it can become a support for the rack.
- Method of laying on timber.
- More modern variety manufacturing ridge knot can be considered the method shown in the photo.
- Cutting method.
After the rafter system is installed, we perform major fastening of all structural elements.
5. Installation of roof sheathing
The sheathing is installed in any case, and is designed for more convenient movement along the roof during work, as well as for fastening roofing material.
The sheathing pitch depends on the type of roofing material, for example:
- for metal tiles - 350 mm (the distance between the two lower boards of the sheathing should be 300 mm).
- for corrugated sheets and slate - 440 mm.
- under soft roof We lay a continuous sheathing.
Rafter system of a gable roof with an attic - video:
Conclusion
As you can see, despite its apparent simplicity, the installation of a gable roof rafter system contains many pitfalls. But, based on the recommendations given, you can build without any problems reliable design with your own hands.
-> Calculation of the rafter systemThe main element of the roof, which absorbs and resists all types of loads, is rafter system. Therefore, in order for your roof to reliably withstand all environmental influences, it is very important to do correct calculation rafter system.
For self-calculation I provide the characteristics of the materials required for installation of the rafter system simplified calculation formulas. Simplifications have been made to increase the strength of the structure. This will cause a slight increase in lumber consumption, but on small roofs of individual buildings it will be insignificant. These formulas can be used when calculating gable attic and mansard roofs, as well as single-pitch roofs.
Based on the calculation method given below, programmer Andrey Mutovkin (Andrey’s business card - mutovkin.rf) for own needs developed a rafter system calculation program. At my request, he generously allowed me to post it on the site. You can download the program.
The calculation methodology is based on SNiP 2.01.07-85 “Loads and Impacts”, taking into account “Changes...” from 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.
In addition to the above, the rafter system is also subject to loads from roof elements:
3. Roof weight.
4. Weight of rough flooring and sheathing.
5. Weight of 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 - desired value of snow load, kg/m²
µ - coefficient depending on the roof slope.
Sg - standard snow load, kg/m².
µ - coefficient depending on the roof slope α. Dimensionless quantity.
The roof slope angle α can be approximately determined by 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 using the formula:
µ = 0.033·(60-α);
Sg - standard snow load, kg/m².
For Russia it is accepted according to map 1 of mandatory appendix 5 of SNiP 2.01.07-85 “Loads and impacts”
For Belarus, the standard snow load Sg is determined
Technical code of PRACTICE Eurocode 1. EFFECTS ON STRUCTURES Part 1-3. General impacts. Snow loads. TKP EN1991-1-3-2009 (02250).
For example,
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.
Using Map 1 of Mandatory Appendix 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
Determine the roof slope angle α.
To do this, divide the roof height (H) by half the span (L): 2.5/3.5=0.714
and from the table we find the slope angle α=36°.
Since 30°, the calculation µ will be produced using the formula µ = 0.033·(60-α) .
Substituting the value α=36°, we find: µ = 0.033·(60-36)= 0.79
Then S=Sg·µ =240·0.79=189kg/m²;
the maximum possible snow load on our roof will be 189 kg/m².
2. Wind loads.
If the roof is steep (α > 30°), then due to its windage, the wind puts pressure on one of the slopes and tends to overturn it.
If the roof is flat (α, then the lifting aerodynamic force that arises when the wind bends around it, as well as turbulence under the overhangs, tend to lift this roof.
According to SNiP 2.01.07-85 “Loads and impacts” (in Belarus - Eurocode 1 IMPACTS ON STRUCTURES Part 1-4. General impacts. Wind impacts), the standard value of the average component of the wind load Wm at a height Z above the ground surface should be determined by the formula :
Where,
Wo is the standard value of wind pressure.
K is a coefficient that takes into account the change in wind pressure with height.
C - aerodynamic coefficient.
K is a coefficient that takes into account the change in wind pressure with 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 mats.
This can be 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 matrices 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 one-story house with the height of the ridge from the ground - 6 m. , 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 a given 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 (bitumen slate) 4 - 6 kg/m²;
3. Ceramic tiles 35 - 50kg/m²;
4. Cement-sand tiles 40 - 50 kg/m²;
5. Bituminous shingles 8 - 12 kg/m²;
6. Metal tiles 4 - 5 kg/m²;
7. Corrugated sheeting 4 - 5 kg/m²;
4. Weight of rough flooring, sheathing and rafter system.
The weight of the rough flooring is 18 - 20 kg/m²;
Sheathing weight 8 - 10 kg/m²;
The weight of the rafter system itself is 15 - 20 kg/m²;
When calculating the final load on the rafter system, all of the above loads are summed up.
And now I'll tell you 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 rafter system.
To refute this statement, I will give the following example.
Calculation of the load on the rafter system when using various roofing materials.
Let's calculate the load on the rafter system when using the heaviest one (Cement-sand tiles
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
Sheathing weight - 20 kg/m²
Total - 303 kg/m²
Metal tiles:
Snow load - 189kg/m²
Wind loads - 24kg/m²
Roof weight - 5 kg/m²
Sheathing weight - 20 kg/m²
The weight of the rafter system itself is 20 kg/m²
Total - 258 kg/m²
Obviously, the existing difference in design loads (only about 15%) cannot lead to any significant savings in lumber.
So, we figured out the calculation of the total load Q acting per square meter of roof!
I especially draw your attention: when making calculations, pay close attention to the dimensions!!!
II. Calculation of the rafter system.
Rafter system consists of separate rafters (rafter legs), so the calculation comes down to determining the load on each rafter leg separately and calculating the cross-section of an individual rafter leg.
1. Find the distributed load per linear meter of each rafter leg.
Where
Qr - distributed load per linear meter of rafter leg - kg/m,
A - distance between rafters (rafter pitch) - m,
Q is the total load acting on a square meter of roof - kg/m².
2. Determine the working area in the rafter leg maximum length Lmax.
3. We calculate the minimum cross-section of the rafter leg material.
When choosing material for rafters, we are guided by the table standard sizes 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 arbitrarily set the width of the section in accordance with standard dimensions, and determine the height of the section using the formula:
H ≥ 8.6 Lmax sqrt(Qr/(BRben)), if the roof slope α
H ≥ 9.5 Lmax sqrt(Qr/(BRben)), if the roof slope α > 30°.
H - section height cm,
B - section width cm,
Rbend - bending resistance of wood, kg/cm².
For pine and spruce Rben is equal to:
1st grade - 140 kg/cm²;
2nd grade - 130 kg/cm²;
3rd grade - 85 kg/cm²;
sqrt - square root
B. We check whether the deflection value is within the standard.
The normalized deflection of the material under load for all roof elements should not exceed L/200. Where, L is the length of the working section.
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 rafter leg - kg/m,
Lmax - working section of the rafter leg with maximum length m,
B - section width cm,
H - section height cm,
If the inequality is not met, then increase B or H.
Condition:
Roof pitch angle α = 36°;
Rafter pitch A= 0.8 m;
The working section of the rafter leg of maximum length Lmax = 2.8 m;
Material - 1st grade pine (Rbending = 140 kg/cm²);
Roofing - cement-sand tiles (Roofing weight - 50 kg/m²).
As it was calculated, the total load acting on a square meter of roof is Q = 303 kg/m².
1. Find the distributed load per linear meter of each rafter leg Qr=A·Q;
Qr=0.8·303=242 kg/m;
2. Choose the thickness of the board for the rafters - 5cm.
Let's calculate the cross-section of the rafter leg with a section width of 5 cm.
Then, H ≥ 9.5 Lmax sqrt(Qr/BRben), since the roof slope α > 30°:
H ≥ 9.5 2.8 sqrt(242/5 140)
H ≥15.6 cm;
From the table of standard sizes of lumber, select a board with the closest cross-section:
width - 5 cm, height - 17.5 cm.
3. We check whether the deflection value is within the standard. To do this, the following 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, which means the cross-section of the rafter material 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.