Another name for a gable type of roof is a gable roof.
It has two identical inclined surfaces. The structure of the roof frame is represented by a truss system.
At the same time, pairs of rafters leaning against each other are combined with a crate. At the ends, triangular walls are formed, or in other words, tongs.
A gable roof is quite simple .
At the same time, very important point for installation is the correct calculation of the necessary parameters.
In the attic truss system there are the following elements:
- Mauerlat. This element serves as the basis for the entire roof structure, is attached along the perimeter of the walls from above.
- Rafter. Boards of a certain size, which are attached at the required angle and have support in the Mauerlat.
- Skate. These are designations of the place of convergence of the rafters in the upper part.
- Crossbars. They are located in a horizontal plane between the rafters. They serve as an element of adhesion of the structure.
- Racks. Supports that are placed in a vertical position under the ridge. With their help, the load is transferred to bearing walls.
- Strut. Elements located at an angle to the rafters to divert the load.
- Sill. It is similar to Mauerlat, only it is located on the internal load-bearing floor.
- Fight. A bar located vertically between the supports.
- . Roof construction.
Calculation of the gable roof truss system - online calculator
Field designations in the calculator
Specify roofing material:
Select a material from the list -- Slate (corrugated asbestos-cement sheets): Medium profile (11 kg/m2) Slate (corrugated asbestos-cement sheets): Reinforced profile (13 kg/m2) Corrugated cellulose-bitumen sheets (6 kg/m2) Bituminous (soft , flexible) tiles (15 kg/m2) Galvanized sheet metal (6.5 kg/m2) Sheet steel (8 kg/m2) Ceramic tiles (50 kg/m2) Cement-sand tiles (70 kg/m2) Metal tiles, corrugated board (5 kg/m2) Keramoplast (5.5 kg/m2) Seam roof (6 kg/m2) Polymer-sand tile (25 kg/m2) Ondulin (Euro slate) (4 kg/m2) Composite tile (7 kg/m2) ) Natural slate (40 kg/m2) Specify the weight of 1 square meter of coating (? kg/m2)
kg/m2
Enter the roof parameters (photo above):
Base Width A (cm)
Base length D (cm)
Lift height B (cm)
Length of side overhangs C (cm)
Front and rear overhang length E (cm)
Rafter:
Rafter step (cm)
Type of wood for rafters (cm)
Working section of the side rafter (optional) (cm)
Lathing calculation:
Purlin board width (cm)
Lathing board thickness (cm)
Distance between decking boards
F(cm)
Snow load calculation (pictured below):
Choose your region
1 (80/56 kg/m2) 2 (120/84 kg/m2) 3 (180/126 kg/m2) 4 (240/168 kg/m2) 5 (320/224 kg/m2) 6 (400/280 kg/m2) 7 (480/336 kg/m2) 8 (560/392 kg/m2)
Wind load calculation:
Ia I II III IV V VI VII
Height to building ridge
5 m from 5 m to 10 m from 10 m
Terrain type
Open area Closed area Urban areas
Calculation results
Roof pitch: 0 degrees.
The angle of inclination is suitable for this material.
The angle of inclination for this material is desirable to increase!
It is desirable to reduce the angle of inclination for this material!
Roof surface area: 0 m2.
Approximate weight roofing material: 0 kg.
Number of rolls of insulation material with 10% overlap (1x15 m): 0 rolls.
Rafter:
Load on the truss system: 0 kg/m2.
Rafter length: 0 cm
Number of rafters: 0 pcs
Lathing:
Number of rows of lathing (for the entire roof): 0 rows.
Uniform distance between the boards of the crate: 0 cm
The number of boards of the crate with a standard length of 6 meters: 0 pcs
Volume of boards of an obreshetka: 0 m 3 .
Approximate weight of the boards of the crate: 0 kg.
Snow load region
Description of calculator fields
It is quite simple to make all the calculations before starting work on the construction of the roof. The only thing what is required is scrupulousness and attentiveness, you should also not forget about checking the data after the process is completed.
One of the parameters, without which the calculation process cannot be dispensed with, will be total area roofs. It should be initially understood what this indicator represents, for a better understanding of the entire calculation process.
There are some general provisions, which are recommended to be followed in the calculation process:
- The first step is to determine the length of each of the slopes. This value is equal to the intermediate distance between the points in the uppermost part (on the ridge) and the lowest (cornice).
- Calculating such a parameter all additional roofing elements must be taken into account, for example, an overhang and any kind of structure that adds volume.
- At this stage also material must be defined from which the roof will be constructed.
- Doesn't need to be taken into account when calculating the area, ventilation and chimney elements.
ATTENTION!
The above points are applicable in the case of a conventional roof with two slopes, but if the plan of the house suggests the presence of an attic or another kind of roof shape, then it is recommended that calculations be carried out only with the help of a specialist.
The truss system calculator will help you best in calculations. gable roof.
Calculation of the gable roof truss system: calculator
Calculation of rafter parameters
In this case, you need to push off from the step, which is selected taking into account the design of the roof individually. This parameter is affected by the selected roofing material and the total weight of the roof.
This indicator can vary from 60 to 100 cm.
To calculate the number of rafters you need:
- Find out the length of the slope;
- Divide by the selected step parameter;
- Add 1 to the result;
- For the second slope, multiply the indicator by two.
The next parameter to determine is the length of the rafters. To do this, you need to remember the Pythagorean theorem, this calculation is carried out according to it. The formula requires the following data:
- Roof height. This value is chosen by each individually, depending on the need to equip the living space under the roof. For example, this value will be equal to 2 m.
- The next value is half the width of the house, in this case - 3m.
- The quantity to be known is triangle hypotenuse. Having calculated this parameter, starting from the data for the example, it turns out 3.6 m.
Important: to the result of the length of the rafters, you should add 50-70 cm with the expectation of washing down.
Moreover, it is necessary to determine what width to choose rafters for mounting.
Rafters can be made by hand, you can read how to do it.
For this parameter, you need to consider:
Determining the angle of inclination
It is possible for such a calculation proceed from roofing material, which will be used in the future, because each of the materials has its own requirements:
- For the size of the slope angle must be more than 22 degrees. If the angle is smaller, then this promises water to enter the gaps;
- For this parameter should exceed 14 degrees, otherwise, sheets of material may be torn off by a fan;
- For the angle can be no less than 12 degrees;
- For shingles this indicator should be no more than 15 degrees. If the angle exceeds this indicator, then there is a possibility of material slipping from the roof during hot weather, because. attachment of the material is carried out on the mastic;
- For roll-type materials, the variation in the angle value can be between 3 and 25 degrees. This indicator depends on the number of layers of material. A larger number of layers allows you to make the angle of inclination of the ramp larger.
It should be understood that the greater the slope angle, the greater the area of free space under the roof, however, more material is required for such a design, and, accordingly, costs.
You can read more about the optimal angle of inclination.
Important: the minimum allowable slope angle is 5 degrees.
The formula for calculating the angle of the slope is simple and obvious, given that initially there are parameters for the width of the house and the height of the ridge. Having presented a triangle in a section, you can substitute data and perform calculations using Bradis tables or an engineering-type calculator.
You need to calculate the tangent of an acute angle in a triangle. In this case, it will be equal to 34 degrees.
Formula: tg β \u003d Hk / (Losn / 2) \u003d 2/3 \u003d 0.667
Determining the angle of the roof
Calculation of loads on the truss system
Before proceeding to this section of calculations, you need to consider all kinds of loads on the rafters. , which also affects the load. Types of loads:
Types of load:
- Constant. This type of load is constantly felt by the rafters, it is provided by the roof structure, material, lathing, films and other small elements of the system. The average value of this parameter is 40-45 kg/m 2 .
- Variable. This type of load depends on the climate and the location of the building, since it is formed by precipitation in this region.
- Special. This parameter is relevant if the location of the house is a seismically active zone. But in most cases, additional strength is enough.
Important: the best when calculating strength, make a margin, for this, 10% is added to the value obtained. It is also worth taking into account the recommendation that 1 m 2 should not take on weight more than 50 kg.
It is very important to take into account the load exerted by the wind. Indicators of this value can be taken from SNiP in the section "Loads and impacts".
- Find out the snow weight parameter. This indicator varies mainly from 80 to 320 kg / m 2 .;
- Multiply by a factor that is needed to account for wind pressure and aerodynamic properties. This value is indicated in the SNiP table and is applied individually. Source SNiP 2.01.07-85. (v this example), which will need to be purchased for construction.
- The length of the roof in this example is 10m. To find out such a parameter, you need to measure the length of the skate;
- The length of the rafter was calculated and equals 3.6m (+0.5-0.7m.);
- Based on this, the area of \u200b\u200bone slope will be equal to - 41 m 2. The total value of the area is 82 m 2, i.e. the area of one slope, multiplied by 2.
- The width of the gable roof depends on the dimensions of the box and the type of coating, which in turn affects the selection of the steepness of the slopes.
- The slope of the roof depends on the climatic features of the construction area and on the type of roofing material.
- The combination of the above circumstances, width and slope, determines the height of the structure, which in the end may not meet architectural requirements and aesthetic considerations.
- Layered, according to which the top and bottom of the rafters have a strong fulcrum. The walls of the house, equipped with a Mauerlat, serve as the lower support. The top of the layered rafter legs rests on a running beam that forms a ridge. The running beam is supported on a support system built specifically for it, on inner wall or on the stone pediments of the box, erected to the roof device. The layered method is mainly used in the arrangement of large houses with an internal bearing wall or near columns.
- hanging, according to which the tops of the rafters rest only against each other. The walls serve as a support for the bottom, as in the previous case. Hanging rafter legs form an equilateral triangle, the base of which is called a puff. Taken together, such a system does not create thrust, i.e. does not transfer the bursting load to the walls of the box. Rafter triangles are installed either ready for installation, i.e. assembled on the ground, or constructed from separate rafters on site. The absence of an upper support makes adjustments to the scope of use: the hanging method is used in the arrangement of only small buildings with small spans.
- When mounted on floor beams, it is they who form the cornice overhang, i.e. determine the dimensions of the roof.
- When installed on a Mauerlat, the width of the roof is determined by adding three values. You need to sum up the width of the box and two projections of the width of the cornice overhang. However, only the bearing part of the width of the roof, equal to the width of the box, is used in the calculations.
- For slate roof no more than 10 cm;
- For bituminous tiles in the range of 30-40cm;
- For metal tiles 40-50cm;
- For profiled sheet 50cm;
- For ceramic tiles 50-60cm.
- The type of coating, coupled with the weight of the crate intended for it. The type of roofing material determines the installation technology and the method of arranging the base for its fastening. The denser the roof is, the lower the value of the slope can be. The fewer overlaps and joints between the elements of the coating, the lower the roof is allowed to be. And vice versa.
- Roof weight with. A heavy coating located at an angle to the horizon presses on the base only with its projection. In short, the higher the slope, the less mass is transferred to the floor. Those. under a heavy roof you need to build a steep roof.
- Climatic specificity of the region. The high slope helps to quickly drain snow and water, which is highly desirable in areas with significant rainfall. However, high slopes are very sensitive to the effects of winds that tend to overturn them. Therefore, in regions with characteristic strong winds, it is customary to build gently sloping structures, and in areas with abundant rainfall, roofs with a high slope.
- We draw a diagram of the box of the house on a scale.
- We are looking for the middle of the upper floor.
- From the middle up we lay the axis of symmetry.
- On either side from the middle, we set aside half the width of the roof - we get the extreme point of the overhang.
- With the help of a protractor, from the extreme point of the overhang, we draw a straight line at an angle recommended by the roofing manufacturer. The point of its intersection with the axis will be the top of the roof. We measure the distance from the top to the overlap, we get the height.
- Beam for the Mauerlat device. In residential construction, lumber with a cross section of 100 × 150 mm to 200 × 200 mm is used. The footage is calculated around the perimeter of the box with a 5% margin for processing and connections. A similar material is purchased for the bed device, if it is designed.
- Board for the manufacture of rafters. Most often, for the manufacture of rafter legs, material is used with a cross section from 25 × 150 mm to 100 × 150 mm. The footage is determined by multiplying the length of the outer edge by the number. The material is purchased with a margin of 15-20%.
- A board or bar for making struts, puffs and supports with a section of 50 × 100, 100 × 100 mm, depending on the project. You also need a margin of about 10%.
- Material for the device of the crate. Its consumption depends on the type of finish coating. The crate is constructed either solid, if it will be produced, or sparse for corrugated board, metal tiles, ordinary tiles, slate, etc.
- Roll waterproofing, the footage of which determines the type of roof and the steepness. High roofs are covered with a waterproofing carpet only along the overhangs, the ridge and in convex or concave corners. Gentle ones are covered with a continuous carpet.
- Finish coating. Its amount is calculated by summing the area of the slopes. If there are embedded dormer windows, then their areas are also calculated. Only calculated as a rectangle, not in fact. The amount of laying stock is recommended by the coating manufacturers.
- Material for sheathing gables and overhangs.
- Corners, plates, self-tapping screws, staples, nails. We need anchors and studs, their number will tell the project.
- 10x10 or 15x15 cm - for Mauerlat timber;
- 10x15 or 10x20 cm - for the rafter leg;
- 5x15 or 5x20 cm - for running and brace;
- 10x10 or 10x15 cm - for the rack;
- 5x10 or 5x15 cm - for lying down;
- 2x10, 2.5x15 cm - for purlins.
- type of building raw materials, because the "exposure" of logs, ordinary and glued beams varies;
- rafter leg length;
- type of wood from which the rafters were planed;
- the length of the gap between the rafter legs.
To do this, it is necessary to divide the resulting value of the roof area by the area of \u200b\u200bone sheet of metal.
Important: do not forget about allowances for roof peaks of 0.5-0.7 m.
Roofing kit
Conclusion
All calculations are best checked several times to avoid errors. When this painstaking preparatory process is completed, you can safely proceed to the purchase of material and prepare it in accordance with the received dimensions.
After that, the installation process of the roof will be simple and fast. And our gable roof calculator will help you with the calculations.
Useful video
Video instruction for using the calculator:
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The roof is an important structural part of the house, performing a number of the most important functions. It protects against atmospheric adversity and removes precipitation, provides insulation and makes a solid contribution to the formation of its own building style. In order for such a significant structure to "excellently" cope with the entrusted work, it is necessary to thoroughly think over the project and scrupulously figure out the dimensions.
Careful analysis and calculation of a gable roof is required for both independent craftsmen and owners of suburban property who resort to the services of construction organizations. Let's figure out how to do it right.
The roof, resembling an inverted V in a section, leads the list of pitched structures for a reason. In terms of simplicity of construction and economy, a gable roof has practically no rivals. For centuries, proven in practice, they are the basis for the construction of most roofing structures.
Unpretentious pitched planes do not require complex cutting of the coating and other materials, which results in an impressive amount of waste. No specific tricks are needed to implement intricate configurations. Precipitation does not linger on sloping surfaces, so there is no need to strengthen the waterproofing. As a result, the installation of a gable roof is often cheaper than a shed roof.
A roof with two slopes can be an independent object or part of a complex of structures of a similar or different form. Its simplest version does not have built-in dormer windows and canopies over the entrance porch, i.e. there are no additional fractures, ridges and accompanying valleys.
The absence of convex and concave corners deprives the master of "pleasure" to suffer with a number of difficult operations. Again, the owners will not get imaginary pleasure from leaks, which often appear at the joints of the pitched roof elements.
In principle, no one bothers fans of bizarre architecture to equip two slopes with numerous built-in structures. True, there are climatic limitations: in areas with a high volume of winter precipitation, the construction of roofs with numerous components is undesirable. In the grooves formed by excesses, favorable conditions are created for the accumulation of snow deposits. They will have to be cleaned faster than usual, and excessive zeal in the field of snow removal can cause damage to the coating with all the consequences.
However, adherents of simple and clear forms should not relax either. The corner roof configuration must be perfectly matched and calculated, otherwise it will not be able to perform the entrusted work flawlessly.
Despite the deceptive elementarity, there are tricks in determining the optimal form of the structure. It is impossible to overcome and circumvent them without knowledge technological subtleties, because all the parameters of the structure are interconnected:
The impeccably designed roof has all the proportions perfectly matched. Its width and height determine the rise and slope necessary for the removal of precipitation in a particular area. Lower is impossible for technical reasons, higher is expensive and unreasonable, unless the unique architecture requires it.
Note that, coupled with an increase in steepness, the construction budget also increases. According to the slope, roofing material is selected. Focusing on its weight and specifics, design and calculate the truss frame. The calculation of the truss frame is carried out taking into account the listed parameters and taking into account the loads acting from the outside on the structure.
The interdependence of the proportions of the roof, the complexity of the construction of the truss frame and the nuances of the selection of the coating makes it necessary to determine the best shape through a banal selection. If something does not fit, replace or strengthen the supporting structures. Fortunately, the assortment on the construction market is now plentiful, and all kinds of methods have been developed to strengthen the structure.
If you are afraid of the upcoming calculations and shuffling of data, it is better to resort to a win-win solution - standard project. It is not for nothing that abroad all the houses of one settlement are equipped with roofs of equal height and covered with material of the same color and characteristics. Typification allows you to maintain landscape identity and reduce design costs.
However, even a typical design solution is not a panacea for technical troubles and aesthetic shortcomings. We must not forget about the individual dimensions of the box over which it is planned to build a roof. Compatriots deny leveling in height and steepness, therefore it is still desirable for us to deal with the proportions of the roof structure.
Step by step calculations
The configuration and dimensions of any pitched roof are set by the truss frame. On the edges of the rafter legs, slopes are laid, forming a dihedral angle. They construct truss systems from rolled metal and wood, use industrial structures and lumber in construction.
Let's look at the options available for the efforts of an independent master, i.e. construction method of erecting a roof frame from lumber.
Stage # 1 - choosing the type of truss system
The method of constructing a gable roof is indirectly related to the dimensions, but without taking into account the difference in the arrangement of structures, it will be difficult to understand the geometric parameters.
In the construction of gable roofs, two traditional technologies are used:
Scheme truss systems both types include a minimum structural elements when overlapping boxes up to 8-10m wide.
When arranging spans larger, there is a danger of deformation of the rafter legs. To eliminate sagging and deflection wooden parts from lumber, install reinforcing elements: struts, contractions, side runs, etc.
Additional details provide rigidity and stability of a large structure, but increase the load. How the total load is determined and produced, we have already analyzed.
Step #2 - Width Calculation
Both types of wooden truss systems are built along the floor beams or along the Mauerlat. How the width of the roof is calculated depends on the type of base:
Mauerlat function in frame buildings performs the upper strapping, at the same time connecting the disparate elements into a single frame. In wooden construction, the upper crown, folded with a bar or log, serves as a Mauerlat.
In the case of using the "beam" scheme of the device, the so-called matrices are used - bars or logs laid under the upper crown of the foot as an overlap.
Eaves overhangs of roofs installed on the Mauerlat can be formed directly by rafter legs, fillies sewn to them or a brick ledge. The latter option, of course, is used in the construction brick walls. The choice of the width of the overhang is dictated by the type of roofing and the material from which the walls are composed.
Walls made of logs and timber require enhanced protection from slanting rains, therefore the overhangs above them are usually increased by 10-15 cm. If the limit value of the overhang width recommended by the manufacturer is exceeded, it is necessary to provide for measures to strengthen it.
It is possible to install external struts on the walls or support pillars, which can simultaneously play the role of structural elements of the terrace, porch, veranda.
Stage # 3 - determining the slope
The angle of inclination of the slopes is allowed to vary over the widest limits, on average from 10º to 60º s tolerances round trip. Traditionally, both planes of a gable roof have equal angles of inclination.
Even in asymmetric structures for residential buildings, they are mainly placed at an equal angle, and the effect of asymmetry is achieved by constructing different-sized slopes. Most often, differences in the slope of the main parts of the roof are observed during construction. country houses and household items.
The procedure for determining the optimal steepness of a gable roof is significantly influenced by three factors:
In the regulatory documentation used in calculating the angles for the construction of gable roofs, there are units that can confuse inexperienced home builders in roofing. The simplest value is expressed in dimensionless units, the most understandable - in degrees.
The second version conveys the ratio of the height of the roof to half its width. To determine it, a line is drawn from the central point of overlap to the top of the roofing triangle. The real line is drawn on the diagram of the house, imaginary at the facility. The value is indicated either as a percentage, or as a mathematical ratio of the type 1: 2.5 ... 1: 5, etc. In percentages, it is wiser and more inconvenient.
Stage # 4 - determining the height of the skate
A roof with two slopes, at the request of the owner, may or may not have an attic. In the attic spaces of gable roofs, it is not supposed to arrange useful premises. There is for this. However, the height of the attic used for servicing and inspecting roofs at an angle is not arbitrary.
According to the requirements of the fire service from the top to the ceiling should be at least 1.6 m. The upper limit is dictated by the aesthetic beliefs of the designers. They argue that if the height of the roof is greater than the height of the box, then it seems to “press” on the building.
The height of the ridge top for hanging roofs arranged on beams is easiest to determine by the drawing method:
To get a complete picture, on the diagram you need to draw a second slope in a similar way. Parallel to the lines of the drawn slopes, two more lines must be drawn at a distance equal to the thickness of the rafter legs on the same scale.
If the configuration of the roof does not suit you, you can "play" with the height on paper, changing the position of the vertex point and the slope of the roof within reasonable limits. The same manipulations can be carried out in one of the drawing programs.
When drawing the outline of a roof constructed using layered technology, the thickness of the running beam should be taken into account. With impressive power, it will slightly shift the position of the slopes.
Craftsmen believe that the calculations of the elements of the truss system for the construction of a gable roof can generally be reduced to calculating only the section of the run. This is the most loaded element, all the others have the right to be thinner. For example, if calculations show that 100 × 150 mm material is required for a ridge run, then 50 × 150 mm boards are enough for rafters, supports, struts.
The process of finding the height of structures with overhangs formed by filly is slightly different from the described method. It’s just that the slope angle is drawn not from the extreme point of the overhang, but from the lower attachment point of the rafter to the Mauerlat. In any case, it is better to choose variations with the steepness and dimensions of the gable roof planned for construction on “paper” than on the construction site.
Stage # 5 - calculation of material consumption
A normal owner thinks ahead of time about the construction budget. True, in the preliminary estimate, by definition, there will be inaccuracies. The process of erecting a gable roof will impose its own adjustments on the initial calculation of the material, but it will help to find out the amount of basic expenses.
The preliminary estimate should include:
You will also need shaped elements for arranging through passages through the roof, valleys, overhangs, ridge. The cost estimate presented is valid for a cold design. For an insulated roof, it will be necessary to purchase insulation and a vapor barrier film, a bar for a control batten and material for roof sheathing from the inside.
The gable roof is formed on the basis of a frame that combines the elementary nature of the device and unsurpassed reliability. But the backbone of the roof in two rectangular slopes can boast of these advantages only in the case of a careful selection of rafter legs.
Parameters of the gable roof truss system
It is worth starting the calculations if you understand that the truss system of a gable roof is a complex of triangles, the most rigid elements of the frame. They are assembled from boards, the size of which plays a special role.
Rafter length
The formula will help determine the length of durable boards for the truss systema²+b²=c², derived by Pythagoras.
The length of the rafter can be found by knowing the width of the house and the height of the roof
The parameter "a" denotes the height and is self-selected. It depends on whether the under-roof space will be residential, and also has certain recommendations if an attic is planned.
Behind the letter "b" is the width of the building, divided in two. And "c" represents the hypotenuse of the triangle, that is, the length of the rafter legs.
Let's say that the width of half of the house is three meters, and it was decided to make the roof two meters high. In this case, the length of the rafter legs will reach 3.6 m (c=√a²+b²=4+√9=√13≈3.6).
To the figure obtained from the Pythagorean formula, 60–70 cm should be added. Extra centimeters will be needed to take the rafter leg out of the wall and make the necessary cuts.
The six-meter rafter is the longest, therefore it is suitable as a rafter leg
The maximum length of the beam used as a rafter leg is 6 m. If a strong board of greater length is required, then they resort to the method of fusion - nailing a segment from another beam to the rafter leg.
Section of rafter legs
For various elements truss system has its own standard sizes:
The thickness of each part of the supporting structure of the roof is determined by the load that it will experience.
A beam with a section of 10x20 cm is ideal for creating a rafter leg
The section of the rafter legs of a gable roof is affected by:
The pitch of the rafters affects the cross section of the rafter legs most significantly. Increasing the distance between the beams entails increased pressure on the supporting structure of the roof, and this obliges the builder to use thick rafter legs.
Table: cross-section of rafters depending on length and pitch
Variable impact on the truss system
The pressure on the rafter legs is constant and variable.
From time to time and with varying intensity, wind, snow and precipitation affect the supporting structure of the roof. In general, the roof slope is comparable to a sail, which is under pressure natural phenomena may break.
The wind tends to overturn or raise the roof, so it is important to make all the calculations correctly.
The variable wind load on the rafters is determined by the formula W \u003d Wo × kxc, where W is the wind load indicator, Wo is the value of the wind load characteristic of a certain section of Russia, k is a correction factor determined by the height of the structure and the nature of the terrain, and c is the aerodynamic coefficient.
The aerodynamic coefficient can range from -1.8 to +0.8. A minus value is typical for a rising roof, and a positive value is for a roof that is being pressed by the wind. In a simplified calculation with a focus on improving strength, the aerodynamic coefficient is considered equal to 0.8.
Calculation of wind pressure on the roof is based on the location of the house
The standard value of wind pressure is recognized from map 3 of Appendix 5 in SNiP 2.01.07–85 and a special table. The coefficient that takes into account the change in wind pressure with height is also standardized.
Table: standard value of wind pressure
Table: value of coefficient k
The wind load is not only affected by the terrain. The housing area is of great importance. Behind the wall of tall buildings, the house is almost in no danger, but in open space the wind can become a serious enemy for it.
The snow load on the rafter system is calculated by the formula S = Sg × µ, that is, the weight snow mass per 1 m² is multiplied by a correction factor, the value of which reflects the degree of slope of the roof.
The weight of the snow layer is indicated in the SNiP "Truss Systems" and is determined by the type of area where the building was built.
Snow load on the roof depends on where the house is located
The correction factor, if the roof slopes heel less than 25 °, is equal to one. And in the case of a roof slope of 25–60 °, this figure decreases to 0.7.
When the roof is tilted more than 60 degrees, the snow load is discounted. Still, snow rolls off a steep roof quickly, without having time to have a negative impact on the rafters.
Permanent loads
Continuous loads are considered to be the weight of the roofing pie, including the lathing, insulation, films and Decoration Materials for the attic.
Roofing cake creates constant pressure on the rafters
The weight of a roof is the sum of the weights of all the materials used in the construction of the roof. On average, it is 40–45 kg / sq.m. According to the rules, 1 m² of the truss system should not account for more than 50 kg of the weight of roofing materials.
So that there is no doubt about the strength of the rafter system, 10% should be added to the calculation of the load on the rafter legs.
Table: weight of roofing materials per 1 m²
| Type of roof finish | Weight in kg per 1 m² |
| Rolled bitumen-polymer sheet | 4–8 |
| Bitumen-polymer soft tile | 7–8 |
| Ondulin | 3–4 |
| metal tile | 4–6 |
| Decking, seam roofing, galvanized metal sheets | 4–6 |
| Cement-sand tiles | 40–50 |
| Ceramic tiles | 35–40 |
| Slate | 10–14 |
| slate roof | 40–50 |
| Copper | 8 |
| green roof | 80–150 |
| Draft flooring | 18–20 |
| crate | 8–10 |
| The truss system itself | 15–20 |
Number of bars
How many rafters will be needed to equip the frame of a gable roof is set by dividing the width of the roof by a step between the bars and adding one to the resulting value. It indicates an additional rafter that will need to be placed on the edge of the roof.
Suppose it is decided to leave 60 cm between the rafters, and the length of the roof is 6 m (600 cm). It turns out that 11 rafters are needed (taking into account the additional timber).
truss system gable roof- this is a structure of a certain number of rafters
The step of the beams of the supporting structure of the roof
To determine the distance between the beams of the supporting structure of the roof, you should pay close attention to such points as:
- weight of roofing materials;
- the length and thickness of the beam - the future rafter leg;
- degree of slope of the roof;
- level of wind and snow loads.
After 90-100 cm, it is customary to place the rafters in the case of choosing a light roofing material
A step of 60–120 cm is considered normal for rafter legs. The choice in favor of 60 or 80 cm is made in the case of the construction of a roof inclined by 45˚. The same small step should be, if desired, to cover wooden frame roofs with heavy materials such as ceramic tiles, asbestos-cement slates and cement-sand tiles.
Table: rafter pitch depending on length and section
Formulas for calculating the truss system of a gable roof
The calculation of the truss system comes down to setting the pressure on each beam and determining the optimal section.
When calculating the truss system of a gable roof, they act as follows:
- According to the formula Qr \u003d AxQ, they find out what is the load on running meter each rafter leg. Qr is the distributed load per linear meter of the rafter leg, expressed in kg/m, A is the distance between the rafters in meters, and Q is the total load in kg/m².
- They proceed to the determination of the minimum cross-section of the beam-rafter. To do this, study the data of the table listed in GOST 24454–80 “Softwood lumber. Dimensions".
- Focusing on the standard parameters, choose the width of the section. And the height of the section is calculated using the formula H ≥ 8.6 Lmax sqrt (Qr / (B Rbend)) if the roof slope α< 30°, или формулу H ≥ 9,5·Lmax·sqrt(Qr/(B·Rизг)), когда уклон крыши α >30°. H is the height of the section in cm, Lmax is the working section of the rafter leg of maximum length in meters, Qr is the distributed load per linear meter of the rafter leg in kg / m, B is the section width cm, Rbend is the resistance of wood to bending, kg / cm². If the material is made from pine or spruce, then Rizg can be equal to 140 kg / cm² (wood grade 1), 130 kg / cm² (grade 2) or 85 kg / cm² (grade 3). Sqrt is the square root.
- Check whether the deflection value complies with the standards. It should not be more than the figure that results from dividing L by 200. L is the length of the working area. The compliance of the deflection value with the L / 200 ratio is feasible only if the inequality 3.125 Qr (Lmax)³ / (B H³) ≤ 1 is true. Qr indicates the distributed load per linear meter of the rafter leg (kg / m), Lmax is the working section of the rafter leg maximum length (m), B is the width of the section (cm), and H is the height of the section (cm).
- When the above inequality is violated, the indicators B and H increase.
Table: nominal dimensions of thickness and width of lumber (mm)
| Board thickness - section width (B) | Board width - section height (H) | ||||||||
| 16 | 75 | 100 | 125 | 150 | - | - | - | - | - |
| 19 | 75 | 100 | 125 | 150 | 175 | - | - | - | - |
| 22 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | - | - |
| 25 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 32 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 40 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 44 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 60 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 75 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 100 | - | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 125 | - | - | 125 | 150 | 175 | 200 | 225 | 250 | - |
| 150 | - | - | - | 150 | 175 | 200 | 225 | 250 | - |
| 175 | - | - | - | - | 175 | 200 | 225 | 250 | - |
| 200 | - | - | - | - | - | 200 | 225 | 250 | - |
| 250 | - | - | - | - | - | - | - | 250 | - |
An example of the calculation of the supporting structure
Assume that α (roof pitch) = 36°, A (rafter spacing) = 0.8 m, and Lmax (maximum rafter length) = 2.8 m. , which means that Rizg \u003d 140 kg / cm².
Cement-sand tiles were chosen for the roof covering, and therefore the weight of the roof is 50 kg/m². The total load (Q) experienced by each square meter, is equal to 303 kg / m². And for the construction of the truss system, bars 5 cm thick are used.
From this follow the following computational steps:
- Qr=A·Q= 0.8·303=242 kg/m - distributed load per linear meter of rafter beam.
- H ≥ 9.5 Lmax sqrt(Qr/B Rbend).
- H ≥ 9.5 2.8 sqrt(242/5 140).
- 3.125 Qr (Lmax)³/B H³ ≤ 1.
- 3.125 242 (2.8)³ / 5 (17.5)³ = 0.61.
- H ≥ (approximate height of the rafter section).
Table standard sizes you need to find the height of the rafter section, close to 15.6 cm. A suitable parameter is 17.5 cm (with a section width of 5 cm).
This value is quite consistent with the deflection index in the regulatory documents, and this is proved by the inequality 3.125 Qr (Lmax)³ / B H³ ≤ 1. Substituting into it the values (3.125 242 (2.8)³ / 5 (17, 5)³), it turns out that 0.61< 1. Можно сделать вывод: сечение пиломатериала выбрано верно.
Video: detailed calculation of the truss system
The calculation of the gable roof truss system is a whole complex of calculations. In order for the bars to cope with the task assigned to them, the builder needs to accurately determine the length, quantity and cross section of the material, find out the load on it and find out what the step between the rafters should be.
The roof is one of the main elements of the roof, which takes on all the impacts coming from the atmosphere.
The main function is to drain water and disperse the load on the top of the building after snow falls.
Quality roofing is valued for long-term operation and nice appearance.
Roof calculation online (calculator with drawings) - will help you make a reliable calculation of the amount of roofing, rafters and battens.
In construction, there are several types of coatings, which in turn are further divided into subspecies. The most common building surfaces are flat(sometimes operated and non-operated) and attic(this includes a whole group of roofs:, conical and others). Without a doubt, when it comes to choosing the type of roof, a further definition of the surface material becomes relevant.
The most popular types include:
- , aluminum seam and other metal roofs;
- slate coating;
- roof made from natural materials.
Roofing materials
As part of the truss system includes many construction "spare parts", but the main ones in this wide list are:
- slopes (inclined planes),
- crate,
- rafters,
- mauerlat bar.
In addition, a gutter, aerator, drainage pipe and others take a certain role in the process of shelter and further functioning of the shelter.
The truss system is represented as a carrier system, which is based on inclined rafter legs, vertical racks, as well as inclined struts. In some cases, it becomes necessary to use rafter beams, which will “tie” the rafter legs. There are hanging and layered rafters. In the first group, trusses with sleepers are separately distinguished.
Roof device
The next layer in the design mansard roof serves as crate, which is laid over the legs of the truss system. Thus, a certain foundation for the roofing deck appears, and the spatial component of the eaves also expands significantly. Most often, this element is made of either wood or metal.
Mauerlat also adheres to its niche of responsibility. It acts as a support for the rafters along the edges., and put it on outer wall along the perimeter. The beam is usually lumber (tobish made of wood), but it is quite reasonable if, in the case of a special metal frame, similar contents will be used to prepare the Mauerlat.
Roof calculation online calculator
How to calculate the roof of a house and how to calculate the material for the roof quickly and without errors? In this you can specially designed service - construction calculator for calculating the roof of a private house. The calculator calculates the amount, weight, and more.
Calculator field designations
Specify roofing material:
Select a material from the list -- Slate (corrugated asbestos-cement sheets): Medium profile (11 kg/m2) Slate (corrugated asbestos-cement sheets): Reinforced profile (13 kg/m2) Corrugated cellulose-bitumen sheets (6 kg/m2) Bituminous (soft , flexible) tiles (15 kg/m2) Galvanized sheet metal (6.5 kg/m2) Sheet steel (8 kg/m2) Ceramic tiles (50 kg/m2) Cement-sand tiles (70 kg/m2) Metal tiles, corrugated board (5 kg/m2) Keramoplast (5.5 kg/m2) Seam roof (6 kg/m2) Polymer-sand tile (25 kg/m2) Ondulin (Euro slate) (4 kg/m2) Composite tile (7 kg/m2) ) Natural slate (40 kg/m2) Specify the weight of 1 square meter of coating (? kg/m2)
kg/m2
Enter the roof parameters (photo above):
Base Width A (cm)
Base length D (cm)
Lift height B (cm)
Length of side overhangs C (cm)
Front and rear overhang length E (cm)
Rafter:
Rafter step (cm)
Type of wood for rafters (cm)
Working section of the side rafter (optional) (cm)
Lathing calculation:
Purlin board width (cm)
Lathing board thickness (cm)
Distance between decking boards
F(cm)
Snow load calculation (pictured below):
Choose your region
1 (80/56 kg/m2) 2 (120/84 kg/m2) 3 (180/126 kg/m2) 4 (240/168 kg/m2) 5 (320/224 kg/m2) 6 (400/280 kg/m2) 7 (480/336 kg/m2) 8 (560/392 kg/m2)
Wind load calculation:
Ia I II III IV V VI VII
Height to building ridge
5 m from 5 m to 10 m from 10 m
Terrain type
Open area Closed area Urban areas
Calculation results
Roof pitch: 0 degrees.
The angle of inclination is suitable for this material.
The angle of inclination for this material is desirable to increase!
It is desirable to reduce the angle of inclination for this material!
Roof surface area: 0 m2.
Approximate weight of roofing material: 0 kg.
Number of rolls of insulation material with 10% overlap (1x15 m): 0 rolls.
Rafter:
Load on the truss system: 0 kg/m2.
Rafter length: 0 cm
Number of rafters: 0 pcs
Lathing:
Number of rows of lathing (for the entire roof): 0 rows.
Uniform distance between the boards of the crate: 0 cm
The number of boards of the crate with a standard length of 6 meters: 0 pcs
Volume of boards of an obreshetka: 0 m 3 .
Approximate weight of the boards of the crate: 0 kg.
Snow load region
Explanation of calculator fields
Loads acting on the roof
It is likely that when it comes to choosing the type of roof and roofing, one should be guided by more than just visual requirements. First of all, it is necessary to pay attention to studying the issue of the load on the hip.
NOTE!
The roof is affected not only by precipitation and their volumes- temperature instability and various causes of physical and mechanical origin also exert serious pressure on the surface.
There are many reasons and sources of influence, but the leading ones are snow and wind. What can we say, if building codes require mandatory calculations for a future canopy. The calculation has a pronounced individuality in view of the differences in the volume of snow cover that falls in a particular region.
The wind load is not as harmless as it might seem at first glance. In some cases, we have to talk about the load due to the weight of one of the elements of the hip. Most often, the crate or roof acts as a weighting agent.
The topical issue of load is faced by those who is going to use the attic space all year round. In this case, large-scale insulation is necessary (slopes, side walls, etc.), which leads to a significant increase in the pressure force on the surface of the walls. When the attic is not planned to be transferred to a living space, then only one floor needs to be insulated.
The load-bearing structure of the eaves can also exert a noticeable load due to its own weight. In this situation, the load indicators are determined taking into account the average density of materials and the design values of the parameters of a constructive and geometric nature.
All of the above factors of influence are not so easy to analyze, but fortunately, all the necessary SNiPs have long been developed, the norms of which can be consulted at any time.
Cover area calculation
Inevitable in any canopy design. If 
the surface of the house will be displayed in a shed plane, then you are very lucky with the calculations.
In such conditions, measure the length and width of the structure, add up the indicators of conditional overhangs and then multiply the two results one by the other.
When it comes to the roof, then several more positions should be used in the calculation, including the angle of inclination of one or another element. First of all, we recommend dividing all capacious parts of the coating into certain parts (for example, into triangles).
In the case of a gable surface, the area of each inclination should be multiplied individually by the cosine of the oblique angle. The slope angle is a figure taken from the intersection of the slope and the floor. As for measuring the length of one inclined, the mentioned parameter should be fixed at the available distance from the ridge to the edge of the eaves.
Roof area calculation
Therefore, the solution algorithm in all projects that use pitched eaves is similar. Upon completion of the marked actions, in order to find out the area of \u200b\u200bthe house dome, you will need to sum up the results obtained.
At construction warehouses and in related stores, slopes with the shape of an irregular polygon can be sold. In this case, remember the advice that has already sounded in the material - divide the plane into identical geometric shapes and, after completing the calculations, simply add them together.
Calculation of the amount of materials for the roof on the example of metal tiles
The metal tile should begin to be considered from the angle of inclination, which was already mentioned in the previous paragraph. If we talk about extremes, then there are all theoretical grounds for saying about 11-70 degree interval. That's just practice, as you know, makes its own adjustments and they do not always coincide with theory.
Experts claim that 45 degrees is the optimal angle of inclination.
Especially when it comes to the roof of the house, which is located in an area with minimal rainfall, which does not require significant slopes. If snow is a fairly frequent guest, then 45 degrees will be the most the best options, that's just because of the increase in wind pressure, it will be necessary to strengthen the crate and truss system. In addition, the greater the slope, the more material will go to the eaves.
Consider the calculation algorithm using the example of a gable roof:
- Let the oblique angle be expressed by the letter A, and ½ of the covered span - B, the height will be H.
- We introduce an action to find the tangent, which is solved by dividing H by B. We know the mentioned values, therefore, using the Bradis table, we find the value of the angle of inclination A through the arc tangent (H / B).
- It is better to use a calculator that can calculate inverse trigonometric functions to solve such serious actions. Then, multiplying B by the length of the cover, we find the area of \u200b\u200beach inclination.
Regarding material costs, such calculations are already addressed at the final design stage. First you need to calculate the surface area that will be laid and directly the dimensions of the roofing material. Let's take a metal tile as an example.
roof area
So, the parameter of the real width is 1180 mm, the effective one is 1100 mm. Now we turn to calculating the length of the coverage of the house, which we have already talked about. Since we are analyzing a fictitious calculation as an example, let the mentioned indicator be equal to 6 meters.
We divide this number by the effective width and get 5.45. The decision of the action displays the number of sheets needed, and since the number is not an integer, for obvious reasons, we round it up.
Thus, we need 6 sheets of metal tiles for flooring one row along the length of the eaves. We proceed to the calculation of the number of sheets vertically.
For measuring vertical row the size of the overlap should be taken into account (usually taken at a value of 140-150 mm), the distance between the ridge and the cornice, as well as the length of the cornice overhang.
Let the distance be 4 meters, and the overhang - 30 cm. Having made a simple addition, we get a size of 4.3 meters. Let's take the conditional length of a metal tile sheet as 1 meter. Taking into account the overlap, the effective length of one roofing unit will be 0.85 m.
After that, we divide the result of 4.3 m by the effective length and at the end we get 5.05 sheets. In such a small deviation from a whole number, we advise you to round down.
Calculation of steam and waterproofing
- and it is considered very simple. To do this, you just need to divide the covered area by the same parameter of the roofing deck. For example, we are talking about a gable canopy.
Conventionally, we take a slope length of 5 meters and a width of 4 m. Therefore, the area of \u200b\u200bone unit is 20 square meters. m, and the total figure for two slopes will be 40 square meters. m. Steam and waterproofing material is considered to be in rolls.
Useful video
Video instruction for calculating the roof:
In contact with
The pitched roof has a system of inclined planes (slopes). The design of the truss system is selected and calculated, taking into account the presence of supports for it, the type of coverage, the size and shape of the building to be covered. A special calculation will help you choose the required size of the rafter leg and ensure the strength of the roof.
Types of gable roof truss systems
The scheme of the truss system is selected based on the conditions for the number of supports for it and the distance between them.
The rafters rest on the external load-bearing walls of the buildings and on additional internal supports, if the distance between the main supports exceeds 4.5 m. The upper end is connected to the ridge run and the other rafter leg.
1, 2 - hanging truss system. 3, 4 - layered truss system. a - rafters, b - tightening, c - crossbar, d - run, e - Mauerlat, f - strut, g - rack.
The hanging type of truss systems has a tightening at the level of the lower support nodes or above them and does not imply intermediate supports. The distance between the external bearing supports must not exceed 6.5 m. This version of the device roof structure can be attributed to triangular farms. The distance in plan between them is assumed to be 1.3-1.8 m.
Coating composition
Roof
Eternite roofs are flat or wavy sheets of asbestos cement. This is a cheap type of roofing that is quite easy to install. V Lately research has shown it bad influence on human health.
Slate roofs also belong to slate. They are built from natural material layered structure of shale. Euroslate, ondulin are descendants of ordinary slate. They are compressed fiberglass or cellulose, which are impregnated with bitumen.
Metal coating is often used in the construction of residential buildings. It reliably protects the house from atmospheric influence, has small weight and is not laborious in installation. This type of roofing includes corrugated board, galvanized steel, aluzinc.
Rolled are soft types of roofs. They are waterproof, weather resistant and easy to install. These include the following types:
- roofing material (rubemast, glass mast, euroroofing material, roofing felt, etc.);
- bitumen-polymer (stekloizol, steklokrom, linokrom, etc.);
- membrane roofs (PVC, thermoplastic membranes, synthetic rubber films, etc.).
If earlier tiled roofs were only ceramic, today there are: cement-sand, bituminous and metal tiles.
Wooden roofs are rarely used due to the difficulty of the device. They are shingled, dranichny, shindebl, ploughshare, hewn.
Light-transmitting roofs are made of polymeric materials and glass. These include cellular polycarbonate, corrugated polyvinyl chloride, triplex, polyester, etc.
crate
Roof decking or sheathing is the basis for the roof. It is made from boards or bars. When constructing a metal, wooden or tiled roof, the lathing timber is taken with a section:
- 50x50 mm with a distance between the rafters - 1.0-1.1 m;
- 50x60 (h) mm with a rafter pitch - 1.2-1.3 m;
- 60x60 mm with a step - 1.4-1.5 m.
For other types, boards 2.5 cm thick can be used. Under roll roofing a double flooring of boards is arranged. The working bottom layer is laid perpendicular to the direction of the rafters with gaps. The top layer is laid at an angle of 45° to the underlying layer. The width of the boards for it is taken no more than 8 cm, and the thickness is 2 cm.
rafters
Wooden rafters are used log, cut down on one edge, from sawn wood (beam, board laid on the edge). For layered rafters, a round section of a log is better suited. Their diameter is 12-20 cm. The advantages of using a log compared to a board or beam are as follows:
- wood savings (to withstand the same loads for a circular section, a smaller diameter is needed source material);
- higher fire resistance limit;
- less consumption of metal fasteners;
- higher rates of rigidity and durability.
Calculation of a layered rafter leg
A step of 1.0-1.5 m is allowed between the rafter legs. Their cross section is determined by calculation, based on the strength and rigidity of the structure. For this, the calculated constant load on the rafters is determined, which includes the calculation of constant loads per linear meter of the roof and snow load.
Scheme of load distribution along the rafter leg: α - angle of inclination of the roof, q - total constant loads, q
The initial data for the calculation are:
- installation step of the rafter legs;
- the angle of the roof;
- roof width and height.
The choice of parameters, as well as the selection of most coefficients, depends on the roofing material and the detailed composition of the roofing cake.
For sloped roofs, permanent loads are calculated using the formula:
The rafter leg is also calculated for stiffness (deflection). Here is the normative load:
- α is the angle of inclination of the roof;
- n, n c - safety factors for loads from snow - 1.4, loads from the roof - 1.1;
- g - weight 1 m 2, which is perceived by the rafter leg (roof, lathing, rafters);
- a - the step of the rafter legs (along the axis).
- S g - snow weight per 1 m 2, which depends on the climatic region;
- c e - coefficient of snow drift due to the influence of wind and other atmospheric influences, depends on the mode of operation of the roof;
- c t is the thermal coefficient.
Coefficients e and c t are taken in accordance with the requirements of SP 20.13330.2011 section 10 "Snow loads" in accordance with 10.5 and 10.6. For a private house with a pitched roof with a roof slope of more than 20 °, the coefficients c e and c t are equal to one, therefore, the snow cover formula:
µ is a coefficient that depends on the angle of the roof and is determined in accordance with Appendix D of SP 20.13330.2011:
- for roofs with a slope less than 30° µ = 1;
- for roofs with a slope over 60° µ = 0;
- otherwise for an inclination angle of 30°<α<60° µ = 0,033 х (60°-α).
The weight of snow cover by region can be specified in SP 20.13330.2011 "Loads and Impacts", which also determines the number of the region according to the map of Appendix G.
Snow cover weight S g
| District | I | II | III | IV | V |
| S g kg / m 2 | 80 | 120 | 180 | 240 | 320 |
Since the rafter leg is subjected to bending from the effects of loads on it, it is tested for strength as a bending element, according to the formula:
M< m и R и W нт
- M is the design bending moment;
- R and - design resistance to wood bending;
- m and - coefficient reflecting the working conditions;
- W nt - moment of resistance of a given section;
- R and \u003d 130 kg / cm 2 - for pine and spruce;
- m and is equal to 1.0 for sections up to 15 cm high and 1.15 for sections more than 15 cm high.
The moment of resistance and the moment of inertia for the material of the rafters are calculated individually. According to the data obtained, the required size of the structural elements of the rafters is selected.
The proposed calculation is approximate and requires additions in the form of the maximum allowable length of the supporting elements, the arrangement of spacer or retaining beams and racks.
Example #1
Consider a tiled ceramic roof on a gable roof in the Moscow region (III climatic region).
Tilt angle 27°; cosα = 0.89; rafter pitch along the axis - 1.3 m; the estimated span of the rafters is 4.4 m. The crate is taken from a beam of 50x60 mm.
Roof weight per 1 m 2:
- roof weight - 45 kg;
- rafter weight - 10 kg.
Total: g n \u003d 62 kg / m 2
- q \u003d (1.1 x 62 x 0.89 + 1.4 x 126 x 0.89 2) x 1.3 \u003d 260 kg / m.
- q n \u003d (62 x 0.89 + 126 x 0.89 2) x 1.3 \u003d 201 kg / m
- M \u003d 0.125 x q x l 2 \u003d 0.125 x 2.60 x 440 2 \u003d 62 920 kg ∙ cm
Moment of resistance:
The moment of inertia (I), which is necessary from the condition of a possible deflection f = 1/150 l; E \u003d 100,000 kg / cm 2; qn = 201 kg.
According to specially designed tables, you can determine the diameter of the log for the rafters.
Log diameter (cm) depending on W and J (for logs hewn to one edge).
| Conventions | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| J | 1359 | 1828 | 2409 | 3118 | 3974 | 4995 | 6201 |
| W | 211 | 263 | 324 | 393 | 471 | 559 | 658 |
According to the table below, we determine the diameter of the log - 18 cm.
Example #2
Let's take all the data from the previous example, but for an ondulin roof. It is necessary to calculate the cross section of the rafter leg from the beam.
Tilt angle 27°; cosα=0.89; rafter pitch along the axis - 1.3 m; the estimated span of the rafters is 4.4 m. The crate is taken from a beam of 50x60 mm.
Roof weight per 1 m 2:
- ondulin roof weight - 3.4 kg;
- crate - 0.05 x 0.06 x 100 x 550/25 = 7 kg;
- rafter weight - 10 kg.
Total: gn \u003d 20.4 kg / m 2
- q \u003d (1.1 x 20.4 x 0.89 + 1.4 x 126 x 0.89 2) x 1.3 \u003d 207.6 kg / m.
- qn \u003d (20.4 x 0.89 + 126 x 0.89 2) x 1.3 \u003d 153.3 kg / m
- M \u003d 0.125 x q x l 2 \u003d 0.125 x 2.08 x 440 2 \u003d 50 336 kg ∙ cm
Moment of resistance:
The moment of inertia (I), which is necessary from the condition of a possible deflection f = 1/150 l; E \u003d 100,000 kg / cm 2; qn = 153.3 kg.
We accept a beam with a height of 15 cm. For a bar with a height of more than 14 cm R and \u003d 150 kg / cm 2. So:
According to the table, we determine the size of the section of the beam for the rafters.
Width (b) and height (h) of the beam depending on W and J.
| Conventions | ||||||||
| 8 | 9 | 10 | 11 | 12 | 13 | 14 | ||
| 1829 | 2058 | 2287 | 2515 | 2744 | 2973 | 3201 | ||
| 261 | 294 | 327 | 359 | 392 | 425 | 457 | ||
| 2250 | 2531 | 2812 | 3094 | 3375 | 3656 | 3937 | ||
| 300 | 337 | 375 | 412 | 450 | 487 | 525 | ||
We accept a bar with a section of 10x15 cm for the rafter leg.
The above formulas can be used to calculate other roof coverings. In this case, the load on the rafter leg is calculated based on their chosen option. Formulas can change:
- rafter length;
- rafter step;
- roof pitch;
- snow load, which is selected according to the region of construction;
- crate weight.
The pairing of the rafter legs between themselves and the run must be reliable. This ensures that there is no destructive thrust on the walls of the building. Wooden structures need to be inspected from time to time, therefore, when constructing layered rafters, the distance from the mark of the top of the attic floor to the lower mark of the Mauerlat is assumed to be at least 400 mm.
Gable roofs are still a tradition of private housing construction today. The right roof structure is a strong, durable and beautiful house.
