Metal tiles appeared in the range of roofing materials relatively recently, but quickly gained popularity. This can be explained simply - when correct installation such a cover provides reliable protection of the house from precipitation, while at the same time giving the roof a reliable imitation of natural classic tiles.
The popularity of this coating is also based on the fact that its installation is not particularly difficult, and the owner of the house must cope with it even on his own, naturally, having an assistant, but without resorting to hiring a team. The clear profile of the metal tile allows you to combine adjacent sheets without much difficulty, and it is very difficult to make a mistake even if you want to. But all this will be fair only if high-quality sheathing is installed under such a roof. A calculator for calculating lumber for lathing under metal tiles will help you figure out how many boards or timber will be needed to create it.
Below are some comments about working with the program.
Before you start building a roof, it is of course desirable that it be designed for strength. Immediately after the publication of the last article ““, I began to receive questions in the mail regarding the choice of the cross-section of rafters and floor beams.
Yes, understanding this issue in the vastness of our beloved Internet is indeed quite difficult. There is a lot of information on this topic, but as always it is so scattered and sometimes even contradictory that an inexperienced person, who in his life may not even have encountered such a subject as “Sopromat” (lucky someone), can easily get confused in these wilds.
I, in turn, will now try to create a step-by-step algorithm that will help you independently calculate the rafter system of your future roof and finally get rid of constant doubts - what if it won’t hold up, or what if it will fall apart. I’ll say right away that going deeper into the terms and various formulas I won't. Well, why? There are so many useful and interesting things in the world that you can fill your head with. We just need to build a roof and forget about it.
The entire calculation will be described using an example. gable roof, which I wrote about in
So, Step #1:
Determine the snow load on the roof. To do this, we need a map of snow loads in the Russian Federation. To enlarge the picture, click on it with the mouse. Below I will give a link where you can download it to your computer.
Using this map, we determine the number of the snow region in which we are building a house and from the table below we select the snow load corresponding to this region (S, kg/m²):
If your city is located on the border of regions, choose higher value loads. There is no need to adjust the resulting figure depending on the angle of inclination of the slopes of our roof. The program we will use will do this itself.
Let's say in our example we are building a house in the Moscow region. Moscow is located in the 3rd snow region. The load for it is 180 kg/m².
Step #2:
Determine the wind load on the roof. To do this, we need a map of wind loads in the Russian Federation. It can also be downloaded from the link below.
Using this map, we also select the corresponding region number and determine the wind load value for it (the values are shown in the lower left corner):
Here, column A is the open coasts of seas, lakes and reservoirs, deserts, steppes, forest-steppes and tundra; Column B - urban areas, forests and other areas evenly covered with obstacles. It should be taken into account that in some cases the type of terrain may differ in different directions (for example, a house is located on the outskirts of a populated area). Then select the values from column “A”.
Let's return to our example again. Moscow is located in I-th wind region. The height of our house is 6.5 meters. Let's assume that it is being built in locality. Thus we take the value correction factor k=0.65. Those. the wind load in this case will be equal to: 32x0.65=21 kg/m².
Step #3:
You need to download a calculation program made in the form of an Excel table to your computer. We will continue to work in it. Here is the download link: ". Also here are maps of snow and wind loads in the Russian Federation.
So, download and unpack the archive. Open the file “Calculation” rafter system", and we get to the first window - “Loads”:
Here we need to change some values in the filled cells blue. All calculations are done automatically. Let's continue with our example:
In the “Initial data” plate we change the angle of inclination to 36° (whatever angle you have, write that, well, I think this is clear to everyone);
We change the pitch of the rafters to the one we chose. In our case it is 0.6 meters;
Load roof (self-weight load roofing material) — we select this value from the table:
For our example, we choose metal tiles with a weight of 5 kg/m².
Snow. region - here we enter the sum of the values of snow and wind loads that we received earlier, i.e. 180+21=201 kg/m²;
Insulation (mans.) - we leave this value unchanged if we lay insulation between the rafters. If we do cold attic without insulation - change the value to 0;
We write in the “Lathing” sign required dimensions sheathings. In our case, for metal tiles, we will change the sheathing pitch by 0.35 m and the width by 10 cm. We leave the height unchanged.
All other loads (from the own weight of the rafters and sheathing) are taken into account by the program automatically. Now let's see what we got:
We see the inscription “The load-bearing capacity of the sheathing is ensured!” We don’t touch anything else in this window; we don’t even need to understand what the numbers are in other cells. If, for example, we choose a different rafter pitch (more), it may turn out that load bearing capacity sheathing will not be provided. Then it will be necessary to select other dimensions of the sheathing, for example, increase its width, etc. In general, I think you will figure it out.
Step #4:
Sling.1"and go to the window for calculating rafters with two support points. Here, all the input data we previously entered is already entered by the program automatically (this will be the case in all other windows).
In our example from the article “Do-it-yourself gable roof of a house,” the rafters have three support points. But let’s imagine that there are no intermediate posts and let’s do the calculation:
On the rafter diagram we change the length of its horizontal projection (the cell is filled in blue). In our example, it is 4.4 meters.
In the “Calculation of rafters” plate, change the value of the rafter thickness B (specified) to what we have chosen. We set 5 cm. This value must be greater than that indicated in the cell Tue (stable);
Now in the line " We accept N"We need to enter the selected rafter width in centimeters. It must be greater than the values specified in the lines “ Ntr.,(strong)" And " Ntr., (deflection)". If this condition is met, all the inscriptions at the bottom under the rafter diagram will look like “Condition met.” In the line " N, (by variety)" indicates the value that the program itself offers us to choose. We can take this number, or we can take another. We usually choose sections available in the store.
So, what we got is shown in the figure:
In our example, to meet all the strength conditions, it is necessary to choose rafters with a section of 5x20 cm. But the roof diagram I showed in the last article has rafters with three support points. Therefore, to calculate it, we move on to the next step.
Step #5:
Click on the tab " Sling.2" or " Sling. 3″. This opens a window for calculating rafters with 3 support points. We select the tab we need depending on the location of the middle support (rack). If it is located to the right of the middle of the rafter, i.e. L/L1<2, то пользуемся вкладкой "Sling.2". If the post is located to the left of the middle of the rafter, i.e. L/L1>2, then use the tab "Sling.3". If the stand is exactly in the middle, you can use any tab, the results will be the same.
On the rafter diagram, we transfer the dimensions in cells filled with blue (except for Ru);
Using the same principle as described above, we select the cross-sectional dimensions of the rafters. For our example, I took the dimensions 5x15 cm. Although 5x10 cm was also possible. I’m just used to working with such boards, and there will be a larger margin of safety.
Now it is important: from the drawing obtained during the calculation, we will need to write down the value of the vertical load acting on the post (in our example (see figure above) it is equal to 343.40 kg) and the bending moment acting on the post (Mop. = 78.57 kghm). We will need these numbers later when calculating the racks and floor beams.
Next, if you go to the “ Arch“, a window will open for calculating the rafter system, which is a ridge arch (two rafters and a tie). I won’t consider it; it’s not suitable for our roof. We have too large a span between the supports and a small angle of inclination of the slopes. There you will get rafters with a cross section of about 10x25 cm, which is of course unacceptable for us. For smaller spans such a scheme can be used. I am sure that those who understand what I wrote above will understand this calculation themselves. If you still have questions, write in the comments. And we move on to the next step.
Step #6:
Go to the “Rack” tab. Well, everything is simple here.
We enter the previously determined values of the vertical load on the post and the bending moment in the figure in the cells “N=” and “M=”, respectively. We recorded them in kilograms, we enter them in tons, and the values are automatically rounded;
Also in the figure we change the height of the rack (in our example it is 167 cm) and set the dimensions of the section we have chosen. I chose a 5x15 cm board. At the bottom in the center we see the inscription “Central secured!” and “Off-center.” secured." So everything is fine. The safety factors "Kz" are very large, so you can safely reduce the cross-section of the racks. But we will leave it as it is. The calculation result in the figure:
Step #7:
Go to the tab "Beam". Floor beams are subject to both distributed and concentrated loads. We need to take both into account. In our example, beams of the same section overlap spans different widths. Of course, we make calculations for a wider span:
— in the “Distributed load” plate we indicate the pitch and span of the beams (from the example we take 0.6 m and 4 m, respectively);
— we take the values Load (normal) = 350 kg/m² and Load (calc.) = 450 kg/m². The values of these loads in accordance with SNiP are averaged and taken with a good margin of safety. They include the load from the dead weight of the floors and the operational load (furniture, people, etc.);
- in the line " B, given» enter the section width of the beams we have chosen (in our example it is 10 cm);
In the lines " N, strength" And " N, deflection» the minimum possible cross-sectional heights of the beams will be indicated at which it will not break and its deflection will be acceptable. We are interested in the larger of these numbers. We take the height of the beam section based on it. In our example, a beam with a cross section of 10x20 cm is suitable:
So, if we didn’t have racks resting on the floor beams, the calculation would have ended there. But in our example there are racks. They create a concentrated load, so we continue to fill out the “” and “ Distributed + concentrated«:
In both plates we enter the dimensions of our spans (here I think everything is clear);
In the “” plate, we change the values of Load (normal) and Load (calculated) to the figure that we received above when calculating rafters with three points of support - this is the vertical load on the rack (in our example, 343.40 kg);
In both plates we enter the accepted width of the beam section (10 cm);
The height of the beam section is determined by the sign “ Distributed + concentrated." . Again we focus on a larger value. For our roof we take 20 cm (see figure above).
This completes the calculation of the rafter system.
I almost forgot to say: the calculation program we use is applicable for rafter systems made of pine (except Weymouth), spruce, European and Japanese larch. All wood used is 2nd grade. If you use other wood, some changes will need to be made to the program. Since other types of wood are rarely used in our country, I will not describe now what needs to be changed.
Introducing a free calculator for calculations gable roof. 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 (wavy 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) From 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 of 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 standard length 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. The end sides of a structure 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 required quantity 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 insulating 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 a roof truss system 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 given value must be divided by 2.
Uniform distance between sheathing boards
To eliminate waste of materials and save yourself from extra work for trimming, 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).
The online gable roof calculator will help you calculate the angles of the rafters, required amount lathing, maximum roof load, as well as materials necessary for roof construction of this type at given sizes. You can calculate the roof from such popular roofing materials as slate, ondulin, ceramic, cement-sand and bitumen tiles, metal tiles and other materials.
The calculations take into account the parameters given in TKP 45-5.05-146-2009 and SNiP “Loads and Impacts”.
A gable roof (also known as a gable or gable roof) is a type of roof that has two inclined slopes that extend from the ridge to the exterior walls of the building. This is the most common type of roof today. This is explained by its practicality, low construction costs, effective protection of premises and aesthetic appearance.
The rafters in a gable roof structure rest on each other, connecting in pairs. On the end side, gable roofs have the shape of a triangle; such ends are called gables or gables. Usually, an attic is installed under such a roof, which is illuminated using small windows on the gables (attic windows).
When entering data into the calculator, be sure to check additional information, marked with an icon.
At the bottom of this page you can leave feedback, ask your own question to the developers, or suggest an idea to improve this calculator.
Explanation of calculation results
Roof angle
The rafters and roof slope are inclined at this angle. It is understood that it is planned to build a symmetrical gable roof. In addition to calculating the angle, the calculator will inform you how the angle complies with the standards for the roofing material you have chosen. If you need to change the angle, then you need to change the width of the base or the height of the roof, or choose a different (lighter) roofing material.
Roof surface area
Total roof area (including overhangs of a given length). Determines the amount of roofing and insulating materials that will be needed for the work.
Approximate weight of roofing material
The total weight of roofing material required to completely cover the roof area.
Number of rolls of overlapping insulation material
The total amount of insulating material in rolls that will be required to insulate the roof. The calculations are based on rolls 15 meters long and 1 meter wide.
The maximum load on the rafter system. The calculations take into account the weight of the entire roofing system, the shape of the roof, as well as the wind and snow loads of the region you specify.
Rafter length
The full length of the rafters from the beginning of the slope to the ridge of the roof.
Number of rafters
The total number of rafters required to construct a roof at a given pitch.
Minimum section of rafters, Weight and Volume of timber for rafters
The table shows the recommended dimensions of rafter sections (according to GOST 24454-80 Lumber coniferous species). To determine compliance, the type of roofing material, the area and shape of the roof structure, and the loads placed on the roof are taken into account. The adjacent columns display total weight and the volume of these rafters for the entire roof.
Number of rows of sheathing
The total number of rows of sheathing for the entire roof. To determine the number of rows of sheathing for one slope, it is enough to divide the resulting value by two.
Uniform distance between sheathing boards
To install the sheathing evenly and avoid unnecessary overspending, use the value indicated here.
Number of sheathing boards standard length
To sheath the entire roof, you will need the number of boards indicated here. For calculations, a standard 6-meter board length is used.
Volume of sheathing boards
The volume of boards in cubic meters will help you calculate the cost of sheathing.
Approximate weight of sheathing boards
Estimated total weight of sheathing boards. The calculations use average values of density and moisture content for coniferous wood.
-> 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 impacts environment, it is very important to do correct calculation rafter system.
To independently calculate the characteristics of the materials required for installing the rafter system, I provide 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 methodology given below, programmer Andrey Mutovkin (Andrey’s business card - mutovkin.rf) for his 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 - normative 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 constructing 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 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 certain types of roofing materials as one of the positive properties note their lightness, 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, with the calculation of the total load Q acting on square meter We figured out the 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.
