Erection of the roof on our own– the task is quite realistic. Of course, this requires a certain amount of knowledge, and first of all this concerns rafter system- the main element of the roof, which perceives and resists all types of loads.
The rafter system actually provides rigidity to the roof structure, since it distributes the load from the sheathing with the laid roofing material to external and internal supports. Therefore, the reliability of the roof and its ability to withstand all impacts depends on how to calculate the rafter system.
How to correctly calculate the rafter system
Calculation of the elements of the rafter system is carried out in order to determine optimal parameters structures that ensure its ability to withstand the impact of the total weight of the roof, including coating and thermal insulation, under conditions of maximum exposure to external loads, wind and snow. In this regard, the question naturally arises of how to calculate the rafter system for the total impact of possible loads. For example, the weight of the coating, interior decoration ceilings, hail, wind, ice on the roof during the period, etc. In the calculations, reliability coefficients are used, say, 1.1 and 1.4. The first increases the strength of the calculated roof by 10%, and the second – by 40%.
As a rule, the calculation scheme used in calculations is “idealized”. The roof is assumed to be exposed evenly distributed load, that is, it experiences an equal and even force, which equally affects all slopes. In fact, such a picture practically never occurs. For example, when the wind sweeps snow bags onto one slope, it simultaneously blows it off another. The force on the slopes thus turns out to be uneven.
Rafter loads
Rafters experience two types of impact - temporary and permanent. The second includes the weight of roof elements, including roofing, sheathing, purlins and rafters. The second is snow and wind. Temporary also includes useful, if any.
Snow
This type of impact can pose a serious risk to the integrity of the structure, as large volumes of snow accumulated on the roof have a significant impact on it. The amount of snow load is determined in horizontal projection using the formula:
S=Sg * µ ,
- Sg – mass of snow cover per unit area horizontal plane. This parameter depends on the location of the building.
- µ is a coefficient expressing the dependence on the angle of inclination of the roof. For example, for flat roofs up to 25⁰ – 1.0, for slopes with a slope of more than 25⁰< α < 60⁰ – 0,7. При крутом уклоне, свыше 60°, снеговая нагрузка не учитывается.
Wind
To calculate the average wind load at a given height, use the following formula:
W=W o x k,
wherein
- W o – standard value, it is selected from the table, according to the wind region;
- k is the coefficient of dependence of wind pressure on height, it differs depending on the area where construction is carried out:
An adjustment for wind is made in the calculation of rafters only if the roof slope is more than 30°.
The choice of terrain type depends on the wind direction used in the calculation.
How to calculate taking into account wind and snow
Let's calculate climatic loads using the example of the Moscow region, which is part of middle lane RF. The calculated values are selected from SNiP 2.01.07-85*, namely “Loads and impacts”.
(1.1 MiB, 1,547 hits)
Let's say the roof slope is 22⁰. This is the third snow region, for which the calculated value is 180 kg/m2, and µ=1.0, then 180 x 1.0 = 180 kg/m2. For pitched roofs with a coefficient µ=0.7 this value decreases to 126 kg/m 2.
When a snow bag is formed, the value of this indicator can increase to 400-500 kg/m2.
The estimated wind load for the same region is 32 kg/m2. Assuming that we're talking about about a 10-meter house, then the magnitude of the wind impact will be equal to 32 x 0.65 = 20.8 kg/m2.
Other
- The load created by the under-roof structure and the roof itself is calculated according to the size of the structure and the volume of materials used.
- The useful value is taken into account for structures “connected” with trusses. For example, ceilings suspended from them, ventilation chambers or water tanks located on farms, etc.
When designing a roof, two types of calculations are carried out:
- in strength, which eliminates damage rafter legs;
- by deformation, which determines the maximum degree of deflection of such a beam. So, calculation of the rafter system sloping roof must take into account that the deflection of the rafters for such a structure should not be more than 0.004 of the length of the section, that is, for example, the maximum deflection of a 6-meter beam reaches 2 cm. At first glance it may seem that this is not so much, however, if even slightly exceed the magnitude of the deformation, it will become visually noticeable. And large deflections will make the roof look like a Chinese pagoda.
Calculation of elements
The design of the system is determined taking into account the following parameters:
- roof slope,
- the size of the overlapped span,
- cross-section of rafters and laths,
- total load from roofing, wind and snow,
- the distance between the rafters, its optimal value determined by the limit method, that is, the value upon reaching which partial or complete destruction can be expected.
The cut (section) of the rafters is selected based on their length and the magnitude of the loads experienced.
The values given in this table, of course, are not the result of a full calculation; they are only recommended for use when carrying out rafter work for simple structures.
A full calculation of the system is possible with sufficient theoretical knowledge and certain drawing and drawing skills. Fortunately, the design task is greatly simplified today, thanks to convenient computer programs designed specifically for developing projects of all kinds. building elements. They are suitable not only for professionals, but also for private users.
Example of calculation using programs
Step 1. Load calculation
At the first stage, select the “Loads” window from the menu and enter it into the table cells blue color necessary changes:
"Initial data"
- Change the slope of the slope and the pitch of the rafters to the expected ones. The next line of the table “Load. Roofs" is filled with data from the table below.
- In the next cell the sum of the pre-calculated loads from wind and snow is entered. Next comes " Insulation (mans.)» – the cell is left unchanged for a warm attic or entered 0 – for a cold one.
- The values in the “Lathing” table are also adjusted.
If the filled in data is correct, the message “The load-bearing capacity of the sheathing is ensured!” should appear at the bottom of the window. Otherwise, you will need to change the dimensions of the sheathing or the distance between the rafters.
Step 2 Rafters with two supports
At this stage, work with the “Sling” tab. 1".
Starting from this tab, the data already entered into the table will be inserted into the cells automatically by the program.
What edits are made at this stage?
- Changes are made to the value of the horizontal projection of the rafters in the diagram and begin to fill out the table “Calculation of rafters”.
- The value of the rafter thickness that is entered into the cell “B (specified)” must be greater than the specified “Btr (stable)”.
- The width of the rafters entered in the line “Accept N” must exceed the values indicated in the lines “Ntr., (deflection)” and “Ntr., (strength)”. If all values are entered correctly, the program will “write” under the diagram: “The condition is met.”
The line “N, (by grade)” is filled in by the program itself, but you should know that you can change the data yourself.
Step 3 Rafters with three supports
Such rafters are calculated on the “Sling.2” or “Sling.3” tab.
Which one to choose depends on the location of the intermediate support. The tabs differ in the location of the middle pillar (support). In case of L/L1<2, иначе говоря, она находится правее середины стропила, пользуются «Строп.2 », в противном случае – «Строп.3 ». Стойка может располагаться точно посередине, тогда не принципиально, какую из них выбрать – результат будет тот же. С этими вкладками работают аналогично «Строп. 1 ».
Step 4 Stand
The magnitude of the bending moment of the rack and the vertical impact on it is entered (in tons) in the cells “M=” and “N=”, respectively. The inscriptions “Off-center. secured" and "Central secured!" in the center means admission to the next stage.
-> 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 - standard snow load, kg/m².
µ - coefficient depending on the roof slope α. Dimensionless quantity.
The roof slope angle α can be approximately determined by dividing the height H by half the span - L.
The results are summarized in the table:
Then, if α is less than or equal to 30°, µ = 1 ;
if α is greater than or equal to 60°, µ = 0;
If 30° is calculated using the formula:
µ = 0.033·(60-α);
Sg - standard snow load, kg/m².
For Russia it is accepted according to map 1 of mandatory appendix 5 of SNiP 2.01.07-85 “Loads and impacts”
For Belarus, the standard snow load Sg is determined
Technical code of PRACTICE Eurocode 1. EFFECTS ON STRUCTURES Part 1-3. General impacts. Snow loads. TKP EN1991-1-3-2009 (02250).
For example,
Brest (I) - 120 kg/m²,
Grodno (II) - 140 kg/m²,
Minsk (III) - 160 kg/m²,
Vitebsk (IV) - 180 kg/m².
Find the maximum possible snow load on a roof with a height of 2.5 m and a span of 7 m.
The building is located in the village. Babenki Ivanovo region. RF.
Using Map 1 of Mandatory Appendix 5 of SNiP 2.01.07-85 “Loads and Impacts” we determine Sg - the standard snow load for the city of Ivanovo (IV district):
Sg=240 kg/m²
Determine the roof slope angle α.
To do this, divide the roof height (H) by half the span (L): 2.5/3.5=0.714
and from the table we find the slope angle α=36°.
Since 30°, the calculation µ will be produced using the formula µ = 0.033·(60-α) .
Substituting the value α=36°, we find: µ = 0.033·(60-36)= 0.79
Then S=Sg·µ =240·0.79=189kg/m²;
the maximum possible snow load on our roof will be 189 kg/m².
2. Wind loads.
If the roof is steep (α > 30°), then due to its windage, the wind puts pressure on one of the slopes and tends to overturn it.
If the roof is flat (α, then the lifting aerodynamic force that arises when the wind bends around it, as well as turbulence under the overhangs, tend to lift this roof.
According to SNiP 2.01.07-85 “Loads and impacts” (in Belarus - Eurocode 1 IMPACTS ON STRUCTURES Part 1-4. General impacts. Wind impacts), the standard value of the average component of the wind load Wm at a height Z above the ground surface should be determined by the formula :
Where,
Wo is the standard value of wind pressure.
K is a coefficient that takes into account the change in wind pressure with height.
C - aerodynamic coefficient.
K is a coefficient that takes into account the change in wind pressure with height. Its values, depending on the height of the building and the nature of the terrain, are summarized in Table 3.
C - aerodynamic coefficient,
which, depending on the configuration of the building and the roof, can take values from minus 1.8 (the roof rises) to plus 0.8 (the wind presses on the roof). Since our calculation is simplified in the direction of increasing strength, we take the value of C equal to 0.8.
When building a roof, it must be remembered that wind forces tending to lift or tear off the roof can reach significant values, and therefore, the bottom of each rafter leg must be properly attached to the walls or mats.
This can be done by any means, for example, using annealed (for softness) steel wire with a diameter of 5 - 6 mm. With this wire, each rafter leg is screwed to the matrices or to the ears of the floor slabs. It's obvious that The heavier the roof, the better!
Determine the average wind load on the roof one-story house with the height of the ridge from the ground - 6 m. , slope angle α=36° in the village of Babenki, Ivanovo region. RF.
According to map 3 of Appendix 5 in “SNiP 2.01.07-85” we find that the Ivanovo region belongs to the second wind region Wo= 30 kg/m²
Since all buildings in the village are below 10m, coefficient K= 1.0
The value of the aerodynamic coefficient C is taken equal to 0.8
standard value of the average component of the wind load Wm = 30 1.0 0.8 = 24 kg/m².
For information: if the wind blows at the end of a given roof, then a lifting (tearing) force of up to 33.6 kg/m² acts on its edge
3. Roof weight.
Different types of roofing have the following weight:
1. Slate 10 - 15 kg/m²;
2. Ondulin (bitumen slate) 4 - 6 kg/m²;
3. Ceramic tiles 35 - 50kg/m²;
4. Cement-sand tiles 40 - 50 kg/m²;
5. Bituminous shingles 8 - 12 kg/m²;
6. Metal tiles 4 - 5 kg/m²;
7. Corrugated sheeting 4 - 5 kg/m²;
4. Weight of rough flooring, sheathing and rafter system.
The weight of the rough flooring is 18 - 20 kg/m²;
Sheathing weight 8 - 10 kg/m²;
The weight of the rafter system itself is 15 - 20 kg/m²;
When calculating the final load on the rafter system, all of the above loads are summed up.
And now I'll tell you little secret. Sellers of 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 Lumber coniferous species. 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.
This article provides a simplified method for calculating a rafter system. You will learn how to quickly and correctly make a decision on the cross-section of the rafters and the width of the span. Adapted mathematical calculation contains a minimum of formulas and leads to fairly accurate results.
There is a standard calculation method truss structure, brought into compliance with SNiP 2.01.07-85 “Loads and impacts”. It includes many rather complex calculations and reference values. A popular website service - online calculation of the rafter system of a gable roof - will allow you to determine the amount of material extremely accurately.
Note. The article discusses the methodology for calculating the rafter system of a gable roof with a hip, half-hip or pediment without additional structural elements- canopies, birdhouses, towers, etc. and a slope angle of at least 45°.
Where to begin
The traditional method assumes the following approach: the roof structure and beam cross-section are selected for the design load. This does not fully meet the requirements today and the initial data in our case will be the following indicators:
- Requirements (wishes) for the roof structure. First of all, this means the presence of an attic (residential) floor, the location skylights or the presence of an attic technical room.
- Existing sizes houses, or the boundaries of a building. 70% of private houses are located in relatively dense buildings, and this should also be taken into account when designing the roof. Limited area of the site and possible requirements neighbors may make their own adjustments regarding sunlight.
- Unification. The rafter system is a multi-element structure. It is reasonable to try to bring maximum amount elements to one standard - the section of a board or timber.
The most difficult, oddly enough, is the first point. However, once you have a complete understanding of what functions the rafter system should perform (direct or combined), you can proceed to the design stage.
Create a sketch
This stage is one of the decisive ones, since in it we find out the approximate sizes of the elements. The main one - the truss - will become the basis for further calculations. The drawing itself will be based on two initial parameters:
- Span between load-bearing walls. It is highly desirable that the support points of the rafter system, which transmit vertical loads, be located along the axes of load-bearing walls or supports. The distance from the projection of the ridge to the wall is called the half-span.
- The height of the ridge from the ceiling. This parameter consists of functional features structures - the height of the ceiling of the attic, accessible attic or “dead” attic space.
As you know, 75% of simple rafter systems are roofs with straight and “broken” slopes. This significantly affects the calculations, so we will immediately separate these types. Since the basis of any standard roof is a triangular structure, we will try to limit ourselves to one formula (the Pythagorean theorem):
- c 2 = a 2 + b 2
At this stage, you can quite accurately calculate the area of the slopes and the consumption of roofing material along with the sheathing. To do this, just use the online calculation of the rafter system for a gable roof, which is provided by many websites.
Straight equilateral slope
We transfer to the sketch the dimensions of the floor or the location of the load-bearing walls (the design does not always imply the presence of a wooden floor) to scale. Then we mark the ridge point and draw straight lines to the walls, taking into account the accepted roof overhang. These straight lines can already be measured and multiplied by a scale - we get the length of the rafter leg.
In accordance with the chosen organization structure internal space(combined or divided), we place the rafter tie (crossbar) and determine its length. We place stops, slopes and vertical posts on the drawing, observing the requirements that the portal website cited in the article “Do-it-yourself gable roof rafter system.” The spans should not be more than 2 m, and the rafters must have an intermediate brace. In this case, it is enough to adhere to the approximate tolerance limits.
Using the formula for the ratio of the sides of a right triangle, you can calculate any of the sizes of the truss. The remaining dimensions can be taken from the drawing using scale. the main task— get the dimensions of each element.
"Broken" slope
This type of roofing is always adopted in connection with the construction of an attic or the addition of a residential floor. He has one characteristic feature- a series of vertical posts at the intersection of the slopes and a rafter crossbar, which can be located either at the level of the top of these posts or under the ridge. Rows of posts and crossbars form the walls and ceiling of the attic space.
In a similar way, we transfer the main elements to the drawing - first the walls and ceiling, then a series of racks and crossbars (at the ceiling level), then we connect them with lines that will quite accurately show the shape of the break in the slopes.
After measurements and calculations, you should add up the lengths of all elements of the truss and add 10% to the resulting number. This will be the total length of the structure of one truss (ODK 1).
Selection of rafter sections and unification
The cross-section of the system elements, especially the rafter legs, directly depends on the span between the supports in the central part. Of all lumber, timber and boards are suitable for the rafter system (not counting factory-made laminated trusses). Moreover, the board has much best indicator ratio of section to flexural strength. In our case, we are talking about the reliability of the rafters, for which the board is used, because There is a reserve depth of the sinus for laying insulation.
Table of dependence of span width and rafter thickness
Arrange flyovers roof trusses more than 6 meters without intermediate supports Not recommended.
Advice. When joining two boards to create vertical support, lay between them in places where the boards are fastened with 25 mm pieces (“bobs”) in increments of 300-400 mm. So the strength of the support will be higher compared to direct splicing.
After determining the sufficient cross-section of the board, you can calculate the volume of one truss. To do this, multiply ODK-1 by the cross-sectional area of the board. The resulting volume of one farm (OF 1) will be used when calculating the total volume.
Calculation of the pitch of trusses
The pitch of the rafters of the attic rafter system depends on the thickness and design of the trusses.
Table of pitch versus thickness
By dividing the length of the longitudinal (parallel to the ridge) wall by the selected step, we get the number of trusses (N). Accordingly, we can calculate the length of the board for the trusses:
- ODK 1 x N
truss board volume:
- OF 1 x N or ODK 1 x S board sections x N
Mauerlat calculation
If the rafter system is arranged on wooden floor, then the entire horizontal piping relates to it. We will consider the option of using a mauerlat on a stone wall.
Since vertical posts, struts and purlins are included in the calculation of the truss, we only need to calculate the horizontal strapping. There is a simple rule here - it must be at least twice as thick as a rafter. If total weight the roof (together with the sheathing and roofing material and snow) is noticeably high, three layers of boards should be used.
The volume of the board for the mauerlat will be equal to length load-bearing walls, multiplied by the cross-section of the board and the number of layers. A Mauerlat made of several layers will bond better at the corners.
Total count
We add all the resulting volumes together and add 20% for waste and trimming. Quantity metal products And fastening elements determined individually. What is certain is that the more there are, the better.
Note. All given values and proportions of dependence are taken from normative and reference literature.
Despite its apparent simplicity, this adapted calculation can compete in accuracy with online rafter system calculators. However, the final word always remains with those who will implement the project.
Video on the topic
rmnt.ru, Igor Maksimov
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 accept the value of the 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. We open the file “Calculation of the rafter system”, and we get into 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 roofing (load from the roofing material’s own weight) - 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.
The roof of a building is designed to hold external loads and redistribute them to load-bearing walls or support structures. Such loads include the weight of the roofing pie, the weight of the structure itself, the weight of the snow cover, and so on.
The roof is located on the rafter system. So called frame construction, on which the roof is fixed. It accepts all external loads, distributing them across supporting structures.
The rafter system of a gable roof includes the following elements:
- Mauerlat;
- Struts and braces;
- Lateral and ridge purlins;
- Rafter legs.
A rafter truss is a structure that includes all of the listed elements with the exception of the Mauerlat.
Calculation of gable roof loads
Constant loads
The first type refers to those loads that always act on the roof (in any season, time of day, and so on). These include the weight of the roofing pie and various equipment installed on the roof. For example, the weight of a satellite dish or aerator. It is necessary to calculate the weight of the entire truss structure along with fasteners and various elements. To perform this task, professionals use computer programs, as well as special calculators.
Calculation gable roof is based on calculating the loads on the rafter legs. First of all, you need to determine the weight of the roofing cake. The task is quite simple, you just need to know the materials used, as well as the dimensions of the roof.
As an example, let’s calculate the weight of a roofing cake with ondulin material. All values are taken approximately high accuracy not required here. Usually builders perform calculations of the weight per square meter of roofing. And then this figure is multiplied by the total roof area.
The roofing pie consists of ondulin, a layer of waterproofing (in this case - insulation on a polymer-bitumen basis), a layer of thermal insulation (weight calculation will be carried out basalt wool) and lathing (the thickness of the boards is 25 mm). Let's calculate the weight of each element separately, and then add up all the values.
Calculation of the roof of a gable roof:
- A square meter of roofing material weighs 3.5 kg.
- A square meter of waterproofing layer weighs 5 kg.
- A square meter of insulation weighs 10 kg.
- A square meter of sheathing weighs 14 kg.
Now let's calculate the total weight:
3.5 + 5 + 10 + 14 = 32.5
The resulting value must be multiplied by the correction factor (in this case it is equal to 1.1).
32.5 * 1.1 = 35.75 kg
It turns out that a square meter of roofing cake weighs 35.75 kg. It remains to multiply this parameter by the roof area, then you can calculate a gable roof.
Variable roof loads
Variable loads are those that act on the roof not constantly, but seasonally. A striking example is the snow in winter time. Snow masses settle on the roof, creating additional impact. But in the spring they melt, and accordingly, the pressure decreases.
Variable loads also include wind. This is also a weather phenomenon that does not always work. And there are many such examples. Therefore, it is important to take into account variable loads when calculating the length of the rafters of a gable roof. When calculating, you need to take into account many different factors affecting the roof of a building.
Now let's take a closer look snow loads. When calculating this parameter, you need to use a special map. The mass of snow cover is marked there different regions countries.
To calculate this type of load, the following formula is used:
Where Sg is the terrain indicator taken from the map, and µ is correction factor. It depends on the roof slope: the stronger the slope, the lower the correction factor. And here there is important nuance- for roofs with a slope of 60 o or more it is not taken into account at all. After all, the snow will simply roll off of them, and not accumulate.
The whole country is divided into regions not only by the mass of snow, but also by the strength of the winds. Available special card, where you can find out this indicator in a certain area.
When calculating roof rafters, wind loads are determined using the following formula:
Where x is the correction factor. It depends on the location of the building and its height. And W o is the parameter selected from the map.
Calculation of the dimensions of the rafter system
When the calculation of all types of loads is finished, you can proceed to calculating the dimensions of the rafter system. The work performed will differ depending on what kind of roof structure is planned.
In this case, a gable one is considered.
Section of the rafter leg
The calculation of the rafter leg is based on 3 criteria:
- Loads from previous section;
- Remoteness of the railings;
- Rafter length.
There is a special table of sections of rafter legs, in which you can find out this indicator based on the criteria described above.
Length of rafters in a gable roof
Manual calculations will require basic knowledge of geometry, in particular the Pythagorean theorem. The rafter is the hypotenuse of a right triangle. Its length can be found by dividing the length of the leg by the cosine of the opposite angle.
Let's look at a specific example:
It is required to calculate the length of the rafters of a gable roof for a house with a width of 6 m, in which the slope of the slopes is 45 o. Let L be the length of the rafters. Let's substitute all the data into the formula.
L = 6 / 2 / cos 45 ≈ 6 / 2 / 0.707 ≈ 4.24 meters.
You need to add the length of the visor to the resulting value. It is approximately 0.5 m.
4.24 + 0.5 = 4.74 meters.
This completes the calculation of the length of the rafters for a gable roof. It was manual method completing the task. There are special computer programs designed to automate this process. The easiest way is to use Arkon. This is completely free program, which even a person with little computer knowledge can easily understand.
It is enough to simply specify the input parameters based on the size of the house. The program will independently perform calculations and show the required cross-section, as well as the length of the gable roof rafters.
