Distance between rafters for different types of roofs and materials. Distance between rafters: correct calculation

The distance between the rafters under the metal tile without fail takes into account the efforts made up of the wind, snow load, own weight of structures, roofing. In addition, the following factors affect the pitch of the rafters under the metal tile:

• the location of the pipes - the wooden elements of the roof should be 25-35 cm from the chimney, should not interfere with the direct paths of the ventilation ducts, fan pipes;
• roof configuration - it is necessary to have a rafter leg at the junction of the ridge of a gable, hipped roof.

All wooden elements truss system are made from coniferous trees, the humidity of which does not exceed 20%.

The step of the rafter legs is calculated at the design stage for budgeting. This will significantly reduce the amount of waste, cuttings of sawn timber.

What you need to know when choosing the optimal distance between the rafters?

The scheme of the roof with hanging rafters.

Having collected the loads present during the strength calculation, the designer evenly distributes them on the load-bearing walls. The calculation principle is the same for layered, hanging rafters, only the schemes for fastening the elements in the ridge, on the Mauerlat, differ.

The minimum, maximum step of wooden rafters under the metal tile is regulated by 0.7 m, 1.2 m, respectively.

When choosing a step of 60 - 100 cm, the length of the rafters cannot exceed 6 m, with its decrease, a run-up of up to 1.2 m is allowed. If you put your feet more often than 60 cm, this will unnecessarily make the roof heavier and increase the construction budget. If you increase the step more than 1.2 m, the bearing capacity and the resource of the structure will sharply decrease.

A solid crate of wood-containing boards adds strength and rigidity to the truss system. In this case, it is allowed to increase the step by 0.3 - 0.2 m compared to a periodic crate made of a bar or edged board. However, to save the construction budget, a continuous crate for metal tiles is used extremely rarely. The material has sufficient strength and rigidity due to additional transverse profile ribs.

A step of more than 1.2 m is not used even when using rolled metal rafters, despite a sufficient margin of safety of the material. This is due to the possible deflection of the roof sheets during heavy snowfalls, hurricane winds.

The cross section of the beam from which the rafter legs are made also affects the step of the rafters, since the area of ​​\u200b\u200bsupport of the crate and the weight of the roof change. The best option a beam of 150 x 50 mm is considered with a discharged crate with a step of 4 - 7 cm, depending on the step of the transverse wave.

Calculation example for a gable roof

During the execution of the project by specialists on initial stage known roofing material. In order to find out the recommended pitch of the rafters, you can use the SNiP tables, and then adjust the value in accordance with the operating conditions. An example table is shown below:

Leg section (cm)	Rafter pitch (cm) depending on their length (m)
	5	4	3
board 20 x 2	70	120	–
board 18 x 2	–	100	–
board 16 x 2	–	70	130
timber 22 x 6	–	120	–
timber 20 x 5	–	110	–
timber 18 x 5	–	90	150
log 180	90	150	–
log 150	–	90	150
log 140	–	70	140
log 130	–	–	110

The table values ​​correspond to the rafters of simple single-gable roofs. First, the section of the leg, the length of the element, the distance between the centers of the log, the beam is obtained automatically. At the next stage, the length of the slope in the ridge is divided by the pitch of the rafters with the addition of one. Thus, the number of legs is counted, rounding the number up. Then it remains to adjust the distance between the wooden rafters in fact. For example, with a ridge length of 7.5 m, a rafter leg with a section of 16 x 2 cm (board) 4 m long, you get:

7.5 / 0.7 \u003d 10.7 + 1 \u003d 11.7 pcs. round up to 12 rafters.

The specification of the size allows you to calculate the center-to-center distance for mounting after installing the outer legs:

7.5/12 = 62.5 cm.

Dormer windows are located between adjacent rafters, in the places where pipes and chimneys pass, the legs are displaced by the distance specified in SNiP. All other elements of the system remain in place, the area of ​​​​adjacency to the pipes, if necessary, is enhanced:

• a bed is cut into two adjacent legs;
• a short rafter cuts into it at one end, the second adjoins the element of the opposite slope in the ridge;
• the offset legs in the upper part rest on a ridge run attached to at least two roof trusses.

Thus, the system receives the necessary rigidity without losing bearing capacity fire safety requirements are met wooden parts roofs.

Rafter leg material

The material of the rafters is often a beam of 25 x 10 cm - 15 x 4 cm, which allows to reduce the construction budget.

When choosing lumber of natural moisture, the developer is guaranteed to shrink the structure in the first year and a half by 5-7 cm in height. By increasing the cost estimate for the arrangement of the truss system by 70%, you can purchase glued laminated timber, significantly reducing structural loads, and doubling the roof resource.

The distance between the rafters will remain unchanged, however, instead of a planed beam of 17.5 x 5 cm, recommended building codes for five-meter legs spaced every 0.6 m, you can get by with a glued beam of a smaller section of 15 x 4 cm. Transportation costs will be reduced, work at height will be facilitated, cutting the material.

Prefabricated rafters from boards are used with the same scheme for attaching hip roof trusses. The upper slopes are made of single boards, the lower ones are made of three boards sewn with self-tapping screws with an offset in the rows.

The choice of metal rafters is justified with a complex configuration of the roof, an abundance of ventilation pipes, chimneys, which cannot be bypassed in compliance with the requirements of SNiP, fire safety. In this case, the step between the rafters is maximized, since rolled metal is much stronger than lumber.

If the rafters are attached at the bottom to the Mauerlat, the step of the legs is not critical, the elements can, if necessary, move to the desired distance in any direction. If the scheme of support on puffs, which are floor beams, is used, it is much more difficult to displace individual elements. In this case, the amount of cut waste increases when sheathing the draft ceiling, the floor of the attic or attic space.

The roof structure is one of the main enclosing elements of the building, the quality characteristics of which are subject to rather stringent requirements.

One of the most common roof sheathing materials is metal shingles, which are made from thin sheets of steel, aluminum, or copper.

From above, the elements are equipped with a polymer coating, which protects metal from aggressive external influences.

Externally, the metal tile is similar to ceramic, but it is more durable. This material is used to cover pitched roofs, the slope of which must be at least 14 degrees.

This is the national team roof frame structure, consisting of many wooden or metal parts. She rests on load-bearing walls, which are a reliable basis for all overlying elements. The rafter system serves as a kind of skeleton, on the basis of which it is made, - and the roof, as well as laying the roofing finish roofing layer.

truss system

Elements roof truss, and their main characteristics:

• Mauerlat. A softwood beam, which is a connecting element between the rafters and the underlying structures. It has a square cross section with a side of 100 or 150 mm. Mauerlat is laid along bearing wall along its entire length. With the help of the Mauerlat, the loads from the roof are evenly distributed throughout the building.
• Sill. A beam having a square section similar to a Mauerlat. It is laid transversely to the bearing walls, as it serves to redistribute the load from the roof racks.
• Rafter leg. From these elements, the main triangular roof structure is created, which experiences the full severity of external atmospheric influences (rain, wind, snow, hail, etc.).
• Rack. Vertical connecting elements that distribute compressive loads from the ridge assembly over the entire area of ​​​​bearing walls. They are made of square bars, the length of the edge of which is determined by calculation.
• Puff. It is the final horizontal element of the triangle of rafter legs, which does not allow them to creep under the pressure of external loads and the own weight of the roof. It is used in systems with hanging rafters.
• Struts. Perceive and redistribute bending loads from the ridge assembly.
• Crate. It consists of boards, bars or plywood sheets (in the case of subsequent laying of bituminous tiles), which are located at a right angle relative to the rafter legs, while being an additional rigid element.
• . The junction of two roof slopes.
• Overhang. A roofing element protruding from load-bearing wall structures at a distance of about 0.4 m. Its purpose is to limit the penetration of moisture to the walls.
• Filly. These elements are attached to the ends of the rafters if they are not long enough to organize an overhang.

Varieties of pitched roofs

Depending on the number of inclined planes, roof structures can be divided into:

In private housing construction, the most commonly used option gable roof, since he has a number of advantages. These include:

1. Practicality. The gable roof has a significant angle of inclination, due to which rainwater does not accumulate on its surface, and the snow and wind load are distributed most optimally.
2. Ease of device and operation. The assembly and joining of two pitched elements is much easier than with complex roof structures. In addition, the repair of such a roof will also be simple.
3. Aesthetics. A roof with a gable structure is organically written into the surrounding infrastructure.
4. Reliability(if done correctly).
5. Democratic price constituent materials.

Types of pitched roofs

Gable roof - truss system for metal tiles

Frame from rafters under a gable roof from a metal tile has no significant differences from structures with other covering roofing materials.

But, in view of the fact that metal thin sheets have a low specific gravity, the rafters will experience less constant load.

This makes it possible to reduce their cross section, due to which can save a lot on the purchase of wood materials.

Ideal for metal roofing the angle of inclination must be at least 14 degrees.

For a roof with two pitched elements, the following apply: frame options:

Laminated rafters under a metal tile.

In this case, 2 load-bearing rafter legs are fastened together using lying down(horizontally) and racks(vertically). The bed is laid parallel to the Mauerlat element, while taking on some of the force effects. The rafter system under the metal tile is taken over only bending loads, which significantly affects the selection of the calculated cross section. Such a system can be used for buildings with large and small spans.

Types of rafters

Hanging rafters.

Unlike layered systems, in this embodiment, two rafter legs fastened together only in the ridge knot. In this case, significant bursting forces arise on the supporting elements, which limits the use of hanging rafters only for buildings with a span of not more than 6 m.

They can be made of wood or metal, as well as installed at the bottom (acting as a supporting beam) or at the top of a triangular structure. It is worth considering that the higher the puff is located, the greater the effort it will take.

NOTE!

To ensure the quality of the tightening, care must be taken on the reliability of fastening with load-bearing rafter legs.

Combined variant

Used to create an original roof structure. Includes elements of both hanging and layered systems.

How to calculate the angle of inclination of the rafters?

For implementation gable roof need to know a few geometric values ​​of the building, namely:

• Half span - L;
• The distance from the load-bearing wall to the roof ridge (or the height of the support post) - H.

Standard formula: α = arctg(L/H)

Where α is the desired angle of inclination of the roof.

Knowing this value, you can calculate the length of the supporting rafter leg:

l = H/sinα.

Where l is the length of the truss element.

Rafter Angle

How to calculate the load?

To carry out the correct selection of parts of the roof frame, it is necessary calculate live and permanent load values acting on its structural elements.

The constant load includes the weight of all elements, as well as the mass of the load-bearing elements themselves and the crate.

The composition of temporary loading options includes force effects from wind, snow cover, rain masses, as well as the weight of a person (to take into account options for subsequent repairs).

Dead Load Calculation

Roofing cake weight.

It is determined by adding the masses of all its elements, namely steam, hydro and thermal insulation, as well as roofing from metal tiles. In this case, the weight of one linear meter (can be found in the regulatory documentation) is multiplied by the value of its length.

The weight of the truss system.

It is determined by adding the weight values ​​​​of the crate, rough flooring, as well as the supporting frame. The mass of each element is calculated by the formula:

M=V*p,

Where V is the volume of the element, calculated depending on geometric characteristics cross section and length elements;

P - The density of the wood used (depending on the species).

Total permanent load \u003d weight of the rafter system + weight of the roofing pie.

Calculation of live loading

Conducted in accordance with regulatory documents ( SNiP 2.01.07-85 "Loads and impacts" or Eurocode "Actions on structures" part 1-4).

To determine the value of the wind effect, the roof structure is conventionally divided by height into several parts. For each of them, the value of the wind load is calculated. To obtain the total wind pressure, they must be summed.

Formula for calculation:

Wm=Wo×k×c,

Where Wm is the value of the wind load;

Wo is the normative value of wind pressure determined from zoning maps;

k - wind pressure coefficient (determined depending on the height according to the regulatory documentation);

c - aerodynamic coefficient (for a gable roof - 0.8).

Determined by the formula:

S = µ×So;

Where So is the normative value of the snow load, determined from the zoning map.

µ is a coefficient that is determined depending on the angle of the roof:

• For α≤30 deg. — µ=1
• For α≥60deg. -µ=0
• For 30≤α≤60 deg. – µ=0.033×(60-α)

Snow load areas

How to choose a beam and calculate the pitch of the rafters under the metal tile?

Determining the value of the cross section of the beam of the truss element is carried out in several stages.

Calculation of the load distributed on each linear meter of the structure:

Qр = L×Q;

L - Step of the rafters.

The L value is calculated as follows:

The length of the roof slope is divided by the estimated step of the structures (for convenience, it is most often taken equal to 1). Then 1 is added to the resulting value. The resulting value reflects the number of rafters that need to be installed on one pitched roof surface. At the last stage, the value of the axial distance between the rafter elements is determined by dividing the length of the roof slope by the number of rafters.

The distance between the rafters under the metal tile - the standard step is 0.6-0.95 m.

Rafter step

Then we determine the maximum working area of ​​\u200b\u200bthe rafter leg (Lmax). We proceed to the calculation of the cross section. To do this, we find its height using the formula:

H ≥ 8.6*lmax * sqrt(Qp/(b*r)), with roof slope α<30 град;

H ≥ 9.5*lmax * sqrt(Qp/(b*r)), with a roof slope α≥30 degrees;

Where b is the width of the cross section,

r is the value of the normative resistance of wood to bending loads (determined according to normative documentation depending on the type of wood).

To simplify the calculations, you need to use the standardization table for truss elements (GOST 24454-80 “Softwood lumber. dimensions").

If the inequality is not observed, it is necessary to increase the value of the geometric characteristics of the section and repeat the calculation.

What is the difference between the truss system for cold and warm roofs?

The main difference between these two roofs is the support system of the truss elements. In the case of a warm attic, the main supporting element is the Mauerlat, as well as the supporting beam system. In a cold roof, rafters are installed directly on load-bearing walls.

Installation of rafters under the metal tile

All installation work on the installation of the roof is carried out at a sufficiently high height. To minimize the risk of falls, as well as greatly simplify work at height, you can assemble the frame of the supporting truss system on the ground.

To do this, you need to create a template from the boards, according to which further assembly will be carried out.

It is made in several stages:

• The boards are raised above the walls of the building, leveled, and then fasten together with the help of a nail.
• Align the angle of the boards in accordance with the project, by lowering and raising them. The elements are fixed.
• The result should be a structure that resembles in shape the future truss system, made in accordance with the estimated geometric dimensions of the roof.
• The template is lowered to the ground, in accordance with it, the finishing elements are fixed to each other. More details in the video below.

Then you should take care of installing the support element - Mauerlat. As mentioned earlier, it is laid on load-bearing walls in the longitudinal direction. Fastening is carried out using studs (on an armored belt or masonry) or using a wire rod (for buildings with a small roof height).

CAREFULLY!

When using a hairpin connection, connecting elements do not need to be tightly sealed into the wall. They should protrude from the wall by 30-40 mm, as the nut will be screwed onto the studs.

The next step is to create ridge run, serving as a supporting part for the entire structure of a gable roof. It is made from timber or hewn logs. If the span of the building is not more than 6 m, it can be supported without additional supporting elements. Otherwise, construction trusses must be used for installation.

Mounting. Part 1

After installing these elements, it is possible to lift and install the main truss element, assembled according to the template. Fastening with a Mauerlat can be carried out in 2 ways:

Rigid connection. It is carried out with the help of corners and beams. Less often, fastening is used by washing down on rafter legs, followed by fixation with nails or staples.

Features: in addition to the main connection, it is necessary to tie the rafters to the wall using anchors or a wire structure.

Sliding. It is based on the creation of a swivel joint. It is made by joining elements using cuts. The elements are connected with a metal embedded part with holes for bolts, or with 2 nails that need to be hammered in at an angle.

It is necessary to carry out the installation of wooden trusses in a certain sequence. First, extreme trusses are installed, located at the ends of the building. Then a cord or rope is pulled between them, with the help of which the verticality of their installation is checked. Further, under the cord, further installation of truss structures is carried out in accordance with the specified design step.

Mounting. Part 2

Creating a roof from a metal tile is a rather laborious process that requires certain skills and a full hand. Therefore, for proper installation, you must at least work under the supervision of a competent specialist.

Useful video

Video instruction for self-installation of rafter legs:

-> Calculation of the truss system

The main element of the roof, perceiving and resisting all types of loads, is rafter system. Therefore, in order for your roof to reliably resist all influences environment, it is very important to make the correct calculation of the truss system.

For self-calculation of the characteristics of the materials necessary for the installation of the truss system, I give simplified calculation formulas. Simplifications are made in the direction of increasing the strength of the structure. This will cause some increase in lumber consumption, but on small roofs of individual buildings it will not be significant. These formulas can be used when calculating gable attic and mansard, as well as shed roofs.

Based on the calculation methodology below, programmer Andrey Mutovkin (Andrey's business card - Mutovkin.rf) developed a truss system calculation program for his own needs. At my request, he generously allowed me to post it on the site. You can download the program.

The calculation methodology was compiled on the basis of SNiP 2.01.07-85 "Loads and impacts", taking into account the "Changes ..." of 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.

On the truss system, in addition to the above, the load from the roof elements also acts:

3. Roof weight.

4. The weight of the rough flooring and lathing.

5. The weight of the 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 - the desired value of the snow load, kg / m²
µ is a coefficient depending on the slope of the roof.
Sg - normative snow load, kg/m².

µ - coefficient depending on the slope of the roof α. Dimensionless value.

You can approximately determine the angle of the roof slope α by the result of 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 by the formula:

µ = 0.033 (60-α);

Sg - normative snow load, kg/m².
For Russia, it is accepted according to map 1 of mandatory annex 5 of SNiP 2.01.07-85 "Loads and impacts"

For Belarus, the normative snow load Sg is determined
Technical code of GOOD PRACTICE Eurocode 1. EFFECTS ON STRUCTURES Part 1-3. General impacts. Snow loads. TCH 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.

According to map 1 of the mandatory annex 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

We determine the angle of the roof slope α.
To do this, we divide the height of the roof (H) by half the span (L): 2.5 / 3.5 \u003d 0.714
and according to the table we find the slope angle α=36°.

Since 30° , calculation µ will be produced according to the formula µ = 0.033 (60-α) .
Substituting the value α=36° , we find: µ = 0.033 (60-36)= 0.79

Then S \u003d Sg µ \u003d 240 0.79 \u003d 189 kg / m²;

the maximum possible snow load on our roof will be 189kg/m².

2. Wind loads.

If the roof is steep (α > 30°), then because of its windage, the wind presses on one of the slopes and tends to overturn it.

If the roof is flat (α , then the lifting aerodynamic force that occurs when the wind bends around it, as well as turbulence under the overhangs, tend to raise this roof.

According to SNiP 2.01.07-85 "Loads and actions" (in Belarus - Eurocode 1 IMPACTS ON STRUCTURES Part 1-4. General actions. Wind actions), the standard value of the average component of the wind load Wm at a height Z above the ground should be determined by the formula :

Where,
Wo - normative value of wind pressure.
K is a coefficient that takes into account the change in wind pressure along the height.
C - aerodynamic coefficient.

K is a coefficient that takes into account the change in wind pressure along the 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 to the mats.

This is 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 mats 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 - 6m. , 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 this 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 (bituminous slate) 4 - 6 kg/m²;
3. Ceramic tiles 35 - 50kg/m²;
4. Cement-sand tiles 40 - 50 kg/m²;
5. Bituminous tiles 8 - 12 kg/m²;
6. Metal tile 4 - 5 kg/m²;
7. Decking 4 - 5 kg/m²;

4. The weight of the rough flooring, lathing and truss system.

Draft flooring weight 18 - 20 kg/m²;
Lathing weight 8 - 10 kg/m²;
The weight of the rafter system itself is 15 - 20 kg / m²;

When calculating the final load on the truss system, all of the above loads are summed up.

And now I will tell you a little secret. Sellers of some types of roofing materials note their lightness as one of the positive properties, which, according to them, will lead to significant savings in lumber in the manufacture of the truss system.

As a refutation of this statement, I will give the following example.

Calculation of the load on the truss system when using various roofing materials.

Let's calculate the load on the truss system when using the heaviest (Cement-sand tile
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
Lathing weight - 20 kg/m²

Total - 303 kg/m²

Metal tile:
Snow loads - 189kg/m²
Wind loads - 24kg/m²
Roof weight - 5 kg/m²
Lathing weight - 20 kg/m²
The weight of the truss system itself is 20 kg / m²
Total - 258 kg/m²

Obviously, the existing difference in design loads (only about 15%) cannot lead to any tangible savings in lumber.

So, with the calculation of the total load Q acting on square meter We got the roof!

I especially draw your attention: when calculating, carefully follow the dimension !!!

II. Calculation of the truss system.

truss system consists of separate rafters (rafter legs), so the calculation is reduced to determining the load on each rafter leg separately and calculating the section of a separate rafter leg.

1. Find the distributed load on running meter each rafter leg.

Where
Qr - distributed load per linear meter of the rafter leg - kg / m,
A - distance between rafters (rafter pitch) - m,
Q - total load acting on a square meter of roof - kg / m².

2. We determine in the rafter leg the working section of the maximum length Lmax.

3. We calculate the minimum cross section of the material of the rafter leg.

When choosing a material for rafters, we are guided by the table standard sizes sawn timber (GOST 24454-80 Softwood lumber. Dimensions), which are summarized in Table 4.

Table 4. Nominal dimensions of thickness and width, 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

A. We calculate the cross section of the rafter leg.

We set the width of the section arbitrarily in accordance with the standard dimensions, and the height of the section is determined by the formula:

H ≥ 8.6 Lmax sqrt(Qr/(B Rbend)), if the slope of the roof α

H ≥ 9.5 Lmax sqrt(Qr/(B Rbend)), if the roof pitch α > 30°.

H - section height cm,


B - section width cm,
Rizg - resistance of wood to bending, kg / cm².
For pine and spruce Rizg is equal to:
Grade 1 - 140 kg / cm²;
Grade 2 - 130 kg / cm²;
Grade 3 - 85 kg / cm²;
sqrt - square root

B. We check whether the deflection value fits into the standard.

The normalized deflection of the material under load for all roof elements should not exceed the value L / 200. Where, L is the length of the working area.

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 the rafter leg - kg / m,
Lmax - working section of the rafter leg of maximum length m,
B - section width cm,
H - section height cm,

If the inequality is not met, then increase B or H .

Condition:
Roof slope angle α = 36°;
Rafter pitch A = 0.8 m;
The working section of the rafter leg is maximum length Lmax = 2.8 m;
Material - pine 1 grade (Rizg = 140 kg / cm²);
Roof - cement-sand tiles (Roof weight - 50 kg / m²).

As it was calculated, the total load acting on a square meter of the roof is Q \u003d 303 kg / m².
1. We find the distributed load per linear meter of each rafter leg Qr=A·Q;
Qr=0.8 303=242 kg/m;

2. Let's choose the thickness of the board for the rafters - 5cm.
We calculate the cross section of the rafter leg with a section width of 5 cm.

Then, H ≥ 9.5 Lmax sqrt(Qr/B Rbend), since the slope of the roof α > 30°:
H ≥ 9.5 2.8 sqrt(242/5 140)
H ≥15.6 cm;

From the table of standard lumber sizes, select a board with the nearest section:
width - 5 cm, height - 17.5 cm.

3. We check whether the deflection value is within the standard. For this, the 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, then the cross section of the material of the rafters 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.

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 the load-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 pitch (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

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 roof area. 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:

1. 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).
2. 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.
3. At this stage also material must be defined from which the roof will be constructed.
4. 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 house plan suggests an attic or other type of roof shape, then it is recommended that calculations be carried out only with the help of a specialist.

The gable roof rafter system calculator will help you best in calculations.

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 information:

• 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.

Besides, 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 the material of the roof, 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 figure 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. Large quantity layers allows you to make the angle of inclination of the slope large.

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:

1. 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 .
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.
3. 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.
(in this example) that will need to be purchased for construction.

To do this, it is necessary to divide the resulting value of the roof area by the area of ​​\u200b\u200bone sheet of metal.

• 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. General value area - 82 m 2, i.e. the area of ​​one slope, multiplied by 2.

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 dimensions obtained.

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:

In contact with

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

Calculations should be started if you understand that the rafter system gable roof- This is a complex of triangles, the most rigid frame elements. 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 a 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 of the rafter system, there are standard sizes:

• 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.

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:

• 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.

The pitch of the rafters affects the cross section of the rafter legs most significantly. Increasing the distance between the bars 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 slope of the roof is comparable to a sail, which can break under the pressure of natural phenomena.

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. Great importance has a housing area. 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 of the 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 down from a steep roof quickly, not having time to 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:

1. According to the formula Qr \u003d AxQ, they find out what is the load per linear meter of 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.
2. 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".
3. 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 width of the section, cm, Rizg 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.
4. 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).
5. 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 foot 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 303 kg/m². And for the construction of the truss system, bars 5 cm thick are used.

From this follow the following computational steps:

1. Qr=A·Q= 0.8·303=242 kg/m - distributed load per linear meter of rafter beam.
2. H ≥ 9.5 Lmax sqrt(Qr/B Rbend).
3. H ≥ 9.5 2.8 sqrt(242/5 140).
4. 3.125 Qr (Lmax)³/B H³ ≤ 1.
5. 3.125 242 (2.8)³ / 5 (17.5)³ = 0.61.
6. H ≥ (approximate height of the rafter section).

In the table of 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 in normative documents, and this is proved by the inequality 3.125 Qr (Lmax)³/B H³ ≤ 1. Substituting the values ​​(3.125 242 (2.8)³ / 5 (17.5)³) into it, we find 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.