Maximum length of rafters. “Lay out on the shelves”: dimensions of the elements of the rafter system
In any building important role plays roof structure. The final cost of the project and the service life of the building depend on its quality and strength. It is this part that will take over most atmospheric influences. The strength of the roof largely depends on the choice, proper calculation and installation of the rafter system.
There are two types of roof structures using rafters: layered and hanging rafter systems. In this article we will discuss the last option, analyze in what cases it is applicable, how it works and the existing varieties.
Rafters are the main part of the roof structure that bears the entire load. The choice of hanging or layered structures depends on the presence of internal load-bearing walls in the building. If they are, then the rafters will rest on them through the rack and this scheme is called layered. Otherwise, only external load-bearing walls serve as foundations, and the maximum distance between them can be up to 14 meters.
Although hanging rafters are on a slope, they do not push the walls, but transmit only strictly vertical loads. This is achieved by using a brace at the base of the roof. They are made from beams and, depending on the required length, can be solid or composite. If you need to use a double stretch, then make an overlap connection, an oblique or straight tooth, overlays, and so on.
The rafter legs themselves can be made of logs, timber or edged boards. They are processed before use by special means, protecting against mold, mildew, fire and rot.
Hanging rafter system is applicable in residential buildings, retail warehouses and industrial facilities.
Factors influencing design calculations
Before starting the construction of a roof with hanging rafters, it is necessary to make a competent calculation. He will help you choose suitable materials, determine the required variety and save money while maintaining structural strength. Although you can do this yourself, it is better to trust a specialist, then you will sleep more peacefully under such a roof. For an error-free calculation, you will need the following information:
- dimensions of the building;
- wall materials;
- layout of additional supporting elements, for example, columns;
- Availability attic floor;
- bearing capacity of walls;
- roof shape.
With the help of this data, the material for the rafters, the cross-section and with what step the installation should be determined.
In addition, roofers take into account climatic conditions (amount of precipitation, wind strength and direction). Based on this information, a decision is made on the angle of inclination and the choice roofing material.
Main design elements
Before you begin to study the types and design features of hanging rafters, you need to get acquainted with the basic elements of the roof. This will help you better imagine the system and not get confused in concepts.
In the construction of such a roof, six main elements are used:
- Mauerlat. A beam with a section of 100x100 or 150x150 mm located on top part load-bearing walls. The rafter legs rest on them. The main task of this part is to evenly distribute the load and transfer it to the foundation.
- Rafter legs. The base of the roof slope. Typically, edged boards with a section of 50x150 or 100x150 mm are used. A step of 0.6-1.2 m is maintained between individual elements. Dimensions and distance depend on the planned load and bearing capacity walls
- Puff. A horizontal beam or board fastened to opposite lower parts of a structure. The main task is to contain the bursting load from the rafters.
- Rigel. Essentially the same puff, only located near the ridge. This part bears more load, so a stronger beam is used.
- Grandma. A suspension element located under the ridge that supports a draw that is too long. Can be wooden or metal.
- Strut. Supports used on buildings with large spans. They help prevent the rafters from sagging too much. The headstock serves as a support for the struts.
Some hanging rafter system designs retain the necessary strength without the use of a Mauerlat.
Varieties of hanging rafter designs
The choice of one or another scheme for installing hanging rafters depends on the span between the load-bearing walls. The greater this distance, the more complex the design and the greater the number of additional elements required.
Basic three-hinged triangular arch
This is the basis of the entire structure and has the shape of a triangle. It is assembled from two rafter legs, which are fastened at the ridge. The lower parts are connected with a wooden tie. The maximum permissible height at the ridge is equal to one-sixth of the span length. However, such a design is allowed to be used only in buildings where the distance between walls is no more than 6 meters.
In such a product, the rafters experience only bending loads, and the tightening - tensile loads. It is allowed to use a metal rod or cord at the base. But usually the tree is left as it serves as beams for the attic floor.
Articulated arch with headstock
This system is used in buildings with a span of more than 6 meters. A tightening of this length will bend greatly, and to avoid this, use a headstock. Usually the suspension is made of timber, but in some situations a metal rod is used. The metal element tolerates tensile loads well and is light in weight.
Using the headstock, roofers adjust the degree of deflection of the horizontal part. At this length, the puff is made from two equal parts, and they are joined exactly under the suspension. Apply different connections knots: oblique or straight cuts, secured with bolts. The suspension and tightening are secured together with a clamp.
Articulated arch with raised drawstring
This option involves installing a tie close to the ridge. Although in this position the part experiences heavy loads, it becomes possible to equip the attic floor. You can adjust the height of the ceilings by changing the height of the tie rod.
In such a situation, the rafters have to rest on the Mauerlat. Since with increasing load, increasing humidity and temperature, the dimensions of the beams change, a sliding connection is used. They are made of metal and attached directly to the mauerlat and rafters. Thanks to this design, the roof retains its geometry and can “breathe.”
In winter, on slopes, hanging rafters with tightening experience different snow loads. Because of this, there is a threat of distortion and leaks. Therefore, in such structures, the ends of the rafters are placed outside the walls.
When constructing an attic floor with a raised roof, the beam serves as the basis for attaching the ceiling. To prevent it from sagging, thicker beams are used. In some situations, hangers are installed connecting the tie and the ridge. If the beam is too long, use several hanging fasteners.
Articulated arch with crossbar
The only difference in this design from the previous one is the method of implementing the attachment points for the rafter legs. They are rigidly fixed to the Mauerlat and can no longer freely change their position. To do this, use nails, screws, and metal plates.
Due to changes in the method of fastening, the effect of loads also changes. Now the rafters are pushed apart by the load-bearing walls. Because of this, the tightening begins to experience compression and in this position it is called a crossbar.
If the calculations show a large load, then in addition to the roof with a crossbar, a classic tie is installed in the lower part of the structure. In this case, attachment to the Mauerlat will not be needed. The result is the first described structure with an additional beam under the ridge.
Arch with headstock and struts
Span lengths up to 9 to 14 meters require reinforcement of the structure with struts. In this situation, the rafter beams begin to bend. With a layered roof structure, the struts rest against the internal load-bearing wall. In our case, the only available stop is the headstock. Here all the loads acting on the frame change: the rafters press on the struts, they stretch the suspension and attract the ridge, then the load is distributed over the rafters, compressing them.
All schemes of hanging rafter systems require accurate calculations that take into account external and internal loads. The only drawback can be considered the complexity of installation. You either have to submit ready-made designs crane, or collect them at height. But, in some situations there are no other options to assemble the roof.
Even at the design stage of the building, it is necessary to decide on the design option for the roof truss system. However, the choice is not difficult. If there is an internal main partition wall, layered rafters are used to form the roof. If there are no such partitions, then hanging rafters are installed, which rest solely on external walls.
Hanging rafters are used in the construction of single-bay houses, industrial buildings, workshops, trade pavilions, when installing attics without internal walls.
Design features of hanging rafters
Why are rafters called “hanging”? Because they literally hang in the interspan space, relying only on the outer walls. There is no internal support. However, hanging systems, due to their design, do not bend and are able to cover spans of up to 14-17 m!
Of course, hanging rafters are only part of the rafter system; they are not used by themselves. Only in conjunction with other elements (bolts, headstocks, crossbars, struts, etc.), together with which the rafters form trusses or arches.
In the case of hanging rafters, the simplest truss is made up of two rafter beams connected at the top point at an angle (in the form of a triangle). Horizontally, the rafters are fastened with a tie, which is usually wooden beam. But it can also be metal, for example, made of profile metal. Then such a puff is called a cord.
Tightening performs an important function. The rafters, fastened at the ridge and resting against the walls, tend to move apart. And the tightening holds them, allowing you to maintain the triangular shape of the arch. The resulting thrust is not transmitted to the walls, and horizontal forces are neutralized. Thus, only vertical forces act on external walls when using hanging rafters.
The tie is not necessarily located at the bottom of the truss; sometimes it moves up, closer to the ridge. It depends on the type of arch structure and what kind of work the tightening has to do. If the tie is located at the base of the rafters, then at the same time it serves as the floor beam of the underlying floor. When constructing an attic, it is convenient to place the tie rod (crossbar) above the base of the rafter legs, so that it becomes possible to arrange a floor with a full ceiling height.
If the span between the walls is more than 6 m, the hanging rafters are supported with braces and hangers (headstocks) for strength. And the tie is not made whole, but consisting of two spliced beams.
There are several design options using hanging rafters. Let's look at them all separately.
Design #1. Triangular articulated arch
The simplest farm in the form of a triangle. Consists of two rafter beams that meet at the ridge. The lower bases rest against a horizontal beam. A tie is secured at the bottom of the triangle. For the system to work correctly, the height of the ridge in the structure should not be less than 1/6 of the span of the truss.
This scheme can be called classic. In it, the rafters work to bend, trying to move apart, and the tightening holds them and receives tensile loads (works in tension). Load-bearing element the tightening is not, so it can be replaced with a rolled metal tie.
To reduce the degree of bending of the rafter beams, the ridge assembly is cut with eccentricity. Due to this, when the rafters are exposed to external loads (atmospheric phenomena, roof weight, own weight, etc.), along with the expected bending, a bending moment in the opposite direction appears. This allows not only to reduce bending deformations, but also to use beams of a smaller cross-section for the rafters. Accordingly, this helps reduce the cost of construction.
Typically, this hanging rafter design is used in construction attic attic. In this case, the tie rods play the role of attic floor beams.
Design #2. Articulated arch with headstock
More complex circuit, which is needed in case of overlapping spans of more than 6 m.
The problem with such a system is the long string, which will experience enormous loads and, as a result, bend under its own weight. To prevent deflection, the tie is suspended from the ridge. How? Using additional element- grandmas. She represents wooden block, playing the role of a suspension. If the suspension is made of metal, then it is called a cord. An ordinary metal rod is often used for these purposes, which in practice works well in tension.
Thus, with the help of a headstock suspension, it is possible to support a long draw and level out its deflection. The tie itself is made up of two parts-beams, joined to each other (in the center of the structure).
The design of the headstock is simple, but builders often make mistakes in its design. The most important thing: the headstock should only work in tension, not compression. It should not be confused with a stand, resting against the beam and the cornice assembly. In this case, the element will compress rather than stretch.
Such confusion may arise because the post and headstock are very similar in design. But their purpose, as well as their operating principle, are completely different. The headstock, unlike the stand, is not rigidly secured with a tightening. It is suspended on a curtain rod, and a tie is attached to its lower part using clamps.
The required tightening length is selected from components, connecting them with an oblique or straight cut and securing with bolts. The tie is connected to the suspension through a clamp.
The considered scheme is suitable for agricultural and industrial buildings with large spans. However, in original form it is no longer used and is considered obsolete. But some of its elements are very successfully used in construction practice, in the development of other types of arches.
Design #3. Articulated arch with raised drawstring
In this scheme, the tie is not installed at the bottom of the arch, but moves upward, closer to the ridge. The higher the tension is installed, the more it stretches.
The raised-tie structure is used in the construction of attic spaces. The height of the ceilings directly depends on how high the tie is located.
The rafter beams of the structure rest on the mauerlat, and not on the tightening. Moreover, the mount is not rigid, but movable, sliding like a slider. It allows you to compensate for changes in the size of beams (their movements) that occur with fluctuations in humidity and temperature.
If a uniform load is applied to the slopes, then the system will be stable in any case. If the load is greater on one side, the rafter system will move towards the prevailing load. To prevent this from happening and to ensure that the roof remains stable, the rafters are installed with extensions in both directions, outside the walls.
The tie in such an arch is not a support; it is subject to tensile loads when constructing an attic, and tensile-bending loads when constructing an attic.
IN attic rooms The tie is often a beam for attaching a suspended ceiling or insulation. To protect it from sagging, a suspension is installed. With small expected loads and a short tightening, the suspension is nailed to the crossbar and the ridge, fastening the joints with two boards on both sides.
If the tightening is relatively long, then several pendants are used, and each of them is secured with nails. Large loads require additional use of clamps.
Design #4. Hinged arch with crossbar
The scheme is similar to the previous one, but has a difference: the lower sliding support in the cornice assembly is replaced with a similar rigid one. Rafter beams are cut into the mauerlat or support bars are used for fixed fixation.
Replacing the support changes the nature of the stresses arising in the arch. The structure becomes spacer, exerting pushing forces on the walls and the mauerlat.
The tightening is installed at the top of the arch. At the same time, its purpose changes. It no longer works on tension, its operating principle is based on compression. A tightening that works in compression is called a crossbar.
An arch with one raised crossbar is designed for a small thrust load. For heavy loads, a tie rod is installed in addition to the crossbar. The result is hanging rafters, the design and components of which are similar to a conventional three-hinged arch. Mauerlat is no longer required for them.
Design #5. Arch with suspension and struts
A diagram that complements the arch and headstock system. It is used when the length of the rafters is so large (up to 14 m) that it creates a significant deflection under its own weight. To level out bending stresses, the system is supplemented with struts that support the rafter beams.
Usually the struts rest against the internal walls. But in hanging systems there are none, so the struts rest against the only existing stop - the headstock. The result is a rigid structure with the following principle of operation: the rafters bend under the influence of an external load, press on the struts, the suspension stretches and attracts the ridge beam, at the same time the upper parts of the rafters are also attracted, the rafters press the struts.
Since this scheme uses long rafters, a long tie is used accordingly. As a rule, it consists of two parts-beams (although it can also be single-element), connected in the middle of the span by an oblique or straight cut. The connection between the tightening and the headstock is made through a clamp.
Essentially, all existing hanging arches are variations of the conventional three-hinged arch. All other additions - headstocks, crossbars, struts - only increase the rigidity of the rafters. And the load-bearing capacity is not changed.
Main nodes: types of element connections
Any of the designs discussed above will work correctly only if all the main components are properly connected. Only then will they perform their function without deforming under the influence of external factors.
From above, the rafter beams are combined at an angle and connected end-to-end, overlapping or by cutting. This knot is called a ridge knot. Butt fastening involves joining the ends of beams cut at an angle and fastening them with metal or wood overlays. When joining with an overlap, the upper parts of the rafters overlap each other and are secured with a bolt and nut or stud.
A half-timber notch joint is similar to an overlap joint. But in this case, the tops of the rafters are placed on top of each other after cutting out recesses half the thickness of the timber. Then the sawn parts are connected, a through hole is drilled in them and they are tightened with a bolt.
In arch designs there is also (for example, in a regular three-hinged arch) a connection of the lower part of the rafters with a tie - a cornice unit. The connection is made by frontal cutting with a single or double tooth and fastening with bolts. Also, for fastening, short boards or metal plates can be used, placed at the joint of the rafters with a tie and fastened with nails.
The raised tie is cut into the rafters in an overlapping half-way, followed by bolting.
In a scheme with a raised tie or transom, the rafters are connected to the mauerlat. In this case, a sliding (like a slider) or rigid mount supports Sliding fastening is carried out using metal sliding supports that allow small movements of the rafters. For rigid fastening, a tooth cut is used; a support block can also be used.
General principles for calculating hanging rafters
As you have already seen, the hanging rafter system refers to complex structures and requires correct calculation based on many factors. Incorrect final parameters will lead to the fact that the roof will not be able to withstand potential loads, which can lead to deformations and collapses.
Therefore, it is advisable to entrust the calculation of hanging rafters to professionals or use already finished project Houses. As a last resort, calculations can be performed using one of the online calculators, of which there are quite a few on the Internet.
The following data is used for calculation:
- dimensions of the overlapped room;
- presence of an attic;
- slope angle;
- type of rafter system;
- wall material;
- roofing material.
As a result of the calculation, the following is determined:
- rafter section;
- rafter pitch size;
- farm shape.
Installation of hanging rafters
After selecting the truss structure and calculating it, you can begin installation work.
The installation of hanging rafters at a construction site is carried out according to the following scheme:
- For installation accuracy and convenience, mark the center of the roof and the height of the ridge. To do this, two boards are temporarily fixed along the gables in the center, and a mark is made on them according to the height of the ridge.
- A template is made for the rafter legs. Take a board, lean it against the mauerlat with the lower end, and against the height mark of the ridge with the upper end. Mark the locations of the upper and lower cuts.
- Using the template, make required amount rafter beams. Depending on their future location in the farm, they are marked on the right and left rafters. They are laid out in pairs (since each truss consists of two rafters - right and left).
- Begin assembling the first truss (arch). Two rafter beams are connected at the top with an overlap, butt or by cutting.
- Install the tightening and, if provided for in the design diagram, the headstock and struts.
- They lift the truss onto the roof and install it from the end of the building (on the pediment). Fastening is carried out to the Mauerlat using corners and nails or self-tapping screws.
- The same arch is installed on the side of the second pediment.
- A string is pulled between the pediment pair of arches so that the remaining arches are installed clearly along the line and at the designated level.
- The remaining arches are placed between the gables with the spacing provided for by the project. The height of the arches is controlled with a stretched string. To correct small errors in size, the height is adjusted by placing wooden planks under the rafters.
This completes the installation of the rafters. Now you can proceed to the next roofing work: lay insulation and waterproofing, fill the sheathing, install roofing material.
What is the difference between layered and hanging rafters? How to choose the optimal section rafter leg? What is the maximum span of hanging rafters? How to connect the rafters with the Mauerlat and ridge run? In our article we will try to find answers to these and some other questions.
Hanging rafter system covered with roofing material.
Types of rafters
The differences in the structural elements of layered and hanging rafters are presented in the photo.
To understand what the design of hanging rafters is, you need to have a good understanding of the structure of roof frames different types. In this case, we are interested in only two types:
- Gable roof, in cross section usually representing an isosceles triangle. Triangular arches are often mounted with vertical gables (sometimes with an attic door and skylights);
- hip roof, in which instead of vertical pediments there are two additional slopes. This type of roof is popular in regions with strong winds.
Frame house with hip roof.
The rafters of the roofs listed above can be one of four types:
- Layered rafters(metal or wood) rest on an internal wall or rack, which, in turn, transfers the weight of the roof to the main wall of the house;
- Hanging rafters unlike layered ones, they rest only on the external walls of the building. As a result, they experience both bending and compression loads.
The compressive load is transferred to the outer walls of the house; to compensate for it, a pair of rafter legs is usually equipped with a tie - a beam or metal profile tying the legs at the base or closer to the skate. When positioned at the bottom, the tie rods serve as the basis for the attic floor;
Schemes of hanging and layered rafter systems.
- Diagonal rafters connect the ridge girder of the hip roof with the corners of the building;
- Narozhny rest on the mauerlat (a beam that encircles the walls around the perimeter and acts as a support for the rafter system) and on diagonal rafters.
Diagonal and outer rafters.
Let's clarify: side slopes hip roof the device does not differ from the gable one and rests on the same hanging or layered rafter legs.
Peculiarities
In practical terms, how do the nodes of a hanging system differ from layered ones? Alas, all the differences are not for the better:
- Larger spans means an increased cross-section of the rafters, which leads to increased costs for materials;
- High breaking force tightening requires reliable connections between it and the rafter legs: ordinary nails or self-tapping screws are not suitable here. Typically, the rafters are joined with a raised lap joint and secured with bolts or washers with wide studs.
In the ridge area, you can also use ordinary self-tapping screws.
This does not apply to the connection between the rafters in the ridge area. It experiences only compressive load; as a result, galvanized linings and even ordinary self-tapping screws screwed through the rafter into the ridge girder can be used here.
Material
What is the rafter system made of? There aren't many options here:
- Profile pipe, I-beam or channel. Their use is justified under particularly stringent requirements for strength - significant wind or snow loads. They have bending strength that is not much inferior to that of a rod of the same section;
Metal rafter system for a gable roof.
- Beam or board. In most cases, hanging and layered rafters are made from the specified materials. As a rule, lumber is mounted in the “edge” position: this ensures maximum structural rigidity with a minimum cross-section of the frame.
The photo shows an example roof trusses made of wood
Requirements
What kind of lumber are they made from? hanging structures? As a rule, the raw material is coniferous wood (pine, spruce, fir, less often cedar or larch).
Wood should not have defects that affect its strength, compression and bending:
The wood of the rafters (like all other elements of the rafter system) must be treated with an antiseptic. It will not only protect the tree from fungus and insects, but will also make it less flammable: all modern antiseptic primers contain fire retardant additives.
Section
The calculation of the span width of hanging rafters is linearly related to their cross-section and vice versa - to the pitch of the rafters. Here are the recommended beam cross-section values for different spans with a rafter pitch of 90 centimeters:
- On gentle slopes with significant snow loads;
- On slopes with a significant slope in regions with strong winds;
- When using heavy roofing materials- ceramic tiles or slate.
The load-bearing capacity of rafters can be increased not only by increasing the cross-section of the timber, but also by connecting boards of a fixed size in pairs.
The rafters are assembled from a pair of boards measuring 150x50 mm.
Maximum size gable roof is determined not only by the cross-section of the beam, but also by the design of the rafter system:
- Hanging rafters tied at the level of the top of the wall can be used in the construction of roofs up to 6 meters wide;
- A gable roof with a crossbar (a tie raised relative to the level of the walls) can have a similar width;
- A rafter system with a bottom tie and a crossbar can have a width of up to 9 meters;
Maximum dimensions for different versions of the rafter system.
- The same width can be achieved by a roof with a central pillar resting on the lower tie;
- Finally, when using multiple posts or struts gable roof can cover a building up to 12-14 meters wide. In this case, a triangular three-hinged arch is used.
The maximum width is 14 meters.
Wooden beams longer than 6 meters will experience enormous bending loads, even without taking into account the weight of the roof and the snow lying on it. They usually use not timber, but a metal or wooden I-beam.
Assembly
How to connect rafters with a ridge, mauerlat, tie, crossbar, rack or strut?
Horse
At the connection with the ridge girder, the rafter is cut at an oblique angle and attached to the girder with screws screwed in at an angle. Additional fixation can be provided with galvanized corners.
Connection of rafter legs with ridge purlin.
When assembling the rafter system, it is better to use not black (phosphated), but white (galvanized) or yellow (brass-plated) screws. They are more durable and corrosion resistant.
Puff
This connection is one of the most responsible. Capital or internal load-bearing walls experience a lateral load pushing them apart, and tightening them removes them:
- The board or beam is overlapped and tightened with bolts or studs with wide washers;
- Additional fixation can be provided by glue - any carpentry or universal PVA glue.
The crossbars are attached to the rafters with overlapping bolts and wide washers.
Mauerlat
Depending on the design of the hanging rafter system, both a rafter leg and a tie can be attached to the mauerlat. In both cases, the connection is made by cutting the Mauerlat into the rafter and fixed with galvanized plates and self-tapping screws.
Connection of the rafter leg with the Mauerlat.
How is the Mauerlat itself attached? It is anchored to the armored belt laid on top of the masonry walls. There are a couple of subtleties here:
- It is more convenient not to drill holes for anchors, but to lay anchor threaded rods when pouring the armored belt. After the concrete gains strength, holes are marked and drilled in the timber, after which it is pulled to the walls through wide washers;
- Waterproofing is required between the armored belt and the Mauerlat. This role is played by the layer bitumen mastic or a couple of layers of roofing felt. Waterproofing will prevent capillary suction of water from the walls and wood rotting. This is especially true for residential attic space.
Installation of the Mauerlat on a wall made of cinder concrete sides.
Racks, struts
Both the strut and the stand are cut so that their end is adjacent to the rafter leg with the maximum area. To fix the connection, pads are used here too - galvanized steel or cut from plywood with a thickness of 18-22 mm.
Conclusion
We hope that our material will help the reader choose optimal solution when building your own home. The attached video will allow you to more clearly see how hanging rafters are installed. We would appreciate your additions and comments. Good luck!
If you want to express gratitude, add a clarification or objection, or ask the author something - add a comment or say thank you!
-
Rafters 7.5 meters without intermediate supports
- Registration: 03/05/11 Messages: 10,919 Thanks: 25,362
- Registration: 12/27/08 Messages: 2,086 Thanks: 674
- Registration: 10.21.11 Messages: 8 Thanks: 0
Last edited by moderator: 11/21/17
- Registration: 10.21.11 Messages: 8 Thanks: 0
- Registration: 02/07/10 Messages: 2,006 Thanks: 856
Axe
I live, but not here, and I won’t say with whom
Ax I live, but not here, and I won’t say with whom
- Registration: 05.26.10 Messages: 1,391 Thanks: 876
- Registration: 07/30/11 Messages: 5,757 Thanks: 12,372 OZLOCKer I build for pleasure
- Registration: 01/21/11 Messages: 837 Thanks: 280
- Registration: 05.26.10 Messages: 1,391 Thanks: 876
- Registration: 12/27/10 Messages: 47 Thanks: 18
- Registration: 07/30/11 Messages: 5,757 Thanks: 12,372 OZLOCKer I build for pleasure
Do you want to calculate the rafter system quickly, without studying theory and with reliable results? Take advantage online calculator Online!
Can you imagine a person without bones? In the same way, a pitched roof without a rafter system is more like a structure from a fairy tale about the three little pigs, which can easily be swept away by natural elements. A strong and reliable rafter system is the key to the durability of the roof structure. In order to design a high-quality rafter system, it is necessary to take into account and predict the main factors affecting the strength of the structure.
Take into account all the bends of the roof, correction factors for uneven distribution of snow over the surface, wind drift of snow, slope of the slopes, all aerodynamic coefficients, impact forces on structural elements roofs and so on - calculating all this as close as possible to the real situation, as well as taking into account all the loads and skillfully assembling their combinations is not an easy task.
If you want to understand it thoroughly - list useful literature is given at the end of the article. Of course, a strength of strength course for a complete understanding of the principles and impeccable calculation of the rafter system cannot be fit into one article, so we will present the main points for simplified versioncalculation.
Load classification
Loads on the rafter system are classified into:
1) Basic:
- permanent loads: the weight of themselves truss structures and roofs,
- long-term loads- snow and temperature loads with a reduced design value (used when it is necessary to take into account the influence of load duration when testing endurance),
- variable short-term influence- snow and temperature effects at the full calculated value.
2) Additional- wind pressure, weight of builders, ice loads.
3) Force majeure- explosions, seismic activity, fire, accidents.
To carry out the calculation of the rafter system, it is customary to calculate the maximum loads in order to then, based on the calculated values, determine the parameters of the elements of the rafter system that can withstand these loads.
Calculation of the rafter system pitched roofs produced according to two limit states:
a) The limit at which structural failure occurs. The maximum possible loads on the structural strength of the rafters should be less than the maximum permissible.
b) Limit state at which deflections and deformations occur. The resulting deflection of the system under load should be less than the maximum possible.
For more simple calculation Only the first method applies.
Calculation of snow loads on the roof
To count snow load use the following formula: Ms = Q x Ks x Kc
Q- the weight of snow cover covering 1 m2 of a flat horizontal roof surface. Depends on the territory and is determined from the map in Figure No. X for the second limit state - calculation for deflection (when the house is located at the junction of two zones, select snow load with a higher value).
For strength calculations according to the first type, the load value is selected according to the area of residence on the map (the first digit in the indicated fraction is the numerator), or is taken from table No. 1:
The first value in the table is measured in kPa, in parentheses the desired converted value is in kg/m2.
Ks- correction factor for the roof slope angle.
- For roofs with steep slopes with an angle of more than 60 degrees, snow loads are not taken into account, Ks=0 (snow does not accumulate on steeply pitched roofs).
- For roofs with an angle from 25 to 60, the coefficient is taken 0.7.
- For others it is equal to 1.
The angle of the roof can be determined online roof calculator the appropriate type.
Kc- coefficient of wind removal of snow from roofs. Assuming a flat roof with a slope angle of 7-12 degrees in areas on the map with a wind speed of 4 m/s, Kc is taken = 0.85. The map shows zoning based on wind speed.
Drift factor Kc is not taken into account in areas with January temperatures warmer than -5 degrees, since an ice crust forms on the roof and snow does not blow off. The coefficient is not taken into account if the building is blocked from the wind by a taller neighboring building.
The snow falls unevenly. Often, a so-called snow bag is formed on the leeward side, especially at joints and kinks (valley). Therefore, if you want a strong roof, keep the rafter spacing to a minimum in this place, and also pay close attention to the recommendations of roofing material manufacturers - snow can break off the overhang if it is of the wrong size.
We remind you that the calculation given above is presented to your attention in a simplified form. For a more reliable calculation, we recommend multiplying the result by the load safety factor (for snow load = 1.4).
Calculation of wind loads on the rafter system
We've sorted out the snow pressure, now let's move on to calculating the wind influence.
Regardless of the angle of the slope, the wind has a strong impact on the roof: it tries to throw off a steeply pitched roof, more flat roof- lift from the leeward side.
To calculate the wind load, its horizontal direction is taken into account, while it blows bidirectionally: on the facade and on the roof slope. In the first case, the flow is divided into several - part goes down to the foundation, part of the flow tangentially from below vertically presses on the roof overhang, trying to lift it.
In the second case, acting on the roof slopes, the wind presses perpendicular to the slope, pressing it in; a vortex is also formed tangentially on the windward side, going around the ridge and turning into a lifting force on the leeward side, due to the difference in wind pressure on both sides.
To calculate the average wind load use the formula
Mv = Wo x Kv x Kc x strength factor,
Where Wo- wind pressure load determined from the map
Kv- wind pressure correction factor, depending on the height of the building and the terrain.
Kc- aerodynamic coefficient, depends on the geometry of the roof structure and wind direction. Values are negative for the leeward side, positive for the windward side
For pitched roof it is necessary to take the coefficient from the table for Ce1.
To simplify the calculation, it is easier to take the maximum value of C, equal to 0.8.
Calculation of own weight, roofing pie
To calculate permanent load you need to calculate the weight of the roof ( roofing pie-see Figure X below) per 1 m2, the resulting weight must be multiplied by a correction factor of 1.1 - the rafter system must withstand such a load throughout its entire service life.
The weight of the roof consists of:
- the volume of wood (m3) used as sheathing is multiplied by the density of the wood (500 kg/m3)
- weight of the rafter system
- weight of 1m2 roofing material
- weight 1m2 of insulation weight
- weight of 1m2 of finishing material
- weight 1m2 of waterproofing.
All these parameters can be easily obtained by checking this data with the seller, or looking at the main characteristics on the label: m3, m2, density, thickness, and perform simple arithmetic operations.
Example: for insulation with a density of 35 kg/m3, packed in a roll 10 cm or 0.1 m thick, 10 m long and 1.2 m wide, weight 1 m2 will be equal to (0.1 x 1.2 x 10) x 35 / (0.1 x 1.2) = 3.5 kg/m2. The weight of other materials can be calculated using the same principle, just do not forget to convert centimeters to meters.
More often the roof load per 1 m2 does not exceed 50 kg, therefore, when making calculations, this value is used, multiplied by 1.1, i.e. use 55 kg/m2, which itself is taken as a reserve.
More data can be taken from the table below:
10 - 15 kg/m² |
|
Ceramic tiles | 35 - 50kg/m² |
Cement-sand tiles | 40 - 50 kg/m² |
8 - 12 kg/m² |
|
Metal tiles | |
Corrugated sheet | |
Subfloor weight | 18 - 20 kg/m² |
Sheathing weight | 8 - 12 kg/m² |
Rafter system weight | 15 - 20 kg/m² |
Collecting loads
According to the simplified version, now it is necessary to add up all the loads found above by simple summation, we will get the final load in kilograms per 1 m2 of roof.
Calculation of the rafter system
After collecting the main loads, you can already determine the main parameters of the rafters.
falls on each rafter leg separately, convert kg/m2 to kg/m.We calculate using the formula: N = rafter spacing x Q, Where
N - uniform load on the rafter leg, kg/m
rafter pitch - distance between rafters, m
Q - final roof load calculated above, kg/m²
It is clear from the formula that by changing the distance between the rafters, you can regulate the uniform load on each rafter leg. Typically, the pitch of the rafters is in the range from 0.6 to 1.2 m. For a roof with insulation, when choosing a pitch, it is reasonable to focus on the parameters of the insulation sheet.
In general, when determining the installation pitch of the rafters, it is better to proceed from economic considerations: calculate all the options for the location of the rafters and choose the cheapest and optimal in terms of quantitative consumption of materials for the rafter structure.
- Calculation of the cross-section and thickness of the rafter leg
In the construction of private houses and cottages, when choosing the section and thickness of the rafters, they are guided by the table below (the cross section of the rafters is indicated in mm). The table contains average values for the territory of Russia, and also takes into account the sizes building materials presented on the market. In general, this table is enough to determine what cross-section of timber you need to purchase.
However, we should not forget that the dimensions of the rafter leg depend on the design of the rafter system, the quality of the material used, constant and variable loads exerted on the roof.
In practice, when building a private residential building, boards with a cross section of 50x150 mm (thickness x width) are most often used for rafters.
Independent calculation of rafter cross-section
As mentioned above, rafters are calculated based on maximum load and deflection. In the first case, take into account maximum torque bending, in the second - the section of the rafter leg is checked for resistance to deflection over the longest section of the span. The formulas are quite complex, so we have chosen for you simplified version.
The section thickness (or height) is calculated using the formula:
a) If the roof angle< 30°, стропила рассматриваются как изгибаемые
H ≥ 8.6 x Lm x √(N / (B x Rben))
b) If the roof slope is > 30°, the rafters are flexurally compressed
H ≥ 9.5 x Lm x √(N / (B x Rben))
Designations:
H, cm- rafter height
Lm, m- working section of the longest rafter leg
N,
kg/m- distributed load on the rafter leg
B, cm- rafter width
Rizg, kg/cm²- bending resistance of wood
For pine and spruce Rizg depending on the type of wood is equal to:
It is important to check that the deflection does not exceed the permitted value.
The deflection of the rafters should be less L/200- length of the thing being checked longest span between supports in centimeters divided by 200.
This condition is true if the following inequality is satisfied:
3,125 xNx(Lm)³ / (BxH³) ≤ 1
N (kg/m) - distributed load on linear meter rafter leg
Lm (m) - working section of the rafter leg of maximum length
B (cm) - section width
H (cm) - section height
If the value is greater than one, it is necessary to increase the rafter parameters B or H.
Sources used:
- SNiP 2.01.07-85 Loads and impacts with latest changes 2008
- SNiP II-26-76 “Roofs”
- SNiP II-25-80 “Wooden structures”
- SNiP 3.04.01-87 “Insulating and finishing coatings”
- A.A. Savelyev “Rafter systems” 2000
- K-G. Goetz, Dieter Hoor, Karl Mohler, Julius Natterer “Atlas wooden structures»
The 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.
For self-calculation I provide the characteristics of the materials required for installation of the rafter system simplified formulas calculation. 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), normative meaning the average component of the wind load Wm at height Z above the ground 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. Bitumen shingles 8 - 12 kg/m²;
6. Metal tiles 4 - 5 kg/m²;
7. Corrugated sheeting 4 - 5 kg/m²;
4. Weight of rough flooring, sheathing and rafter system.
The weight of the rough flooring is 18 - 20 kg/m²;
Sheathing weight 8 - 10 kg/m²;
The weight of the rafter system itself is 15 - 20 kg/m²;
When calculating the final load on the rafter system, all of the above loads are summed up.
And now I'll tell you little secret. Sellers of certain types of roofing materials as one of the positive properties note their lightness, which, according to them, will lead to significant savings in lumber in the manufacture of the rafter system.
To refute this statement, I will give the following example.
Calculation of the load on the rafter system when using various roofing materials.
Let's calculate the load on the rafter system when using the heaviest one (Cement-sand tiles
50 kg/m²) and the lightest (Metal tile 5 kg/m²) roofing material for our house in the village of Babenki, Ivanovo region. RF.
Cement-sand tiles:
Wind loads - 24kg/m²
Roof weight - 50 kg/m²
Sheathing weight - 20 kg/m²
Total - 303 kg/m²
Metal tiles:
Snow load - 189kg/m²
Wind loads - 24kg/m²
Roof weight - 5 kg/m²
Sheathing weight - 20 kg/m²
The weight of the rafter system itself is 20 kg/m²
Total - 258 kg/m²
Obviously, the existing difference in design loads (only about 15%) cannot lead to any significant savings in lumber.
So, with the calculation of the total load Q acting on square meter We figured out the roof!
I especially draw your attention: when making calculations, pay close attention to the dimensions!!!
II. Calculation of the rafter system.
Rafter system consists of separate rafters (rafter legs), so the calculation comes down to determining the load on each rafter leg separately and calculating the cross-section of an individual rafter leg.
1. Find the distributed load per linear meter of each rafter leg.
Where
Qr - distributed load per linear meter of rafter leg - kg/m,
A - distance between rafters (rafter pitch) - m,
Q is the total load acting on a square meter of roof - kg/m².
2. Determine the working area in the rafter leg maximum length Lmax.
3. We calculate the minimum cross-section of the rafter leg material.
When choosing material for rafters, we are guided by the table standard sizes lumber (GOST 24454-80 Softwood lumber. Dimensions), which are summarized in Table 4.
| Board thickness - section width (B) | Board width - section height (H) | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 16 | 75 | 100 | 125 | 150 | |||||
| 19 | 75 | 100 | 125 | 150 | 175 | ||||
| 22 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | ||
| 25 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 32 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 40 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 44 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 60 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 75 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 100 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 | |
| 125 | 125 | 150 | 175 | 200 | 225 | 250 | |||
| 150 | 150 | 175 | 200 | 225 | 250 | ||||
| 175 | 175 | 200 | 225 | 250 | |||||
| 200 | 200 | 225 | 250 | ||||||
| 250 | 250 |
A. We calculate the cross-section of the rafter leg.
We arbitrarily set the width of the section in accordance with standard dimensions, and determine the height of the section using the formula:
H ≥ 8.6 Lmax sqrt(Qr/(BRben)), if the roof slope α
H ≥ 9.5 Lmax sqrt(Qr/(BRben)), if the roof slope α > 30°.
H - section height cm,
B - section width cm,
Rbend - bending resistance of wood, kg/cm².
For pine and spruce Rben is equal to:
1st grade - 140 kg/cm²;
2nd grade - 130 kg/cm²;
3rd grade - 85 kg/cm²;
sqrt - square root
B. We check whether the deflection value is within the standard.
The normalized deflection of the material under load for all roof elements should not exceed L/200. Where, L is the length of the working section.
This condition is satisfied if the following inequality is true:
3.125 Qr (Lmax)³/(B H³) ≤ 1
Where,
Qr - distributed load per linear meter of rafter leg - kg/m,
Lmax - working section of the rafter leg with maximum length m,
B - section width cm,
H - section height cm,
If the inequality is not met, then increase B or H.
Condition:
Roof pitch angle α = 36°;
Rafter pitch A= 0.8 m;
The working section of the rafter leg of maximum length Lmax = 2.8 m;
Material - 1st grade pine (Rbending = 140 kg/cm²);
Roofing - cement-sand tiles (Roofing weight - 50 kg/m²).
As it was calculated, the total load acting on a square meter of roof is Q = 303 kg/m².
1. Find the distributed load per linear meter of each rafter leg Qr=A·Q;
Qr=0.8·303=242 kg/m;
2. Choose the thickness of the board for the rafters - 5 cm.
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.
Let the construction of the rafter system seem quite simple matter, but it requires precise mathematical calculations. Correct sizes elements load-bearing structure will not allow the roof to be fragile and will save the owner of the house from excessive spending.
Calculation of rafter system parameters
The rafter system is formed not only by the rafter legs. The design includes a Mauerlat, racks, struts and other elements, the dimensions of which are strictly standardized. The fact is that the components of the rafter system are supposed to withstand and distribute certain loads.
The elements of the rafter system of a simple gable roof are rafters, purlin (ridge board), racks, beds, mauerlat and rafter legs (struts)
This is a structure of four beams connecting brick, concrete or metal walls houses with a wooden load-bearing roof structure.
The Mauerlat beam should occupy 1/3 of the space at the top of the wall. The optimal cross-section of this lumber is 10x15 cm. But there are others suitable options, for example, 10x10 or 15x15 cm.
The main thing is not to take beams less than 10 cm wide to create a mauerlat, as they will seriously let you down in terms of strength. But lumber with a width of more than 25 cm will not raise doubts about its reliability, but it will put pressure on the house so that it will soon begin to collapse.
The Mauerlat must be narrower than the walls, otherwise it will put excessive pressure on the walls
The ideal length of the beam for the base under the rafter system is equal to the length of the wall. It is not always possible to meet this condition, so the Mauerlat can also be constructed from segments that are completely or at least approximately equal in length.
The bed acts as an element of the rafter system, which is in a lying position and serves as the basis for the rack (headstock) of the supporting roof structure.
A beam of the same cross-section as the Mauerlat is usually taken as a beam. That is optimal size horizontal element on the inside load-bearing wall- 10x10 or 15x15 cm.
The size of the bench is no different from the Mauerlat
Ridge beam
Due to the size ridge beam, into which the rafters rest at the upper end, the weight of the roof should not exceed the permissible limits. This means that for the ridge it is necessary to take a beam that is quite strong, but not heavy, so that other elements of the supporting structure of the roof do not bend under its pressure.
The most suitable pine lumber for the roof ridge is a beam with a section of 10x10 cm or 20x20 cm, like the racks of the structure.
The ridge purlin should not be thicker than the rack of the rafter system
filly
A fillet is a board that extends the rafter if it is unacceptably short.
When using fillies, the rafter legs are cut flush with outer wall. And the boards that extend them are selected in such a way that they form the necessary overhang of the roof and are no thicker than the rafters themselves.
An extra 30–50 cm must be added to the length of the filly, which will be used to combine the rafters with the additional board and make the connection between the frame and the roof overhang as strong as possible.
The thickness of the filly is inferior to the rafter leg
Racks
The post is the same as the center support. Height vertical beam in the rafter system it is customary to find it using the formula h = b 1xtgα – 0.05. h is the height of the rack, b 1 is half the width of the house, tgα is the tangent of the angle between the rafters and the mauerlat, and 0.05 is the approximate height of the ridge beam in meters.
The main requirement for racks is stability, so they choose beams as thick as a bench
A strut is an element of the rafter system, which is mounted at an angle of at least 45° (relative to the horizontal cut of the walls) with one end on the rafter, and the other on a tie laid in the direction from one wall of the house to the other, close to the vertical post.
The length of the strut is determined by the cosine theorem, that is, by the formulaa² =b² +c² - 2xbxcxcosα for a plane triangle. a denotes the length of the brace, b is part of the length of the rafter, c is half the length of the house, and α is the angle opposite to side a.
The length of the strut depends on the length of the rafters and the house
The width and thickness of the struts should be identical to the same dimensions of the rafter leg. This will greatly facilitate the task of securing the element to the roof frame.
The tie is installed at the base of the rafter system and plays the role of a floor beam. The length of this element is determined by the length of the building, and its cross-section does not differ from the parameter of the rafter legs.
The tightening can be called a ceiling joist in another way.
A sliding support or element of the rafter system, allowing it to adapt to changes in configuration, must be characterized by the following parameters:
- length - from 10 to 48 cm;
- height - 9 cm;
- width - 3–4 cm.
The size of the sliding support should allow the rafters to be well fixed to the roof base
Boards or beams for rafters
The size of the boards that will become the rafters of the roof with symmetrical slopes is not difficult to determine. The formula from the Pythagorean theorem c² = a²+ b² will help with this, where c acts as the required length of the rafter leg, a denotes the height from the base of the roof to the ridge beam, and b is ½ part of the width of the building.
The parameters of rafters that differ in asymmetry are also recognized using the Pythagorean formula. However, the indicator b in this case will no longer be half the width of the house. This value will have to be measured separately for each slope.
Using the Pythagorean formula, you can calculate both the length of the rafters and the height of the rack
Rafters are usually boards with a thickness of 4 to 6 cm. The minimum parameter is ideal for commercial buildings, such as garages. And the rafter system of ordinary private houses is created from boards 5 or 6 cm thick. Average the width of the main elements of the supporting structure of the roof is 10–15 cm.
With a large pitch and a significant length, the cross-section of the rafters will certainly be increased. Let’s say that when the distance between the legs of the supporting roof structure reaches 2 m, a section of 10 × 10 cm is chosen for the rafters.
The length of the rafters is influenced by the degree of roof slope and the length of the space between the walls located opposite each other. As the roof slope increases, the length of the rafter leg increases, as does its cross-section.
The size of the rafters is determined by the size of the gap between them
Table: correspondence of the length of the rafter leg to its thickness and pitch
| Rafter leg length (m) | Space from one rafter to another (m) | |||||||
| 1,1 | 1,4 | 1,75 | 2,13 | |||||
| Rafter thickness (mm) | ||||||||
| Bruschi | Logs | Bruschi | Logs | Bruschi | Logs | Bruschi | Logs | |
| Until 3 | 80×100 | Ø100 | 80×130 | Ø130 | 90×100 | Ø150 | 90×160 | Ø160 |
| From 3 to 3.6 | 80×130 | Ø130 | 80×160 | Ø160 | 80×180 | Ø180 | 90×180 | Ø180 |
| From 3.6 to 4.3 | 80×160 | Ø160 | 80×180 | Ø180 | 80×180 | Ø180 | 100×200 | Ø180 |
| From 4.3 to 5 | 80×180 | Ø180 | 80×200 | Ø200 | 100×200 | Ø200 | - | - |
| From 5 to 5.8 | 80×200 | Ø200 | 100×200 | Ø220 | - | - | - | - |
| From 5.8 to 6.3 | 100×200 | Ø200 | 120×220 | Ø240 | - | - | - | - |
Rafter angle
The value of the rafter angle is determined by the formula α = H / L, where α is the angle of inclination of the roof, H is the height of the ridge beam, and L is half the span between the opposite walls of the house. The resulting value is converted into percentages according to the table.
How the rafters will be inclined depends on two indicators - the height of the ridge and the width of the house
Table: determining the rafter angle as a percentage
Video: calculating the size of rafter legs
For each element of the rafter system, there are averaged size data. You can use them as a guide, but it is better to calculate the parameters of the racks, struts and other components of the supporting structure of the roof in special programs on a computer or using complex geometric formulas.
Collectionloads
First, to determine the loads, we set the cross-section of the rafter leg to 75x225 mm. The constant load on the rafter leg is calculated in table. 3.2.
Table 3.2 Calculated constant load on the rafter leg, kPa
|
Exploitation- |
Limit |
||
|
Elements and Loads |
γ fm |
meaning |
|
|
meaning |
loads |
||
|
loads | |||
|
Rafter leg 0.075*0.225*5/0.95 | |||
|
g page e =0.372 |
g c tr. m = 0.403 |
Estimated maximum load on the rafter leg (combination of constant plus snow)
Geometric pattern of rafters
Schemes for calculating the rafter leg are shown in Fig. 3.2. With the width of the corridor in axes 
=3.4 m distance between the longitudinal axes of the outer and inner walls.
The distance between the axes of the power plate and the bed, taking into account the reference to the axis ( 
=0.2 m)m. We install the brace at an angle β = 45° (slope 2 = 1). The slope of the rafters is equal to the slope of the roof i 1 =i = 1/3 = 0.333.
To determine the dimensions necessary for the calculation, you can draw a geometric diagram of the rafters to scale and measure the distances with a ruler. If the mauerlat and the leg are on the same level, then the spans of the rafter leg can be determined using the formulas
Node heights h 1 =i 1 l 1 =0.333*4.35=1.45 m; h 2: = i 1 l=0.333*5.8=1.933 m. Height mark: take the crossbar 0.35 m below the point of intersection of the axes of the rafter leg and the post h = h 2 - 0.35 (m) = 1.933 -0.35 = 1.583 m.
Efforts in the rafter leg on the crossbar
The rafter leg acts as a three-span continuous beam. Support settlements can change the supporting moments in continuous beams. If we assume that due to the subsidence of the support, the bending moment on it has become equal to zero, then we can conditionally cut the hinge into the place of zero moment (above the support). To calculate the rafter leg with a certain safety margin, we assume that the subsidence of the strut has reduced the supporting bending moment above it to zero. Then the design diagram of the rafter leg will correspond to Fig. 3.2, c.
Bending moment in rafter leg
To determine the thrust in the crossbar (tightening), we assume that the supports have sagged in such a way that the supporting moment above the strut is equal to M 1 and above the racks - zero. Conventionally, we cut the hinges into places of zero moments and consider the middle part of the rafters as a three-hinged arch with a span l cp = 3.4 m. The space in such an arch is equal to
Vertical component of the strut reaction
Using the diagram in Fig. 3.2.g, we determine the force in the strut
Rice. 3.2. Schemes for calculating rafters
a-cross section of the attic covering; b - diagram for determining the estimated length of the rafter leg; c - design diagram of the rafter leg; d - diagram for determining the thrust in the crossbar; l - also for a scheme with one longitudinal wall; 1 - Mauerlat; 2 - lying down; 3 - run; 4 - rafter leg; 5 - stand; 6 - strut; 7 - crossbar (tightening); 8 - spacer; 9, 10 - thrust bars; 11 - filly; 12 - overlay.
Calculation of rafter legs based on the strength of normalsections
Required moment of resistance of the run
According to adj. M we take the width of the rafter leg b = 5 cm and find the required section height
According to adj. We take a board with a section of 5x20 cm.
There is no need to check the deflections of the rafter leg since it is located in a room with limited access by people.
Calculation of board jointsrafter leg.
Since the length of the rafter leg is more than 6.5 m, it is necessary to make it from two boards with an overlapping joint. We place the center of the joint at the point where it rests on the strut. Then the bending moment at the joint during subsidence of the strut M 1 = 378.4 kN*cm.
We calculate the joint in the same way as the joint of purlins. We accept the overlap length l nahl =1.5 m= 150cm, nails diameter d= 4 mm = 0.4 cm long l guards = 100 mm.
Distance between axes of nail connections
150 -3*15*0.4 =132 cm.
Force perceived by a nail connection
Q=M op /Z=378.4/ 132 =3.29 kN.
Estimated nail pinching length taking into account the normalized maximum gap between boards δ W = 2 mm with board thickness δ D = 5.0 cm and nail tip length l.5d
a p = l gv -δ d -δ w -l.5d = 100-50-2-1.5*4 = 47.4 mm = 4; 74 cm.
When calculating a dowel (nail) connection:
– thickness of the thinner element a= a p =4,74 cm;
– thickness of the thicker element c = δ d =5.0 cm.
Finding a relationship a/c = 4,74/5,0 = 0,948
According to adj. T, we find the coefficient k n =0.36 kN/cm 2.
We find the load-bearing capacity of one seam of one nail from the conditions:
– crushing in a thicker element
= 0.35*5*0.4*1*1/0.95 = 0.737 kN
– crumpling in a thinner element
= 0.36*4.74*0.4*1*1/0.95 = 0.718 kN
– nail bending
=
(2,5* 0,4 2
+ 0,01* 4,74 2)
/0.95=0.674 kN
– but not more than kN
Of the four values, select the smallest T = 0.658 kN.
Finding the required number of nails P guards ≥ Q/ T =2,867/0,674=4,254.
We accept P guards = 5.
We check the possibility of installing five nails in one row. The distance between the nails across the wood fibers is S 2 = 4d = 4 * 0.4 = 1.6 cm. The distance from the outer nail to the longitudinal edge of the board is S 3 = 4d = 4 * 0.4 = 1.6 cm.
According to the height of the rafter leg h = 20 cm should fit
4S 2 +2Sз=4*1.6+2*1.6 = 9.6 cm<20 см. Устанавливаем гвозди в один ряд.
Calculation of the connection between the crossbar and the rafter leg
According to the assortment (Appendix M), we accept a crossbar made of two boards with a cross-section bxh = 5x15 cm each. The force at the joint is relatively large (N = 12, kN) and may require the installation of a large number of nails under construction site conditions. To reduce the complexity of installing the covering, we design a bolted connection between the crossbar and the rafter leg. We accept bolts with a diameter d = 12 mm = 1.2 cm.
In the rafter leg, dowels (bolts) crush the wood at an angle to the fibers α = 18.7 0. According to adj. We find the coefficient k α =0.95 corresponding to the angle α =18.7 0.
When calculating a dowel connection, the thickness of the middle element is equal to the width of the rafter c = 5 cm, the thickness of the outermost element is the width of the crossbar board a = 5 cm.
We determine the load-bearing capacity of one seam of one dowel from the conditions:
– crushing in the middle element 
= 0.5*5* 1.2*0.95* 1 *1/0.95 = 3.00 kN
– crushing in the outermost element 
= 0.8*5*1.2*1*1/0.95 = 5.05 kN;
– dowel bend = (l.8* 1.2 2 + 0.02* 5 2) 
/0.95=3.17 kN
- but not more than kN
Of the four values, select the smallest T = 3.00 kN.
We determine the required number of dowels (bolts) with the number of seams n w =2
We accept the number of bolts n H =3.
There is no need to check the cross-section of the cross-bar for strength since it has a large margin of safety.
4. ENSURING SPATIAL RIGIDITY AND GEOMETRICAL STABILITY OF THE BUILDING