Rafter system of a gable roof and its structure. Frame roof: arrangement of the rafter system, calculation and installation of the structure Roof without supports

Rafters perform a number of significant roofing functions. They set the configuration of the future roof, absorb atmospheric loads, and hold the material. Among the rafter's duties are the formation of smooth planes for laying the covering and providing space for the components of the roofing pie.

In order for such a valuable part of the roof to flawlessly cope with the listed tasks, information is needed about the rules and principles of its design. The information is also useful for those who are constructing the rafter system gable roof with their own hands, and for those who decide to resort to the services of a hired team of builders.

In device rafter frame for pitched roofs, wooden and metal beams. The starting material for the first option is a board, log, timber.

The second is constructed from rolled metal: channel, profile pipe, I-beam, angle. There are combined structures with the most heavily loaded steel parts and wood elements in less critical areas.

In addition to its “iron” strength, metal has many disadvantages. These include thermal qualities that are unsatisfactory to the owners of residential buildings. The need to use welded joints is disappointing. Most often, industrial buildings are equipped with steel rafters, and less often, private cabins assembled from metal modules.

In business self-construction Wood is the priority for rafter structures for private houses. It is not difficult to work with, it is lighter, “warmer”, and more attractive in terms of environmental criteria. In addition, to perform nodal connections you will not need welding machine and welding skills.

Rafters - a fundamental element

The main “player” of the frame for constructing a roof is the rafter, which among roofers is called a rafter leg. Beams, braces, headstocks, purlins, ties, even a Mauerlat may or may not be used depending on the architectural complexity and dimensions of the roof.

Rafters used in the construction of gable roof frames are divided into:

  • Layered rafter legs, both heels of which have reliable structural supports under them. The lower edge of the layered rafter rests against the mauerlat or the ceiling crown of the log house. The support for the upper edge can be a mirror analogue of the adjacent rafter or a purlin, which is a beam laid horizontally under the ridge. In the first case, the rafter system is called spacer, in the second, non-spacer.
  • Hanging rafters, the top of which rests against each other, and the bottom is based on an additional beam - a tie. The latter connects the two lower heels of adjacent rafter legs, resulting in a triangular module called a rafter truss. Tightening dampens the tensile processes, so that only vertically directed load acts on the walls. Although a structure with hanging rafters is braced, the bracing itself does not transmit to the walls.

In accordance with the technological specifics of rafter legs, the structures constructed from them are divided into layered and hanging. For stability, the structures are equipped with struts and additional racks.

To support the top of the layered rafters, planks and purlins are installed. In reality, the rafter structure is much more complex than the elementary templates described.

Note that the formation of a gable roof frame can generally be done without truss structure. In such situations, the supposed planes of the slopes are formed by slabs - beams laid directly on the load-bearing gables.

However, what interests us now is specifically the structure of the rafter system of a gable roof, and it can involve either hanging or layered rafters, or a combination of both types.

Subtleties of fastening rafter legs

The rafter system is fastened to brick, foam concrete, aerated concrete walls through a Mauerlat, which in turn is fixed with anchors.

Between the Mauerlat, which is wooden frame, and walls made of the specified materials must be laid with a waterproofing layer of roofing material, waterproofing material, etc.

The top of brick walls is sometimes specially laid out so that along the outer perimeter there is something like a low parapet. This is so that the mauerlat placed inside the parapet and the walls do not push apart the rafter legs.

Roof frame rafters wooden houses rest on the upper crown or on ceiling beams. The connection in all cases is made by notches and is duplicated with nails, bolts, metal or wooden plates.

How to do without mind-boggling calculations?

It is highly desirable that the cross-section and linear dimensions of wooden beams be determined by the project. The designer will provide clear calculation justification for the geometric parameters of the board or beam, taking into account the entire range of loads and weather conditions. If available home handyman there is no design development, its path lies on the construction site of a house with a similar roofing structure.

You don’t have to pay attention to the number of floors of the building being constructed. It is easier and more correct to find out the required dimensions from the foreman than to find out them from the owners of a shaky self-built building. After all, in the hands of the foreman is documentation with a clear calculation of the loads per 1 m² of roof in a specific region.

The installation pitch of the rafters determines the type and weight of the roofing. The heavier it is, the smaller the distance between the rafter legs should be. For laying clay tiles, for example, the optimal distance between the rafters will be 0.6-0.7 m, and for corrugated sheets 1.5-2.0 m is acceptable.

However, even if the pitch required for proper installation of the roof is exceeded, there is a way out. This is a reinforcing counter-lattice device. True, it will increase both the weight of the roof and the construction budget. Therefore, it is better to understand the pitch of the rafters before constructing the rafter system.

Craftsmen calculate the pitch of the rafters according to the design features of the building, simply dividing the length of the slope into equal distances. For insulated roofs, the pitch between the rafters is selected based on the width of the insulation slabs.

You can find it on our website, which may also help you a lot during construction.

Rafter structures of layered type

Layered rafter structures are much simpler to construct than their hanging counterparts. A reasonable advantage of the layered scheme is to ensure adequate ventilation, which is directly related to long-term service.

Distinctive design features:

  • It is mandatory to have support under the ridge heel of the rafter leg. The role of support can be played by the run - wooden beam, resting on racks or on the internal wall of the building, or the upper end of an adjacent rafter.
  • Using a Mauerlat to erect a truss structure on walls made of brick or artificial stone.
  • The use of additional purlins and racks where the rafter legs, due to the large size of the roof, require additional support points.

The disadvantage of the scheme is the presence of structural elements that affect the layout of the internal space of the attic in use.

If the attic is cold and organization is not expected in it useful premises, then the layered structure of the rafter system for installing a gable roof should be given preference.

Typical sequence work on the construction of a layered truss structure:

  • First of all, we measure the heights of the building, the diagonals and horizontality of the upper cut of the frame. When identifying vertical deviations of brick and concrete walls, we remove them with a cement-sand screed. Exceeding the heights of the log house is cut off. By placing wood chips under the mauerlat, vertical flaws can be combated if their size is insignificant.
  • The floor surface for laying the bed must also be leveled. It, the Mauerlat and the girder must be clearly horizontal, but the location of the listed elements in the same plane is not necessary.
  • We treat all wooden parts of the structure with fire retardants and antiseptics before installation.
  • We lay waterproofing on concrete and brick walls for installation of the Mauerlat.
  • We lay the mauerlat beam on the walls and measure its diagonals. If necessary, we slightly move the bars and turn the corners, trying to achieve the ideal geometry. Align the frame horizontally if necessary.
  • We mount the Mauerlat frame. The beams are joined into a single frame using oblique notches; the joints are duplicated with bolts.
  • We fix the position of the Mauerlat. Fastening is done either with staples to wooden plugs placed in the wall ahead of time, or anchor bolts.
  • Mark the position of the prone position. Its axis should recede from the mauerlat bars at equal distances on each side. If the run will rest only on posts without supports, we carry out the marking procedure only for these posts.
  • We install the bed on a two-layer waterproofing. We fasten it to the base with anchor bolts, with internal wall we connect with wire twists or staples.
  • We mark the installation points of the rafter legs.
  • We cut out the racks to uniform sizes, because... Our bench is pointed at the horizon. The height of the racks should take into account the cross-sectional dimensions of the purlin and beam.
  • We install racks. If provided by the design, we secure them with spacers.
  • We lay the purlin on the racks. We check the geometry again, then install brackets, metal plates, and wooden mounting plates.
  • We install a test rafter board and mark the cutting areas on it. If the Mauerlat is set strictly to the horizon, there is no need to adjust the rafters on the roof after the fact. The first board can be used as a template for making the rest.
  • We mark the installation points of the rafters. For marking, folk craftsmen usually prepare a pair of slats, the length of which is equal to the clearance between the rafters.
  • According to the markings, we install the rafter legs and fasten them first at the bottom to the mauerlat, then at the top to the purlin to each other. Every second rafter is screwed to the Mauerlat with a wire bundle. In wooden houses, the rafters are screwed to the second crown from the top row.

If the rafter system is made flawlessly, the layer boards are installed in any order.

If there is no confidence in the ideal structure, then the outer pairs of rafters are installed first. A control string or fishing line is stretched between them, according to which the position of the newly installed rafters is adjusted.


The installation of the rafter structure is completed by installing fillets, if the length of the rafter legs does not allow forming an overhang of the required length. By the way, for wooden buildings the overhang should “extend” the contour of the building by 50 cm. If you plan to organize a canopy, separate mini-rafters are installed under it.

Another useful video about building a gable rafter base with your own hands:

Hanging rafter systems

The hanging variety of rafter systems is a triangle. The two upper sides of the triangle are folded by a pair of rafters, and the base is the tie connecting the lower heels.

The use of tightening allows you to neutralize the effect of the thrust, therefore, only the weight of the sheathing, roof, plus, depending on the season, the weight of precipitation, acts on walls with hanging rafter structures.

Specifics of hanging rafter systems

Characteristic features of hanging type rafter structures:

  • The obligatory presence of a tie, most often made of wood, less often of metal.
  • Possibility to refuse to use the Mauerlat. A timber frame can be successfully replaced by a board laid on double-layer waterproofing.
  • Installation of ready-made closed triangles – trusses – on the walls.

The advantages of the hanging scheme include the space under the roof free from racks, which allows you to organize an attic without pillars and partitions. There are disadvantages.

The first of them is restrictions on the steepness of the slopes: their slope angle can be at least 1/6 of the span of a triangular truss; steeper roofs are strongly recommended. The second disadvantage is the need for detailed calculations for the proper installation of cornice units.

Among other things, the angle of the truss will have to be installed from jeweler's precision, because the axes of the connected components of the hanging rafter system must intersect at a point, the projection of which must fall on the central axis of the Mauerlat or the backing board replacing it.

Subtleties of long-span hanging systems

The tie is the longest element of a hanging rafter structure. Over time, as is typical for all lumber, it becomes deformed and sags under the influence of its own weight.

Owners of houses with spans of 3-5 meters are not too concerned about this circumstance, but owners of buildings with spans of 6 meters or more should think about installing additional parts that exclude geometric changes in tightening.

To prevent sagging, there is a very significant component in the installation diagram of the rafter system for a long-span gable roof. This is a pendant called a grandmother.

Most often it is a block attached with wooden pegs to the top of the truss. The headstock should not be confused with the racks, because its lower part should not come into contact with the puff at all. And the installation of racks as supports in hanging systems is not used.

The bottom line is that the headstock hangs, as it were, on the ridge assembly, and a tightening is attached to it using bolts or nailed wooden plates. To correct sagging tightening, threaded or collet-type clamps are used.

The tightening position can be adjusted in the area of ​​the ridge assembly, and the headstock can be rigidly connected to it by a notch. Instead of a bar in non-residential attics, reinforcement can be used to make the described tension element. It is also recommended to install a headstock or hanger where the tie is assembled from two beams to support the connection area.

In an improved hanging system of this type, the headstock is complemented by strut beams. The stress forces in the resulting rhombus are extinguished spontaneously due to the proper placement of vector loads acting on the system.

As a result, the rafter system is stable with minor and not too expensive modernization.


Hanging type for attics

In order to increase usable space the tightening of the rafter triangles for the attic is moved closer to the ridge. A completely reasonable move has additional advantages: it allows you to use the puffs as a basis for lining the ceiling.

It is connected to the rafters by cutting with a half-pan and duplicating with a bolt. It is protected from sagging by installing a short headstock.

A noticeable disadvantage of the attic hanging structure lies in the need for accurate calculations. It is too difficult to calculate it yourself; it is better to use a ready-made project.

Which design is more cost effective?

Cost is an important argument for an independent builder. Naturally, the price of construction for both types of rafter systems cannot be the same, because:

  • In the construction of a layered structure, a board or beam of small cross-section is used to make rafter legs. Because layered rafters have two reliable supports underneath them; the requirements for their power are lower than in the hanging version.
  • In the construction of a hanging structure, the rafters are made of thick timber. To make a tightening, a material with a similar cross-section is required. Even taking into account the abandonment of the Mauerlat, the consumption will be significantly higher.

It will not be possible to save on the grade of material. For the load-bearing elements of both systems: rafters, purlins, beams, mauerlat, headstocks, racks, 2nd grade lumber is needed.

For crossbars and tensile ties, grade 1 will be required. In the manufacture of less critical wooden overlays, grade 3 can be used. Without counting, we can say that in the construction of hanging systems, expensive material is used in greater quantities.

Hanging trusses are assembled in an open area next to the facility, then transported, assembled, upstairs. To lift weighty triangular arches from timber, you will need equipment, the rental of which will have to be paid. And the project for complex nodes of the hanging version is also worth something.

Video instruction on the installation of a hanging category truss structure:

There are actually many more methods for constructing rafter systems for roofs with two slopes.

We have described only the basic varieties that are actually applicable for small country houses and buildings without architectural tricks. However, the information presented is enough to cope with the construction of a simple truss structure.

Each roof is based on a large number of beams, rafters, posts and purlins, which are collectively called the rafter system. Over the centuries-old history, many types and methods of its organization have accumulated, and each has its own characteristics in the construction of nodes and cuts. Let's talk in more detail about what the rafter system of a gable roof can be and how the rafters and other elements of the system should be attached.

Design of a gable roof truss system

In cross-section, a gable roof is a triangle. It consists of two rectangular inclined planes. These two planes are connected at the highest point into a single system by a ridge beam (purlin).

Now about the components of the system and their purpose:

  • Mauerlat is a beam that connects the roof and walls of a building, serves as a support for rafter legs and other elements of the system.
  • Rafter legs - they form inclined planes roofs and are a support for the sheathing under the roofing material.
  • Ridge purlin (bead or ridge) - combines two roof planes.
  • A tie is a transverse part that connects opposite rafter legs. Serves to increase structural rigidity and compensate for thrust loads.
  • Lezhny - bars located along the mauerlat. Redistribute the load from the roof.
  • Side purlins - support the rafter legs.
  • Racks - transfer the load from the purlins to the beams.

There may still be fillies in the system. These are boards that extend the rafter legs to form an overhang. The fact is that to protect the walls and foundation of the house from precipitation, it is desirable that the roof ends as far from the walls as possible. To do this, you can take long rafter legs. But the standard length of lumber of 6 meters is often not enough for this. Ordering non-standard is very expensive. Therefore, the rafters are simply extended, and the boards with which this is done are called “fillies”.

There are quite a few designs of rafter systems. First of all, they are divided into two groups - with layered and hanging rafters.

With hanging rafters

These are systems in which the rafter legs rest only on the external walls without intermediate supports (load-bearing walls). For gable roofs, the maximum span is 9 meters. When installing a vertical support and a strut system, it can be increased to 14 meters.

The good thing about the hanging type of gable roof rafter system is that in most cases there is no need to install a mauerlat, and this makes the installation of rafter legs easier: there is no need to make cuts, just bevel the boards. To connect the walls and rafters, a lining is used - a wide board, which is attached to studs, nails, bolts, crossbars. With this structure, most of the thrust loads are compensated, the impact on the walls is directed vertically downwards.

Types of rafter systems with hanging rafters for different spans between load-bearing walls

Gable roof rafter system for small houses

Exists cheap option rafter system when it is a triangle (photo below). Such a structure is possible if the distance between the external walls is no more than 6 meters. For such a rafter system, you can not calculate the angle of inclination: the ridge must be raised above the tie to a height of at least 1/6 of the span length.

But with this construction, the rafters experience significant bending loads. To compensate for them, either rafters of a larger cross-section are taken or the ridge part is cut in such a way as to partially neutralize them. To give greater rigidity, wooden or metal plates are nailed on both sides at the top, which securely fasten the top of the triangle (also see the picture).

The photo also shows how to extend rafter legs to create a roof overhang. A notch is made, which should extend beyond the line drawn from the inner wall upward. This is necessary to shift the location of the cut and reduce the likelihood of the rafter breaking.

Ridge knot and fastening of rafter legs to the backing board when simple version systems

For mansard roofs

Option with installing a crossbar - used when. In this case, it serves as the basis for lining the ceiling of the room below. For reliable operation of a system of this type, the crossbar cut must be hingeless (rigid). The best option- half frying pan (see picture below). Otherwise, the roof will become unstable to loads.

Please note that in this scheme there is a Mauerlat, and the rafter legs must extend beyond the walls to increase the stability of the structure. To secure them and dock them with the Mauerlat, a notch is made in the form of a triangle. In this case, with an uneven load on the slopes, the roof will be more stable.

With this scheme, almost the entire load falls on the rafters, so they need to be taken with a larger cross-section. Sometimes the raised puff is reinforced with a pendant. This is necessary to prevent it from sagging if it serves as a support for ceiling cladding materials. If the tie is short, it can be secured in the center on both sides with boards nailed to the nails. With a significant load and length, there may be several such belays. In this case, too, boards and nails are enough.

For large houses

If there is a significant distance between the two outer walls, a headstock and struts are installed. This design has high rigidity, since the loads are compensated.

With such a long span (up to 14 meters), it is difficult and expensive to make the tie in one piece, so it is made from two beams. It is connected by a straight or oblique cut (picture below).

For reliable joining, the connection point is reinforced with a steel plate mounted on bolts. Its dimensions must be larger than the dimensions of the notch - the outer bolts are screwed into solid wood at a distance of at least 5 cm from the edge of the notch.

In order for the circuit to work properly, it is necessary to make the struts correctly. They transfer and distribute part of the load from the rafter legs to the tie and provide structural rigidity. Metal pads are used to strengthen connections

When assembling a gable roof with hanging rafters, the cross-section of lumber is always larger than in systems with layered rafters: there are fewer load transfer points, therefore each element bears a greater load.

With layered rafters

In gable roofs with layered rafters, their ends rest on the walls, and the middle part rests on load-bearing walls or columns. Some schemes push through the walls, some don't. In any case, the presence of a Mauerlat is mandatory.

Non-thrust schemes and notch units

Houses made of logs or timber do not respond well to thrust loads. For them they are critical: the wall may fall apart. For wooden houses, the rafter system of a gable roof must be non-thrust. Let's talk about the types of such systems in more detail.

The simplest non-thrust rafter system diagram is shown in the photo below. In it, the rafter leg rests on the mauerlat. In this version, it bends without pushing the wall.

Pay attention to the options for attaching the rafter legs to the Mauerlat. In the first, the support area is usually beveled, its length being no more than the section of the beam. The depth of the cut is no more than 0.25 of its height.

The top of the rafter legs is laid on the ridge beam, without fastening it to the opposite rafter. The structure results in two pitched roofs, which in the upper part are adjacent (but not connected) to one another.

The option with rafter legs fastened at the ridge part is much easier to assemble. They almost never push against the walls.

To operate this scheme, the rafter legs at the bottom are attached using a movable connection. To secure the rafter leg to the mauerlat, one nail is driven from above or a flexible steel plate is placed from below. See the photo for options for attaching rafter legs to the ridge girder.

If you plan to use heavy roofing material, it is necessary to increase the load-bearing capacity. This is achieved by increasing the cross-section of the rafter system elements and strengthening the ridge assembly. It is shown in the photo below.

Reinforcing the ridge assembly for heavy roofing material or for significant snow loads

All of the above gable roof schemes are stable in the presence of uniform loads. But in practice this practically never happens. There are two ways to prevent the roof from sliding towards a higher load: by installing a screed at a height of about 2 meters or by struts.

Options for rafter systems with contractions

Installing contractions increases the reliability of the structure. In order for it to work properly, it needs to be secured to them with nails at the places where it intersects with the drains. The cross-section of the timber for the scrum is the same as for the rafters.

They are attached to the rafter legs with bots or nails. Can be installed on one or both sides. See the figure below for attaching the screed to the rafters and ridge girder.

In order for the system to be rigid and not “crawl” even under emergency loads, it is enough in this option to ensure rigid fastening of the ridge beam. In the absence of the possibility of its horizontal displacement, the roof will withstand even significant loads.

Layered rafter systems with struts

In these options, for greater rigidity, rafter legs, also called struts, are added. They are installed at an angle of 45° relative to the horizon. Their installation allows you to increase the span length (up to 14 meters) or reduce the cross-section of beams (rafters).

The brace is simply placed at the required angle to the beams and nailed on the sides and bottom. An important requirement: the strut must be cut accurately and fit tightly to the posts and rafter leg, eliminating the possibility of it bending.

Systems with rafter legs. The top is a spacer system, the bottom is a non-spacer system. The correct cutting nodes for each are located nearby. Below are possible strut mounting schemes

But not in all houses the average load-bearing wall is located in the middle. In this case, it is possible to install struts with an angle of inclination relative to the horizon of 45-53°.

Systems with struts are necessary if significant uneven shrinkage of the foundation or walls is possible. Walls can settle differently on wooden houses, and foundations can settle on layered or heaving soils. In all these cases, consider installing rafter systems of this type.

System for houses with two internal load-bearing walls

If the house has two load-bearing walls, install two rafter beams, which are located above each of the walls. The beams are laid on the intermediate load-bearing walls, the load from the rafter beams is transferred to the beams through the racks.

In these systems, a ridge run is not installed: it provides expansion forces. The rafters in the upper part are connected to one another (cut and joined without gaps), the joints are reinforced with steel or wooden plates, which are nailed.

In the upper non-thrust system, the pushing force is neutralized by the tightening. Please note that the tightening is placed under the purlin. Then it works effectively (top diagram in the figure). Stability can be provided by racks, or joints - beams installed diagonally. In the spacer system (in the picture it is below) the crossbar is a crossbar. It is installed above the purlin.

There is a version of the system with racks, but without rafter beams. Then a stand is nailed to each rafter leg, the other end of which rests on the intermediate load-bearing wall.

Fastening the rack and tightening in the rafter system without a rafter purlin

To fasten the racks, 150 mm long nails and 12 mm bolts are used. Dimensions and distances in the figure are indicated in millimeters.

The construction of the roof truss system and the subsequent roofing are the most important stages in any construction. This is a very complex matter, involving comprehensive preparation, which includes the calculation of the main elements of the system and the acquisition of materials of the required cross-section. Not every novice builder will be able to design and renovate a complex structure.

However, often when building adjoining buildings, utility or utility structures, garages, sheds, gazebos and other objects, the special complexity of the roof is not required at all - the simplicity of the design, the minimum amount of costs for materials and the speed of work, which are quite feasible, come first For independent execution. It is in such situations that the rafter system becomes a kind of “lifesaver”

In this publication, the main emphasis is on calculations of a pitched roof structure. In addition, the most typical cases of its construction will be considered.

The main advantages of pitched roofs

Despite the fact that not everyone likes the aesthetics of a building over which a pitched roof is installed (although the question itself is ambiguous), many owners of suburban areas, when constructing buildings, and sometimes even a residential building, choose this option, guided by a number of advantages similar design.

  • Very little materials are required for a single-pitch rafter system, especially if it is being built over a small outbuilding.
  • The most “rigid” flat figure is a triangle. It is this that underlies almost any rafter system. In a single-slope system, this triangle is rectangular, which greatly simplifies calculations, since all geometric relationships are known to everyone who graduated from high school. But this simplicity does not in any way affect the strength and reliability of the entire structure.
  • Even if the presenter self-construction the owner of the site has never encountered the construction of a roof before, the installation of a lean-to rafter system should not cause him excessive difficulties - it is quite understandable and not so complicated. Often, when covering small outbuildings or other adjacent structures, it is quite possible to do without not only calling a team of specialists, but even without inviting assistants.
  • When erecting a roof structure, the speed of work is always important, naturally, without loss of quality - you want to protect the structure from the vagaries of the weather as quickly as possible. In terms of this parameter, the pitched roof is clearly the “leader” - its design contains practically no complex connecting units that take a lot of time and require high-precision adjustment.

How significant are the disadvantages of a lean-to rafter system? Alas, they exist, and they also have to be taken into account:

  • An attic with a pitched roof is either not intended at all, or it turns out to be so small that one has to forget about its wide functionality.

  • Based on the first point, there are certain difficulties in ensuring sufficient thermal insulation of rooms located under a pitched roof. Although, of course, this can be corrected - nothing prevents you from insulating the roof slope itself or placing an insulated attic floor under the rafter system.
  • Shed roofs, as a rule, are made with a slight slope, up to 25–30 degrees. This has two consequences. Firstly, not all types of roofing are suitable for such conditions. Secondly, the significance of the potential snow load increases sharply, which must be taken into account when calculating the system. But with such slopes, the influence of wind pressure on the roof is significantly reduced, especially if the slope is positioned correctly - in the windward direction, in accordance with the prevailing winds in a given area of ​​the area.

  • Another drawback, perhaps, can be attributed to very conditional and subjective - this appearance pitched roof. It may not be to the liking of lovers of architectural delights, they say, it greatly simplifies the appearance of the building. This can also be objected to. First, the simplicity of the system and the cost-effectiveness of construction often play a decisive role in the construction of auxiliary structures. And three times - if you look at the overview of residential building projects, you can find very interesting design options, in which the emphasis is placed specifically on the pitched roof. So, as they say, there is no arguing about tastes.

How is a lean-to rafter system calculated?

General principles of system calculation

In any case, a shed roof system is a structure of layered rafter legs installed parallel to each other. The name itself, “layered”, means that the rafters rest (lean) on two rigid support points. For ease of understanding, let us refer to simple scheme. (By the way, we will return to this same diagram more than once – when calculating the linear and angular parameters of the system).


So, two points of support for the rafter leg. One of the points (IN) located above the other (A) by a certain excess value (h). Due to this, a slope of the slope is created, which is expressed by the angle α.

Thus, as already noted, the basis for constructing the system is a right triangle ABC, in which the base is the horizontal distance between the support points ( d) – most often this is the length or width of the building being built. Second leg – excess h. Well, the hypotenuse becomes the length of the rafter leg between the support points - L. Base angle (α) determines the steepness of the roof slope.

Now let's look at the main aspects of choosing a design and carrying out calculations in a little more detail.

How will the required slope of the slope be created?

The principle of arranging the rafters - parallel to each other with a certain pitch, with the required slope angle - is general, but this can be achieved in various ways.


  • The first is that even at the stage of developing a building project, the height of one wall (shown in pink) is immediately set in excess h relative to the opposite ( yellow). The two remaining walls, running parallel to the roof slope, are given a trapezoidal configuration. The method is quite common, and although it somewhat complicates the process of building walls, it extremely simplifies the creation of the roof truss system itself - almost everything for this is already ready.
  • The second method can, in principle, be considered a variation of the first. In this case we are talking about frame construction. Even at the project development stage, it is built into it, then the vertical posts of the frame on one side are higher by the same amount h compared to the opposite.

In the illustrations presented above and in those that will be placed below, the diagrams are made with simplification - the Mauerlat running along the upper end of the wall is not shown, or the strapping beam - on frame structure. This does not change anything fundamentally, but in practice it is impossible to do without this element, which is the basis for installing the rafter system.

What is a Mauerlat and how is it attached to the walls?

The main task of this element is to uniformly distribute the load from the rafter legs to the walls of the building. Read the rules for selecting materials for the walls of the house in a special publication on our portal.

  • The following approach is practiced when the walls are of equal height. The excess of one side of the rafter legs over the other can be ensured by installing vertical racks required height h.

The solution is simple, but the design turns out, at first glance, to be somewhat unstable - each of the “rafter triangles” has a certain degree of freedom to the left and to the right. This can be easily eliminated by attaching the transverse beams (boards) of the sheathing and covering the rectangular gable part of the roof on the front side. The remaining gable triangles on the sides are also sewn up with wood or other material convenient for the owner.

rafter mount

  • Another solution to the problem is to install a roof using single-pitch trusses. This method is good because it is possible, after making calculations, to ideally assemble and fit one truss, and then, taking it as a template, make the required number of exactly the same structures on the ground.

This technology is convenient to use in cases where, due to their large length, they require a certain amplification (this will be discussed below).


The rigidity of the entire rafter system is already inherent in the design of the truss - it is enough to install these assemblies on the Mauerlat with a certain pitch, fasten to it, and then connect the trusses with strapping or cross beams battens.

Another advantage of this approach is that the truss serves as both a rafter leg and a floor beam. Thus, the problem of thermal insulation of the ceiling and lining of the flow is significantly simplified - everything for this will be immediately ready.

  • Finally, one more case - it is suitable for the situation when a pitched roof is planned over an extension being built near the house.

On one side, the rafter legs rest on the frame posts or the wall of the extension being built. WITH opposite side there is a main wall of the main building, and the rafters can rest on a horizontal purlin fixed on it, or on individual fastenings (brackets, embedded bars, etc.), but also aligned horizontally. The attachment line for this side of the rafter legs is also made in excess h.


Please note that although there are differences in installation approaches single slope system, in all options there is the same “rafter triangle” - this will be important for calculating the parameters of the future roof.

In which direction should the roof slope be provided?

It would seem like an idle question, however, it needs to be decided in advance.

In some cases, for example, if there are no special options - the slope should be located only in the direction from the building to ensure the free flow of storm water and melted snow.

A free-standing building already has certain options to choose from. Of course, the option is rarely considered in which the rafter system is positioned in such a way that the direction of the slope falls on the façade (although such a solution is not excluded). Most often, the slope is organized backwards or to one side.


Here you can take as selection criteria the external design of the building under construction, the features of the site, the convenience of laying communications for the storm water collection system, etc. But you should still keep in mind certain nuances.

  • The optimal location of a pitched roof is in the windward direction. This allows us to minimize the wind effect, which can work with the lifting application of the force vector, when the slope turns into a kind of wing - the wind tries to rip the roof upward. It is for pitched roofs that this is of utmost importance. If there is wind blowing into the roof, especially at small slope angles, the wind impact will be minimal.
  • The second aspect of choice is the length of the slope: in case of a rectangular building, it can be placed along it or across it. It is important to take into account here that the length of the rafters without reinforcement cannot be unlimited. In addition, the longer the rafter span between the support points, the thicker the cross-section of the lumber used to make these parts should be. This dependence will be explained a little later, during the calculations of the system.

However, the rule of thumb is that the free length of the rafter leg should usually not exceed 4.5 meters. As this parameter increases, additional structural reinforcement elements must be provided. Examples are shown in the illustration below:


So, if the distance between opposite walls is from 4.5 to 6 meters, it will be necessary to install a rafter leg (strut), located at an angle of 45°, and resting from below on a rigidly fixed support beam (bench). At distances of up to 12 meters, you will have to install a vertical post in the center, which should rest either on a reliable ceiling, or even on a solid partition inside the building. The stand also rests on the bed, and in addition, a strut is also installed on each side. This is all the more relevant due to the fact that standard length lumber usually does not exceed 6 meters, and the rafter leg will have to be made composite. So in any case it will not be possible to do without additional support.

A further increase in the length of the slope leads to an even greater complication of the system - it becomes necessary to install several vertical racks, with a pitch of no more than 6 meters, supported by capital walls, and with the connection of these racks with contractions, with the installation of the same struts both on each rack and on both external walls.

Thus, you should think carefully about where it would be more profitable to orient the direction of the roof slope, also for reasons of simplifying the design of the rafter system.

wood screws

What slope angle will be optimal?

In the vast majority of cases, when it comes to a pitched roof, an angle of up to 30 degrees is chosen. This is explained by a number of reasons, and the most important of them has already been mentioned - the strong vulnerability of the lean-to structure to wind loads from the façade side. It is clear that, following the recommendations, the direction of the slope is oriented to the windward side, but this does not mean that the wind from the other side is completely excluded. The steeper the slope, the greater the lifting force created, and the greater the load on the roof structure will experience.


In addition, pitched roofs with a large angle of inclination look somewhat awkward. Of course, this is sometimes used in bold architectural and design projects, but we are talking about more “mundane” cases...

A slope that is too gentle, with a slope angle of up to 10 degrees, is also not very desirable, for the reason that the load on the rafter system from snow drifts increases sharply. In addition, with the beginning of snow melting, it is very likely that ice will appear along the lower edge of the slope, impeding the free flow of melt water.

An important criterion for choosing the slope angle is what is planned. It is no secret that for various roofing materials there are certain “frames”, that is, the minimum permissible roof slope angle.

The slope angle itself can be expressed not only in degrees. Many masters find it more convenient to operate with other parameters - proportions or percentages (even in some technical sources you can find a similar measurement system).

Proportional calculus is the ratio of the span length ( d) to the height of the slope ( h). It can be expressed, for example, by the ratio 1:3, 1:6 and so on.

The same ratio, but already in absolute value and reduced to percentages, gives a slightly different expression. For example, 1:5 - this will be a slope slope of 20%, 1:3 - 33.3%, etc.

To simplify the perception of these nuances, below is a table with a graph-diagram showing the ratio of degrees and percentages. The diagram is fully scaled, that is, it can be easily converted from one value to another.

The red lines show the conditional division of roofs: up to 3° - flat, from 3 to 30° - roofs with a low slope, from 30 to 45° - medium slope, and above 45 - steep slopes.

Blue arrows and their corresponding numerical designations (in circles) show the established lower limits for the use of a particular roofing material.


Slope amount Type of permissible roof covering (minimum slope level) Illustration
1 from 0 to 2°Absolutely flat roof or with an inclination angle of up to 2°.
At least 4 layers of roll bitumen coating applied using “hot” technology, with a mandatory top coating of fine gravel embedded in molten mastic.
2 ≈ 2°
1:40 or 2.5%
The same as in point 1, but 3 layers of bitumen material will be enough, with mandatory topping
3 ≈ 3°
1:20 or 5%
At least three layers of bitumen roll material, but without gravel backfill
4 ≈ 9°
1:6.6 or 15%
When using rolled bitumen materials - at least two layers glued to the mastic using a hot method.
The use of certain types of corrugated sheets and metal tiles is allowed
(according to manufacturer's recommendations).
5 ≈ 10°
1:6 or 17%
Asbestos-cement corrugated slate sheets with reinforced profile.
Euroslate (odnulin).
6 ≈ 11÷12°
1:5 or 20%
Soft bitumen shingles
7 ≈ 14°
1:4 or 25%
Flat asbestos-cement slate with reinforced profile.
Corrugated sheeting and metal tiles - practically without restrictions.
8 ≈ 16°
1:3.5 or 29%
Sheet steel roofing with seam connection of adjacent sheets
9 ≈ 18÷19°
1:3 or 33%
Asbestos-cement wavy slate of regular profile
10 ≈ 26÷27°
1:2 or 50%
Natural ceramic or cement tiles, slate or composite polymer tiles
11 ≈ 39°
1:1.25 or 80%
Roofing made of wood chips, shingles, natural shingles.
For lovers of special exoticism - reed roofing

Having such information and having outlines for the future roofing covering, it will be easier to determine the slope angle.

metal tiles

How to set the required slope angle?

Let's turn again to our basic “rafter triangle” diagram posted above.

So, to set the required slope angle α , it is necessary to ensure that one side of the rafter leg is raised by the amount h. Parameter Relationships right triangle are known, that is, determining this height will not be difficult:

h = d × tg α

The tangent value is a tabular value that is easy to find in reference books or in tables published on the Internet. But in order to simplify the task as much as possible for our reader, below is a special calculator that will allow you to perform calculations in just a few seconds.

In addition, the calculator will help you solve, if necessary, inverse problem– by changing the slope angle in a certain range, select the optimal value of the excess when this particular criterion becomes decisive.

Calculator for calculating the excess of the upper installation point of the rafter leg

Specify the requested values ​​and click the "Calculate the value of excess h" button

Basic distance between rafter support points d (meters)

Planned roof slope angle α (degrees)

How to determine the length of the rafter leg?

There shouldn’t be any difficulties in this question either - using two known sides of a right triangle, it won’t be difficult to calculate the third using the well-known Pythagorean theorem. In our case, applied to the basic diagram, this relationship will be as follows:

L² =d² +

L = √ (d² +h²)

When calculating the length of the rafter legs, one nuance should be taken into account.

With small slope lengths, the length of the rafters is often increased by the width of the eaves overhang - this will make it easier to mount this entire assembly later. However, with large lengths of rafter legs, or in the case where, due to circumstances, it is necessary to use material of a very large cross-section, this approach does not always look reasonable. In such a situation, lengthening the rafters is used using special elements systems - fillies.


It is clear that in the case of a pitched roof there can be two eaves overhangs, that is, on both sides of the building, or one, when the roof is attached to the wall of the building.

Below is a calculator that will help you quickly and accurately calculate required length rafter leg for a pitched roof. If desired, you can carry out calculations taking into account the eaves overhang or without it.

Calculator for calculating the length of the rafter leg of a pitched roof

Enter the requested values ​​and click the "Calculate rafter length L" button

Elevation height h (meters)

Basic length d (meters)

Calculation conditions:

Required width of eaves overhang ΔL (meters)

Number of overhangs:

It is clear that if the length of the rafter leg exceeds standard sizes commercially available lumber (usually 6 meters), you will either have to abandon shaping using rafters in favor of fillets, or resort to splicing timber. You can immediately assess what consequences this “results in” in order to make the optimal decision.

How to determine the required rafter section?

The length of the rafter legs (or the distance between the points of their attachment to the Mauerlat) is now known. The parameter for the height of raising one edge of the rafter has been found, that is, there is also a value for the slope angle of the future roof. Now you need to decide on the cross-section of the board or beam that will be used to make the rafter legs and, in conjunction with this, the steps for their installation.

All of the above parameters are closely interrelated and must ultimately correspond to the possible load on the rafter system in order to ensure the strength and stability of the entire roof structure, without distortions, deformation or even collapse.


Principles for calculating distributed load on rafters

All loads falling on the roof can be divided into several categories:

  • Constant static load, which is determined by the weight of the rafter system itself, the roofing material, its sheathing, and in the case of insulated slopes - the weight of thermal insulation, the inner lining of the attic ceiling, etc. This total indicator largely depends on the type of roofing material used - it is clear that the massiveness of corrugated sheeting, for example, cannot be compared with natural tiles or asbestos-cement slate. And yet, when designing a roofing system, they always strive to keep this figure within 50÷60 kg/m².
  • Temporary loads on the roof caused by external causes. This is certainly a snow load on the roof, especially characteristic of roofs with a slight slope. Wind load plays a role, and although it is not so great at small slope angles, it should not be completely discounted. Finally, the roof must also withstand the weight of a person, for example, when carrying out any repair work or when clearing the roof of snowdrifts.
  • A separate group includes extreme loads of a natural nature, caused, for example, by hurricane winds, snowfalls or rains that are abnormal for a given area, tectonic tremors of the earth, etc. It is almost impossible to foresee them, but when calculating for this case, a certain reserve of strength of structural elements is laid down.

Total loads are expressed in kilograms per square meter roof area. (IN technical literature Often they operate with other quantities - kilopascals. It’s easy to translate - 1 kilopascal is approximately equal to 100 kg/m²).

The load falling on the roof is distributed along the rafter legs. Obviously, the more often they are installed, the less pressure will be applied to each linear meter rafter leg. This can be expressed by the following relationship:

Qр = Qс × S

— distributed load per linear meter of rafters, kg/m;

— total load per unit roof area, kg/m²;

S— step of installation of rafter legs, m.

For example, calculations show that an external impact of 140 kg is likely on the roof. with an installation step of 1.2 m, for each linear meter of the rafter leg there will already be 196 kg. But if you install the rafters more often, in increments of, say, 600 mm, then the degree of impact on these structural parts decreases sharply - only 84 kg/m.

Well, based on the obtained value of the distributed load, it is no longer difficult to determine the required cross-section of lumber that can withstand such an impact, without deflections, torsion, fractures, etc. There are special tables, one of which is given below:

Estimated value of the specific load per 1 linear meter of rafter leg, kg/mSection of lumber for making rafter legs
75 100 125 150 175 from round timber from a board (timber)
diameter, mmboard (beam) thickness, mm
40 50 60 70 80 90 100
Planned length of rafters between support points, m board (beam) height, mm
4.5 4 3.5 3 2.5 120 180 170 160 150 140 130 120
5 4.5 4 3.5 3 140 200 190 180 170 160 150 140
5.5 5 4.5 4 3.5 160 - 210 200 190 180 170 160
6 5.5 5 4.5 4 180 - - 220 210 200 190 180
6.5 6 5.5 5 4.5 200 - - - 230 220 210 200
- 6.5 6 5.5 5 220 - - - - 240 230 220

Using this table is not difficult at all.

  • In its left part, the calculated specific load on the rafter leg is found (with an intermediate value, the closest value is taken in the larger direction).

Using the found column, they lower down to the required length of the rafter leg.

This line on the right side of the table shows the necessary parameters of lumber - the diameter of the round timber or the width and height of the timber (board). Here you can choose the most convenient option for yourself.

For example, calculations gave a load value of 90 kg/m. The length of the rafter leg between the support points is 5 meters. The table shows that you can use a log with a diameter of 160 mm or a board (timber) of the following sections: 50 × 210; 60×200; 70×190; 80×180; 80×180; 90×170; 100x160.

The only thing left to do is to determine the total and distributed load.

There is a developed, rather complex and cumbersome calculation algorithm. However, in this publication we will not overload the reader with an array of formulas and coefficients, but will suggest using a calculator specially designed for these purposes. True, to work with it it is necessary to make several explanations.

The entire territory of Russia is divided into several zones according to the probable level of snow load. In the calculator you will need to enter the zone number for the region in which construction is taking place. You can find your zone on the diagram map below:


The level of snow load is affected by the angle of the roof slope - we already know this value.

Initially, the approach is similar to that in the previous case - you need to determine your zone, but only by the degree of wind pressure. The schematic map is located below:


For wind load, the height of the roof being erected matters. Not to be confused with the exceedance parameter discussed earlier! In this case, it is the height from ground level to the highest point of the roof that is of interest.

The calculator will ask you to determine the construction zone and the degree of openness of the construction site. The criteria for assessing the level of openness are given in the calculator. However, there is a nuance.

We can talk about the presence of these natural or artificial barriers to the wind only if they are located no further than a distance of no more than 30×N, Where N– this is the height of the house being built. This means that to assess the degree of openness for a building with a height of, for example, 6 meters, you can take into account only those features that are located no further than within a radius of 180 meters.

In this calculator, the rafter installation step is a variable value. This approach is convenient from the point of view that by varying the pitch value, you can trace how the distributed load on the rafters changes, and therefore choose the most appropriate option in terms of selecting the necessary lumber.

By the way, if the pitched roof is planned to be insulated, then it makes sense to adjust the rafter installation step to the dimensions of standard insulation boards. For example, if pitas will be used basalt wool size 600×1000 mm, then it is better to set the rafter pitch to either 600 or 1000 mm. Due to the thickness of the rafter legs, the “clear” distance between them will be 50÷70 mm less - and these are almost ideal conditions for the tightest fit of the insulating blocks, without gaps.

However, let's return to the calculations. All other data for the calculator is known, and calculations can be carried out.

Rafters supported on two supports without any additional supports are used for single-pitched roofs with a span of 4.5 m or gable roofs with a span of up to 9 m (Fig. 30). The rafter system can be used with the transfer of thrust to the mauerlat (walls) and without the transfer of thrust.

Rice. 30. Layered rafters without struts

Non-thrust layered rafters

A rafter that works in bending and does not transmit thrust to the walls must have one support fixed but freely rotating, the other freely rotating and movable.

Three options for fastening the rafters meet these conditions:

1. The bottom of the rafter leg is hemmed with a support bar or a notch (notch) is made on it with a tooth and rests against the mauerlat, and at the top of the rafter an enlarged horizontal notch (notch) with a bevel is made (Fig. 31). The depth of the cut (notch) in the upper part of the rafters should not exceed a = 0.25h. The length of the trim (support area) is made no more than the height of the rafter section (h). It is recommended to bevel the undercut so that it does not interfere with the bending of the rafters, otherwise the side of the notch will rest against the purlin and we will get a spacer rafter system. The length of the beveled trim is made at least two depths A. If trimming the top of the rafter leg cannot be done, it is hemmed with rafter trim with double-sided fastening with mounting plates or wooden nails. The upper ends of the rafter legs are laid loosely on the purlin. In gable roofs, they are attached to the purlin like a sliding support, and are not fastened together. Gable roof, in this case, we consider them as two single-pitched ones, adjacent to each other with a high side. Please note this extremely important condition: The upper support notch or the hemming of the top of the rafters with grooves is made horizontally. One has only to change the support pattern for the purlin, and the rafter immediately shows a spread. This calculation scheme for installing rafters, due to the rigidity of the manufacturing conditions of the upper unit (any inaccuracy in the execution of the unit immediately turns the non-thrust scheme into a spacer one), is practically not used for gable roofs, so it is more often used in pitched roofs. In addition, in gable roofs, for the lack of expansion on the mauerlat when the rafters deflect under the influence of a load, you have to pay for the opening of the roof ridge assembly.

At first glance, this scheme is generally paradoxical. We clearly see in the lower part of the rafter leg the support in the Mauerlat and the system seems to have to exert a horizontal force on it. However, it does not show expansion. If anyone wants to know why, then read the proof in the course of lectures by Professor V. G. Zalessky on pages 414–415.


rice. 31. Supporting the bottom of the rafters with a notch in the mauerlat, and the top of the rafters on the run with a horizontal notch, with a beveled cheek, does not give support to the walls

2. The most common method of installing rafters is related to gable roofs. The bottom of the rafter leg is made on a slider, and the top is secured (Fig. 32): tied with a nail or a bolt, or rested against each other and tied with wooden hammers or metal toothed plates (MZP).

rice. 32. Supporting the bottom of the rafters without cutting into the mauerlat with securing the top of the rafters does not give support to the walls

What you need to pay special attention to is the fastening of the rafter leg to the mauerlat. It comes down only to securing the rafters in the design position that ensures the step of their installation. To do this, it is enough to drive one nail diagonally from both sides into the side surface of the rafters or one long nail from above, or place a flexible steel plate. If fashionable fastening corners are used, then to secure the bottom of the rafter, one nail will be enough, or you need to press the rafter with corners on both sides without nails at all. Do not screw as many screws or nails into the corners as there are holes in the corner. Otherwise, you will turn the slider into an imperfect hinge and get a spread on the Mauerlat. Flexible twisted wires hold the roof against wind overturning; there is no need to transfer this function to the corners, or the rafter system should be designed as a spacer.

3. Rigid pinching of the ridge assembly does not give expansion when the bottom of the rafter leg is placed on a slider and the top is rigidly fixed (Fig. 33). However, a bending moment appears in the ridge unit, tending to destroy it. The maximum bending moment in this design occurs at the ridge support, and the rafter legs themselves receive less deflection. It is quite difficult to calculate such a unit, and then accurately manufacture it on a construction site, so it is better to use formulas for calculating the bending moment and deflection as for ordinary single-span beams.


rice. 33. Supporting the bottom of the rafters without cutting into the mauerlat with pinching the ridge assembly, does not give support to the walls

In all three options, the rule is followed: one end of the rafter leg is placed on sliding support, allowing rotation, the other on a hinge, allowing only rotation. Fastening rafters on sliders and fixed hinges are made in a variety of designs. Nowadays they are often performed on mounting plates. You can also fasten it the old fashioned way: with staples, nailing, or using short bars and boards. You just need to choose the right type of fastener so that it allows or prevents the rafters from sliding in the support.

When calculating the rafter system, an “idealized” design scheme is adopted. It is believed that a uniformly distributed load presses on the roof, i.e. an equal and even force acting uniformly along all planes of the slopes. In fact, there is almost never a uniformly distributed load on the roof slopes. Wind sweeping snow bags on one of the slopes and blowing snow away from the other, the sun melting the snow on the southern slopes, snow sliding in the spring - make the load on the slopes uneven. Under the influence of an uneven load, all three of the above options for rafter systems are statically stable, but only if the ridge girder is rigidly secured. Which ends are inserted into the gables of the walls or supported by slanted rafters of hip roofs. That is, the rafter system will be stable only if the ridge purlin on which the top of the rafters rests is securely secured against horizontal displacement.

When making gable roofs and supporting the purlins only on the posts (without resting their ends on the gable walls), the situation changes for the worse (Fig. 34). In the second and third options, with a significant decrease in the load on one of the slopes, against the calculated one on the other slope, the roof will try to “move” towards a higher load. The first option, in which the bottom of the rafter leg is made with a notch or with a support beam hemmed, and the top is laid on a purlin with a horizontal notch, holds an uneven load well, but only if the posts holding the ridge purlin are absolutely vertical.


rice. 34. Loss of stability of the rafter system

To give the rafter system stability, a horizontal grip is introduced into it (Fig. 35). It increases the stability of the system, but only slightly. Therefore, in all places where the scrum intersects with the posts supporting the ridge girder, it is attached to the posts with nails. There is a persistent misconception that the contraction always works to stretch, this is not so. The grip is a multifunctional element: in non-thrust rafter structures, it does not work at all if there is no snow on the roof, or it works in compression when a slight uniform load appears on the slopes. It works in tension only in a pre-emergency situation when the ridge girder subsides or bends under maximum loads. In essence, a screech is an emergency element of the rafter system that comes into operation when the roof is filled with the maximum possible amount of snow and the ridge girder bends to its full calculated value, or when unexpected and uneven settlement of the foundations occurs and, as a consequence, uneven settlement of the walls and the ridge girder. The lower the contractions are set, the better. Usually they are installed at a height of at least 1.8–2 m from the floor surface so that they do not interfere with a person when walking through the attic.

If in the second and third variants the lower support unit of the rafter leg (slider) is replaced with a slider of a slightly different design (Fig. 35, c) - with the end of the rafter being moved beyond the wall, then this will further strengthen the entire system, making it a statically stable structure at any combination of loads.

rice. 35. The grip between the rafters increases the stability of the rafter system

Another measure to increase the stability of the entire system is to rigidly (which is not always possible) secure the bottom of the racks supporting the purlin. They are cut into the frame and attached to the ceilings using any possible way, transforming the lower support node of the rack from a hinged one (in the plane of the rafters) into a node with rigid pinching (Fig. 36).


rice. 36. An example of securing the rack support unit

Due to the development of small stresses in them, the cross-section of contractions is not calculated; they are taken constructively. In order to reduce the standard size of the parts used in the construction of the rafter system, the scrum section is used in the same dimensions as the rafters, but thinner boards can also be used. Screws are installed on one or both sides of the rafters and attached to them with nails and/or bolts (Fig. 37). When calculating the cross-section of rafters, contractions are not considered additional supports, i.e. the rafter system is calculated as if there were no contractions in it at all. However, if the screeds are bolted to the rafters, then the load-bearing capacity of the wood due to weakening by the bolt holes is reduced using a factor of 0.8. In other words, if holes are drilled in the rafter for installing tie bolts, then its design resistance is used equal to 0.8R. When attaching the screed to the rafters only with nails, there is no weakening of the calculated resistance of the wood of the rafter leg, but you need to make a calculation on the number of nails driven in. Calculations are made for cutting (bending) nails. The calculated shear force is taken to be the thrust that may occur in the event of an emergency condition of the rafter system. In general, a spacer is introduced into the calculation of the nail connection between the scrum and the rafter (H), which is not present during normal operation of the rafters.


rice. 37. Screw fastening unit

Let us remind you once again that the static instability of a non-thrust rafter system manifests itself only in roofs where it is not possible to secure the ridge girder against horizontal displacement. In houses with hip roofs and in houses with gables made of brick and stone, non-braced rafter systems are quite stable and there is no need for measures to ensure stability. However, “emergency-proof” structures - contractions - still need to be installed.

When thrust is introduced into the calculation of the rafter system (even if it is not there), the calculation of the compressive force S changes. Now it is calculated by dividing the resultant distributed load by the sine of the angle of inclination of the rafter S = (qL/2)/sinα. Without going into details of the decomposition of force vectors, let us explain this with a small example. Let's assume we have a rafter system with a steep slope angle. When a load is applied to it in an emergency condition, for example, during subsidence, departure from the vertical or destruction of the ridge girder, tensile stresses will appear in the contraction, neutralizing the so-called thrust. With a constant external load, the smaller the angle of inclination of the slopes, the greater the expansion will increase and the more the rafter legs will be compressed. And vice versa, if the rafter legs are not connected by contractions, then they work like ordinary beams laid in an inclined position. In this case, reducing the angle of inclination, with a constant load, reduces the compressive stresses in the rafters and increases the normal (perpendicular) force directed at bending the beam. Therefore, the compressive force in rafter systems without contractions is considered as S=(qL/2)×sinα and with contractions S=(qL/2)/sinα. Since gable truss systems are almost never built without contractions, and calculations are always carried out for the worst operating conditions, then in all diagrams the compressive stresses will be written as S = (qL/2)/sinα, regardless of whether there will be a thrust or No.

When installing studs or bolts for fastening the contractions, pay special attention to the diameter of the hole for them. It should be equal to the diameter of the studs (bolts) or even 1 mm less. In an emergency, the screed will not work until it selects a gap between the pin and the wall of the hole, at which time the bottom of the rafter legs will “corrode” by several millimeters or centimeters (depending on the installation height of the screech), which can move or unscrew the Mauerlat and destroy the cornice of the walls, and in spacer rafter systems, where the Mauerlat is rigidly fixed, to “push apart” the light walls.

Spacer layered rafters

A rafter working in bending, transmitting thrust to the walls, must have two fixed supports.

We take the same variants of rafter schemes and replace the lower supports with two degrees of freedom (sliders) with supports with one degree of freedom (hinges). Simply, where there are none, we nail support bars to the bottom of the rafter leg. Usually a block of about a meter in length and a cross-section of 50×50(60) mm is used with the calculation of a nail connection. Or we make support on the Mauerlat in the form of a tooth. In the first version of the design scheme, in the ridge where the rafters are horizontally supported on the purlin, we sew the upper ends of the rafter legs together with nails or fasten them with a bolt and thus obtain a hinged support.

rice. 38. Rafters resting both ends on the mauerlat and on each other show expansion

The design diagrams of rafter systems change slightly (Fig. 38), all internal compression and bending stresses remain the same, but in the lower supports of the rafters a thrust equal to H = (qL/2)×ctg α, (kg). In the upper nodes, the thrust in one rafter leg is destroyed by an oppositely directed thrust from the end of the other rafter leg, so here it does not bring much trouble. However, the ends of rafter legs resting directly against each other or through a purlin can be checked for wood compression, although in most cases this is not required.

In fact, spacer layered rafters are a transitional scheme between non-spaced layered and hanging rafters. They already show the scheme hanging rafters, but a rudiment in the form of a ridge girder still remains. When the rafters rest against the walls at the bottom and against each other at the top, the girder is like the fifth wheel in a cart. On the one hand, it doesn’t seem to hurt, but on the other hand, you can do without it. The rafter system exhibits duality in its operation, which depends on the tightness of the top of the rafters to the purlin and to each other. Force vector pressing on ridge knot distributed both to the rafters and to the purlin. When subsidence occurs, as a result of shrinkage of the walls or deflection from its own weight, the purlin goes out of work and the force vectors are completely distributed over the rafters, and the rafters themselves turn into hanging ones.

In spacer rafter systems, the purpose of the contraction is somewhat different - in emergency situations it works for compression. When it starts working, it reduces the thrust on the walls of the bottom of the rafters, but does not completely remove it. She will be able to remove it completely if it is located at the very bottom, fixed between the ends of the rafter legs, but that’s another story design diagram and the contraction in it is called tightening.

What changes with the inclusion of scrum in the scheme? We will not burden you with the layout of force vectors, just imagine a pre-emergency situation when maximum loads are applied to the roof. Where there are no racks under the ridge girder, the girder deflects and the layered rafters, tightened with a contraction, instantly turn into a pattern of hanging rafters with a compressed crossbar, and the bottom of the rafter legs receives expansion according to the corresponding design scheme. Where there are posts under the ridge girder or the girder is rigid, the contraction also works for compression and the bottom of the rafter legs also transmits thrust, but weaker in the same way as the top of the rafters holds the ridge girder. However, the calculation is based on the worst-case scenario.

The use of spacer layered rafter systems requires taking into account the influence of the spacer on the walls. The expansion can be reduced by installing rigid ridge girders. For these rafter schemes, it will be better if the calculated deflection of the ridge girder is much less than that normalized by SNiP. Try to increase the rigidity of the girder by installing racks, struts or cantilever beams (changing the height of the section) or make a construction lift on it. This is especially true for houses made of lightweight concrete, timber and chopped logs. Massive brick, concrete and panel houses more easily transfer the thrust to the walls.

It should be noted that by thrust is meant the horizontal force arising from the compressive stress S rolling down the rafter leg. In other words, thrust is a horizontal vector of forces arising from the action of a vertical load. It should not be confused with the expansion from the deflection of the rafters. In the design diagram, rafters are considered to be rod elements that have no height, so the expansion due to deflection is not taken into account. This is what the standardization of deflection in building structures is aimed at. SNiP, by introducing normalized deflection values, brings idealized design schemes closer to real ones. In other words, if the deflection building structure does not exceed the normalized value, then you shouldn’t even think about the thrust from the deflection, it’s as if it doesn’t exist. Although in fact it exists, and in the spacer scheme it manifests itself to a greater extent than in the non-spacer one. You need to pay attention to the expansion from deflection when building the walls of a house from aerated concrete. These blocks do not hold bends at all and can be destroyed by thrust even from the deflection of the rafters. Do not use braced rafter systems on these walls. In other cases, the thrust from deflection does not cause much harm, for example, in brick walls it is absorbed by the elasticity of the Mauerlat and steel fasteners.

A rafter system made according to the spacer option is a statically stable system under any combination of loads and requires rigid fastening of the Mauerlat to the wall. To maintain the thrust, the walls must be quite massive or equipped with an unbreakable monolithic reinforced concrete belt around the entire perimeter, like a hoop on a wooden barrel. In emergency situations, in contrast to non-thrust systems, in a spacer system the contraction working in compression does not save the situation; it only partially reduces the thrust transmitted to the walls (Fig. 38.1). In order to emergency situations It didn’t happen and we are collecting to the maximum the loads acting on the roof.

rice. 38.1. The contraction working on compression partially removes the thrust from the walls

The calculation of a rafter system with a compressed tension introduced into it is done using two combinations of loads. The section of the rafter leg is selected according to the maximum bending moment and deflection without taking into account the work of the compressed contraction. Imagine that there is an uneven load on the roof: on one side of the slope the snow lies, and on the other it has melted or slid. The bending rafter leg will simply push the compressed scrum and work like a regular single span beam. On the contrary, we will select the cross-section of the compressed contraction and determine the thrust on the walls for a uniformly distributed load along both slopes. In this case, the contraction will be compressed on both sides and will receive maximum voltage compression, the bottom of the rafter leg will give a reduced thrust to the wall, and the rafter leg itself will turn into a continuous beam on three supports.



 
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