The ridge beam is the top crossbar to which the rafters in the roof are attached. Installing ridge beams is considered a special skill in the work of builders: they must make a special calculation of the dimensions of the room, the mounting location, and the attic.
Skate wooden beam and the rafters attached to it are designed to perform the following tasks during housing construction:
- Create a stable structure of the rafter system.
- Evenly distribute the pressure force and area along the lateral perimeters.
- Correctly distribute the weight of the roof onto the gables.
- Maintaining the geometry of a roof whose length is more than 4.5 m. This allows you to install rafters without using a template. If the roof dimensions are large, then a rafter beam (upper part) is placed on the ridge wooden beam, and the lower one is attached to the mauerlat.
An important condition for installing a ridge beam is to calculate the correct cross-section of such a support, which will make it possible to create a stable structure.
Let's figure out how to calculate and fasten the timber. The cross section of the purlin is calculated very simply: add all the load data with horizontal projection roofs. The dimensions of the ridge beam depend on 2 main parameters:
- Timber runs.
- Dimensions of the building.
The calculation of the beam parameters provides that large buildings require a powerful, heavy and rather weighty girder. But it is worth considering that such dimensions of the ridge beam will require the use of a crane. Average length ordinary timber is approximately 6 m, so to make a larger purlin you will need to look for wood or a so-called laminated beam.
The fixed ends of the ridge, pre-treated with an antiseptic, rest against the wall into which they are embedded. Additional processing carried out with roofing felt and roofing felt, which perfectly protects the wood from rotting. A solid wood beam is installed differently:
- The end is cut at an angle of 60°.
- The ends are left open so that the ends do not touch the walls.
As a result, when building a house, 2 problems are solved at once. Firstly, the end area becomes larger. Secondly, moisture exchange processes are normalized.
Then they calculate the dimensions of the ridge beam, which must be installed in the wall and pass through it; contact with the wall must be taken into account. Therefore, the end of the run must be well treated with an antiseptic and wrapped roll material. Similar design used to make an unloading console.
When choosing the right section for a solid wooden beam, you need to take into account that the beam in the ridge can bend at any time under the weight of its own weight. Experienced builders It is recommended to install a construction truss so that the fixed wooden ridge beam does not break.
Calculation of the cross section of a ridge beam
Section calculation requires taking into account following parameters, which will be used to calculate the required size:
- deflection data;
- strength to destruction.
To determine the cross section, it is necessary to use special formulas in which each indicator has important. A separate calculation determines the following data:
- Internal stress (Σ = M:W).
- Purlin deflection (according to the formula f = 5qL³L:384EJ).
- The dimensions of the beam section are determined by the formula h = √¯(6W:b).
The data for each formula is listed below:
Σ = M:W (definition of internal stress), where Σ is the quantity to be found. M is the maximum bending moment, which is calculated in kg/m. W is the deflection resistance of the established section.
Calculation of the deflection of the purlin is carried out using other data that must be substituted into the formula f = 5qL³L:384EJ. The letter J means the moment of inertia, to obtain which you need to know the dimensions of the purlin section (height and width, denoted by the letters h and b). Then the exponent h needs to be cubed and multiplied by b. The resulting value is divided by 12. Parameter E is the elasticity of the modulus, which is taken into account and is individual for each type of wood.
The bending moment must be calculated using the formula h = √¯(6W:b), where b is the width of the beam in centimeters, W is the bending resistance of the purlin. You can get W by dividing M (the largest bending moment) by 130.
The width and height values obtained after calculation must be rounded upward. If a builder is afraid of making a mistake, you need to contact specialists who will calculate the parameters and determine what the beam and girder to be fixed should be.
Installation of ridge beams
Let's look at how to attach ridge bars. They are made only from high-quality lumber, which is due to the importance of the structure, which must perform the functions of long-term and reliable operation, bear the load, and be safe for the residents of the building. It is important that the purlin does not increase the weight of the roof, otherwise the strength of the structure will be in question. The rafters must serve for a long time, fulfilling their assigned functions. For this purpose, pine lumber with a cross-section of 20x20 cm is often used for ridge beams.
The fastening of the rafters to the ridge beam is selected depending on the type of building: residential or commercial. Depending on this, the material of the ridge, its cross-section and dimensions will be selected. For example, for a bathhouse, well-dried larch is usually used, which is heavier in weight and more resistant to stress. Larch also copes well with steam, retains heat and holds tiles. Residential buildings are built from pine, since the roof is usually covered with so-called flexible tiles.
Larch is used to make timber if the house will be covered with heavy tiles, which require durable and strong building materials. frame construction. It is important that the rafters not only support the roof itself, but also do not become extra weight for the walls. They must hold the purlins perfectly and not bend under them.
In order to give the rafters a central support, you need to install a beam. Its ends will rest against parallel load-bearing walls. Correct installation This design requires the calculation of data such as:
- The average annual amount of precipitation that falls in a particular area.
- Whether there are strong winds in the region or not.
- Design width of the house.
Ridge beams allow you to avoid such processes in the construction of a house as hammering nails or drilling. As a result, it is possible to avoid the formation of cracks, maintain the integrity of the timber and ensure the reliability of the entire rafter system.
A gable roof also requires the use of a ridge purlin, which subsequently serves as the roof ridge. In order to build a residential building measuring 6x6 m, it is recommended to take a purlin made of logs or solid timber. The purlin will rest on 2 gables and no supports will be needed. If the length of the house is more than 6 m, then it is allowed to use construction trusses and a composite ridge girder. It is important that the timber lies on the external gables.
The ridge beam is fastened different methods, which allows you to connect the bars in the desired way. The main goal of each connection is to make the structure strong and reliable. Modern technologies allow you to connect the beams together so as not to use any Additional materials for insulation. If project documentation If it is compiled correctly, the house will not only be strong and able to support the roof, but will also become environmentally friendly and reliable for habitation.
Building a house from the foundation to the top is an amazing event! Especially if you do some of the work with your own hands, you live and breathe the future nest. And you know that no matter how tired you may be finishing work, still everything needs to be done competently and thoroughly. Especially when it comes to the roof, where any mistakes can lead to expensive and unpleasant repairs.
Therefore, in order for the “umbrella” of your dream home to serve properly, perform all structural components correctly, especially splicing the rafters in the area of the ridge - this is the highest point! And we will help you understand the types of connections and important technological nuances.
What is a roof ridge?
So, first, let's understand the concepts a little.
So, a purlin is an additional beam that is placed parallel to the roof ridge and the mauerlat. Speaking in simple language, this is the same Mauerlat, only raised in level. And as a result, the ridge should be located at a certain distance from the purlin - depending on what angle of the roof was chosen.
A ridge is a horizontal roof element that connects both roof slopes at the top point.
And the main task of the connecting elements in the ridge is to create reliable rigidity and strength of the entire roof structure. This is what we will talk about now.
Types of rafter splicing in the ridge
There are three ways to do this:
This method differs from all previous ones in that here the rafters are connected by side planes and tightened with a pin or bolt. Enough popular technology to date.
If the house is wooden, then the top log or timber will be suitable as a support for this method, but you will have to put a mauerlat on the blocks.
The most popular type of fastening is splicing rafters into half a tree:
Overlapping ridge rafters are most often connected using nails. Usually these are the roofs of gazebos, sheds, bathhouses and garages - there are no special requirements for the strength of the rafter system.
Method number 2. Butt connection
To do this you need:
- Cut the edge of the rafter at an angle so that this angle is equal to angle roof slope.
- Support the rafters.
- Apply fastener.
It is much easier to make such trims using a template - just make it in advance. So all the planes will fit tightly against each other.
If you are fastening rafters with nails, use at least two of them. Hammer each of the nails into the upper cavity of the rafters at an angle so that the nail goes into the cut of the second rafter being joined. Additionally, strengthen the splice of the rafters at the ridge with a metal plate or wooden overlay.
Or partially end-to-end:
The essence of this design is that the edges of the two rafters are adjusted so precisely that they evenly distribute the load placed on them with each other. But it will not be enough to secure this connection with one nail - you also need metal or wooden attachments. Take a board 30 mm thick, secure it to one (preferably two) sides of the assembly and nail it.
Method No. 3. Connection to timber
In this method we will attach the rafters directly to ridge beam. This design is good in that the beam can be provided with central supports, and each rafter can be fastened separately and at a convenient time. This method is irreplaceable if you don’t have time to make a template.
A connection to a ridge beam is recommended in cases where the roof is wide enough - wider than 4.5 meters. This design is quite reliable, but sometimes it requires the installation of additional supports underneath, which reduces the functionality of the attic significantly. After all, there are now beams in the middle of the room! For small ones attic roofs This, of course, is not a problem, but in the attic it will have to be used as an element of the interior. But no template is needed for this design, and small discrepancies are not scary.
Variation:
You can, of course, use a metal fixing plate - but this is only a connection, not a tightening. The essence of the tightening is that it is located lower and takes on part of the load.
This is a combined splicing of rafters, because it is performed end-to-end, exactly the same as when focusing on the mauerlat.
How to splice? Selection of fasteners
The rafter legs form the contour of the roof and transfer the point load from the roof to the mauerlat, and the mauerlat, in turn, evenly distributes it to the load-bearing walls.
The following elements have long been used to fasten rafters:
- Overlays.
- Bars.
- Wooden pins.
- Wedges.
- Nageli.
- Metal staples.
And here modern market offers more functional fasteners that make splicing rafters in the ridge area much easier and more reliable. At any angle, the desired rigidity and strength are obtained. This:
- Nail and perforated plates.
- Self-tapping screws.
- Bolts and screws.
- And much more.
But the choice of one or another fastening element no longer depends on how much it costs and how strong it turns out to be, but on what the load is on a particular ridge unit and what it requires.
So, here’s how, for example, rafters in a ridge are spliced with self-tapping screws:
And here it is with nail and perforated plates:
But in order to use these plates, you will have to work with the press:
And now - from simple to complex.
Splicing rafters at the ridge of a gable roof
When resting on the ridge girder of a gable roof, the rafter legs can either rest against each other with their beveled ends or be apart.
- If the rafters rest against each other with their ends, in other words, end-to-end, then their ends need to be connected with overlays on nails or bolts.
- If the ends of the rafter legs in the ridge assembly are located apart, then they are connected with corner brackets and bolts.
- If the rafter legs rest on two purlins at once, then the ends of the legs also rest on each other. Naturally, a certain thrust arises, the tension of which is relieved with the help of horizontal crossbars.
- If there is no purlin at all, then the junction of the rafter legs in the ridge unit is made by placing the beveled ends of the legs against each other. Additionally, such joints need to be secured with paired overlays, which are nailed to the legs or connected with bolts.
- To secure the rafter leg with the crossbar, the joint is made using wooden side plates. They are nailed directly to the crossbar or bolted - it all depends on cross sections materials used. Next, a block is placed under the crossbar to absorb transverse forces.
- But rafter legs made of logs with a crossbar are already attached without overlays. Only at the end of the crossbar itself is a notch made ½ from the section of the truss. To ensure that the system ultimately turns out to be stable, the rafter legs are reinforced in the transverse direction with struts and crossbars. Especially when it comes to the span width between external load-bearing walls of 8 meters or more.
- If strong winds are not uncommon in the area, it is extremely important to protect the roof ridge from possible displacement. And for this purpose, the ends of the rafters are additionally connected to the ridge girder with corner brackets. Plus, the rafter legs and masonry of the house must be secured with wire.
- If you are splicing a rafter system from logs in a ridge, round timber, then expect it to be quite heavy.
Note that with significant loads on the rafter system, the tie-in rafter leg It is not recommended to do this at all - just use intermediate scarves.
Here's more detailed information:
If rafter diagram are inclined, external loads are transmitted by supports (mauerlat, purlins, racks, struts and beams), while compressive and bending stress forces arise in the rods themselves. And the steeper the pitched roof, i.e. The more vertically the rods are tilted, the bending is less, but the horizontal loads, on the contrary, only increase.
Simply put, the steeper the roof, the more durable everything should be horizontal structures, and the flatter the slope, the stronger it should be vertical structures rafter system.
The joining of rafters on a hip roof follows a completely different scenario than on a gable roof. So, there are already new elements here - slanted rafters, which need to be installed using a certain technology. And these parts must be attached to the ridge beam using the cutting method with additional fixation with upper ties and crossbars. Adding to its complexity is the fact that the hip roof has sloping slopes containing skylights and ventilation holes, which are often located directly under the ridge.
If there is only one purlin in a hip roof, its diagonal rafter leg is supported on the purlin console. The consoles themselves need to be extended 10-15 cm beyond the rafter frame. Moreover, do it in such a way as to cut off the excess, and not build up what is missing.
If there are two purlins, then in the ridge directly to the rafters you need to sew a short board, up to 5 cm thick - a groove. We will rest the slanted rafters and diagonal rafter legs on it.
Now let's look at the outer valley. The rafter legs that rest on it are also called slanted and diagonal. Moreover, the diagonal rafters are longer than ordinary ones, and shortened rafters from the slopes - narozhniki - rest on them. In another way, they are also called rafter half-legs. In this case, the slanted rafters already carry a load that is one and a half times greater than that of conventional rafters.
Such diagonal rafters are longer in themselves regular boards, and therefore they should be made paired. This immediately solves three problems:
- Double the cross-section carries double the load.
- The beam turns out to be long and not cut.
- The dimensions of the parts used become unified.
- For the installation of slanted rafters, you can use the same boards as for ordinary ones.
To summarize and speaking in simple terms, the use of boards of the same height for the ridge unit greatly forgives everything Constructive decisions hip roof.
Let's move on. To ensure multi-span, one or two supports need to be installed under the slanted legs. After all, slanted rafters in their essence are a bent and bifurcated ridge girder, a kind of continuation of it. Therefore, these boards need to be spliced along the length so that all joints are at a distance of 15 m from the center of the support. Select the length of the rafter leg depending on the length of the spans and the number of supports.
Technically, this node is performed like this:
A couple of technical points:
- If you are making a support for fastening the rafters at the ridge of the hip roof directly above the dormer window, then the support of the diagonal rafter legs should be on the side struts and the crossbar.
- If the rafter legs of the hip roof are fused directly above the ventilation vent, then there is no need to place a central emphasis on the struts.
- For a hip roof, be sure to make sure that the joining surfaces at the ridge joints fit tightly, almost perfectly. Therefore, it is much easier to manufacture the required configuration of all ridge elements on the ground, and only then mount each rafter leg separately on the roof.
Here is a visual master class:
A prerequisite for installing layered rafters is to provide their upper part with support. In pitched roofs, this issue is solved simply: the walls are built different heights, mauerlat beams are laid on them, on which rafters in turn are laid.
In a gable roof, you can do the same: build the inner wall to the required height and lay the mauerlat on it. Then lay the rafters on the low external and high internal walls. However, this decision limits the layout options attic space, which is increasingly used as an attic. And for ordinary attic roofs, this option is not profitable, because... requires significant financial costs for the construction of a high internal main wall. Therefore, in the attic, the internal wall is replaced with a horizontal beam mounted on supports or supported on the opposing gables of the walls. A horizontal beam laid on a roof is called a purlin.
The name itself: purlin, suggests that this beam is “thrown” from wall to wall, although in fact, for example, in hip roofs it may be shorter. The simplest design solution for installing a ridge girder is to lay a powerful beam on the gables of the walls without any additional supports (Fig. 24.1).
rice. 24.1. An example of installing a ridge girder, without additional supports, on the walls of an attic.
In this case, to calculate the cross-sections of the purlins, the load acting on them must be collected from half the horizontal projection of the roof area.
In large buildings, the purlins are long and heavy; most likely, they will have to be installed by a crane. To make a purlin, find flat timber made of solid wood longer than 6 m is quite problematic, so for these purposes it is better to use a laminated beam or log. In any case, the ends of the purlins, walled up in the walls of the gables, must be treated with antiseptics and wrapped in rolled waterproofing material. The ends of solid wood beams are beveled at an angle of approximately 60° and left open; in the niche they should not rest against the wall material (Fig. 25). Bevelling the end of the beam increases the end area and promotes better moisture exchange throughout the beam. If the purlin passes through the wall, then where it rests on the wall, it is also wrapped waterproofing material. Beams are passed through the walls for architectural reasons in order to provide an overhang of the roof over the gables, although this can also be achieved by moving the sheathing beyond the wall. Purlins passed through the wall form unloading consoles. The pressure load on the console tries to bend the girder upward, and the load acting on the span tries to bend it downward. Thus, the total deflection of the purlin in the middle of the span becomes smaller (Fig. 24.2).
Rice. 24. 2. Run with consoles.
If you use a log as a purlin, then it is not necessary to cut it into two edges; it is enough to trim it at the place where the rafters support and at the place where the purlin rests on the walls. It is not advisable to make long purlins made of solid wood; they are designed for strength and deflection; however, they can bend under their own weight. It is better to replace them with construction trusses.
The cross section of the run is selected according to the calculations for the first and second limit state- to destruction and deflection. A beam working in bending must meet the following conditions.
1. Internal stress arising in it during bending from the application external load, should not exceed the design bending resistance of wood:
σ = M/W ≤ Rben, (1)
where σ - internal stress, kg/cm²; M - maximum bending moment, kg×m (kg×100cm); W - moment of resistance of the section of the rafter leg to bending W = bh²/6, cm³; Rbend - the calculated bending resistance of wood, kg/cm² (accepted according to the table SNiP II-25-80 " Wooden structures"or according to the table);
2. The amount of deflection of the beam should not exceed the normalized deflection:
f = 5qL³L/384EJ ≤ fnorm, (2)
where E is the modulus of elasticity of wood, for spruce and pine it is 100,000 kg/cm²; J is the moment of inertia (a measure of the inertia of a body during bending), for rectangular section equal to bh³/12 (b and h are the width and height of the beam section), cm4; fnor - the normalized beam deflection, for all roof elements (rafters, purlins and sheathing bars) it is L/200 (1/200 of the length of the checked beam span L), see.
First, the bending moments M (kg × cm) are calculated. If on design scheme several moments are depicted, then all are calculated and the largest is selected. Further, by means of simple mathematical transformations of formula (1), which we omit, we obtain that the dimensions of the beam section can be found by specifying one of its parameters. For example, arbitrarily setting the thickness of the beam from which the beam will be made, we find its height using formula (3):
h = √¯(6W/b) , (3)
where b (cm) is the width of the beam section; W (cm³) - the moment of resistance of the beam to bending, calculated by the formula: W = M/Rbending (where M (kg×cm) is the maximum bending moment, and Rbending is the bending resistance of wood, for spruce and pine Rbending = 130 kg/cm²) .
You can, conversely, arbitrarily set the height of the beam and find its width:
After this, the beam with the calculated parameters of width and height according to formula (2) is checked for deflection. Here it is necessary to focus your attention: in terms of load-bearing capacity, the rafter is calculated based on the highest stress, that is, the maximum bending moment, and the section that is located on the longest span is checked for deflection, that is, on the section where the greatest distance between the supports is. The deflection for all: one-, two- and three-span beams is easiest to check using formula (2), that is, as for single-span beams. For two- and three-span continuous beams, such a deflection test will show a slightly incorrect result (slightly larger than it actually will be), but this will only increase the safety factor of the beam. For a more accurate calculation, you need to use deflection formulas for the corresponding design scheme. For example, such a formula is indicated in Figure 25. But we repeat once again that it is better to include a certain margin of safety in the calculation and consider the deflection according to the simple formula (2) at a distance L equal to itself long span between the supports, than to find the formula corresponding to the design load diagram. And one more thing you need to pay attention to, according to the old SNiP 2.01.07-85, both calculations (for bearing capacity and deflection) were carried out under the same load. The new SNiP 2.01.07-85 states that the snow load for calculating deflection must be taken with a coefficient of 0.7.
rice. 25.1. An example of the location of purlins on a T-shaped roof
rice. 25.2. An example of the location of purlins on a T-shaped roof
rice. 26. Loads acting on the purlins of a T-shaped roof.
If, after checking the beam for deflection, it is no more than L/200 in the longest section, then the section is left as it turned out. If the deflection is greater than the standard one, we increase the height of the beam or place additional supports under it, but the cross-section must be recalculated again according to the appropriate design scheme (taking into account the introduced supports).
If anyone managed to read this far, then let’s say that the most difficult thing in this calculation is not to get confused in the units of measurement (in converting meters to centimeters), but everything else... Multiplying and dividing several numbers on a calculator does not require much knowledge.
Ultimately, only two numbers will appear: required for a given load, which are rounded up to the nearest whole number.
If a log is used instead of a beam (solid, glued or assembled on an MZP), then it should be taken into account that when working in bending, due to the preservation of the fibers, the load-bearing capacity of the log is higher than that of the timber and amounts to 160 kg/cm². Moment of inertia and resistance round section determined by the formulas: J = 0.0491d³d; W = 0.0982d³, where d is the diameter of the log at the top, cm. The moments of resistance and inertia of a log hewn on one edge are equal to J = 0.044d³d, W = 0.092d³, on two edges - J = 0.039d³d; W = 0.088d³, with a panel width of d/2.
The height of purlins and rafters, depending on the loads and architectural solution roofs can be very diverse. In addition, the forces pressing on the walls, especially when it comes to purlins, reach large values, so the roof, like everything else, must be designed in advance, even before the house is built. For example, in the layout of a house, you can introduce an internal load-bearing wall and relieve the purlins, or make capitals on the gables of the walls, put slopes under the purlins and thereby reduce their deflection. Otherwise, it will be quite difficult to connect purlins of different heights to each other and to coordinate the elevations with the gables of the walls.
When using long and heavy runs, you can use the so-called “construction lift”. This is the manufacture of a beam in the form of a rocker arm. The height of the “rocker arm” is made equal to the standard deflection of the purlin. The loaded beam will bend and become level. The method came to us from our ancestors. They're in log houses when laying the mats and beams (beams), the logs were undercut from below, along the entire length, making the undercut deeper in the middle part, and, if necessary, undercutting the edges of the beams from above. Over time, the rocker-shaped beams sagged under their own weight and became straight. This technological technique is used quite often, for example, pre-stressed reinforced concrete structures. IN Everyday life you simply don’t notice it, because the structures bend, and the already small construction rise becomes completely invisible to the eye. To reduce the deflection of the beam, you can also introduce additional struts under it. If it is impossible to install struts or make a “construction lift,” you can increase the rigidity of the beam by changing its section: to a T-beam, I-beam or lattice - a truss with parallel chords, or change the cross-section by placing cantilever beams under the supports, that is, making its bottom in the form of an imperfect arch.
The support of the purlins on the wall is ensured by a transverse side support and must be designed for wood compression. In most cases, it is enough to provide the required depth of support and place a wooden lining under the block on two layers of roofing felt (waterproofing material, etc.). However, it is still necessary to crush the wood. If the support does not provide the required area at which collapse will not occur, the area of the wooden pad must be increased, and its height should distribute the load at an angle of 45°. The crushing stress is calculated using the formula:
N/Fcm ≤ Rc.90°,
where N is the pressure force on the support, kg; Fcm-crumple area, cm²; Rcm90 - calculated resistance to wood crushing across the grain (for pine and spruce Rcm90 = 30 kg/cm²).
Need to pay Special attention on the wall under the support of the ridge girder. If there is a window below, then there must be at least 6 rows from the top of the lintel to the bottom of the purlin reinforced masonry, otherwise reinforced concrete lintels must be laid over the window inside pediment. If the layout of the house allows, the ridge purlins should not be made long and heavy; it is better to divide them into two single-span purlins or leave one and add a support under it. For example, the layout of the house shown in Figure 25 involves installing a partition in the room under the second purlin. This means that you can install a truss truss in the partition and unload the ridge girder, and then hide the truss with sheathing, say, plasterboard.
Rice. 26.1. Rafterless roof
Another way to unload ridge purlins is that you can simply increase the number of stacked purlins, for example, install one or two unloading purlins along the roof slopes. With a significant increase in the number of beams, the question arises: why do we need rafters here at all? The sheathing can be done directly along the purlins. This is true. Such roofs are called rafterless (Fig. 26.1). However, in attic insulated roofs the issue of drying the insulation becomes acute, so something like rafters will still have to be made. To ensure air circulation, it will be necessary to fill the purlins along the slopes (in the same direction as the rafters are laid). wooden blocks, for example, 50x50 or 40x50 mm, thereby providing a vent height of 50 or 40 mm.
Note. Earlier, here and further in the text, the following absurdities are found in the formulas: d³d, this hurts the eyes a little, but from a mathematical point of view this is the correct notation. It shows that the variable is in the 4th power. Since writing the 4th degree in the language of the website “breaks” the beauty of the formula, we have to resort to such a notation. The same applies to radical expressions: everything in brackets is included under the root sign.
An example of calculating the cross section of purlins.
Given: Vacation home 10.5×7.5 m. Design load on the roof at the first limit state Qр=317 kg/m², at the second limit state Qн=242 kg/m². Roof plan with dimensions indicated on.
1. Find the loads based on the limit states acting on the first run:
qр = Qр×a = 317×3 = 951 kg/m
qн = Qн×a = 242×3 = 726 kg/m = 7.26 kg/cm
2. We calculate the maximum bending moment acting on this run (formula for):
M2 = qр(L³1 + L³2)/8L = 951(4.5³ + 3³)/8×7.5 = 1872 kg×m
3. We arbitrarily set the width of the purlin, b = 15 cm, and using formula (3) we find its height:
h = √¯(6W/b) = √¯(6×1440/15) = 24 cm,
where W=M/Rben = 187200/130 = 1440 cm³
According to the assortment of lumber, the nearest suitable beam has dimensions of 150x250 mm. We select it for subsequent calculations.
4. On the longest span, we check the purlin for deflection using formula (2).
First, we determine the standard deflection: fnorm = L/200 = 450/200 = 2.25 cm,
then calculated: f = 5qнL²L²/384EJ = 5×7.26×450²×450²/384×100000×19531 = 2 cm,
where J = bh³/12 = 15×25³/12 = 19531 cmˆ4
Condition met 2 cm< 2,25 см, прогиб прогона получился меньше нормативно допустимого. Сечение первого прогона определили, будет применен брус размерами 150×250 мм. Если бы расчетный прогиб получился больше нормативного, то нужно увеличить сечение (better height) run.
5. Find the load acting on the second run.
From the calculated uniformly distributed for the first limit state it will be equal to: qр = Qр×b = 317×3 = 951 kg/m;
for the second limit state qн = Qн×a = 242×3 = 726 kg/m = 7.26 kg/cm
At the point of connection of the purlins, a concentrated force P will be applied from the action of the first purlin to the second purlin (formula for):
according to the first limit state Рр=RB = qр b/2 - M2/b = 951×3/2 + 1872/3 = 2051 kg
according to the second limit state Рн=RB = qн b/2 - Mн/b = 726×3/2 + 1429/3 = 1566 kg,
where Мн = qн(L³1 + L³2)/8L = 726(4.5³ + 3³)/8×7.5 = 1429 kg×m
6. First, we need to determine by what formula we will calculate the maximum bending moment on the second run; to do this, we find the ratios of forces P/qрL and lengths of application of force c/b (see):
Рр/qрL = 2051/951×7.5 =0.29; c/b = 4.5/3 = 1.5
c/b turned out to be greater than p/qрL, which means we calculate the maximum moment using the formula:
Mmax = ab(qрL + 2Pр)/2L = 4.5×3(951×7.5 + 2×2051)/2×7.5 =10112 kg×m
7. We arbitrarily set the width of the purlin, b = 20 cm, and using formula (3) we find the height of the purlin:
h = √¯6W/b = √¯(6×7778/20) = 48 cm,
where W=Mmax/Rbend = 1011200/130 = 7778 cm³
There are no beams of this height in the lumber assortment, so we decide to take two beams measuring 200×250 mm, lay them on top of each other, twist them with pins and sew them together with steel MZP plates or we will make a beam with wooden ties. This way we get a beam with a width of 200 and a height of 500 mm.
8. We check the composite beam for deflection using the formula. First we determine the standard deflection:
fnor = L/200 = 750/200 = 3.75 cm
Then the calculated one, in our case it is calculated as the sum of deflections from the application of a uniform load and a concentrated force to the beam:
f = 5qнL²L²/384EJ + PнbL²(1 - b²/L²)√¯(3(1- b³/L³)/27EJ) = 5×7.26×750²×750²/384×100000×208333 + 1566×300×750² (1 - 300²/750²)√¯(3(1 - 300³/750³)/27×100000×208333) = 1.4 + 0.7 = 2.1 cm,
where J = bh³/12 = 20×503/12 = 208333 cmˆ4
The calculated deflection was less than the standard 2.1 cm< 3,75 см, значит составная балка удовлетворяет нашим требованиям. Таким образом, первый прогон принимаем из цельного бруса 150×250, второй - составным, общей высотой 500, а шириной 200 мм.
The calculation clearly shows that by introducing an additional support under the intersection of the purlins, it would be possible to eliminate the concentrated force and reduce the cross-section of the second purlin, and, given the dimensions of the structure given in the example, make it equal to the first purlin.
An example of checking the support units of purlins for crushing.
We check the area of support of the purlins on the walls to ensure that irreversible collapse of the wood or destruction of the wall material does not occur. Let's assume that the walls of the gables are made of gas silicate D500. The compressive strength of gas silicate D500 is 25 kg/cm², the compressive strength of pine wood in supporting parts of structures at an angle of 90° to the fibers is 30 kg/cm². To prevent destruction of the wall material and irreversible collapse of the wood, the following conditions must be met:
N/F ≤ Rсж - for wall material;
N/Fcm ≤ Rc.90° - for wood
IN in this example It turned out that wood has greater strength than the wall material. We will make calculations to prevent destruction of the wall material, i.e. compression stress should not exceed 25 kg/cm².
We find the pressure value of the first purlin on the walls (formulas for , load qр on the example page for calculating a purlin):
RA = qр а/2 - M2/а = 951×4.5/2 +1872/4.5 = 2556 kg
RС = qр L/2 + M2L/аb = 951×7.5/2 - 1872×7.5/4.5×3 = 2526 kg
We calculate the supporting area of the ends of the first run:
F=N/Rсж = 2556/25 =103 cm
where N = 2556 kg (the greatest of the forces pressing on the wall), and Rcom = 25 kg/cm².
It turns out that to support a purlin with a width of 15 cm, you need a “hook” on the wall equal to only 103/15 = 7 cm, and in this case irreversible collapse of the wood and destruction of the gas silicate blocks of the wall will not occur. Therefore, we will take the length of support of the purlin on the wall constructively, for example, equal to 15 cm.
Find the amount of pressure on the walls of the second run:
RD = qр L/2 + bPр/L =951×7.5/2 +4.5×2051/7.5 =4797 kg
RE = qр L/2 + aPр/L =951×7.5/2 +3×2051/7.5 =4387 kg
We calculate the supporting area of the ends of the second run:
F=N/Rсж = 4797/25 =192 cm,
where N=4797 kg (the greatest force pressing on the wall).
To support the second purlin with a width of 20 cm, you need a “hook” on the wall of at least 192/20 = 10 cm. And here we will take the length of support of the purlin on the wall to be constructively equal to 15 cm.
At the heart of every roof is a large number of beams, rafters, posts and purlins, which are collectively called the rafter system. Behind 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. Read more about what a rafter system can be gable roof and how the rafters and other elements of the system should be attached, let’s talk in more detail.
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 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. A lining is used to connect the walls and rafters - 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 interior wall up. 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 systems 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, the 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 turns out to be 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 “creep” 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. 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 depending on wooden houses, and the foundations are 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 on the image). 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.
Calculation of ridge beams and purlin dimensions. If you follow the wording, then a run is load-bearing beam, which rests on the wall at both ends. In most cases, the ridge rests on two pediments, but sometimes this formulation does not entirely correspond to reality. So, in hip roofs the ridge does not rest on the walls. The simplest option is a beam laid on the gables without the use of supports. In any case, it is necessary to correctly determine the cross-section of the ridge girder.
The nuances of choosing and laying a purlin
To calculate the cross-section of the ridge girder, it is necessary to sum up the loads from half the roof, or rather, from its horizontal projection. The dimensions of the run depend on its length and the dimensions of the building. In a large building, the purlin will be so powerful and heavy that installation will require the use of crane. However, find an even solid timber a length of more than 6 meters is very difficult, so to make such a ridge it is better to take an ordinary log or a laminated beam.
In this case, the ends of the ridge element, which will rest on the wall and are actually walled up in it, must be treated with antiseptics and wrapped in roofing felt or roofing felt to protect it from rotting. If an all-wood beam is used, then its end must be cut at an angle of 60 degrees and left open, that is, this end should not come into contact with the wall material. This measure is needed in order to increase the area of the end, which will improve moisture exchange in the wood.
If the ridge girder will pass through the entire wall, then that part of it that is in contact with the wall should also be treated with an antiseptic and wrapped with rolled material. Such an overhang of the ridge outside the wall allows you to form an unloading console. If in the middle of the ridge the load from the roof tries to bend the beam down, then on the consoles the pressing force promotes deflection in the opposite direction, thereby reducing the deflection of the purlin in the middle part.
Important: even if the cross-section of a long solid wood purlin is chosen correctly and it is suitable for deflection strength, the beam can bend under its own weight. Therefore, instead of such a long wooden ridge, it is better to use a construction truss.
Section calculation
To select the cross-section of a ridge beam, it is necessary to carry out a calculation based on two indicators:
- for deflection;
- and calculate the fracture strength.
- First, you need to determine the internal stress that occurs in the beam when bending under the influence of an external load. This value should not be greater than the calculated bending resistance of the material, which can be found in the table or in SNiP number II-25-80. We find the internal stress using the formula: Σ = M:W, where:
- Σ is the desired value, which is determined in kg per cm²;
- M – maximum bending moment (kg X m);
- W is the moment of resistance to deflection at the selected rafter section (found by the formula bh²: 6).
- The deflection of the purlin must be compared with the normalized value, which is equal to L/200. He should not exceed it. The deflection of the beam is found by the formula f = 5qL³L:384EJ, where:
- J is the moment of inertia, which is determined by the formula bh³:12, where h and b are the dimensions of the purlin section;
- E – elastic modulus value (for wood coniferous species it is equal to 100 thousand kg/cm²).
First you need to calculate the bending moment. If there are several of them on the beam diagram, then after the calculation the largest one is selected. Next, to determine the dimensions of the beam section, we can arbitrarily set the beam width parameter and then determine its required height using the formula: h = √¯(6W:b), where:
- b is the beam width we set in cm;
- W is the bending resistance of the run, the value is determined by the formula: W = M/130, where M is the largest bending moment.
You can do the opposite, set an arbitrary width of the purlin and calculate its height using the formula b = 6W:h². After you calculate the dimensions of the purlin section, it must be checked for deflection using the formula from point 2.
Attention! It is better to include a small margin of safety in the calculated deflection value.
When the ridge beam is designed for deflection, it is necessary to compare this value with the value L:200. If the deflection in the longest section does not exceed this value, then the section of the beam is left as it turned out. Otherwise, it is necessary to increase the height of the run or use additional supports from below. In the latter case, the resulting section must be double-checked by again performing the calculation taking into account the supports used.
The resulting values for the width and height of the ridge must be rounded up. In principle, this calculation is not difficult to perform. The most important thing is to indicate the values in the required units of measurement, that is, do not get confused when converting meters to centimeters and back.