The main parameters of the drawing of the truss system for the hip roof. Do-it-yourself hip roof drawings: step-by-step process and photo Complex hip roof truss system
Country plots are not large. Therefore, many build houses of small area and increase living space by creating additional living quarters in the attic. This is possible if the hip roof truss system is correctly installed.
Such a roof is made in the form of four slopes. Two of them are classic lateral ones in the form of a trapezoid, and two more are triangular at the ends of the roof. Unlike a hip roof, where all four slopes converge at one point, a hip roof has two peaks connected by a ridge.
Hip roof with four slopes
It is the side triangular gables, which are performed with a slope, and are called hips. gable roof also has triangular end gables, but they are located strictly vertically, at the hip roof these slopes are inclined, which is hallmark this type of roof.
Double pitched roof
A hip roof is called if the end slopes, starting from the ridge, reach the outer wall, that is, to the eaves. But there are options when the ramp is interrupted and in one place goes into a vertical plane. Then such a roof is called half-hip or Dutch.
According to the method of installation and use different material such roofs can be classified as complex structures. In general, the design of the hip roof consists of a Mauerlat, a ridge beam, rafters - angular, short and intermediate.
Mauerlat is wooden beam, mounted around the entire perimeter of the house at the very top of the walls. It serves for the correct transfer and distribution of loads exerted by wind, snow cover, the weight of the roof and itself on the load-bearing walls of the building. This element is a connecting upper trim for walls made of piece materials - brick, concrete blocks.
Mauerlat hip roof
For walls made of logs or timber, the Mauerlat is not suitable. Its role is performed by the upper crowns of the log house.
The ridge beam is the main element of the truss system, which connects all the roof slopes into a single structure. It must be of the same section with the rafter legs. Otherwise, in the future, a distortion of the entire roof structure and roofs in general.
Corner rafters, otherwise called slanted or diagonal rafters, are the basic power parts that connect the corners of the building box with the ridge beam. For their manufacture, you will need a board equal in thickness to a ridge beam. At one end it is attached to the ridge, the other rests on the Mauerlat. Depending on the roof project, a different number of such rafters is used, but not less than four.
Corner rafters hip roof
Short rafters can be of different lengths, but when assembling the roof structure, they are all displayed at the same angle and are parallel to the intermediate rafters. When the necessary calculation of their number is made, first of all, the area of \u200b\u200bthe entire roof is taken into account. At one end, the short rafter legs are connected to the corner rafter, and at the other they rest on outer wall building.
The central rafters are installed with the upper end on the ridge beam, the lower end rests on the load-bearing walls of the house. As a rule, their calculation is as follows: three on one side of the roof and the same number on the other, but when designing truss systems for large houses, an increase in their number is allowed.
Intermediate rafters are elements that are mounted on a ridge on one side and rest on a Mauerlat on the other. They are usually not used on hip slopes, since the entire area is covered with short rafters. The calculation of the cross section and the number of intermediate elements is based on the bearing capacity of the truss structure and the type roofing material.
At large sizes the building will require the installation of additional reinforcing elements in the form of struts and vertical posts supporting the ridge beam, and trussed structures to prevent sagging of the diagonal rafters.
Rafter systems in these types of roofs are carried out in various options. For example, if the hip slope does not reach the ridge, as a result of which a vertical small triangular pediment is formed at the top, then such a roof is called Dutch.
Dutch hip roof
Hip roofs also stand out. They have all four slopes of the same shape, and there are simply no side gables in such designs. Hips in this embodiment are triangular surfaces, the slope of which is made at the same angle with other slopes. As a rule, such systems are used for buildings that have a square-shaped area in the projection. In the group of hip roofs there are semi-hip mansard roofs, four-slope, gable, multi-gable and gable.
Hip roof
In addition, there are broken roofs, consisting of slopes of various sizes, the angle of inclination of which is different. Such structures are very complex in design, and it is also difficult to calculate them. Therefore, they are not common, but it should be noted that they have a very attractive appearance. You can evaluate the effectiveness of roofs with a broken structure of the truss system in the video, which also talks about the features of their construction.
The device of hip truss systems begins with the development of their project. A correct and competent project will allow you to assemble the roof in a short time. The optimal choice of the angle of inclination of the slopes is determined depending on the climatic conditions:
- In a region where windy weather prevails, the angle of inclination should be smaller, this will reduce the wind load on the roof.
- During snowier winters, the angle of inclination of the slopes, on the contrary, is increased so that ice and snow do not accumulate on the roof.
Hip truss system project
When choosing the angle of inclination of the rafters, accordingly, the calculation of the required amount of material is also carried out. And if for the lathing in almost all cases the calculation is made based on the total area of \u200b\u200bthe roof, then the number and cross section of angular and short rafters are calculated separately, depending on the type of roof chosen.
In addition to the climatic features of the region, when choosing the angle of inclination, the type of roofing material is taken into account:
- If type-setting material is used, for example, slate or metal tiles, then in order not to increase the load on the rafters, it is better to make the angle at least 22 °.
- When using roll coatings, the number of layers is taken into account. The more of them, the less you can make the slope of the slopes.
- The device of a larger angle of inclination of the slopes allows the use of roofing material - corrugated board, but the height of the profile is taken into account. The angle of inclination in this case can vary in the range from 20 to 45 degrees.
The choice of the angle of inclination of the roof according to the material
The correct calculation of the angle of inclination of the roof begins with the determination of the end axis of the building on the upper trim. After that, it is necessary to mark the middle of the ridge beam, at this point the central rafter leg will be located. Then it is necessary to determine the location of the next intermediate rafter, for which the distance corresponding to the calculation of the distribution of intermediate rafter legs is measured. In most cases, it does not exceed 70–90 cm.
The length of the rafters is determined so that their lower end protrudes 40–50 cm above the outer wall, and the upper end rests on the ridge beam.
A similar calculation is carried out on all four sides of the roof to calculate the location of the intermediate rafter legs on the ridge beam. An example of their correct location is shown in the photo.
When designing hip roofs, two types of rafters can be used - hanging and layered. Hanging ones rest only on the walls of the building, transferring all spacer loads to the Mauerlat. If an attic device is planned, then additional installation of metal or wood screeds will be required, which are laid on the load-bearing walls of the building and subsequently serve as the basis for the floor device. The photo shows how mansard hip roofs with a hanging truss system are arranged.
Mansard hip roof with hanging truss system
Rafter rafters are used if they have support in the form of columns or internal bearing walls. When designing the system, alternation of two types of rafters is allowed. Where internal walls they play the role of supports, they are attached to the layers, and in other places they are hanging.
The fastening of the rafters is mainly carried out by means of sawing (saddles). But their depth cannot exceed a quarter of the width of the rafter board. In order for the wash to be the same on all legs, you need to make a template. In addition, the elements of the truss system are attached using metal corners, self-tapping screws, nails. Fastening can also be done with brackets, bolts and studs.
Fastening the elements of the hip roof truss system
When installing the Mauerlat, do not forget to lay a layer of waterproofing along the top of the walls. If the walls are made of brick, then in back rows masonry, embedded parts are installed for further fastening of the Mauerlat. Such fasteners can be made in the form of vertical studs or bolts, installed in increments of no more than one and a half meters.
Hip roofs are complex structures, but this does not in the least reduce their popularity. Despite the complexity of the construction, they make it possible to arrange additional living quarters in the attic space, and if you carry out high-quality work, you can also use it in winter time.
The most important structure of the house, which affects the entire structure as a whole, is its roof. The basic design features of a roof depend on many factors, such as the maximum permissible load on walls, type of construction, type of roofing material, etc. Hip roof rafter system which is not quite simple, is nevertheless a fairly popular design during construction. Its main advantage is considered to be its excellent self-cleaning ability, as well as good resistance to heavy snow and wind loads.
Design features of the hip roof
The hip roof has found wide application in construction due to its durable design feature, durability and sufficient original design having a beautiful appearance.
The roof structure allows you to equip a spacious living attic floor with magnificent cut-in windows, and the streamlined shape reduces aerodynamic loads from strong winds.
The truss system of the hip roof consists of four slopes: two of which are lateral (having the shape of a trapezoid), and two more are hip (in the form of triangles). Thus, the structure has two vertices, united by a ridge run.
Main structural units
- Skate run- the main bearing axis in the upper part of the roof, which is the junction of all four slopes. Executed from edged board 50x200 mm.
- Diagonal (sloping rafters)- an important load-bearing element of the frame, connecting the corners of the house with the horse run. It is carried out from the same board as the ridge run.
- Side roof rafters- made from a board 50x200 mm. It is attached to the ridge run and the side walls of the building or the Mauerlat. Their main task is to evenly distribute the lateral load on the load-bearing walls.
- Shortened rafters (spiders)- a board sawn at a certain angle, which is attached to the diagonal rafters and the hip part of the wall of the house or Mauerlat. Thus, there is no connection between the sprigs and the horse run.
It is important to follow the basic rules for linking structural units; the reliability and strength of the entire structure will depend on the quality of their fastening. To do this, use only high-quality lumber and "ruffed" nails.
Scheme of connection of the main components of the structure
Types of hip roofs
There are quite a lot of options for the execution of hip roofs, in addition to the standard one, there are also: (half-hip Dutch and Danish, hipped roofs, as well as broken roofs).
- If, for example, the length of the hip roof slope is less than the side ones, such a design is called half-hip (Dutch). Such a design with dignity withstands strong blast loads, and thanks to sharp slopes, snow almost never lingers on it for a long time. This type is more similar to the classical one, however, in terms of its characteristics, it significantly exceeds it.
- The Danish half-hip roof is a little more difficult to implement. The design difference lies in the fact that the hip part is already located not from below, but from above, a vertical pediment, which can be replaced with a beautiful frame with glass.
- For buildings with walls of the same length (square), a hipped roof is perfect. Unlike the hip one, which has a ridge run, the hipped one does not have one. The design is as follows, four absolutely identical roof slopes converge at one top point. thus forming a pyramidal geometric figure.
- Broken roofs due to the complexity of the design are very rare. However, their appearance is so mesmerizing that long time you can't take your eyes off her. It represents itself, a set of many slopes, arranged at different angles relative to the walls. With your own hands, without having enough experience behind you, it is very problematic to make such a roof, so it is better to entrust this matter to professional roofers.
Do-it-yourself hip roof
Correct calculations are the key to the reliability and durability of any roof. Having drawn the design diagram correctly, you can easily assemble it yourself, while having 2-3 partners as an apprentice. It will not be necessary to resort to the help of a team of builders, it is enough to do everything according to the plan and adhere to the given calculations.
Tilt angle
When designing any roof, its angle of inclination is chosen based on climatic conditions, which in Russia are very different, depending on the region. If the building is being built in a region with heavy snowfall prevailing in winter, then it is desirable to make the angle of inclination large, so the snow cannot linger on the roof and will constantly slide off it under its own weight.
In the southern regions, where precipitation is quite rare, and only in the form of rain, but strong gusts of wind are not uncommon, roofs are erected with a slight slope. The main task of which is to resist these wind loads.
Also an important factor in calculating the slope is the type roofing. The fact is that some of them have a recommended corner height limit, which should not be neglected. And so, in order not to make mistakes, read each of them:
- Slate - Recommended Slope Angle 15º - 65º. Failure to comply with these parameters can lead to moisture ingress between the joints of the sheets;
- Ceramic tiles - the best sloped angle for slopes 35° - 65°. Neglecting the slope recommended by the manufacturer will lead to the possibility of condensation;
- Metal tiles - minimum slope for this material is 13°, the maximum is not set by manufacturers;
- Soft tiles - optimal size slope is considered not less 15º. Roof installation can be carried out at any other value of the angle above the minimum;
- Ondulin - any slope angle is not less than 5°, the step of the crate will directly depend on the size of the corner.
- Metal seam roofing - should be used when the slope of the slopes is over 25° degrees.
Correct area calculation
In order to correctly calculate total area surface of the hip roof, first we need to calculate the area of \u200b\u200beach slope separately, then add the resulting numbers together. As we remember, hip roof slopes are geometric figures two trapezoids and triangles. Remembering the school curriculum, it is easy to calculate their total area.
If you are still afraid to make a mistake, the specialists from whom you will purchase roofing material can correctly calculate, or you can use any of the online calculators that are convenient for you, which are full on the Internet.
Having accurately indicated all the parameters of the future roof, they will help to calculate everything with an accuracy of up to a square meter.
Calculation of the truss system
For an accurate calculation of the rafter system, you must use the table below of the relationship between length and their placement.
| Roof angle ratio | Correction factor for corner rafters | Correction factor for intermediate rafters |
| 3:12 | 1.016 | 1.031 |
| 4:12 | 1.027 | 1.054 |
| 5:12 | 1.043 | 1.083 |
| 6:12 | 1.061 | 1.118 |
| 7:12 | 1.082 | 1.158 |
| 8:1 2 | 1.106 | 1.202 |
| 9:1 2 | 1.131 | 1.250 |
| 10:12 | 1.161 | 1.302 |
| 11:12 | 1.192 | 1.357 |
| 12:12 | 1.225 | 1.414 |
Based on the above table, the length of the rafter leg is equal to its product of the coefficient and the projection. The use of the table will help to make all the necessary calculations as accurately as possible.
The calculation itself is carried out in the following sequence:
- Using a regular rail, find the laying (horizontal projection) of the intermediate rafter leg. Find your slope coefficient in the table and multiply by the presented coefficient;
- From the ridge run to the attachment point of the lower part of the stacking leg, we measure the length of the rafter;
- In the same way, multiplying the correction factor by the laying (horizontal projection), we find the length of the overhang of the rafters. Or you can use the Pythagorean theorem (see Fig. 1).
- Now find the length of the corner rafters. It will be easier to visualize this using the figure below.
Installation of rafters
Frame reinforcement
In order to give the structure greater rigidity, it must be strengthened with additional corner braces and vertical posts. Their required number is calculated based on the maximum load of the truss system. Weight includes: roofing cake and coatings, as well as the mass of snow and wind loads.
After the hip roof truss system is reinforced, you can safely proceed with the installation of the crate. Its step and design depends on the type of roofing material you choose. For example, under it should have a solid carpet.
Roofs hip design are gaining more and more popularity among homeowners. This is not surprising, since such a scheme is distinguished by a number of undeniable advantages of operational properties, and besides, it looks very original, giving the house a special aesthetic.
Some DIY homeowners may be put off by the fact that the hip roof truss system looks too complicated. Yes, it is certainly not as simple as a conventional gable gable roof. Nevertheless, this rafter system is also completely subject to the laws of geometry, and it is quite possible to make its preliminary calculation. Installation, of course, will require some experience in carpentry, but with good helpers, and even better with a qualified consultant, you can take on this large-scale undertaking.
What are the advantages of a hip roof?
The hip roof is one of the varieties of four-pitched roof structures. In terms of the complexity of the arrangement, hip roofs are superior to classic and gable roofs - it is not very easy to place four slopes on the house, exactly coordinated with each other and joined at the same angles. But with a strong desire, even the most difficult activities become clear and simple. Check out the guide and get started.
The hipped roof system has a number of distinctive features. So, the hip roof includes a pair of long slopes with a pronounced trapezoidal shape, as well as a pair of short slopes made in the form of inclined triangles.
The main difficulties in the arrangement of a traditional hip roof arise at the stage of erection of a truss structure, consisting simultaneously of sloping, ordinary and outdoor rafters.
Hip roofs perfectly withstand wind loads and generally have high performance characteristics. In order for the finished roof to serve as long and efficiently as possible, at the design stage it is necessary to solve a number of important issues, namely:
- choose the best material for the arrangement roof structure;
- determine the intensity of precipitation typical for the region of construction;
- set the average and maximum wind loads.
Based on the figures above, you can calculate optimal values angles of inclination of the slopes and the height of the roof structure.
To perform calculations and draw up a project, you can contact a specialist or find a suitable project in one of the many open sources. If you have the proper skills, you can handle the above activities with your own hands.
The roof in question, as already noted, has a very interesting design. And if large slopes can be seen on almost all roofs, then short slopes make the system in question truly unique.
The design of the roofing system is such that the slopes do not overlap the area of the house along the length and the remaining free space is filled with two short hips.
When drawing up a diagram of a hip roof structure on your own, you will need to use a marking rail and Pythagorean tables.
It is important that the roof project is as accurate as possible - this is the only way you can make the correct cuts from the rafters yourself and install all the components of the system yourself.
What do you need to know before getting started?
In order for the system to fully comply with all the requirements put forward, remember the following recommendations:
- the intermediate components of the hip roof truss system are steeper when compared with the corner parts, therefore, the boards used to equip the intermediate elements must have a size of at least 5x15 cm;
- fastening of short elements is carried out to the corner truss components, and not to the ridge board. Intermediate boards must be fixed with the same slope as the short bars;
- the ridge roof system and truss elements must be made from the same material;
- intermediate rafter legs are fixed along the edges of the ridge board. They must simultaneously dock with the upper end of the harness and with the ridge board;
- rafters and ridge beams must be of equal thickness. Only if this rule is observed, you can count on the reliability and strength of the roofing system. If any rafters are thinner, after a while the roof frame will deform and the integrity of the system will be seriously compromised;
- hip roofing system can be of almost any height. However, when arranging a too low roof, it is necessary to use additional supports;
- to ensure the longest possible life of the hip roof, it is necessary to use carefully dried and high-quality timber for its arrangement conifers. Before assembling the structure, all wooden components must be treated with antiseptic impregnation.
Hip roof construction guide
Proceed to the arrangement of the roof. Start by creating the layout of the building object.
markup
Competently executed markup, correct drawing and the most reliable calculations - these are the three fundamental factors for successful construction. Carry out the markup in accordance with the drawings. Stick to the following sequence.
First step. Mark the axis along the highest trim on the end side of the building;
Second step. Calculate 50% of the thickness of the ridge and set the location of the first element of the rafter system.
Third step. Attach one end of the measuring stick to the previously marked line. Place the other end along the line of the side wall. So you set the placement point for the intermediate rafter element.
Fourth step. Determine the length of the rafter overhang. To do this, place the beam with one edge on outer corner walls, and the other install it on the roof overhang.
Fifth step. Calculate the next component of the center rafters. Move the rail to the edge of the side wall and mark the place where the rafters are attached. The element will be located between the upper roof trim and the side wall.
Repeat for the remaining three corners. So you will find out where the intermediate rafter legs and ends of the ridge will be installed in the future.
Calculation
First step. Take the marking rail and determine the value of the horizontal projection of the intermediate rafter element. In accordance with the standardized documentation, find the appropriate roof slope for your situation and multiply the determined values.
Second step. Measure the length of the rafter. Do this from the selection at the roof ridge to the selection at the place where the support is fixed. Measure along the bottom line.
Third step. Determine the length of the overhang in the same way. To do this, multiply the value of the horizontal projection by the appropriate correction factor. You can use the position of the Pythagorean theorem, known since school days: c2=a2+b2. In the situation under consideration, a is a vertical projection, and b, respectively, a horizontal projection.
Fourth step. Proceed to the calculations of the corner components. On one side of the rafter legs there are oblique cuts, due to which reliable fixation of the elements to the roof ridge is ensured. Directly at the ridge there is an undercut with a special double bevel used for attaching corner components.
Corner rafter legs are calculated in the following order:
- from any corner of the house, the length of the truss element is measured;
- a projection is set equal to the squares of the length of the projections of the used central rafter legs, multiplied by each other;
- the resulting value is multiplied by a correction factor, which allows you to determine the length of the corner rafter leg.
Rafter installation
First step. Proceed with the installation of vertical racks, due to which the ridge beam will be supported. Fasten the elements to the central beam using the sloping system.
Second step. Install diagonal rafters. All elements must be the same length. In the case of roof overhangs, the figure will vary from 500 to 700 mm. Pay special attention to the correct joining of the hip, diagonal rafters and ridge.
Third step. Install the rafters, and then the ordinary rafters with a step of about 600 mm. Attach ordinary rafters to the Mauerlat and ridge beam using the cutting method. To strengthen the fixation, use crossbars and ties.
It is important that ordinary rafters do not come into contact with the studs, due to which the Mauerlat is fastened to the walls of the house.
Fourth step. Attach sprigs to each side of the diagonal planks, due to which the rafters will be connected to the Mauerlat.
Both ordinary truss elements and sprigs must be mounted strictly perpendicular to the ridge.
Strengthening the roof structure
When choosing a method of strengthening the rafters, be guided, first of all, by the size of the building. Among the most popular methods of amplification, the following options should be distinguished:
- at the corners of the roof, trusses are fixed with a special stand that acts as a support for the diagonal rafter element. Sprengel in this situation is a bar that you need to throw between the two angular arms of the supporting Mauerlat. If the installation of the truss has to be carried out at a great distance from the mentioned corner, professionals recommend installing a reliable truss truss;
- on reinforced concrete floor or the racks are stuffed by tightening. They will perform the function of the so-called. "Shelves" supporting the truss elements in the middle;
- if the diagonal rafters are too long, double beams should be used instead of one beam.
Ventilation
For the device of the required level of ventilation of the under-roof space, make a hole in the windproof film for air inlet. It must be placed on top, closer to the roof ridge.
If the wind filing is made of wood, it is enough just to fix the boards with a gap of 2-3 mm. In the event that for the manufacture of filings are used plastic products, the elements must first be perforated.
If the wind sheeting of the roof is already assembled, you can mount ordinary ventilation grilles into it. The standard diameter of such gratings is 50 mm. The mesh of the product can have any color. Lattices are placed along the entire length of the windshield with a step of about 800 mm.
In conclusion, you just have to lay the insulation, equip the waterproofing layer, fill the boards of the crate and mount the selected finish.
Now you know the main features and the procedure for self-arranging a hip roof. The work can hardly be called too easy, but using the knowledge gained in practice, you can cope with the implementation of all related activities with your own hands.
Successful work!
Video - Do-it-yourself hip roof
Hip roofs have many advantages. They are beautiful, reliable in all weather conditions, the four-sided design allows you to effectively insulate the house from the side of the roof. Some difficulty is the device of the truss system. We will deal with its schemes and calculations in this article.
Hip roofs, sometimes called Dutch and Danish, are distinguished by good quality, reliability and spectacular European design. The truss base of such roofs consists of many basic and reinforcing elements that require drawings or three-dimensional drawings, accurate calculations and execution.
Hip roof varieties
Hip roofs, in addition to the basic classical design, consisting of two trapezoidal slopes and two triangular end hips, also include their varieties:
- Half hip double slope.
- Semi-hip four-slope.
- Shatrovaya.
- Hip-pediment.
Each variety has its own scheme of the truss system. Next, we consider and calculate the classic hip roof.
Scheme and main elements
To perform the calculation of the truss system, you need to familiarize yourself with its basic scheme, the main and auxiliary elements.
The main elements of the truss system
The main elements include (see the figure below):
- Mauerlat. It is a beam fixed along the perimeter of the outer walls, indented from the outer edge. Attaches to the wall. Mauerlat disperses the load from the pressure of the rafters, connects the truss system with the walls of the house, and is the basis of the roof.
- Skate. Upper crossbar for fastening the rafters of the roof slopes. The height of the ridge depends on the angle of inclination of the slopes. Gives the system rigidity and strength.
- The central rafters of the slopes. The ends of the ridge are supported on the sides of the Mauerlat. There are 4 such elements in the system. - 2 pcs. on every slope.
- The central rafters of the hips. The ends of the ridge are supported on the end sides of the Mauerlat. There are 2 such elements in the system. - 1 pc. on every hip.
- Skew legs (diagonal, corner rafters). Connect the corners of the Mauerlat with the ends of the ridge. They are part of the supporting structure. There are 4 of them in the rafter system.
- Intermediate rafters of slopes. They are installed parallel to the central rafters of the slope between them with the same pitch, relying on the side of the Mauerlat and the ridge beam. If the length of the ridge is insignificant, they may not be used.
- Shortened rafters of slopes. They are installed parallel to the central rafters of the slopes and have a variable length - the closer to the corner, the shorter. They rely on the side of the Mauerlat and slanted legs. The number of elements depends on the installation step.
- Shortened hip rafters or sprigs. They are installed parallel to the central rafters of the hips and have a variable length - the closer to the corner, the shorter. They rely on the end part of the Mauerlat and oblique legs. The number of elements depends on the installation step.
Scheme and main elements of the truss system
You can read more about attaching rafters to the Mauerlat in our article.
The above elements are basic, basic. Other elements are designed to reinforce the main ones and are used in critical buildings, for example, for residential buildings:
- Vertical racks for supporting the ridge beam. They rely on crossbars (see below), laid parallel to the end of the house or a bed located along the longitudinal axis of the building (if there is a main wall under it).
- Crossbars or puffs. The rafter legs of the slopes are connected in pairs. They serve as a support for racks and diagonal struts (see below). They can serve as floor beams if they are built into the Mauerlat or installed directly into the longitudinal walls of the house. If the puffs are placed closer to the ridge, they will become the basis of the attic ceiling.
- Diagonal braces (braces). They are used to increase the rigidity of the system if the length of the rafters is more than 4.5 m. The use of struts allows you to reduce the cross section of the rafters, which they reinforce.
- Sprengel. Beam installed in the corners of the Mauerlat. Serves for mounting a stand that supports and reinforces the oblique leg.
- Wind beam. Serves to resist deformation of the rafter legs during gusty, strong winds. It is attached to the rafters of the slopes from the inside, obliquely, on one or both sides - it depends on the wind load in the construction area.
- filly. An element of a smaller section than the rafters themselves. Extends the leg of the rafters to provide a roof overhang when a single piece is not available due to limited lumber length or for cost reasons.
Gain elements
Calculation of the truss system
The calculation of the system includes the choice of the angle of inclination of the slopes and hips and the calculation of the lengths of its main and auxiliary elements.
The choice of the angle of inclination of the longitudinal and end slopes
The choice of the angle of the slopes and hips ranges from 25-45 ° and depends on the desire to have an attic, the roofing material adopted, the assessment of static (roof weight) and dynamic (wind, snow) loads.
In hipped roofs, the angle of inclination of the hips and slopes is the same. In hip roofs, the same angles are also often taken in terms of aesthetics, but they may differ if this is the architect's idea.
Recommendations for the use of roofing materials
For a better understanding of the calculation algorithm, consider as an example a hip roof of a house with sides of 8 and 12 m, and a ridge height of 2.5 m. Let's take the angle of inclination of the slopes at 35 °, and the angle of inclination of the hips - 45 °.
Calculation of the main truss elements
The classic hip roof consists of two slopes in the form of trapezoids connected in a ridge, and two hips - end slopes in the form of triangles.
First you need to remember some formulas from the school algebra curriculum. This is the ratio of the lengths of the sides of a right triangle, expressed in terms of the trigonometric function of the angle and the Pythagorean theorem.
Trigonometric functions of an acute angle of a right triangle
Let's depict the frame of the truss system in an axonometric view:
Let's calculate the main elements of the truss system.
1. Calculate the length of the central hip rafter CD, which is the height of an isosceles triangle (hip) and the hypotenuse of a right triangle whose height is equal to the height of the ridge (CE = 2.5 m). Angle of inclination of the hip α = 45°. Sin 45° = 0.71 (according to the Bradis table).
According to the trigonometric relation:
- CD = CE / sin α = 2.5 / 0.71 = 3.52 m
2. Determine the length of the skate K. To do this, from the previous triangle we find the length of the base ED, using the Pythagorean theorem:
House length: BL = 12 m.
Skate length:
- CF \u003d 12 - 2.478 x 2 \u003d 7.044 m
3. The length of the corner rafters CA can also be obtained from the Pythagorean theorem for triangle ACD. Half the width of the house AD = 8 / 2 = 4 m, CD = 3.52 m:
4. The length of the central rafters of the slope GF is the hypotenuse of the triangle, the legs of which are the height of the ridge H (CE) and half the width of the house AD:
The intermediate rafters of the slopes have the same length. Their number depends on the pitch and section of the beams and is determined by calculating the total load, including weather.
These tables correspond to the atmospheric loads of the Moscow region
| Rafter pitch, cm | Rafter length, m | ||||||
| 3,0 | 3,5 | 4,0 | 4,5 | 5,0 | 5,5 | 6,0 | |
| 215 | 100x150 | 100x175 | 100x200 | 100x200 | 100x250 | 100x250 | — |
| 175 | 75x150 | 75x200 | 75x200 | 100x200 | 100x200 | 100x200 | 100x250 |
| 140 | 75x125 | 75x125 | 75x200 | 75x200 | 75x200 | 100x200 | 100x200 |
| 110 | 75x150 | 75x150 | 75x175 | 75x175 | 75x200 | 75x200 | 100x200 |
| 90 | 50x150 | 50x175 | 50x200 | 75x175 | 75x175 | 75x200 | 75x200 |
| 60 | 40x150 | 40x175 | 50x150 | 50x150 | 50x175 | 50x200 | 50x200 |
Let's compare the maximum, average and minimum section of a beam with a length of 4.717 m (see the values for 5.0 m).
At section 100x250 mm the step will be 215 cm. With a ridge length of 7.044 m, the number of intermediate rafters will be: 7.044 / 2.15 = 3.28 segments. We round up - up to 4. The number of intermediate rafters of one slope - 3 pcs.
- 0.1 0.25 4.717 3 2 = 0.708 m 3
At section 75x200 mm the step will be 140 cm. With a ridge length of 7.044 m, the number of intermediate rafters will be: 7.044 / 1.4 = 5.03 segments. The number of intermediate rafters of one slope - 4 pcs.
The volume of lumber for both slopes:
- 0.075 0.2 4.717 4 2 = 0.566 m 3
At section 50x175 mm the step will be 60 cm. With a ridge length of 7.044 m, the number of intermediate rafters will be: 7.044 / 0.6 = 11.74 segments. We round up - up to 12. The number of intermediate rafters of one slope - 11 pcs.
The volume of lumber for both slopes:
- 0.05 0.175 4.717 11 2 = 0.908 m 3
Therefore, for our geometry, the optimal option from the point of view of economics would be a section of 75x200 mm with a step of 1.4 m.
5. To calculate the lengths of the shortened slope rafters MN, you again have to remember the school curriculum, namely the triangle similarity rule.
Similar triangles on three sides
The large triangle that we need to reinforce with shortened rafters has known dimensions: GF = 4.717 m, ED = 2.478 m.
If the shortened rafters are installed with the same step as the intermediate ones, their number will be 1 in each corner:
- 2.478 m / 1.4 m = 1.77 pcs.
That is, two segments are formed with one shortened rafter in the middle. A small triangle will have a leg, 2 times smaller than ED:
- BN = 2.478 / 2 = 1.239 m
We compose the proportion of similar triangles:
Based on this ratio:
At this height, the cross section of the rafters is taken according to the table - 75x125 mm. The total number of shortened rafters of both slopes is 4 pcs.
6. Determining the length of shortened hip rafters (spreaders) is also performed from the ratio of similar triangles. Since the length of the central hip rafters CD = 3.52 m, the step between the shortened rafters may be greater. With AD \u003d 4 m, shortened rafters with a step of 2 m will be one on each side of the central hip rafter:
- (2 3.52) / 4 = 1.76 m
With such a height, we take the rafter section 75x125 mm. The total number of shortened rafters of both hips is 4 pcs.
Attention! In our calculations, we did not take into account the overhang.
Calculation of the roofing area
This calculation comes down to determining the areas of a trapezoid (slope) and a triangle (hip).
Let's do the calculation for our example.
1. The area of one hip with CD = 3.52 m and AB = 8.0 m, taking into account the overhang of 0.5 m:
- S \u003d ((3.52 + 0.5) (8 + 2 0.5)) / 2 \u003d 18.09 m 2
2. The area of one slope at BL = 12 m, CF = 7.044 m, ED = 2.478 m, taking into account overhangs:
- S \u003d (2.478 + 0.5) ((12.0 + 2 0.5) + 7.044) / 2 \u003d 29.85 m 2
Total roofing area:
- S Σ \u003d (18.09 + 29.85) 2 \u003d 95.88 m 2
Advice! When buying material, consider cutting and inevitable losses. The material produced by large area elements is not the best option for hip roofs.