In private housing construction, in addition to common gable roofs more durable and rigid four-slope structures are often used. They are distinguished by the absence of pediments, which replace the triangular slopes that cut off the ends of the ridge ridge. This configuration makes four-pitched roofs very attractive and economical, despite the fact that during their construction the length of the eaves overhangs increases, the number downpipes and gutters. Therefore, they deserve the closest attention.
Varieties of truss systems for hipped roofs
The device of the truss system depends on the shape of the four pitched roof. The following configurations are the most common today.
- Hip structure. All four slopes occupy the area from the ridge to the cornice overhang, while two side slopes are trapezoid in shape, and two end slopes (hips) are triangular. A feature of the truss hip frame is the presence of two pairs of diagonally installed layered rafters that extend from the edge of the ridge and serve as supports for sprenels and sprengels.
The hip four-slope design is characterized by the fact that the slopes occupy the entire area of the roof - from the ridge to the cornices
- Dutch half hip. A device with truncated end slopes that do not reach the eaves. As a rule, they are 2-3 times smaller than trapezoidal ones. The advantage of this four-slope roof structure is the possibility of installation at the ends of the house normal window, as well as the absence of a typical gable roofs a sharp protrusion, which greatly increases the wind resistance of the structure.
The Dutch half-hipped roof has truncated triangular slopes and part of the gable into which a conventional vertical window can be installed.
- Danish half hip. It is characterized by the presence in the triangular slopes of the pediment at the ridge, which allows for full natural lighting of the under-roof space without installing skylights.
- Tent construction. It is installed on houses with a square frame. All four slopes of a hipped roof are the same isosceles triangles connected at one point. When building such a roof, an important aspect is the observance of symmetry.
The structure of the four-slope truss system depends on the chosen roof configuration
Features of the supporting frame of the hipped roof
We note right away that the truss system of a four-pitched roof will be more complex than traditional gable roof structures for two reasons.
- Due to the increase in the number of inclined planes and their docking with each other. At its core, the connection of the slopes is the intersection lines running at a certain angle to the horizon. The joints that form an angle protruding above the surface of the slopes are called roof ribs. From them, water flows down the slopes and accumulates in the grooves (valleys) - the lines of intersection with the inner corner. If all planes have the same slope, then the ribs and valleys divide the base angle at the junction of adjacent slopes in two and create a slope of 45 ° to the perimeter of the building.
Four-pitched truss systems are distinguished by the absence of full gables, instead of which there are two triangular end slopes, as well as the presence of two lateral trapezoidal inclined planes, grooves and ribs
- Due to the fact that the runs in the four-slope structure form a closed loop, where the hip (diagonal) rafter legs are located along the lines of the ribs and valleys. They are longer than ordinary beams, which are installed longitudinally to the slopes at a distance between intersections. hip rafters in the top harness. But between the lower parts of the diagonal legs, short rafters, called sprigs, are mounted. A distinctive feature of the four-pitched roof frame is the presence of sprengels - wooden struts under the hip rafters.
Support runs in four-slope structures have a closed contour, where diagonal rafter legs are located along the lines of valleys and ribs
The main structural elements of the truss system of a hipped roof are:
Thus, the number of elements of the truss system of a four-pitched roof is much greater than, for example, gable design, and this, of course, increases the cost of its construction. However, in general, as we noted above, the arrangement of a four-pitched roof will cost a little more due to savings on laying a roofing pie, since there will be much less waste of insulating materials and covering flooring when cutting into a multi-pitched structure.
Despite the fact that the truss system of the four-slope structure is more complex and expensive, the construction of the entire roof is more profitable due to savings on the arrangement of the roofing pie.
In addition, the four-slope design:
Video: gable or four-pitched roof - what to choose
How to calculate the truss system of a four-pitched roof
The supporting structure of a four-pitched roof can be layered if the building has solid internal walls, or hanging when intermediate supports are not included in the building. With a hanging device, the rafters rest on the walls of the house and exert a bursting force on them. To relieve the load on the walls in such cases, a puff is mounted at the base of the rafter legs, connecting the rafters to each other.
The use of a layered structure makes the frame lighter and more economical due to the fact that less lumber is required for its arrangement. Because of this, the layered truss system is used much more often in the construction of multi-pitched roofs. But regardless of the type of rafters used, only correct calculation supporting frame and accurate marking will increase economical effect from the construction of a four-slope structure.
Marking and calculation of the supporting frame of a hipped roof
When calculating the truss system, you must adhere to the following rules.
To determine the installation location of the rafters and find their length, you will need a template.
Using a template will make measurements and calculations much easier. roof frame hipped roof
The length of the rafter leg can be determined by its laying (horizontal projection). For this, there is a special table of coefficients, presented below. The length of the rafter is determined by the size of its projection, multiplied by a coefficient corresponding to the slope of the slope.
Table: the ratio between the length and laying of the rafters
| Roof pitch | Coefficient for calculating the length of intermediate rafters | Coefficient for calculating the length of the corner rafters |
| 3:12 | 1,031 | 1,016 |
| 4:12 | 1,054 | 1,027 |
| 5:12 | 1,083 | 1,043 |
| 6:12 | 1,118 | 1,061 |
| 7:12 | 1,158 | 1,082 |
| 8:12 | 1,202 | 1,106 |
| 9:12 | 1,25 | 1,131 |
| 10:12 | 1,302 | 1,161 |
| 11:12 | 1,357 | 1,192 |
| 12:12 | 1,414 | 1,225 |
| Note: when erecting a roof frame for which there are no data in the table (for non-standard slopes of slopes), the parameters should be calculated using the Pythagorean theorem or a mathematical proportion should be used. | ||
Consider an example: a private house is being built in Yekaterinburg with a size of 7.5x12 m with a planned height hip roof from metal tiles 2.7 m.
- First of all, we draw a drawing or a sketch of the roof.
Before calculating the truss system, it is necessary to make a sketch of the building and apply all the initial data to it
- We find the angle of inclination of the slopes using the formula: the tangent of the angle of inclination is equal to the ratio of the height of the roof to half the length of the span, in our case, to half of the end side L = 7.5 / 2 = 3.75. Thus, tg α = 2.7 / 3.75 = 0.72. According to the reference tables, we determine: α = 36 °, which corresponds to the standards providing for a roof slope for metal tiles of at least 14 °, and the climatic conditions of Yekaterinburg.
The tangent of the angle of inclination of the slopes is determined by the well-known formula for calculating the sides right triangle as the ratio of the opposite leg to the adjacent
- We determine the position and edge of the ridge ridge, for which we apply the template at an angle of 36 ° in the middle top harness end (place of installation of the first central intermediate rafter) to a height of 2.7 m and design the outline on the sketch.
- We retreat ½ of the thickness of the ridge beam from the axial (key) line and set the end of the measuring rail at this point. At the other end of the rail, we make marks for the outer and inner contours of the side wall, as well as the overhang. We turn the rail to the side and from inner corner external strapping, we mark the laying of the intermediate rafter at the mark of the inner contour, thus determining the installation location of the second intermediate central rafter.
When arranging the truss frame of a four-pitched roof, the position of the central rafter legs is initially determined using a template and a measuring rail
- We carry out similar actions at all corners, determining the edges of the ridge ridge and the location of all central rafter legs.
- After planning the intermediate rafters, we determine their length from the table. In our example, the slope angle is 36°, its tangent is 0.72, which corresponds to a ratio of 8.64:12. There is no such value in the table, so we calculate the coefficient relative to the line with the parameter 8:12 - 8.64/ 8 = 1.08. Hence, the desired coefficient is 1.202 1.08 = 1.298.
- Multiplying the depth of the intermediate rafters by the calculated coefficient, we find their length. Let's take into account the laying depth of 3 m, then L str \u003d 3 1.298 \u003d 3.89 m.
The length of ordinary and central intermediate rafters depends on the angle of inclination of the roof and the depth of their laying
- Similarly, we determine the length of the diagonal rafters, having previously calculated the laying, equal to the distance from the angle of connection of the side and end slopes to the first intermediate central rafter. According to the initial data, the laying of the corner rafters is 7.5 / 2 = 3.75 m. Then the estimated length of the corner rafters will be 3.75 1.298 = 4.87 m.
Corner rafters differ from intermediate device undercuts with double bevel in the ridge area, deeper and longer undercuts for the bearing part
- We calculate the overhang according to the Pythagorean theorem according to the markings made, or simply add the desired size to the length of the rafters, for example, 0.6 m plus at least 0.3 m for arranging an external drain.
To calculate the length of the overhang, you need to multiply its placement by the coefficient for an intermediate or corner rafter, or add the planned length of the overhang and at least 0.3 m to the estimated length of the rafters to organize an external drainage system
- Having marked all the elements of the truss frame, we determine the length of the ridge ridge, which is equal to the difference in the length of the side and twice the value of laying the intermediate rafters: 12 - 2 3 = 6 m. It is at this distance that ordinary rafters will be installed. If you take a step of 1 m, then you need 5 ordinary rafters, equal in length to the central ones. In addition, at the site of laying the intermediate central rafters, having a length of 3 m, two short rafters will be installed from one and the other edge of the side.
- Since the short rafters (spreaders) are attached to the diagonal ones, it means that two rafters will also be installed on the end sides between the corner and central intermediate rafters on the left and right.
Let's summarize the preliminary result - for the truss frame of a four-pitched roof you will need:
- two pairs of hip (corner) rafters with a length of 4.87 + 0.6 + 0.3 = 5.77 m;
- three pairs of intermediate central rafters 3.89 + 0.6 + 0.3 = 4.79 m long;
- five pairs of ordinary rafters 4.79 m long.
Only ten pairs of rafters, the total length of which will be approximately 100 running meters. We add here 6 m for the ridge beam, as well as a ten percent margin, and we get that approximately 117 linear meters of lumber are needed to make a simple hip truss frame with struts, struts, crossbars, trusses and fillies. But if racks and a bed are provided in the design, then they will have to be calculated separately or a larger percentage of the stock should be added.
Video: four-pitched roof truss system, installation technology
https://youtube.com/watch?v=n_Yr2QB3diMThe measuring rail makes the work very easy and helps to avoid grossest mistakes during measurements. It is most often made independently from plywood 50 mm wide.
A few words need to be said about short rafters. They are calculated in the same way as the intermediate ones: the laying multiplied by the coefficient for the intermediate rafters from the table. However, the task can be facilitated and the length of the sprigs can not be calculated specifically, since the percentage of the stock is taken sufficient, and the trimming of the boards will be needed for the manufacture of structural reinforcing elements - struts, struts, crossbars, etc.
The length of short rafters (spiders) can not be calculated, since lumber trimmings are useful for the manufacture of reinforcing structural elements
Video: hip roof truss frame, element marking and assembly
Calculation of the section of lumber
After marking the position of the components of the truss frame, it is necessary to select suitable lumber, i.e., determine their allowable cross section. For calculations, you will need a zoned map of snow and wind loads and thermal resistance, as well as auxiliary tables based on regulations- SNiP II-3-79, SP 64.13330.2011, SNiP 2.01.07-85 and SP 20.13330.2011.
The device of a four-pitched roof includes the determination of the required section of lumber, which is carried out on the basis of an analysis of the loads on the truss structure during operation
The load from the snow cover is determined by the formula S = S g µ, where S is the desired snow load (kg / m²); S g - standard load for real terrain, indicated in the map, µ - correction factor depending on the slope of the roof. Since our tilt angle is in the range from 30 to 60 °, we calculate µ using the formula 0.033 * (60 - 36) = 0.792 (see note to the table below). Then S \u003d 168 0.792 \u003d 133 kg / m² (Ekaterinburg is located in the fourth climatic region, where S g \u003d 168 kg / m 2).
Table: determination of the µ index depending on the slope of the roof
| Determining the angle of the roof | |
| Tangent value | Angle α° |
| 0,27 | 15 |
| 0,36 | 20 |
| 0,47 | 25 |
| 0,58 | 30 |
| 0,7 | 35 |
| 0,84 | 40 |
| 1 | 45 |
| 1,2 | 50 |
| 1,4 | 55 |
| 1,73 | 60 |
| 2,14 | 65 |
| Note: if the slope angle (α) ≤ 30°, then the coefficient µ is taken as 1; if the angle α ≥ 60°, then µ = 0; if 30°< α < 60°, µ высчитывают по формуле µ = 0,033 · (60 - α). |
|
Table: normative snow loads by region
| region number | I | II | III | IV | V | VI | VII | VIII |
| S g, kg / m 2 | 56 | 84 | 126 | 168 | 224 | 280 | 336 | 393 |
The wind load is calculated by the formula W = W o k c, where W o is the standard indicator on the map, k is the tabular index, c is the aerodynamic drag coefficient, which varies from -1.8 to +0.8 and depends on the slope of the slopes . If the angle of inclination is more than 30°, then according to SNiP 2.01.07–85 p. 6.6, the maximum positive value aerodynamic index equal to 0.8.
Yekaterinburg belongs to the first zone in terms of wind load, the house is being built in one of the districts of the city, the height of the building with the roof is 8.7 m (zone "B" in the table below), which means W o = 32 kg / m², k = 0 .65 and c = 0.8. Then W \u003d 32 0.65 0.8 \u003d 16.64 ≈ 17 kg / m². In other words, it is with this force that the wind at a height of 8.7 m presses on the roof.
Table: k value for different types of terrain
| Building height Z, m | k coefficient for terrain types | ||
| BUT | AT | FROM | |
| ≤ 5 | 0,75 | 0,5 | 0,4 |
| 10 | 1,0 | 0,65 | 0,4 |
| 20 | 1,25 | 0,85 | 0,55 |
| 40 | 1,5 | 1,1 | 0,8 |
| 60 | 1,7 | 1,3 | 1,0 |
| 80 | 1,85 | 1,45 | 1,15 |
| 100 | 2,0 | 1,6 | 1,25 |
| 150 | 2,25 | 1,9 | 1,55 |
| 200 | 2,45 | 2,1 | 1,8 |
| 250 | 2,65 | 2,3 | 2,0 |
| 300 | 2,75 | 2,5 | 2,2 |
| 350 | 2,75 | 2,75 | 2,35 |
| ≥480 | 2,75 | 2,75 | 2,75 |
| Note: "A" - open coasts of the seas, lakes and reservoirs, as well as deserts, steppes, forest-steppes, tundra; "B" - urban areas, forests and other areas evenly covered with obstacles more than 10 m high; "C" - urban areas with buildings over 25 m high. |
|||
Table: standard wind load by region
| region number | Ia | I | II | III | IV | V | VI | VII |
| W o , kg / m 2 | 24 | 32 | 42 | 53 | 67 | 84 | 100 | 120 |
Now we calculate the load on the supporting frame from the weight of the roof. To do this, add up the weight of all layers of the roofing cake laid on top of the rafters. We leave the rafters exposed to achieve a decorative effect, which means we lay all the layers on top of the rafters. The load of the roof on the elements of the truss system will be equal to the sum of the weights of the metal tile, lathing and counter lathing, insulating films, insulation, additional lathing and ventilation rails, a solid plywood base and facing material roof space.
When determining the load on the supporting frame from the weight of the roof, the weights of all layers of the roofing pie laid on top of the rafters are summed up
The mass of each layer can be found in the manufacturer's instructions by selecting highest value density. The thickness of the heat insulator is calculated from the map of thermal resistance for a certain area. We find it by the formula T = R λ P, where:
- T is the thickness of the heat insulator;
- R is the standard of thermal resistance for a particular area, according to the map enclosed in SNiP II-3–79, in our case 5.2 m 2 °C / W;
- λ is the thermal conductivity coefficient of the insulation, which for low-rise construction is assumed to be 0.04;
- P is the highest density value thermal insulation material. We will use basalt insulation"Rocklight", for which P = 40 kg / m².
So, T \u003d 5.2 0.04 40 \u003d 8.32 ≈ 9 kg / m². Thus, the total load of the roof will be equal to 5 (metal tile) + 4 (solid decking) + 23 (basic lathing, additional and counter lathing) + 0.3 2 (insulating films) + 9 (insulation) + 3 (cladding) = 44 ,6 ≈ 45 kg/m².
Having received all the necessary intermediate values, we determine the total load on the supporting frame of the hipped roof: Q \u003d 133 + 17 + 45 \u003d 195 kg / m².
The allowable cross-section of lumber is calculated by the formulas:
- H ≥ 9.5 L max √ if angle α > 30°;
- H ≥ 8.6 L max √ if α< 30°.
The following notation is used here:
- H - board width (cm);
- L max - the maximum working length of the rafters (m). Since the layered rafter legs are connected in the ridge area, the entire length is considered to be working and L max = 4.79 m;
- R izg - an indicator of the resistance of wood to bending (kg / cm). According to the set of rules 64.13330.2011 for wood grade II R izg = 130 kg/cm;
- B is the thickness of the board, taken arbitrarily. Suppose B = 5 cm;
- Q r - load per linear meter of one rafter leg (kg / m). Qr \u003d A Q, where A is the pitch of the rafters, which in our case is 1 m. Therefore, Q r \u003d 195 kg / m.
Substitute the numerical values into the formula → H ≥ 9.5 4.79 √ = 9.5 4.79 0.55 = 25.03 cm ≈ 250 mm.
Table: nominal dimensions of softwood edged boards
| Board thickness, mm | Width (H) of boards, mm | ||||||||
| 16 | 75 | 100 | 125 | 150 | - | - | - | - | - |
| 19 | 75 | 100 | 125 | 150 | 175 | - | - | - | - |
| 22 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | - | - |
| 25 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 32 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 40 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 44 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 60 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 75 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 100 | - | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 125 | - | - | 125 | 150 | 175 | 200 | 225 | 250 | - |
| 150 | - | - | - | 150 | 175 | 200 | 225 | 250 | - |
| 175 | - | - | - | - | 175 | 200 | 225 | 250 | - |
| 200 | - | - | - | - | - | 200 | 225 | 250 | - |
| 250 | - | - | - | - | - | - | - | 250 | - |
From the table, the thickness of the board with a width of 250 mm can vary from 25 to 250 mm. The table of dependence of the section on the pitch and length of the rafters will help to determine more specifically. The length of the intermediate rafters is 4.79 m, the step is 1.0 m - we look at the table and select the appropriate section. It is equal to 75X250 mm.
Table: section of lumber depending on the length and pitch of the rafters
| 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 | 100X200 | 100x250 | - |
| 175 | 75X150 | 75X200 | 75X200 | 100X200 | 100X200 | 100X200 | 100x250 |
| 140 | 75X125 | 75X175 | 75X200 | 75X200 | 75X200 | 100X200 | 100X200 |
| 110 | 75X150 | 75X150 | 75X175 | 75X175 | 75X200 | 75X200 | 100X200 |
| 90 | 50X150 | 50X175 | 50X200 | 75X175 | 75X175 | 75X250 | 75X200 |
| 60 | 40X150 | 40X175 | 50X150 | 50X150 | 50X175 | 50X200 | 50X200 |
Here is another table for those who will use hardwood lumber.
Table: limit deviations from the nominal dimensions of boards
We check the correctness of the calculations by substituting the numerical parameters in the following inequality / ≤ 1. We get (3.125 195 x 4.79³) / (7.5 x 25³) = 0.57 - the section is chosen accurately and with a good margin. Let's check less powerful beams with a section of 50x250 mm. Substitute the values again: (3.125 195 x 4.79³) / (5 x 25³) = 0.86. The inequality is again fulfilled, so a 50x250 mm beam is quite suitable for our roof.
Video: calculation of the hip roof truss system
After all the intermediate calculations, we summarize: for the construction of the roof, we need 117 linear meters edged board section 50X250 mm. This is approximately 1.5 m³. Since it was initially agreed that for a four-pitched hip structure it is desirable to use lumber of the same section, then for the Mauerlat you should purchase the same timber in an amount equal to the perimeter of the house - 7.5 2 + 12 2 = 39 running meters. m. Taking into account the margin of 10% for cutting and marriage, we get 43 running meters or approximately 0.54 m³. Thus, we need approximately 2 m³ of lumber with a section of 50X250 mm.
The length of the rafters is the gap from the undercut for the supporting part to the undercut for the ridge beam.
Video: an example of calculating the roof on an online calculator
Rafter system installation technology
The arrangement of a four-slope structure has its own characteristics, which must be taken into account:
Manufactured and assembled in compliance with all the rules, a rafter frame of a layered type for a four-slope roof will be a non-spreading structure. It is possible to prevent the appearance of spacers if, in the places of support on the Mauerlat, the planes of the rafters are made horizontal.
In most cases, two schemes are used to support the rafter legs.
In four-slope hip structures, the length of the corner legs is often greater than the typical length of lumber. Therefore, the timber and boards are spliced, trying to locate the joints at a distance of 0.15 of the span length (L) from the center of the supports, which is approximately equivalent to the interval between the support points. The rafters are connected using the oblique cut method, tightening the joints with bolts Ø12–14 mm. Wash down is recommended to be done on the rafters, and not on the support beam, so that the cut does not weaken the supports.
Because the standard length most lumber does not exceed 6 m, the diagonal rafters are increased in length using the oblique cut and connected with bolts when using timber or with nails and clamps if boards are spliced
Table: position of supports for corner rafters
| Span length, m | Support types | Location of supports |
| less than 7.5 | stand or brace | at the top of the rafters |
| less than 9.0 | stand or brace | at the top of the rafters |
| sprengel or rack | at the bottom of the rafters - 1/4L pr | |
| over 9.0 | stand or brace | at the top of the rafters at the bottom of the rafters - 1/4L pr |
| sprengel or rack | in the center of the rafters | |
| rack | in the center of the rafters | |
| Note: Lpr - the length of the span, which is covered by rafters. | ||
To join the sprigs with the rafters, the top of the half-rafters is ground down, keeping it in the same plane with the corner legs, and fixed with nails. When placing the rafters on the rafters, they strictly monitor that they do not converge in one place. If you use not a cut, but cranial bars 50X50 mm, stuffed in the lower zone of the rafters on both sides, when installing the sprigs, then the rigidity of the rafter legs will be higher, which means that their bearing capacity will increase.
To increase the rigidity of the rafter frame, it is recommended to use cranial bars, stuffed on both sides at the bottom of the rafter legs, when installing sprigs.
Do-it-yourself installation of a truss structure
The construction of the four-pitched roof frame is carried out in several stages.
- The materials are laid out and calculated, after which the roofing material is laid as a waterproofing around the entire perimeter of the building. A support for racks and a Mauerlat are laid on top of it, fixing it to the walls, fixing it especially well in the corners.
Mauerlat in four-slope structures is laid around the entire perimeter and is well fixed to the walls, especially at the corners, to create a strong knot for attaching diagonal rafters
- They install a frame for the ridge run and lay the run itself, rigidly maintaining the height and spatial arrangement skate, since the strength and reliability of the entire roof structure.
- Support posts are placed using a water level for leveling and secured under the ridge with inclined supports. The arrangement of the racks is done based on the configuration of the roof - in the hip structure, the racks are installed in one row with an interval of no more than two meters, and in hipped roof- diagonally at the same distance from the corner.
- Mount the central intermediate rafters, and then ordinary ones, filling the middle of the side slopes.
- According to the markup, corner rafters are installed, preferably made with reinforcement, resting them with their lower part on the corner of the Mauerlat, and with the upper fragment on the rack. Here they make a bookmark of the cornice overhang and drain.
- Next, half-rafters (springs) are placed, strengthening the lower part of the diagonal legs with trusses, which will partially unload the corner rafters, and sheathe the roof with a wind board around the perimeter of the roof.
Sprengel grating is used for steep roofs and relatively large spans in order to avoid deflection of the diagonal rafters
- After the installation of the truss system, the roofing pie is laid, equipped cornice overhangs and drainage system.
When installing the truss system of a four-pitched roof, you need to carefully consider the joining of the diagonal rafters, the central rafter from the side of the end of the building, as well as the ridge beam
Video: hipped roof on nails and a stool
Self erection a hipped roof is, of course, not an easy process. But if you have measuring instruments, as well as necessary tools, you will succeed. The main thing is the desire to assemble the structure with your own hands and the desire to adhere to general principles. And so that the roof lasts as long as possible and retains its amazingly beautiful appearance, try not to save on the elements of the truss frame and use modern reliable metal fasteners for wood to fix them.
The roof is no less important element of the house than the foundation and walls. Its design sets the mood for the entire architectural ensemble, makes the building neat and attractive. The four-pitched roof has gained wide popularity not only because of its high reliability and external attractiveness, but also due to the opportunity to equip additional structures - attic and dormer windows, bay windows, etc. Despite the fact that the installation of such a roof is a little more expensive and more complicated than a gable structure, it is still easy to build it yourself.
Advantages of hipped roofs over gable roofs
One of the main tasks that appears even at the stage of designing your own house is the choice of the type of roof. The presence of many options among gable and four-slope structures requires an answer to the question of which roof to give preference to. And although the aesthetics of the building plays an important role, the criteria for reliability and practicality still come to the fore.
The gable roof is a classic structure, which is formed by two opposite slopes and a pair of vertical end parts, called gables. Spacious roof space allows you to equip the attic, living space or use the attic for domestic purposes.
The classic gable roof is easily recognizable by a pair of rectangular slopes that adjoin each other along the central axis of the building, and two triangular gables from its endsStructures of this type, due to their simplicity and practicality, for a long time remained the most popular in individual construction. At the same time, the dependence of the geometry of the roof on the size of the building, as well as the complication and increase in the cost of the structure during the arrangement of the attic, forced the search for other, more practical and functional options. And they were found in the form of a variety of hipped roofs, which basically have a pair of triangular and two trapezoidal slopes. The latter are often called hips, and the roof itself is called hip. When erecting a structure of this type, there is no need for gables and it becomes possible to make the building more modern and original.
The slopes of the simplest hip roof define surfaces in the form of two trapezoids and a pair of triangles There are several advantages of hip roofs over traditional gable structures:
- the possibility of arranging attic windows directly on the slopes;
- increased strength, reliability and stability of the truss system;
- increased resistance to weather factors;
- the possibility of increasing the area attic space a simple decrease in the width of the base of the hip;
- more even weight distribution of the roof;
- improved temperature regime when arranging an attic room.
Don't be fooled by the numerous advantages of a more stylish hipped roof - it also has its drawbacks. These include a more complex design, a slight decrease in the size of the attic space and uneconomical consumption of roofing material. As for the costs, the budget that will be required for the construction of one and the other roof differs slightly.
The four-pitched roof is not a know-how in architecture - its design has been known since ancient times Classification of hip roofs
Differences in the form of buildings, as well as the requirements for functionality and practicality of traditional hip roofing, contributed to the emergence of many variations. If we do not consider the most exotic of them, then we can distinguish several main types of hipped roofs.
- Traditional hip roof, the side slopes of which reach the level of the eaves. For the construction of its main surfaces, straight rafters are used, and the hip ribs form bars extending from the ends of the ridge. The well-designed design and weight distribution of the roof over an increased area allows not only to place the overhangs on the same line, but also to increase their overhang. Thanks to this, the facade of the building is reliably protected from rain even with strong gusts of wind.
Glazing elements are often built into the slopes of a classic hip roof. - A hipped roof can be installed on a house that has the shape of a square in plan. A feature of this design are slopes of the same configuration. Their edges converge to one point, and the hips have the shape of isosceles triangles.
Hip roofs are widely used in modern individual construction. - Half-hip roofs got their name because of the shortened hips. Unlike traditional roofing, their length is reduced by 1.5–3 times compared to the dimensions of the main slopes.
The side slopes of half-hipped roofs have a shortened length, so they do not reach the cornice line - The Danish semi-hip roof has a small pediment under the ridge and a short hip from the side of the eaves. This design allows you to install elements of ventilation and lighting directly into the vertical end of the roof, thereby eliminating the need to install skylights.
The Danish project is good because it allows you to easily equip the attic - The semi-hipped Dutch roof has a vertical pediment that divides the hip into two short slopes. truss system"Dutch", although it has increased complexity, but it allows you to make the attic space more spacious and practical. In addition, this design is great for installing vertical glazing in the attic.
The roof built according to the Dutch project is still rare in our area - The broken hipped roof has several slopes different size on one slope. Thanks to their different inclination, it is possible to increase the amount of under-roof space. Though broken structure and cannot be called simple, houses with such a roof are very common. The reason for the popularity is the ability to equip additional living rooms on the upper tier. For this reason, a roof with broken slopes is often called a mansard.
broken roof somewhat burdens the architecture of the building, but it allows you to equip several living quarters in the attic space
There are also more complex structures of many hips, as well as those in which a hipped roof is combined with roofing systems of other types. The design and installation of such a roof requires many years of experience and knowledge, so it is better to entrust the construction of a tricky roof to specialists.
Design of pitched roofs
When developing a hip roof, all types of loads that will affect it are taken into account. To do this, first of all, several important questions must be addressed:
- purpose of the attic space;
- roofing material;
- degree of atmospheric impact in the region of construction.
Based on these factors, the degree of inclination of the slopes and the roof area are determined, the loads are calculated and a decision is made on the design and parameters of the truss system.
Geometric parameters of slopes
The angle of inclination of the slopes depends on the snow and wind load, therefore it varies over a very wide range - from 5 to 60 degrees. In areas with rainy weather and high snow cover, roofs are erected with a slope of 45 to 60 degrees. If the region is different strong winds and a minimum amount of precipitation, the slope can be reduced down to the very minimum.
When determining the angular parameters of the roof, it is necessary to take into account what material it will be covered with:
- slate sheets, ondulin, roofing metal and rolled materials are laid on slopes with a slope of 14 to 60 degrees;
- tiles are mounted on the surface with a degree of slope from 30 to 60 degrees;
- roll coating use on sloping slopes - from 5 to 18 degrees.
Having decided on the angle of inclination of the roof, it is not at all difficult to calculate at what height the ridge will be. To do this, use simple trigonometric formulas for a right triangle.
Roof area
Even the most complex hip roof consists of individual slopes that follow the contours of the simplest geometric shapes, therefore, most often for calculations it is enough to know the linear dimensions of the base and the angles of inclination of the hips.
To determine the quadrature of the roof, it is necessary to add the area of \u200b\u200bthe slopes of which it consists total area roofs are calculated by summing the quadrature of individual hips. stingrays complex configuration divided into several simple surfaces, after which separate calculations are carried out for each of them.
The principles for calculating the geometric parameters of hipped roofs are based on calculations for simple surfaces Load calculation
The loads acting on the hipped roof are divided into two types:
- permanent,
- periodic.
The first includes the weight of roofing materials, rafters, battens and other frame parts. The second is the effort exerted by precipitation and the force of the wind. In addition, the calculation should take into account the payload in the form of a variety of engineering systems and communications attached to the elements of the truss system.
Focusing on SNiP, when designing a roof, it is necessary to take a snow load of 180 kg / sq. m. If there is a danger of snow accumulation on the roof, this parameter rises to 400–450 kg / sq. m. m. If the roof has a slope angle of more than 60 degrees, then the snow load can be ignored - precipitation does not linger on surfaces with such steep slopes.
The strength of wind loads is much less - up to 35 kg / sq. m. If the slope of the roof is from 5 to 30 degrees, then the impact that the wind has can be neglected.
The above parameters of atmospheric effects are average values taken for the middle band. When performing calculations, correction factors should be used depending on the region of construction.
Calculation of the truss system
When calculating the rafter system, the pitch of the rafters and the maximum load that they can carry are determined. Based on these data, a decision is made to install braces that contribute to the redistribution of the load, and puffs that protect the frame from loosening.
The main load of the hip roof falls on the diagonal rafters The presence of hips on four-pitched roofs, in addition to ordinary rafters, also requires the installation of diagonal (in other words, slanting) - those that are attached to the ridge and go to the corners of the building. Their length is greater than the transverse nodal elements of the roof. In addition, shortened elements - sprigs - are attached to the diagonal ribs. Compared to conventional rafters, slanting legs experience a load increased by 1.5–2 times, so their cross section is doubled, and to ensure multi-span, they are supported by one or two racks.
Often, hip roofs have a complicated truss system, which, unlike a simple four-slope structure, exerts an additional load at the installation sites of vertical supports. This feature must be taken into account when calculating the strength of the wooden frame of the roof.
The distance of laying the rafters is called a step and is determined based on the length of the rafter leg and the cross section of the lumber used. It is most convenient to determine this parameter using special tables, one of which is given below.
Table: dependence of the section and pitch of the rafters on their length
Manual calculations are quite laborious. To reduce design time, you can use one of the online calculators to determine the parameters of hip roofs. With its help, you can determine not only the geometric parameters, but also a lot of other equally important factors:
- the amount of moisture and heat insulation, taking into account overlaps;
- the amount of roofing material, including waste generated during cutting;
- the volume of lumber required for arranging the truss system;
- length of overhangs, etc.
Video: using a construction calculator to calculate the roof
What materials will be needed to assemble the truss system
For the construction of a hip roof, timber and a board made of larch, pine and other coniferous wood are best suited. When choosing a material for construction, it is necessary to carefully reject defective boards. Fungal damage, knots and cracks reduce the strength of the boards and affect the durability of the roof. When the moisture content of the wood is more than 22%, the lumber is stacked in the open air and dried. It should be understood that under-dried boards can warp, and this, in turn, will lead to a violation of the geometry of the roof with possible damage finish coat.
To assemble a wooden frame, a rectangular beam with a section from 80x80 mm to 150x150 mm is used - the exact parameters are determined by calculation or using the table above. Alternatively, you can use a board with a section of 50x100 mm or 50x200 mm. If there is a need to strengthen the rafter leg, then paired boards are used.
For reliable fastening, as well as increasing the rigidity of the wooden frame, steel staples and other metal elements are used. Often, under especially loaded ridge runs, not wooden ones are installed, but steel supports. Combined frames have increased strength and reliability.
Features of the truss system
In order to properly design and install a four-pitched roof, it is necessary to understand in detail its design, as well as the features of the arrangement of hip roofs of the most common types.
The device of the truss system in detail
The frame of the hip roof consists of most of the same parts as the gable roof, but a more complex truss system requires installation additional elements. Upon closer examination, the following components can be found:
All these elements can be found in a hipped roof of any type. The only exception is the hipped roof, which does not have side rafters and a ridge beam.
In wooden and frame houses, the truss system is mounted without a Mauerlat. In the first case, its functions are taken over by the extreme crowns, and in the second - by the upper harness.
Varieties of hip roof truss systems
Since the hip roof truss system is based on rafters, the following rules must be followed when installing the roof frame:
- In structures where the sloping legs experience an increased load, a beam of double thickness is used for their manufacture.
- The splicing of individual parts of the diagonal rafters is performed in places with maximum load (most often in their upper part) and strengthened with the help of struts and uprights installed at an angle of 90 ° to the rafter legs.
- In the manufacture of rafters, a margin for trimming in place should be provided, therefore, the estimated length of the timber is increased by 5–10%.
- Responsible joints of the rafter legs must be reinforced with metal fasteners - staples, twists or perforated building strips.
When choosing a rafter system, it is necessary to take into account the size of the building and the presence of internal supports or capital walls. Based on specific conditions, choose a scheme with hanging or layered rafters.
Hanging rafter system
roof structure with hanging rafters it has no supports along the midline, so the main weight falls on the walls of the outer perimeter. This feature manifests itself in the redistribution of internal forces - the rafter system is subjected to compressive and bending loads. As for the walls, significant bursting forces are transmitted to them. To eliminate this factor, each pair of rafters is interconnected by so-called puffs - jumpers from wooden beam or rolled metal.
The puff can be located both at the base of the rafter legs and above. In the first case, the jumper will also play the role of a transverse beam, which is good option during the construction of a mansard roof. If the puff is installed in the region of the midline or higher, then it will only serve as a fixing link. It should be noted that the cost of the truss system depends on such a seemingly insignificant moment as the installation height of the puffs. The higher they are located cross bridges, the larger should be the cross section of all components of the wooden frame.
Hip roofs with layered and hanging rafters have differences between supporting elements designs Structural rafter construction
A hip roof with layered rafters is only suitable for those houses inner space which is divided into two equal parts by a main wall or installed to support the ceiling supporting pillars. In this case, the lower edge of the rafter legs rests on the Mauerlat, and middle part- on the bearing wall. The presence of additional support points allows you to unload the elements of the truss system, removing sign-variable horizontal forces from them, as well as from the walls of the building. Like roof beams, rafters begin to work only in bending. The frame with layered rafters becomes more rigid and durable compared to the design that uses unsupported rafters. And this despite the fact that in the first case, you can use a beam of a smaller section. And this helps to reduce the weight of a wooden structure and reduces the cost of purchasing lumber.
Installation of a pitched roof
The assembly of the truss system must be carried out in a strictly defined order. This is necessary in order to properly install and secure all structural elements of the roof.
- To redistribute the load that is exerted on the walls roof structure, wind and precipitation, on external walls lay mauerlat. In individual construction, a bar with a section of at least 100x150 mm is used for these purposes. Anchor studs are used to fasten the longitudinal beams of the structure. They must be laid in the upper rows of masonry even at the stage of building walls. Mauerlat waterproofing is performed using two layers of roofing material, which is laid on top of the load-bearing walls.
Mauerlat is fixed to the load-bearing wall with bolts or anchors. - If it is necessary to install vertical supports, beds are laid on the bearing walls. For horizontal alignment of the elements of the truss system, wooden linings are used. In the future, this will greatly simplify the installation of racks and runs. If capital partitions are not provided for by the building plan, then vertical supports are mounted on floor beams. To do this, they are reinforced by splicing two boards 50x200 mm or using one bar 100x200 mm.
The support of vertical racks on beams is allowed only if the structure will rest on the main pier - Set up support stands. To level them, use a plumb line or laser level, after which temporary supports are installed. For fastening vertical support to a bed or a horizontal beam use metal corners and plates.
- Runs are laid on top of the racks. The traditional hip roof requires the installation of one run, which, in fact, forms the ridge. Tent structures need to install four runs. As with the installation of racks, fastening is carried out using metal corners and self-tapping screws.
The ridge run can be fastened both directly to the rafter leg and by means of wooden slips - Rafter preparation. The side rafter legs of simple four-slope roofs are mounted in the same way as the rafters on a gable roof. First you need to make a template. To do this, from the side of the extreme support, a board of the same width as the rafters is applied to the ridge. Its thickness should not exceed 25 mm - the template should be light. On this board, they mark the gash, which is necessary for reliable support and precise fit of the rafter leg to the ridge beam, as well as a cutout corresponding to the place of joining with the Mauerlat. The marked places are cut out and then used for fast training rafter legs.
Making a template can reduce the time it takes to prepare rafters for installation - When applying the manufactured sample to the running beam, it is necessary to check whether an exact fit of the rafters is needed. If there are gaps, cuts in the rafters are performed taking into account the amendments. After all the supporting legs are ready, they are set in increments of 50–150 cm and attached to the Mauerlat and the ridge. Staples are best suited for mounting, but powerful metal corners can also be taken.
- As already mentioned, diagonal rafters are made from spliced boards or a beam of increased cross section. For their installation, you will also need a template, which is prepared in full accordance with the method described above. Since the rafters on one side adjoin the corner of the Mauerlat, and on the other they rest on the racks, the sawing is performed at an angle of 45 ° to the plane.
The layout of the rafters and joists on the hip roof is performed according to the template - In the intervals between the slanting rafters, sprigs are attached. Their step corresponds to the distance between the rafters, and the diagonal legs and the Mauerlat act as support points. The load experienced by the rafters cannot be compared with the weight that falls on the rafters, so the first can be built from boards 30–50 mm thick. To speed up the installation, you will need a template with cuts from the side of the diagonal rafter and Mauerlat, but the cutouts on half of the sprigs must be made in a mirror image.
The use of metal fasteners makes the truss system more rigid and stable - If there is a need, then fillies are attached to the rafters and sprigs. ends roof elements cut along the cord.
Fastening rafters to the Mauerlat can be done in several ways - Strengthen the side and side rafters. In the first case, vertical trusses are used, and in the second, struts installed at an angle of 45 °. They are supported on beds or beams.
- After the rafter system is assembled, a roofing pie is installed on top of it.
The truss system is prepared for the installation of roofing materials
Sheathing and insulation
Before proceeding with the installation of the battens, a vapor barrier is laid on top of the rafters, and, if necessary, roll thermal insulation. Top layer of insulation is closed waterproofing film, which is mounted with an overlap of 10–20 mm wide and attached to the timber with a construction stapler. After that, the slats of the counter-lattice are nailed to the rafters. If the roofing pie is mounted without insulation, then vapor barrier is not required - a layer of moisture-resistant material will suffice. Of course, additional slats will not be needed, since the boards supporting the roof will be attached directly to the sprigs and rafter legs.
Depending on the type of roofing material, one of two types of lathing is used on hip roofs:
- solid;
- sparse.
The first is most often equipped under soft roof and only in individual cases- for the arrangement of the attic space. The crate of this type is made of boards with a width of 100 to 200 mm and a thickness of at least 20–25 mm. Installation is carried out without gaps. In addition, the use of plywood sheets and OSB boards. Their dignity is extremely Smooth surface, which allows you to lay roofing material with minimal cost time and effort.
Under a soft roof, a continuous sheathing of OSB, plywood or boards stuffed without a gap is equipped For a sparse crate, the same boards are used as in the first case, however, they are mounted with a gap. Since this type of base is used for laying slate, corrugated board, metal tiles and roofing iron, the distance between the individual boards must take into account the characteristics of the roofing material.
The fastening of the crate is carried out with nails, the length of which is equal to three times the thickness of the boards. If self-tapping screws are used for fixing, then a shorter threaded fastener with a length corresponding to twice the thickness of the lumber can be used.
For fixing slate, ondulin and other sheet materials, a sparse crate is used The wooden base of the roofing pie is mounted from the bottom up, while the first board of each slope is set parallel to the Mauerlat. First, the crate is stuffed on the hips, after which the protruding edges are cut with a hacksaw flush with the diagonal ribs. Next, they begin to fasten the lumber on the main slopes, releasing the edges of the boards behind the rafters. After that, the ends of the boards are cut down similarly to the first case.
Video: we build a hip roof with our own hands
Typical hip roof project
When building a simple hip roof, you can use a typical project that was developed by specialists. Project documentation includes:
- technological map;
- roofing design;
- schemes of the truss system;
- drawings of sections and corner joints;
- statement and specification with a complete list of materials used.
As a sample, below is the documentation for a typical design of a hip roof for a house with an area of 155 square meters. m.
Gallery: drawings and diagrams of a hipped roof
The drawing indicates the exact dimensions of all elements of the roof. At the base of the truss truss are triangles. Rafters of trapezoidal slopes rest on the long load-bearing walls of the building. Puffs are installed at the base of the rafters and act as floor beams. rafter fastenings are used wooden and metal products Fastenings allow you to transfer the load from one element of the system to another
Despite the apparent complexity of a four-slope roof, it is not much more difficult to build it with your own hands than a gable structure. It is only important to carefully understand the appointment individual elements and principles of construction of the truss system. Otherwise, the reliability and durability of the roof will still depend on compliance with the technology and accuracy of installation. As for the additional difficulties and costs, they will pay off with complete satisfaction from the work, which will make the building brighter and more attractive.
For buildings of a large area, a gable roof does not provide the required protection and reliability. This design relies only on 2 external load-bearing walls, so the load on the rafters is excessively large. For big house it is better to choose a hipped roof that effectively withstands atmospheric loads and distributes pressure more evenly on the external load-bearing walls and foundation.
pitched roof configurations
The geometric design of such a roof combines 4 inclined planes, the bases of which are the load-bearing walls of the house around the perimeter. There are several configurations that determine the shape and relative position of inclined surfaces.
hip roof
A simple design, outwardly somewhat reminiscent of a gable: in parallel long walls form 2 planes, which are connected in the center by a ridge floor. Opposite pediments are replaced with sloping triangles-hips. The design is used for large buildings, the two sides of which are much longer than the others. 
Half hip roof
Differs in a configuration of end slopes. The bases of the triangles rise above the bottom edge of the structure. The remaining space is filled by the pediment. The corners at the base of large slopes are cut vertically. This allows you to make a spacious attic under the roof and install a double-glazed window.
Suitable for square houses or buildings in which all walls are approximately equal. Four slopes are triangles connected by vertices at a common central point. There is no horizontal ridge in such structures.
These configurations are the basis for the construction of all hipped roofs, including the combination of various elements into complex structures.
Many country arbors have the shape of a regular polygon, often a hipped roof is erected to them. Why a hipped roof is used for a small structure is explained by the practicality and aesthetic completeness of such a design. Build a roof with two inclined surfaces for country gazebo impractical: the absence of closed gables will leave part of the structure unprotected from precipitation, for example, during slanting rain. The four-pitched roof wins in this.
Types of truss systems
There are hanging and layered structures. The first type is distinguished by the fact that the rafters lean against each other. This variety is used for buildings that do not have central load-bearing walls. The load is bursting. To increase strength, ties are made between opposite rafters, racks, struts and other devices are used.
The sloped design of the hipped roof includes additional supports for the rafters. They are reinforced under the ridge run and transfer part of the load to the load-bearing walls inside the building.
System differences: 1) Hanging 2) Layered
Description of the roof structure
The construction of a hip roof requires the master professional knowledge and experience. Drawings of the truss system of this type of hipped roof include the following elements:
- Mauerlat - the base of the frame, laid on load-bearing walls. Since all sides of the house are supporting, the element is attached around the perimeter of the building. Since hipped roofs are built on large objects, the Mauerlat must be of high strength. Usually use a bar 150x150 or 100x100. Mauerlat is not required if the structure is made of wood. In this case, the upper wall trim serves as the base.
- The ridge run is installed horizontally on the line of intersection of trapezoidal slopes and serves as a connecting element.
- From each end of the run, 3 supports, called the central rafters, depart. They are erected regardless of the pitch of the remaining elements.
- Diagonal (corner) rafters connect the ridge beam to the corners of the building. These are the longest supports with the greatest slope.
- Parallel to the directions of the slopes, short rafters are erected on the hips, fastening the corner supports (sides of the triangles) with the Mauerlat.
- The lateral edges of the trapezoid with the base are connected by sprigs, and two parallel sides are connected by intermediate supports.
- Sprengel is used to increase strength. It is a bar located closer to the corner of the building, the ends of which are installed on adjacent walls.
- When installing struts and racks, a truss truss is formed - an additional structural unit.
- Puffs are used in a hanging truss system. They are mounted on two opposite supports.
- In the layered structure there is a bed, which is laid on bearing wall in the center of the building and takes on part of the load.
The peculiarity of the semi-hip roof is that the lower edge of each triangular slope rises to the height of the pediment, thereby shortening the diagonal rafters. The four-pitched hipped roof is simpler. The frame design includes similar components of the hips and the internal ligament. All reinforcement elements are designed for one purpose - to pull the frame into knots and make it rigid.
System features and calculation
The roof with four slopes is able to withstand high wind and snow loads. In order for the roof to be practical, reliable and perfectly perform the functions assigned to it, an accurate calculation of all elements is carried out. The slope of the slopes of the hip roof does not exceed 40 °. The construction of the tent system provides for an angle of 40 to 60 °.
Calculation supporting structure based on the interdependence of the span length, rafter step and beam sections. The second parameter is selected individually based on the available material and ease of attachment. In the longest structures, the rafter pitch is 2.15 m, and in most cases 90 cm is chosen.
The distance determines the cross section of the supports. The farther apart the rafters are placed, the thicker the board will be required. The size of the section also depends on the length of the supports themselves. Communication is directly proportional. In order for the rafters to withstand the bending force, a material of a larger section is chosen. For 6-meter supports with a step of 90, the cross-sectional area is 75 × 200 mm, and for 3-meter supports it is only 50 × 150.
Carrying out construction activities
The material for the frame must be well dried. Wood moisture content is limited to 20%. Work order:
A professional approach to assembling a solid frame determines the performance of a hipped roof. Resilience to weather conditions and the service life of the structure as a whole depend on the reliability of the structure.
In private housing construction, in addition to the common gable roofs, more durable and rigid four-pitched structures are often used. They are distinguished by the absence of pediments, which replace the triangular slopes that cut off the ends of the ridge ridge. This configuration makes four-pitched roofs very attractive and economical, even though their construction increases the length of the cornice overhangs, the number of downpipes and gutters. Therefore, they deserve the closest attention.
Varieties of truss systems for hipped roofs
The device of the truss system depends on the shape of the hipped roof. The following configurations are the most common today.
- Hip structure. All four slopes occupy the area from the ridge to the cornice overhang, while two side slopes are trapezoid in shape, and two end slopes (hips) are triangular. A feature of the truss hip frame is the presence of two pairs of diagonally installed layered rafters that extend from the edge of the ridge and serve as supports for sprenels and sprengels.
The hip four-slope design is characterized by the fact that the slopes occupy the entire area of the roof - from the ridge to the cornices
- Dutch half hip. A device with truncated end slopes that do not reach the eaves. As a rule, they are 2-3 times smaller than trapezoidal ones. The advantage of such a four-slope roof structure is the possibility of installing an ordinary window at the ends of the house, as well as the absence of a sharp protrusion typical of gable roofs, which greatly increases the wind resistance of the structure.
The Dutch half-hipped roof has truncated triangular slopes and part of the gable into which a conventional vertical window can be installed.
- Danish half hip. It is characterized by the presence in the triangular slopes of the pediment at the ridge, which allows for full natural lighting of the under-roof space without installing skylights.
- Tent construction. It is installed on houses with a square frame. All four slopes of a hipped roof are identical isosceles triangles connected at one point. When building such a roof, an important aspect is the observance of symmetry.
The structure of the four-slope truss system depends on the chosen roof configuration
Features of the supporting frame of the hipped roof
We note right away that the truss system of a four-pitched roof will be more complex than traditional gable roof structures for two reasons.
- Due to the increase in the number of inclined planes and their docking with each other. At its core, the connection of the slopes is the intersection lines running at a certain angle to the horizon. The joints that form an angle protruding above the surface of the slopes are called roof ribs. From them, water flows down the slopes and accumulates in the grooves (valleys) - the lines of intersection with the inner corner. If all planes have the same slope, then the ribs and valleys divide the base angle at the junction of adjacent slopes in two and create a slope of 45 ° to the perimeter of the building.
Four-pitched truss systems are distinguished by the absence of full gables, instead of which there are two triangular end slopes, as well as the presence of two lateral trapezoidal inclined planes, grooves and ribs
- Due to the fact that the runs in the four-slope structure form a closed loop, where the hip (diagonal) rafter legs are located along the lines of the ribs and valleys. They are longer than ordinary beams, which are installed longitudinally to the slopes at a distance between the intersections of the hip rafters in the upper harness. But between the lower parts of the diagonal legs, short rafters, called sprigs, are mounted. A distinctive feature of the four-pitched roof frame is the presence of sprengels - wooden struts under the hip rafters.
Support runs in four-pitched structures have a closed contour, where diagonal rafter legs are located along the lines of valleys and ribs
The main structural elements of the truss system of a hipped roof are:
Thus, the number of elements of the truss system of a hipped roof is much greater than, for example, that of a gable roof, and this, of course, increases the cost of its construction. However, in general, as we noted above, the arrangement of a four-pitched roof will cost a little more due to savings on laying a roofing pie, since there will be much less waste of insulating materials and covering flooring when cutting into a multi-pitched structure.
Despite the fact that the truss system of the four-slope structure is more complex and expensive, the construction of the entire roof is more profitable due to savings on the arrangement of the roofing pie.
In addition, the four-slope design:
Video: gable or four-pitched roof - what to choose
How to calculate the truss system of a four-pitched roof
The supporting structure of a four-pitched roof can be layered if the building has solid internal walls, or hanging when intermediate supports are not provided in the building. With a hanging device, the rafters rest on the walls of the house and exert a bursting force on them. To relieve the load on the walls in such cases, a puff is mounted at the base of the rafter legs, connecting the rafters to each other.
The use of a layered structure makes the frame lighter and more economical due to the fact that less lumber is required for its arrangement. Because of this, the layered truss system is used much more often in the construction of multi-pitched roofs. But regardless of the type of rafters used, only the correct calculation of the supporting frame and accurate marking will increase the economic effect of the construction of a four-slope structure.
Marking and calculation of the supporting frame of a hipped roof
When calculating the truss system, you must adhere to the following rules.
To determine the installation location of the rafters and find their length, you will need a template.
Using a template will make it much easier to measure and calculate the truss frame of a four-pitched roof
The length of the rafter leg can be determined by its laying (horizontal projection). For this, there is a special table of coefficients, presented below. The length of the rafter is determined by the size of its projection, multiplied by a coefficient corresponding to the slope of the slope.
Table: the ratio between the length and laying of the rafters
| Roof pitch | Coefficient for calculating the length of intermediate rafters | Coefficient for calculating the length of the corner rafters |
| 3:12 | 1,031 | 1,016 |
| 4:12 | 1,054 | 1,027 |
| 5:12 | 1,083 | 1,043 |
| 6:12 | 1,118 | 1,061 |
| 7:12 | 1,158 | 1,082 |
| 8:12 | 1,202 | 1,106 |
| 9:12 | 1,25 | 1,131 |
| 10:12 | 1,302 | 1,161 |
| 11:12 | 1,357 | 1,192 |
| 12:12 | 1,414 | 1,225 |
| Note: when erecting a roof frame for which there are no data in the table (for non-standard slopes of slopes), the parameters should be calculated using the Pythagorean theorem or a mathematical proportion should be used. | ||
Consider an example: a private house is being built in Yekaterinburg with a size of 7.5x12 m with a planned height of a hip roof made of metal tiles of 2.7 m.
- First of all, we draw a drawing or a sketch of the roof.
Before calculating the truss system, it is necessary to make a sketch of the building and apply all the initial data to it
- We find the angle of inclination of the slopes using the formula: the tangent of the angle of inclination is equal to the ratio of the height of the roof to half the length of the span, in our case, to half of the end side L = 7.5 / 2 = 3.75. Thus, tg α = 2.7 / 3.75 = 0.72. According to the reference tables, we determine: α = 36 °, which corresponds to the standards providing for a roof slope for metal tiles of at least 14 °, and the climatic conditions of Yekaterinburg.
The tangent of the angle of inclination of the slopes is determined by the well-known formula for calculating the sides of a right triangle as the ratio of the opposite leg to the adjacent
- We determine the position and edge of the ridge ridge, for which we apply the template at an angle of 36 ° in the middle of the upper trim of the end (the installation site of the first central intermediate rafter) to a height of 2.7 m and project the outline onto the sketch.
- We retreat ½ of the thickness of the ridge beam from the axial (key) line and set the end of the measuring rail at this point. At the other end of the rail, we make marks for the outer and inner contours of the side wall, as well as the overhang. We turn the rail to the side and from the inner corner of the outer trim we mark the laying of the intermediate rafter at the mark of the inner contour, thus determining the installation location of the second intermediate central rafter.
When arranging the truss frame of a four-pitched roof, the position of the central rafter legs is initially determined using a template and a measuring rail
- We carry out similar actions at all corners, determining the edges of the ridge ridge and the location of all central rafter legs.
- After planning the intermediate rafters, we determine their length from the table. In our example, the slope angle is 36°, its tangent is 0.72, which corresponds to a ratio of 8.64:12. There is no such value in the table, so we calculate the coefficient relative to the line with the parameter 8:12 - 8.64/ 8 = 1.08. Hence, the desired coefficient is 1.202 1.08 = 1.298.
- Multiplying the depth of the intermediate rafters by the calculated coefficient, we find their length. Let's take into account the laying depth of 3 m, then L str \u003d 3 1.298 \u003d 3.89 m.
The length of ordinary and central intermediate rafters depends on the angle of inclination of the roof and the depth of their laying
- Similarly, we determine the length of the diagonal rafters, having previously calculated the laying equal to the distance from the angle of connection of the side and end slopes to the first intermediate central rafter. According to the initial data, the laying of the corner rafters is 7.5 / 2 = 3.75 m. Then the estimated length of the corner rafters will be 3.75 1.298 = 4.87 m.
Corner rafters differ from intermediate undercuts with a double bevel in the ridge area, a deeper laying and a longer undercut for the supporting part
- We calculate the overhang according to the Pythagorean theorem according to the markings made, or simply add the desired size to the length of the rafters, for example, 0.6 m plus at least 0.3 m for arranging an external drain.
To calculate the length of the overhang, you need to multiply its placement by the coefficient for an intermediate or corner rafter, or add the planned length of the overhang and at least 0.3 m to the estimated length of the rafters to organize an external drainage system
- Having marked all the elements of the truss frame, we determine the length of the ridge ridge, which is equal to the difference in the length of the side and twice the value of laying the intermediate rafters: 12 - 2 3 = 6 m. It is at this distance that ordinary rafters will be installed. If you take a step of 1 m, then you need 5 ordinary rafters, equal in length to the central ones. In addition, at the site of laying the intermediate central rafters, having a length of 3 m, two short rafters will be installed from one and the other edge of the side.
- Since the short rafters (spreaders) are attached to the diagonal ones, it means that two rafters will also be installed on the end sides between the corner and central intermediate rafters on the left and right.
Let's summarize the preliminary result - for the truss frame of a four-pitched roof you will need:
- two pairs of hip (corner) rafters with a length of 4.87 + 0.6 + 0.3 = 5.77 m;
- three pairs of intermediate central rafters 3.89 + 0.6 + 0.3 = 4.79 m long;
- five pairs of ordinary rafters 4.79 m long.
Only ten pairs of rafters, the total length of which will be approximately 100 running meters. We add here 6 m for the ridge beam, as well as a ten percent margin, and we get that approximately 117 linear meters of lumber are needed to make a simple hip truss frame with struts, struts, crossbars, trusses and fillies. But if racks and a bed are provided in the design, then they will have to be calculated separately or a larger percentage of the stock should be added.
Video: four-pitched roof truss system, installation technology
https://youtube.com/watch?v=n_Yr2QB3diMThe measuring rail greatly facilitates the work and helps to avoid gross errors in measurements. It is most often made independently from plywood 50 mm wide.
A few words need to be said about short rafters. They are calculated in the same way as the intermediate ones: the laying multiplied by the coefficient for the intermediate rafters from the table. However, the task can be facilitated and the length of the sprigs can not be calculated specifically, since the percentage of the stock is taken sufficient, and the trimming of the boards will be needed for the manufacture of structural reinforcing elements - struts, struts, crossbars, etc.
The length of short rafters (spiders) can not be calculated, since lumber trimmings are useful for the manufacture of reinforcing structural elements
Video: hip roof truss frame, element marking and assembly
Calculation of the section of lumber
After marking the position of the components of the truss frame, it is necessary to select suitable lumber, i.e., determine their allowable cross section. For calculations, you will need a regionalized map of snow and wind loads and thermal resistance, as well as auxiliary tables based on regulations - SNiP II-3–79, SP 64.13330.2011, SNiP 2.01.07–85 and SP 20.13330.2011.
The device of a four-pitched roof includes the determination of the required section of lumber, which is carried out on the basis of an analysis of the loads on the truss structure during operation
The load from the snow cover is determined by the formula S = S g µ, where S is the desired snow load (kg / m²); S g - standard load for real terrain, indicated in the map, µ - correction factor depending on the slope of the roof. Since our tilt angle is in the range from 30 to 60 °, we calculate µ using the formula 0.033 * (60 - 36) = 0.792 (see note to the table below). Then S \u003d 168 0.792 \u003d 133 kg / m² (Ekaterinburg is located in the fourth climatic region, where S g \u003d 168 kg / m 2).
Table: determination of the µ index depending on the slope of the roof
| Determining the angle of the roof | |
| Tangent value | Angle α° |
| 0,27 | 15 |
| 0,36 | 20 |
| 0,47 | 25 |
| 0,58 | 30 |
| 0,7 | 35 |
| 0,84 | 40 |
| 1 | 45 |
| 1,2 | 50 |
| 1,4 | 55 |
| 1,73 | 60 |
| 2,14 | 65 |
| Note: if the slope angle (α) ≤ 30°, then the coefficient µ is taken as 1; if the angle α ≥ 60°, then µ = 0; if 30°< α < 60°, µ высчитывают по формуле µ = 0,033 · (60 - α). |
|
Table: normative snow loads by region
| region number | I | II | III | IV | V | VI | VII | VIII |
| S g, kg / m 2 | 56 | 84 | 126 | 168 | 224 | 280 | 336 | 393 |
The wind load is calculated by the formula W = W o k c, where W o is the standard indicator on the map, k is the tabular index, c is the aerodynamic drag coefficient, which varies from -1.8 to +0.8 and depends on the slope of the slopes . If the angle of inclination is more than 30°, then according to SNiP 2.01.07–85, clause 6.6, the maximum positive value of the aerodynamic index equal to 0.8 is taken into account.
Yekaterinburg belongs to the first zone in terms of wind load, the house is being built in one of the districts of the city, the height of the building with the roof is 8.7 m (zone "B" in the table below), which means W o = 32 kg / m², k = 0 .65 and c = 0.8. Then W \u003d 32 0.65 0.8 \u003d 16.64 ≈ 17 kg / m². In other words, it is with this force that the wind at a height of 8.7 m presses on the roof.
Table: k value for different types of terrain
| Building height Z, m | k coefficient for terrain types | ||
| BUT | AT | FROM | |
| ≤ 5 | 0,75 | 0,5 | 0,4 |
| 10 | 1,0 | 0,65 | 0,4 |
| 20 | 1,25 | 0,85 | 0,55 |
| 40 | 1,5 | 1,1 | 0,8 |
| 60 | 1,7 | 1,3 | 1,0 |
| 80 | 1,85 | 1,45 | 1,15 |
| 100 | 2,0 | 1,6 | 1,25 |
| 150 | 2,25 | 1,9 | 1,55 |
| 200 | 2,45 | 2,1 | 1,8 |
| 250 | 2,65 | 2,3 | 2,0 |
| 300 | 2,75 | 2,5 | 2,2 |
| 350 | 2,75 | 2,75 | 2,35 |
| ≥480 | 2,75 | 2,75 | 2,75 |
| Note: "A" - open coasts of the seas, lakes and reservoirs, as well as deserts, steppes, forest-steppes, tundra; "B" - urban areas, forests and other areas evenly covered with obstacles more than 10 m high; "C" - urban areas with buildings over 25 m high. |
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Table: standard wind load by region
| region number | Ia | I | II | III | IV | V | VI | VII |
| W o , kg / m 2 | 24 | 32 | 42 | 53 | 67 | 84 | 100 | 120 |
Now we calculate the load on the supporting frame from the weight of the roof. To do this, add up the weight of all layers of the roofing cake laid on top of the rafters. We leave the rafters exposed to achieve a decorative effect, which means we lay all the layers on top of the rafters. The load of the roof on the elements of the truss system will be equal to the sum of the weights of the metal tile, lathing and counter lathing, insulating films, insulation, additional lathing and ventilation rails, a solid plywood base and facing material of the under-roofing room.
When determining the load on the supporting frame from the weight of the roof, the weights of all layers of the roofing pie laid on top of the rafters are summed up
The mass of each layer can be found in the manufacturer's instructions by selecting the highest density value. The thickness of the heat insulator is calculated from the map of thermal resistance for a certain area. We find it by the formula T = R λ P, where:
- T is the thickness of the heat insulator;
- R is the standard of thermal resistance for a particular area, according to the map enclosed in SNiP II-3–79, in our case 5.2 m 2 °C / W;
- λ is the thermal conductivity coefficient of the insulation, which for low-rise construction is assumed to be 0.04;
- P - the highest value of the density of the heat-insulating material. We will use Rocklight basalt insulation, for which P = 40 kg / m².
So, T \u003d 5.2 0.04 40 \u003d 8.32 ≈ 9 kg / m². Thus, the total load of the roof will be equal to 5 (metal tile) + 4 (solid decking) + 23 (basic lathing, additional and counter lathing) + 0.3 2 (insulating films) + 9 (insulation) + 3 (cladding) = 44 ,6 ≈ 45 kg/m².
Having received all the necessary intermediate values, we determine the total load on the supporting frame of the hipped roof: Q \u003d 133 + 17 + 45 \u003d 195 kg / m².
The allowable cross-section of lumber is calculated by the formulas:
- H ≥ 9.5 L max √ if angle α > 30°;
- H ≥ 8.6 L max √ if α< 30°.
The following notation is used here:
- H - board width (cm);
- L max - the maximum working length of the rafters (m). Since the layered rafter legs are connected in the ridge area, the entire length is considered to be working and L max = 4.79 m;
- R izg - an indicator of the resistance of wood to bending (kg / cm). According to the set of rules 64.13330.2011 for wood grade II R izg = 130 kg/cm;
- B is the thickness of the board, taken arbitrarily. Suppose B = 5 cm;
- Q r - load per linear meter of one rafter leg (kg / m). Qr \u003d A Q, where A is the pitch of the rafters, which in our case is 1 m. Therefore, Q r \u003d 195 kg / m.
Substitute the numerical values into the formula → H ≥ 9.5 4.79 √ = 9.5 4.79 0.55 = 25.03 cm ≈ 250 mm.
Table: nominal dimensions of softwood edged boards
| Board thickness, mm | Width (H) of boards, mm | ||||||||
| 16 | 75 | 100 | 125 | 150 | - | - | - | - | - |
| 19 | 75 | 100 | 125 | 150 | 175 | - | - | - | - |
| 22 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | - | - |
| 25 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 32 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 40 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 44 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 60 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 75 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 100 | - | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
| 125 | - | - | 125 | 150 | 175 | 200 | 225 | 250 | - |
| 150 | - | - | - | 150 | 175 | 200 | 225 | 250 | - |
| 175 | - | - | - | - | 175 | 200 | 225 | 250 | - |
| 200 | - | - | - | - | - | 200 | 225 | 250 | - |
| 250 | - | - | - | - | - | - | - | 250 | - |
From the table, the thickness of the board with a width of 250 mm can vary from 25 to 250 mm. The table of dependence of the section on the pitch and length of the rafters will help to determine more specifically. The length of the intermediate rafters is 4.79 m, the step is 1.0 m - we look at the table and select the appropriate section. It is equal to 75X250 mm.
Table: section of lumber depending on the length and pitch of the rafters
| 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 | 100X200 | 100x250 | - |
| 175 | 75X150 | 75X200 | 75X200 | 100X200 | 100X200 | 100X200 | 100x250 |
| 140 | 75X125 | 75X175 | 75X200 | 75X200 | 75X200 | 100X200 | 100X200 |
| 110 | 75X150 | 75X150 | 75X175 | 75X175 | 75X200 | 75X200 | 100X200 |
| 90 | 50X150 | 50X175 | 50X200 | 75X175 | 75X175 | 75X250 | 75X200 |
| 60 | 40X150 | 40X175 | 50X150 | 50X150 | 50X175 | 50X200 | 50X200 |
Here is another table for those who will use hardwood lumber.
Table: limit deviations from the nominal dimensions of boards
We check the correctness of the calculations by substituting the numerical parameters in the following inequality / ≤ 1. We get (3.125 195 x 4.79³) / (7.5 x 25³) = 0.57 - the section is chosen accurately and with a good margin. Let's check less powerful beams with a section of 50x250 mm. Substitute the values again: (3.125 195 x 4.79³) / (5 x 25³) = 0.86. The inequality is again fulfilled, so a 50x250 mm beam is quite suitable for our roof.
Video: calculation of the hip roof truss system
After all the intermediate calculations, we summarize: for the construction of the roof, we need 117 running meters of edged boards with a section of 50X250 mm. This is approximately 1.5 m³. Since it was initially agreed that for a four-pitched hip structure it is desirable to use lumber of the same section, then for the Mauerlat you should purchase the same timber in an amount equal to the perimeter of the house - 7.5 2 + 12 2 = 39 running meters. m. Taking into account a margin of 10% for cutting and marriage, we get 43 linear meters or approximately 0.54 m³. Thus, we need approximately 2 m³ of lumber with a section of 50X250 mm.
The length of the rafters is the gap from the undercut for the supporting part to the undercut for the ridge beam.
Video: an example of calculating the roof on an online calculator
Rafter system installation technology
The arrangement of a four-slope structure has its own characteristics, which must be taken into account:
Manufactured and assembled in compliance with all the rules, a rafter frame of a layered type for a four-slope roof will be a non-spreading structure. It is possible to prevent the appearance of spacers if, in the places of support on the Mauerlat, the planes of the rafters are made horizontal.
In most cases, two schemes are used to support the rafter legs.
In four-slope hip structures, the length of the corner legs is often greater than the typical length of lumber. Therefore, the timber and boards are spliced, trying to locate the joints at a distance of 0.15 of the span length (L) from the center of the supports, which is approximately equivalent to the interval between the support points. The rafters are connected using the oblique cut method, tightening the joints with bolts Ø12–14 mm. Wash down is recommended to be done on the rafters, and not on the support beam, so that the cut does not weaken the supports.
Since the standard length of most lumber does not exceed 6 m, the diagonal rafters are increased in length using the oblique cut and connected with bolts when using timber or with nails and clamps if boards are spliced.
Table: position of supports for corner rafters
| Span length, m | Support types | Location of supports |
| less than 7.5 | stand or brace | at the top of the rafters |
| less than 9.0 | stand or brace | at the top of the rafters |
| sprengel or rack | at the bottom of the rafters - 1/4L pr | |
| over 9.0 | stand or brace | at the top of the rafters at the bottom of the rafters - 1/4L pr |
| sprengel or rack | in the center of the rafters | |
| rack | in the center of the rafters | |
| Note: Lpr - the length of the span, which is covered by rafters. | ||
To join the sprigs with the rafters, the top of the half-rafters is ground down, keeping it in the same plane with the corner legs, and fixed with nails. When placing the rafters on the rafters, they strictly monitor that they do not converge in one place. If you use not a cut, but cranial bars 50X50 mm, stuffed in the lower zone of the rafters on both sides, when installing the sprigs, then the rigidity of the rafter legs will be higher, which means that their bearing capacity will increase.
To increase the rigidity of the rafter frame, it is recommended to use cranial bars, stuffed on both sides at the bottom of the rafter legs, when installing sprigs.
Do-it-yourself installation of a truss structure
The construction of the four-pitched roof frame is carried out in several stages.
- The materials are laid out and calculated, after which the roofing material is laid as a waterproofing around the entire perimeter of the building. A support for racks and a Mauerlat are laid on top of it, fixing it to the walls, fixing it especially well in the corners.
Mauerlat in four-slope structures is laid around the entire perimeter and is well fixed to the walls, especially at the corners, to create a strong knot for attaching diagonal rafters
- They install a frame for the ridge run and lay the run itself, rigidly maintaining the height and spatial arrangement of the ridge, since the strength and reliability of the entire truss structure directly depends on this.
- Support posts are placed using a water level for leveling and secured under the ridge with inclined supports. The arrangement of the racks is done based on the configuration of the roof - in the hip structure, the racks are installed in one row with an interval of no more than two meters, and in a hipped roof - diagonally at the same interval from the corner.
- Mount the central intermediate rafters, and then ordinary ones, filling the middle of the side slopes.
- According to the markup, corner rafters are installed, preferably made with reinforcement, resting them with their lower part on the corner of the Mauerlat, and with the upper fragment on the rack. Here they make a bookmark of the cornice overhang and drain.
- Next, half-rafters (springs) are placed, strengthening the lower part of the diagonal legs with trusses, which will partially unload the corner rafters, and sheathe the roof with a wind board around the perimeter of the roof.
Sprengel grating is used for steep roofs and relatively large spans in order to avoid deflection of the diagonal rafters
- After the installation of the rafter system, the roofing pie is laid, the cornice overhangs and the drainage system are equipped.
When installing the truss system of a four-pitched roof, you need to carefully consider the joining of the diagonal rafters, the central rafter from the side of the end of the building, as well as the ridge beam
Video: hipped roof on nails and a stool
Self-construction of a hipped roof is, of course, not an easy process. But if you have measuring instruments, as well as the necessary tools, you will succeed. The main thing is the desire to assemble the structure with your own hands and the desire to adhere to general principles. And in order for the roof to last as long as possible and retain its amazingly beautiful appearance, try not to save on the elements of the truss frame and use modern reliable metal fasteners for wood to fix them.
