DIY hipped roof: drawings, calculation of the rafter system

Recommendation points

• Hip roof options
• Basic diagrams and elements of the rafter system
• Main elements
• Reinforcement elements
• Calculation of the rafter system of the hipped roof
• Calculation of the lengths of rafter elements
• Calculation of the roof area taking into account overhangs

A hipped roof can be one- and two-level, have four or more slopes. For the correct selection of the sections of its elements, it is necessary to perform a sketch and correct calculation, which boils down to several formulas. In the article we will talk about the structure of the hipped roof and the method of calculating its rafter system.

A hipped roof is one of the most common options for building a house or a gazebo, having a circular, square or rectangular shape in plan with a slight difference in the lengths of the sides. This design is a good solution for houses of a relatively small area or two-storey cottages with a small base. The roof got its name from the pyramidal shape of the traditional oriental tent, formed by one top and triangular slopes..

Hip roof options

Under the name “hipped roof” several roofing options are combined that have structural differences.

Classic hipped roof

A single-level four-pitched roof is geometrically a four-sided pyramid. A two-level roof is a more complex structure: the upper part is a pyramid, the middle is a cube or parallelogram, and the lower is a truncated pyramid. It was as if the top of the roof had been cut off from the base and raised. The middle part is sometimes made in the form of a glass lantern or finished in the color of the walls.

Two-level hipped roof

A hip roof can have not only four slopes, but also six and eight slopes. This shape looks more like a cone than a pyramid, and is most common in the construction of arbors with a round base. The most difficult thing in the implementation of such a structure is the connection of the rafters in the center.

Six-sided roof

Roof rafters made of eight gentle slopes

The rafter systems differ not so much aesthetically as structurally:

• hanging;
• layered.

The hanging truss system rests exclusively on the walls of the house, the layered one has a support located in the center of the building and rests on a load-bearing wall or on a post specially erected inside the house.

a – the structure of the hanging rafters; b – the construction of layered rafters; 1 – rafter; 2 – crossbar; 3 – tightening; 4 – rack; 5 – brace; 6 – run; 7 – bed

The choice of design depends on the size of the span (8 m – a hanging system is suitable, 12 m – a layered system is required) and the maximum length of the timber for construction (when connecting a rafter leg in length, a vertical support is required).

In practice, the layered system is often used, as it is more reliable and maintainable. If the house does not have a suitable load-bearing wall or pillar for support, the base can be created from a bar by dressing at the Mauerlat level.

Basic diagrams and elements of the rafter system

As we wrote, the hipped roof is geometrically a pyramid, so all calculations are carried out based on the rules that apply to the pyramids and triangles that make up it.

Geometric image of a hipped roof

Main elements

In order not to be confused in the future with the terms, we will name the main elements of the rafter system of the hipped roof, schematically shown in the figure below, and link them to the geometric image of the hipped roof in the form of a pyramid.

Hanging rafter structure

1. Mauerlat.Roof base and support, especially with hanging rafters. It is located around the perimeter of the building (ABCD), rests on the walls or is mounted on their outside. For the Mauerlat device, a large section bar is used.
2. Slant rafters.Roof corners converging at a central point to form a pyramid. On the pyramid diagram (excluding overhangs): AK = DK = CK = BK = Lн. Longest rafter legs in construction.
3. Ridge knot (K).The most difficult knot in a carpenter’s design. If the base of the house is not square, but the ridge forms an edge, the hipped roof transforms into its “sister” – the vald roof. In a structure with layered rafters, the KF (H) section is the central support.
4. Central rafters.They converge in a ridge knot with nipple rafters. They are the height of each slope, which is an isosceles triangle. On the pyramid diagram (excluding overhangs) – a segment KE, length Lц.
5. Narodniks.These are shortened rafters running parallel to the central one in both directions.

Now consider constructions with layered rafters.

Rig-free construction with layered rafters

Along with the already designated elements: the slant (1) and central (2) rafters, as well as the ridge (3), new elements appear. The central support (rack) or headstock (4), which is supported by the braces (5), connecting the Mauerlat diagonally. This is an embodiment of a rack that rests not on the masonry, but on an element of the rafter system.

Reinforced rafters with crossbars

In the absence of central rafters and to strengthen the ridge knot with the headstock (2), it is complemented by crossbars (3) connecting oppositely placed slant rafters (1) in pairs (see the figure above).

Reinforcement elements

For greater strength and rigidity of the structure, especially in a climate prone to strong winds, or with a large building area, and therefore a large length of rafter legs, the main structural elements are supplemented with reinforcement elements.

Option to strengthen the rafter structure

Along the axis of the building, an additional bar is cut into the opposite beams of the Mauerlat (1) – a bed (2). The basis of the design, as before, is made up of central (4), shortened (rafters) (5) and oblique (3) rafters. The slanting rafters reinforce the cranial bars (6), fixed to the bottom. This reinforcement is for both the slant legs and for the wives who lean on them. The tie rods (7) hold the opposite rafters together and serve as a base for installing the struts (8). They are fixed on top of the Mauerlat and on top of the bed and rest on them.

With especially large lengths of rafter legs, struts are used – supports located not vertically, but at an angle of 45-60 °. In practice, struts are placed with a wall length of more than 9 m (for a gable or four-slope).

The system of strengthening the main elements also contributes to saving lumber. The cross-section of the main elements in such a structure can be taken as reduced. Another way of saving is the formation of overhangs by growing rafters ending in a Mauerlat, filly – bars or boards of a smaller section.

Overhangs with filly

Calculation of the rafter system of the hipped roof

The following initial data are taken as the basis for the calculation:

• the length of the house;
• width of the house
• ridge height.

Consider the order and formulas of calculations on a conditional example, using the geometric image of a hipped roof (see above):

• house length: AB = DC = 9 m;
• house width: AD = BC = 8 m;
• the height of the ridge located in the geometric center of the roof: KF = 2 m.

Calculation of the lengths of rafter elements

1. Length of beams mauerlata.

• AB + DC + AD + BC = 9 + 8 + 9 + 8 = 34 m

2. Central rafters(excluding overhangs). They are the hypotenuse of a right-angled triangle, in which one leg is the height of the ridge, and the other is half the width (8/2 = 4 m) or length (9/2 = 4.5 m) of the house.

We recall the Pythagorean theorem:

3. Slant rafters(excluding overhangs). They are the hypotenuse of a right-angled triangle, in which one leg is half the width or length of the house, and the other is the corresponding central rafter. For a roof with a ridge in the geometric center of the roof, the lengths of the slant rafters are the same.

4. Narodniks.The shortened rafters are located parallel to the central one, with a pitch depending on the length of the rafters. Consider a table compiled taking into account weather loads for the Moscow region.

Table 1. Data correspond to atmospheric loads in the Moscow region

Rafters step, cm	Rafter length, m
3.0	3.5	4.0	4.5	5.0	5.5	6.0
215	100×150	100×175	100×200	100×200	100×250	100×250	–
175	75×150	75×200	75×200	100×200	100×200	100×200	100×250
140	75×125	75×125	75×200	75×200	75×200	100×200	100×200
110	75×150	75×150	75×175	75×175	75×200	75×200	100×200
90	50×150	50×175	50×200	75×175	75×175	75×200	75×200
60	40×150	40×175	50×150	50×150	50×175	50×200	50×200

Our center rafters are 4.472 m and 4.924 m long.The rafters will be shorter, so you can look at the column – 3.5 m.

To calculate the lengths of the beads, let’s remember the school and use the properties of such triangles.

If in the figure AB is the central rafter, then MN is a man, AC is half the length of the wall (4.0 and 4.5 m, respectively), AM is a step depending on the number of people. MC for each spouse is calculated separately.

• MN = (AB MC) / AC

We will calculate the options for choosing the most economical location of the shortened rafters, the results of which will be summarized in a table.

Table 2. Calculation of sawn timber for women

Step of the wives, cm	Bar section, mm	Long side mongrels: AC = 4.5 m, AB = 4.472 m	Short side people: AC = 4.0 m, AB = 4.9242 m
number in half slope	AM, m	length in half slope, m	volume of lumber for two slopes, m3	number in half slope	AM, m	length in half slope, m	volume of lumber for two slopes, m3
215	100×175	1	2.25	2,356	0.165	1	2.0	2.461	0.172
175	75×200	2	1.5	2.981 + 1.491	0.268	1	2.0	2.461	0.148
140	75×175	2	1.5	2.981 + 1.491	0.235	2	1.333	3.282 + 1.641	0.258
110	75×150	3	1.125	3.354 + 2.236 + 1.118	0.302	3	1.0	3.693 + 2.462 + 1.231	0.332
90	50×175	4	0.9	3.578 + 2.683 + 1.789 + 0.894	0.313	3	1.0	3.693 + 2.462 + 1.231	0.259
60	40×175	6	0.643	3.834 + 3.195 + 2.556 + 1.917 + 1.278 + 0.639	0.376	6	0.571	4.218 + 3.515 + 2.812 + 2.109 + 1.406 + 0.703	0.413

Obviously, the less expensive options for our example are options with long strides. However, the requirements for fastening the roofing material and the costs of the lathing should also be taken into account. From this point of view, the answer will not be so obvious..

Calculation of the roof area taking into account overhangs

Since the previous calculation was carried out without taking into account the eaves overhang, which in our example is performed using filly, we will consider this part of the roof again as a simple geometric figure.

Eaves overhang

Let us take the length of the overhang (DC) equal to 0.5 m.To determine the area of ​​the slope, we again use the knowledge about the properties of such triangles:

• EF / BC = AG / AD

BC – 8 and 9 m for short and long walls, respectively.

AD – 4.924 and 4.472 m for short and long walls, respectively.

AG – 4.924 + 0.5 = 5.424 m and 4.472 + 0.5 = 4.972 m for short and long walls, respectively.

• EF = (AG • BC) / AD
• EF = (5.424 x / 4.924 = 8.812 m – for the short side
• EF = (4.972 * 9) / 4.472 = 10.006 m – for the long side

The area of ​​the slope is calculated by the formula:

• S = (EF • AG) / 2
• S = (8.812 * 5.424) / 2 = 23.9 m² – for the short side
• S = (10.006 * 4.972) / 2 = 24.88 m² – for the long side

Total area of ​​roofing material:

• 2 (23.9 + 24.88) = 97.56 m².

Advice! When calculating the material, take into account the cutting, especially if it is sheet material, such as slate or corrugated board.

Attention! The article considers the calculation of only the main elements of the rafter system, which can help in drawing up a preliminary budget for the construction.