The calculation of the rafter system on its own

A vital step in building or remodeling a home is figuring out the rafter system. It entails figuring out the lengths and angles of the rafters that make up the framework for the roof. By using this computation, it is ensured that the roof can support the weight of the covering material in addition to any other loads, such as wind or snow. Accurate computations also aid in material optimization, guaranteeing cost-effectiveness.

Important details like the span of the roof (the space between supporting walls), the intended pitch or slope of the roof, and the kind of roof covering to be used should be gathered before beginning the computation. These elements have an impact on the rafter system’s design. For instance, a shallower pitch might be selected for reasons related to regional architecture or aesthetics, but a steeper pitch works better for snow removal.

Usually, the computation procedure calls for the use of online calculators or mathematical formulas. These tools can be used by DIY enthusiasts or roofing professionals to input the collected data and determine the lengths and angles of the rafters. The measurements for the plumb cut (the top cut where the rafter meets the ridge), seat cut (the bottom cut where it rests on the wall plate), and any birdsmouth cuts (notches where the rafter meets the wall) are provided for each rafter in the output.

For the roof to be structurally sound, the rafter system must be calculated accurately. Inaccurate measurements may result in leaks, sagging roofs, or even structural collapse when large loads are applied. As a result, it is advised to verify calculations again and seek professional advice if necessary, particularly for intricate roof designs or unique building circumstances.

How to calculate the rafter system

Simplified calculating formulas are presented to increase the strength of the system’s elements so that users can calculate the materials used in the rafter system independently. This simplification results in a greater material requirement, but this increase won’t be noticeable if the roof is small in size. You can compute the following kinds of roofs using formulas:

• single -shoe;
• gable;
• The attic.

Video: Calculation of the rafter system

Comprehending the independent computation of a rafter system is essential for roofing construction endeavors. In order to ensure structural integrity and efficiency, this process entails determining important parameters such as roof slope, span, and load-bearing capacity. Homeowners and builders can confidently plan and implement safe and functional roof designs that are suited to particular architectural requirements and environmental conditions by understanding these computations."

Calculation of the load on the rafters of the gable roof

A sturdy supporting frame is required to construct an inclined roof, to which all other components will be fastened. The necessary length and cross-sectional area of the rafter beam and other rafter system components, on which the variable and constant load will act, are calculated during the project’s development.

Loads that are always in motion:

• the mass of all the structural elements of the roof structure, such as roofing material, crate, waterproofing, thermal insulation, internal sheathing of the attic or attic;
• A mass of equipment and various items that are attached to rafters inside the attic or attic.

• the load created by the wind and precipitation;
• The mass of the employee who performs repairs or cleaning.

Seismic loads and other unique loads that impose extra requirements on roof design are also considered variable loads.

The issue of snow load is severe in the majority of Russian Federation’s regions; the rafter system must recognize the resulting mass of snow without causing the structure to distort (this requirement is most pertinent to single-sided roofs). The amount of snow on the roof increases as the roof’s angle decreases. Installing rafters with a large cross-sectional area and a small step is necessary to set up a single shooting with a zero angle of inclination. It will also require cleaning on a regular basis. This is applicable to roofs with an inclination of up to 25 degrees.

The formula for calculating the snow load is s = sg × µ, where

• SG – a mass of snow cover on a flat horizontal surface with a size of 1 m 2 . The value is determined in accordance with the tables in the SNiP “rafter systems” based on the required area in which construction is carried out;
• µ – coefficient taking into account the angle of inclination of the slope of the roof.

When the inclination angle is set to 25 o, the coefficient value is 1.0; when the angle is set to 60 o, it is 0.7; above 60 o, the snow load value is not included in the calculations.

The formula w = wo × k is used to calculate the wind load, where:

• Wo is the magnitude of the wind load, determined according to the tabular values, given the nature of the area where construction is carried out;
• k is the coefficient that takes into account the height of the building and the nature of the area.

The values of the coefficients for a building height of 5 m are KA = 0.75 and KB = 0.85, 10 m – ka = 1 and kb = 0.65, and 20 m – ka = 1.25 and kb = 0.85.

Root section on the roof

It is not difficult to calculate the size of the rafter beam, given the next moment – the roof is a system of triangles (refers to all types of roof). Having the overall dimensions of the building, the value of the angle of the roof or the height of the ridge and using the Pythagore theorem, the size of the length of the rafters from the ridge beam to the outer edge of the wall is determined. The length of the cornice is added to this size (in the case when the rafters protrude behind the wall). Sometimes the cornice is made due to the installation of mares. Having calculated the area of ​​the roof, the values ​​of the lengths of the mares and rafters are summarized, which allows you to calculate the required amount of roofing material.

It is best to use reference books to find the cross-section of the bars used in the construction of any type of roof, according to the required length of the rafters, its installation step, and other parameters.

The rafter beam’s dimensions range from 40 by 150 to 100 by 250 mm. The distance between the walls and the angle of inclination determine the length of the rafters.

An increase in the roof’s slope causes the rafter beam’s length and, in turn, its cross-sectional area to increase. This is required to guarantee that the structure has the required strength. Concurrently, there is less snowfall, allowing for the installation of rafters with a large step. However, increasing the step will result in an increase in the overall load on the rafter beam.

Make sure to account for all the details in your calculation, including the humidity, the density and quality of the lumber (if a wood roof is being built), and the thickness of the rolling used (if a metal roof is being built).

The fundamental idea behind the calculations is that the size of the beam’s cross section is determined by the amount of load applied to the roof. Stronger designs have larger cross sections, but they also have higher total masses, which puts more strain on the building’s foundation and walls.

How to calculate the length of the rafters of the gable roof

The stiffness of the design of the rafter system is a mandatory requirement, and its ensuring excludes the deflection when exposed to loads. The rafters are bended in the case of errors made in the design of the structure and the step size, with which the rafter beam is installed. In the case when this defect is detected after the end of the work, it is necessary to strengthen the structure using struts, thereby increasing its stiffness. With the length of the rafter beam of more than 4.5 m, the use of struts is mandatory, since the deflection will form in any case under the influence of its own weight of the beam. This factor is necessarily taken into account when performing calculations.

Determination of the distance between the rafters

In a residential building, the rafters are typically installed in steps of between 600 and 1000 millimeters. Its worth influences:

• calculated load;
• The cross -section of the beam;
• description of the roof;
• the angle of inclination of the roof;
• The width of the material of the insulation.

The process by which they will be established is taken into consideration when defining the necessary number of rafters. For this:

1. The optimal installation step is selected.
2. The length of the wall is divided into a selected step and a unit is added to the obtained value.
3. The resulting number is rounded to the whole.
4. The length of the wall is re -divided by the resulting number, thereby determining the desired step of installation of the rafters.

The intersostean distance between them must be considered when determining the necessary number of rafters.

The area of the rafter system

The following elements need to be considered when figuring out the gable roof’s area:

1. Total area, which consists of the area of ​​two slopes. Based on this, the area of ​​one slope is determined and the resulting value is multiplied by the number 2.
2. In the case when the sizes of slopes differ among themselves, the area of ​​each slope is individually. The total area is calculated by the addition of the obtained values ​​for each slope.
3. In the case when one of the angles of the ramp is larger or less than 90 o in order to determine the area of ​​the ramp, it is “divided” into simple figures and their area is calculated separately, and then the results are folded.
4. When calculating the area, the area of ​​chimney, windows and ventilation ducts is not taken into account.
5. The area of ​​pediment and cornice overhangs, parapets and firewall walls are taken into account.

For instance, the house is 9 meters long and 7 meters wide, with a 4 meter rafter beam, a 0.4 meter cornice overhang, and a 0.6 meter overhang.

The formula s = (lDD+2 × lFS) × (lC+LKs) can be used to find the value of the slope’s area.

• L_DD – wall length;
• L_FS – the length of the overhang overhang;
• L_C – the length of the rafter beam;
• L_Ks – The length of the cornice overhang.

As it happens, S = (9+2 × 0.6) × (4+0.4) = 10.2 × 4.4 = 44.9 m 2 is the area of the slope.

The roof’s total area is S = 2 × 44.9 = 89.8 m^2.

The length of the slopes will decrease by 0.6–0.8 meters if roofing material is tile or soft coating applied in rolls.

The amount of roofing material needed is calculated based on the size of the gable roof. The amount of material used increases as the roof’s tilt angle increases. About 10% to 15% should be the supply. The cause is the laying of an overlap. It is best to use reference books to calculate the precise amount of material, accounting for the slope of the slopes.

Video: Rail system of a gable roof

How to calculate the length of the rafters of the hip roof

The rafter system is the same in all roof types despite their differences in design. Regarding roofs with holly:

1. Skate supporting beam or skate beam – is a supporting element of the structure of the roof of a roller type. Diagonal rafters are fastened to it. The length of the timber is calculated by the formula: l_skate = L – d, where l and d are equal to the length and width of the sides of the building.
2. The central rafter is a bar, which is located along the edge of the rafter system and forms the angle of inclination of the front -ton slope of the roof. The upper edge rests on the skate. The length of the central rafters is calculated by the formula: l_{center.rafters} = h 2 + d 2, where h is the height of the ridge, and D is the distance from the end of the skate to the wall.
3. Intermediate or ordinary rafters – form the surface of the trapezoidal slope. Installed according to the calculated step. The length of ordinary rafters is calculated according to a similar formula for central rafters.
4. Diagonal rafters (lateral, ribs, clock or corner rafters) – a rafter beam that rests on the end of the skate, and the lower part into the corner of the house. Diagonal rafters determine the shape of roof slopes. The length of the diagonal rafters is calculated by the formula: l_{Dia. rafters}= √ (l 2 +d 2), where l is the length of the central rafters, and D is the distance from the lower part of the rafter beam to the corner of the house.
5. Penetrins or short rafters – a short rafter bar, which is mounted with the upper end to the diagonal rafter and forms the angular part of the trapezoidal slope. The length of the people is calculated according to the following formulas:
6. The first Noshod l₁ = 2L/3, where L is the length of the intermediate rafters;
7. The next Nosyotnik l₂ = L/3, where l is the length of the intermediate rafters.
8. The calculation of the necessary lengthening of the rafters for the formation of the cornice overhang is performed according to the DL = K/COSα formula, where K is the distance from the edge of the cornice overhang to the wall, COSα is the roof angle of the angle of the roof.
9. The angle of inclination of ordinary rafters is determined by the formula β = 9 o – α, where α is the angle of inclination of the slope of the roof.

Video: Hot roof rafter system

Any homeowner or builder taking on a roofing project has to know how to calculate their own rafter system. Gaining control over this process will help you ensure cost-effectiveness and structural integrity in your construction.

First and foremost, it is crucial to ascertain the span and pitch of your roof. The pitch of a roof is its angle, and the span is the amount of horizontal space it will cover. The overall stability and drainage of your roof are directly impacted by these measurements, which also determine the sizes and angles of your rafters.

The next step in determining the rafter length is to apply fundamental trigonometric concepts. You can precisely calculate each rafter’s length by using the sine function and the Pythagorean theorem. This stage is essential for making the right material purchases and guaranteeing accurate construction.

Calculating the rafter spacing is also necessary to ensure that the chosen roofing material is sufficiently supported. The type of roofing material, regional building codes, and the anticipated load-bearing capacity of your roof are some of the variables that affect this spacing.

Furthermore, maintaining the structural integrity of your roof requires knowing how to compute and distribute the load on the rafters. This entails taking wind resistance, snow load, and any potential additional weight from upcoming installations or renovations into consideration.

Finally, becoming proficient in these computations gives you the ability to confidently manage your roofing project and make sure it complies with local environmental regulations and safety standards. You can have a roof that not only protects your house but also increases its value and aesthetic appeal with careful planning and accurate calculations.

Video on the topic

Ritual system of the gable roof / How to fix the rafters / Options for fastening the roof

Installation of rafters with your own hands. Gable roof. Cold attic.

Gable roof.