Although architecture is always presenting new concepts for single and multi-family houses, the gable roof house remains the standard in construction to this day. A timbered roof truss is required with a gable roof. The main load of the roof is dissipated by the rafters, the sloping beams. How to calculate the rafters, you will learn in this text.
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How to calculate rafters?
The type, number and cross-section of the rafters depends on the load they bear under maximum conditions. The load creates bending stress on the rafters. The load acting vertically on the projected area per square meter is always used as the basis. This is important to remember: the more pointed the roof, the longer the rafter placed under the projected square meter will be. However, the compressive stress on the purlins also increases. Overall, calculating a roof truss is a demanding task that should be carried out by a structural engineer.
The following factors are required to calculate the rafter:
- snow load zone
- rafter length
- roof angle
- roof skin
- roof type
- Cross-section of the rafters
- Distance of the rafters to each other
- material of the rafters
- Expansion reserves for additional loads (photovoltaic, solar thermal)
snow load zone
In which snow load zone is the house located?
This question is at the very beginning of calculating the rafters. Europe is divided into so-called “snow load zones”. They depend essentially on the height above sea level at which the house is built. In addition, the snow load zones are also assigned to specific regions. There is a map of Europe that shows the snow load zones.
You have to know: Ten centimeters of fresh new snow already produces 100 kg per square meter, which corresponds to one kilonewton (kN). Ten centimeters of compacted old snow can weigh as much as 300 kg. The exact snow load zone can also be obtained from the local town hall.
Determine rafter length
The rafter length is the diagonal between the ridge and eaves points. Only the distance between these two points is relevant for the calculation of the statics. This means: the rafter can protrude beyond both points. This is largely irrelevant for the statics. The emphasis is on “as far as possible”: it can make sense to extend the rafter well beyond the ridge edge. For example, you can install a vestibule or a carport at the same time. However, the leverage forces that occur must in turn be included in the overall statics. If necessary, the rafter is secured with an additional support.
The more pointed the roof, the lower the snow load. On the other hand, the rafters are getting longer and the wind pressure is increasing. The flatter the roof, the shorter rafters you can use. On the other hand, the usable space under the roof is reduced until it can practically no longer be used at all. In addition, the desired roof skin sometimes dictates the minimum roof pitch.
Formula for roof angle
The roof angle is the angle between the straight line connecting the ridge beams transverse to their direction and the rafters. It’s not the angle in the rooftop. With a symmetrical roof, however, one can easily deduce the angle at the top of the roof: 180 – 2 x roof angle = angle at the top of the roof.
This way, you get a better impression of how pointed or flat the roof will be afterwards. However, this angle is irrelevant for determining the rafter length.
The following minimum roof angles apply to common roof coverings:
- Fiber cement panels: 25°
- Natural slate: 22°
- Concrete roof tiles: 22°
- Roof tiles: 22° – 30°
- Plastic plates: 15°
- Trapezoidal sheets: 4°-7°
This shows how important it is to determine the cover material.
After all, determining the rafter length is quite simple. The rafter forms the hypotenuse in a right triangle. The roof angle is formed between the rafter and the adjacent side. The length of the rafter can be calculated with the help of the law of cosines “adjacent leg / hypotenuse = cosine” : Roof angle = distance between the eaves point and the ridge beam / rafter
These forms are simply converted to determine the rafter length and you get:
Rafter = distance between eaves point and ridge beam / roof angle
Conversely, this also results in the roof height. The perpendicular between the peak of the roof and the attic forms the opposite side of the triangle. The law of sine “opposite leg / hypotenuse = sine” applies here. Alternatively, you can use the Pythagorean theorem.
When determining the rafter length, the desired overhang is now added. Now the cross-section has to be determined. This requires the type of roof, the desired spacing between the joists and the material of the rafters.
The simplest roof construction is the purlin roof. The purlins are beams that run across the rafters and provide the support for them. However, the purlins must be supported. This took up space and restricted the usability of the roof truss. The rafters are particularly lightly loaded with a purlin roof.
The collar beam roof has no middle purlins or ridge beams. The rafters meet sharply and support each other. In addition, boards running across the rafters are nailed to the side of the rafters halfway up the rafters. A collar beam roof is ideal for large attic spaces. They allow light, wide spaces. With clever planning, an additional attic is even possible. However, the bending stresses on the unsupported rafters are quite high
The rafter roof also has no purlins and no collar beams. The rafters meet sharply. This construction is statically very critical and requires precise execution. The bending stresses on the beams are quite high, which is why the rafter roof is only suitable for small roofs.
Distance between the rafters
As a house planner, you have a legitimate interest in constructing a roof structure with as few rafters as possible. The fewer rafters used, the greater the distance between them. This allows the installation of ever larger windows or dormers. In addition, a roof truss with fewer rafters is quicker to erect. Of course, the rafters have to be more stable the fewer of them are installed. This stability is achieved through the material and/or cross-section of the rafters.
Material of the rafters
Of course, wood is the common building material for roof structures. But there are big differences in the stability of the types of wood. The common material for rafters today are cut spruce or fir trunks. Laminated beams are only used when particularly thick beams are required.
Spruce, pine, Douglas fir and fir are the standard wood used for roof trusses today due to availability and low price. Oak, which used to be commonly used, is practically irrelevant today. With 13 – 17 N/mm², they all have a comparable bending stress, which is completely sufficient for use as a normal roof truss. As solid wood, the strength of the beams made from them is limited. The following dimensions of rafter beams are available as standard today:
|Rafter Dimensions||Max. bending stress (in kN/mm²)||Costs (per running meter in euros)|
|40mm x 60mm (2400mm²)||31.2 – 40.8||1.60|
|60mm x 60mm (3600mm²)||46.8 – 61.2||2.40|
|60mm x 80mm (4800mm²)||62.0 – 81.6||3.20|
|60mm x 100mm (6000mm²)||78.0 – 102||4.00|
|60mm x 120mm (7200mm²)||93.6 – 122.4||4.80|
|60mm x 140mm (8400mm²)||109.2 – 142.8||5.60|
|60mm x 240mm (14400mm²)||187.2 – 244.8||9.50|
|80mm x 80mm (6400mm²)||83.2 – 108.8||4.30|
|80mm x 100mm (8000mm²)||104.0 – 136.0||5.30|
|80mm x 120mm (9600mm²)||124.8 – 163.2||6.40|
|80mm x 140mm (11200mm²)||145.6 – 190.4||7.40|
|80mm x 160mm (12800mm²)||166.4 – 217.6||8.50|
|80mm x 200mm (16000mm²)||208.0 – 272.0||10.60|
|80mm x 240mm (19200mm²)||249.6 – 326.4||12.70|
|100mm x 100mm (10000mm²)||130.0 – 170.0||6.70|
|100mm x 120mm (12000mm²)||156.0 – 204.0||8.00|
|100mm x 140mm (14000mm²)||182.0 – 238.0||10.00|
|100mm x 160mm (16000mm²)||208.0 – 272.0||10.60|
|120mm x 120mm (14400mm²)||187.2 – 244.8||10.00|
|120mm x 200mm (24000mm²)||312.0 – 408.0||16.00|
|140mm x 140mm (19600mm²)||254.8 – 333.2||13.00|
|140mm x 240mm (33600mm²)||436.8 – 517.2||22.50|
If the required bending stresses are not reflected in this table, a laminated truss or a double-T steel girder must be used. Caution: In the entire construction industry, static factors must never be rounded down, but must always be rounded up!
Rafters and roof beams are always installed “upright”, never “lying”!
In the case of rafters that are cut to rest on a purlin, the perpendicular from the cut edge to the solid wood must be subtracted from the rafter height! Otherwise you build many predetermined breaking points in the roof, which sooner or later become noticeable!
In order to calculate the rafters, the maximum load to be expected (snow load, battens, roof skin, insulation, internal formwork, additional loads such as solar modules…) is determined and the compressive stress per square meter is calculated from this. The desired rafter spacing is offset against this. This gives a cross-sectional area of the rafter beam. The rafter height and width are read from the cross-sectional area. Finally, the cut edge for the purlin support must be included in the rafter height.
Conclusion: Don’t take it lightly!
We do not recommend relying on rules of thumb or simplified formulas when calculating rafters. Especially as a layman, mistakes can quickly creep in, which either make the construction unnecessarily expensive or endanger its statics. This article is intended to raise awareness and sensitivity to leave these tasks to a professional structural engineer. This is always money well invested and gives a secure feeling when building a house.