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You can imagine a man without bones? Similarly, the pitched roof and no roof system is more similar to the structure of the tale about three pigs that easily swept away the natural elements. Sturdy and reliable system of rafters – a pledge of longevity of the roof structure. In order to construct a system of rafters, it is necessary to take into account and forecast the main factors affecting the strength of the structure.

To take into account all the curves of the roof, the correction factors for uneven distribution of snow on the surface, the demolition of snow by the wind, slope of ramps, all aerodynamic coefficients, forces impact on the structural elements of the roof, and so on - to calculate all this as close as possible to the real situation, and consider all loads, and artfully to collect the combination – not an easy task.

If you want to understand thoroughly – the list of useful literature is given in the end of the article. Of course, the course strength of materials for a full understanding of the principles and impeccable calculation of the truss system in one article does not fit, and the following are highlights **for the simplified version ****of the calculation**.

**Classification of loads**

The load on the truss system are classified into:

1) **Main**:

*constant load*: the weight of themselves-truss and roof*long loads*– snow and temperature loads low design value (used if necessary, taking into account the influence of duration of loads, with the test of endurance),*variable short-term effect*- snow and temperature effects on the full design value.

2) **Supplementary **– wind pressure, the weight of builders, ice load.

3) ** Force majeure** , such as explosions, seismic activity, fire, accident.

For the calculation of the rafter system adopted to calculate the limit load, then, based on the counted values, determine the parameters of the elements of the truss system that can withstand these loads.

The calculation of roof systems of pitched roofs is made **for two limit States: **

a) the Limit at which the destruction of the structure. The maximum possible load on the structural strength of the rafters must be less than the maximum allowable.

b) Limit state, which causes a deflection and deformation. The resulting deflection of the system under load should be less than the maximum possible.

For a more simple calculation is used only the first method.

**The calculation of the snow loads on the roof**

For calculation of **snow loads** use the following formula: Ms = Q x Ks x Kc

where **Ms** is the snow load,

**Q** - the weight of the snow cover, covering 1m2 flat horizontal surface of the roof. Depends on the territory and is defined by the map in figure X for the second limit state based on deflection (at the location of the house at the junction of two zones, select a snow load with a large value).

For strength calculation for the first type value of the load is selected according to the area on the map (the first digit in the specified fraction is the numerator), or taken from the table №1:

The first value in the table is measured in kPa in brackets need a translated value in kg/m2.

**Ks** - correction coefficient on the angle of the roof.

- For roofs with steep slopes with an angle over 60 degree snow loads are not considered Ks=0 (the snow accumulates on pitched roofs cool).
- For roofs with an angle of from 25 to 60, the factor is taken as 0.7.
- For the rest it is equal to 1.

The angle of the roof, you can determine **online calculator the roof** of the appropriate type.

**Kc** – coefficient of wind drift of snow from the roof. Subject to the gently sloping roof with the angle of the slope 7-12 degrees in the areas on the map with wind speed 4 m/s, was adopted by Kc = 0.85. The map shows the zoning of the wind speed.

The ratio of drift **Kc **is not taken into account in areas with a January temperature is warmer than -5 degrees, as the roof forms an ice crust, and blowing snow is not happening. Not taken into account the coefficient in the case of closure of the building from the wind higher neighbouring building.

Snow falls unevenly. Often on the leeward side forming the so-called snow bag, especially in the joints, fractures (valley). Therefore, if you want a durable roof, step to the minimum of the rafters in this place, also pay close attention to the recommendations of manufacturers of roofing material, the snow can break off the overhang, if it is wrong size.

Remember that the above calculation, proposed in a simplified form. For more reliable calculation of the suggest to multiply the result by the reliability coefficient for the load (snow load = 1,4).

**Calculation of wind loads on the truss system**

With pressure snow settled, we now turn to the calculations of wind influence.

Regardless of the angle of the slope, the wind strongly affects the roof: the roof crotonate trying to lose, more flat roof – lift to leeward.

To calculate load shifting into consideration taking it a horizontal direction, while it is blowing bi-directionally: on the facade and roof slope. In the first case the flow is divided into several part goes down to the Foundation, part of the flow tangentially from the bottom vertically presses on the overhang of the roof, trying to lift it.

In the second case, acting on the roof, the wind pressure perpendicular to the slope, pressing it; it also creates turbulence at a tangent on the windward side, skirting the ridge and turning into a lifting force on the leeward side, in connection with the difference in wind pressure from both sides.

For calculating the average **wind load** use the formula

**Mv = Wo x Kv x Kc x the coefficient of strength**,

where **Wo** is the wind load pressure specified on the map

**Kv** - correction factor wind pressure depending on height of building and terrain.

**Kc** - aerodynamic coefficient depends on the geometry of the roof structure and direction of the wind. Negative values for leeward, windward positive for

For a shed roof you need to take the factor from the table for Ce1.

To simplify the calculation, the value of C is easier to take a maximum of 0.8.

For more reliable results suggest multiply by **the factor of safety** for wind load = 1,2.

**Calculation of self-weight, roofing**

**For calculating the continuous load** you need to calculate the weight of the roof (roof –see figure X below) per 1 m2, the weight obtained must be multiplied by a correction factor of 1.1 to a load of the truss system must withstand during the entire period of operation.

The weight of the roof consists of:

- the volume of forest (m3), used as sheathing, is multiplied by the wood density (500 kg/m3)
- the weight of the truss system
- the weight of 1m2 of roofing material
- the weight of the weight of 1m2 of insulation
- the weight of 1m2 of surfacing material
- the weight of 1m2 of waterproofing.

All these parameters are easy to specify these details from the seller, or look up the label key features: m3, m2, density, thickness, to produce simple arithmetic operations.

**Example:** for insulation of density 35 kg/m3, Packed by roll thickness 10 cm or 0.1 m with a length of 10m and a width of 1.2 m, **weight of 1 m2** will be equal to (0.1 x 1.2 x 10) x 35 / (0.1 x 1.2) = 3.5 kg/m2. The weight of the rest of the materials can be calculated on the same principle, but do not forget centimeters to meters translate.

**Most often** the load of the roof on 1 m2 does not exceed 50 kg, therefore, when calculating the lay that is the value multiplied by 1.1, i.e. 55 kg/m2, which is itself taken stock.

More data can be taken from the table below:

Slate |
10 - 15 kg/m2 |

Onduline |
4 - 6 kg/m2 |

Ceramic tile |
35 - 50kg/m2 |

Cement-sand tile |
40 - 50 kg/m2 |

Shingles |
8 - 12 kg/m2 |

Metal |
4 - 5 kg/m2 |

Corrugated sheet |
4 - 5 kg/m2 |

Weight rough flooring |
18 - 20 kg/m2 |

The weight of the crates |
8 - 12 kg/m2 |

The weight of the truss system |
15 - 20 kg/m2 |

**Collect load**

Simplified version now, you need to add all the found load by simple summation, we get the final load in kilograms per 1 m2 of the roof.

**The calculation of the rafter system**

After collecting the key pressures, you can already determine the main parameters of the rafters.

- What is the
**distributed load**per truss leg separately, translate kg/m2 in kg/m.

Consider the formula: ** N = pitch of rafters x Q**, where

N - uniform load on the rafter foot, kg/m

step rafters - distance between rafters, m

Q is calculated above the total roof load, kg/m2

From the formula it is clear that the change of the distance between the rafters can be adjusted uniform load on each rafter foot. Typically, the pitch of rafters is in the range from 0.6 to 1.2 m. For roof insulation when choosing step it is reasonable to focus on the parameters sheet of insulation.

In General, when defining the step of installation of the rafters it is better to come for economic reasons: to calculate all the arrangements of the rafters and to choose the cheapest and the best quantitative material consumption for the truss.

**Calculation of the cross section and the thickness stropilnoj feet**

In the construction of private houses and cottages, the choice of cross-section and thickness of the rafters, guided by the table below (a section of rafters in mm). In the table average values for the territory of Russia, and also takes into account the dimensions of building materials on the market. In General, this table is enough to determine what section you need to purchase a forest.

However, we should not forget that the dimensions of the truss legs depend on the design of roof system, quality of the material used, the permanent and the variable loads exerted on the roof.

In practice, in the construction of private residential houses are most commonly used for rafters and boards section 50h150 mm (thickness x width).

**Independent calculation of the cross section of the rafters**

As mentioned above, rafters are calculated based on the maximum load and deflection. In the first case, consider the maximum bending moment in the second section of the truss legs are checked for resistance to the deflection on the longest stretch of stairs. The formula is quite complex, so we have selected for you **a simplified version.**

If you want to calculate select the width of the cross section in accordance with the table:

The thickness of the section (or height) is calculated using the formula:

a) If the angle of the roof < 30°, rafters are treated as flexible

H ≥ 8.6 x Lm x √(N / (B x Rизг))

b) If the roof pitch > 30°, rafters bent-compressed

H ≥ 9.5 x Lm x √(N / (B x Rизг))

Designations:

**H, cm** - the height of the rafters

**Lm, m **- the working portion of the longest truss legs

**N****,** **kg/m** distributed load on the rafter foot

**B, cm **- the width of the rafters

**Rизг**, **kg/cm2** - resistance of wood to bending

For pine and spruce** Rизг **depending on the type of wood is equal to:

1st grade |
140 kg/cm2 |

2nd grade |
130 kg/cm2 |

3 grade |
85 kg/cm2 |

It is important to check whether the deflection exceeds the allowed value.

The amount of deflection of the rafters must be less than **L/200 **- check the length of the greatest span between supports in inches divided by 200.

This condition is true if the following inequality:

**3,125 ****x****N****x****(****Lm****)3 / (****B****x****H****3) ≤ 1**

N (kg/m) distributed load per meter rafter feet

Lm (m) is the working portion of the rafter feet maximum length

B (cm) - width of the section

H (cm) - height cross-section

If the value is greater than one, you must increase the parameters of rafters **B** , or **H**.

**Sources:**

- SNiP 2.01.07-85 Loads and impacts from recent changes 2008.
- SNiP II-26-76 "Roof"
- SNiP II-25-80 "timber structures"
- SNiP 3.04.01-87 "Insulation and finishes"
- A. A. Savel'ev "roof system" 2000
- K-G. Goetz, Dieter with a stay at Karl Meller, Julius Natterer "Atlas of wooden structures"

Useful links for automated calculations: