# Snow Load on Monopitch and Duopitch Roofs

### Technical Article

In order to combine the snow loads with other actions (imposed loads, wind, etc.) in defined design situations according to the combination standard DIN EN 1990, the load is classified accordingly as variable, fixed and static action [1], [2]. It is important whether normal or exceptional conditions are present at the corresponding place of construction. A normal condition is assumed if exceptional snowfalls are unlikely to happen at this location. In this case, the load for the persistent/transient design situation has to be determined. An exceptional condition is assumed if snowfalls are likely to happen at this location. In the North German Plain, snow loads up to a multiple of the numerical values have been recorded in rare cases. In this case, the load for the persistent/transient and accidental design situation has to be determined. Drifted snow loads are, according to the National Annex, no accidental actions.

[3] | Normal conditions | Exceptional conditions |
---|---|---|

Case | Case A DIN EN 1991-1-3 3.2(1) | B1 DIN EN 1991-1-3 3.3(1) |

Description | No exceptional snowfalls No exceptional drifted snow load | Exceptional snowfalls No exceptional drifted snow load |

Design situation 1 | Persistent/transient | Persistent/transient |

Snow load s on the roof | Not drifted: ${\mathrm\mu}_\mathrm i\;\cdot\;{\mathrm C}_\mathrm e\;\cdot\;{\mathrm C}_\mathrm t\;\cdot\;{\mathrm s}_\mathrm k$ | Not drifted: ${\mathrm\mu}_\mathrm i\;\cdot\;{\mathrm C}_\mathrm e\;\cdot\;{\mathrm C}_\mathrm t\;\cdot\;{\mathrm s}_\mathrm k$ |

Drifted: ${\mathrm\mu}_\mathrm i\;\cdot\;{\mathrm C}_\mathrm e\;\cdot\;{\mathrm C}_\mathrm t\;\cdot\;{\mathrm s}_\mathrm k$ | Drifted: ${\mathrm\mu}_\mathrm i\;\cdot\;{\mathrm C}_\mathrm e\;\cdot\;{\mathrm C}_\mathrm t\;\cdot\;{\mathrm s}_\mathrm k$ | |

Design situation 2 | - | Exceptional (if snow is the accidental action) |

Snow load s on the roof | - | Not drifted: ${\mathrm\mu}_\mathrm i\;\cdot\;{\mathrm C}_\mathrm e\;\cdot\;{\mathrm C}_\mathrm t\;\cdot\;{\mathrm s}_\mathrm{Ad}$ with ${\mathrm s}_\mathrm{Ad}\;=\;{\mathrm C}_\mathrm{esl}\;\cdot\;{\mathrm s}_\mathrm k$ |

Drifted: ${\mathrm\mu}_\mathrm i\;\cdot\;{\mathrm C}_\mathrm e\;\cdot\;{\mathrm C}_\mathrm t\;\cdot\;{\mathrm s}_\mathrm{Ad}$ with ${\mathrm s}_\mathrm{Ad}\;=\;{\mathrm C}_\mathrm{esl}\;\cdot\;{\mathrm s}_\mathrm k$ | ||

${\mathrm\mu}_\mathrm i$ = Snow load shape coefficient ${\mathrm C}_\mathrm e$ = Exposure coefficient (according to NA, ${\mathrm C}_\mathrm e\;=\;1.0$ to be applied) ${\mathrm C}_\mathrm t$ = Thermal coefficient (according to NA, ${\mathrm C}_\mathrm t\;=\;1.0$ to be applied) ${\mathrm s}_\mathrm k$ = Characteristic value of the snow load on the ground ${\mathrm s}_\mathrm{Ad}$ = Design value for accidental snow load on the ground ${\mathrm C}_\mathrm{esl}$ = Accidental snow load coefficient (according to [5], ${\mathrm C}_\mathrm{esl}\;=\;2.3$ in the North German Plain) |

#### Characteristic Value of Snow Load on Ground

"The characteristic value of snow load on the ground is a fractile value of 98 % with an annual probability exceedance value of 0.02 and a return period of 50 years." [3] This value is defined in the National Annex of Germany and is calculated depending on the snow load zone and the height above sea level. The National Annex [2] shows in Figure NA.1 a map of Germany with zone indications. The exact assignment of snow loads of administrative units, particularly at the edges of the zones, has to be checked with the competent authorities. The German Centre of Competence for Construction (DIBt) offers in German the table "Categorization of snow load zones according to administrative limits" for each land on this subject on its website. Moreover, this table indicates for each administrative area the assignment to the North German Plain concerning the implementation of the accidental design situation.

Figure 01 - Snow Load Zones of Germany

Zone [2], [4] | Characteristic value of the snow load on the ground in kN/m² ${\mathrm s}_\mathrm k$ |
---|---|

1 | $0.19\;+\;0.91\;\cdot\;\left(\frac{\mathrm A\;+\;140}{760}\right)^2\;\geq\;0.65$ |

1a | $1.25\;\cdot\;\left[0.19\;+\;0.91\;\cdot\;\left(\frac{\mathrm A\;+\;140}{760}\right)^2\right]\;\geq\;0.81$ |

2 | $0.25\;+\;1.91\;\cdot\;\left(\frac{\mathrm A\;+\;140}{760}\right)^2\;\geq\;0.85$ |

2a | $1.25\;\cdot\;\left[0.25\;+\;1.91\;\cdot\;\left(\frac{\mathrm A\;+\;140}{760}\right)^2\right]\;\geq\;1.06$ |

3^{1)} | $0.31\;+\;2.91\;\cdot\;\left(\frac{\mathrm A\;+\;140}{760}\right)^2\;\geq\;1.10$ |

3a and > 3a^{2)} | $1.25\;\cdot\;\left[0.31\;+\;2.91\;\cdot\;\left(\frac{\mathrm A\;+\;140}{760}\right)^2\right]\;\geq\;1.10$ |

A = Ground elevation above sea level in m^{1)} In Zone 3, higher values may be governing than according to the equation mentioned above for certain locations (e.g. Oberharz, high altitudes of Fichtelgebirge, Reit im Winkl, Obernach/Walchensee). Information on snow load in this regions has to be requested from the competent authorities.^{2)} New zones 3a and > 3a on the basis of [4] according to the information of the Building Supervision Authority of the Bavarian Ministry for Internal Affairs of 19.01.2018 |

#### Determination with Dlubal Online Service

The Dlubal online service Snow load zones, wind zones and earthquake zones combines the standard specifications with digital technologies. The service places, depending on the selected load type (snow, wind, earthquake) and the country-specific standard, the respective zone map over the map of Google Maps. By using the search, it is possible to place a marker on the planned place of construction by defining the address, geographical coordinates or the local conditions. The application then determines through the exact height above sea level and the given zone data the characteristic load or the acceleration at this location. If the new place of construction cannot be identified by a specific address, it is possible to zoom in and to shift the focus to the correct place. With the displacement of the marker, the calculation is adapted to the new altitude and displays the correct loads.

The online service is available on the Dlubal website at Solutions → Online Services.

By defining the parameters...

1. Load type = snow

2. Standard = EN 1991-1-3

3. Annex = Germany | DIN EN 1991-1-3

4. Address = Zellweg 2, Tiefenbach

the following results are obtained for the selected location:

5. Snow load zone

6. If applicable: additional information

7. The characteristic value of snow load ${\mathrm s}_\mathrm k$

Figure 02 - Dlubal Online Service

If you select a position in the North German Plain, the online service displays at point 6 the note "North German Plain". Then the calculated load has to be considered as exceptional snow action in the exceptional design situation.

#### Shape Coefficient of Selected Roofs

Snow can occur in many different load distributions on the roof [1]. Amongst others, the snow load depends on the shape of the roof, the insulating properties, the surface roughness, the heat build-up under the roof, the neighboring buildings, the surrounding area and, of course, the local climate. Hence, it is essential that a non-drifted and drifted distribution of the snow load is considered during the design. The snow load to be applied acts perpendicular and refers to the horizontal projection of the roof surface.

Figure 03 - Projected Snow Load

Fundamentally, the shape coefficient ${\mathrm\mu}_\mathrm i$ depends on the inclination $\mathrm\alpha$ of the considered roof surface.

Shape coefficient | Roof inclination in $\mathrm\alpha$ | ||

$0^\circ\;\leq\;\mathrm\alpha\;\leq\;30^\circ$ | $30^\circ\;\leq\;\mathrm\alpha\;\leq\;60^\circ$ | $\mathrm\alpha\;>\;60^\circ$ | |

${\mathrm\mu}_1\left(\mathrm\alpha\right)$ | 0.8 | $\frac{0.8\;\cdot\;\left(60^\circ\;-\;\mathrm\alpha\right)}{30^\circ}$ | 0 |

The shape coefficients apply if the snow can slide off the roof unobstructedly. If sliding off is obstructed, for example, by a snow guard, attic, etc., the shape coefficient 0.8 has to be applied. |

A uniformly distributed load has to be applied with and without drift for flat and monopitch roofs.

Figure 04 - Shape Coefficient on Flat and Monopitch Roof

Three load arrangements have to be analyzed for duopitch roofs. Case a) shows the distribution without wind effects. Cases b) and c) show the distribution with influences from drift and melting. These two additional distributions are often governing for structures which are sensitive to unequally distributed loads.

Figure 05 - Shape Coefficient on Duopitch Roof

#### Keywords

snow zone plain monopitch duopitch shape coefficient

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