# Snow Load on Monopitch and Duopitch Roofs

## Technical Article on the Topic Structural Analysis Using Dlubal Software

### Technical Article

In Germany, DIN EN 1991-1-3 with National Annex DIN EN 1991-1-3/NA regulates snow loads. The standard applies to civil engineering works at altitudes of up to 1,500 m above sea level.

In order to combine snow loads with other actions (imposed loads, wind, etc.) in defined design situations according to combination standard DIN EN 1990, the load is classified accordingly as variable, fixed, or static action [1], [2]. The conditions present at the corresponding place of construction (normal or exceptional) are important. A normal condition is assumed if exceptional snowfall is 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 snowfall is 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. According to the National Annex, drifted snow loads are not accidental actions.

[3]Normal conditionsExceptional conditions
CaseCase A
DIN EN 1991-1-3 3.2(1)
B1
DIN EN 1991-1-3 3.3(1)
DescriptionNo exceptional snowfall
Exceptional snowfall
Design
Situation 1
Persistent/transientPersistent/transient
Snow load s on the roofNot drifted:

Formula 1

$$μi · Ce · Ct · sk$$

Not drifted:

Formula 1

$$μi · Ce · Ct · sk$$

Drifted:

Formula 1

$$μi · Ce · Ct · sk$$

Drifted:

Formula 1

$$μi · Ce · Ct · sk$$

Design
Situation 2
-Exceptional (if snow is the accidental action)
Snow load s on the roof-Not drifted:

Formula 2

$$μi · Ce · Ct · sAd$$

with
Drifted:

Formula 2

$$μi · Ce · Ct · sAd$$

with
# formula@000346# = shape factor for snow loads
# formula@000347# = environmental coefficient (# formula@000348# must be applied according to NA)
# formula@000349# = temperature coefficient (# formula@000350# must be applied according to NA)
# formula@000351# = characteristic value of the snow load on the ground
# formula@000352# = design value for accidental snow loads on the ground
# formula@000353# = coefficient for exceptional snow loads (according to [5] ,# formula@000354# in the North German Lowlands)

#### 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. In Figure NA.1 the National Annex [2] shows  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 [5]. The German Center of Competence for Construction (DIBt) offers (in German) the table "Categorization of snow load zones according to administrative limits" for each land area 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.

Zone [2], [4]Characteristic value of the snow load # formula@000351 # on the ground in kN/m²
1

Formula 13

$$0.19 0.91 · A 1407602 ≥ 0.65$$

1a

Formula 14

$$1.25 · 0.19 0.91 · A 1407602 ≥ 0.81$$

2

Formula 15

$$0.25 1.91 · A 1407602 ≥ 0.85$$

2a

Formula 16

$$1.25 · 0.25 1.91 · A 1407602 ≥ 1.06$$

31)

Formula 17

$$0.31 2.91 · A 1407602 ≥ 1.10$$

3a and> 3a 2)

Formula 18

$$1.25 · 0.31 2.91 · A 1407602 ≥ 1.10$$

A = Ground elevation above sea level in m
1) In Zone 3, higher values may govern than according to the equation mentioned above for certain locations (e.g., Oberharz, high altitudes of Fichtelgebirge, Reit im Winkl, Obernach/Walchensee). Information on the snow load in these regions has to be requested from the competent authorities.
2) New zones 3a and> 3a on the basis of [4] according to the notification of the Supreme Building Authority in the Bavarian State Ministry of the Interior of January 19, 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 the respective zone map over the Google Maps map, depending on the selected load type (snow, wind, earthquake) and the country-specific standard. Using the search, a marker can be placed on the planned construction location by defining the address, geographical coordinates, or local conditions. The application determines the characteristic load or the acceleration at this location using the exact height above sea level and the given zone data. If it is impossible to define the location by means of a specific address, you can zoom in to the map and select the correct location. When selecting the correct location on the map, the calculation will be adapted to the new altitude and will display the updated loads.

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

By defining the parameters...

2. Standard = EN 1991-1-3
3. Annex = Germany | DIN EN 1991-1-3
May address = Zellweg 2, Tiefenbach

...it results in the following for the selected location:

7. The characteristic value of the snow load

If you select a location in the North German Plain, the online service displays the message "North German Plain" at step 6. 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 a roof [1]. Among other things, the snow load depends on the shape of the roof, the insulating properties, the surface roughness, the heat buildup 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 perpendicularly and refers to the horizontal projection of the roof surface.

The shape factor # formula@000346 # basically depends on the inclination # formula@000361 # of the considered roof surface.

 Shape factor Roof slope in Formula 20 $$0° ≤ α ≤ 30°$$ Formula 21 $$30° ≤ α ≤ 60°$$ Formula 22 $$α > 60°$$ Formula 23 $$μ1α$$ 0.8 Formula 24 $$0.8 · 60° - α30°$$ 0 The shape coefficients apply if the snow can slide off the roof without being obstructed. If the sliding is obstructed (for example, by a snow guard, attic, etc.), 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.

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 often govern for structures that are sensitive to unequally distributed loads.

#### Dipl.-Ing. (BA) Andreas Niemeier, M.Eng.

Product Engineering & Customer Support

Mr. Niemeier is responsible for the development of RFEM, RSTAB, and the add-on modules for tensile membrane structures. Also, he is responsible for quality assurance and customer support.

#### Reference

 [1] Eurocode 1: Actions on structures - Part 1‑3: General actions - Snow actions; EN 1991‑1‑3:2003 + AC:2009 [2] National Annex - Nationally determined parameters - Eurocode 1: Actions on structures - Part 1‑3: General actions - Snow actions; EN 1991‑1‑3/NA:2010‑12 [3] Albert, A. (2018). Schneider - Bautabellen für Ingenieure mit Berechnungshinweisen und Beispielen (23rd ed.). Cologne: Bundesanzeiger. [4] Wichura, B.; Hoffmann, K.: Flächenhafte Analyse von Schneelastmesswerten in fünf Landkreisen und ihr Vergleich mit den Schneelastzonendaten der DIN 1055-5:2005 als Pilotuntersuchung für die Überarbeitung der Schneelastzonenkarte. Stuttgart: Fraunhofer IRB, 2017 [5] Deutsches Institut für Bautechnik: Zuordnung der Schneelastzonen nach Verwaltungsgrenzen. Berlin: Deutsches Institut für Bautechnik, 2018

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