# Determination of snow bag for height changes on roofs according to EN 1991-1-3

### Technical Article

New

001611

11/06/2019

Annexes are often found on buildings. If the roof levels are not at the same depth, this elevation jump (if more than 0.5 m) must additionally be considered for the snow load assumption.

In addition to the normal snow load, which is applied to the roof below, an additional load from slipping and blown snow has to be considered. These two additional loads are distributed triangularly over the length of the flywheel l s .

Additional impact loads due to the snow slipping off the higher roof may also have to be taken into account.

γ = weight of snow = 2 kN/m³

h = depth of the eavesdropping

s k = characteristic value of the snow load on the ground in kN/m²

l s = drift length = $2 \; \ cdot \; \ mathrm h \; \ left \ {\ begin {array} {l} \ geq \; 5 \; \ mathrm m \\ leq \; 15 \; \ mathrm m \ end {array} \ right.$
If the length of the underlying roof b 2 is shorter than the length of the gougule wedge l s , then the load ordinates must be cut off at the edge of the roof.

μ 1 = 0.8 (assuming the lower roof is flat)

μ 2 = μ s + μ w

μ s = shape coefficient for derived snow
α ≤ 15 °: μ s = 0
α> 15 °: μ s results from an additional load that is distributed triangular to length l s . As an additional load, 50% of the resulting snow load is applied to the adjoining roof side of the higher roof.

μ = shape coefficient of the roof at a higher level = 0.8 (regardless of the roof inclination)

μ w = shape coefficient for snow with consideration of wind = $\ frac {{\ mathrm b} _1 \; + \; {\ mathrm b} _2} {2 \; \ cdot \; \ mathrm h} \ le \ \ ; \ frac {\ mathrm \ gamma \; \ cdot \; \ mathrm h} {{\ mathrm s} _ {\ mathrm k}}$

In addition, the sum of the shape coefficients μ w + μ s can be limited by the National Annex (Germany) as follows.

Common case:
0.8 ≤ μ w + μ s ≤ 2.4

Canopies open at the side and accessible for evacuation (b 2 ≤ 3 m):
0.8 ≤ μ w + μ s ≤ 2

For snow regions s k ≥ 3.0 kN/m², the upper limit applies for the alpine region according to DIN EN 1991-1-3: 2010-12 and DIN EN 1991-1-3/A1: 2015-12, Figure C.2 Limitation:
1.2 ≤ μ w + μ s ≤ (6.45/s k 0.9 )

Exceptional actions (North German Plain) in general:
0.8 ≤ μ w + μ s ≤ 2.4

When arranging snow guards or similar structures, it is not necessary to use μ s .

#### Example:

b 1 = 10 m
b 2 = 5 m
h = 3 m
Roof inclination of the roof at a higher level = 30 °
A = 100 m
μ 1 = 0.8
s k = 0.25 + 1.91 ⋅ ((A + 140)/760) ² ≥ 0.85 → 0.85 kN/m²

Uniformly distributed snow load on the roof below:
μ 1 ⋅ s k = 0.8 ⋅ 0.85 kN/m² = 0.68 kN/m²

Length of drift wedge:
${\mathrm l}_{\mathrm s}\;=\;2\;\cdot\;\mathrm h\;\left\{\begin{array}{l}\geq\;5\;\mathrm m\\\leq\;15\;\mathrm m\end{array}\right.=\;2\;\cdot\;3\;\mathrm m\;=\;6\;\mathrm m$

Shape coefficient for derived snow:
μ s = 0.67

Shape coefficient for snow with consideration of wind:
$µ_{\mathrm w}\;=\;\frac{{\mathrm b}_1\;+\;{\mathrm b}_2}{2\;\cdot\;\mathrm h}\;\leq\;\frac{\mathrm\gamma\;\cdot\;\mathrm h}{{\mathrm s}_{\mathrm k}}\;\\µ_{\mathrm w}\;=\;\frac{10\;\mathrm m\;+\;5\;\mathrm m}{2\;\cdot\;3\;\mathrm m}\;\leq\;\frac{2\;\mathrm{kN}/\mathrm m³\;\cdot\;3\;\mathrm m}{0,85\;\mathrm{kN}/\mathrm m²}\;=\;2,50$

Limitation of shape coefficients (general case):
0.8 ≤ μ w + μ s ≤ 2.4
μ 2 = μ w + μ s = 2.5 + 0.67 = 3.17 → 2.4

μ 2 ⋅ s k = 2.4 ⋅ 0.85 kN/m² = 2.04 kN/m²

In RFEM and RSTAB, it is possible to conveniently apply the load arising from drifted snow and shifting snow as a linearly variable surface load. For frameworks, for example, you can apply the load with the load generator.

#### 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:2019‑04 [3] Albert, A.: Schneider - Bautabellen für Ingenieure mit Berechnungshinweisen und Beispielen, 23. Auflage. Köln: Bundesanzeiger, 2018