1-05 Derivation of Snow Load

› Note 5 Level 1

22

TheStructuralEngineer March 2012

Technical Technical Guidance Note

Derivation of snow load Introduction

This Technical Guidance Note concerns the derivation of snow load onto structures. It is based on Eurocode 1: Actions on Structures Part 1-3; General Actions – Snow Loads. With this Eurocode being focused on an action that is sensitive to environmental effects, the UK annex to it plays a significant role, as it makes reference to projected snow falls that are unique to the British Isles. There are a large number of variations and conditions the designer must be aware of when determining snow loads onto structures. As such, the reader is referred to the code text more frequently than in other Technical Guidance Notes. All of the guides in this series have an icon based navigation system, designed to aid the reader.

Design principles The derivation of snow load requires the designer to make judgements on the environment the structure is placed in as well the form of the structure itself. The potential for the build up of snow must be allowed for when determining the magnitude of the resulting persistent snow load onto a structure. Eurocode 1-1-3 addresses these issues by establishing a base load and then applying factors to that load that represent snowdrift.

Determining Basic Snow Load (sk)

The basic snow load (sk) is defined as the amount of snow on the ground based on an altitude of 100m above mean sea level. Clause 1.6.1 of Eurocode 1-1-3 sets the probability of exceeding this value at 1 in 50 per year. Clause NA.2.8 defines (sk) by the following expression:

sk [= 0.15 + (0.1Z +0.05)] + �

A–100 525

�

Where: Z is the zone number (i.e. 1,2,3 etc) taken from Figure NA.1 in the UK Annex to Eurocode 1-1-3 and not the ground snow load figure at 100m above mean sea level.

A is the altitude in meters of the ground level of the site where the structure is situated above mean sea level. This part of the expression is ignored when considering sites near coastal regions that are below 100m above mean sea level.

Shape Coefficient (�1)

To allow for snowfall thickness variances depending upon the shape of roof structures, Eurocode 1-1-3 uses coefficient �1 to take geometric changes into account. It is applied to the basic snow load sk and is based on the type of roof the structure has; be it flat, mono-pitch, duo-pitch or a multi-span roof. The proximity of protrusions such as taller elements of the structure or chimney stacks also has an impact when determining the value of shape coefficient �1.

Shape Coefficient (�1) for Flat, Mono- & Duo-Pitch Roofs

The relative angle (�) of the roof pitch affects the shape coefficient �1 value. This is shown in Figure 5.1 of Eurocode 1-1-3. For flat roofs the value of �1 is 0.8. For mono-pitch roofs, it’s the pitch angle � that is plotted against �1, referenced in Figure 5.1 or Table 5.2 of Eurocode 1-1-3. For roofs with a pitch angle of 60° or more the value of �1 is 0.

Icon Legend

• Design principles

• Applied practice

• Worked example

• Further reading

• Web resources

In the case of duo-pitched roofs, pitch angle � of each side of the roof is read against �1. In cases where there are differing pitch angles, each section of the roof will have its own unique shape coefficient. In this condition a series of snow load patterns must be considered before arriving at a definitive snow load. The patterns that need to be reviewed are: a) Both sides loaded using the �1 coefficient for each side of the roof drawn from Figure 5.1 or Table 5.2 b) One side loaded using NA Figure NA.2 and Table NA.1 c) Other side loaded using NA Figure NA.2 and Table NA.1 The worst case from the conditions listed above is considered to be the persistent snow load. For more information on this, see Clause 5.3.3(3) and Figure 5.3 of Eurocode 1-1-3. It’s important to note that load cases (ii) and (iii) cited in Clause 5.3.3(4) have been replaced by Clause NA 2.17 in the UK National Annex of Eurocode 1-1-3.

Shape Coefficient (�1) for Multi-Span Roofs Snow formation is not often uniform when it lands upon on multi-span roofs. To allow for this, two loading conditions are considered to determine the persistent snow load case.

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The first requires the separate pitches of each part of the roof to have the relevant coefficient applied to them, in a similar fashion to duopitched roofs previously described. The second condition allows for the build up of snow within the valley of the multi-span roof. Annex B2 of Eurocode 1-1-3 should be used to determine the value of �1 for drifts forming in the valleys. Taking the lowest value from the following:

�1 = 2h / sk

�1 = 2b3 / (ls1 +ls2)

�1 = 5

Figure B1 in Annex B of Eurocode 1-1-3 provides a definition of the above variables. It is very important to note that these load cases are exceptional in that they are considered in exclusion to the blanket snow load. See Clause B1(2) in Eurocode 1-1-3 for further guidance on this.

Shape Coefficients (�1) & (�3) for Roofs Adjacent to Tall Structures

When a roof is situated adjacent to or within 1.5m of a vertical element, a barrier exists against which snow can build up. To address this, alternative shape coefficients �1 and �3 need to be applied to the basic snow load as a separate case.

conjunction with Table B1 in Eurocode 1-1-3, which provides definitions for the variables shown. Again as with snowdrift in multi-span roofs, snow loads defined by guidelines stated within Appendix B of Eurocode 1-1-3 are exceptional and must not be considered in conjunction with the blanket snow load.

Shape Coefficient (�1) for Projections and Obstructions Small projections from the side elevation of structures, such as canopies and obstructions within roofs, including chimneys and parapets have an impact on snow load. They are barriers around which snow can drift and create localised heaped areas of snow. When assessing snow loads onto a structure, shape codes that represent these increased volumes of snow are applied to the base load. For snowdrifts due to obstructions such as chimneys, the reader is directed to Clause B4(1) and Figure B3 of Annex B of Eurocode 1-1-3 for the derivation of shape coefficient �1. For canopies over entrances, Clause B4(2)b in Eurocode 1-1-3 needs to be followed. This clause states that where it is not possible for more than 1m depth of snowdrift to form, no shape factor needs to be applied.

For smaller doorways that are less than 2m wide, the depth ‘h’ of the snowdrift is limited to the lesser of the height of the projection or its width that is perpendicular to the wind direction.

For flat roofs abutting taller structures, the shape factor �1 is 0.8. The snowdrift that appears on top of the snow covered roof is arrived at via the application of shape coefficients.

The shape coefficient �1 for canopies is defined by Clause B4(2)c in Eurocode 1-1-3 thus:

Figure 1 explains how the extent of the snowdrift is defined. It should be read in

For canopies over doors that do not project more than 5m, the value of �1 cannot exceed 2b / ls1, with ‘b’ being the larger value of b1 and b2. See Figure 2 for clarification of the previously referenced variables.

�1 = 2h / sk or 5, which ever is the lesser.

For the derivation of snowdrift shape factors near parapets, the reader is directed to Clause B4(3) and Figure B4 in Annex B of Eurocode 1-1-3. The snowdrift factor (�1) is defined as the lowest value from the following expressions:

�1 = 2h / sk �1 = 2b / ls �1 = 8

The length of drift ls is either 5h, b1 or a maximum of 15m. All of the variables mentioned in these expressions are defined in Figure B4.

Partial Factors for Snow Loads Eurocode 1-1-3 defines snow loads as variable fixed actions. The partial factors (Qk) for snow loads are dependent on the likelihood of the snowfalls that are projected by the Eurocode, actually occurring. In the case of flat, mono- and duo-pitched roofs, the loads are considered to be transient/persistent actions. All snow loads derived using Annex B of Eurocode 1-1-3, are deemed to be an extreme condition and are therefore classified as accidental actions (Ad).

Partial factor for snow load in isolation: 1.5Qk, Partial factor for snow load in conjunction with dead and imposed loads:

(0.5ψ0) 1.5Qk

Partial factor for snow load in conjunction with dead, imposed and wind loads: (0.2ψ1) 1.5Qk

Where Qk is the partial factor for the snow load and ψ0 and ψ1 are the combination factors to be used when snow load is considered with others. The numbers stated adjacent to the factors above are their respective values.

When snow loads are derived using Annex B of Eurocode 1-1-3 no partial factor is applied to them. This is because they are considered to only occur in extreme cases and are therefore classified as accidental.

Applied practice The applicable codes of practice for the derivation of snow loads are as follows: BS EN 1991-1-3 Eurocode 1: Actions on Structures – Part 1-3: General Actions – Snow loads Figure 1 Snowdrift condition for roofs abutting tall structures shown with basic snow coverage of roof. Note that these two conditions are never applied simultaneously.

Figure 2 Variables definition of snowdrift shape factor for entrance canopies

BS EN 1991-1-3 UK National Annex to Eurocode 1: Actions on Structures – Part 1-3: General Actions – Snow loads

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Worked example An indoor sports hall is to be constructed adjacent to an existing further education college. It is located 1 km south of Inverness city centre and is 90m above mean sea level. Calculate the characteristic snow load on the roof and entrance canopy to the new sports hall. The roof pitch angle � to the sports hall is 8°.

Technical Technical Guidance Note

Initially, the basic snow load is calculated using Figure NA.1:

The shape factor for the overall snow load on the duo-pitch roof for the new sports hall is then determined and the corresponding snow load is calculated.

Note that this load is a variable static action and therefore would have a partial factor of 1.5Qk if it were being considered in isolation to other loads. The shape factor for the canopy entrance is determined and the projected snow load onto it is calculated using Clause B4(2)b in Eurocode 1-1-3.

This is considered to be an accidental action as it is classified as an extreme condition. Therefore in Ultimate Limit State (ULS) and Equilibrium (EQU) analyses, no partial factor would be applied to this load.

Figure 3 Isometric view of new sports hall

Finally, we consider the snowdrift load onto the main roof due to the adjacent existing structure, which is significantly taller than the sports hall. It is at this point when Table B1 in Eurocode 1-1-3 is used.

Like the canopy load, this is deemed to be an accidental action and therefore no partial factors are applied to it within ULS and EQU analyses.

Glossary and further reading

Partial factor – A factor that is applied to characteristic loads when carrying out design of structures and the elements they are constructed from.

Action – An applied load, both due to a direct application or as a consequence of an indirect effect such as thermal expansion of the structure.

Variable static action – A load that is static and variable in magnitude. Loading due to snowfall is typical of this type of action.

Accidental action – A loading condition that is unlikely to occur. Partial factors are not applied to them within ULS analysis.

National Annex – A part of the Eurocode that has been written specifically for a particular region.

Characteristic load – A base load that has not had any partial factors applied to it.

Further Reading Manual for the design of building structures to Eurocode 1 and Basis of Structural Design — Institution of Structural Engineers – April 2010

Web resources For more information on this subject, please visit: www.istructe.org/resources-centre/ library