ISO/DIS 4355

ISO/TC 98/SC 3

Secretariat: JISC

Date: 2025-11-10

Bases for design of structures — Determination of snow loads on roofs

Bases du calcul des constructions — Détermination de la charge de neige sur les toitures

DIS stage

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Contents

Foreword

Introduction

Scope

Normative references

Terms and definitions

Snow loads on roofs

General function describing intensity and distribution of the snow load on roofs

Approximate formats for the determination of the snow load on roofs

Partial loading due to melting, sliding, snow redistribution, and snow removal

Ponding instability

Characteristic snow load on the ground

Snow load coefficients

Exposure coefficient

Thermal coefficient

Surface material coefficient

Shape coefficients

(informative) Background on the determination of selected snow parameters

(informative) Snow load distribution on selected types of roof

(informative) Determination of the exposure coefficient for small roofs

(informative) Determination of thermal coefficient

(informative) Roof snow retention devices

(informative) Snow loads on roof with snow control

(informative) Alternative methods to determine snow loads on roofs not covered by this document

Bibliography

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

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This document was prepared by Technical Committee ISO/TC 98, Bases for design of structures, Subcommittee SC 3, Loads, forces and other actions, Working Group WG 1, Snow loads, with the following members:

• Thiis, Thomas K. (convenor, SN)
• Meløysund, Vivian (secretary, SN)
• O'Rourke, Michael (ANSI)
• Chiba, Takahiro (JISC)
• Takahashi, Toru (JISC)
• Tsutsumi, Takuya (JISC)
• Dutkiewicz, Maciej (PKN)
• Li, Honghai (SAC)
• Xue, Yuan (SAC)
• Zhou, Xuanyi (SAC)
• Hong, Hanping (SCC)
• Frimannslund, Iver (SN)
• Croce, Pietro (UNI)
• Formichi, Paolo (UNI)
• Sykora, Miroslav (UNMZ).

This fourth edition cancels and replaces the third edition (ISO 4355:2013), which has been technically revised.

The main changes are as follows:

• updated guidance on use of basic meteorological data: snow density, rain on snow surcharge load and climate change;
• inclusion of guidance on snow load distribution for roofs with solar panels;
• improved guidance on determination of exposure coefficient for small roofs;
• improved guidance on determination of thermal coefficient;
• improved guidance on snow loads on roofs with snow load control;
• updated bibliography.

Any feedback or questions on this document should be directed to the user’s national standards body. A complete listing of these bodies can be found at www.iso.org/members.html.

Introduction

The intensity and distribution of snow load on roofs can be described as functions of climate, topography, shape of building, roof surface material, heat flow through the roof, and time. Only limited and local data describing some of these functions are available. Consequently, for this document it was decided to treat the problem in a semi-probabilistic way.

The characteristic snow load on a roof area, or any other area above ground which is subject to snow accumulation, is in this document defined as a function of the characteristic snow load on the ground, s0, specified for the region considered, and a shape coefficient which is defined as a product function, in which the various physical parameters are introduced as nominal coefficients.

The shape coefficients will depend on climate, especially the duration of the snow season, wind, local topography, geometry of the building and surrounding buildings, roof surface material, building insulation, etc. The snow can be redistributed as a result of wind action; melted water can flow into local areas and refreeze; snow can slide or can be removed.

In order to apply this document, each country will have to establish maps and/or other information concerning the geographical distribution of snow load on ground in that country. Procedures for a statistical treatment of meteorological data are described in Annex A.

Bases for design of structures — Determination of snow loads on roofs

This document specifies methods for the determination of snow load on roofs.

It can serve as a basis for the development of national codes for the determination of snow load on roofs.

National codes should supply statistical data of the snow load on ground in the form of zone maps, tables, or formulae.

The shape coefficients presented in this document are prepared for design application, and can thus be directly adopted for use in national codes, unless justification for other values is available.

For determining the snow loads on roofs of unusual shapes or shapes not covered by this document or in national standards, it is advised that special studies be undertaken. These can include testing of scale models in a wind tunnel or water flume, especially equipped for reproducing accumulation phenomena, and should include methods of accounting for the local meteorological statistics. Examples of numerical methods, scale model studies, and accompanying statistical analysis methods are described in Annex G.

In some regions, single winters with unusual weather conditions can cause severe load conditions not taken into account by this document.

Specification of standard procedures and instrumentation for measurements is not dealt with in this document.

The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 2394, General principles on reliability for structures

For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminology databases for use in standardization at the following addresses:

• ISO Online browsing platform: available at https://www.iso.org/obp
• IEC Electropedia: available at https://www.electropedia.org/

characteristic value of snow load on the ground

s0

load with a specified annual exceedance probability

Note 1 to entry: It is expressed in kilonewton per square metre (kN/m²).

Note 2 to entry: In meteorology, the term “weight of the ground snow cover” is also used.

shape coefficient

μ

coefficient which defines the amount and distribution of the snow load on the roof over a cross section of the building complex and primarily depends on the geometrical properties of the roof

value of snow load on roofs

s

function of the characteristic snow load on the ground, s₀, and appropriate shape coefficients

Note 1 to entry: The value of s is also dependent on the exposure of the roof and the thermal conditions of the building.

Note 2 to entry: It refers to a horizontal projection of the area of the roof.

Note 3 to entry: It is expressed in kilonewton per square metre (kN/m²).

basic load coefficient

µb

coefficient defining the reduction of the snow load on the roof due to a slope of the roof, β, and the surface material coefficient, C_m

drift load coefficient

µd

coefficient which defines the amount and redistribution of additional load on a leeward side or part of a roof, depending on the exposure of the roof to wind, C_e, and the geometrical configurations of the roof

slide load coefficient

µs

coefficient defining the amount and distribution of the slide load on a lower part of a roof, or a lower level roof

exposure coefficient

Ce

coefficient defined as the ratio of the snow load remaining on the roof when some snow has been eroded by wind to the reference snow load on a flat unheated roof under normal exposure

exposure coefficient for small roofs

Ce0

exposure coefficient for small roofs with effective roof length shorter than 50 m

effective roof length

lc

length of the roof influenced by exposure coefficient given as a function of roof dimensions

thermal coefficient

Ct

coefficient defining the change in snow load on the roof as a function of the heat flux through the roof

Note 1 to entry: C_t, in some cases, can be greater than 1,0. Further guidance is given in 6.2 and Annex D.

surface material coefficient

Cm

coefficient defining a reduction of the snow load on sloped roofs made of surface materials with low surface roughness

equivalent snow density

ρe

density for calculating the annual maximum snow load from annual maximum snow depth

snow density

ρ

ratio between snow load and snow depth

Formally, the snow load on roofs can be defined as a function, F, of several parameters:

(1)

where the symbols are as defined in Clause 3.

While C_e, C_t, and C_m are assumed constant for a roof or a roof surface, µ_b, µ_d, and µ_s generally vary throughout the roof.

This document defines the snow load on the roof as a combination of a basic load part, s_b, a drift load part, s_d, and a slide load part, s_s. Thus, for the most unfavourable condition (lower roof on leeward side):

(2)

where “+” implies “to be combined with”.

Effects of the various parameters are simplified by the introduction of product functions.

(3)

(4)

(5)

The basic roof snow load, s_b, is uniformly distributed in all cases^[1][2], except for curved roofs, where the distribution varies with the slope, β (see information in Clause B.4).

The basic load defines the load on a horizontal roof, and the load on the windward side of a pitched roof. Since any direction can be the wind direction, the basic load is treated as a symmetrical load on a symmetrical roof, thus defining a major part of the total load on the leeward side as well.

The drift load is the additional load that can accumulate on a roof due to wind-driven drifting, typically on:

• the leeward side on a pitched or curved roof;
• the lower roof of a multilevel roof;
• roofs with obstructions.

The slide load is the load that can slide from an upper roof onto a lower roof, or a lower part of a roof.

NOTE 1 For information on roof snow retention devices, see Annex E.

NOTE 2 For information on snow loads on roof with snow control, see Annex F.

A load corresponding to severe imbalances resulting from snow removal, redistribution, sliding, melting, etc. (e.g. zero snow load on specific parts of the roof) should always be considered.

Such considerations are particularly important for structures which are sensitive to unbalanced loading (e.g. curved roofs, arches, domes, collar beam roofs, continuous beam systems, roof trusses spanning from side wall to side wall) which are addressed in other clauses of this document.

Roofs shall be designed to preclude ponding instability. For flat roofs (or with a small slope), roof deflections caused by snow loads shall be investigated when determining the likelihood of ponding instability from rain-on-snow or from snow meltwater.

The characteristic snow load on the ground, s₀, is determined by statistical treatment of snow data.

Snow load measurements on the ground should be taken in an undisturbed area not subject to localized drifting.

Information on methods for the determination of the characteristic snow load on the ground, s₀, are described in Annex A.

The exposure coefficient, C_e, should be used for determining the snow load on the roof. The choice of C_e should consider the future development around the site. For regions where there are no sufficient winter climatological data available, it is recommended to set C_e = 1,0.

NOTE In the case of significant uncertainties about the future development of wind exposure conditions, a safe-sided choice of C_e can be appropriate.

For most cases, the exposure coefficient, C_e, is equal to the exposure coefficient for small roofs, C_e0. However, for very large flat roofs, wind is less effective in removing snow from the whole roof. To compensate for this, the exposure coefficient for large roofs is higher than for smaller roofs.

(6)

where

l_c is the effective roof length equal to in metres;

C_e0 is the exposure coefficient for small roofs.

Information on methods for the determination of C_e0 are given in Annex C.

In the expression for l_c, W is the length of the shorter side of the roof and L is the length of the longer side (see Figure 1).

Figure 1 — Rectangular roof dimensions

For non-rectangular roofs, W and L can be taken as the shorter and longer side of the roof’s major dimensions along two orthogonal axes. For example, for an elliptical shape, W is measured along the short axis and L along the long axis.

An overview of the exposure coefficient is shown in Figure 2.

Figure 2 — Exposure coefficient, C_e, as a function of effective roof length, l_c

The thermal coefficient, C_t (see 3.10), is introduced to account for the effect of thermal transmittance of the roof. C_t adjusts the snow load caused by melting and/or freezing of water in the snow layer.

The snow load is reduced on roofs with high thermal transmittance because of melting caused by heat loss through the roof. For such cases and for glass-covered roofs in particular, C_t, can take values less than unity.

For buildings where the internal temperature is intentionally kept below 0 °C (e.g. freezer buildings, ice skating arenas), C_t, can have values higher than unity. For all other cases, C_t = 1,0 applies.

Bases for the determination of C_t are the thermal transmittance of the roof, U_roof, and the lowest temperature, θ_in, to be expected for the space under the roof, and the snow load on the ground, s₀.

Information on methods for the determination of C_t for roofs with high thermal transmittance are described in Annex D.

The amount of snow which slides off the roof will, to some extent, depend on the surface material of the roofing; see 6.4.2.

The surface material coefficient, C_m (see 3.11), is defined to vary between unity and 1,333, and takes the following fixed values:

• C_m = 1,333 for slippery, unobstructed surfaces for which the thermal coefficient C_t < 0,9 (e.g. glass roofs);
• C_m = 1,2 for slippery, unobstructed surfaces for which the thermal coefficient C_t > 0,9 (e.g. glass roofs over partially climatic conditioned space, metal roofs, etc.);
• C_m = 1,0 corresponds to all other surfaces.

NOTE C_m = 1,2 can also be applied for slippery unobstructed surfaces with C_t < 0,9 if this is assumed to be more reasonable.

The shape coefficients define distribution of the snow load over a cross section of the building complex and depend primarily on the geometrical properties of the roof.

For pitched roof buildings with rectangular plan form, the distribution of the snow load in the direction parallel to the eaves is assumed to be uniform, corresponding to an assumed wind direction normal to the eaves.

The shape coefficients presented for selected types of roof (see information in Annex B), are illustrated for one specific wind direction. Since prevailing wind directions can not correspond to the wind directions during heavy snow falls, the condition that the wind during snow fall can have any direction with reference to the roof location should be considered when designing roofs.

When snow on sloped roofs can slide off unobstructed, snow load on the roof will be reduced. The reduction of the snow load on the roof due to the slope, β, of the roof and the surface material coefficient, C_m, is defined by the shape coefficient, μ_b (see 3.4), which is given by Formula (7):

(7)

An overview of the basic load coefficient is shown in Figure 3.

Figure 3 — Basic load coefficient, µ_b, as a function of surface material coefficient, C_m

The drift load coefficient, µ_d (see 3.5), is dependent on the roof geometry and the exposure coefficient, C_e, see information in Annex B.

Slide load from an upper part of a roof onto a lower part of a roof will depend on the amount of snow that can slide down, and on the geometrical configuration of the roof.

The distribution of the slide load and the spreading out of the load will, in addition to the geometrical shape of the roof, depend on the properties of the sliding snow and on the friction on the upper roof from which the snow is sliding.

The slide load magnitude and distribution is incorporated in the slide load coefficient, µ_s (see 3.6).

In the cases when slide load should be considered, the slide load coefficient for different roof types can be found using the guidance in Annex B.

NOTE It can be relevant to consider impact loading due to slide load in the design.

1. 
   (informative)
   
   Background on the determination of selected snow parameters
   1. Snow zones and maps

The characteristic snow load on the ground, s₀, with an annual exceedance probability of 0,02 or other values taking into account the importance of the building and the limit state considered, should be available in national standards.

Investigations have shown that near the coasts, not only the altitude but also the distance from the coast can influence the snow load.

NOTE On the treatment of statistical values, see guidance in Clause A.3.

• 1. Use of basic meteorological data
     1. General

To determine snow load on the ground, s₀, a sequence of maximum yearly snow loads is used. This parameter can be determined on the basis of recordings of water equivalents, snow depths, precipitation, etc.

For areas where there is snow every year, a preferable minimum recording length is 20 years.

Snow sampling equipment and the observation procedure should be in accordance with WMO recommendations ^[3]. Preferably, snow courses with records of water equivalents should be used ^[4], ^[5]. However, if water equivalent data are scarce, available data on snow depth can be used.

For regions with missing or scarce ground snow load measurements, validated models may be used to estimate snow loads on the ground based on common meteorological data; these may include for instance hydrological, snowmelt, or temperature-index models ^[4], ^[5]. Relevant uncertainties should be considered, e.g.:

• model uncertainties;
• uncertainties in the basic variables including statistical uncertainty;
• uncertainty in the climate change effect.

NOTE A period of winter season, rather than a calendar year, is more appropriate to specify a maximum snow load on the ground.

• • 1. Density of snow

The average density of snow layer is an important parameter for determining snow load, since the snow depth has more recordings than the water equivalent at many stations.

When determining annual maximum snow load by means of snow depth and density, it should be considered that these two parameters usually have a significant positive correlation before the occurrence of a year’s snow depth maximum, and negative afterwards. In heavy snow regions, there is usually a time lag between the annual maximum snow depth and the annual maximum snow load. This difference is due to densification of snow layers. Therefore, an equivalent density of snow needs to be used for determining s₀ when based on the annual maximum snow depth ^[6].

Many formulae have been proposed due to different climates in different countries.

A formula for equivalent snow density on the ground with a return period of 100 years used in Japan ^[6] is Formula (A.1):

(A.1)

where

ρ_e is the equivalent snow density (kg/m³);

d is the snow depth (m);

d_ref is the reference snow depth of 1 m.

Formula (A.2) is for snow density in the USA. It relates the snow density at one point in time to the snow load at the same point in time:

(A.2)

where

ρ is the snow density (kg/m³);

s₀ is the snow load on the ground (kN/m²).

Formula (A.2), written in terms of snow depth, is shown in Formula (A.3):

(A.3)

where

ρ is the snow density (kg/m³);

d is the snow depth (m).

Based on observations of the German Weather Service (Deutscher Wetterdienst DWD)^[7][8] the approach in Formula (A.4) has been developed:

(A.4)

where

d is the snow depth (m);

ρ₀ is the density of snow at the surface (kg/m³);

ρ_∞ is the upper limiting value of the snow density;

d_ref is the reference snow depth of 1 m.

For Germany, the snow density at the surface usually is in the range from 170 kg/m³ to 190 kg/m³, and the upper limiting value ranges from 400 kg/m³ to 600 kg/m³. The latter value is valid for wet climates.

In China, Formula (A.5) has been proposed ^[9] to estimate the relationship between snow depth and snow density with a return period of 50 years for Northeast China where heavy snowfalls are frequently encountered:

(A.5)

where

ρ is the snow density (kg/m³);

h₅₀ is the snow load on the ground (m) with a return period of 50 years.

Figure A.1 shows a comparison of Formula (A.1), Formula (A.3), Formula (A.4) and Formula (A.5) for snow density ^[10].

NOTE For Formula (A.4) : a) dry climate with surface density 170 kg/m³ and upper limit density 400 kg/m³, b) wet climate with surface density 190 kg/m³ and upper limit density 600 kg/m³.

Figure A.1 — Snow density, ρ, as a function of snow depth, d, according to Formula (A.1), Formula (A.3), Formula (A.4) and Formula (A.5)

• • 1. Snow intensities for short periods of time

For roofs with high values of heat loss, the snow fall intensity for short periods of time, 24 h or even shorter, can be of particular interest of design.

Normally, only recordings from various kinds of rain gauges can be obtained for this purpose. Such data on snow fall should never be used without corrections. The data shall be corrected for errors caused by wind effects at the gauge. Recommendations on such adjustments of the data, based on observations in Nordic countries, are available in ^[11].

• • 1. Rain on snow surcharge load

Rain on snow surcharge load depends on roof length and slope. In the USA, following value have been used, ^[12]. For locations where 0 < s₀ < 1 kN/m², all roofs with slopes less than W/15,2 (in degrees) shall have a 0,38 kN/m² rain-on-snow surcharge. This rain-on-snow-augmented design load applies only to the basic load case and need not be used in combination with drift, sliding, unbalanced, or partial loads.

Another formula for rain on snow surcharge load in Japan (^[13]) is Formula (A.6):

(A.6)

(A.7)

where

S_r is the surcharge loads [kN/m²];

a is the factor for roof span length W and slope [kN/m²/m^1/2];

d is the snow depth on roof [m];

W is the projected horizontal eave to ridge distance (5 m ≤ W);

β is the roof angle (β < 10°).

• • 1. Climate change

When developing national or regional maps for snow loads on the ground, climate change effects, inducing possible positive or negative trends in confined ensembles of annual extremes or peaks over a specific threshold, should be considered.

Climate change scenarios may be used to obtain information on the basic shape of trends and their associated uncertainties.

Climate change effects may be considered in the elaboration of values for snow loads on the ground by means of change factor values derived from the analysis of future climate projections ^[14].

Factors of change at the time window t, F_C(t), may be derived as given in Formula (A.8):

(A.8)

where

is the characteristic values obtained from the ensemble of climate projections at the investigated time window t;

is the characteristic values at the time window corresponding to the observation period (t = 1).

NOTE The length of time windows (t) is typically taken as not less than the recording length used for the evaluation of the characteristic value of snow load on the ground (s₀) (see Clause A.2).

The characteristic value of snow load on the ground in future time windows s₀(t) may be obtained as given in Formula (A.9):

(A.9)

where

is the factor of change at the time window t;

is the characteristic value of snow load on the ground.

Maximum values of the snow load on the ground in the investigated time windows may be used to update snow values including potential climate change effects as given in Formula (A.10):

(A.10)

Effects of climate change estimated from climate model projections may only be considered in the updating values of snow load on the ground when leading to increased values of the action.

• 1. Statistical treatment of basic data

When applying statistical methods to basic snow measurement data, it should generally be noted that the regional significance of such data is highly dependent on the method of observation and the sheltering of the observation area. Whether or not a meteorological station typifies a region shall therefore be carefully considered in snow load calculations.

• • 1. Statistical distributions

For snow climates with a permanent snow cover for most of the winter, the annual maximum snow loads provide the appropriate basis for extreme value statistics. For those snow climates which have more than one independent period of permanent snow cover over the winter season, the statistical stability of the estimated parameters can be increased by using peaks over a specific threshold. Since confined ensembles inevitably contain random information, it can be difficult to identify the “true” probability distribution and the corresponding “true” parameters. Detailed comparisons of different probabilistic distributions should be made to identify an appropriate distribution for annual maxima of snow loads on the ground. For snow climates not having snow every year, the fitting of data should only use non-zero snow load amplitudes. Special care has to be taken if the observations include unusual large values in terms of outliers.

• • 1. Possible climatic dependence in choice of distribution

Research indicates that the best fit of local data to the LogNormal or the Type 1 distribution is often governed by certain climatic conditions of the region ^[12]. Detailed analyses comparing different distributions are recommended to aid selection of the type of distribution,

If detailed analyses comparing different distributions are unavailable, it is recommended that in regions with an annual extreme snow load resulting from accumulation during a long part of the winter season, the Type 1 is selected. In other regions with extreme load as a result of only one, or a few, snowfalls, the LogNormal distribution may apply.

The conservatism of the two distributions depends on the magnitude of the coefficient of variation, i.e. for low values, Type 1 is more conservative, and for high values, LogNormal is most conservative when calculating long return period loads.

The standard error of estimate for the return period considered can be used in comparing different parameter estimation methods.

Often the return period considered is greater than the number of maximum snow load recordings available. The degree of goodness of fit for a theoretical distribution to the sample data cannot always be relied upon for extrapolated values corresponding to long return periods. It is recommended also to consider climatic conditions and expected effects of climate change in the decision making.

1. 
   (informative)
   
   Snow load distribution on selected types of roof
   1. Simple pitched roofs

Snow load distribution for simple pitched roofs is described in Figure B.1. For asymmetrical simple pitched roofs, each side of the roof shall be treated as one-half of a corresponding symmetrical roof.

Figure B.1 — Snow load distribution on simple pitched roof

Basic load case:

• windward side: s = s_b;
• leeward side: s = s_b.

Drifted load case:

• windward side: s = 0;
• leeward side: s = s_b + s_d.

Basic load part s_b is given by Formula (B.1):

(B.1)

where

s₀ is the characteristic value of snow load on the ground;

C_e is the exposure coefficient;

C_t is the thermal coefficient;

μ_b is the basic load coefficient.

Drifted load part s_d is given by Formula (B.2), Formula (B.3) and Formula (B.4):

(B.2)

(B.3)

(B.4)

where

μ_d is the drift load coefficient;

β is the roof angle with 5° < β < 60°;

w is the length of the drifted load part;

W is the length of the roof.

In Figure B.2 the product µ_bµ_d is illustrated as a function of roof slope β in case of C_m = 1,0.

Figure B.2 — µ_bµ_d as a function of roof slope β in case of C_m = 1,0

• 1. Simple flat and monopitched roofs

For simple flat and monopitched roofs only the basic roof snow load, s_b, shall be considered, see Figure B.3.

(B.5)

Figure B.3 — Snow load distribution on monopitched roof

• 1. Multipitched roofs

For a simple pitched roof, one expects snow to slide off the roof when the slope is steep. However, for a multipitched roof, the snow slides and results in a redistribution of load on the same roof. This is covered by separate basic and sliding load cases as shown in Figure B.4. The sliding load case accounts for the potential for sliding snow and possible drifted snow. It is recommended to set ρ = 300 kg/m³. External slopes of multipitched roofs is according to Clause B.1.

Figure B.4 — Snow load distribution — multipitched roof

Basic load case:

(B.6)

Sliding load case 1:

(B.7)

(B.8)

(B.9)

(B.10)

Sliding load case 2:

(B.11)

(B.12)

(B.13)

(B.14)

• 1. Simple curved roofs, pointed arches, and domes

For curved and pointed arch roofs with h/b ≥ 0,05, the basic load and drifted load distributions are determined according to Figure B.5. For h/b < 0,05, the snow loads are determined according to Clause B.2. Pointed arches with β ≥ 5° at the ridge line (x = 0) should be treated as pitched roofs, see Clause B.1.

For domes of circular plan form, the basic load is that in Figure B.6 applied in an axially symmetric manner. The drifted load along the central axis parallel to the wind is the same as for an arch and µd varies as shown in Figure B.5 with distance y from this axis.

Figure B.5 — Basic and drifted snow load distribution on curved roofs

Basic load case:

(B.15)

Drifted load case:

(B.16)

(B.17)

(B.18)

(B.19)

where

x₃₀ is x at β = 30° and x₃₀ ≤ b/2

Drift load coefficient on domes (see Figure B.6):

(B.20)

NOTE The arrow indicates wind direction.

Figure B.6 — Plan view of drift load coefficient on dome

• 1. Multilevel roofs (lower roofs with slope β_l)

For lower roofs, Figure B.7, the basic part of the load is determined from:

(B.21)

(B.22)

where

x is the horizontal distance from the step;

h is the height of step.

The drift part of the snow load, s_d(x), is determined as the most severe of three possible cases, illustrated in Figure B.8:

Case a: Step faces in the downwind direction and snow drifts off the upper roof into the sheltered zone at the step.

Case b: Step faces into the wind and snow drifts over the lower roof into the step region.

Case c: End region of a step that faces in the downwind direction where snow drifts into the sheltered step region from around the corner.

s_d(x) is a triangular function of x, being a maximum at x = 0 and decreases linearly to zero at the tail of the drift, at x = l_d. Where the tail of the drift would extend beyond the edge of the lower roof, the drift is truncated to a trapezoidal form.

NOTE C_e and μ_d are also given in Table B.1.

Figure B.7 — Snow distribution and snow load coefficients for lower level adjacent roofs

The length of the drift is as follows:

(B.23)

The maximum of the drift load is given by Formula (B.24) , Formula (B.25) , Formula (B.26) , Formula (B.27) and Formula (B.28) :

(B.24)

(B.25)

(B.26)

(B.27)

(B.28)

where

h_p is the height of the roof perimeter parapet of the source area;

s_bs is the basic snow load of the source area;

ρ is the snow density;

g is the acceleration due to gravity.

h_p shall be taken as zero unless all the roof edges of the source area have parapets.

It is recommended to set ρ = 300 kg/m³. Alternatively, see Annex A for information on density formulae.

Table B.1 — Coefficients C_e and µ_d

The appropriate values of the parameter ξ for each of cases a), b), and c) are tabulated in Table B.2. l_cs is the representative length of the appropriate source area for snow drifting for each of the three cases shown in Figure B.8.

(B.29)

where

L is the longer dimension of the source area.

If the upper roof is pitched, the dimensions W and L are based on the overall dimensions of the upper roof for case a).

Key

1 lower roof

2 upper roof

3 length of step

source area for snow in drift

snow drift

wind direction

NOTE The directions of the dimensions L and W shown in the diagrams will interchange depending on which is larger.

Figure B.8 — Snowdrift cases and parameters for lower level roofs

Table B.2 — Values of the parameter ξ for each of cases a), b), and c)

Figure B.9 shows µ_d(0) plotted as a function of ρgl_cs/s0 for cases a) and b) for several values of ρgh_p/s₀. For case c) the plot for case b) with ρgh_p/s₀ = 0 applies.

Key

A upper limit for C_e = 0,8

B upper limit for C_e = 1,0

C upper limit for C_e = 1,2

NOTE For case c), the plot for case b) applies with ρgh_p/s₀ = 0.

Figure B.9 — Variation of µ_d(0) with ρgl_cs/s₀ for cases a) and b)

At an outside corner where two step faces meet (see Figure B.10) the triangular drift load from the more lightly loaded step region shall be assumed to extend radially from the corner. At an inside corner the drift loads calculated for each step face shall be applied as far as the bisector of the corner angle, as shown in Figure B.11.

Key

1 step face with higher µ_d(0)

2 step face with lower µ_d (0)

NOTE Radius of drift surcharge, r, is equal to l_d.

Figure B.10 — Drift loading at outside corner

Key

1 lower roof

2 upper roof

3 step face 1

4 step face 2

5 bisector of angle between two step faces

Figure B.11 — Drift loading at inside corner

When a building roof is closer than 5 m to a higher level roof of an adjacent building, it shall be designed for the tail portion of the triangular drift load, as shown in Figure B.7.

If the upper roof is sloped greater than 5° and has no edge parapet or snow fence to prevent sliding, the additional sliding snow load, s_s(x), on the lower roof shall be assumed to take a triangular form (see Figure B.12) and is calculated as follows:

(B.30)

(B.31)

(B.32)

(B.33)

where

(B.34)

(B.35)

(B.36)

Figure B.12 — Sliding snow load factor

The sliding snow load should be considered as simultaneous with the basic load and 50 % of the drift load.

NOTE The sliding snow load defined above does not include the effect of the impact of the snow as it lands on the lower roof.

• 1. Additional drift load and sliding load on ground or on lower level roof, acting against the upper arch or pitched roof

A lower level roof should be checked for the sliding load as an alternative load case as compared with the load cases of Clause B.5. Impact effects shall be considered (see Figure B.13).

Figure B.13 — Additional drift load and sliding load acting on upper arch or pitched roof

(B.37)

(B.38)

(B.39)

(B.40)

µ_b = 1,0 (B.41)

µ_d = 3,0 (B.42)

where

β is the roof angle;

ρ is the snow density;

g is the acceleration due to gravity.

• 1. Roofs with local obstructions

The basic part of the load, s_b, for roofs with local obstructions, such as elevator, air-conditioning and fan housings, small penthouses, and wide chimneys, is determined in the same way as for lower roofs (see Clause B.5). The drift load, s_d(x), in areas adjacent to the obstructions is determined as a triangular function of distance x from the obstruction, being a maximum at x = 0 and decreasing linearly to zero at the tail of the drift, at x = l_d.

(B.43)

where

l₀ is the longest horizontal dimension of the obstruction (see Figure B.14).

Figure B.14 — Drift load coefficient for local obstructions

(B.44)

The drift load shall extend from all sides of the obstruction and in a radial manner from the corners (see Figure B.10). Drift loads need not be considered when l₀ < 3 m. Note that, as the horizontal dimension l₀ of the obstruction increases, the drift load from Formula (B.44) can surpass that for a lower level roof as determined in Clause B.5. At this point it will be preferable to treat the projection or obstruction as an upper level roof and use Clause B.5 to determine the drift loads adjacent to it.

• 1. Roofs with solar panels

The drift coefficient (µ_d) for a roof with solar panels should be calculated as given in Formula (B.45) and illustrated in Figure B.15 and Figure B.16 :

(B.45)

where

µ_a is the accumulation coefficient;

µ_r is the redistribution coefficient.

The accumulation coefficient (µ_a) should be calculated according to Formula (B.46). The length and width of the area with µ_a should be according to Formula (B.47).

(B.46)

(B.47)

where

ρ is the snow density;

h_pv is the height of the panel;

s₀ is the characteristic snow load on the ground [kN/m²];

µ_b is the basic load coefficient.

The redistribution coefficient (µ_r) shall be calculated if both conditions in Formula (B.48) is satisfied.

(B.48)

where

s₀ is the characteristic snow load on the ground [kN/m²];

l_f is the upwind distance without obstacles [m].

The redistribution coefficient µ_r should be calculated using Formula (B.49) :

(B.49)

Only a limited amount of rows are influenced by µ_r. The number of influenced rows n should be calculated according to Formula (B.50), Formula (B.51), Formula (B.52) and Formula (B.53):

(B.50)

(B.51)

(B.52)

(B.53)

where

Q_p is the total redistribution potential;

Q_C is the snow drifts capacity for each row;

l is the length from the upwind edge of the roof to the first panel row;

C_e is the exposure coefficient;

a is the length of the panel not covered by snow/length of windward/sliding snow [m];

b is the length of leeward snowdrift [m];

c is the distance between the rows [m].

NOTE 1 If the length of leeward (b) and windward (a) drifts overlap, the drift coefficient (µ_r) is not affected.

NOTE 2 When secondary beams are aligned with solar panel rows and the load width is similar to the drift lengths, it is advisable to reposition the solar panels to distribute the load more evenly across the beams.

Key

a) section through snow layer

b) section through roof and solar panels

c) plan view

µ_b basic load coefficient

µ_r redistribution coefficient

µ_a accumulation coefficient

l_f upwind distance without obstacles [m]

l_d minimum drift area

z length of rows [m]

Figure B.15 — Spatial snow load distribution for a flat roof with solar panels

Key

µ_b basic load coefficient

µ_r redistribution coefficient

µ_a accumulation coefficient

l_d minimum drift area

c distance between rows [m]

a length of the panel not covered by snow/length of windward/sliding snow [m]

b length of leeward snowdrift [m]

h_pv height of panel

Figure B.16 — Variable definitions in the solar panel system

1. 
   (informative)
   
   Determination of the exposure coefficient for small roofs
   1. General

The exposure coefficient for small roofs, C_e0, is a general coefficient reflecting the effect of snow removal at a roof location independent of the roof shape. The definition of C_e0 is given in 3.7 and expresses the ratio between:

• the snow load remaining on the roof when some snow has been eroded by wind, and
• the reference snow load on a flat unheated roof under normal exposure, i.e. accounting for normal erosion effects (typically taken as 80 % of the ground snow load for small- and medium-size flat roofs and normal exposure conditions).

The exposure coefficient may be written (^[15]):

(C.1)

where

s_g is the ground snow load [kg/m per unit width];

L is the dimension of the flat roof parallel to the wind direction [m];

s_e,mv is the eroded snow amount from a flat roof during the drifting period [kg/m per unit width];

D_mw is the duration of the snow drifting period until the value of C_e reaches its minimum [days];

s_e is the daily erosion rate [kg/m/day].

NOTE 1 According to Formula (C.1) C_e can reach a maximum value of 1,25, with a lower (physical) bound equal to 0. In this document the maximum value of C_e0 is set to 1,20 and the minimum value are set is set to 0,8 as a minimum erosion level is expected to occur as well as extremely low C_e values are unlikely to be registered in inhabited areas.

Since Formula (C.1) can be complicated to use due to the need for extensive data with high temporal resolution, C_e0 may be determined as described in Clause C.4 based on the characteristics of the regional wind category (see in Clause C.2), temperature climate (see Clause C.3) and terrain roughness category.

NOTE 2 For very large roofs it is expected that C_e will approach 1,25, regardless of the wind and temperature regime, since at a sufficiently large size the roof becomes no different from the ground from a snow drifting point of view. Therefore the calculation of C_e in Clause B.5 assumes a basic value of C_e = C_e0 for small roofs, with dimensions less than about 50 m, and then increases C_e as the roof size increases so that it approaches 1,25 asymptotically, see 6.1.

• 1. Winter wind exposure

The mean frequency of wind speed above a threshold value (5 m/s) is used rather than the monthly mean of wind speed as the main parameter for drifting. This is due to the fact that the effectiveness of drifting of both falling and old snow depends on the occurrence of relatively strong wind during and a few days after snow falls.

The normal terrain is suburban, urban or wooded areas. Sheltered terrain is for sites with completely sheltered by other higher buildings or trees in all directions.

The winter wind climates given in Table C.1 should be considered, normally by using the average values of the three coldest months of the year.

Table C.1 — Winter wind categories

Data on the wind frequency are available for meteorological stations recording the wind speed in open terrain 10 m above ground level.

• 1. Winter temperature climate

In regions with a relatively warm winter climate, only drifting of falling snow is usually possible. In such regions snow falls are accompanied by the lowest temperature of the winter. This is normally not the case in cold regions. A common variable reflecting the temperature during snow falls for different climates is therefore difficult to obtain. For practical reasons, the parameter used in this Annex is the lowest monthly mean temperature of the year. Note that this parameter has lower values than the winter mean temperature being referred to in Clause C.5.

The monthly mean temperatures, θ, for the coldest month of the year given in Table C.2 should be considered.

Table C.2 — Winter temperature categories

• 1. Exposure coefficient

When winter wind category has been determined from Table C.1 and winter temperature category has been determined from Table C.2, the exposure coefficient can be determined from Table C.3.

Table C.3 — Exposure coefficient for small roofs, C_e0

• 1. Climates not having snow every year

For climates not having snow every year, a more consistent approach to the analysis of the winter wind and temperature climate uses only those situations where a considerable snow load on the ground has occurred.

1. 
   (informative)
   
   Determination of thermal coefficient

This Annex gives values for the thermal coefficient for adjustment of snow load on roofs caused by heat flow through the roof.

The thermal coefficient, C_t, adjusts the snow load caused by melting and/or freezing of water in the snow layer and should be given by Formula (D.1) , ^[16].

In areas where large sudden snowfall is expected C_t ≥ 1,0 should apply.

NOTE 1 Large sudden snowfall can be defined as snowfall with more than 50 % of characteristic snow load on ground during 24 hours.

(D.1)

where

θ_in is the indoor temperature during the winter [°C];

U_roof is the thermal transmittance of the roof [W/(m²K)];

s₀ is the characteristic snow load on the ground (s₀ ≥ 1,5 kN/m²).

For unheated buildings or canopy roofs, T_in = −5 [°C] and U_roof = 1,0 [W/(m²K)] should apply.

It is assumed that melting water can be drained from the roof surface without risk of icing.

If the calculated additional local maximum load due to drifting exceeds 30 % of the mean snow load on the roof surface excluding drifting, the drift load part shall not be reduced by the thermal coefficient C_t.

If sliding onto the roof surface is possible, C_t = 1,0 should be applied.

NOTE 2 Values of C_t are given in Figure D.1.

Figure D.1 — Thermal coefficient C_t for T_in = 22 °C and T_in= -25 °C

1. 
   (informative)
   
   Roof snow retention devices
   1. General

Forces on snow fences associated with the snow load on a sloped roof are mainly the component of the mass of the snow along the roof surface, the frictional forces, and the compression force at the eave. Adhesive or tensile forces are important when the snow is frozen to the roof surface material, or when the snow is anchored to the ridge or any obstructions on the roof surface.

Friction and adhesion are the primary resisting forces. These forces will be decreased by a thin layer of water on the roof surface from melting snow or rain.

• 1. Static load

Snow fences may in most cases be designed for static loads assuming zero adhesion and tension forces. Under these assumptions, the snow fence may be designed for the static load, F₀, parallel to the slope of the roof, defined by Formula (E.1):

(E.1)

where

s_b0 is the basic snow load according to Clause B.1 with roof slope β = 0;

l₁ is the horizontal projection of the distance along the roof from the snow fence to the top of the roof;

k₁ is the coefficient of friction;

β is the slope of the roof above the snow fence.

The static load, F₀, may in most cases be assumed to act on the fence at a vertical height, h₁, as given by Formula (E.2), above the roof surface:

(E.2)

where

ρ is the density of the snow on the ground;

g is the acceleration due to gravity.

The density of the snow on the ground may be set ρ = 300 kg/m³unless a different value is specified for location of the structure.

• 1. Height of snow fence

Sufficient height of the snow fence to prevent sliding is mainly dependent on the snow depth on the roof, the roof angle, and the friction between separate layers of snow. If the friction is relatively low, sliding from a top layer is possible for roof angles above approximately 25°.

In this Annex, the design value of snow fence height, h₂, should be given by Formula (E.3). This height is considered to be conservative due to an assumption of low friction between separated snow layers.

(E.3)

The density of the snow on the ground should be set to ρ = 300 kg/m³.

• 1. Dynamic load

The dynamic force on a snow fence from sliding snow can be theoretically estimated by the use of a model based on a chain or a rope sliding along the roof surface with zero friction.

If this model is applied and l₂ is set equal to l₁ (see Figure E.1), the dynamic force, F_dyn, may be calculated from Formula (E.4):

(E.4)

where

k₂ is a coefficient equal to 3,0;

F₀ is given by Formula (E.1).

When l₂ is of the order 0,5l₁ to 0,8l₁, and the snow layer cannot accelerate to a stop due to internal forces, k₂ should be set k₂ = 1,75 in Formula (E.4).

Figure E.1 — Parameters to be considered when determining dynamic forces on a snow fence

1. 
   (informative)
   
   Snow loads on roof with snow control
   1. General

When sufficiently reliable control device or method is used, snow load on the roof may be reduced using the following concept.

• 1. Specification of snow load on roof with snow control

Snow load on the roof with snow control is given by Formula (F.1):

(F.1)

where

μ_b is the basic load coefficient defined in 3.4;

s_n is the snow load on the ground with accumulation for n days (kN/m²) defined in F.3.1;

s_c is the controlled snow load (kN/m²) defined in Clause F.4.

• 1. Ground snow load with accumulation for n days
     1. Formula for ground snow load with accumulation for n days

When the roof snow is reliably controlled, snow load on the ground, s_n, is determined from Formula (F.2):

(F.2)

where

C_e is the exposure coefficient that takes into account local topography;

d_n is the representative snow depth on the ground (m) when the snow load on the roof is controlled, as defined in F.3.2;

ρ_n is the equivalent density for ground snow with roof snow control; see A.2.2 if the equivalent density is not available;

g is the acceleration due to gravity.

• • 1. Representative snow depth with accumulation for n days

Representative snow depth on the ground, d_n, is defined as the annual maximum value of snow accumulation for n days with a return period of certain years (50 or 100 years, for example), and is estimated from meteorological data of the ground snow depth as specified in Clause A.2. n is typically corresponding with the duration of single event of snow duration of each building site.

• 1. Controlled snow load

Controlled snow load, s_c, is generally determined after field research and experiments investigating the capacity and reliability of snow controlling devices ^[17]. In other words, s_c is the difference between initial snow load expected when heavy snow fall starts (μ_bs_n) and residual snow load after removal (s) by the device whose performance is guaranteed even during heavy snow fall. This can be devices for:

• melting of snow;
• initiating snow sliding; or
• manual snow removal equipment.

In the case of using melting devices, the length of evaluation period n (day) for snow accumulation is decided with the performance and reliability of the roof snow control system. It is important to ensure a reliable energy supply during a heavy snow fall period. The system should satisfy the design performance requirements, based on appropriate maintenance over a specified period.

Monitoring roof snow could also be useful in ensuring the reliability of the system ^[18].

Risks related to the situation with malfunction of the snow control system shall be assessed and a safety plan shall be developed in accordance with ISO 2394.

1. 
   (informative)
   
   Alternative methods to determine snow loads on roofs not covered by this document

The analytical snow load provisions in this document and its annexes are based primarily on full-scale observations of snow accumulations on simple common shapes of roof, including allowances for the non-uniform loads that can arise due to drifting and sliding. For unusual roof shapes and surrounding conditions, for shapes not covered by this document, and for large span roofs where snow loads significantly impact the balance between cost and safety, scale model studies in wind tunnels or water flumes and/or special computational studies are recommended.

The physical process of snow accumulation occurs due to precipitation with or without wind, redistribution of existing snow cover, and the combination of both. Snow removal occurs due to scouring by wind, melting, and sliding. The snow loads at any given instant depend on the preceding history of these processes in the hours, days, and weeks beforehand. The length of this history that is relevant will depend on the winter climate at the site. Where prolonged cold periods are experienced, the length of history that needs to be considered will be longer. Theoretical and physical models of these processes can be used to make predictions of snow loads. There are a range of types of snow with varying terminal velocities, angles of repose, and ability to be picked up by wind. The modelling methods selected should take into consideration these variations.

The methods that have been used to model snow loading fall into three categories:

1. those in which the consequences of particular storms are simulated by using scaled models and introducing particles into the wind tunnel or water flume to simulate snow particles and their accumulations;
2. those in which the wind velocity patterns are measured on scaled models and the snow drifting and accumulation is numerically inferred with reliance on field data on snow transport rates and other information. Snow particles are not physically simulated in this approach;
3. those that use the methods of computational fluid dynamics, including the interaction effects of snow particles and the air flow.

All these methods are useful for identifying the potential formation of unusual snowdrifts, due to winds blowing from selected directions. However, in climatic regions where below freezing temperatures persist for lengthy periods, maximum snow loads can be the result of cumulative snowfalls and drifting events from a variety of directions over a prolonged part of the winter season. In such situations, it is desirable to track snow accumulations on a 1 h to 3 h basis by recognizing the consequences of each snowfall and wind event. Numerical methods are needed to keep track of the snow fall, snow drifting, snow melting, refreezing, rainfall, and the percolation and runoff of melt and rainwater. Method 2 is best suited for this purpose as it is able to rapidly re-evaluate the snow load every hour, using the historical hourly meteorological data as well as the heat transfer representatives of the roof, thus enabling statistical predictions to be made of extreme loads. However, methods 1 and 3 are capable of providing better detail of certain drift shapes due to individual events. Therefore, a mixture of methods is often desirable. Examples of the use of alternative prediction methods can be found in ^[19], ^[20], ^[21], ^[22], ^[23] , ^[24] and ^[25].

Since all prediction methods involve a number of simplifications and assumptions about snow accumulation processes, it is important that where possible they be calibrated against field data (e.g. ^[26], ^[27]).

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[2] Thiis T., O’Rourke M. (2012), A model for the distribution of snow load on gable roofs, in Proc. of 7th Int. Conf. on Snow Engineering, Fukui, Japan

[3] World Meteorological Organization. Guide to meteorological instruments and methods of observation. WMO No. 8. WMO, Geneva, Switzerland, 2010

[4] Takahashi T., Kawamura T., Kuramoto K. (2001), Estimation of Ground Snow Load Using Snow Layer Model. Journal of Structural and Construction Engineering, Architectural Institute of Japan, Vol. 66, No. 545, pp. 35–41 DOI https://doi.org/10.3130/aijs.66.35_1

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[9] Mo, H.M., Cao, X.L., Hong, H.P., Fan, F.. Development of a Relation between Return Period Values of Annual Maximum Snow Load and Snow Depth and Its Implication in Structural Reliability for Northeastern China. J. Struct. Eng. 2022, 148(8). 04022100

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[11] The Coordination Committee for Hydrology in the Nordic Countries (KOHYNO). The improvement of point precipitation data on an operational basis. NHP-Report No. 17, 1986, Nordic Hydrological Programme, Stockholm, Sweden

[12] ASCE 7-16: 2016, Minimum design loads and associated criteria for buildings and other structures (ISBN 9780784479964)

[13] Otsuki, M., Takahashi, T., Tomabechi, T., Chiba T., Tsutsumi, T., Kamiishi, I., Kikitsu, H., Iwata, Y., Ishihara, T., Okuda, Y. (2017). Study on Estimation Method for Surcharge Snow Load Due to Rainfall. Journal of Structure and Construction Engineering, Architectural Institute of Japan, Vol.82, No.739, 1329-1338, DOI https://doi.org/10.3130/aijs.82.1329, and its Errata DOI https://doi.org/10.3130/aijs.85.449

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[18] Diamantidis D., Sykora M., Lenzi D. (2018). Optimising monitoring: standards, reliability basis and application to assessment of roof snow load risks. Structural Engineering International 28(3), 269–279

[19] Anno, Y. and Tomabechi, T. Development of a snowdrift wind tunnel. Cold Regions Science and Technology, No. 10, 1985

[20] O'Rourke M., Degaetano A., Tokarczyk J.D. Snow Drifting Transport Rates from Water Flume Simulation. J. Wind Eng. Ind. Aerodyn. 2004 December, 92 pp. 1245–1264

[21] Irwin P.A., Williams C.J. (1983), Application of Snow Simulation Model Tests to Planning and Design, in Proceedings of the Eastern Snow Conference, 40th Annual Meeting, Vol. 48, pp. 118-130

[22] Gamble S.L., Kochanski W.K., Irwin P.A. Finite Area Element Snow Loading Prediction – Applications and Advancements. J. Wind Eng. Ind. Aerodyn. 1992, 4a pp. 1537–1548

[23] Irwin P.A., Gamble S.L., Taylor D.A. Effects of Roof Size and Heat Transfer on Snow Load: Studies for the 1995 NBC. Can. J. Civ. Eng. 1995, 22 pp. 770–784

[24] Tominaga Y., Okaze T., Mochida A. CFD Modelling of Snowdrift Around a Building: An Evaluation of New Approach. Build. Environ. 2011, 46 pp. 899–910

[25] Delpech P., Guilhot J. (2008), Quantitative assessment of snow load on complex and extended roof shapes, in Proc. of the 6th Int. Conf. on Snow Engineering, Whistler, Canada

[26] Tsutsumi T., Chiba T., Tombechi T. (2012), Snowdrifts On and Around Buildings Based on Field Measurement, in Proc. of the 7th Int. Conf. on Snow Engineering, Fukui, Japan

[27] Oikawa S., Tomabechi T. (2000), Daily observation of snow drifts around a model cube, in Proc. of the 4th Int. Conf. on Snow Engineering, 137-141