chapter 5 snow loads

CHAPTER 5 SNOW LOADS - C5-1-

CHAPTER 5 SNOW LOADS

5.1 Procedure for Determining Snow Load on Roof C5-2

5.2 Snow Load on the Ground C5-4

5.2.1 Characteristic snow load on the ground C5-4

5.2.2 Snow depth on the ground C5-8

5.2.3 Equivalent unit weight for ground snow C5-15

5.2.4 Environmental coefficient C5-16

5.3 Ground Snow Load with Accumulation for n Days C5-18

5.3.1 Characteristic ground snow load with accumulation for n days C5-18

5.3.2 Ground snow depth accumulation for n days C5-19

5.3.3 Equivalent unit weight for ground snow with roof snow control C5-20

5.4 Snow Load on the Roof C5-22

5.4.1 Design snow load on the roof C5-22

5.4.2 Shape coefficient C5-22

5.5 Snow Load on the Roof with Control C5-25

5.5.1 Design snow load on the roof with control C5-25

5.5.2 Controlled snow load C5-25

5.6 Partial Snow Load on the Roof C5-27

5.7 Other Snow Loads C5-27

References C5-28

- C5-2 - Commentary on Recommendations for Loads on Buildings

CHAPTER 5 SNOW LOADS

5.1 Procedure for Determining Snow Load on Roof

Because the Japanese islands are surrounded by sea and scattered over a wide range of latitudes,

snow fall mechanisms and snow depth distributions vary from region to region. Hokkaido and

northwestern Honshu are covered with heavy snow during winter. These areas are subjected to the

snowfall mechanism shown in Fig. 5.1.1. However, areas on the Pacific Ocean side sometimes

receive heavy snow at the end of winter due to approaching low pressures in the temperate zone.

Figure 5.1.1 A typical snowfall mechanism in Japan

In spite of the regional climate differences and the two different snowfall mechanisms, the present

recommendation uses unified concepts as much as possible in determining snow loads on roofs, on the

basis of recent studies. A flowchart of the procedure for determining snow loads on roofs is shown in

Fig. 5.1.2. The main portion of the procedure is subdivided into three parts: setting up the design

concept for dealing with roof snow loads, considering snow conditions at the construction site, and

considering snow conditions on the roof itself.

First of all, the designer should set up the design concept for the roof snow load, whether or not an

active control system is to be introduced to reduce the snow load accumulating on the roof. An

appropriate system will reduce the design snow load on the roof. Because there have been many

accidents in which buildings with control apparatuses have failed, the reliability of the control

apparatuses needs to be critically assessed, also taking human error into account. Recent

developments in control system technologies have been remarkable in Japan. This new

recommendation is expected to encourage their further development.

Snow loads on roofs vary as a function of the characteristic snow load on the ground, climate

(including temperature and wind speed during the winter), roof shape, roofing material, and from one

winter to another. Most available snow load data comprises snow depth on the ground. This

recommendation assumes that the snow load on the roof is proportional to that on the ground.

As the second step, snow depth on the ground at the construction site is estimated by a statistical

treatment and by an interpolation technique. The basic load value in this recommendation is defined

as one for the snow depth on the ground with a return period of 100 years. If a building is designed

for another return period, a conversion factor is introduced to modify the value. The snow load on the


ground is calculated from the snow depth multiplied by an equivalent snow density. The other ways

to estimate ground snow weight using observed precipitation and temperature are also introduced.

Figure 5.1.2 Flowchart of procedure for determining snow load on roof


For the third step, the snow load on the roof is estimated from the snow load on the ground

multiplied by a ground-to-roof conversion factor, that is, a shape coefficient. Because the shape

coefficient varies according roof shape, temperature, snow type (dry or wet), wind direction and wind

speed, it is impossible to determine precisely. Therefore, it is recommended in principle that the shape

coefficient for the roof is estimated by an experimental study with models. However, tables in this

recommendation give values for several typical shapes. For a large roof, even if the shape is simple,

an experimental study is also recommended because the shape coefficient is usually different from

those used for small roofs.

5.2 Snow Load on the Ground

5.2.1 Characteristic snow load on the ground (1) Estimation of ground snow weights based on the data of snow depth on the ground and equivalent

unit weight for ground snow Because direct observation of snow loads on roofs are limited, characteristic snow loads on the

ground are used as characteristic values. For ordinary buildings without control systems, the annual

maximum load for the whole season is used as the characteristic snow load S0, which is given by

Eq.(5.2.1) as the product of factors:

S0 = kenv d0 p0 (5.2.1)

where

S0 (kN/m2) : characteristic snow load on the ground used for design when snow load on the roof

is not controlled

kenv : environmental coefficient, as defined in 5.2.4

d0 (m) : characteristic snow depth on the ground when the snow load on the roof is not

controlled, as defined in 5.2.2

p0 (kN/m3) : equivalent unit weight for ground snow as defined in 5.2.3

(2) Estimation of ground snow weights based on the data of daily precipitation and daily mean air temperature In order to estimate the ground snow weights besides the conventional method using the equivalent

snow density in Chapter 5.2.3, this section presents a new method based on the meteorological data

such as daily precipitation and daily mean air temperature. Three kinds of equations due to Joh &

Sakurai, Kamimura & Uemura and Takahashi etc., are proposed as follows;

1) Joh and Sakurai’s equation1)

The authors have proposed a practical method to estimate ground snow weights during snow cover

period as defined below;

!"

=

=1

1

n

i

inPP (Ti < 2 °C) (5.2.2)


where

Pi (N/m2) : daily snowfall weight converted from the daily precipitation (mm)

Pn (N/m2) : ground snow weight of the n-th day: accumulated value of Pi from the first day

(i=1) of a period of continuous snow cover to the (n-1) day

Data of Pi should be accumulated when daily mean air temperature Ti (℃) is less than the air

temperature limit , +2℃, which is used to judge that the data of Pi means the value of snowfall or not.

Here, the daily melting snow weight is neglected for practical application.

Figures 5.2.1(a)~(d) show the examples of the comparison of the estimated value due to Equation

(5.2.2) with the observed value of snow weights at Sapporo, Kamabuchi, Nagaoka and Tokamachi

located in heavy snow regions, respectively. In these four cases, the continuous snow cover periods

are almost three months at Sapporo and five months at other three observatories. It is obvious from

these examples that the proposed equation can approximately trace the increasing process of ground

snow weights from the starting day to the day of peak value.

2) Kamimura and Uemura’s equation2)

This equation is expressed as follows;

!

Sm

= Sm"1 + C

b# P

m"C

a#T

m (5.2.3)

!

Ca

=

0

Ca1

Ca 2

"

# $

% $

T < 0°C( )0°C & T and C

bPm

> 0( )0°C & T and C

bPm

= 0( )

!

Cb

=

1

Tu"T( ) / Tu "Tl( )

0

#

$ %

& %

T ' Tl( )

Tl

< T ' Tu( )

Tu

< T( )

where

Sm (N/m2) : estimated ground snow weight on m-th day after the starting day of calculation

Pm (N/m2) : snowfall weight on m-th day which is converted from the daily precipitation (mm)

Tm (°C) : daily mean air temperature on m-th day

Ca (N/m2°C) : snowmelt factor

Cb : reference coefficient to judge whether Pm means snow or rain

Tu (°C) : upper limit temperature

!

Tl (°C) : lower limit temperature

“Cb·Pm” and “Ca·Tm” in Equation (5.2.3) means the increasing snow weight and the melting snow

weight on m-th day, respectively. Figures 5.2.2(a) and (b) show the examples at Nagaoka and

Tokamachi using Equation (5.2.3), in which the estimated values are compared with the observed

values for ground snow weights. It is clearly that this Equation can approximately trace the ground


snow weights over the continuous snow cover period.

The calculation is done to use different and suitable value of snowmelt coefficient Ca at each

observatory, which can be obtained from the data of snow weights etc. Therefore, further

investigation is needed how to search the suitable snowmelt coefficient Ca at other observatory, which

has no data of snow weights.

Fig.5.2.1 Estimation of ground snow weight with Equation (5.2.2)1)



3) Takahashi’s equation3)

It is assumed that the each day’s snowfall formed one snow layer on the ground snow. After a

snowfall, the snow consolidates and metamorphoses in proportion to the number of days and air

temperature. Finally, it melts and it is assumed to percolate into the ground. In Equation (5.2.4),

numerator means the estimated snow weight of m-th snow layer and the denominator means the

estimated snow density of m-th snow layer.

!

mdn

= mP"

mPc

#min

n+mk

(5.2.4)

where

m : number of days from the start of continuous snow cover

n : number of days from the snowfall of the layer

mdn (m) : estimated depth of m-th snow layer

mP (kN/m2) : snowfall weight on m-th day which is converted from the daily precipitation (mm)

Pc (kN/m2) : melting snow weight on m-th day

!

Pc

=mPc

= C T "T0( )

m

# (T > T0)

0 (T $ T0)

%

& '

( '

C (N/m2°C) : snowmelt factor

T (°C) : daily mean air temperature

T0 (°C) : reference temperature for snowmelt fixed as -2 °C

mk : correction number for the initial condition

!

mk =

m"0( )2

"min( )

2

mρ0 (kN/m2) : unit snow weight of a snowfall on the m-th day

!

m"0

=

"min

"min

+mT "

max# "

min( ) 3

"max

T $ 0°C( )0°C < T $ 3°C( )3°C < T( )

%

& '

( '

ρmin (kN/m2) : minimum unit snow weight of a snowfall

ρmax (kN/m2) : maximum unit snow weight of a snowfall fixed as 4.9kN/m3

This equation is one-day step repeating calculation using minimum snow unit snow weight ρmin and

snowmelt factor C as unknown factors. The minimum value of the estimated error between the

estimated daily snow depth and observed daily snow depth leads to the optimum solution for the

transition process of snow depth.

Figures 5.2.3(a)~(f) show the examples at Sapporo, Shinjo, Takada, Toyama and Fukui using

Equation (5.2.4), in which the estimated values are compared with the observed values for ground

snow weights. It is clear that this equation can approximately trace the ground snow weights over the


continuous snow cover period.

As a result, considering the difficulty to decide the suitable value about the regional characteristics

of snowmelt coefficient in advance, Equations (5.2.2) and (5.2.4) are recommended at present.


5.2.2 Snow depth on the ground

For a roof snow load without a control system, the basic snow depth on the ground d0 is defined as

the annual maximum value for the whole season with a return period of 100 years. Statistical

properties of a snow depth at 423 meteorological observatory points in Japan were studied to estimate

a value with a long return period4). Five types of probability distribution functions were applied with

two plotting techniques: Hazen and Thomas. Statistical properties in Japan were subdivided into three

groups as shown in Fig. 5.2.4. Finally, it was concluded that statistical properties of the annual

maximum snow depth could not be explained by any single distribution or plotting technique. As a

result, a new method was proposed in which a linear regression analysis was applied to the upper 1/3

of all the data plotted on Gumbel probability paper.


Figure 5.2.4 Type classification on Gumbel probability paper4)

In this recommendation, statistical values with a return period of 100 years were estimated by the

proposed method for the annual maximum snow depth for the whole season and for the annual

maximum increasing snow depth. Because the Gumbel distribution is given by Eq.(5.2.5), the snow

depth on the ground with a return period of r years (10<r<200) can be estimated by Eq.(5.2.6).

FX(x) = exp{-exp[-a(x-b)]} -! <x<! (5.2.5)

where

a: scale parameter

b: position parameter

d0 = b + 1/a ln(r) (5.2.6)

It is usually impossible to obtain meteorological data over a long period at the construction site.

Therefore, this recommendation gives an empirical equation for estimating the snow depth at a

location without any observatories. According to previous studies5), the dominant topographic factors

influencing snow depth on the ground are altitude and sea ratio, which is defined as the ratio of sea

area to total area around the site (see Fig. 5.2.5). In this recommendation, the annual maximum value

of snow depth on the ground is estimated for a given point by:

d = (α ･ altitude) + (β ･ sea ratio) + γ (5.2.7)


where coefficients α for altitude and β for sea ratio and constant γ are given in tables in Appendix of

the original Japanese version. (Appendix 5.2, Table A5.2.4, A5.2.5)

Fig.5.2.5 Definition of sea ratio5) Fig. 5.2.6 Relation between snow depth

and altitude of observatories5)

Fig.5.2.7 Effectiveness of snow depth estimation based on two parameters5)

Snow depth is almost proportional to the altitude where the site is inland and in a narrow limited

area (Fig. 5.2.6). Although the altitude alone is not sufficient to interpolate in general (Fig. 5.2.7 (a)),

values estimated by Eq.(5.2.7) almost coincide with the observed data, as shown in Fig. 5.2.7 (b). Fig.

5.2.8 (a) ~ (h) shows the distribution of the annual maximum snow weight in Japan. The maps were

created with Kriging estimation which equation is expressed as follows.6)

!

" d ds( ) =1

2N ds( )S0si( ) # S0 s j( )[ ]

2

N ds( )

$ (5.2.8)

where, N(ds) is the number of observatories with distance of ds, S0(si) is the observed value of

observatory si.

Nishikawa-cho (Yamagata Prefecture)


Fig. 5.2.8 (a) Annual maximum snow weight (Return period: 100 years, Hokkaido)

Fig. 5.2.8 (b) Annual maximum snow weight (Return period: 100 years, Tohoku)


Fig. 5.2.8 (c) Annual maximum snow weight (Return period: 100 years, Kanto)

Fig. 5.2.8 (d) Annual maximum snow weight (Return period: 100 years, Chubu)


Fig. 5.2.8 (e) Annual maximum snow weight (Return period: 100 years, Kinki)

Fig. 5.2.8 (f) Annual maximum snow weight (Return period: 100 years, Chugoku)


Fig. 5.2.8 (g) Annual maximum snow weight (Return period: 100 years, Shikoku)

Fig. 5.2.8 (h) Annual maximum snow weight (Return period: 100 years, Kyushu)


5.2.3 Equivalent unit weight for ground snow

Usually snow cover of the annual maximum depth comprises several layers, each of which has

accumulated one after another and with varying properties from snowflakes to granular snow, as

shown in Fig. 5.2.10. Fig. 5.2.9 shows typical examples of the relation between snow depth and the

snow mass that is defined as snow weight per unit area. Until the annual maximum snow depth is

recorded, the mass increases in proportion to snow depth. After that, the mass still increases and then

the maximum value is recorded, even though the depth decreases. Although there is usually a time lag

between the dates of the annual maximum depth and of the annual maximum mass, in most cases the

meteorological observation data give only the snow depth. Therefore, we need to use the equivalent

unit weight for ground snow, which is the ratio of the annual maximum snow mass to the annual

maximum snow depth, in order to evaluate the annual maximum snow mass from the annual

maximum snow depth.

Fig. 5.2.9 Relation between snow depth and Fig. 5.2.10 Layers of different types of snow

snow mass7) (section of accumulated snow)8)

Statistical properties of the annual maximum snow depth and the annual maximum snow mass were

studied for data measured at 12 meteorological observatories which were located in heavy snow

regions in Japan. Fig. 5.2.11 shows the relation between snow depth d (m) and equivalent unit weight

for ground snow p0 (kN/m3) with return periods of 100 years and 10 years.9) The relation is described

by:

32.272.0ref00+= ddp (5.2.8)


Fig.5.2.11 Relation between annual maximum snow depth and equivalent unit snow weight

at 12 observatories in Japan9)

Fig. 5.2.12 shows the relation between snow depth d and equivalent unit weight p for data calculated

by the method of snow weight evaluation using daily precipitations and daily average air temperatures

(mentioned in 5.1), which observed at 126 meteorological observatories not only in heavy snow

regions but also in little snow regions. Equation 5.2.8 shows overestimation for the snow depth less

than about one meter. Therefore it is possible to use smaller equivalent unit weight for the snow depth

less than about one meter against the equivalent unit weight obtained by the equation.

Fig.5.2.12 Relation between annual maximum snow depth and equivalent unit snow weight

with return period of 100 years calculated at 126 observatories in Japan10)

5.2.4 Environmental coefficient

Snow loads on roofs vary according to various factors due to the environmental conditions. Table

5.2.1 shows environmental factors influencing the depth of snow on roofs.


Table 5.2.1 Environmental factors influencing depth of snow on roof Macrofactors distance from the nearest seaside, altitude, topographical

inclination, topographical curvature, etc. Mesofactors trees, neighboring buildings, local topography, etc. Microfactors Thermal condition on the roof surface, roofing materials,

orientation of the roof, etc.

Macrofactors are mostly included in the estimated depth of snow on the ground. Microfactors are

too variable to consider in determining the design snow load. In this recommendation, only

mesofactors are considered by the environmental coefficient (kenv).

Table 5.2.2 shows an example of how the environmental condition influences the ground-to-roof

conversion factor, that is, shape coefficient. Fig. ○ shows the location of three buildings with flat

roofs. Building A is usually heated and the snow on the roof is slowly melted. In years of ordinary

winter climates, the snow depth on the roof of building B is higher than those of the other two

buildings. This might be because building B is located to the leeward of building A. In heavy snow

years, the snow depth on the roof of building B is almost the same as that in ordinary years, though the

other two buildings are more heavily loaded than in ordinary years.

Table 5.2.2 Ratio of snow depths on the ground and on roofs7)

Ratio Year

Roof of Bldg. A / Ground

Roof of Bldg. B / Ground

Roof of Bldg. C / Ground

Light Snow Year (1978 – 1979) 0.81 1.03 0.91

Heavy Snow Years ('79-'80, '80-'81) 0.81 1.03 0.96

Ordinary Snow Years (’77-’78, ’81-’82 & ’82-’83) 0.56 1.02 0.81

Here, mean values are shown for heavy snow years and ordinary snow years.

The environmental coefficient (kenv) is generally defined as unity. When the snow depth on the

ground is estimated to increase locally because of the environmental condition, kenv should be

correspondingly larger than the unity.

Figure 5.2.13 Block plan of the buildings7)


5.3 Ground Snow Load with Accumulation for n Days

5.3.1 Characteristic ground snow load with accumulation for n days

(1) Estimation of ground snow weights based on the data of snow accumulation for n days on the

ground and equivalent unit weight for ground snow

A heavy short-term snowfall produces a critical condition in buildings whose snow loads are usually

controlled by reliable systems. In such cases, the annual maximum snow load for the whole season

leads to an overestimation and increasing snow depth for certain days needs to be statistically

estimated. In this recommendation, the increasing snow depth for n days is considered. The duration

n is determined by sufficient consideration. For buildings with reliable control systems, the

characteristic snow load on the ground Sn is given by Eq.(5.3.1) as the product of several factors:

Sn = kenv dn pn (5.3.1)

where

Sn: characteristic snow load (kN/m2) on the ground used for design when snow load on

the roof is controlled,

kenv: environmental coefficient, it is the same as defined in 5.2.4,

dn: characteristic snow depth (m) on the ground when the snow load on the roof is

controlled, as defined in 5.3.2,

pn: equivalent unit weight for ground snow (kN/m3), as defined in 5.3.3.

(2) Estimation of the snow weights on the ground based on the data of daily precipitation and daily

mean air temperature

In section 5.2.1(2), it is described that the new proposed method is practical and useful for

estimating ground snow weights. In order to estimate the characteristic snow weights on the ground,

the above-mentioned method can be applied easily. Fig. 5.3.1 shows the examples at Sapporo,

Kamabuchi, Nagaoka and Tokamachi using Equation (5.2.1), in which the estimated values are

compared with the observed values for snow weights increasing intensity for 7 days. As seen in the

Figures, the estimated values approximately agree with the observed values.


Figure 5.3.1 Example of observed and estimated snow weight increasing intensity for 7 days due to

Eq. (5.2.2)10)

5.3.2 Ground snow depth accumulation for n days

The basic snow depth accumulation for n days on the ground dn is defined as the annual maximum

value of snow accumulation for n days with a return period of 100 years for snow load on a roof with a

reliable control system. The annual maximum increasing intensity of snow depth is defined as shown

in Fig. 5.3.2. Because of the limited number of meteorological observatories, the basic snow depth at

the construction site is estimated from topographical data.

To clarify the difference between the annual maximum snow depth for the whole season (AMD) and

the annual maximum increasing snow depth for 3 days (AMI-3) and for 7 days (AMI-7), two

antithetical examples plotted on Gumbel probability paper are shown in Fig. 5.3.3. In Hokkaido,

values of AMD become larger at the end of winter in spite of smaller AMI values because of the low

temperature. In Gifu, located in the middle of Honshu, however, values of AMI are closer to values of

AMD because this area is rather warmer and snow depth increases rather rapidly. A different snow

accumulation mechanism can also be recognized in Fig. 5.3.4.


Fig. 5.3.2 Annual maximum increasing snow Fig. 5.3.4 Ratio of AMI-7 to AMD11)

depth for n days11)

Fig. 5.3.3 Comparison of AMD, AMI-3 and AMI-7 (Gumbel probability paper, Hazen plot)11)

5.3.3 Equivalent unit weight for ground snow with roof snow control

Because there are quite few data of snow weight observed daily, the equivalent unit weight for

ground snow accumulation for n days (pn) is discussed here with data calculated by the method of

snow weight evaluation using daily precipitations and daily average air temperatures at 126

meteorological observatories. Fig. 5.3.5 shows the relation between snow depth dn and equivalent unit

weight pn based on the annual maximum snow depths accumulating for 3 and 7 days with return

periods of 100 years. The values of pn shown in Fig. 5.3.5 are smaller than those of p0 for the snow

depth larger than 0.5 m in heavy snow regions shown in Fig. 5.2.8, because the snow density increases

according to accumulation days. However they are similar to the values of p0 for the annual maximum

snow depth less than 0.5 m in little snow regions because snow melts away within several days. These

tendencies exhibit also in Fig. 5.3.7, that is the equivalent unit weights dn and d are almost constant for

Tokyo or Sendai located in Pacific Ocean side being relatively warm in winter, but they are different


for Fukui or Sapporo located in Japan Sea side being cold.

The equivalent unit weight for 1, 3 and 7 days are 1.37, 1.41 and 1.57, respectively, which were

obtained as the average values of 126 observation points, as shown in Fig. 5.3.6. However, it is

considered for estimation in safety side that the equivalent unit weight for n-days accumulation snow

with roof snow control pn is the same as that for the annual maximum snow without roof snow control

p.

Fig. 5.3.5 Relation between annual maximum snow depth accumulating for 3 and 7 days and

equivalent unit snow weight with return period 100 years calculated at 126 observatories in

Japan10)

Fig. 5.3.6 Frequency of equivalent unit snow weight for 1, 3 and 7 days’ accumulation10)


Fig. 5.3.7 Relation between accumulating days and equivalent unit snow weight in some cities in

Japan10)

5.4 Snow Load on the Roof

5.4.1 Design snow load on the roof

Generally, design snow load on the roof can not be determined directly. In this recommendation, it

is estimated from ground snow load. Snow load on the roof is usually less than on the ground because

of wind, sunshine, and so on. In addition, roof shape and slope influences the ratio of roof snow to the ground snow. Therefore, shape coefficients µ0 and µn are introduced, taking into account

meteorological conditions. Partial snow load such as snowdrift caused by projecting structures, snow

eaves, and sliding snow from upper roofs at the eaves or lower levels of multilevel roofs are

considered in 5.6.

The format equations of design snow load on roofs differ depending on whether or not snow on the

roof is controlled. If the roof snow is not controlled, the design snow load on the roof S is the characteristic snow load on the ground S0 multiplied by µ0:

S = µ0 S0 (5.4.1)

5.4.2 Shape coefficient

According to recent works, snow load on roofs depends on wind speed and temperature.12)13) In cold

regions, snow on roofs is easily removed, as shown in Photo 5.4.1 and 5.4.2. However, in warm

regions, especially in calm wind conditions, snow on the roof is similar to that on the ground.14)


Photo 5.4.1 Snow drift on a roof Photo 5.4.2 Snow accumulation on a roof

In this recommendation, shape coefficient µ0 is defined as:

µ0 = µb + µd + µs (5.4.1)

where µb: basic shape coefficient

µd: shape coefficient for irregular distribution caused by snowdrift

µs: shape coefficient for irregular distribution caused by sliding

This coefficient is only applied to normal shaped buildings. For special forms or large scale

buildings, shape coefficient should be determined from special research or experimentation.

(1) Basic shape coefficient

The relationship between the ratio of roof snow depth to ground snow depth (basic shape

coefficient) and wind speed is shown in Fig. 5.4.1. In the figure, the solid line shows the former

recommendation of AIJ (1986), the pointed dashed line shows the recommendation of the former

Soviet Union15), the dashed line shows the equation proposed by Mihashi et. al. (1988)16), and the

dotted line shows the equation proposed by Tomabechi et. al. (1991)17). Every study shows that the

basic shape coefficient decreases as wind speed increases.

Roof snow also depends on roof shape. According to wind tunnel tests16), the ratio of roof snow

depth to ground snow depth increases for roof slopes up to 25° and decreases for roof slopes over 25°.

In these ways, basic shape coefficient is determined as shown in Fig. 5.1. For roof slopes larger than

50°, the same value as 50° is used.


Figure 5.4.1 Relationship between ratio of roof snow depth to ground snow depth and wind speed

(2) Shape coefficient for irregular distribution caused by snow drift

In the troughs of M-shaped roofs, multiple pitched roofs and multispan roofs, snow accumulates by

snow drift and it is always deeper in the troughs than at the ridge, as shown in Fig. 5.4.218). This

phenomenon is also observed in wind tunnel tests19). Therefore, shape coefficient for irregular

distribution caused by snow drift µd is defined for the troughs and is zero at the ridges. For multilevel

roofs, snow accumulation on lower roof levels increases especially at the edge of high roofs. The

same thing occurs when there is a parapet or similar structure on the roof.

Figure5.4.2 Observation of snow accumulated on multispan pitched roof (Ottawa)18)

(3) Shape coefficient for irregular distribution caused by sliding

Sliding of snow on the roof depends on characteristics of the snow, temperature, shape of the roof, roofing materials, and so on. Its mechanism is difficult to accurately define. When (2µb+µd)d is larger

than roof gap shown as Fig. 5.4.3 (b), this should be adjusted as shown Fig. 5.4.3 (c).


Figure5.4.3 Treatment of µs

5.5 Snow Load on the Roof with Control

5.5.1 Design snow load on the roof with control

In this recommendation, design snow load on the roof with control is defined as:

S = Sn µn – Sc (5.5.1)

where

Sc: controlled snow load, as defined in 5.5.2.

In this case, µn might be different from µ0. However, because Sn is determined from snow

accumulation for n days, it is difficult to clarify the difference by wind tunnel tests or other estimation methods. That also depends on the method of snow control. Therefore, in this recommendation, µn

takes the same value as µ0. When the snow load is controlled, Sc is calculated as difference of the

initial snow load of snow remaining on the roof when another heavy snowfall is expected and the

snow load removed by a device whose performance is guaranteed even during a heavy snowfall. The

performance should be estimated by research or experiments and then the value Sc should be

determined.

5.5.2 Controlled snow load There are three methods of artificially removing snow from a roof:

1. Mechanical snow removal (including snow removal with man power)

2. Positive snow sliding

3. Snow melting

A combination of methods 2 and 3 is also used. In methods 1 and 2, snow is removed after it

accumulates, and it is unclear how much snow has accumulated when removal starts. In method 3,

there are two possibilities: all snow is melted and some snow remains. Therefore, design snow load

on the roof should be decided by the planner. Fig. 5.5.1 (a) shows the daily snow depth and Fig. 5.5.1

(b) shows the ground snow load on the ground simulated from snow depth after Eq. (5.2.4).


Figure 5.5.1 Simulations of roof snow control (in case of Sapporo 1980-1981)

When snow is removed by manpower, the time during which snow load exceeds the design snow

load on the roof should be considered. If the time is long as in Fig. 5.5.1 (c), the designer cannot

consider the controlled snow load. Fig. 5.5.1 (d) shows the case where snow is removed mechanically

with short delay. In the worst case, we should consider the case where a heavy snowfall starts when

the existing snow load is just over the design load level. Fig. 5.5.1 (e) shows reliable snow removal

system, and only such a case we can take controlled snow load into the design. Fig. 5.5.1 (f) simulates

a snow melting system that is run continuously during the snow season. Its capacity and reliability

against heavy snowfalls should be considered. When the performance of the device is guaranteed even during heavy snow falls, the controlled snow load Sc may be reduced from Sn µn as expressed in

Eq. (5.5.1).

According to some research, a melting system that melts all the snow on a roof all the time

consumes a lot of energy, and a melting system that only works after some snow has accumulated is

inefficient because of snow caving between the snow and the roof (see Fig. 5.5.2)20)21). After this trial,

a new method was studied22)23). With this method, a thin ice layer is created and then melted, thus


inducing snow sliding and consuming little energy.

In snow control, it is important to ensure a reliable energy supply in a heavy snow fall. In Hokkaido,

since the 1970s, roads (national route) closed by heavy snow have been reopened in four days at most.

5.6 Partial Snow Load on the Roof

Snow load on roofs partially increases because of snowdrift caused by projecting objects like

chimneys, ventilators and so on. This load might not be critical for the main frame, but it should be

considered in design of secondary members. The load should be considered as concentrated.

Therefore, to determine the point of accumulation, wind direction should be considered. Snow eaves

are sometimes up to 2 to 3 meters long. Therefore, it should be considered as a concentrated load with

a density of about 4kN/m3. Snow sliding from the upper roof should be resisted first. However, if it

cannot be resisted, the distance and impact of sliding should be considered. The impact force might be

twice the gravity force.

5.7 Other Snow Loads

Side pressure from snow drifts on the outside walls of buildings may be categorized as A or B, as

shown in the Fig. 5.7.1. The load for case B might be larger than for case A. Side pressure might be

assumed as follows, after Matsushita et. al.24):

!

Fl

= 9.8 "10#3 15 ~ 20( )ds2 (5.7.1)

where

!

Fl: Side pressure [kN/m2].

When the building might be buried under snow, snow load caused by sedimentation should be

considered because eaves or braces at the outside might be broken.

When snow adheres to the building or snow covers the building, snow mushrooms at the tops of the

projecting objects sometimes grow to over 1 meter, and therefore cannot be neglected. When snow

blows into balconies or outside corridors, it accumulates in sheltered zones.


Figure 5.7.1 Side pressure and sedimentation25) Figure5.7.2 Observation of

side pressure24)

References

1) Sakurai, S., Joh, O. and Shibata, T.: Estimation of ground snow weight based on daily

precipitation and daily mean air temperature, Snow Engineering: Recent Advances, pp.185-192,

Balkema, 1997.

2) Kamimura, S., Umemura, T.: Estimation of daily snow mass on the ground using air temperature

and precipitation data, Second International Conference on Snow Engineering, CRREL Special

Report 92-27 pp.157-167, 1992.

3) Takahashi, T., Kawamura, T., Kuramoto, K.: Estimation of ground snow load using snow layer

model, Journal of Structural and Construction Engineering (Transactions of AIJ)，No.545,

pp.35-41, 2001.

4) Izumi, M., Mihashi, H. and Takahashi, T., Statistical properties of the annual maximum series and

a new approach to estimate the extreme values for long return periods, Proc. of 1st. Int. Conf. on

Snow Engineering, CRREL Special Report 89-6, pp.25 - 34, 1989.

5) Takahashi, T., Fukaya, M., Mihashi, H. and Izumi, M., Influence of altitude and sea area ratio for

geographic distribution of snow depth, Summaries of Technical Papers of Annual Meeting, Vol. B,

AIJ, pp.219 - 220, 1992.8 (in Japanese).

6) Takahashi, T., Shitara, T. and Ellingwood, B.R.: Ground snow load estimation with Kriging, Snow

Engineering V, pp.135-140, Balkema, 2004.

7) Takahashi, H. and Nakamura, T., Disaster Prevention of Snow and Ice, Hakuashobo, pp.213 - 218,

1986 (in Japanese).

8) Maeda, H.: Fundamental Study on Estimation of Snow Load, Transactions of AIJ, No.319,

pp.32-37, 1982 (in Japanese with English abstract).


9) Joh, O., Sakurai, S., Equivalent snow density in heavy snowing area, Journal of Snow Engineering,

JSSE, Vol.9, No.2, pp.112 - 114, 1993.4 (in Japanese)

10) Sakurai, S., Joh, O. and Shibata, T.: Estimation of equivalent density of snow accumulation for

short period, Snow Engineering, Recent Advances and Developments, pp.143-148, Balkema, 2000.

11) Izumi, M., Mihashi, H. and Takahashi, T.: Statistical Properties and Regional Characteristics of

Annual Maximum Increasing Intensity of Snow Depth, Journal of Structural and Construction

Engineering (Transactions of AIJ), No.392, pp.68-77, 1988.10 (in Japanese with English abstract).

12) Tomabechi, T., Izumi, M. and Endo, A, A Fundamental study on the evaluation method of

roof-snowfall-distributions of buildings, Journal of Structural Engineering, AIJ, Vol.32B, pp.49 -

62, 1986.3 (in Japanese with English abstract).

13) Izumi, M., Mihashi, H., Sasaki, T., Takahashi, T., Matsumura, T., Fundamental study on

estimation of roof snow loads part 15, Summaries of Technical Papers of Annual Meeting, Vol. B,

AIJ, pp.1405 - 1406, 1987.10 (in Japanese).

14) Yamada, K. and Matsumoto Y., Observation of snow cover on real flat roofs in the Hokuriku

region, 1982 - 1989, Summaries of Technical Papers of Annual Meeting, Vol. B, AIJ, pp.117 - 118,

1990.10 (in Japanese).

15) ISO 4355, Bases for design of structures - Determination of snow loads on roofs, 1998.

16) Mihashi, H., Takahashi, T. and Izumi, M., Wind effects on snow loads, Proc. of 1st. Int. Conf. on

Snow Engineering, CRREL Special Report 89-6, pp.158 - 167, 1989.

17) Tomabechi, T., Influence of meteorological conditions for snow depth on roofs, Summaries of

Technical Papers of Annual Meeting, Vol. B, AIJ, pp.51 - 52, 1989.10 (in Japanese).

18) Taylor, D.A., Roof snow loads in Canada, Canadian Journal of Civil Engineering, Vol.7, No.1,

pp.1 - 8, 1980.

19) Endo, A. and Tomabechi, T., Wind channel experiment of the forming conditions of the snow

depth on various roof with model snow, Memoirs of the Hokkaido Institute of Technology, No.11,

pp.163 - 178, 1983 (in Japanese with English abstract).

20) Morino, K., Kobayashi, M., Takebayashi, Y., Kawai, M., Kawashima, M., A snow melting

experiment on a pneumatic structure (air supported dome) No.2 a snow melting experiment by a

wind box, Summaries of Technical Papers of Annual Meeting, Planning division, AIJ, pp.789 -

790, 1984.10 (in Japanese).

21) Nishi, Y., Nishikawa, K., Ishii, H., Analysis of snow melting process of the air supported

structure -2, Summaries of Technical Papers of Annual Meeting, Vol. D, AIJ, pp.895 - 896, 1986.8

(in Japanese).

22) Ohtsuka, K., Joh, O., Homma, Y., Miyagawa, Y., Masumo, T. and Okada, H., A Study on the

removal of snow from membrane structures, Proc. of Membrane Structures Association of Japan,

No.4, pp.55 - 68, 1990 (in Japanese with English abstract).

23) Tomabechi, T., Yamaguchi, H., Ito, T., Hoshino, M., Fundamental study on sliding of snow on

the roof of membrane structure, Journal of Structural and Construction Engineering, AIJ, No.426,


pp.99 - 105, 1991 (in Japanese with English abstract).

24) Matsushita, S., Nakajima, H. and Izumi, M., A study on side pressure of snow, Transactions of the

AIJ, No.89 (Summaries of Technical Papers of Annual Meeting) p.82, 1963.9 (in Japanese).

25) Kubodera, I.: Side pressure of snow on buildings, Kenchiku Gijutsu, No.384, pp.203-204, 1983

(in Japanese).

chapter 5 snow loads

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