Prediction of Local Snow Loads on Roofs

Prediction of local snow loads on roofs

Vivian Melysund

Dissertation submitted for the Philosophiae Doctor Degree (PhD) in Structural Engineering at the Faculty of Engineering Science and Technology, Department of Structural Engineering, Norwegian University of Science and Technology (NTNU)

Contact information: SINTEF Building and Infrastructure P.O.Box 124 Blindern, NO-0314 Oslo, Norway Telephone +47 22 96 55 55 Or Norwegian University of Science and Technology (NTNU) Department of Structural Engineering Richard Birkelands vei 1 A, NO-7491 Trondheim, Norway Telephone +47 73 59 47 00 [email protected]

ISBN Printed version: 978-82-471-2491-8 ISBN electronic version: 978-82-471-2490-1 ISSN 1503-8181 Doctoral thesis serial number 2010:247

Printed by Tapir Uttrykk, Trondheim, Norway 2010.

This PhD study has been carried out within the SINTEF research & development programme Climate 2000 Building constructions in a more severe climate (2000-2007) tjenester.byggforsk.no/prosjekter/klima2000

Melysund, V./ Prediction of local snow loads on roofs

AcknowledgementsThis PhD study has been carried out within the SINTEF research programme Climate 2000 Building constructions in a more severe climate (2000-2007), strategic institute project Impact of climate change on the built environment. I gratefully acknowledge the programme management for giving me the opportunity to carry out this study. I also thank all construction industry partners of the programme and the Research Council of Norway (NFR reference no. 154002). I would like to express a warm appreciation and thank my two supervisors at NTNU, Professor Karl Vincent Hiseth and Professor Bernt J. Leira, for many discussions and advices. I would also like to thank the University of Life Sciences, especially Professor Emeritus Egil Berge and Professor Emeritus Halvor Hib, permitting the use of their field observation data in my work and useful help in the search for background information. I also wish to thank Research Director PhD Kim Robert Lis for many discussions and thorough reviews. March 2010 Vivian Melysund

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SummaryLarge snow loads on roofs during the winter season of 2005 - 2006 led to the collapse of several buildings in Norway. In Central Europe, during the same winter season, there were several serious accidents related to heavy snow loads where many people were killed or injured. Hence, there is a need for evaluating the background for snow loads used in the design of buildings and an assessment of the reliability of buildings which are subjected to roof snow loads. The snow load represents one of the most important structural loads in Norway. The magnitude of the snow load varies throughout the country depending on local climate. In the current Norwegian standards, characteristic snow loads on roofs are found by means of simple expressions for the relationship between snow depth on the ground and snow loads on the roof. In addition, rules are given in order to account for the effects of wind, roof geometry and heat transfer on roof snow loads. An investigation is performed in order to obtain a reliable indicator as to whether existing buildings in Norway meet current regulatory requirements concerning safety against collapse caused by snow loads and wind actions. The analysis comprises studies of 20 existing buildings in five high-snowfall and five high-wind municipalities in Norway. The investigation demonstrates that most of the buildings considered have higher calculated probability for collapse owing to snow loads than the regulations now require. It also indicates too low calculated reliability for a considerable number of buildings in Norway, when evaluating the possible implications of the findings. An unexpected result in this study is the discovery that many buildings have even lower calculated reliability than the historical increase in design loads should imply. Weather data from meteorological stations in Norway for a reference period of 30years, 1961-1990, are used to quantify the effects of wind exposure on roof snow loads according to the definitions in the Norwegian standard NS 3491 and the international standard ISO 4355. It is shown that the procedure in an informative annex of the standard does not reflect the actual effects of wind exposure on roof snow loads in Norway, the main reasons being oversimplifications in the definition of the exposure coefficient and the extreme variations of the climate in Norway. As a result of the present work, the Norwegian snow load standard NS-EN 1991-1-3, which recently has been published, includes an improved definition of the exposure coefficient. Whether it is beneficial to differentiate roof snow loads in view of material costs, is studied by means of a selected house concept. This study lead to unexpected conclusions which challenge the prevailing view that increased calculated capacity results in unacceptable increased costs for the individual house owner. In this investigation, a timber detached house is designed for different roof snow load levels. Some differences are found when evaluating the degree of building material consumption, but the economic effect is small. When comparing the costs of increased reliability of all houses to the total damage insurance payments, conclusions may be drawn that it is more reasonable not to increase the reliability.v


From an environmental perspective reduced material consumption is however highly appreciated. Since the costs of increasing the calculated reliability and the negative effects on the environment probably are limited, an individual property owner would most likely prefer to invest in increased reliability. Models for predicting roof snow loads and snow density on the ground are developed using meteorological data as input which extends the application of the models. Snow load and density measurements performed at 105 sites by Professor Hib at the Agricultural University of Norway (now the University of Life Sciences, UMB) in the period 1966 to 1986 are analysed. New knowledge of the influence of local climate on resulting maximum snow loads is achieved. A clear correlation is found between observed climate and the measurements. The study also reveals that the relation between local climate and snow load is complex. The results are a step forward in the process of understanding these relations. The work has revealed that wind velocity as a single parameter probably is of less importance in relation to maximum snow loads than previous research has indicated. Additional work is necessary and should focus on further developing the method for predicting snow loads on roofs, which in turn can be used to improve standards and regulations. The snow measurements performed by Hib were done within a small area in Norway. Additional work should also aim at investigating the results in view of data from other parts of the country. The methods developed in the current study for predicting snow loads on roofs are important in order to understand the climates significance on the accumulation of roof snow loads. In a longer perspective it can be used to improve the European standards recommendations with respect to design roof snow loads. It is also demonstrated in which way the methods can be used to estimate roof snow loads in areas subjected to large snow falls with short duration. In this way, snow clearance of roofs can be carried out in time. Roof snow loads for buildings located in the city of Kristiansand in Norway are calculated. Methods for collection and preparation of the necessary meteorological input are presented, including development of parameters for building sites where limited meteorological data exist.

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Table of contentsACKNOWLEDGEMENTS .................................................................................... III SUMMARY ................................................................................................................V TABLE OF CONTENTS ...................................................................................... VII LIST OF PAPERS ................................................................................................... IX 1 INTRODUCTION ............................................................................................. 1 1.1 1.2 1.3 1.4 1.5 1.6 2 BACKGROUND............................................................................................... 1 PURPOSE AND OBJECTIVES ............................................................................ 3 THE WINTER CLIMATE IN NORWAY ............................................................... 3 WIND AND SNOW LOADS ON ROOFS............................................................... 5 BUILDING REGULATIONS AND DESIGN STANDARDS ..................................... 14 STRUCTURAL SAFETY ................................................................................. 16

MAIN FINDINGS ............................................................................................ 20 2.1 INTRODUCTION AND METHODOLOGY .......................................................... 20 2.2 PART A: STRUCTURAL SAFETY AND RELIABILITY ....................................... 21 Increased snow loads and wind actions on existing buildings: Reliability of the Norwegian building stock (Paper I) .................................................................. 21 2.3 PART B: ANALYSES OF CURRENT DESIGN RULES ......................................... 23 Effects of wind exposure on roof snow loads (Paper II).................................... 23 Economical effects of reduced roof snow loads (Paper III) .............................. 23 2.4 PART C: METHODS FOR IMPROVED CALCULATION OF ROOF SNOW LOADS .. 25 Predicting snow density using meteorological data (Paper IV) ........................ 25 Predicting roof snow loads using meteorological data (Paper V) .................... 26

3 EXAMPLE OF APPLICATION: LOCAL SNOW LOADS ON ROOFS IN KRISTIANSAND ..................................................................................................... 28 4 5 FURTHER WORK .......................................................................................... 33 CONCLUSIONS .............................................................................................. 35

REFERENCES......................................................................................................... 38 COMPLEMENTARY WORK CARRIED OUT AS PART OF THE PHD STUDY ...................................................................................................................... 41 INDIVIDUAL PAPERS ............................................................................................ 1

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List of papers

Part A Structural safety and reliability

I.

Melysund, V., Lis, K.R., Siem, J. and Apeland, K. (2006) Increased snow loads and wind actions on existing buildings: Reliability of the Norwegian building stock. Journal of structural engineering, 132(11), 1813 1820.

Part B Analyses of current design rules

II.

Melysund, V., Lis, K.R., Hygen, H.O., Hiseth, K.V and Leira, B. (2007) Effects of wind exposure on roof snow loads. Building and Environment 42(10): 37263736. Melysund, V., Hiseth, K.V., Leira, B. and Lis, K.R. (2008) Economical effects of reduced roof snow loads. Proc. of the 6th International Conference on Snow Engineering, Whistler, British Columbia, Canada 2008. Engineering Conference International, Brooklyn, New York, U.S.A.

III.

Part C Methods for improved calculation of roof snow loads

IV.

Melysund, V., Leira, B., Hiseth, K.V. and Lis, K.R. (2007) Predicting snow density using meteorological data. Meteorological Applications 14: 413-423. Melysund, V., Hiseth, K.V., Leira, B., Lis, K.R. and Berge, E. (2010) Predicting roof snow loads using meteorological data Meteorological Applications (submitted).

V.

These papers will be referred to by their Roman numerals.

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1 Introduction

1.1 BackgroundLarge snow loads on roofs during the winter season of 2005 - 2006 led to the collapse of several buildings in Norway. Schools, sports halls and shops were among the building types with damage. There were no death casualties in the accidents, only material damage was reported. In Central Europe, during the same winter season, there were several serious accidents related to heavy snow loads, where many people were killed or injured. The two most serious accidents were the collapse of a market hall in Moscow, where 66 people died, and the roof collapse of an exhibition hall in southern Poland, where 62 people died. There were also reports of serious accidents in the Czech Republic and Germany. After these accidents, it has been a matter of concern whether the design regulations concerning roofs to withstand snow loads are adequate or if they should be improved. The climate differences in Norway imply large variations in snow loads. Due to the rugged topography of the country, the amount of precipitation and the magnitude of wind actions in exposed western locations are highly different from sheltered inland areas in the eastern part. The temperatures are generally higher in southwest parts of the country compared to eastern and northern parts. Previously, the design roof snow loads did not reflect these differences in a proper way. The building regulations of 1949 (valid until 1970), for instance, referred to a general snow load on roofs corresponding to 1.5 kN/m2 (National Office of Building Technology and Administration 1949). This value could be reduced or increased by local building authority. Current regulations are more differentiated; however they are not based on a thorough registration of roof snow loads throughout the country. The regulations rely on an assumed relationship between ground snow loads and roof snow loads. This relationship is expressed as a function of roof slope, energy flux trough the roof and wind exposure. The snow loads on the ground vary from 1.5 to 9.0 kN/m2 in the current regulations. There are few scientifically documented measurements of snow loads on roofs in Norway. Consequently, the regulations do not account for the large climatic variations in the country (ref. paper II). There is a need for more thorough knowledge of roof snow loads as a function of local climate. With this knowledge, the effects of future climate change on roof snow loads could be evaluated and taken into consideration. In NS 3491-3 Design of structures - Design actions - Part 3: Snow loads (Standards Norway 2001), snow loads on roofs are expressed by s = Ce Ct sk (1)

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where s k is snow load on the ground and the parameters , C e and C t describe the conditions on the roof. A similar expression can be found in ISO 4355 Bases for design of structures Determination of snow loads on roofs (International Organization for Standardization 1998). The exposure coefficient C e takes into account that wind removes snow from flat roofs. The coefficient gives a snow load on a sheltered roof twice as large as that on a windswept roof. The shape coefficient describes the distribution of snow load on the roof due to geometry. The thermal coefficient C t defines the reduction of the snow load on the roof as a function of the heat flux through the roof. In practice, it has turned out to be difficult for consultants in structural engineering to determine the exposure coefficient C e . The main reason is the meteorological input which is needed. According to an informative annex in ISO 4355 and NS 3491-3, the exposure coefficient is a function of: , the mean temperature in the coldest winter month N, the number of days with a wind velocity above 10 m/s, where N is defined as an average for the three coldest months of the year.

Mean values for many years are recommended, usually 30 years. This meteorological information is available from advanced weather stations, merely. If a building site happens to be located near such a station, the data needed is still not easily accessible. In NS 3491-3, snow loads on the ground are specified for the municipality centre in each of the 434 Norwegian municipalities (50-year return period). Rules are given for increasing these values with respect to the buildings sites height above sea level compared to that of the municipal centre. The standard also allows using other reliable sources for the ground snow load in particular cases, for instance measurements performed close to the building site and over a long period (at least 20 years). Due to the topography in Norway, it is not always appropriate to apply height as the only parameter for differentiating local ground snow loads. As a particular example, a maximum snow depth of 275 cm was measured in the winter season 1999/2000 at the meteorological station Grnligrotten situated at 87 m above sea level in the municipality of Rana (at the arctic circle in Northern Norway), while at the meteorological station Mo i Rana III (40 m a.s.l.) 6 km away, the corresponding measured maximum snow depth was only 105 cm (ref. www.met.no). Furthermore, meteorological stations are placed in order to enable a good representation of regional climate, i.e. the differences in measured snow depth are not likely to be explained by the degree of wind exposure. The current methods for calculating roof snow loads found in the Norwegian standard do not reflect the differences in climate which can be observed within short distances. As a result, a majority of the roofs may be designed for snow loads which deviate from the prescribed design load with 50 years return period. There is a need for methods which include the effects of local wind actions, local precipitation

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amounts and local temperatures on roof snow loads. Developing models which use meteorological data as input will ensure results which easily can be used by structural engineers all over the country, without the need of advanced computer software. On the other hand, increased geographic differentiation and more complex calculation methods can contribute to higher risk of errors and evasions. Investigations carried out by SINTEF Building and Infrastructure indicates that the cost of repairing building process induced building defects in Norway amounts to 5% of the annual capital invested in new buildings. Correcting faults and repairing defects which arise in buildings during the construction process are estimated to cost another 4%. The construction industry in Norway therefore seeks solutions which contribute to a reduction of the amount of building defects.

1.2 Purpose and objectivesThe main purpose of the present work is to contribute to improved methods for adapting roof snow loads to local climate. In this work the effects of wind on roof snow loads will have a special focus. The work is intended to contribute to the development of more accurate criteria and standards of practice concerning snow loads on roofs. The objectives are accordingly: To study the reliability of the Norwegian building stock identifying the vulnerability with respect to snow loads, To analyze selected topics of current design rules for snow loads in order to find areas with potential of improvement, To contribute to improved design methods for predicting roof snow loads based on local climate, To evaluate the importance of differentiated roof snow loads through a case study.

Data from the Norwegian Institute of Meteorology are applied. It may simplify use and further development of the results in equivalent studies, for instance in the development of methods for other climatic zones or analyses of the impact of future climatic changes.

1.3 The winter climate in NorwayThe Norwegian climate is extremely varied. From its southernmost point (Lindesnes) to its northernmost (North Cape) there is a span of 13 degrees of latitude, or the same as from Lindesnes to the Mediterranean Sea. Furthermore, the rugged topography of Norway gives large local differences over short distances. Norway is often regarded as a cold and wet. The country shares the same latitude as Alaska, Greenland and Siberia, but has a rather pleasant climate compared to these areas. Thanks to its

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westerly location, on the east side of a vast ocean with a huge, warm and steady ocean current near its shores and a dominating south-westerly air flow from the Atlantic Ocean, Norway has a much more friendly climate than the latitude indicates. The highest winter temperatures can be found in the coastal areas of the southern and western part of Norway (see Figure 1). Vgsy (Sogn og Fjordane County) on the southwest coast has monthly normal temperatures in the period November to March varying from 2.6 C to 5.5 C. Sviny at Hery (Mre og Romsdal County) recorded the highest mean monthly temperature ever, with 9.1 C in November 2000. Except for uninhabited mountain areas, the coldest area throughout the winter season is the Finnmark Plateau (inland area, Finnmark County). One of the weather stations there, Karasjok, has monthly normal temperatures in the period from November to March varying from 9.4 C to 17.1 C. The coldest month ever was in 1966, when Karasjok recorded a mean monthly temperature of 27.1 C. The inland climate of Norway is subject to extreme changes in temperature on short temporal scales. Rros (Sr-Trndelag County, south-east of Norway), for instance, experienced in March 2005 a maximum monthly temperature of 13,2 C while the minimum monthly temperature was 39,4 C. There are also large differences in the normal winter precipitation in Norway. The largest monthly normal precipitation is found some tens of kilometres from the coast of Western Norway. These amounts are among the highest in Europe. Grndalen at Flora (Sogn og Fjordane County) has a monthly normal precipitation varying from 261 to 425 mm in the period November to March. Several other stations in this area follow closely. Grndalen has also the record for one-month precipitation, with 1190 mm in January 1989. The inner part of south-east Norway), the Finnmark Plateau (Finnmark County), and some smaller areas near the Swedish border, are all lee areas in relation to the large weather systems which mainly arrive from the west. Common for these areas are the low annual precipitation and that a showery precipitation during summer is the largest contributor. Kautokeino (Finnmark County) has lowest monthly normal precipitation varying from 7 to 18 mm in the period November to March. One of the lowest recorded winter precipitation amounts for the same period (November to March) is only 23 mm, measured at this station in 1942-43. Large precipitation amounts result in high snow depth on the ground. At a meteorological station in Odda (Hordaland County in the southwest) a snow depth of 490 cm were measured in March 1983. Norway is a mountainous country with the main settlements being located in valleys and along the coast. This gives two characteristic types of wind climate for the built environment. Inland settlements experience a wind climate governed by valleys. The main wind direction is along the valley, with a decrease in wind speed due to topographic effects. The costal areas suffer a higher frequency of extreme winds due to less topographic effects. The strongest wind registered at any location in Norway was 62 m/s at the Sviny lighthouse (Mre og Romsdal County on the western coast of Norway) in January 1992. The climate statistics in this section are obtained from www.met.no.

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Figure 1 Map of Norway

1.4 Wind and snow loads on roofsDuring snowfall, the presence of wind makes the snow load on roof different from that on undisturbed ground. Drifting occurs even for light winds (0.3 1.5 m/s). At higher wind velocities (1.6 3.3 m/s) the snow particles move in a more horizontal than vertical direction. Drifting affects the deposition of snow; particles are transferred through areas with high wind velocities and accumulate in areas with low wind velocities. At wind velocities between 3.4 m/s and 5.4 m/s the snow moves considerably faster horizontally than vertically, and significant redistribution may occur. Higher winds often blow the snow away leaving the roofs almost bare. The same winds may deposit large drifts on the ground or against structures and may result in the formation of snow ramps of such size that ground snow begins drifting onto the roofs (Nordli 2000, Taylor 1979).

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Snowdrift formations are highly dependent on the detailed wind velocity patterns across the roof, which in turn are functions of wind direction and duration, roof geometry, and the local surroundings near the building (Figure 2). In areas where the wind is accelerating, there will be removal of snow, since a higher volume is drifting out of the area than into it. In areas of decelerating wind, the snow will accumulate, since a higher volume drifts in than out (Irwin et al. 1995, Isyumov 1971).

Figure 2 Local wind velocity around buildings (SINTEF Byggforsk Research Sheets no. 471.043)

The wind produces both static and pulsating pressures on structures. According to Bernoullis equation the sum of static and velocity pressure is constant along a streamline: p + U2 = const (2)

The magnitude and distribution of the wind velocity pressure are dependent on the geometry of the structure and the intensity of the wind load. Wind pressure at a point of a structure can be expressed as q point = C p U tot 2 (3)

where is the air density and U tot is the total wind velocity (i.e. the sum of mean velocity and fluctuating velocity). The pressure coefficient C p is defined as the ratio of velocity pressure on the building surface and velocity pressure on the undisturbed upstream air flow. Considering only along-wind turbulence U tot can be separated into the mean velocity U and the fluctuating velocity component u (see Figure 3): U tot = U + u (4)

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Figure 3 Wind profile (Dyrbye and Hansen 1997)

The mean wind profile can be expressed by a logarithmic expression:U ( z ) = u* 1

ln

z z0

(5)

where u * is the friction velocity, is von Krmns constant (equal to 0.4) and z 0 is the roughness length. The friction velocity is defined as:u* =

0

(6)

where 0 is the surface shear stress and is the air density. The value of u * depends on the roughness length z 0 and is about 3 4 % of the wind velocity at a height of 10 m (Mellor, 1965). The roughness length z 0 is a function of the terrains roughness which retards the mean wind at the ground surface, see Figure 4. According to NS 3491-4 Design of structures - Design actions - Part 4: Wind loads the roughness length z 0 has a value of 0,003 at rough, open sea and a value of 1 in urban areas or areas with spruce forest.

Figur 4

The terrains roughness retards the mean wind at the ground surface (Dyrbye and Hansen 1997)

The turbulence component of the wind, u, can be expressed by means of the turbulence intensity, I z :

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(7) U ( z) where u (z) is the standard deviation for the turbulence component and U(z) is the mean velocity. The turbulence intensity I u can be assumed constant in homogeneous terrain but varies as a function of height above ground z and roughness length z 0:I u ( z) = 1 ln( z / z 0 )

I u ( z) =

u ( z)

(8)

When the wind meets topographical elements (like escarpments or hills) or obstacles (like buildings) the wind properties will change. The shape and roughness of the structure which is subjected to the wind is decisive for the resulting velocity pressure on a structure. The pressure coefficient C p (defined in connection with Equation 3) is a measure of the decrease or increase of pressure relative to that of the undisturbed upstream air flow. Figures 5 and 6 show areas with increased pressure on pitched roofs.Dir.

Flat roofs

Mono pitched roofs

Duo pitched roofs

Area with increased wind loads

Figure 5 Areas with increased pressure (high values of C p ) on pitched roofs (SINTEF Byggforsk Research Sheets no. 471.041).

The wind flow field is disturbed for buildings in the wake of other buildings. In the near wake the mean flow and turbulence intensity are affected by separating shear

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layers and vortices shed from the upstream building edges. The mean wind decreases and the turbulence increases in the direction of the flow. The near wake may have a length up to a few building heights. In the far wake the effects on the wind flow field decays. The wind profile may be significantly affected for a length of 10 to 20 building heights downwind and 2 to 3 building heights/widths in other directions see Arya (2001). If a building is more than twice as high as the average height of the neighbouring buildings, the design of the neighbouring building should be designed for an increased wind velocity according to NS-EN 1991-1-4, section A.4. Reference is made to Davenport (1962), Dyrbye and Hansen (1997), Simiu and Scanlan (1986) for a detailed description of wind loads on structures. When snow falls in the presence of wind, the snow may accumulate on buildings in wake areas such as valleys, the lee side of peaked or arched roofs, lower roofs sheltered by higher roofs or behind obstructions on roofs (Boyd et al. 1981). This occurs in such a way that it tends to smooth out details. This accumulation may change the wind flow field through lower roughness and thereby result in less turbulence.

Figure 6 Areas with higher pressure (high values of C p ) (SINTEF Byggforsk Research Sheets no. 471.043)

Redistribution of snow may also occur in periods without snowfall. Snow may be transferred onto the roof from its surroundings, snow may be redistributed across the roof or snow may blow off the roof. Snow transport can be divided into suspended transport and unsuspended transport, see Figure 7. Unsuspended transport takes place in a layer 125 cm above the surface. Saltation and creep are the two kinds of unsuspended transport. Saltation refers to the way in which the drifting snow particles appear to jump along the surface, and is the dominant mode of transport for particles larger than 0.1 mm (Tabler 1988). Creep describes particles that roll along the surface. Suspended transport or suspension is defined as snow transported by turbulent wind at a higher level (approximately 1 100 m) than unsuspended transport (Norem 1974, Mellor 1965).

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Figure 7 Snow transport (Norem 1974, based on Mellor 1965)

Whether unsuspended transport or suspended transport will dominate the snow redistribution depends on the properties of the snow and the wind velocity. In order to move snow particles by creep or saltation the friction and cohesive forces of the snow particles have to be exceeded. The threshold wind velocity is defined as the wind velocity where this kind of transport begins. Only unsuspended transport is possible at a wind velocity just above the threshold velocity. At higher wind velocities the particles are lifted further up into the suspension layer and suspended transport takes place (Schmith 1980, Li and Pomeroy 1997). According to Otstavnov and Rosenberg (1989) drifting occurs at average wind velocities above 4 m/s during snowfall and above 6.5 m/s with no snowfall. Other studies have focused on a more instant threshold wind velocity and not a wind velocity averaged over a longer period as applied in that study. According to Mellor (1965), threshold wind velocities of 3 to 8 m/s at a height of 10 m are needed in order to transport loose and unbounded snow. If the surface snow is densely packed and firmly bounded, a threshold wind velocity can be above 30 m/s. According to Kind (1981) the threshold wind velocity is approximately 5 m/s at a height of 10 m for fresh dry snow, 11 m/s for slightly aged or hardened snow and 23 m/s for snow hardened by very strong winds. Li and Pomeroy (1997) evaluated 1-hour observations from the period 1970 to 1976 at 16 meteorological stations in the Canadian prairies. Based on these studies, threshold wind velocities were recorded and presented as a function of temperature. It was concluded that threshold wind increased nonlinearly with ambient air temperature above 25 C. An average threshold wind velocity of 9.9 and 7.7 m/s was observed for respectively wet and dry snow transport. An average threshold wind velocity of 7.5 and 8.0 m/s was observed for respectively fresh and aged snow. Wind makes the snow particles split and become smaller. Smaller particles imply a higher ratio of suspended transport (Tabler 1988). Once at the surface, snow crystals rapidly become bonded to each other, and these larger particles inhibit wind transport (Schmith 1980). Snow deposited during windy conditions becomes more densely packed than snow deposited during calm air. The amounts of snow redistributed by the wind is dependent on the particle-, windand surface properties (particle weight, cohesion forces, wind velocity, non-erodible

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surface elements etc.). The properties of the snow layer will change with time. Snow particle bonding tends to increase as a result of mass and energy fluxes and changes in the state of the snow crystals, mainly through the process called metamorphism. Temperature gradient metamorphism makes water condensate in the colder outer layer of the snow and causes snow crystals to grow. Equitemperature metamorphism causes growth of ice bonds by sintering and strong cohesion between crystals, and is a result of local differences in vapour pressure due to the crystal geometry. Metamorphism generally results in increase of surface snow density, mechanical continuity and hence strength over time (Li and Pomeroy 1997). High temperatures increase the cohesion forces between the snow particles and thereby the threshold wind velocity. Measurements show an exponentially increase in cohesive forces with increasing temperatures (Schmidt 1980). ura et al. (1967) presented data showing that the threshold wind velocity increased with increasing temperature above 7 C, presumably due to cohesive forces (based on meteorological observations). Other observations indicated that the threshold wind velocity for fresh snow seemed to be constant and equal to 3 m/s at temperatures below 2.5 C. Transport rates for drifting snow based on mean wind velocity are developed based on the study of for instance drifting ground snow in Antarctica, Canadian Prairies and Siberia. The expression developed by Pomeroy et al. (1991) is a function of mean velocity U (in m/s, 10 m above the ground) and is based on integration over a height of 5 m:4 qT = 2.2 106U10.04

(9)

where q T is expressed in kg/s per metre perpendicular to the wind. Similar expressions for redistribution of snow on multi-level flat roofs are developed where the amount of available drifted snow is the main parameter (ORourke and Kuskowski 2005). The total duration of wind will determine the mass of snow accumulated or depleted on the roof. Even low velocities of long duration may give significant drifts and unbalanced loads. The drifts are influenced by the rate of snowfall, its duration, and the time between snowfalls (Taylor 1979). Prevailing calculation methods for snow loads on roofs are mainly based on results from field investigations and wind tunnel experiments rather than analytical calculations of the wind field, snow transport and erosion/deposition. One reason is the lack of a theoretical basis for such analysis. Another reason may be the large variation in meteorological parameters, roof structures and surroundings. The amount of snow on a roof has often been measured in the field, expressed in terms of the ratio to ground snow load. The differences in roof and ground loads are mainly due to changes in wind climate, sliding and heat transfer through the roof. These changes have been expressed through the shape coefficient (accounting for wind effects and sliding), the exposure coefficient C e (accounting for wind effects)

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and the thermal coefficient C t (accounting for heat transfer) in the Norwegian standard NS 3491-3 (Standards Norway 2001): s = Ce Ct sk (10)

where s k is the snow load on the ground and s is the roof snow load. Shape coefficients and exposure coefficients have been developed for simple roof geometries through field investigations. These results have been supported by laboratory experiments (wind tunnel and water flume) where also more complex roof geometries have been examined. Table 1 summarizes field investigations for flat roofs with varying wind climate. The values for the exposure coefficient and shape coefficients for flat and pitched roofs found in many standards are based on the listed field investigations.Table 1 Ground to roof snow conversion factors for flat roofsa) Reference Ratio ground snow load/roof snow load Sheltered SemiWindsheltered swept Otstavnov and Rosenberg 1989b) 0.98 0.72 0.46 Lutes 1970 0.90 0.60 0.30 Taylor 1979 0.80c) ORourke 1983d) 0.76 0.57 0.55 Hib 1988 s k = 1.0 kN/m2 0.82 e) 2 s k = 3.5 kN/m 0.62 e) Lberg 1976 0.55 0.27 Com. European Communities 1999 0.90 0.74 0.58a) To be compared to C e in NS 3491-3, i.e. 0.8C e for flat roofs b) Assumed snow cover for 3.5 months. Average winter wind velocity in sheltered, semi-sheltered and windswept area are assumed to be respectively 2 m/s, 4 m/s and 6 m/s c) Snow ground load with 30-year return period was used when calculating roof-to-ground ratio d) Values are recalculated by the author in order to be applicable for unheated roofs e) Degree of wind exposure was not registered. s k ground snow load. The ratio ground snow load/roof snow load is found to depend on the amount of snow load on the ground.

In the European Snow Load Program 1997-1999 (Commission of the European Communities 1999) wind tunnel tests were performed on pitched, flat, multilevel and curved roofs for a single snowfall in order to verify measured roof snow loads in nature. The roof shape coefficients for flat roofs and roofs with small roof slope were basically confirmed, although the values found in the experiments were generally larger than those obtained from full-scale measurements. For large roof slopes the tests suggested a slight increase of the shape factors for both the leeward and the windward side of pitched roofs compared to shape factors in the current EN standard.

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Figure 8 Wind tunnel experiments (Commission of the European Communities 1999)

Sliding of snow on pitched roofs depends on several factors. The component of the snow weight which is parallel to the roof produces the driving force of the sliding. This force is restrained by anchoring forces for instance over the ridge or chimneys, and compression forces due to frozen snow at the eaves. On the roof surface, sliding is restrained by cohesion and friction. The friction forces increase with increasing roof snow loads while the cohesion forces are not affected by the magnitude of snow loads (Taylor 1983, Taylor 1985).

Figure 9 Load components of sliding snow (Taylor 1983)

Several field investigations have documented the effects of sliding (Taylor 1985, Hib 1988). The results of these investigations show a reduction of snow loads for roof angles larger than 20 30, and no roof snow loads at all for angles larger than 60 70. The reduction is larger for smooth roofing materials than materials with a high coefficient of friction. In figure 10, which shows the results of the investigations done by Hib, it can be seen that roofs with metal roofing has a lower coefficient of friction, and consequently less snow loads, than roofs with other roofing material. It can also be seen that the snow loads are generally higher at the leeward side of the roof than at the windward side. This is due to drifting.

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Figure 10 Reduction of snow loads for high roof angles proposed by Hib (Hib 1988)

A method for quantifying snow load reduction due to heat transfer through glass roofs has been suggested by Sandvik (1989). By combining a simple numerical heat transfer model with meteorological observations of temperature, precipitation and wind velocity in Norway, a conservative amount of melting snow has been prescribed. In the report to The Commission of the European Communities (1999), a more detailed model is discussed, which also accounts for heat transfer within the snow cover and to/from the atmosphere. A method for taking into account increased sliding due to water film on the boundary between glass/snow, as a function of roof angle, is also suggested. The concept of using ground snow loads as basis for determination of roof snow loads is useful because it covers the influence of local differences in climate parameters, such as precipitation and temperature. In field investigations where the ratio of ground snow load/roof snow load is documented, it is therefore particularly important to measure undisturbed ground snow loads. For sites exposed to wind this can obviously be difficult. An alternative would be to prescribe roof snow loads as a function of observed precipitation amounts; however this would disregard the influence of other parameters, such as melting, and catchment errors. Calculation methods primarily based on field investigations may be inaccurate due to a high degree of generalisation with respect to climate, topography and building geometry. Some of the derived ground to roof conversion factors are based on a too small number of measurements. Shape factors for curved roofs and multilevel roofs are areas where more research should be performed. Field investigations documenting shape coefficients and exposure coefficients are to a high extent performed for medium to small buildings, and do not sufficiently take into consideration the redistribution which may occur on large roofs. Shape and exposure coefficients as a function of roof size should therefore be focused on.

1.5 Building regulations and design standardsThe building regulations of 15 December 1949 (National Office of Building Technology and Administration 1949) referred to a general snow load on roofs equal to 1.5 kN/m2. This value could be reduced or increased by the individual building authority with the Ministrys approval. The influence of the roof shape on the snow load was calculated in a simple way. The snow load was multiplied by a shape factor equal to 1.0 for roof slopes less than 30. For roof slopes between 30 and 60, the 14 of 42


shape factor should be reduced linearly from 1.0 to 0.0. The regulations prescribed that accumulation of snow on the roof should be taken into consideration. In the case of pitched roofs, the roof structure should be calculated for unbalanced snow load, i.e. snow load on only one side of the roof. In the building regulations of 1 August 1969 (National Office of Building Technology and Administration 1969), the requirement concerning general snow load equal to 1.5 kN/m2 was maintained, but the guidance to the regulations indicated a few municipalities in which the snow load should be taken as 1.0 kN/m2, 2.0 kN/m2 or 3.0 kN/m2. To account for the roof shape, reference was made to the shape factors in NS 3052 (Standards Norway 1970). In March 1970, the first standard on structural loads, NS 3052 Calculation of loading, was issued. The general basic value for snow loads on roofs was still unchanged at 1.5 kN/m2, and the shape factors also remained as before. This standard indicated that, for areas with especially high snowfall, the basic value was to be assessed with the aid of snow maps. Reference was made to zones with values of up to 1.5 kN/m2, between 1.5 and 2.5 kN/m2 and above 2.5 kN/m2. Areas of high, shortterm snowfall with subsequent melting needed to be assessed in particular. In February 1979, the 1st edition of NS 3479 Design loads for structures (Standards Norway 1979a) was issued. The section dealing with snow loads contained a direct translation of ISO 4355 Snow loads on roofs. The concept of characteristic snow loads on the ground was introduced. The concept was defined as the load that had a probability P = 0.8 of not being exceeded in a single year, i.e. a return period of (1/(1-0.8)) = 5 years. Snow loads on roofs were calculated as the product of the characteristic snow load on the ground and a shape factor for the roof structure. Characteristic snow loads on the ground were largely between 1.5 kN/m2 and 3.5 kN/m2. In previous standards, only shape factors had been given for pitched roofs. The new standard quoted shape factors for a number of typical roof shapes such as pitched roofs, shed roofs, curved roofs, multi-span roofs, multilevel roofs and roofs with superstructures. In the case of roofs for which snow removal was difficult, a return period of at least 20 years needed to be designed for. To prevent that traditional small timber houses would have to be strengthened, the standard which applied to timber structures, NS 3470 Timber structures Design rules(Standards Norway 1979b), was brought into line with the new snow load design rules and issued during that same year. In the 3rd edition of NS 3479 (Standards Norway 1990), which was published in October 1990, a thermal coefficient C t was introduced, that reduced the theoretical snow load on transparent roofs as a result of heat transfer through the roof. The snow load could be reduced if the lowest expected indoor temperature in the winter was higher than 5 C. In the same revision, the characteristic snow load on the ground was changed for a number of municipalities. NS 3490 Design of structures Requirements to reliability (Standards Norway 1999) was issued in 1999, and prescribed that a 50-year return period should be adopted for environmental loads in general. This means that the characteristic snow load on the ground, s k , was redefined. A 50-year return period for a snow load means

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that it has a probability equal to P = 0.98 of not being exceeded in a single year. Until new characteristic snow loads were issued, NS 3479 was to be used for determination of loads with a return period of 50 years. In NS 3491-3 Design of structures Design actions Part 3: Snow loads (Standards Norway 2001) a number of revisions has been made. The most important change is that a characteristic snow load on the ground with a 50-year return period, s k , is specified for all 434 municipalities in Norway. This results in a significant increase in the snow load on the ground in certain municipalities. The basic value for s k is quoted for the centre of each municipality. In addition, rules are introduced concerning the adjustment of s k based on the building sites height above sea level compared to that of the municipal centre. The bulk of the municipalities now have a value for snow loads on the ground between 3.0 kN/m2 and 4.5 kN/m2. A few coastal municipalities have values as low as 1.5 kN/m2, and in some inland municipalities values of up to 9.0 kN/m2 are introduced. Another change that is important for many buildings, is the change in the shape factors for pitched roofs. For roof slopes between 15 and 60, the shape factor on the lee side has been reduced. The reduction is largest for roof slopes of about 30, where the shape factor on the lee side has been reduced from 1.2 to 0.8. The shape factor for pitched roofs has been changed so that the value never exceeds 0.8. Shed roofs and curved roofs have also undergone certain changes associated with the shape factor. A new coefficient, known as the exposure coefficient, has also been introduced in NS 3491-3. This is a dimensionless constant which accounts for the effect of wind drifting dry snow off the roof. The coefficient depends on the local temperature and wind climate during the coldest winter months, and its value ranges between 0.6 and 1.2. In the calculations, s k must be multiplied by the exposure coefficient. Rules for calculating snow guards and snow overhanging the edge of a roof have also been introduced in the standard. In April 2010 NS-EN 1991-1-3 Eurocode 1: Actions on structures - Part 1-3: General actions - Snow loads (Standard Norway 2008) will supersede NS 3491-3. Only minor revisions have been performed in this standard compared to NS 3491-3. For instance, there is an adjustment of the shape factor for curved roofs.

1.6 Structural safetyIn view of the currently valid snow load standard several roof structures in Norway have presumably such a low load carrying capacity that they may be in danger of collapse for large snow loads. Table 2 provides an overview of a number of large buildings where snow has triggered or caused significant damage or collapse. The summary is not complete, but gives an idea of which types of buildings that are especially vulnerable to damage. The table is based on information from insurance companies, SINTEF Building and Infrastructure and newspapers (Lis et al. 2000).

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Table 2 Cases of collapse as a result of major snow loadsBuilding Type of building County Built (year) Time of collapse/ damage 2010 2009 2008 2007 2007 2006 2006 2006 2006 2006 2006 2006 2000 2000 2000 2000 2000 2000 1999 1999 1996 1994 1994 1988 1987 1987 1983 1975

Swimming bath Shop Industrial facility Sports hall Shop Storehouse Sports hall Barn Sports hall Barn Barn Industrial facility Swimming pool Community hall School Community hall School Sports hall Sports hall Sports hall Industrial facility Sports hall School Industrial facility Sports hall Industrial facility Drill hall (military facility) Troms Industrial facility * Year of rebuilding or reconstruction.

Hatlestrand skule Rimi, Larvik Gameleveien, Lrenskog Gimlemoen, Kristiansand Europris, Kristiansand Rudshgda, Ringsaker Lier Skien Ringerike ridesenter Rnholt, Porsgrunn vre Mosby, Kristiansand Larvik Stongelandet skole Bardufoss Samfunnshus Lenangen Skole Mlselv Storvoll Skole Troms Tennishall Lkens-hallen Lofothallen Aukra Asker Tennishall Drammen Harstad Birkenes-hallen Svelvik Karosseri Epokehallen

Hordaland Vestfold Akershus Vest-Agder Vest-Agder Hedmark Buskerud Telemark Buskerud Telemark Vest-Agder Vestfold Troms Troms Troms Troms Nordland Troms Akershus Nordland Romsdal Akershus Buskerud Troms Aust Agder Vestfold Troms Troms

1974

1971 1965 1970 1990* 1978/ 1996*

1982

For most of the collapsed buildings, defects during planning or construction have been identified as the most likely cause of damage. In some cases, the damage has resulted from applicable building regulations not being adhered to, or construction at the site not being in accordance with the design calculations. In a few cases, the snow load assumed in the calculations has been lower than the actual loading. Safety level of structures One of the most important functions of building legislation has always been to ensure technically sound structures. Although it is not possible to build structures that have zero probability of failure, methods have been developed for documenting the inherent safety level. Two such methods are based on an explicit probabilistic representation of loads and resistance. These are frequently referred to as the fully probabilistic method (sometimes the level III method) and the second-moment method (or level II method), respectively. A third method is based on a semiprobabilistic representation, and is commonly referred to as the partial factor method (or the level I method). This latter method is the one which is most commonly adopted by current design standards. The second-moment method is 17 of 42


employed when use of the partial factor method must be calibrated against higherlevel failure reliability requirements. The fully probabilistic method is used to develop basic formats regarding design of structures. For ready reference the different methods for reliability calculations are briefly discussed below. Reliability calculations by the fully probabilistic (level III) method The level III method represents the most general and academic approach. To allow reliability calculations based on this method, the probability distributions for the factors important for structural failure must be known. The probability of failure can then be calculated and compared to a given requirement concerning the maximum annual probability of failure. The Norwegian Technical Regulations under the Planning and Building Act (National Office of Building Technology and Administration 1997) prescribes higher-level requirements of this kind with respect to the maximum annual probability of failure of building structures. The structures are categorized into reliability classes depending on the consequences of a possible failure, and the requirements become stricter as the consequences of failure increases. The second-moment method (level II) The second-moment method (level II) is a simplified and more practical approach than fully probabilistic reliability calculations. The expected value and the standard deviation for the factors of importance must be known when using the method. It is not required that complete statistical information is available (i.e. the joint probability distributions). Partial factor method (level I) The partial factor method is the most convenient method and is used virtually always when building structures or structural components must be designed by engineers in accordance with current regulations. The method is a semi-probabilistic method in which the total safety is represented by separate safety factors being applied to the structural capacity and the load effect. The main principle is that the factored design resistance (or capacity) must be greater than or equal to the value of the factored design load. Characteristic resistance is usually defined as the 5 % fractile value of the resistance. This corresponds to the value for which 5 % of the capacity measurements in an infinitely long series of samples have lower values, and accordingly 95 % will have higher values. Partial factors for material properties take into account uncertainties in material properties, mechanical model uncertainties and dimensional variations. The characteristic value for load action is defined in terms of an established probability P based on annual extremes, so that it is not likely to be exceeded within a single year. In the case of environmental loads, a return period of 50 years is usually assumed (i.e. P = 0.98). The partial factors for load actions take into account uncertainties associated with the actions themselves, load model uncertainties and dimensional variations.

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When the partial factor method is used, it is theoretically possible to build two completely different buildings that have approximately the same safety level. This can be done even if the buildings have different applications, are located at two geographically different sites, have different construction methods, have different quality management systems, are built from different materials etc. If, for example, the buildings have different geographical locations, the same safety level will be achieved by different values being applied for the environmental loads. With detailed regulations concerning the load and design aspects, it is possible to achieve the same safety level for different buildings. The more detailed the regulations, the more accurately it is possible to construct a building with the desired safety level. The drawback of detailed specific regulations is, of course, that the planning and design phase requires a high level of expertise and becomes time-consuming and expensive. Design of structures and structural safety Prior to the new series of design standards introduced in 1973, a calculation method referred to as the allowable stress principle was used. The safety level was then expressed in terms of a single safety factor by which the characteristic capacity of the material was divided. In light of the fact that snow loads and wind actions were minimally adapted to the variable climatic conditions pertaining in Norway, there is no doubt that the structures that were built in accordance with these regulations at various locations in Norway had widely different safety levels. With the introduction of NS 3052 in 1970, and the new generation of design standards in 1973, the partial factor method was also introduced. Theoretically, the change in the rules led to less variation of safety levels for buildings that were built at various geographical locations and with various materials than had been the case before. In the last regulation amendment process, the reliability standard NS 3490 (Standards Norway 1999) and the snow load and wind action standards NS 3491-3 (Standards Norway 2001) and NS 3491-4 Design of structures Design actions Part 4: Wind loads (Standards Norway 2002a) were introduced. The reliability standard prescribes a 50-year return period for environmental loads as mentioned earlier, also for snow loads. The partial factors for design loads (or design actions) depend on the reliability classes and a more detailed and extensive system for combinations of loads has been introduced. When NS 3490 was introduced, the partial factor for snow loads in the ultimate limit state was reduced from 1.6 to 1.5. A reduction factor k L by which the partial factor should be multiplied was also introduced (with a value of 0.8 1.0 depending on the reliability class). Thus, the magnitude of the partial factor for design loads has been reduced, particularly for the low reliability classes. With respect to the partial factors for the materials, it is now possible to make them dependent on the reliability class. In April 2010 Eurocodes will supersede the Norwegian standards in the series NS 3491. Generally, there are minor alterations in these standards as compared to NS 3491.

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2 Main findings

2.1 Introduction and methodologyThe presentation of the main findings in this thesis is divided into three parts. In part A, the structural safety and reliability of the Norwegian building stock is studied. According to the objectives of the study, the vulnerability with respect to snow has a special focus. In Part B the current design rules for snow loads are studied in order to find areas with potential for improvement. Finally, in Part C, methods for improved calculation of roof snow loads are presented. Part A describes the results of an analysis of the reliability of the Norwegian building stock considering snow loads and wind actions. An evaluation of the most exposed building types is performed, including considerations of the historical development of design loads and experiences from registered roof collapses. Based on this evaluation a selection of existing buildings is made. It is assessed whether they meet the safety requirements set in the current regulations through field investigations and design calculations. On this background, possible implications for buildings in Norway are discussed. Through the case histories in section 1.6 and this investigation, it is demonstrated that snow loads on roofs are important and that a high number of existing buildings most likely do not have the reliability level required by the authorities for new buildings. In Part B, a critical eye is cast at the current snow load regulations. It is found to be difficult to use the methods proposed for determining the effect of wind exposure on roof snow loads. It is investigated whether the presently codified method is appropriate. The development of modern design standards often implies an increase in the degree of detailing. It is evaluated whether this development is beneficial through an analysis of the effects of differentiation of roof snow loads for a timber detached house. This investigation considers the differences in safety in addition to economic and environmental aspects. The results in part B demonstrate that the current regulations have weak points. Further development of standards and regulations has to consider the benefits of increased detailing versus the risk of errors and evasions. Advanced calculation models, which have been developed in geophysics and hydrology, can be used to predict snow loads with a higher degree of accuracy than the models proposed in this work. The use of advanced models demands thorough insight in meteorology and geophysical processes in order to calculate realistic timeseries of snow loads during the winter season. In part C, methods for predicting snow density and snow loads based on simple meteorological parameters are developed. The methods provide sufficiently accurate results for structural engineering purposes, without the use of advanced computer software.

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In the period from 1966 to 1986 Professor Halvor Hib at UMB performed depth and density measurements of snow on the ground at 105 sites in the area of s. These measurements are analysed in order to evaluate local climate factors which are of importance for roof snow loads. s is situated in Akershus County in the southeast of Norway. The area has a relatively stable winter climate (moist mid-latitude climate with cold winters according to the Kppen Climate Classification System). The measurements of Hib were carried out at the time of maximum snow depths. The registrations were not done exactly at the same time every year. However, most of the data were usually collected in mid-February. A total of 608 measurements were carried out. No measurements were performed during winter seasons with maximum snow loads on ground below approximately 0.40 kN/m2. The following research methods have been applied to obtain the presented results: Field investigations of buildings (Paper I). Field measurements of snow loads on roofs (Papers IV and V). Structural design calculations (Papers I and III). Analyses of climate data from the Norwegian Meteorological Institutes Climate archive (Papers II, IV-V). Literature surveys (all papers).

Methods and delimitations are thoroughly described in the referred individual papers.

2.2 Part A: Structural safety and reliabilityIncreased snow loads and wind actions on existing buildings: Reliability of the Norwegian building stock (Paper I)Referring to the number of roof collapses and the recurrent discussions on high roof snow loads as to whether it is necessary to clear the roofs or not, it is relevant to quantify the reliability of the building stock in Norway. The high number of roof collapses due to snow loads in Germany and strategies to handle the problems are also discussed in Strasser (2008). The principal objective of the investigation has been to obtain a reliable indicator as to whether existing buildings in Norway meet current regulatory requirements concerning safety against collapse owing to snow loads and/or wind actions, and also to establish a basis for the analysis of future climate change impacts on the Norwegian building stock. The analysis comprises design documentation investigations and field studies of 20 existing buildings in five high-snowfall and five high-wind municipalities in Norway (Siem et al. 2003; Melysund et al. 2004). Statistical data for e.g. building type, year of construction and geographical localization of the approximately 3.7 million registered buildings in Norway are available in the Ground Property, Address and Building Register (GAB). Special attention has been paid to exposed types of buildings, and the buildings have been randomly selected within the exposed building categories. Assessments of whether the regulations are satisfactory, and theoretical parameter studies of the regulations, are not included in the investigation. The investigation focuses on assessing the

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buildings main load-bearing structures and, to a lesser extent, their secondary loadbearing structures. Some clear indications of aspects that ought to be considered as a representative trend for the building types investigated have been found. 18 out of 20 buildings have a utilization ratio of more than 1.0 (90 % of the buildings investigated). The design requirements for 95 % of the buildings have increased since they were built. Nevertheless, one would assume that the buildings had built-in reserve capacities resulting in fewer buildings experiencing a utilization ratio of more than 1.0. As many as 11 out of 20 buildings have higher utilization ratio than the load increase should imply. It is difficult to obtain structural drawings and design calculations for existing buildings. Such documentation is particularly important when buildings are to have alterations or when reconstructions are carried out. Public authorities should therefore establish a system ensuring that such documentation is made and maintained. The rules for determining wind loads that were introduced in 2002 have led to most of the buildings investigated having greater calculated reliability against collapse owing to wind load than the current regulations require for new buildings. However, for buildings in municipalities exposed to wind, for tall buildings or in places with special topographical conditions, safety may, on the other hand, decrease. The rules for determining snow loads, introduced in 2001, have led to most of the buildings investigated having lower calculated reliability against collapse owing to snow loads than the regulations now require. The exposure coefficient is set to unity in these calculations. The investigation indicates too low reliability according to the structural codes for a considerable number of buildings according to current building regulations, when evaluating the possible implications for buildings in Norway. The exposed building types amount to 5 % of the total bulk of buildings in Norway (11 % of total building floor area). Potentially 4.5 % of the total bulk of buildings in Norway may have too low capacity according to current regulations. Design snow loads may have increased for 4.7 % of the total bulk of buildings. The investigation indicates that a somewhat careless approach is often applied in relation to planning, or that this process is completely omitted, in the case of alteration and additional work. This may lead to significant exceeding of design capacity. It is therefore also important that rebuilding, reconstruction and addition (extension) projects are adequately designed. Scenarios for future climate change indicate both increased winter precipitation and increased temperature, and will result in changes regarding snow loads on roofs in parts of the country. An increase in frequencies of strong winds in areas also exposed today is estimated (IPCC 2007, Benestad 2005). According to these scenarios, the future reliability of buildings in these areas could decrease.

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2.3 Part B: Analyses of current design rulesEffects of wind exposure on roof snow loads (Paper II)In this paper, weather data from meteorological stations in Norway, for the 30-year reference period 1961-1990, are applied in order to determine the exposure coefficient C e according to the definition in ISO 4355 Bases for design on structures - Determination of snow loads on roofs (International Organization for Standardization 1998). An equivalent expression is used in NS 3491-3. First, historical field investigations of snow loads on roofs are evaluated, giving the background for the exposure coefficient. Next, values for the exposure coefficients are calculated for 389 meteorological stations, and the ability of the coefficient to take wind effects into consideration is discussed. Finally, possible approaches for improving the calculations of wind exposure on roof snow loads are suggested. It is shown that the exposure coefficient as defined in an informative annex of ISO 4355 does not reflect the actual effects of wind exposure on roof snow loads in Norway. The main reason is the coarse simplifications of snow transport theories in combination with extreme climate variations. It must be revised and improved to serve as an applicable tool for calculating design snow loads on roofs, using the best available data from meteorological stations in Norway. As a result of the present work, the Norwegian snow load standard NS-EN 1991-1-3 (Standards Norway 2008), which recently has been published, includes an improved definition of the exposure coefficient. In Norway there are large areas subjected to heavy snow fall in combination with strong - and frequent wind. In these areas the wind affects roof snow loads, and one would expect the exposure coefficient to have a low value. However, the definition of the exposure coefficient, as given in ISO 4355, apparently does not consider transport of snow off the roof in these areas. Hence, a too heavy design snow load is prescribed. On the other hand, in areas which should be characterized as shielded (i.e. no reduction due to wind exposure) a too low design snow load may be used according to this definition.

Economical effects of reduced roof snow loads (Paper III)Improved calculation methods and tools have made it possible to increase the degree of detailing in modern building design. The environmental loads to be used in design calculations, such as snow loads and wind actions, can reflect the local topography and climate more accurately than before. Current design tools allow each structural component to be optimized, regarding dimensions. The paper deals with the possible benefits that can be achieved by differentiation of roof snow loads with respect to the material costs of a selected house concept. Differentiation within a specific snow load zone is examined - in addition to a more general differentiation between different zones. The importance of these differences when considering the total building costs is evaluated. Finally, the extent of damage related to snow loads is examined.

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Figure 11 Exposure coefficients according to ISO 4355 for 389 meteorological stations (weather data from the reference 30-year period 1961 1990) and characteristic snow load on the ground (kN/m2, 50-year return period) for municipality centres.

A detached timber house is selected as case-study. It is designed to resist six levels of roof snow load: three different snow load zones with varying degree of wind exposure (high/low). Obviously, the material consumption depends on the loading, but the economic significance is small. The cost difference is 3 % for the two highest snow zones, for the lowest snow zone there is almost no economic benefits to be

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gained. When comparing the buildings designed with highest/lowest roof snow loads, the cost difference is 6 %. The material costs constitute 33 % of the total building costs, and 24 % of the total house costs (includes also installations like plumbing, heating and ventilation). When including other costs, such as ground costs, projecting, VAT etc. the material costs becomes 17 %. The maximum cost difference due to snow loads is hence 1.8 % of the total building costs, 1.3 % of the total house cost and 1.0 % of the total project costs, respectively. The degree of damage can be reduced by means of an excessive built-in safety. According to statistics for residential buildings developed by the Norwegian Financial Services Association (FNH) for the period 1997 2005, damage payments for the category where roof snow load is included constitute only 6 % of the total payments and have an annual average of 27.6 million (see www.fnh.no). Snow loads as a cause of damage is probably a small part of this category, but assume that it constitute half of the payments. Divided by the total number of residential buildings (1.4 million), the annual payment is 10. Anticipating that the economic lifetime of the building is 60 years, the total average payment for each building is 600. It has to be emphasized that the share of this sum resulting from snow load damage is rather uncertain. The price differences in the present study can also be seen as the costs for increasing the reliability for this type of building. The level of damage can be reduced with a higher built-in safety. A key unknown is the ratio of increase in material cost divided by the decrease in damage cost (further assuming there is no human injury involved). If it is assumed that the decrease in damage cost is small for a given increase of material cost, conclusions may be drawn that it is more reasonable not to increase the material cost. If, on the contrary, it is assumed that the decrease in damage cost is significant, the investment in additional material cost will be worthwhile. Quantification of this effect is beyond the scope of the present study and should be performed as part of future investigations.

2.4 Part C: Methods for improved calculation of roof snow loadsPredicting snow density using meteorological data (Paper IV)Due to extreme differences in local climate and topography, a large variation in snow loads on the ground can be observed within short distances in Norway. NS 3491-3 (Standards Norway 2001) does not take this variation into account. As a result, many buildings are designed with a doubtful estimation of characteristic snow load on the ground. Adequate equipment for surveillance of snow depths, in combination with more advanced calculation methods, should be used to improve the national maps for snow loads on the ground. This will require detailed information of snow density depending on geographical location and climate during the period of snow accumulation. Advanced calculation models, which have been developed in geophysics and hydrology, can be used to calculate snow density and associated loading with a 25 of 42


higher degree of accuracy than the method proposed in this paper (for instance multilayered models; Loth and Graf, 1998; Xue et al., 2003). The use of advanced models demands thorough insight in meteorology and geophysical processes in order to calculate realistic time-series of snow loads during the winter season. The objective of the current study is to develop a method for predicting characteristic snow density based on simple meteorological parameters. The method should provide sufficiently accurate results for structural engineering purposes, without the use of advanced computer software. 608 snow density (bulk weight density) measurements from the period 1967 1986 are used in a multiple regression analysis. The measurements are performed at 105 sites in the s area. A clear correlation is found between observed climate and measured snow density (here in kg/m3). The analysis results are promising, with a coefficient of determination equal to 70 % and a standard deviation equal to 24 kg/m3 (0.24 kN/m3) compared to measured values. The equation is expressed as

= 230 + 0,0167 RH snow + 2,23 f drift 1,84d 4,66 10 4 ptot + 2,4t sun 1,89 R p

(10)

This suggested equation has six predictors and one constant. The most important predictor concerns the climate during snowfalls and is the sum of relative air humidity when it is snowing (RH snow ). Other important parameters reflect the climate during the whole accumulation period, like the amount of solar radiation (t sun ) and the frequency of high wind velocity and simultaneous snow, which is able to drift (f drift ). The parameters RH snow , f drift and t sun are found to increase the density. The parameters snow depth (d), sum of atmospheric pressure (p tot ) and sum of precipitation as rain (R p ) are found to decrease the density. The most important parameters in generally applied density equations, as given in an informative annex of ISO 4355, are snow depth, mean wind and mean temperature. Combinations of these parameters are investigated without achieving satisfactory correlation. These results are not included in the present paper. Snow density values calculated by use of the Norwegian standard NS 3491-3 will in most cases be overestimated. The expressions in ISO 4355 are less applicable to prescribe snow density for a climate as studied in the present investigation. Still, they can be used as simple and rough estimates.

Predicting roof snow loads using meteorological data (Paper V)According to works by Isyumov (1971), Isyumov et al. (1974) and Isyumov et al. (1977) snow load on a particular roof is the running sum of incremental loads added by individual snowfalls during the course of winter and the depletion of the roof snow load by wind action and various thermodynamic processes:

R(t ) = Ri r ( )di =1 0

N (t )

t

(11)

Both the roof snow load deposition R and the depletion r are functions of roof properties (geometry, heat loss etc.), surrounding environment (terrain roughness, 26 of 42


shelter etc.) and meteorological parameters (snowfalls, wind velocity, temperature etc.). In this paper similar models as for the snow density are utilised for prediction of roof snow loads using meteorological data as input, thus extending the application. Snow load measurements performed at 105 sites in the area of s are considered. The distances between the measurement sites and the meteorological station in the area, vary between 0.6 and 14 km. 608 measurements were carried out at the time of maximum snow depth. No measurements were performed during winter seasons with maximum snow loads on ground below approximately 0.40 kN/m2. A clear correlation is found between observed climate and measured roof snow loads. Multiple regression equations for prediction of overall maximum roof snow load, s max , and maximum roof snow load at the windward side of the roof, s windw , are developed (both in kN/m2). The results of the analysis are promising, with a coefficient of determination for the overall maximum roof snow load equal to 74 % and a standard deviation of 0.19 kN/m2. The coefficient of determination for maximum roof snow at the windward side is 68 % and the standard deviation of the error is 0.18 kN/m2. The equations are expressed as smax = 0.87 + 0.136 d + 0.00364Tsnow 0.00223t 0.00477 + 0.733 3 vmean (12)

3 swindw = 0.527 + 0.208 d 7.59 103 + 0.04vmean 0.012 Pr 4.36 103 vsnow,loc (13)

The most important predictor in both models is the snow depth on the ground (d) observed at the meteorological station. The roof angle () and the mean wind velocity (v mean ) at the meteorological station are also important parameters. In addition, a parameter describing the temperature during snowfalls (T snow ) and the age of the snow cover (t) are predictors in the model for overall maximum roof snow load. A parameter describing the local wind velocity during snowfall (v snow,loc ), where local topography and shielding in the wind direction are included, is important for the snow loads at the windward side. In addition, the amount of rain (P r ) is important at the windward side of the roof. The methods presented in this paper are based on simple meteorological parameters and provide sufficiently accurate results for structural engineering purposes. Other advanced prediction models are not easily accessible for structural engineers in general.

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3 Example of application: local snow loads on roofs in KristiansandResults from paper V are used in this chapter in order to calculate maximum roof snow loads in the area of Kristiansand, in Norway. Methods for collection and preparation of the necessary meteorological input are presented, including selection of parameters for building sites with limited meteorological data available. It is difficult, especially for the owners of large properties, to determine the roof snow loads and to decide whether clearing of roofs is necessary. Kristiansand is a municipality in the south-east of Norway (Vest-Agder County, see Figure 1), which often experiences heavy snowfalls within short time spans. An example is February 1960, when the registered diurnal precipitation at the meteorological station in Mestad was 128.7 mm (water equivalent). Three buildings collapsed in this area in the winter season of 2006 2007, see section 1.6 and Table 2. The application of the methods, which are developed in this work for prediction of roof snow load, is demonstrated for buildings located in this area.

Mestad Kjevik

Eg

Figure 12 Map of Kristiansand

Measurements from three meteorological stations in the municipality of Kristiansand are employed. These are: Eg, Kjevik and Mestad (see Figure 12 and Table 3). Temperature and wind data are not measured at the meteorological station at Mestad.Table 3 Meteorological stations and observed parametersMeteorological station Eg Kjevik Mestad * height above sea level ** precipitation Height* (m) 22 12 151 Operation years 1957 - 75 1946 - 02 1900 Measured meteorological data Wind Snow depth Prec.** Temp. x x x x x x x x x x -

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Temperature and precipitation variations within the Kristiansand area give local differences in snow loads, see the table below.Table 4 Extreme monthly values in the period January - MarchMeteorological station Kjevik Mestad Kristiansand S Eg Mean wind velocity (m/s) Value Date 6.0 Jan. 84 7.3 Feb. 69 Precipitation (mm water) Value Date 341 Jan. 88 443 Jan. 75 333 Feb. 14 Snow depth (cm) Value Date 170 Feb. 70 204 Mar. 37 165 Mar. 54

Maximum roof snow loads are calculated by application of the results from paper V where an equation for the overall maximum snow load is given on the basis of meteorological parameters (see chapter 2): smax = 0.87 + 0.136 d + 0.00364Tsnow 0.00223t 0.00477 + 0.733 3 vmean (12)

The parameter T snow (measure of temperature during snowfalls) describes the climate during snow fall. The parameter v mean (in m/s) concerns the wind climate for the whole accumulation period. In addition, the snow depth d (in cm), age t (total number of observations) and roof angle are applied parameters. The meteorological input needed is daily precipitation, snow depth, wind velocity and air temperature. Based on these data the parameters T snow and the age t are developed. Mestad has the largest snow depths as can be seen in Figure 13. There is a large variation in the annual extreme snow depth; some years there are almost no snow on the ground. Mestad has an average annual maximum snow depth of 79 cm (109 measurement years) while Kjevik (57 measurement years) and Eg (72 measurement years) have mean snow depths of 44 cm and 56 cm, respectively. A larger fraction of the snow covers, at the time when the annual extreme values occur, have a higher age at Mestad than at the other two stations, see Figure 14. Mestad is situated farther away from the coast and at a higher elevation. Hence, it experiences both higher precipitation amounts and lower temperatures.

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A nnual extr eme snow depthsLognormal

Frequency

20

10

Loc Scale N

3,503 0,8177 59

0 0 40 80 120 160 200 Annual extreme snow depths (cm) KJEVIK 240

Frequency

20 10

LognormalLoc Scale N 3,835 0,6352 72

0 0 40 80 120 160 200 Annual extreme snow depths (cm) EG 240

Lognormal

Frequency

20 10 0 0 40 80 120 160 200 Annual extreme snow depths (cm) MESTAD 240

Loc Scale N

4,247 0,5429 109

Figure 13 Distribution of annual extreme snow depths (cm) at three meteorological stations fitted to a lognormal distribution.

A ge of snow cover at maximum snow depth50 WeibullShape Scale N 0,8363 68,74 58

Frequency

25

0 0 100 200 300 400 Age (no. of observations) KJEVIK 500

Weibull

Frequency

20 10 0 0 100 200 300 Age (no. of observations) EG 400 500

Shape Scale N

0,7069 58,90 19

30

WeibullShape Scale N 1,122 131,9 108

Frequency

15

0 0 100 200 300 400 Age (no. of observations) MESTAD 500

Figure 14 Distribution of age of snow cover (no. of observations) at meteorological stations fitted to a Weibull distribution. With three observations a day, the number of days are 1/3 x Age (i.e. total number of observations).

No wind and temperature parameters are registered at Mestad. Adjusted data from the other two stations are used in order to describe both air temperature and wind

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velocity. The daily temperatures for Mestad are computed by assuming a constant deviation relative to the observed temperatures at Kjevik: 2.5 C. Temperatures at both Eg and Kjevik are evaluated. With a constant temperature deviation of 2.5 C, the ratios of the calculated roof snow loads for flat roofs at Mestad, Eg and Kjevik are approximately similar to the corresponding ratios of ground snow depths at the three sites. The wind climate at the meteorological stations is not expected to be very different. Both the stations at Eg and Mestad are surrounded by terrain elements which tend to decelerate the wind. Kjevik is situated at an airport and is more exposed. The differences in mean wind velocity for the observed snow covers at Eg and Kjevik are on the average 11 % (Kjevik highest). The corresponding mean wind for Kjevik is taken to be representative for the mean velocity at Mestad. For the years where no wind data are available for Kjevik, the average mean wind velocity at that station is applied (equal to 4.4 m/s). Roof snow loads can be calculated for each winter season and for various roof angles based on Equation 12. The results for flat roofs can be seen in Figure 15. The results are based on daily observations during 58 winter seasons at Kjevik, 19 winter seasons at Eg and 59 winter seasons at Mestad. Winter seasons with a maximum snow depth on the ground equal to 20 cm or below are excluded from the analysis.

20

20

20 15 15

15

Frequency

Frequency

10

Frequency0 1 2 3 4 Eg (kN/m2) 5

10

10

5 5

5

0

0

1

2 3 Kjevik (kN/m2)

4

5

0

0

0

1

2 3 4 Mestad (kN/m2)

5

Figure 15 Calculated roof snow loads for flat roofs.

A lognormal distribution is found to provide the best fit for the calculated roof snow loads at the three meteorological stations. However, the results for Eg (see Figure 15) indicate that multi-peak distributions might be required in order to fit the histograms well. According to the Norwegian Standard NS 3490 (Standards Norway 1999) environmental loads to be used when designing buildings shall have a return period 31 of 42


of 50 years, i.e. an annual probability of 0.02 to be exceeded. The statistical computer program Minitab Statistical Software (www.minitab.com) is used in order to find the characteristic design values for each data set (Kjevik, Eg and Mestad). For flat roofs the characteristic roof snow loads for Kjevik, Eg and Mestad are 2.84 kN/m2, 4.83 kN/m2 and 5.00 kN/m2, respectively (50 years return period).K

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Prediction of Local Snow Loads on Roofs

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