Snow Loads Coeff.pdf

SNOW LOADS Preparation of Standards for Snow Loads on Roofs in Various Countries, with Particular Reference to the U.S.S.R. and Canada by W.R. Schriever* and V.A. Otstavnov**

I. A Rational Approach To Design Snow Loads 1. The i m ~ o r t a n c eof snow loads In nothern countries with cold winters and frequent snowstorms, roofs a r e subjected to heavy loads from snow accumulations. In countries with a milder climate, snow falls less frequently but can still produce significant loads. Proper standards for snow loads a r e of vital importance a s the choice of proper design values will affect both the safety and the economy of roof construction on a country-wide basis. The choice of such design values is, however, not an easy one. Many standards for snow loads in use at present a r e quite inaccurate and not in keeping with the refinement of methods of structural analysis. It is common today to use methods of analysis that by themselves provide excellent accuracy, and to assume a design snow load that under- ( o r over-) estimates by a factor of two o r more the true maximum load to be supported. Snow loads on roofs vary according to geographicallocation (climate), elevation above sea level of the site, wind exposure ( o r shelter) of the roof, shape and type of roof, and, of course, from one winter to another. Obviously, then, the choice of proper design snow loads must take into account many factors and be based to some extent, on a statistical approach. And before snow loads on roofs can be discussed, snow loads on the ground must be considered because the latter generally form the basis for the determination of the roof loads. 2. Effects of climate The wide climatic variations that exist across countries such a s the U.S.S.R. and Canada produce great variation in snow load conditions. In regions with frequent thaws, such a s some coastal regions, snow loads may be of short duration, caused by a single snowstorm. In contrast to this, many interior regions and also certain mountainous regions a r e subject to snow loads that accumulate and last through the entire winter. Areas with a continental climate such a s prairie and northern regions in Canada experience cold winters but low average annual snowfalls. Yet, owing to frequent strong winds, deep drifts of snow may occur on roofs and on the ground. On the other hand, in certain mountainous regions such a s the Rocky Mountains (and the Alps) heavy snowfalls of up to 200 to 300 in. (500 to 750 cm) may occur under very calm conditions leading to very unifurm and very deep snow covers on the ground and on roofs. In mountain a r e a s within the same climatic zone, snow loads vary mainly with elevation. Small countries that lie completely within a given climatic zone may specify snow loads simply a s a function of elevation above sea level. F o r large countries such a s the U.S.S.R. and Canada, this is not possible, and graphical presentation of snow loads in the form of isolines of equal snow load on a map is the more common approach. 3. Density of snow Freshly fallen snow is very loose and light and has a specific gravity of about 0.05 to 0.1. Immediately after falling, however, the snow crystals start to change. The beaufiful needle-like projections begin to sublime and the crystals gradually become more rounded. This results in consolidation of the snow and

* **

Division of Building Research, National Research Council, Ottawa, Canada. Scientific Research Institute of Building Structures, Gosstroy, Moscow, U.S.S.R.

after a few days o r weeks the specific gravity will have increased to about 0.2 o r higher, even a t below freezing temperatures. The specific gravity of old snow generally ranges from 0.2 to 0.4. Sometimes only the depth of snow is known and the specific gravity of the snow must then be estimated to determine the load. In the U.S.S.R. the following empirical expression, based on analysis of field records, has been used a s a firstapproximation:

where d = snow density, kg/m 3 h = the height of snow cover, cm t = average temperature in OC (plus o r minus) for the three coldest months of the winter under consideration. (Formula not to be used for temperatures below -20Oc.I Densities calculated in this way should, however, be corrected on the basis of actual values observed under different climatic conditions. In Canada, a i r temperature and windconditions a r e considered to be the two factors that affect snow density the most. Attempts to relate these two factors to snow density separately have not shown significant results. By using a "weather index" that combines these two factors, however, a correlation has been established at least for exposed stations in colder regions1). As wind, occasional thaws, and rainfalls all have important effect on the density, the estimation of the density of the snow cover is relatively inaccurate. Because of this no refinement in the assumed density has been considered justified in Canada, and a single specific gravity value of 0.2 has been used to calculate snow loads from the available snow depth data. Maximum snow loads often occur immediately after an unusually heavy f r e s h snowfall and hence a large proportion of the snow has a low density. Therefore a relatively low value of 0.2 for the average specific gravity is used to calculate the weight of the snow cover. 4. Determination of ground snow loads Although observations of actual loads on roofs a r e now available, this information is generally considered too heterogeneous to form a sound basis for determining the basic design snow load on a country-wide basis. Snow observations on the ground a r e therefore used a s an indicator of precipitation in form of snow to provide the basis for roof loads. In Canada, records of snow depth only, rather than weight, a r e generally available. Records of annual maximum depths of snow on the ground a r e available from over 200 stations for periods ranging from 12 to 20 years. To determine pasic design loads for all of Canada, these recorded depths were assembled o r )each . station and analysed with an extreme value method developed by Gumbel, a s explained by ~ o ~ dF ~ an extreme value distribution of the form y = -loge (-logeP) was fitted to the observed values of the annual maximum snow depths and then used to obtain the maximum snow depth for a 30-year return period; in other words the snow depth which will probably be equalled o r exceeded, on the average, only once in 30 years. Because the heaviest snow loads often occur when an early spring rain falls into, and is retained by, the snow cover, it was considered advisable to increase the snow load by the load of a certain amount of rain water. To do this it was found convenient (although not always very accurate) to use the maximum 24-h rainfall data for the period of the year when snow depths a r e the greatest2).

The groun snow loads calculated in this way, which vary from l e s s than 20 psf (100 kg/m2) to over 120. psf (600 kg/m ), a r e shown on a map (fig. l), in a supplement3a) to the National Building Code of canada3), together with a table giving specific values f o r l a r g e r cities and towns. Maps on such a s m a l l s c a l e obviously cannot show ,all local differences. Since a l l weather observations used in preparing the map were, of necessity, taken a t inhabited locations, the map applies generally to the m o r e populated areas. In mountainous a r e a s this means that the map applies mainly to the valleys. The lines on the map, therefore, do not apply to the mountain slopes and tops where, in many cases, much g r e a t e r snow depths occur and must be taken into account in the design of roofs.

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In the U.S.S.R., r e c o r d s of both depth and density of snow cover were used to determine the ground snow load. The specific gravity used f o r different regions of the U.S.S.R. varied f r o m about 0.17 to 0.30 in accordance with actually observed values. The U.S.S.R. Code of practice4) provides, in addition to "standardP values, "design" values of snow loads. The standard value i s the average of the annual maxima of the snow load on the ground. The design values a r e obtained a s follows. Based on statistical studies of the variability of the ground snow load from y e a r to y e a r and assuming that the average value of snow loads on roofs of building i s , in most cases, lower than the ground load by a t least 5 to the design values have been determined a t the standard value ofcthe ground load multiplied by an overloading factor, n = 1.4. This corresponds to a load that i s exceeded, on the average, once in 10 to 15 years. F o r code purposes the U.S,S;R. i s divided into 6 regions with standard values of 50, 70, 100, 150, 200 and 250 kg/m2 (10, 14, 20, 30, 40 and 50 psf)

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In regions with strong winds representative ground loads a r e often difficult to obtain. The most reliable method of determining the ground load i s to measure the weight of the snow cover on the ground by means of direct sampling in a place that i s well sheltered from the wind. A f o r e s t of deciduous t r e e s i s usually the best place. In exposed open a r e a s without t r e e s i t i s almost impossible to find any snow that i s not affected by drifts. Measurements, recently taken in Ottawa, Canada, indicate that the average snow depth over a s m a l l a r e a on a certain day was 15 in. (38 cm) in a forest, 1 3 in. (33 cm) in a sparsely treed a r e a and 8 in. (20 cm) in open fields (based on over 300 ground depth measurements). On the other hand, the specific gravity measured a t the s a m e time showedno significant pattern and varied only from 0.20 to 0.25. In view of these large variations of ground snow loads, roof-to-ground ratios obtained in the surveys must be viewed with some caution. Sometimes sheltered a r e a s a r e unavailable within reasonable distance. The s a m e problem is experienced in the U.S.S.R. T o a s s i s t with this problem a specially large snow gauge, consisting of a weight-table within a c i r c u l a r fence 3 m high and 6 m in diameter, h a s been developed in the U.S.S.R. for use in windy areas5). 5. Effects of wind and shelter on snow accumulations on roofs In perfectly calm weather falling snow would cover a l l roofs and the ground with a uniform blanket of snow. If this calm continued the snow cover would remain undisturbed (except f o r temperature effects) and the calculation of the design loads would be relatively simple. The design snow load could then be considered a s a uniformly distributed load and equal to a suitable statistical maximum of the ground snow load.

Fig. 2. Example of v e r y uniform snow load in c a l m a r e a . T h i s c a s e a l s o i l l u s t r a t e s the fact that on unheated buildings snow will not s l i d e even f r o m v e r y s t e e p m e t a l roofs. Ratio of maximum roof load to ground load w a s approximately 1 :1, of a v e r a g e roof load to ground load 0.8:l. ( R o g e r s P a s s , B r i t i s h Columbia, Canada).

Truly uniform loading conditions (fig. 21, however, a r e relatively r a r e , and a r e observed only in certain calm a r e a s and occasionally in windy a r e a s on roofs that a r e well sheltered on a l l s i d e s by high trees. In many regions of northern countries, snowfalls a r e usually accompanied o r followed by winds that drastically change the loads. Snowflakes, having a large surface a r e a for their weight, a r e easily transported horizontally by the wind. Consequently, on roofs that a-re exposed to winds, little snow will accumulate. T h i s i s the c a s e particularly on flat and low-sloped roofs without any obstructions. Over protected p a r t s of roofs, however, the wind speed will be slowed down sufficiently t o let the snow "drop out" and accumulate in the form of snow drifts. These roof a r e a s could be called "areas of aerodynamic shade", and occur, for example, behind vertical projections on roofs. Low roofs situated adjacent to higher roofs a r e particularly susceptible to heavy drift loads because the upper roof, if it is large, can provide a large supply of snow. The drift loads that accumulate on such roofs often reach several times the ground load. These drift loads depend mainly on the differences in elevation of the two roofs, the s i z e of the upper r ~ o f ,and the wind direction. The drifts produced in this way a r e often triangular in cross-section. Two examples, which illustrate the severity of drift loads that may occur even in the relatively moderate winter climate of southeastern Canada, may be mentioned. In 1962 a snow drift 14 ft deep (4.3 m) maximum load of 260 psf (1300 kg/m2) caused the collapse of a low flat roof adjacent to a large higher roof n e a r Montreal, Quebec. The ratio of maximum drift load to ground load was 6:l. In 1965 a maximum drift load of approximately 180 psf (900 kg/m2) was measured on a one-storey roof adjacent to a two-storey section of a school in Ottawa. In this c a s e the ratio of maximum drift load to ground load was 12:l. Peaked roofs subjected to winds at approximately right angles to the ridge often receive heavy unbalanced loads when snow is blown f r o m the windward slope over to the leeward slope. On curved roofs, s i m i l a r o r even m o r e extreme distributions have been observed. In 1965 a curved roof in Sarnia, Ontario, 200 ft (61 m) in span with a 27 f t (8.2 m) r i s e , collapsed due to unbalanced snow load produced by a single snowstorm with strong winds perpendicular to the axis of the building. The windward side of the curved roof was practically f r e e of snow whereas the leeward side had approximately 3 ft (1 m) of snow a t the q u a r t e r span and over 6 ft ( 2 m) of snow a t the base of the arch. The ground snow depth was about 1 ft (30 cm). Most of the c a s e histories collected in Canada, a s well a s the roof failures in northern Japan after a recent exceptionally long and heavy snowfall, indicate that i t is not safe merely to rely on shovelling snow f r o m roofs in exceptional winters (the usual last resort). Roof a r e a s where large drifts accumulate a r e often too f a r away f r o m the edge of the roof to make shovelling a practical solution. Furthermore, during exceptionally heavy s t o r m s , traffic incities may be immobilized s o that workers and equipment may not be available. 6. Effects of s o l a r radiation and heat loss Various other factors besides wind modify snow loads, although some of them such a s s o l a r radiation and heat loss a r e effective only under certain conditions. It has been found, f o r example, that s o l a r radiation has little effect in reducing loads in very cold weather. Although heat loss f r o m the building i s not very effective in reducing the snow load by melting on roofs over a well ventilated attic space, there a r e many roofs where, even in very cold regions, the OOC isotherm moves into the snow if the snow layer i s deep. This r e s u l t s in melting, and sometimes a reduction of load. Under m o r e moderate winter temperatures n e a r e r the freezing point, melting may reduce the load considerably if good drainage of melting water is provided. The influence of these factors can not always be predicted reliably but a r e of c o u r s e taken into account by measuring the actual roof loads, but c a r e has to be exercised in applying the load data f r o m ordinary roofs to ventilated roofs. 7. Effect of melting and sliding of snow Snow that slides from a sloped roof on to a lower roof can produce a very high additional load on the lower roof, while a reduction of load on the upper roof occurs. The reduction of snow load on sloped roofs due to sliding is difficult to predict, however, and most codes provide only very crude reduction factors a s a function of slope. F o r example, very steep roofs, when unheated, have been observed to retain their full load, whereas under ordinary conditions with some heat loss through the roof, moderately sloped roofs often shed their load after a while. More r e s e a r c h on the relationship between roof inclination and snow load f o r various conditions i s required before much refinement can be developed. Redistribution of snow load can occur due to melting and fefreezing, particularly in the temperature range just below freezing. Ice loads n e a r the eaves and on overhangs of sloped roofs a r e fairly common. If a roof slopes and drains on to a lower one, melt water may refreeze on the lower colder roof o r i t may be retained in the snow there.

As flat roofs in general do not provide a s good drainage a s sloped roofs, snow and ice will remain on flat roofs longer than on sloped roofs. On flat roofs without any slope, which a r e now fairly common, melt water tends to flow into the lower a r e a s in the centre of bays where the snow load has produced maximum deflection in the roof member, particularly when the drains a r e located near columns. This redistribution of load causes further deflection and can lead to a very dangerous situation. 8.. Snow load surveys and ratios of average roof to ground load

Information on which to base a more refined assessment of the magnitude and distribution of snow loads on roofs has, until recently, been relatively scarce and has only become available when country-wide surveys of actual snow loads on roofs were undertaken in some countries, such a s the U.S.S.R. andcanada. The Canadian survey, carried out by the Division of Building Research of the National Research Council, with the help of many voluntary observers6), provided information that allowed the development of the new snow load oefficient diagrams published in a Supplement to the 1965 Edition of the National Building Code of Canada3'). The survey also provided information on the relationship between average roof loads and ground loads. The results show clearly that the average roof loads a r e much lower than the ground load because part of the snow is blown off o r melted. Consequently, the Revision Committee responsible for the Supplement specified, in 1960, that the basic roof load be reduced from 100% to 8 v o of the ground load. In 1965, the Committee recommended a further reduction to 60% of the ground load, but only for roofs well exposed to the wind, and only because at the same time the consideration of higher loads due to drifts and other accumulations on roofs was required. The 80 and 6 v 0 values should be considered a s initial steps only, which will need further refinement depending, among other things, on average winter wind speeds. The results of the survey showed that on the average, 50, 20 and 6% of the observed flat roofs each winter had an average load'that reached 0.3, 0.6, 0.8, respectively, of the ground load. F o r the observed peaked roofs it was found that on the average, 50, 6 and 1% of the roofs each winter had an average roof load that exceeded 0.15, 0.6, 0.8, respectively, of the ground load. These figures were obtained mainly from roofs of single residential buildings in exposed a r e a s and may not be representative of all types of roofs. The figures confirm that sloped roofs have less load than flat roofs but it i s probable that more of the observed sloped roofs were in exposed a r e a s than flat roofs and that more of the sloped roofs were poorly insulated.

Fig. 3. Example of a snow drift on a one-storey roof west of a two-storey flat roof. The maximum load was 180 psf (900 kg/m2), the ground load 15 psf (75 kg/m2) giving a ratio of 12:l. Snow gauge held by o b s e r v e r is 6 ft (1.8 m) long; other gauges a r e 3 ft (0.9 m). (Ottawa, Ontario, Canada).

In reviewing the results generally, i t i s clear that average roof loads a r e very much lower than the ground loads but that further reductions in the basic average roof-to-ground-load ratio should not be made the same for all roofs and for all a r e a s of the country as, certainly in windy areas, each type of roof must be dealt with separately. Local maximum loads, on theother hand, a r e often very much higher than the ground loads (fig. 3) and must be properly estimated by the designer to ensure adequate safety.

11. Code Provisions F o r Snow Loads On Roofs Of Various Shapes 1. General The possibility of drift loads that exceed the average load and other non-uniform snow loads must be considered in design because these loads can produce an overstressing of certain members of a roof structure, and therefore a reduction of safety of the roof on the whole. In some cases, such a s in trusses, high local loads may cause not only an increase of s t r e s s but also a reversal from tension to compression in diagonals. In other cases, for example, at the junction of two adjacent roofs of different height, drift loads can cover significant areas, so that not only a single member but the whole structure may be subjected to overloading. The probability of non-uniform snow accumulations on roofs of complex shape is now becoming recognized, and several standards contain provisions for consideration of these higher loads. The scope and accuracy of these provisions are, however, quite variable. The most detailed provisions appear to be contained in the Codes of the U.S.S.R. and Canada. Codes of practice of other countries usually merely state the need to take possible local snow loads into account in design. (Extracts from some codes on snow loads a r e given in Appendix A to the paper 22.) As the Codes of the U.S.S.R. and Canadadeal more extensively with non-uniform snow accumulation on roofs of complex shape than those of other countries, some requirements from these two Codes with brief explanations a r e given below. 2. Design diagrams for snow loads on roofs of complex shape, provided by the Code of the U.S.S.R. The Code for snow loads of the u.s.s.R.~)provides diagrams of snow loads for the more commonly used roof shapes. Snow loads for more unusual shapes must be estimated on the basis of experience and possibly special tests. The U.S.S.R. Code recommends that the design of all roofs of complex shape should take into account two cases of snow loads a s minimum: (a) a uniformly distributed load that occurs under conditions of low winds ( a s a result of geographic peculiarities of the locality o r sheltering of a roof due to t r e e s o r buildings in the neighbourhood); and (b) non-uniformly distributed loads that occur when a roof is subjected to the action of wind which causes drifting and redistribution of the snow. The design diagrams of snow loads in the U.S.S.R. Code (figs. 1 to 5 and 8) a r e based on observations of snow accumulation on roofs. Although these diagrams were revised recently (in 1959), they still have some shortcomings. (a) Slope reduction Snow loads for sloped and gable roofs a r e determined a s a function of the slope angle a. The snow load coefficient "C* is one for a . 2 20° and zero for a 2 60° with intermediate values being determined by linear in.terpolation. "C" is ratio of snow load on a roof ( o r part of a roof) to the snow load on the ground. This rule is still tentative. It is known, for example, that in regions with average winter wind speeds of about 5 m/sec. (18 mph) o r more, snow may be blown from one slope to the other and a t certain angles (about 30') the coefficient C may reach 1.7 to 1.8 for one slope. It is also known that under calm conditions on some roofings, such a s shingles o r boards,.snow can accumulate to full depth even on relatively steep slopes (up to 450). These examples indicate that on the whole the conditions of snow accumulation on sloping roofs cannot yet be considered to be sufficiently well known, andfurther study will be needed for the refinement of the slope reduction rule.

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FIGURE 4 Figure 4. Design diagrams f o r snow loads on roofs provided by the Standard Code of Practice of the U.S.S.R.

For single-span curved roofs two loads a r e assumed; a uniformly distributed load and a variable load (see fig. 4a). F o r the uniform load, C i s equal to 1/8f, where 1 i s the span of roof and f i s i t s rise. The maximum and minimum values of C a r e set at 1 and 0.4, respectively.

Figure 5. Snow on a curvedroof of 30 m (100 ft) span and 5 m (16 ft) rise in an exposed location in the U.S.S.R. Note the shift of snow due to wind from the right side (lower photograph) and particularly the centre of the arch to the left side (upper photograph). Max. load on the left side 420 kg/m2 (85 psf), on the right 80 kg/m2 (16 psf) and in the centre 25 kg/m2 ( 5 psf), ground load 140 kg/m2 (28 psf). Average winter wind 4.7 m/sec. (10 miles/h).

Under the action of wind, variable loads occur. Recent observations in the U.S.S.R. (fig. 5) have shown that the accumulations a r e triangular, with C = 0 along the top and C = 2.0 at the leeward base. At the windward base of the arch 'the load can vary from zero to 1 1.5 depending on several factors, particularly on the wind force, the slope of the curved roof at the eave and the orientation of the roof with respect to the direction of the wind. Several questions still exist concerning snow loads on this type of roof; to solve them, additional observations will be required. Po The U.S.S.R. Code also specifies a load for curved roofs close to the ground with H 5 (H = distance between the ground surface and the eave of the vault in meters, Po = weight of snow cover of the ground in kg/m2, see fig. 4a) for which the possibility of snow drifts from the ground to the roof i s also considered.

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(c) Roofs with monitors

F o r roofs with monitors with low roof slope two cases of snow load a r e specified (fig. 4b). The first case is a uniformly distributed load, with the load on the monitor reduced to 0.8, because even in areas with very low winter winds some snow i s blown off from the upper roof. F o r lower parts of the roof the load i s correspondingly increased. The second case of snow load takes into account wind action on the lower roof. The volume and the form of snow accumulations on those parts of the roof near the monitor a r e d6pendent on the ratio of width of the monitor to the width of the lower slope, the height of the monitor, dimensions of the roof on the whole, and also on the winter wind directions. The appropriate form of snow accumulation for roofs with spans 1 up to 40 m (130 ft) and monitors of height 4 to 4.5 m (13 to 15 ft) and width about 1/2 to 1/3 1 may be determined as follows. Snow from the monitor drifts, a s a rule, to both sides, because directions of winds vary during winter. The ratio between winds of the prevailing direction under consideration, and those opposite to them can be taken a s 4 to 6, a value which has been found valid for different regions of the U.S.S.R. On this basis the diagram of asymmetric load may be represented by the case when 4% of the snow i s removed to one side and 60% to the other. The average value of snow load on the leeward slope of the roof can be determined a s p(l + 0 . 6 a ) , and on the windward side a s p(l + 0.4%). Although the load is close to a triangular one, for the sake of %mplification it may be presented a s ste ped, with the width of the steps equal to half that of the slope and the !il and 0.5 p(l + 0.6%) for the leeward slope and 1 3 1 + 0.4%) and following ordinates: 1.5 p(l + 0.6 -), b1 0*5p(l + 0-4 a ) for the windward slope.

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Fig. 6. Snow n e a r the monitor of the roof of a one-spanbuilding 30 m (100 ft) wide i m h e U.S.S.R. The monitor was 2 m ( 7 ft) wide 4.0 m (13 ft) hi h. The snow was accumulated in the f o r m of a triangular d r i f t with a maximum load of 700 kg/m (140 p s n . T h e r e was no snow on the monitor. The ground load was 160 kg/m2 (32 psn.

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Fig. 7. Another view of a typical snow accumulation adjacent to a monitor on a roof in the U.S.S.R.

The above mentioned diagrams of snow loads correspond well to observed loads (figs. 6 and 7). When these loads a r e used in design, central diagonals and verticals near the monitor of continuous structures have to be strengthened. The strengthening of certain members of the t r u s s lattices in some existing structures had been prompted by general experience with steel structures a s well a s by several failures of trusses caused by buckling of centre diagonals. From monitors that have deep depressions (such a s M-shaped monitors), snow is not easily removed by the wind blowing across the monitors. When the wind blows along the monitors a small part of the snow slides into the lower portion of the monitor roof. This fact explains in turn the smaller values assumed for the area outside the monitor. An unbalanced snow load on the monitor roof itself i s also taken into account. The Code of the U.S.S.R. gives diagrams of snow loads for the a r e a s of roofs near the monitor ends in addition to the diagrams f o r roofs of single-span buildings described above. These diagrams closely approximate the diagrams of loads presented in figs. 4b and 4c and a r e therefore not represented here. They take account of higher snow accumulation behind monitor ends under the action of wind in the direction parallel to the longitudinal axis of the building. (dl Two-span roofs The U.S.S.R. Code contains diagrams also for two-span roofs, on the basis of which i t i s easy to establish the loads for multi-span roofs (figs. 4d ana 4e). Figure 4e illustrates the treatment for a two-span roof, formed by two roofs of different shape without monitors: the first c a s e takes account of a uniformly distributed snow load; the second provides for a possible higher load in valleys formed by two-sloped roofs intersecting at an angle of 20° to 350, o r by two curved roofs. If the curved roofs have a risef-< 1/6 o r 1 the intersecting angle of the straight sloped roofs i s more than 35O, then allowance should be made f o r a snow load according to the third case. The Code also contains some explanations on how to determine snow loads for multi-span roofs on the basis of the loads for single and two-span roofs. (el Multi-level roofs The fact that large drift loads often occur near the junction of adjacent roofs of different level i s represented by fig. 4f. The magnitude and a r e a covered by such drift loads depend on many factors, mainly the size and configuration of the upper roof, the wind direction, the exposure of the building to the winds and certain meteorological conditions. The definition of snow loads for this case thus presents some difficulties. The principal one i s that to take the worst loads that have been observed would mean overdesigning many

roofs. As the most unfavourable drift loads occur only in districts with high winter winds, and only i f the building i s oriented in a certain way in relation on these winds, a moderate drift load assumption seems appropriate particularly if, a s is the case in the U.S.S.R., the possibility of snow removal from the roof i s also considered. The largest snow load at the junction of the different levels of roofs is assumed to be 4 times the ground load (C = 4); in case of smalldifferences in levels the load i s defined so a s to fill the full height a t the junction of two levels. The average specific gravity is assumed to be 0.28 and the load to have the form of a triangle with a base equal to a double height of the difference in levels, but not larger than 10 m (30 ft) and not l e s s than 5 m (15 ft). Further refinements a r e needed primarily f o r cases of various superstructures and other obstructions on the higher roof that prevent the snow from drifting. In such cases snow loads at the junction of the different levels probably may be somewhat reduced (perhaps to C = 2 to 2.5).

3. General requirements and design diagrams f o r snow loads in the Canadian Code (a) Ground snow load and general requirements In the N tional Building Code of Canada31 the basic load is the ground load, which includes a certain amount of rain2?. This load i s shown on a map (fig. 1) a s well a s in a table (both given in a Supplement to the Code containing climatic i n f ~ r m a t i o n ~ The ~ ) . roof loads a r e then calculated by multiplying the specified ground snow load by appropriate snow load coefficients Cs for which values a r e recommended in a Supplement to the ~ o d e 3 b ) . The basic snow load coefficient is Cs = 0.8, except for roofs *exposed to wind" for which 0.6 may be used. The Code states that the basic snow loadcoefficients of 0.8 and 0.6 a r e to be further increased o r decreased to account for the following influences: the decrease of snow load because of the effect of slope for roof slopes exceeding 30°; the accumulation of unbalanced snow load on gable and hip roofs; the accumulation of non-uniform and unbalanced snow load on arched and curved roofs; the accumulation of increased snow loads in valleys of butterfly a s well a s multi-span curved o r sloped roofs; (V) the accumulation of increased non-uniform snow loads due to drifting snow on the lower of two-level o r multi-level roofs, provided the upper roof is part of the same building o r of an adjacent building not more than 15 ft away; (VI) the accumulation of increased non-uniform snow loads on a r e a s adjacent to roof projections such a s penthouses, large chimneys, and ventilating equipment; (VII) the accumulation of increased snow o r ice loads on a r e a s due to snow sliding onto these a r e a s from an adjacent roof sloping towards this area o r due to melt water draining onto it. (I) (11) (111) (IV)

(b) Exposed roofs The reduction of the basic snow load coefficient f o r exposed roofs from 0.8 to 0.6 shall be used only if: (1) the roof is fully exposed to the winds on all sides, i.e., is not shielded on any side from the direct action of the wind by numerous t r e e s higher than the roof o r by higher roofs of the same o r of neighbouring buildings ; (2) the roof does not have projections, such a s parapet walls, which prevent the snow from being blown off; (3) the building is not located in a mountain a r e a with heavy snow load and low wind speeds during the winter season.

(c) Strip loading

In all cases the design snow loads shall be applied: (1) with a full load distributed over the entire area, o r (2) with half the load distributed on any portion. of the area and full load on the remainder of the area, whichever produces the greatest effect in the members concerned.

(d) Coefficient f o r sloped and peaked roofs

Slrnplr flat and r h r d rnola

Simple a r c h and curved roola

Simple gable and

L o w e r of m u l l i - l e v e l roofs with

ORlFT LO40

lor o S 20' use Case I only f o r o > 20' use C a s e s I and I1

Typical values:

0 lo 30'

60' 70' to 90'

s11c t exp 0. H 0.6

0.2

Case I

cs+,,.0 . 8 - 5 !!! 50

Casc I1

=

2

5

0. 15

(

0

.

Ior for

8

- ~ 50

h

I *muse

Only

F,bUBC case

1

)

11

Design l o w e r roof for Loada a c c o r d i n g to F i g u r e 5 plu8 a porlion of t h e aliding enow f r o m the upper roof a c c o r d i n g t o t e x t , a e c t i o n IV ( 6 ) . D e s ~ g nu p p e r roof for l o a d s a c c o r d i n g t o F i g u r e s I t o 4.

Fig 8d

Fig 8 e

1

/

Fig 89

_---

---

0

,

Roof a r e a e ad,iac?nt t o p r o j e c t i o n s and o b ~ t r u c t i o n s on r o o f s

a L o w e r l e v e l of m u l t i - l e v e l roofa (when u p p e r r o o f in p a r t of the s a m e building o r on a n adjacent building not m o r e than 15 ft away)

Valley a r e a s of two-span and m u l t i - a p a n sloped o r c u r v e d roofs

! : ~ ~ ! ; ! l i : ~ ! ! l ! c:~

CASEI

0 a - 30 Cs = 0 . 8 - 50 h

C B

= 15 when 15

= 10

C B

-h < 0 . 8* u a e

C

= 0. 8'

13

> 3.0

when 1 5

u s e Cs = 3 . 0

when 10

-Q2

B

when 1 <

W - 2 h when h < 5 f t u s e W = 10 It h > 1 5 f t u s e W = 30 f t

F o r load on u p p e r roof uac F i g u r e 8 I t o 4.

!!
when10i>2.0 I3

B

h :d i f f e r e n c e of roof helght8 In ft g = ground snow load in p8f W .: width of d r i f t f r o m h l g h e r bulldlng In It a = d i a t a n c e between bulldlngs < 15 ft

h u8e C

= 0. 8'

u8e C

~ 2 . 0

use C

= 0 . 8 ~

W = Z h when h < 5 It uae W = 10 It when h > 1 5 It u s e W = 30 f t

p=-

O1

+

"2

2

h = heluht of p r o j e c t i o n In ft g = ground nnow load in p a l W = w i d t h of snow d r i f t in It 1 = length of p r o j e c l i o n in ft

for p S 10' uae C a a e 1 only for l o ' < p < 20' u s e C a a e 1 and 11 for p 2 LO' uac C a s e I, 11 and Ill

BR 3782 -3 Figure 8. Design diagrams for snow loads on roofs provided in Supplement No. 3 to the National Building Code of Canada 1965. Notes: For roofs exposed to wind a s described under 3(b) in the paper, all values of Cs marked with an asterisk (*) may be reduced by 25 per cent. All load distributions shown in these figures are also to be applied a s alternating strip loading (full and half load) a s described under 3(c) in the paper. In Figures Bas 8b, and 8d note that the term a - 30 i s valid only for slopes a greater than 300. 50

Two d i a g r a m s (figs. 8a and 8b) a r e provided f o r roofs of various slopes with a single slope (shed roof) and double slope (gable and hip roofs). F o r the c a s e of the single slope the uniform load i s provided with a linear reduction f o r slope angles f r o m 30 to 70°. F o r the peaked roofs two c a s e s a r e given, a uniform load and an unbalanced load with no load on one side and 1.25 t i m e s the basic load on the other. H e r e also the reduction of load f o r slopes exceeding 30' is allowed. (el Simple a r c h and curved roofs F o r simple a r c h and curved roofs, a uniform load a s well a s a triangular unbalanced load with z e r o load on one side and a maximum coefficient of 2.0 on the f t h e r , a r e provided (fig. 8c). The second c a s e is to be used f o r a l l curved roofs where the rise+exceeds 10. The unbalanced load i s more s e v e r e than the unbalanced load condition considered in the U.S.S.R. Code. (f) Sliding snow

A load on a lower roof due to the possible sliding of snow f r o m an upper roof that is sloped towards the lower i n addition to the drift load, i s a l s o considered (fig. 8d). It was not thought possible, however, to provide coefficients f o r this additional load but s o m e guide lines a r e given a s follows. Because of the r e duced probability that both upper and lower roofs will have their full load over the full a r e a s simultaneously when sliding occurs, i t may be assumed that the lower roof would be c a r r y i n g i t s full load according to fig. 8e and that sliding of 50% of the design load f r o m the upper roof would occur. The distribution should be made depending on the relative s i z e s , slopes and positions of the two roofs. If, because of a relatively s m a l l lower roof, all the sliding snow could not be retained on it, appropriate reduction may be made. The density of sliding snow may be r a t h e r high. (g) Multi-level roofs

A triangular load is given to provide f o r the drift loads which frequently accumulate on a lower roof adjacent to a higher roof (fig. 8e). An e m p i r i c a l formula is given to a calculate the peak load. The maximum value of Cs is 3.0 and the width of the triangular load v a r i e s between 1 0 and 30 ft. Recent observations on two level roofs in Canada, where the upper roof was relatively long a t right angles to the edge of the lower roof, indicate that considerably l a r g e r values than Cs = 3.0 may o c c u r under c e r tain wind direction. It may be that in the future the Cs value f o r this c a s e should be made a function of the size of the upper roof a s this determines the amount of snow available f o r the drift process. Certain wind directions may be more c r i t i c a l than others, but in Canada i t is assumed that a l l wind directions must be considered equally by the designer. ( F o r the effect of a wind blowing diagonally o v e r a roof see, f o r example, fig. 9.)

Fig. 9. Example of a deep drift o n a flat onestorey lean-to roof e a s t of large slopedroof, caused by $ind blowing diagonally over the building. The maximum load was 120 psf (480 kg/&, the ground load 12 psf (70 kg/ m2) giving a ratio of 10:l. (Ottawa, Ontario, Canada).

(h) Vallev a r e a s A diagram, patterned after the diagram given in the U.S.S.R. Code, is given for valley a r e a s of two-span and multi-span sloped o r curved roofs (fig. 8f). This takes into account the fact that some of the snow will tend to drift o r slide towards the bottom of the valley.

(i) Proiections on roofs

A triangular drift load diagram for roof a r e a s adjacent to projections and obstructions is given in fig. 8g. The coefficient is a function of the height and length of the projection and reaches a maximum of 2.0. The width of the triangular drift i s assumed to be twice the height of the obstruction.

(i)Unusual roofs In concluding the description of the design diagrams contained in the Canadian Code's Supplement No. 3, some remarks about unusual types of roofs that a r e not covered by the diagrams a r e appropriate. Because the information provided in the Supplement cannot possibly cover all conditions that occur in practice ( a s an example, see fig. 9 ) , and also considering the fact that new information may become available in the future, every designer should try to obtain the latest and the most appropriate design information available. F o r unusual types of roofs o r structures it may be necessary to resort to special information such a s wind tunnel experiments o r other model tests, special theoretical studies, and local experience to provide adequate design values. In this connection it should be noted that the provisions of the Supplement a r e not mandatory, but merely recommended information. It is the designer's responsibility to decide where he must deviate from this information. 4. Consideration of shape in codes of countries other than U.S.S.R. and Canada Codes of other countries give the followin provisions for establishing snow loads for roofs of complex shape. The Standard Code of Switzerland1%) points out that local snow accumulations on roofs must be taken into consideration by appropriate design. The Code of sweden16) says that i f there is a possibility for formation of snow accumulation, then an increased load should be taken into account, and the volume weight of the snow must be taken equal to 400 kg/m3 (80 psf). The Code of 1srael17) points out that, for places of probable snow accumulations, an increased load should be taken. The French ~ e ~ u l a t i o n s ~ l state that where snow accumulations may occur either because of the presence of obstructions o r because of the shape of the roof, such accumulation should be taken into account based on both the "normal" and the "extremes snow load. Examples of typical cases a r e published in a separate Appendix. The combination of snow and wind loads is also mentioned and three examples in the "Commentairess (p. 34 of Reference 21) indicate unbalanced loads to be considered, the difference in load between the windward and leeward sides of the roof being limited to 25 kg/m2 ( 5 psf). The above-mentioned Codes, however, on the whole provide relatively little guidance concerning the magnitude and distribution of the increased loads for various roof shapes. 111. Conclusions 1. In many countries snow loads a r e the most important loads with regard to the safety and economy of roof structures. The problem of standardizing snow loads is of particular interest to northern countries such a s the U.S.S.R., Canada, the Scandinavian countries, but also to countries where snow occurs l e s s frequently o r only in the mountains. 2. The determination of proper design snow loads can be broken down into two parts: (a) the selection of a suitable snow load on the ground (including a certain amount of rain load) for design purposes on the basis of a statistical evaluation of meteorological data, and (b) the modification of the ground load to represent adequately the actual conditions of snow accumulation on roofs of simple and complex shapes. F o r windy climates and exposed locations an adequate assessment of the influence of wind and the shape of roofs is more important than extreme accuracy in determining the basic ground o r roof load when considering safety a s the prime objective of a Code. When considering the economy of roof structures, on the other hand, the proper determination of the basic uniform roof load is also very important.

3. It would appear that the U.S.S.R. and Canada have sufficient experience in standardizing recommendations for design snow loads s o that on the basis of their experience, augmented by that of other countries willing to cooperate, i t should be possible to develop a standard f o r snow loads f o r member countries of CIB and for eventual adoption a s international standards by I.S.O.

4. At the same time, problems concerning local loads on roofs of complex shapes need to be studied further under different climatic conditions, and furthur investigations in all countries in which this problem is of particular importance a r e therefore suggested.

REFERENCES 1. Williams, G.P. and Gold, L.W.; Snow density and climate. Engineering Institute of Canada, May 1958, 2, No. 2, pp. 91-4 (reprint available a s NRC 4833). 2.

Boyd, D.W.; Maximum snow depths and snow loads on roofs in Canada. Proceedings, 29th Annual Meeting, Western Snow Conference, Spokane, Wash., April 1961, pp. 6-16 (reprint available a s NRC 6312).

3.

National Building Code of Canada. Section 4.1, Structural Loads and Procedures, Associate Committee on the National Building Code, National Research Council, Ottawa 1965.

3(a) Climatic information for building design in Canada, 1965. Supplement No. 1 to the National Building Code of Canada. 3(b) Structural information for building design in Canada, 1965. Supplement No. 3 to the National Building Code of Canada.

- Standard Code of

4.

U.S.S.R.

5.

Academy of Building and Architecture of the U.S.S.R., Central Research Institute of Building Construction. State Publishing House of Literature on Building, Architecture and Building Materials, Moscow 1963.

6.

Peter, B.G.W., Dalgliesh, W.A. and Schriever, W.R.; Variations of snow loads on roofs. Transactions of the Engineering Institute of Canada, April 1963, 6, No. A-1, (reprint available a s NRC 7418).

7.

Berechnung und Aiisfuhrung d e r Tragwerke. Schnee

8.

Minimum design loads on.buildings. SAA Int. 350, 1961, Australia.

9.

British standard code of practice CP 3. Code of functional requirements of buildings. Chapter V. Loading. 1952.

Practice. (SNIP) 11-A. 11-62. Loads and Effects.

-

und Eislasten. ONORMA B 4000, 4. Teil.

10.

Lastannahmen fur Bauten. DIN 1055, DDR und Bundesrepublik.

11.

Indian standard code of practice for structural safety of buildings: loading standards. IS:875, 1957.

12.

Regulamento de solicitacoes e m edificiose pontes. NO. 44041, Portugal, 1961.

13.

Normativ Conditionat. Calculul constructiilor la storile limita. I, Rumania, 1963.

14.

CeskoslovenskaStamiNorma. Zatizeni stavebnich konstrukci. CSN 73 1310, 1958.

15.

Normen fGr die Belastungsannahmen, die Inbetriebnahme und die Uberwachung der Bauten, Schweizerischer Ingenieur und Architekten Verein, Nr. 1960, Switzerland, 1956.

16.

Anvisnigar till Byggnadsstadgan BABS. Sweden, 1960.

17.

Israel Draft Standard. Loading of Buildings: Loads. NO. 89/2.1, April 1960.

18.

Loads, external forces and design stresses. (Excerpted from Building Standard Law Enforcement Order, revised in 1959) Japan.

19.

Estratto da Istruzioni per il calcolo, l'esecuzione e la manutenzione delle construzioni metalliche. Italy, 1961.

20.

American standard building code requirements for minimum design loads in building and other structures. American Standards Association, Inc., New York 1955,

21.

R'egles de'finissant l e s effets de la neige e t du vent sur les constructions. fidite' Par la ~ocie'te'de Diffusion des Techniques du ~ " a i m e n et t des TravauiPublics. (R6gles N.V. 65). Paris. November 1965.

22.

Building regulations of 15 December 1949, Volume I; Department of Supply and Reconstruction, Oslo, Norway.

APPENDIX A Extracts from Various Building Codes and Codes of Practice With Regard to Snow Loads

The Interim Code merely indicates that in a r e a s where snow loads a r e likely to occur, their values a r e to be determined according to local records.

The value of snow load is determined depending on the elevation of the area above the sea level and assumed a s 75, 120, 200, 260, 320, 450, 550 and 650 kg/sq.m. The smallest load (75 kg/sq m o r 15 lb/sq ft) is valid for the Danube river valley, the largest ones for high mountainous areas. F o r cases where roofs a r e subject to drifts o r other snow accumulations the Code makes allowance for higher loads. The Code, however, gives no detailed recommendations concerning the allowance for such higher loads. The value of snow loads for sloped roofs is determined a s a function of the slope angle a and is assumed with a = 00 to 30°, K = 1; a = 400, K = 0.75; a = 500, K = 0.5; a = 600, K = 0.25 and o c > 700, K = 0.

See text of present report.

For structures being erected at an elevation above sea level up to 600 m, the snow load is equal to 75 kg/ sq m. F o r greater heights the load is to be calculated by the formula:

where h is the height above sea level in meters. The Code permits to allow for higher snow loads in some a r e a s (e.g. in valleys of mountains) in accordance with the records of meteorological stations. With a roof slope exceeding 400 the snow load may be taken a s 50 kg/sq m for any height over sea level. It is noted that it is necessary to watch great snow accumulations on roofs and to take into account the snow load on both sides and on one side only on roofs.

Rules Concerning Snow and Wind Effects on Buildings. Ministry of Reconstruction and Urban Development. The basic design snow load, under the elevation of 200 m, will have the value, 30 kg/m2 for the 1st zone, 45 kg/m2 for the 2nd zone, and 60 kg/m2 for the 3rd zone. Above 200 m the load increases with increasing elevations. The increase between 200 m and 500 m is 1 kg/m2 per 10 m of increase in elevation, and above 500 m 2.5 kg/m2 per 10 m of increase in elevation. The above values may be reduced by 2% for each degree of slope over 250. Trough-shaped roofs need special care; accordingly the amount of snow accumulated on both adjacent sides, without reduction for slope, is taken into account. F o r wind conditions, the snow load may be reduced to one half of the basic load, but for loads exceeding 60 kg/m the differences between the various loaded parts of the roof must not exceed 30 kg/m2 of horizontal projection.

S

In DIN Standard 1055 the minimum snow load on horizontal surfaces is assumed a s 75 gd/sq m. In mountainous areas a higher load should be allowed for in compliance with the local records. F o r sloping surfaces the load should be reduced (if snow accumulations do not occur) due to the slope angle: 30

The Standard provides f o r possible snow concentrations (but t h e r e a r e no detailed instructions). The des i g n e r should take inio account e i t h e r the full value of the snow load o r p a r t of it.

7. G r e a t ~ r i t a i n 9 ) The British Standard Code of P r a c t i c e indicates that f o r a roof-slope of 30° o r l e s s a load of 15 lb/sq f t should be allowed for; f o r a roof-slope of 75O no allowance is necessary. F o r roof slopes between 30 and 75O, the snow load to be allowed f o r may be obtained by linear interpolation. The Code gives no other data on snow loads. (The Building ResearchStation, Garston, Watford has recently begun a survey of snow loads.)

8. India 11) The actual snow loads depend upon the shape of a roof and i t s capacity to retain the snow. Where snow is encountered, the allowance of 10 lb/sq f t (50 kg/sq m) p e r ft (30 c m ) of snow should be made.

Snow load is taken into account only in the northern p a r t of the country. The load is determined from the height above s e a level a s follows: 20 kg/sq m f o r 200m to 400 m; 30 kg/sq m f o r 400 m to 600 m; 40 k g f s q m f o r 600 m to 600 m to 800 m; 50 kg/sq m f o r 800 m to 1000 m; 60 kg/sq m f o r m o r e than 1000 m. F o r heights of l e s s than 200 m no snow load is assumed. On r o o f s a t an inclination to the horizontal g r e a t e r than 35% the snow load may be reduced in accordance with the following; f o r slope of 35% to 5w0 75%; f o r 5wo of the snow load; f o r slopes exceeding 80a/,, the snow load may be neglected. slope of 50% to 80% It is noted that in locations where snow is likely to accumulate, higher loads should be taken into consideration by adding possible additional loads.

-

-

Snow loads a r e determined on the b a s i s of local climatic conditions. It is pointed out that, a s a rule, f o r localities a t a height not g r e a t e r than 500 m above s e a level the snow load should be not lower than 100 kg/ s q m in northern Italy, 70 kg/sq m in c e n t r a l Italy, and 40 kg/sq m in southern Italy and on islands. F o r localities higher than 500 m these loads should be i n c r e a s e d respectively by 0.2 kg/sq m (h - 500) in northern Italy; 0.15 kg/sq m ( h 500) in c e n t r a l Italy, and 0.10 kg/sq m (h 500) in southern Italy and on islands. F o r a roof slope of 450 and m o r e the snow load may be neglected if the roof m a t e r i a l is rough and if t h e r e a r e no snow-retaining structures. F o r a roof slope l e s s than 45O the snow is taken into consideration in full. F o r 'flat roofs (with a slope l e s s than 10') the snow load is i n c r e a s e d by 25% if t h e r e a r e difficulties in the removal of water when snow is melting. F o r gable roofs with a slope exceeding 10% i t is n e c e s s a r y to take into account the snow load on one slope. It a l s o is n e c e s s a r y to allow f o r snow accumulations in gutters.

-

-

Snow loads a r e determined on the b a s i s of the g r e a t e s t height of snow known in the given locality. The volume weight of snow is taken a s not l e s s than 0.2 g/cm3. Local authorities a r e responsible f o r fixing the snow load, and the l a r g e s t depth should correspond to actual conditions. The value of snow load f o r sloping roofs is determined based on the roof slope and should be multiplied by a factor 1 f o r a < 30°; 0.75 f o r a = 30° to 40°; 0.5 f o r a = 400 to 500; 0.25 f o r a = 50° to 60°. F o r slopes exceeding 60° no snow load need be assumed. Local authorities may fix other values of coefficients taking into account the m a t e r i a l of the roof, properties of snow, etc. It is noted that if t h e r e is a possibility of accumulation of snow in an unbalanced way, i t s effect should be considered in the design. F u r t h e r m o r e i t is permissible to take into account reduced snow loads f o r localities where i t is the custom to remove snow f r o m roofs f r o m time to time. (It is believed that this provision h a s since been deleted).

12. Norway 22) Building Regulations of 15 December 1949. Department of Supply and Reconstruction, Norway. (a) The snow load, S, on a horizontal surface is assumed, in general, to be 150 kg/sq m. In districts with relatively little snowfall and in districts with relatively heavy snowfall this value may be changed by the Building Council (local administrative body) with the approval of the Pepartment. (b) The snow load S f o r a roof surface with a slope a greater than 30' i s reduced according to the equation: 60-ff kg/m2 horizontal projection. 30 (c) Where the form of the roof can lead to greater snow accumulations, this must be taken into account in the calculations. (dl With peaked roofs the roof construction is calculated also for one-sided snow load if this causes greater s t r e s s e s than the total load. Larger, continuous, and cantilevered constructions a r e dimensioned for partial snow load. Sa=S-

The a r e a s a r e listed where snow load must be taken into account. The value of the snow load is determined, due to the elevation of the locality, by the formula:

where H is the height in meters above sea level.

For sloping roofs if there a r e norestrictions to snow sliding the load should be taken a s proportional to the cosine of the roof slope angle (for angles from 0 to 450), the minimum of the load being 30 kgysq m, that is also accepted for angles of more than 45'. The Code indicates that if the roof has several slopes the snow should be taken into account only on some of them, if this leads to a more adverse effect in the calculation of the structures.

The territory of the country is divided into two districts with snow loads of 75 and 100 kg/sq m. F o r mountainous a r e a s more than 600 m high the snow load should be determined depending on the height of the locality above sea level by the formula: Qz = 220 hz (in kg/sq m) where hz is the average depth for greatest depths of the snow cover (in meters) assumed according to the data recorded during not less than 10 years. In ultimate strength design the overload coefficient is taken a s n = 1.4. The Code permits one to allow for lower loads for sloping roofs and vaulted r o ~ f as s well a s for the possibility of accumulation of snow concentrations on roofs with superstructures and on roofs of multi-span buildings of complex shape. The numericalvalues of these loads for the mentioned cases coincide with those recommended by the U.S.S.R. Code of Practice. There is no allowance for loads at points of differences in roof levels.

The country is divided into areas with snow loads of 75, 100, 150 and for high mountainous regions 200 to 300 kg/sq m. F o r roofs slopes lower than 300 the snow load should be reduced by one district. At the angle of 60° the snow load should be neglected, and for roofs with angles from 30 to 60° the load is determined by interpolation. If snow concentrations a r e likely to accumulate on roofs, the -load due to them should be taken into consideration at the volume weight of snow of 400 kg/cu m.

The snow load should be determined taking into account the height of the locality above sea level: (a) f o r heights H 5 800 m

but not lower than 90 kg/sq m; (b) for heights H

5

800 m

F o r a roof slope l e s s than4S0, if there a r e no restrictions to snow sliding, the load is taken a s proportional to the cosine of the angle of the roof slope; f o r a roof slope of 45O and more the snow load may be neglected. F o r gable roofs the load should be considered on either side and equal to 5% of the design load. It is indicated that local snow concentrations should be taken into account by appropriate design.

American Standard Building Code Requirements f o r Minimum Design Loads in Buildings and Other Structures. (Note: Several other buildings codes a r e used in the U.S.A., but a r e not listed here because of lack of space). A map shows snow load zones based on studies of the U.S. Weather Bureau. The loads given a r e based on the weight of the snow cover equalled o r exceeded one year in ten. F o r mountainous a r e a s the loads a r e not given. The minimum required design snow load is 20 psf of horizontal projection even in localities where little o r no snowfall occurs, because i t has been considered necessary to provide for occasional loading due to workmen and materials during repair operations. If U.S. Weather Bureau o r local Weather Bureau records a r e not available, the snow load map should be consulted and the indicated unit snow loadforthe locality, if larger, substituted f o r the minimum. Provision is made to the effect that any excess over 20 psf of horizontal projection may be reduced for each degree of pitch over 20° by S/40 1/2, where S is the total snow load in pounds per square foot of horizontal projection. At 60° the load is assumed to disappear:

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