Load factor calibration for the proposed 2005 edition of the National ...

429Load factor calibration for the proposed 2005edition of the National Building Code of Canada:Statistics of loads and load effectsF.M. Bartlett, H.P. Hong, and W. ZhouAbstract: The 2005 edition of the National Building Code of Canada (NBCC) will adopt a companion-action formatfor load combinations and specify wind and snow loads based on their 50 year return period values. This paper summarizesstatistics for dead load, live load due to use and occupancy, snow load, and wind load that have been adoptedfor calibration, and a companion paper presents the calibration itself. A new survey of typical construction tolerancesindicates that statistics for dead load widely adopted for building code calibration are adequate unless the dead load isdominated by thin, cast-in-place concrete toppings. Unique statistics for live load due to use and occupancy are derivedthat pertain specifically to the live load reduction factor equation used in the NBCC. Statistics for snow and wind loadsare normalized using the 50 year values that will be specified in the 2005 NBCC. New statistics are determined for thefactors that transform wind speeds and ground snow depths into wind and snow loads on structures.Key words: buildings, code calibration, companion action, dead loads, live loads, load combinations, load factors, reliability,safety, snow loads, wind loads.Résumé : L’édition 2005 du Code national du bâtiment du Canada (CNBC) adoptera un format compagnon-action pourles combinaisons de charges et elle spécifiera les charges de vent et de neige selon leurs valeurs basées sur une périodede retour de 50 ans. Cet article résume les statistiques pour les charges mortes, les charges vives provenant de l’usagedu bâtiment, les charges de neige et les charges de vent qui ont été adoptées pour le calibrage et un article accompagnantcelui-ci présente le calibrage en temps que tel. Une nouvelle revue des tolérances de constructions typiquesindique que les statistiques pour les charges mortes généralement adoptées pour le calibrage de codes de bâtiments sontadéquates à moins que la charge morte soit dominée par un recouvrement mince de béton armé coulé sur place. Desstatistiques uniques sont dérivées pour les charges vives provenant de l’usage du bâtiment; elles se rapportent spécifiquementaux facteurs de réduction de la charge vive utilisés dans le CNBC. Les statistiques pour les charges de neigeet de vent sont normalisées suivant les valeurs basées sur une période de retour de 50 ans qui seront spécifiées dans leCNBC de 2005. De nouvelles statistiques sont déterminées pour les facteurs qui transforment les vitesses de vent et lesprofondeurs d’accumulation de neige au sol en charges de vent et de neige appliquées sur la structure.Mots clés : bâtiments, calibrage de codes, action compagnon, charges mortes, charges vives, combinaisons de charges,facteurs de charges, fiabilité, sécurité, charges de neige, charges de vent.[Traduit par la Rédaction] Bartlett et al. 439IntroductionThis is the first of two papers summarizing the load factorcalibration carried out for combinations of dead, live, wind,and snow loads specified in the 2005 edition of the NationalBuilding Code of Canada (NBCC). Several changes from theReceived 27 February 2002. Revision accepted 24 September2002. Published on the NRC Research Press Web site athttp://cjce.nrc.ca on 18 April 2003.F.M. Bartlett, 1 H.P. Hong, and W. Zhou. 2 Department ofCivil and Environmental Engineering, Faculty of Engineering,The University of Western Ontario, London, ON N6A 5B9,Canada.Written discussion of this article is welcomed and will bereceived by the Editor until 31 August 2003.1 Corresponding author (e-mail: f.m.bartlett@uwo.ca).2 Present address: C-FER Technologies, 200 Karl Clark Road,Edmonton, AB T6N 1H2, Canada.1995 NBCC have been proposed, including (i) adoption ofthe “companion-action” format and revised load factors, forload combinations involving wind, snow, and live loads dueto use and occupancy at ultimate and serviceability limitstates; (ii) use of the 1 in 50 year value, which has a returnperiod of 50 years, instead of the 1 in 30 year value fornominal (or specified) snow and wind loads; and (iii) adoptionof importance factors for post-disaster shelters andbuildings applied to snow and wind loads. The load factorcalibration was carried out for the NBCC Part 4 Task Groupon Snow and Wind Loads, whose members are acknowledgedat the end of this paper.The companion-action format for load combinations wasrecommended for the 2005 NBCC during a meeting of theTask Group on Snow and Wind Loads in October 1999. Thisformat is widely recognized for its simplicity and appropriatenessfor combining loads that can occur simultaneously(e.g., Turkstra 1972; Ellingwood et al. 1980; Kariyawasamet al. 1997) and has been adopted for many codes and stan-Can. J. Civ. Eng. 30: 429–439 (2003) doi: 10.1139/L02-087 © 2003 NRC Canada

430 Can. J. Civ. Eng. Vol. 30, 2003dards including the CEB (1976), AISC (1986), and ASCE(2000). Structural design based on this format uses loadcombinations of the form[1] α + α S + α S∑p i i ij ji≠jwhere α P is the load factor applied to the effects due to permanentload, P, such as dead load; and α i is the load factorapplied to the effects due to the principal transient load, S i ,assumed to be acting at its maximum value during the lifetimeof the structure. The load factors α ij applied to thecompanion-action transient loads S j represent thecompanion-action load effects that occur during the periodwhile the principal action is acting at its maximum value.An early objective of the calibration process was to determinewhether specified snow and wind loads should correspondto 50 year or 500 year return periods. The Task Groupon Snow and Wind Loads decided in October 2000 to recommendthat specified loads be based on 50 year returnperiods, in part because (i) these values could be readily obtainedfrom existing databases; (ii) preliminary calibrationindicated that load factors less than 1.0 were required if500 year loads were specified; and (iii) 50 year return periodsare used for the loads specified in ASCE7-98 (ASCE2000).In this paper, the bases for the statistical parameters usedto characterize dead, live, snow, and wind loads are presented.These statistical parameters differ slightly from thevalues used to verify the 1977 NBCC reported by Nowakand Lind (1979). A companion paper summarizes results ofthe calibration, describes the evolution of the recommendedload factors in response to comments from the Task Groupon Snow and Wind Loads and others, and summarizes the finalload factors and load combinations recommended for the2005 NBCC.Dead loadDead load consists of the weights of a structural memberand the structural components that it supports, partitions,and permanent equipment. Although uncertain, it is commonlyassumed to remain constant during the service life ofa structure. There is a tendency for the dead load to exceedits nominal value because the designer may overlook somethingin the dead load takeoff, which is typically estimatedto within ±10% for buildings. Dead load uncertainty is becauseof dimensional tolerances and the uncertainty of unitweights of materials. Additional uncertainty is introducedthrough the process of converting the load into a load effect,which for indeterminate structures can be done accuratelyonly if the construction sequence is known. It is commonlyassumed that dead loads are normally distributed, perhapsbecause tolerances tend to be normally distributed, althoughno actual data seem to be available to verify this assumption.The dead load statistical parameters depend to some extenton the size of structure, the construction material used,and the quality control implemented. The weight of largestructural components is relatively insensitive to absolute dimensionaltolerances, so the dead load bias coefficients andcoefficients of variation are reduced. Improved qualitycontrolprocedures have the same effect. Geometric andmaterial unit weight variations are less for steel or precastconcrete components than for cast-in-place concrete construction.In particular, formwork deflections in cast-in-placeconcrete floor construction can often cause the dead load tobe larger than the nominal value.A literature review indicated dead load itself has a bias, orratio of the mean to nominal values, from 1.00 to 1.05 and acoefficient of variation (CoV), the ratio of the standard deviationto the mean value, between 0.06 and 0.09. Modellingand analysis are typically assumed to be unbiased, withCoVs of 0.03–0.07, and increase the CoV of the dead loadeffect to between 0.05 and 0.10. Most investigators (StandardsAssociation of Australia 1985, South African Bureauof Standards 1989, and European Committee for Standardization1994, all reported by Kemp et al. 1998; Tabsh 1997;Ellingwood 1999) adopted a bias of 1.05 and a CoV of 0.10,as reported by Ellingwood et al. (1980), which were used forthe current investigation. For cases where the dead loadcounteracts the effects of other loads, the dead load wasassumed normally distributed with a bias of 1.00 and a CoVof 0.10.In response to comments from members of the TaskGroup on Snow and Wind Loads and the Canadian StandardsAssociation (CSA) Technical Committee on ReinforcedConcrete Design, the statistical basis for dead loadfactors, including the accuracy of the analysis of dead loadeffects, was investigated. Findings are presented in this paperconcerning the original dead load statistics (Ellingwoodet al. 1980) and data from a new survey of concrete floorthickness variability. The companion paper summarizes relatedproposed revisions to NBCC Commentary G that reflectthe accuracy of the analysis of dead load effects.“Original” dead load statistics and load factorsFor the past two decades, code calibrators around theworld have characterized dead load effects as having a biasof 1.05 and a CoV of 0.10. The most detailed rationale forthese numbers is presented in Appendix B of Ellingwood etal. (1980, p. 145) and is based on the statistics shown in Table1. The mean dead load is 1.0 × 4.8 + 1.1 × 1.9 =6.89 kPa, with a standard deviation of [(1.0 × 4.8 × 0.06) 2 +(1.10 × 1.9 × 0.15) 2 ] 1/2 = 0.43 kPa and CoV of 0.43/6.89 =0.062. The bias for the dead load effect, accounting for theload model and analysis parameters, is therefore 6.89/6.70 ×1.0 × 1.0 = 1.03, with a CoV of (0.062 2 + 0.05 2 + 0.05 2 ) 1/2 =0.094. In these computations, the bias and uncertainty of thesuperimposed dead load were relatively large, and the magnitudeof the superimposed dead load is also large. Theimpact of the superimposed dead load was diminished, however,because it is a small fraction of the total dead load.In the derivation of the load factors for the 1975 edition ofthe NBCC, the dead load effect was assumed to have a biasof 1.00 and a CoV of 0.10, which included a CoV of 0.07for the transformation of dead load to dead load effect(Allen 1975). This calibration suggested a dead load factorof 1.30, but this was reduced to 1.25 to maintain the sameratio of dead load factor to live load factor as was used at thetime for ultimate strength design of concrete buildings.Survey in 2000 of concrete floor thickness variabilityMembers of the CSA Technical Committee on ReinforcedConcrete Buildings were invited to estimate typical floor© 2003 NRC Canada

Bartlett et al. 431Table 1. Dead load statistics for cast-in-place concrete (Ellingwood et al. 1980).Variable Bias CoVConcrete density 1.00 0.03Dimensions and density combined150 mm slab 1.00 0.08Slab and beam floor 1.00 0.07Column 1.04 0.04Total (100 pound-force per square foot = 4.8 kPa) 1.00 0.06Superimposed dead load: (40 pound-force per square foot = 1.9 kPa) 1.10 0.15Load model 1.00 0.05Dead load analysis 1.00 0.05thickness deviations for cast-in-place concrete construction.Three responses were received, two with quite detailed (andconsistent) information as summarized in Table 2. The valuesfor one- and two-way slabs are consistent with thicknesstolerances specified in standard CSA-A23.1-00 (CSA 2000).Bias values shown are based on the average of the reporteddeviations. Coefficients of variation are determined assumingthe range represented by the typical difference representstwo standard deviations, and the range represented by theworst difference represents four standard deviations.The tolerances shown in Table 2 indicate that the thicknessof cast-in-place toppings on precast construction andcast-in-place cover slabs on unshored composite constructioncan be extremely variable. It is assumed that the excessthickness is not uniform, but varies parabolically from amaximum, ∆, at midspan to zero at the ends. The extra load(or shear) in this case is equivalent to a uniform excessthickness of 2∆/3 along the full length of the member. Theextra midspan moment for a simply supported member isequivalent to a uniform excess thickness of 5∆/6 along thefull length of the member. If a 50 mm topping is placed on a200 mm precast hollow core slab, then the overall dead loadof topping and precast has a bias of 1.044 and a CoV rangingfrom 0.053 to 0.132. If a 50 mm topping is placed on a400 mm precast double tee beam, then the overall dead loadof topping and precast has a bias of 1.068 and a CoV rangingfrom 0.068 to 0.154. The bias and CoV for these casesare slightly greater than those shown in Table 1.Unshored composite construction was further identified asa potential problem, even though the definition of dead loadin clause 7.1.1 of CSA-S16.1-95 (CSA 1995) was amendedto include “the additional weight of concrete and finishesresulting from deflections of supporting members”. No guidanceabout acceptable tolerances for the cover slab thicknessis given in the CSA-A23.1-00 (CSA 2000) or CSA-S16.1-95(CSA 1995) standards. As noted previously, the impact ofgreater-than-specified slab thickness is more significant forbending moment than for shear force or reactions. Combiningthe worst values shown for cover slabs in Table 2with data for typical steel beams and deck, the overall deadload (or shear) of the concrete slab, deck, and steel beam hasa bias of 1.22 and a CoV of 0.25. The moment of the slab,deck, and beam has a bias of 1.33 and a CoV of 0.25. Theseparameters would require dead load factors in the order of1.8–2.0 to achieve acceptable levels of reliability.The survey responses also indicated that the weight ofconnections in steel roofs is known only after the roof is detailedby the fabricator and can exceed the 10% allowancethat some (but probably not all) designers use. For example,the allowance necessary for connection weight of the roof ofthe Skydome in Toronto was 30% (C.M. Allen, personalcommunication, 2000).The present study assumed a CoV for dead load analysisof roughly 0.050–0.075, which implies that the actual deadload force effects should generally be within 10–15% ofcalculated values. Although this margin may seem small,current codes and standards generally require the user to designductile members and structures that have the capabilityto redistribute the load if the actual distribution of force effectsis not exactly as predicted by an elastic analysis.Live load due to use and occupancyIn the present study, live load refers to that associatedwith the use and occupancy of a building. It includes theweight of people, equipment, and furnishings and materialsin storage. The total live load may be represented by a sustainedlive load component, which remains essentially constantfor a period of time that is often associated with theduration of a tenancy, and a transient (or extraordinary) liveload component that has a short duration or is instantaneous.The magnitude of each component is conventionally modelledby a Gamma distribution (Peir and Cornell 1973;Chalk and Corotis 1980; Ellingwood et al. 1980), and the arrivalof each is modelled as a Poisson process.Maximum lifetime live loadFor most reliability analyses or code calibrations, themaximum live load during the life of the structure has beenrepresented by a time-independent random variable with aGumbel probability distribution (Allen 1975; MacGregor1976; Ellingwood et al. 1980; European Committee forStandardization 1994; Kariyawasam 1996; Tabsh 1997;Ellingwood 1999). The reliabilities obtained by consideringthe live load as a Poisson process may in some cases differfrom those obtained by modelling the maximum live loadduring the life of the structure using an “equivalent” Gumbeldistribution. In practice, however, it is acceptable to representthe maximum live load as a Gumbel variate, and thisrepresentation was adopted.The mean value of the maximum equivalent uniformlydistributed live load for office floors during a 50 year referenceperiod was derived following Kariyawasam (1996).From simulation results (Ellingwood and Culver 1977), the© 2003 NRC Canada

432 Can. J. Civ. Eng. Vol. 30, 2003Table 2. Survey of concrete floor thickness variability from 2000.Thickness difference (mm)TypicalWorstCase Min. Max. Min. Max. Bias CoV Note50 mm topping on precast –5 +10 –10 +20 1.00–1.10 0.140–0.400–10 +10 –40 +50 1.00–1.23 0.077–0.176 Depends on camber of precast member65–75 mm cover slab, –5 +5 — —steel deck–5 +15 –10 +50 1.02–1.06 0.049–0.078 Extreme values are for unshoredconstruction150 mm one-way slabbetween beams–5 +5 –5 +25 Slopes tough, especially if sloped in twodirections–5 +10 –25 +25200 mm two-way slab –10 +20 — — 1.03–1.06 0.062–0.065–10 +15 –15 +40 Always have more around the columns;there is a buildup there300 mm two-way slab –10 +10 — — 1.00–1.06 0.033–0.056–10 +20 –20 +50expected value of the 50 year maximum equivalent uniformlydistributed live load, Lmax (in kN/m 2 ), isFig. 1. Fifty year maximum live load bias coefficient versus influencearea.[2] Lmax = 0. 895 + 76 . / AIwhere A I is the influence area (in m 2 ). The correspondingnominal live load, L (in kN/m 2 ), from the 1995 NBCC is[3] L = 24 . ( 03 . + 98 . / B)where 2.4 is the specified live load (in kN/m 2 ) and B is thetributary area (in m 2 ). According to ASCE7-98 (ASCE2000), the influence area equals the tributary area for twowayslabs, twice the tributary area for interior beams, andfour times the tributary area for columns. Using these relationships,the bias is simply the ratio of eq. [2] to eq. [3] andso depends on the type of element and its influence area.The 50 year maximum live load bias is shown in Fig. 1for realistic ranges of influence areas of two-way slabs,beams, and columns. The ASCE (2000) curve in Fig. 1 indicatesthe bias if the nominal live load is reduced with increasinginfluence area in accordance with ASCE7-98instead of eq. [2]. The 30 year extreme live load model usedfor previous Canadian design code calibration (Allen 1975)has a bias of 0.70 and a CoV of 0.30; the equivalent 50 yearmaximum live load has a bias of 0.78 and a CoV of 0.27 andis also shown in Fig. 1.The present study adopted a bias for the 50 year maximumlive load effect of 0.90, based on several considerations.Two-way slabs and other components with smallinfluence areas have greater bias, but the consequences offailure of these elements are less severe than those for elementssupporting larger tributary areas. Provided they arenot weak in shear, two-way slab systems possess considerablestrength reserves that are not usually considered by thedesigner. The average bias for beams, as computed for the12 values shown by the markers in Fig. 1 and so weightedtowards the smaller influence areas, is 0.94. The averagebias for columns, as computed for the 16 values shown bythe markers in Fig. 1 and so weighted towards the smallerinfluence areas, is 0.87. Although larger bias occurs forlarger influence areas, the large dead load that the columnmust sustain in this case makes the design relatively insensitiveto the magnitude of the live load. Figure 1 also indicatesthat the live load reduction specified in the NBCC is conservativewith respect to that in ASCE7-98 for beams and forcolumns with influence areas less than 1000 m 2 , and so thelive load bias is less than the value of 1.00 used to calibrateASCE7-98 (Ellingwood 1999). The average ratios of NBCCbias to ASCE7-98 bias, as determined by averaging thepoints shown by markers in Fig. 1, are 0.95 for beams and0.84 for columns. Lastly, the bias of 0.90 for use and occupancyload is greater than the value 0.78, which is equivalentto that used to calibrate the 1975 edition of the NBCC(Allen 1975).The CoV of the maximum equivalent uniformly distributedlive load for office floors during a 50 year referenceperiod is also based on the simulation results for officebuildings (Ellingwood and Culver 1977). This study reported2the variance of the 50 year maximum live load, σ L max (inkN/m 2 ), is© 2003 NRC Canada

Bartlett et al. 4332[4] σ L max = 0. 033 + 4. 025/A IThus the CoV of the live load is obtained by dividing thesquare root of eq. [4] by eq. [2]. The resulting relationshipbetween the CoV and the influence area is represented bythe curve marked “load only” in Fig. 2. The CoV values arerelatively insensitive to the influence area considered, rangingfrom 0.162 to 0.182.The transformation of the live load into a live load effectintroduces modelling and analysis factors. The modellingfactor addresses the idealization of the actual live load as anequivalent uniformly distributed load and has been assumedunbiased with a CoV of 0.20 (Ellingwood et al. 1980). Kariyawasam(1996) assumed these values pertain to columns,and a reduced CoV of 0.10 pertains to beams. The analysisfactor reflects the transformation of load to load effect andhas been assumed unbiased with a CoV of 0.05 (Ellingwoodet al. 1980). Using these values, the variation of CoV for the50 year maximum equivalent uniformly distributed load withinfluence area is plotted in Fig. 2. The CoV values forbeams proposed by Kariyawasam are consistently smallerthan those for columns. All CoV values are relatively insensitiveto the influence area. The CoV values for columns aresimilar to that assumed by Allen (1975) for calibration ofprevious editions of the NBCC, if the difference between the30 year and 50 year reference periods is taken into accounted.In past investigations, a Gumbel distribution has beenused to represent the total live load effect, including modellingand analysis factors (Ellingwood et al. 1980;Kariyawasam 1996). In the present investigation, the liveload was assumed to be a Gumbel variate with a bias of 0.9and a CoV of 0.17. The combined effect of the modellingand analysis factors has a bias of 1.0 and a CoV of [0.20 2 +0.05 2 ] 1/2 = 0.206 and was assumed to be time-independent. Itis further assumed that the overall effect of modelling andanalysis is normally distributed, because its uncertainty isdominated by a single factor, the modelling uncertainty, andbecause in the absence of data or studies concerning themodelling uncertainty, a normal distribution seems as reasonableas any other.Point-in-time live loadsStatistical analyses of point-in-time live load have beencarried out by others (Ellingwood and Culver 1977; Chalkand Corotis 1980; Ellingwood et al. 1980). The load may bemodelled as a sustained component, with a duration from 2to 8 years, and an extraordinary live load that occurs once ortwice per year. For the present study, it is assumed that theduration of the point-in-time live load, which includes boththe sustained component and the extraordinary live loadevent, is 6 months.The point-in-time live load is assumed to have a Weibulldistribution, with parameters derived from those of the50 year maximum live load distribution following the procedurespresented by Wen (1990). The bias is 0.273 and theCoV is 0.674. The transformation factors used to convertload into load effect were assumed identical for the 50 yearmaximum live load and the point-in-time live load.Fig. 2. Fifty year maximum live load coefficient of variation(CoV) versus influence area.Wind loadThe simplified procedure in the 1995 NBCC adopts a simple“gust factor” approach to estimate wind load on buildings.The wind pressure, p, against the surface of a buildingis[5] p = qC e C p C gwhere q is the reference velocity pressure, C e is the exposurefactor, C p is the external pressure coefficient, and C g is thegust factor. Although values for each of these variables arespecified in the NBCC, all are uncertain. As described in thenext section, the reference velocity pressure depends on theclimatic conditions at the site and, assuming these conditionsdo not change, can be considered as a stochastic process.Thus the distribution of the maximum pressure that will occurover a given design life can be derived from the annualmaximum pressure distribution. The various coefficients thattransform the reference velocity pressure to a pressure on thesurface of a building will be considered time-independentrandom variables.Reference wind pressuresIn Appendix C of the 1995 NBCC, the 1 in T year referencewind pressure, q T , is determined from the 1 in T yearwind velocity, V T ,as2[6] qT= 1 ρVT2where ρ is the density of air (1.2929 kg/m 3 for dry air at 0°Cand standard atmospheric pressure). The density of air wasconsidered deterministic because its CoV, roughly 2.5–5.0%(Ellingwood et al. 1980; MacGregor et al. 1997), is considerablyless than the CoV of V 2 T .Reference velocity pressures presented in Appendix C ofthe 1995 NBCC are derived from 1 h wind velocity datafrom over 100 sites, typically airports, with 10–22 years ofrecord (NBCC 1995). Maps were prepared showing contoursof the 1 in 30 year wind velocity and dispersion parametersfor Gumbel distributions fit to the data. For the locations© 2003 NRC Canada

434 Can. J. Civ. Eng. Vol. 30, 2003listed in Appendix C, which represent the centres of urbanareas and so generally differ from the sites where data werecollected, 1 in 30 year wind velocities and dispersion parameterswere obtained from the maps by interpolation. Then 1in 10 year and 1 in 100 year velocities were determined foreach site, from which 1 in 10, 1 in 30, and 1 in 100 year referencepressures were computed using eq. [6]. Thus the referencepressures listed in Appendix C of the NBCCgenerally do not exactly fit a Gumbel distribution, though itis possible to back-calculate wind velocities from the publishedreference pressures that do. There is no documentationavailable concerning the factors used to transform thevelocities and dispersion parameters from the data collectionsites to the locations listed in Appendix C. Generally theCoVs of maximum annual wind velocities back-calculatedfrom the wind pressures in Appendix C seem greater thanthe corresponding CoVs for nearby sites where data werecollected.The present investigation considered the wind velocity,not the wind pressure, as a random variable with a Gumbeldistribution to be consistent with the methodology and assumptionsadopted to compute the NBCC reference pressures.The ratio of the mean maximum velocity expected ina 50 year design life, V 50, to the specified 1 in 50 yearvelocity, V 50 , depends on only the CoV of the maximumannual wind velocity, CoV a , and isV 50 1[7] = + 3.050 CoVaV 1 + 2.592 CoV50aAnnual maximum wind velocity data were provided for311 sites by the Engineering Climatology Section of theCanadian Meteorological Centre in Downsview, Ontario, ofwhich 223 had at least 10 years of record. The CoV of themaximum annual wind velocity varies as shown in Fig. 3.The horizontal axis in Fig. 3 is the difference in degrees betweenthe longitude of the site and the Yukon–Alaska border,so the points on the left-hand side of the figurecorrespond to sites in Yukon and British Columbia and thepoints on the right-hand side correspond to sites in the Atlanticprovinces. The CoV a values range from 0.028 (OldGlory Mountain, British Columbia) to a maximum of 0.394(Squamish Airport, British Columbia), with an overall meanvalue of 0.134. For the 223 sites with at least 10 years of record,CoV a ranges from 0.055 (Vancouver Harbour, BritishColumbia) to 0.230 (Iqaluit, Nunavut), and the overall meanis 0.135. For these 223 sites, 90% of the CoV a values arewithin the range 0.087–0.183. There is a marked tendencyfor the standard deviation of the maximum annual wind velocityto increase as the mean value of the maximum annualwind velocity increases, as shown in Fig. 4. A linear regressionline forced through the origin has a slope, which correspondsto the CoV a , of 0.135 as shown.Figure 5 shows the relationship between the referencewind pressures for various return periods and the CoV of themaximum annual velocity distribution. The reference windpressures have been normalized using the 1 in 30 year windpressure. Figure 5 can be used to estimate the wind load factorsfor specified 1 in 50 year reference wind pressures thatgive factored wind loads identical to those in the 1995NBCC, where the load factor of 1.5 is applied to specified 1in 30 year reference wind pressures. For the average CoV aFig. 3. Coefficient of variation (CoV) of maximum annual windvelocity.Fig. 4. Standard deviation of maximum annual wind velocity.Fig. 5. Normalized specified wind pressures.of 0.135, the load factor applied to the 1 in 50 year referencewind pressure is 1.38, and for the CoV a limits of 0.087 to0.183 it corresponds to 1.35 and 1.42, respectively. If theload factor selected for the 1 in 50 year specified wind pres-© 2003 NRC Canada

Bartlett et al. 435sure exceeds these values, and the resistance factors areunchanged, designs to the 2005 NBCC will require a greaternominal resistance than designs to the 1995 NBCC.Figure 5 can also be used to estimate the importance factorfor wind load for post-disaster buildings, which in the1995 NBCC are designed for the 1 in 100 year wind load.These provisions are equivalent to an importance factor thatranges from 1.14 to 1.26, with a mean value of 1.21.Calibration for wind load was carried out for Regina,Rivière du Loup, and Halifax. The annual maximum windvelocity was treated as a Gumbel variate with bias computedusing eq. [7] and CoV a values derived from the CanadianMeteorological Centre data. These values are summarized inTable 3.Transformation factorsAs implied by eq. [5], the reference velocity pressuremust be transformed using gust, exposure, and pressure coefficientsto obtain the pressure applied to the surface of abuilding. Given that the transformation is represented as aproduct of independent random variables, the Central LimitTheorem implies that the overall transformation factor hasa log-normal distribution. It was further assumed that thetransformation factor is time independent. The current literaturepresents a considerable range of statistical parametersfor these coefficients; rationale for the particular values selectedis summarized briefly in the following paragraphs.The literature pertaining to the wind load approach inASCE7-98 (ASCE 2000) has limited relevance becausesome factors differ markedly from those in the NBCC.Statistical parameters for the exposure coefficient, C e , andthe combined gust and pressure coefficients, C g C p , reportedby others are presented in Table 4. The C e parametersadopted for the current investigation are consistent withthose proposed by Davenport (1982, 2000). The C g C p biasadopted is conservative with respect to values proposed forlow (Davenport 1982) or tall buildings (Davenport 2000),and the CoV adopted is at the higher end of the range of valuesreported by others.ASCE7-98 (ASCE 2000) specifies a factor of 0.85 fordirectionality that was neglected in the present investigationbecause the gust and pressure coefficients used for lowbuilding design in the NBCC have been reduced to accountfor directionality and other factors. Also, the pressure coefficientsin the NBCC for taller buildings are less severe thanthose in ASCE7-98 because they permit the designer tocompute the leeward suction at the mid-height of the building,not at the top.Thus the overall bias coefficient accounting for exposure,gust, and pressure coefficients, ignoring wind directionality,is 0.80 × 0.85 = 0.68, with a CoV of 0.219, say 0.22. Asshown in Table 4, these values are similar to those proposedby Ellingwood and Tekie (1999) and are comparable to valuesproposed by Davenport (1981, 1982).Point-in-time wind velocitiesPoint-in-time wind loads were derived assuming that thewind velocity (and therefore pressure) is a stochastic processand the factor that transforms the reference pressure to aload against the building surface is a time-independent randomvariable. The duration of each wind pulse was assumedTable 3. Statistical parameters for maximum wind velocity in50 year and 3 h periods.to be 3 h, so the annual number of pulses is 365.25 × 24/3 =2922. The central tendency and dispersion parameters forthe point-in-time distributions are summarized in Table 3.Snow loadMaximum 50 yearMaximum 3 hSite CoV a Bias CoV Bias CoVRegina 0.108 1.039 0.081 0.130 0.785Rivière du Loup 0.170 1.054 0.112 0.066 1.095Halifax 0.150 1.049 0.103 0.080 1.001The actual snow load on a roof is the difference betweenthe quantity of snow or rain that has accumulated and thequantity that has been removed by wind, melting, or evaporation(Ellingwood and O’Rourke 1985), but data are notreadily available to quantify snow load in this manner. Instead,the model used for design, which expresses the snowload on the roof of a structure, S, as a snow component anda rain component, was adopted:[8] S =(C b C w C s C a )S s + S rwhere S s is the ground snow load, S r is the associated rainload, C b is the basic roof snow load factor and equals 0.8,C w is the wind exposure factor, C s is the slope factor, and C ais the accumulation factor. The transformation factor, C gr ,that converts the ground snow load at a given site to an appropriateroof snow load is[9] C gr = C b C w C s C aAccording to the 1995 NBCC, S r need not be takengreater than C gr S s .Ground snow loadThe ground snow load, S s , is determined in Appendix C ofthe 1995 NBCC as the product of the depth of snow, d, andthe unit weight of snow, γ. These values were computed(NBCC 1995; Newark et al. 1989) by first fitting Gumbeldistributions to maximum annual accumulated snow depthdata for 1618 stations with 7–38 years of record and calculating1 in 30 year values. Then snow densities were determined,for various geographical regions with commonclimatic features as manifested by forest type, that averaged2.01 kN/m 3 east of the continental divide, 2.55–4.21 kN/m 3west of the continental divide, and 2.94 kN/m 3 above thetreeline in the Northwest Territories and Nunavut. The loadswere normalized to account for the site elevation, assuminga linear variation of load above sea level, and smoothed contourmaps were prepared. The final loads corresponding tothe various geographical locations in Appendix C were derivedby interpolation and rectified to account for elevation.There is no documentation available concerning the interpolationweighting factors used to transform the ground snowload values from the data collection sites to the locationslisted in Appendix C.The present investigation considered the maximum annualsnow accumulation depth to have a Gumbel distribution, forconsistency with the basis for computation of the specified© 2003 NRC Canada

436 Can. J. Civ. Eng. Vol. 30, 2003Table 4. Statistical parameters for the exposure coefficient, combined gust and pressure coefficients, and overall wind load transformationfactor reported by others.Source Bias CoV CommentExposure coefficient, C eAllen 1975 — — Bias = 0.85; CoV = 0.13 assumed for combination of C e C g andmodellingEllingwood et al. 1980 1.0 0.16 Exposure factor different from NBCCDavenport 1981 1.0 0.10 As reported by Kariyawasam 1996Davenport 1982 0.80 0.16 Low buildingsEllingwood and Tekie 1999 0.93 0.129 Low buildingDavenport 2000 0.80 0.20 For simplified method; tall buildingCurrent investigation 0.80 0.16Gust coefficient and pressure coefficient, C g C pAllen 1975 1.0 0.10 Pressure coefficient only; model error factor of 0.85 included separatelyEllingwood et al. 1980 1.0 0.11 Gust1.0 0.12 Pressure1.0 0.16 CombinedDavenport 1981 (as reported by 1.0 0.05 GustKariyawasam (1996))1.0 0.10 Pressure1.0 0.11 CombinedDavenport 1982 0.80 0.15 For low buildingsEllingwood and Tekie 1999 0.97 0.093 Gust0.88 0.067 Pressure (same nominal values as NBCC)0.85 0.115 CombinedDavenport 2000 0.80 0.21 For simplified method; tall buildingCurrent investigation 0.85 0.15Overall wind load transformation factorAllen 1975 0.72 0.174 Basis for calibration of NBCCEllingwood et al. 1980 0.85 0.239Davenport 1981 0.85 0.150 Not specifically for low buildings (as reported by Kariyawasam (1996))Davenport 1982 0.54 0.325 Low buildings; only external pressuresRosowsky and Cheng 1999 0.73 0.264 For low buildings, high-wind regionsEllingwood and Tekie 1999 0.70 0.208 Not specifically for low buildings; all factors have normal distributionsDavenport 2000 0.57 0.250 Simple method0.71 0.150 Detailed method1.00 0.087 Wind tunnel and meteorological studyCurrent investigation 0.68 0.22 Log-normalvalues in Appendix C of the 1995 NBCC. Annual maximumsnow depth data were provided for 1278 data-collection sitesby the Engineering Climatology Section of the CanadianMeteorological Centre. The CoV of the annual maximumdepth ranges from 0.08 to 1.34, with a mean of 0.491 and amedian of 0.47. Approximately 95% of the CoV values liebetween 0.22 and 0.95. Statistical parameters for maximumsnow depth in a 50 year reference period are summarized inTable 5. The ratio of the mean value of the maximum depthin a 50 year reference period to the 1 in 50 year specifiedsnow depths were computed using eq. [7]. The ranges ofbias coefficients and CoV values for the normalized maximum50 year distribution are quite small, so the valuesshown in the last row of Table 5 were adopted.Snow densities used to derive the 1 in 30 year valuesspecified in the 1995 NBCC were assigned based on thetype of forest in the region of the site. Kariyawasam (1996)has summarized statistical parameters for snow density, ρ,from Newark (1984), as reproduced in Table 6. In theTable 5. Statistical parameters for maximum snowdepth in 50 year period.CoV a Bias CoVLower 3% fractile 0.220 1.064 0.132Mean 0.491 1.099 0.197Upper 3% fractile 0.953 1.126 0.244Current investigation 1.10 0.20current investigation snow densities were assumed normallydistributed with a bias of 1.0 and a CoV of 0.17. The CoVvalue adopted is the average for all regions except tundraand taiga, which are not densely populated.Associated rain loadThe associated rain load represents the weight of rain fallingon snowpack, and values for Appendix C of the 1995NBCC have been derived based on historical data for winter© 2003 NRC Canada

Bartlett et al. 437Table 6. Statistical parameters for snow density (Kariyawasam 1996).Forest region Mean (kg/m 3 ) SD (kg/m 3 ) CoV Typical sitesAcadian 220 50 0.23 Fredericton, Halifax, St. John’s, CharlottetownAspen grove 220 40 0.18 Edmonton, Saskatoon, Winnipeg, Thunder BayBoreal 190 60 0.32 Northern Prairies, mid-northern Ontario and QuebecCoast 430 25 0.06 Coastal British ColumbiaColumbia 360 35 0.10 Southeastern British ColumbiaGreat Lakes 220 60 0.27 Southern and central Ontario, southern QuebecMontane 260 25 0.10 Interior British Columbia and YukonPrairie 210 40 0.19 Southern Prairies, ReginaSubalpine 360 30 0.08 Vancouver and Fraser ValleyTundra 300 80 0.27 ArcticTaiga 200 80 0.40 Subarctic, YellowknifeCurrent investigation 0.17Note: SD, standard deviation.rainfall (Taylor and Allen 2000). Subjectivity was requiredin the process of sketching 0.1 kPa isolines on maps(Newark et al. 1989). The difficulty of deriving statisticalparameters for this load is further exacerbated because thenecessary data are not readily available and, even if theywere, would require careful filtering to eliminate winterrainfall on nonexistent snowpacks. It was therefore assumedthat probability distributions for the roof snow load includeany further bias and uncertainty due to the associated rainload.Ground-to-roof transformation factorAlthough there is a significant body of literature concerningthe ground-to-roof snow load transformation factor, fewstudies provide results in a format that is compatible withcode calibration. Ellingwood and O’Rourke (1985) cite thefollowing relationship, from O’Rourke et al. (1982):[10] Cgr = 047 . ETεwhere E is a wind exposure factor ranging from 0.9 to 1.3; Tis a thermal characteristic factor ranging from 1.0 to 1.2; andε is the error term, which has a log-normal distribution witha mean value of 1.0 and a CoV of 0.44. The transformationfactor computed using eq. [10] ranges from 0.53 to 0.91times the basic roof snow load factor of 0.8 specified in the1995 NBCC.For the present investigation, parameters were adoptedfrom a recent study by Taylor and Allen (2000) that are consistentwith the definition of the ground-to-roof snow loadfactor as defined in eq. [8]. Various results, summarized inTable 7, consider the ratio of the maximum measured roofsnow load to the corresponding maximum ground snow loadas converted to an equivalent roof load using the NBCC criteria.The statistics are based on 13 years of data for 112roofs in four Canadian cities. The bias for data obtainedin Halifax, Chicoutimi, and Ottawa and the drift locationin Saskatoon tend to fall within the ranges suggested byEllingwood and O’Rourke (1985). The CoV values are alsosimilar.Point-in-time snow loadPoint-in-time snow load parameters were derived assumingthat the snow accumulation is a stochastic process andTable 7. Statistical parameters for ground-to-rooftransformation factor (Taylor and Allen 2000).the factors that transform the depth to a load and the groundsnow load to a roof snow load are time-independent randomvariables. It was assumed that the point-in-time pulse has amagnitude that follows the Weibull distribution and a durationof 14 days during only 3 months of the year, so thereare six events per year. The central tendency and dispersionfor the point-in-time distribution represent a bias with respectto the specified 1 in 50 year snow depth of 0.196 and aCoV of 0.882.Summaryn Bias CoVSheltered locationsHalifax 35 0.61 0.45Chicoutimi 8 0.71 0.44Saskatoon 8 0.30 0.11Recommended value 0.60 0.42Exposed locationsHalifax 11 0.47 0.46Ottawa 12 0.44 0.41Saskatoon 5 0.33 0.22Recommended value 0.50 0.42Drift locationsChicoutimi 4 0.86 0.30Ottawa 6 0.60 0.38Saskatoon 23 0.61 0.43Recommended value 0.60 0.42Current investigation 0.60 0.42Note: n, number of roofs in the sample.This paper summarizes statistical parameters for deadload, live load due to use and occupancy, snow load, andwind load that have been adopted for calibration of load andload combination criteria for the 2005 National BuildingCode of Canada (NBCC). Table 8 summarizes the bias andCoV values and distribution types adopted for the calibrationpresented in a companion paper. A new survey of typicalconstruction tolerances indicates that statistical parametersfor dead load presented by Ellingwood et al. (1980) are ade-© 2003 NRC Canada

438 Can. J. Civ. Eng. Vol. 30, 2003Table 8. Summary of statistical parameters for loads.Load type Bias CoV Distribution typeDead load 1.050 0.100 NormalUse and occupancy live load50 year maximum load 0.900 0.170 GumbelPoint-in-time load 0.273 0.674 WeibullTransformation to load effect 1.000 0.206 NormalWind load (1 in 50 year specified)50 year maximum velocityRegina 1.039 0.081 GumbelRivière du Loup 1.054 0.112 GumbelHalifax 1.049 0.103 GumbelPoint-in-time velocityRegina 0.156 0.716 WeibullRivière du Loup 0.064 1.149 WeibullHalifax 0.084 1.001 WeibullTransformation to load effect 0.680 0.220 Log-normalSnow load (1 in 50 year specified)50 year maximum depth 1.100 0.200 GumbelPoint-in-time depth 0.196 0.882 WeibullDensity 1.000 0.170 NormalTransformation to load effect 0.600 0.420 Log-normalquate unless the dead load is dominated by thin, cast-inplaceconcrete toppings. Statistical parameters for live loaddue to use and occupancy were derived that pertain specificallyto the live reduction factor equation used in the NBCC.Statistics for snow and wind loads were normalized usingthe 1 in 50 year values that will be specified in the 2005NBCC. New statistical parameters were determined for thefactors that transform wind or snow loads to the force effectbecause of these loads.AcknowledgementsPrimary funding for this study from the National ResearchCouncil of Canada Institute for Research in Construction isgratefully acknowledged. Additional funding from the NaturalSciences and Engineering Research Council of Canadaand the Steel Structures Education Foundation is also acknowledged.The Engineering Climatology Section of theCanadian Meteorological Centre in Downsview providedenvironmental data and very helpful assistance concerningtheir interpretation. The authors gratefully acknowledgecomments and suggestions from the National Building Codeof Canada Part 4 Task Group on Snow and Wind Loads:D.E. Allen (Chair), P. Chan, P.A. Irwin, P. Jarrett,D.J.L. Kennedy, J.G. MacGregor, A. Metton, R.S. Riffell,R.G. Sexsmith, C. Taraschuk, and A. Wong. The opinionsexpressed in this paper are those of the authors, however,and not necessarily those of the Task Group.ReferencesAISC. 1986. Specification for structural steel buildings — load andresistance factor design. American Institute of Steel Construction(AISC), Chicago, Ill.Allen, D.E. 1975. Limit states design — a probabilistic study. CanadianJournal of Civil Engineering, 2: 36–49.ASCE. 2000. Minimum design loads for buildings and other structures(ASCE7-98). American Society of Civil Engineers(ASCE), Reston, Va.CEB. 1976. Common unified rules of different types of constructionand material. Vol. 1. Bulletin d’Information No. 116-E,Comité Euro-International du Béton, Paris, France.Chalk, P.L., and Corotis, R.B. 1980. A probability model fordesign live loads. ASCE Journal of the Structural Division,106(ST10): 2017–2033.CSA. 1995. Limit states design of steel structures. Standard CSA-S16.1-95, Canadian Standards Association, Rexdale, Ont.CSA. 2000. Concrete materials and methods of construction. StandardCSA-A23.1-00, Canadian Standards Association, Rexdale, Ont.Davenport, A.G. 1981. Some attributes of the wind load requirementsof the National Building Code of Canada. In Proceedingsof the Canadian Conference on Wind Engineering, Vancouver,B.C., 13–14 April. pp. 1–12.Davenport, A.G. 1982. On the assessment of the reliability of windloading on low buildings. In Proceedings of the 5th Colloquiumon Industrial Aerodynamics, Aachen, Germany, 14–16 June.Davenport, A.G. 2000. A comparison of seismic and windstormhazards. In Proceedings of the 6th Environmental SpecialtyConference of the Canadian Society for Civil Engineering, 7–10June 2000, London, Ont. Canadian Society for Civil Engineering,Montréal, Que. pp. 504–509.Ellingwood, B.R. 1999. A comparison of general design and loadrequirements in building codes in Canada, Mexico and theUnited States. In Proceedings of the North American Steel ConstructionConference, Toronto, Ont., 19–21 May. American Instituteof Steel Construction Inc., Chicago, Ill. pp. 12-1–12-27.Ellingwood, B.R., and Culver, C. 1977. Analysis of live loads inoffice buildings. ASCE Journal of the Structural Division,103(ST8): 1551–1560.Ellingwood, B., and O’Rourke, M. 1985. Probabilistic models ofsnow loads on structures. Structural Safety, 2: 291–299.Ellingwood, B.R., and Tekie, P.B. 1999. Wind load statistics forprobability-based structural design. ASCE Journal of StructuralEngineering, 125(4): 453–464.© 2003 NRC Canada

Bartlett et al. 439Ellingwood, B.R., Galambos, T.V., MacGregor, J.G., andCornell, C.A. 1980. Development of a probability based loadcriterion for American National Standard A58. NBS SpecialPublication 577, National Bureau of Standards, U.S. Departmentof Commerce, Washington, D.C.European Committee for Standardization. 1994. ENV 1991-1:1994 Eurocode 1: basis of design and actions on structures —Part 1: basis of design. European Committee for Standardization,Brussels, Belgium.Kariyawasam, S.N. 1996. Development of probability based resistancefactors and companion-action load factors for concrete designin Canada. Ph.D. thesis, University of Alberta, Edmonton,Alta.Kariyawasam, S.N., Rogowsky, D.M., and MacGregor, J.G. 1997.Resistance factors and companion-action load factors for reinforcedconcrete building design in Canada. Canadian Journal ofCivil Engineering, 24: 593–602.Kemp, A.R., Mahachi, J., and Milford, R. 1998. Developing LRFDcodes in South Africa. In Proceedings of the Structural EngineersWorld Congress, San Francisco, Calif. 19–23 July. ReferenceP315-3.MacGregor, J.G. 1976. Safety and limit states design for reinforcedconcrete. Canadian Journal of Civil Engineering, 3: 484–513.MacGregor, J.G., Kennedy, D.J.L., Bartlett, F.M., Chernenko, D.,Maes, M.A., and Dunaszegi, L. 1997. Design criteria and loadand resistance factors for the Confederation Bridge. CanadianJournal of Civil Engineering, 24: 882–897.NBCC. 1995. National Building Code of Canada. Institute for Researchin Construction, National Research Council of Canada,Ottawa, Ont.Newark, M.J. 1984. A new look at ground snow loads in Canada.In Proceedings of the Eastern Snow Conference, 41st AnnualMeeting, Washington, D.C. Vol. 29, pp. 37–48.Newmark, M.J., Welsh, L.E., Morris, R.J., and Dnes, W.V. 1989.Revised ground snow loads for the 1990 National Building Codeof Canada. Canadian Journal of Civil Engineering, 16: 267–278.Nowak, A.S., and Lind, N.C. 1979. Practical code calibration procedures.Canadian Journal of Civil Engineering, 6: 112–119.O’Rourke, M.J., Redfield, R., and Von Bradsky, P. 1982. Uniformsnow loads on structures. ASCE Journal of the Structural Division,108(ST12): 2781–2798.Peir, J.C., and Cornell, C.A. 1973. Spatial and temporal variabilityof live loads. ASCE Journal of the Structural Division, 99(ST5):903–922.Rosowsky, D.V., and Cheng, N. 1999. Reliability of light-frameroofs in high-wind regions. ASCE Journal of Structural Engineering,125(7): 725–733.South Africa Bureau of Standards. 1989. The general proceduresand loadings to be adopted in the design of buildings: SABS0160:1989. South Africa Bureau of Standards, Pretoria, SouthAfrica.Standards Association of Australia. 1985. Guidelines for conversionto limit states codes, Committee BD16 — Loading ofStructures. Standards Association of Australia, Canberra, Australia.Tabsh, S.W. 1997. Safety of reinforced concrete members designedfollowing ACI 318 building code. Engineering Structures,19(10): 843–850.Taylor, D.A., and Allen, D.E. 2000. Statistical variation and durationof snow load on flat roofs in Canada. Institute for Researchin Construction, National Research Council of Canada, Ottawa,Ont. Unpublished study.Turkstra, C.J. 1972. Theory of structural design decisions. SolidMechanics Study 2, University of Waterloo, Waterloo, Ont.Wen, Y.K. 1990. Structural load modelling and combination forperformance and safety evaluation. Elsevier, Amsterdam, TheNetherlands.List of symbolsA I influence areaB tributary areaC a snow accumulation factorC b basic roof snow load factorC e exposure factor for wind loadC g gust factor for wind loadC gr ground-to-roof snow load transformation factorC p external pressure coefficient for wind loadC s slope factor for snow loadC w wind exposure factor for snow loadCoV coefficient of variationCoV a coefficient of variation of annual maximum loadd snow depthE wind exposure factorL live load due to use and occupancyI max mean 50 year maximum live load due to use and occupancyn number of roofs in the samplep wind pressureP effect due to permanent loadq reference velocity pressureq T reference wind pressure with T year return periodS snow loadS i principal transient loadS j companion-action transient loadS r rain load associated with ground snow loadS s ground snow loadT return period or thermal characteristic factorV T wind velocity with 50 year return periodV max mean 50 year maximum wind velocityV 50 with 50 year return period wind velocityα load factorα i load factor applied to the effects due to the principaltransient loadα ij load factor applied to the companion-action transientloadsα P load factor applied to the effects due to permanent loadsuch as dead loadγ unit weight of snow∆ maximum excess thickness of cast-in-place toppingε error term in ground to roof snow load transformationfactorρ density2σ Lmax variance of 50 year maximum live load due to use andoccupancy© 2003 NRC Canada