International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Variability of time independent wind load components Botha, Jacques; Retief, Johan V.; Viljoen, Celeste Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Variability of Time Independent Wind Load ComponentsJacques BothaPostgraduate Student, Dept. of Civil Engineering, Stellenbosch University, Stellenbosch,South AfricaJohan V. RetiefProfessor, Dept. of Civil Engineering, Stellenbosch University, Stellenbosch, South AfricaCeleste ViljoenSenior Lecturer, Dept. of Civil Engineering, Stellenbosch University, Stellenbosch, SouthAfricaABSTRACT: This paper investigates the variability of the primary time independent components of thedesign wind load formulation. It is shown that the variability of these components has a significantinfluence on the total reliability of wind loads. The use of comparative studies of international wind loadstandards as an indicator of the variability of the time independent wind load components is discussed. Atwo part comparative study is done to determine the variability. It is found that the existing representativeprobability model of wind load components underestimates even a lower limit estimate of the variabilityof these components, particularly for pressure coefficients. Furthermore, insight is gained into the effectsof various structural and wind load parameters on the total variability of wind loads.1. INTRODUCTIONWind is an intrinsically uncertain natural phe-nomenon. This uncertainty is a critical aspect ofwind actions as structural loads that can only betreated probabilistically. This investigation is partof an ongoing project to develop new wind loadprobability models for the South African environ-ment. This paper discusses a critical step this pro-cess, namely, determining the variability of the timeindependent wind load components of the designwind load formulation.2. PROBABILISTIC MODELING OF WINDLOADSThe design wind load formulation is used to repre-sent the combination of multiple physical processeswhich result in wind pressures acting on a struc-ture. As with any physical process, each of theseprocesses is subject to uncertainties. These uncer-tainties need to be quantified and taken into accountin the calibration of the wind load formulation inorder to achieve a desired level of reliability.Probabilistic models describe the uncertainty ofthe design wind load through the use of representa-tive probability distributions of the wind load com-ponents. These distributions are defined by threeparameters: distribution type, mean value and co-efficient of variation. The parameters determinehow the probability models describe the total un-certainty of the wind load, therefore it is imperativethat each one be determined using the best availablereliability sources.The general formulation of design wind loads isgiven in Equation 1. The variables are defined inTable 1, along with the representative statistical pa-rameters of the distributions used to describe eachcomponent. These parameters are normalized withrespect to their characteristic values. It should benoted that there are numerous levels of approxi-mation which may be considered when determin-ing wind loads on structures. Many formulationstake account of factors such as wind directionalityand dynamic effects. Furthermore, most probabilis-tic models also include a model uncertainty factor112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Table 1: Wind load formulation variables and representative distribution parameters.Symbol Variable Distribution Type Systematic Bias Coefficient of VariationQRef Annual extreme pressure Gumbel 1.10 0.18cr Terrain roughness Normal 0.80 0.10ca Pressure coefficient Normal 1.00 0.10cg Gust factor Normal 1.00 0.10when used for reliability calibration. For the pur-poses of this investigation, however, only the fun-damental formulation of design wind loads as givenbelow was considered.Q = QRef cr ca cg (1)The representative probability model of the de-sign wind load formulation given in Table 1 wasadopted from JCSS (2001) and was used in the cal-ibration of the Eurocode 1 wind load stipulationsby Gulvanessian and Holický (2005). However,the reliability basis used for the development of theJCSS model is unclear. This serves as the primarymotivation for the ongoing project to develop a newwind load probability model for the South Africanenvironment based on transparent and reliable data.The development of a new probability model re-quires that the statistical parameters of each windload component be investigated. Research on thevariability of the time dependent wind load compo-nent in South Africa has been presented by Krugeret al. (2013) and Botha et al. (2014). This paperinvestigates the variability of the time independentcomponents, specifically pressure coefficients andterrain roughness factors. The investigation is lim-ited to the global reliability of regular structures inorder to obtain a generic representation of uncer-tainty. Uncertainties representative of special con-ditions such as dynamic effects or special structuresshould be investigated separately.2.1. Time Dependence of Wind Load ComponentsThe design wind load formulation may broadly bedivided into two parts. The first is the descriptionof the free-field wind at the location of the struc-ture, a time dependent process which is subject tothe stochastic nature of strong wind conditions. Thesecond is the conversion of the free-field wind intowind pressure loading on the structure. This con-version is a function of the aerodynamic and terrainroughness effects. Where the free-field wind is timedependent, these factors are time independent as thephysical conditions which influence them, namelythe geometry of the structure and the surroundingterrain, remain relatively constant over time.Free-field wind is often considered to be the pri-mary source of uncertainty in the wind load pro-cess as it forms the basis of wind loads. The timeindependent components act as magnification or re-duction factors of the free-field wind pressure. It isclear that although the aerodynamic factors and ter-rain roughness factors are theoretically time inde-pendent, they are not independent of the free field-wind. These factors do have a significant influenceon the total wind load, however, and the uncertain-ties related to them should not be underestimated.To illustrate the importance of the time inde-pendent wind load components on the reliabil-ity of wind loads, specifically the variability ofthese components, a simple First Order Reliabil-ity Method (FORM) comparison was done. Thewind load formulation was simplified to the prod-uct of two variables, the time dependent free-fieldwind (D) and the combined time independent windload components (I). The deterministic designwind pressure (wd) was varied parametrically. Us-ing a basic limit state function given in Equation 2,FORM analyses were done using two probabilitymodels. The first model was derived using the ba-sic distribution parameters from the representativewind load probability model in Table 1. The sec-ond model used the same distribution parametersfor the time dependent component, but double thevalue for the coefficient of variation of the time in-212th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015dependent components was used. The models usedin the FORM comparison are summarized in Ta-ble 2. The results showing the design wind pres-sure plotted against the calculated reliability indexvalues (β) are given in Figure 1.0 = D ∗ I − wd (2)Table 2: FORM comparison probability modelsSymbol TypeModel 1 Model 2Bias CoV Bias CoVD Gumbel 1.10 0.18 1.10 0.18I Normal 0.80 0.14 0.80 0.28Figure 1: FORM comparison results.The results clearly indicate that the variability ofthe time independent components markedly affectsthe total reliability of the design wind load. Al-though doubling the variability assumed by the rep-resentative probability may seem extreme, this pa-per will show that the coefficient of variation usedin the second model is a reasonable approximationof the total variability of the combined time inde-pendent wind load components.2.2. Wind Load Uncertainty Characterizationand Reliability BasisIn addition to differentiating the wind load compo-nents based on their time dependence, the compo-nents are also characterized by different types ofuncertainties. Much research has been done in thefield of extreme wind prediction. Through the con-tinuous process of gaining additional data and im-proving probability models, the systematic uncer-tainties related to the description of the free-fieldwind are reduced and the aleatoric uncertainties in-herent in strong wind conditions become dominant.Aerodynamic and terrain roughness effects, on theother hand, are dominated by epistemic uncertain-ties due to the simplicity of the models which areused to describe them.As the variability of the time independent com-ponents is due to epistemic uncertainties, a reliabil-ity investigation of these components needs to bebased on information which reflects the systematicuncertainties. Arguably the most important part ofany reliability investigation is obtaining reliable in-formation and data. This is particularly challengingwhen considering pressure coefficients and terrainroughness factors due to the scope of the design sit-uations which may be considered for even the mostbasic structures. This investigation explored and as-sessed the use of the comparison of wind load stan-dards as an indicator of the variability of the windload components considered.Wind load standards may be characterized by atwo-step development process. Firstly, backgroundinformation and research is converted into opera-tional models to describe design wind loads. Thesemodels are then modified and adapted into practi-cal design procedures which systematically coverthe required design situations. The background op-erational models are the true source of the epis-temic uncertainties, and the comparison of thosemodels would provide the closest approximationof the variability. However, without clear back-ground documentation detailing the development ofthe standards, as is often the case, these models arenot readily accessible. The wind load standardsthemselves are accessible, and the standards mayserve as a valuable source of information to com-pare the differences between the theoretical modelsand data.Using the comparison of standards has cleardrawbacks. Foremost among these is the fact thatone cannot use the wind load standard stipulationsas statistical data. As stated above, the basic data312th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015used in the development of the standards may havebeen modified to develop the final design proce-dures. This process may result in additional levelsof conservatism being added or simplification of thebackground models. Furthermore, there are signif-icant differences in the formulations of the variousstandards, such as pressure zone area definitions,pressure coefficients for different roof slope inter-vals and terrain roughness factor cutoff heights. Asa result, the comparison of standards may lead toadditional variability being observed. Careful fil-tering out of the differences due to format can en-sure that the differences in standard generated val-ues will reflect the differences in the backgroundmodels used in their development and may serve asan indication of the true variability.This may be achieved through a comprehensivecomparative study in which the sources of addi-tional variability are identified and treated appropri-ately. This process should consist of the followingsteps:1. A design situation is defined and the corre-sponding codified parameters from selectedwind load standards are determined. Thesecodified values provide an estimation of themean characteristic value of the respective pa-rameters for the specific situation.2. The scatter of the codified parameter valuesaround the mean for the design situation isused to estimate the epistemic variability of theparameters for the given situation.3. The design situation is changed parametricallyand the first two steps repeated. The trendswhich arise in both the characteristic valuesand the variability may then be identified asmore situations are considered.4. By repeating the process within an acceptablesample space of design situations, a estima-tion may be made of the representative vari-ability of the time independent wind load com-ponents.Assuming that each wind load standards is an in-dependent sample and represents a unique formu-lation which integrates data from different sources,comparison of standards provides a reasonable ap-proximation of the variability of the time indepen-dent wind load components. This method under-estimates the true variability where different stan-dards are based on the same models. The variabil-ity is underestimated further due to the nature ofepistemic uncertainties as not all sources of uncer-tainty are considered. It is therefore apparent thatthe methods presented in this paper provide a lowerbound approximation of the true variability of thetime invariant wind load components.3. METHODOLOGYSeven international standards were considered inthis investigation, namely SANS 10160-3 (2011),EN 1991-1-4 (2005), BS NA EN 1991-1-4 (2010),AS-NZS 1170-2 (2011), ISO 4353 (2009), ASCE7 (2010) and NBC (2010). The SANS wind loadstipulations are based on EN 1991, which providesa comprehensive and detailed wind load formula-tion. BS NA EN 1991 is a National Annex to EN1991 which provides different parameters for thesame general formulation. Similarly, the AS/NZS,ISO and ASCE wind load stipulations follow a sin-gle formulation, but each standard provides differ-ent parameters within the overarching formulation.This formulation is slightly less detailed than theEN formulation, but is easily applied to a largescope of design situations. Finally, the NBC stip-ulations for primary wind loads on structures pro-vides yet another formulation. ASCE also includesstipulations for the NBC formulation, but thesewere not considered in this investigation.A comparative study of wind load standards wasdone to investigate the variability of time indepen-dent components. The study was done in two parts.In the first part the pressure coefficients and the ter-rain roughness factors provided in the wind loadstandards were compared individually in order todetermine the variability of each component inde-pendently. The second part investigated the com-bined effects of the time independent wind loadcomponents. Instead of comparing individual pres-sure coefficients or terrain roughness factors, a pa-rameter study was done on representative structuresand the design wind pressures as calculated accord-ing to the stipulations given by each of the stan-dards were compared. Constant values were cho-sen for the time dependent component of the wind412th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015load across all parameter studies to ensure that theobserved variability was solely due to the time in-dependent components.A critical part of the comparative study is the se-lection of the sample space. The sample space mustbe chosen in such a way that it provides the best re-flection of the pure epistemic uncertainties and ex-cludes special cases and outliers which may skewthe results. The scope of this investigation is lim-ited to structures representative of buildings com-monly designed in practice. The parameter rangesselected in this paper were based on engineeringjudgement, but the investigation may be refined infuture through a comprehensive study to determinethe optimal sample space.4. INDIVIDUAL COMPONENT INVESTIGATIONS4.1. Pressure CoefficientsAs pressure coefficients are presented and imple-mented in various ways, the parameter range waschosen so that the values obtained from the differ-ent standards would be comparable. The externalpressure coefficients on walls, mono-pitched andduo-pitched roofs were compared. Comparisonswere done for roof pitch values between 0o to 20o.Furthermore, as the global reliability of structureswas under investigation, only large area-averagedpressure coefficients were considered.Critical positions on the structures were definedand the pressure coefficients specified by each windload standard at those positions were recorded. Thepressure coefficients were normalized with respectto the average value of each position, allowing di-rect comparison of the pressure coefficients at allpositions. The coefficients of variation were thendetermined for each structural component as wellas across all observation positions. The results arepresented in Table 3.4.2. Terrain Roughness FactorsA similar procedure to that used to determine thevariability of pressure coefficients was used. Threerepresentative exposure categories correspondingto sea, open country and suburban terrains were se-lected from Eurocode. The roughness lengths usedare given in Table 4. The equivalent roughness fac-tor profile for each representative exposure cate-Table 3: Coefficients of variation of pressure coeffi-cients.Component Coefficient of VariationWalls 0.27Flat Roof 0.28Mono Pitched Roof 0.30Duo Pitched Roof 0.27Total 0.33Table 4: Representative exposure categories used incomparative study.Category Description Roughness Length1 Sea 0.02 m2 Open Country 0.05 m3 Suburban 0.40 mgory was then calculated using the stipulations ofthe wind load standards. The profiles were sam-pled at 1 m intervals. The roughness factors at eachheight were normalized with respect to the calcu-lated average roughness factor at that height, al-lowing direct comparison of the roughness factorsacross the entire height. The results of the investi-gation are presented in Table 5.4.3. Combined VariabilityBy assuming that both the pressure coefficient andterrain roughness uncertainties are best describedby a Normal distribution, as is the case in the rep-resentative probability model, the total variabilityof the two components may be calculated. This al-lows for a single coefficient of variation of the com-bined components which may then directly com-Table 5: Coefficients of variation of terrain roughnessfactors.Exposure Category Coefficient of Variation1 0.112 0.103 0.12All 0.11512th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015pared to the coefficient of variation obtained fromthe combined component investigation to follow. Acombined coefficient of variation of 0.35 was cal-culated.5. COMBINED COMPONENT INVESTIGATION5.1. Parameter Study MethodologyA comprehensive comparative study of the variousdesign wind load standards requires a large numberof comparisons covering a wide range of represen-tative design situations. This was achieved througha parameter study of the design wind load formu-lation rather than using individual comparisons ofvarious reference structures. This provided an in-dication of the variability of the time independentwind load components as well as insight into whichaspects of the structure’s geometry have the mostsignificant impact on the variability of the windloading process. Furthermore, a parameter study al-lowed identification of the trends of the additionalvariation due to the differences in the developmentof the standards.To this end, a program was written to automatethe process. Every wind load standard consideredin this investigation was studied extensively and aseparate module was developed for each, which al-lowed automatic calculation and comparison of dif-ferent design wind loads. The program calculatedwind loads based on seven primary parameters:• Structure Type: The structure could be de-fined as a mono- or duo-pitch building.• Wind Direction: The program allowed forthree orthogonal wind directions. 0o defineda wind direction perpendicular to the ridgeof the structure blowing onto the low eave,90o running parallel to the ridge of the struc-ture, and 180o perpendicular to the ridge of thestructure blowing onto the high eave.• Exposure Category (EC): The three repre-sentative exposure categories as used in the in-dividual component investigations were usedin the program.• Structure Width (W): Defined as the hori-zontal dimension perpendicular to the ridge ofthe structure.• Structure Length (L): Defined as the hori-zontal dimension parallel to the ridge of theTable 6: Reference structures and parameter ranges.Smaller reference structure parameters given in paren-theses where applicable.Structural Parameter RangesParameter: Reference Lower Upperα: 10◦ 0◦ 20◦H: 5m 5m 35m (25m)W: 25m (15m) 10 m 40m (30m)L: 50m (30m) 10 m 70m (50m)EC: 2 1 3structure.• Wall Height (H): Measured from ground levelto the lowest eave of the building.• Roof Pitch (α): For structures with a roofpitch of less than 5o, the roof was assumed tobe flat and the flat roof procedures for calcu-lating wind pressures were followed.Once these parameters were defined the exter-nal design wind pressure distributions on the struc-ture were calculated. As with the individual com-ponent investigation, only wind pressures resultingin primary structural actions were considered, i.e.cladding and component pressures were not con-sidered. The pressure was then integrated over eachface of the structure and a spatially averaged windpressure value was recorded per face. The coeffi-cient of variation of the design wind loads could bedetermined for each face and across the structure asa whole.The parameter study needed to be done in such away that it allowed investigation of a wide range ofdesign situations as well as effective analysis andcomparison of the results. In order to accomplishthis, a reference structure was defined and each ofthe parameters were varied in turn within selectedparameter ranges. This procedure was done for tworeference structures. The reference structural pa-rameters and parameter ranges used in each param-eter study are given in Table 6.Five combinations of the two structure types andthree wind directions were used in each parameterstudy and their results recorded separately. As theresults for duo-pitch roofs are the same for 0o and180o, the logical sixth combination was ignored.612th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Figure 2: Coefficients of variation plotted against varied parameters for the larger reference structure.Table 7: Maximum, average and minimum coefficient of variation for all parameter studies. Values in parenthesescalculated excluding the "Mono180" case results.Varied Larger Reference Structure Smaller Reference StructureParameter: Maximum Average Minimum Maximum Average MinimumRoof Slope: 0.36 (0.33) 0.26 (0.25) 0.21 (0.21) 0.30 (0.30) 0.25 (0.24) 0.20 (0.20)Wall Height: 0.36 (0.30) 0.26 (0.25) 0.22 (0.22) 0.32 (0.32) 0.26 (0.27) 0.19 (0.19)Width: 0.38 (0.31) 0.28 (0.26) 0.22 (0.22) 0.30 (0.30) 0.24 (0.24) 0.19 (0.19)Length: 0.36 (0.30) 0.27 (0.25) 0.19 (0.19) 0.31 (0.30) 0.25 (0.24) 0.18 (0.18)Exposure Category: 0.36 (0.32) 0.28 (0.26) 0.22 (0.22) 0.31 (0.29) 0.25 (0.24) 0.19 (0.19)5.2. Parameter Study ResultsFigure 2 shows the results of the parameter studyusing the larger reference structure. The coeffi-cients of variation are plotted against each variedparameter for the five structure-direction combina-tions. The vertical black line on the graphs indi-cates the reference structure. The range of resultsobtained for both parameter studies is summarizedin Table 7. The peak values obtained from the pa-rameter study using the larger reference structureare up to 26.7% higher than those obtained fromthe second parameter study, but the average valuesobtained from the two studies only differ by 7.6%.It may be seen from Figure 2 that there are sig-nificant differences between the values obtained foreach structure-direction combination. It is clearthat for the larger reference structure "Mono180"is the dominant case as it consistently yields thegreatest variability. By recalculating the values andexcluding the "Mono180" results, as given by theparenthesized values in Table 7, it is shown thatalthough the calculated maximum values are sig-nificantly lower, the average values change by lessthan 6.0% for the larger reference structure. Fur-thermore, less than 3.8% change is observed in theresults of the parameter study on the smaller refer-ence structure, indicating that "Mono180" is not thedominant case for that design situation. This rein-forces the use of a comprehensive parameter studyacross multiple design situations as a valid indica-tion of the variability as extreme cases have littleeffect on the final calculated average values.712th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Of the varied parameters, the roof slope studyshows the most erratic results, indicating that it hasthe greatest effect on the variability of the windloads, second only to the differences in variabilitybetween the structure-direction combinations. Thewall height parameter study shows erratic resultsfor low wall heights, but the values become stableafter a wall height of 20 m is reached. The buildingwidth, building height and exposure category pa-rameter studies show relatively consistent variabil-ity, indicating that these parameters do not impactthe variability of wind loads significantly.6. CONCLUSIONS• The variability of the time independent windload components has a significant effect on thetotal reliability of wind loads.• This variability is primarily due to epistemicuncertainties in the wind load formulation.• The comparison of wind load standards maybe used as an indicator of the variability of thetime independent wind load components.• The sampling space chosen in this investiga-tion is based on engineering judgement. Theinvestigation may be refined in future by deter-mining the optimal parameter ranges for unbi-ased sampling.• Average coefficients of variation of 0.33 forpressure coefficients and 0.11 for terrainroughness factors were obtained from the in-dividual component investigations. A coeffi-cient of variation of 0.35 was calculated for thecombined effect of both components.• The combined component investigation re-sulted in average coefficients of variation be-tween 0.24 and 0.28 for total variability of thetime independent wind load components.• The results for the variability of the time inde-pendent components of the wind load formu-lation obtained from this investigation are con-sistently greater than the variability accountedfor by existing probabilistic wind load models,particularly for pressure coefficients.• Wind direction and roof type have the largestinfluence on the variability of wind loads. Ofthe structural parameters, the roof slope hasthe greatest on the variability, whereas changesin the plan dimensions of the structure have lit-tle effect on the total variability.7. REFERENCESAS-NZS 1170-2 (2011). “Structural design actions- Part 2: Wind actions.” Standards Australia Lim-ited/Standards New Zealand.ASCE 7 (2010). “Minimum Design Loads for Buildingsand Other Structures.” American Society of Civil En-gineers.Botha, J., Retief, J., Holický, M., and Viljoen, C. (2014).“Development of probabilistic wind load model forSouth Africa.” Proceedings of the Thirteenth Confer-ence of the Italian Association for Wind Engineering.BS NA EN 1991-1-4 (2010). “UK National Annex toEurocode 1: Actions on structures, Part 1-4: Generalactions - Wind actions.” British Standards Institute.EN 1991-1-4 (2005). “Eurocode 1: Actions on struc-tures, Part 1-4: General actions - Wind actions.” CENBrussels.Gulvanessian, H. and Holický, M. (2005). “Eurocodes:using reliability analysis to combine action effects.”Proceedings of the ICE - Structures and Buildings,158, 243 – 252.ISO 4353 (2009). “Wind actions on structrues.” Interna-tional Organization for Standardization.JCSS (2001). “Joint Committee on Structural SafetyProbabilistic Model Code, Parts 1 to 4.Kruger, A., Retief, J., and Goliger, A. (2013). “Strongwinds in South Africa.” Journal of the South AfricanInstitution of Civil Engineering, 55(2).NBC (2010). “National Building Code of Canada -Structural Commentaries.” American Society of CivilEngineers.SANS 10160-3 (2011). “Basis of structural design andactions for buildings and industrial structures, Part 3:Wind actions.” South African Bureau of Standards.8


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