COMPARISON OF WIND LOAD STANDARDS. by SHRINIVAS KOLA, B.S.C.E.. A THESIS CIVIL ENGINEERING

COMPARISON OF WIND LOAD STANDARDS by SHRINIVAS KOLA, B.S.C.E.. A THESIS IN CIVIL ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN CIVIL ENGINEERING Approved December, 1995

\\^ ACKNOWLEDGMENTS I would like to thank my committee chairperson, Dr. Kishor C. Mehta, for his direction and support of this thesis. I also like to express my sincere thanks to Dr. James R. McDonald for his helpful suggestions. u

TABLE OF CONTENTS ACKNOWLEDGMENTS ii ABSTRACT vi LIST OF TABLES vii LIST OF HGURES x CHAPTER I. INTRODUCTION 1 II. NATIONAL STANDARDS 5 2.1 American Standard 7 2.2 Australian Standard 11 2.2.1 Simplified Procedure 12 2.2.2 Detailed Procedure 13 2.2.2.1 Static Analysis 13 2.2.2.2 Dynamic Analysis 15 2.3 British Standard 16 2.3.1 Standard Method 16 2.3.2 Directional Method 17 2.4 Canadian Standard 19 2.5 Summary 21 III. FORMULATION OF WIND LOAD PARAMETERS 23 3.1 Reference Wind Speed 24 3.2 Annual Probability 26 3.2.1 American Standard 30 3.2.2 Australian Standard 30 3.2.3 British Standard 31 3.2.4 Canadian Standard 31 3.3 Terrain Factor 32 3.3.1 American Standard 36 m

3.3.2 Ausualian Standard 38 3.3.3 British Standard 38 3.3.4 Canadian Standard 40 3.4 Gust Effect Factor 40 3.4.1 American Standard 42 3.4.2 Australian Standard 44 3.4.3 British Standard 44 3.4.4 Canadian Standard 45 3.5 Pressure Coefficients 46 3.5.1 American Standard 49 3.5.2 Australian Standard 50 3.5.3 British Standard 51 3.5.4 Canadian Standard 51 3.6 Summary 52 IV. CASE STUDY 54 4.1 Low Building 100 ft X 60 ft X 15 ft 57 4.2 160 ft High Building 100 ft X 200 ft X 160 ft 67 4.3 Use of Standards 84 4.3.1 American Standard 84 4.3.2 Australian Standard 85 4.3.3 British Standard 86 4.3.4 Canadian Standard 87 4.4 Summary 87 4.4.1 Low Building 88 4.4.2 160 ft High Building 88 V. LIMIT STATE LOADING 90 5.1 Low Building 93 5.2 160 ft High Building 93 VI. CONCLUSIONS 94 IV

REFERENCES 96 APPENDICES A. CALCULATIONS USING AMERICAN STANDARD 98 B. CALCULATIONS USING AUSTRALIAN STANDARD 112 C. CALCULATIONS USING BRITISH STANDARD 128 D. CALCULATIONS USING CANADIAN STANDARD 144

ABSTRACT The objective of this thesis is to compare major recognized national standards of wind loads and to determine the correlation among them. The four national standards compared are American Society of Civil Engineering Standard, ASCE 795 (ASCE 795), Australian standard, SAA Loading Code, Part 2: Wind Loads, AS 1170.21989 (SAA, 1989), British standard, Part 2, Code of Practice for Wind Loads, BS 6399, 1994 (BS 1994), and National Building Code of Canada, 1990 (NRCC 1990). The objective was accomplished by calculating wind loads on two buildings: a low building with dimensions of 100 ft x 60 ft x 15 ft and a 160 ft high building with a plan dimensions of 200 ft x 100 ft. Limit state base shear and overturning moments for the two buildings were calculated and then compared. The study shows that the four national standards give similar limit state base shear for the two specific buildings selected for the study. It is also seen that the overturning moment depends largely on the roof uplift. The roof uplift force obtained from using the four national standards vary significantly which indicates that a thorough parametric study on roof uplift loads should be conducted to assess the real loads. The design pressures on components and claddings differ between the standards by as much as 200 percent. While accomplishing the objective it was observed that the comfurtability in using any standard depicts the format of the standard in some manner. The study shows that for that the format of the American and the Canadian standards are easy to follow, while the Australian and the British standard are more difficult to use to when determining the wind loads. VI

LIST OF TABLES 2.1. Parameters and their terminology 6 2.2 Levels of approach 8 2.3 Equations used in the American standard 9 3.1 Probability of exceeding the reference wind speed during the reference period for various values of annual probability 29 3.2 Exposure categories used in the four standards 33 3.3 Gradient heights and the exponential coefficients used in the American standard 37 3.4 Roughness lengths used by the Australian standard 39 3.5 Roughness lengths used by the British standard 39 3.6 Exponential coefficients used by the Canadian standard 41 4.1 Wind load parameters used in the calculations of low building 59 4.2 Base shear, overturning moment and roof uplift for low building 64 4.3 Wind load parameters used in the calculations of 160 ft building 70 4.4 Baseshear, overturning moment and roof uplift for 160 ft building 78 5.1 Limit state base shear, overturning moments and roof uplift for low buildings 92 5.2 Limit state base shear, overturning moments and roof uplift for highrise buildings 92 A. 1 Design wind pressures and extemal pressure coefficient values for CASE A 101 vu

A.2 Design wind pressures and extemal pressure coefficient values for CASE B 102 A.3 External pressure coefficients for components and claddings 104 A.4 Design wind pressures for components and claddings 104 A.5 Velocity pressure exposure coefficients and velocity pressures 105 A.6 Design wind pressures for wind parallel and normal to 100 ft side 107 A.7 Extemal pressure coefficients for components and claddings HO A.8 Design pressures for zone l(roof middle surface), zone 2 (roof edges), and zone 3(roof corners) A.9 Design pressures for zone 4(wall middle surface) and zone 5 wall edges) HI Ill B.l Design pressures for roof 116 B.2 External pressure coefficients for components and claddings 118 B.3 Design wind pressures for components and claddings 118 B.4 Values of terrain and structure height multiplier M(z,cat). design gust wind speed Vz and velocity pressure qz 120 B.5 Design windward wall pressures 122 B.6 External pressure coefficients for components and claddings 125 B.7 Design pressures for zone l(roof middle surface), zone 2 (roof edges), and zone 3(roof comers) 126 B.8 Design pressures for zone 4(wall middle surface) and zone 5 wall edges) 126 C.l External pressure coefficients for components and claddings 133 C.2 Design pressures for components and claddings 133 C.3 External pressure coefficients for components and claddings 137 viii

C.4 Design pressures for zone l(roof middle surface), zone 2 (roof edges), and zone 3(roof corners) 138 C.5 Design pressures for zone 4(wall middle surface) and zone 5 wall edges) 138 C.6 External pressure coefficients for components and claddings 141 C.7 Design pressures for zone l(roof middle surface), zone 2 (roof edges), and zone 3(roof corners) 143 C.8 Design pressures for zone 4(wall middle surface) and zone 5 wall edges) 143 D. 1 External peak pressure coefficients and design pressures on the main windforce resisting system for wind perpendicular to ridge 147 D.2 External peak pressure coefficients and design pressures on the main windforce resisting system for wind parallel to ridge 148 D.3 Extemal peak pressure coefficients for components and claddings 150 D.4 Design pressures on components and claddings 150 D.5 Exposure factors and design pressures on the windward wall 152 D.6 External pressure coefficients for components and claddings 155 D.7 Design pressures for zone l(roof middle surface), zone 2 (roof edges), and zone 3(roof corners) 156 D.8 Design pressures for zone 4(wall middle surface) and zone 5 wall edges) 156 IX

LIST OF FIGURES 3.1 Mean wind speed vector V and turbulent wind speed vector V(t) 25 3.2 Ratio of probable maximum speed averaged over period t to that averaged over one hour (Simiu, 1986) 27 3.3 Wind speed profile 35 3.4 Typical pressure record 47 4.1 Low building 55 4.2 160 ft building 56 4.3 Stmctural system for low building 58 4.4 Design pressures on the main windforce resisting system 63 4.5 Design pressures for wall grits and roof purlins (tributary area 100 sqft) 66 4.6 Design pressures for fasteners (tributary area 5 sqft) 68 4.7 Stmctural system for 160 ft building 69 4.8 Design pressures for the main windforce resisting system, based on American standard 73 4.9 Design pressures for the main windforce resisting system based on Australian standard 74 4.10 Design pressures for the main windforce resisting system based on British standard 75 4.11 Design pressures for the main windforce resisting system based on Canadian standard 76 4.12 Design pressures for components 80 4.13 Design pressures for claddings 83 X

CHAPTER I INTRODUCTION Wind has major effects on mankind, both favorable and unfavorable. Property losses in windstorms and increased concem for human comfort have resulted in a discipline called wind engineering. "Wind engineering is best described as the rational treatment of interaction between wind in the atmospheric boundary layer and man and his works on the surface of the earth" (Cermak, 1975, p. 9). When wind interacts with a building, it produces pressures on both intemal and extemal surfaces. The magnitude of developed pressures on building surfaces depend on the characteristics of the approaching wind and the geometry of the building. These effects are incorporated into a standard in some manner, to form the wind load standard. A wind load standard guides an engineer to use proper wind load for design of a building that is exposed to the action of wind during its anticipated life. Various countries develop their own national standards for wind loads. It is recognized that wind climate in countries can be different resulting in different wind loads. However, windstmcture phenomena is invariant, hence wind loads resulting from different national standards should be the same for a given reference wind speed. The objective of this thesis is to compare major recognized national standards of wind loads and to determine the correlation among them. The four national standards selected for comparison are: (1) American Society of Civil Engineering Standard, ASCE 795 (ASCE 795),

(2) Australian Standard, SAA Loading Code, Part 2: Wind Loads, AS 1170.21989 (SAA 1989), (3) British Standard, Part 2, Code of Practice for Wind Loads, BS 6399, 1994 (BS 1994), (4) National Building Code of Canada, 1990 (NRCC 1990). The American and British standards are in the development process; latest available drafts are used for this thesis work. Since, only the four national standards are used in this thesis, specific references to each standard are not given wherever the standards are mentioned. A comparative study of the earlier editions of these four national standards was conducted by Das (1985). Since 1985, the four national standards have been significantly revised in the methodologies of calculating wind loads. The new editions of standards bring up to date the considerable advances in wind engineering. The latest American standard has adopted a 3second gust reference wind speed (earlier edition used fastest mile wind speed) and has included a topography factor. The latest Australian standard specifies wind speed for the serviceability limit state, ultimate limit state and permissible stress design. The basic wind speed in the new British standard is a mean hourly wind speed, while the previous edition used a 3second gust wind speed. These significant changes in reference wind speeds affect the approach to calculation of wind loads. The provisions in the four national standards use different terminology for similar parameters. The descriptions such as "openings in one wall" and "one wall permeable" are difficult to distinguish and interpret. The provisions of the four national standards

have to be interpreted correctly. In this thesis, the provisions are interpreted by the author to the best of his ability. No responsibihty is assumed by the author or the advising committee in interpretation of the provisions. Chapter II of the thesis deals with the description of wind load equations and parameters used by each standard in determining the design wind pressures. In describing the four national standards no effort is made to explain the equations or background of the provisions; it is beyond the scope of this thesis. The parameters which affect the design wind pressure are reference wind speed, annual probability of wind speed, height and terrain factor, gust effect factor and pressure coefficients. The four national standards consider all of these parameters. However the methods to consider these parameters to compute the design wind pressures are different. The methods and the formulation of each parameter for each of the standard are discussed in chapter HI. Since the methods are different in the four standards, it is meaningless to compare magnitudes of the parameters in the standards. The four national standards can be compared by calculating wind loads on specific buildings. In order to compare the four national standards, wind loads are calculated on two buildings: a low building with dimensions of 100 ft x 60 ft x 15 ft and a 160 ft high building with a plan dimensions of 200 ft x 100 ft. The design pressure are compared in chapter IV. The buildings are assumed to be located in a suburban area in the United States, where the 3second gust wind speed is 110 mph (49 m/s). The reference wind speeds of the British and Canadian standards are made consistent with the reference wind speed of the American standard. Since the Australian standard uses the 3second gust speed, no conversion is necessary to the reference wind

speed. The appendices contain the actual wind load calculations. Chapter V deals with the application of load factors in limit state design and compares the base shear, overtuming moment and roof uplift for the two buildings. Conclusions drawn from this study are presented in Chapter VI.

CHAPTER II NATIONAL STANDARDS "Wind load standards and codes govern design of buildings and structures to resist wind induced loads" (Mehta, 1980, p. 1305). A majority of stmctures can be designed using the prevailing standards. Wind tunnel tests are recommended for unusual structures to determine the specific wind loads. "A standard is a documentation of the stateofknowledge" (Mehta, 1980, p. 1306). Generally, consensus groups, professional societies or govemmental agencies develop the standards. The standard is used by engineers to design building frames and building components to resist wind effects. This chapter highlights equations and parameters used by the four national standards in determining the design wind pressures. The parameters which are used by the four standards for calculation of wind loads are: (1) reference wind speed, (2) a factor which accounts for variation of terrain roughness and height, (3) a factor which accounts for increase in wind speed due to local topography, (4) a factor which modifies wind speed based on the building classification category, (5) a factor which accounts for shielding effect, (6) a factor which accounts for additional loading due to wind gusts and, (7) pressure coefficients. The standards compared in the study address the above mentioned parameters. However, the methods of consideration of these parameters are different in each of the standard. These differences are examined in chapter HI. The parameters used by the four national standards and their terminology is shown in Table 2.1.

Table 2.1. Parameters and their terminology PARAMETER AMERICAN AUSTRALIAN BRITISH CANADL\N STANDARD STANDARD STANDARD STANDARD Reference wind speed at standard height in open terrain 3second gust speed at 10 m height above ground in open 3second gust speed at 10 m height in open terrain mean hourly wind speed at 10 m above ground in mean hourly wind speed at 10 m above ground in open terrain open terrain terrain terrain roughness and height factor Kz, velocity pressure coefficient M(z,cat), terrain and structure height multiplier Sb, terrain and building factor Cc, exposure factor topography factor Kzt, topography Mt, topography multiplier None None factor importance I, importance Mi, structure Sp, probability reference wind factor factor importance factor pressures multiplier based on mean recurrence interval shielding factor None Ms, shielding None None multiplier gust effect G, gust effect None None Cg, gust effect factor factor factor pressure Cp, extemal C C C c C C ' coefficient and internal extemal and extemal and extemal and pressure intemal intemal intemal coefficients pressure pressure pressure coefficients coefficients coefficients

The four national standards divide buildings and stmctures into rigid structures and flexible stmctures. Each standard formulates conditions for which a specific structure is analyzed for static or dynamic loading. The standards use different levels of approach; simple procedures, detailed procedures, and wind tunnel tests in attaining the design wind pressures. Lowrise buildings and all rigid stmctures are analyzed using a simplified procedure. Detailed procedures are used where wind loads govem the economics of structural design. Flexible buildings are analyzed using detailed procedures, which provide the designer with more accurate wind loads. Wind tunnel tests are performed on buildings and stmctures which have complex shapes. Wind tunnel tests are also recommended for monumental stmctures, where the additional design expenses are justified. Apart from the above mentioned procedures, the British standard uses a directional method to evaluate the design wind pressures on a rigid stmcture. Various levels of approaches used by the four national standards are as shown in Table 2.2. 2.1 American Standard American standard ASCE 795 classifies buildings and other structures into rigid stmctures and flexible or dynamically sensitive stmctures. Rigid stmctures are further categorized into partially enclosed, special lowrise buildings and open buildings. Rexible structures are divided into buildings and other stmctures. The equations used for the calculation of design wind pressures p (psf), and forces F (lb) for each category are listed in Table 2.3. The general and simplified equation for evaluating design wind pressures P (pso is

Table 2.2. Levels of approach LEVELS OF AMERICAN AUSTRALIAN BRITISH CANADIAN APPROACH STANDARD STANDARD STANDARD CODE Simple yes yes yes yes procedure Detailed yes yes none yes procedure wind tunnel test yes yes none yes 8

Table 2.3. Equations used in the American Standard RIGID STRUCTURES BUILDING TYPE Partially enclosed building Special lowrise buildings Open buildings and stmctures EQUATION p = qgcp qh(gcpi) p = qh [(GCpf) (GCpi)] F = qzgcfaf FLEXIBLE STRUCTURES BUILDING TYPE Building Other stmctures EQUATION p = qgfcp F = qzgfcfaf

where q: velocity pressure, P = qgcp (2.1) G: gust effect factor, Cp: pressure coefficient. The velocity pressure q is given by the equation q = 0.00256KzKztV'l (2.2) where Kz: velocity pressure exposure coefficient, Kzt: topography factor, V: basic wind speed, I: importance factor. The constant 0.00256 represents air mass density for a standard atmosphere of 0.00237 slugs/ft and constants required to convert wind speed from miles per hour to feet per second. The basic wind speed, V, is a 3second gust speed at 10 m height above ground in open terrain. Basic wind speed is associated with an annual probabihty of occurrence of 0.02 (mean recurrence interval of 50 years). The velocity pressure exposure coefficient Kz accounts for the variations of wind speed with height above ground and terrain roughness. The American standard define four exposure categories: Exposure A for a large city center. Exposure B for urban or suburban areas as well as heavily wooded areas, Exposure C for open, airport terrain, and Exposure D for wind flowing over large bodies of water. The topography factor Kzt accounts for significant variations of wind speed over an isolated hill or escarpment. Significant variations can occur due to the sudden or abrupt changes in topography surrounding the site. The topography factor is 10

applied to buildings and structures which are situated in the upper part of a hill or near the edges of escarpments. The basic wind speed map of ASCE 795 is based on the annual probability of occurrence of 0.02. To modify the basic wind speed to other probabilities, an importance factor I is used. The importance factors are based on the building and stmctural classification categories. Each building and stmctural category is associated with an unique importance factor. The gust effect factor G, accounts for the loading effect due to wind turbulence. Gust effect factors for rigid structures are 0.8 for exposure A and B, and 0.85 for exposure C and D. For flexible buildings the Commentary in the American Standard provides a rational method for calculating gust effect factors Gf. Pressure coefficients account for the variation in wind pressure on surfaces of buildings and structures. Pressure coefficients are basically divided into two categories, buildings of all height and special lowrise buildings. Combined values of pressure coefficients and gust effect factors for special lowrise building and components and claddings, are tabulated. Appropriate pressure coefficients must be used to calculate the design wind pressures. For suiictures, force coefficients Cf are provided for a limited number of shapes. 2.2 Australian Standard The Australian Standard, SAA Loading Code part 2: Wind Loads, describes two procedures, a simplified procedure and a detailed procedure, to calculate the design wind pressures. 11

2.2.1 Simphfied Procedure This procedure is applicable to buildings, which consist of a combination of rectangles in plan, with height and gross area of roof plan less than 15 m and 1000 m^, respectively. The applicability of this procedure is further restricted to buildings with roof slopes less than 30 and ratio of building height to minimum plan dimension less than 5. The design wind pressure p (kpa) is given by p = p'bib2b3b4 (2.3) where p : net basic wind pressure, B1: regional multiplying factor, B2: terrain and height multiplying factor, B3: topography multiplying factor, B4: reduction factor for roofs. The net basic wind pressure p' is obtained by combining the intemal and extemal basic pressures. Values of extemal basic wind pressure p* (standard's nomenclature for net and basic pressures) are tabulated for roofs and walls. Values of p^ are also tabulated for intemal pressures. The factor Bi depends on the geographical region in which the building is located. Four regional factors are specified in the standard: normal, intermediate, tropical cyclone, and severe tropical cyclone. The terrain and height multipher B2 accounts for the changes in height and terrain surrounding the building. The factor B3 is a topographic multiplier applied to buildings siuiated along the upper half of a hill or near the edge of a escarpment. The roof reduction factor B4 is used to reduce the wind forces on roof supporting structures with tributary area greater than 10 m^. 12

2.2.2 Detailed Procedure This procedure evaluates design wind pressures using two methods based on the sensitivity of the stmcture to wind. 2.2.2.1 Static Analysis. Static analysis is applied to buildings and stmctures which are not sensitive to wind action. The height or length to breadth ratio and the first mode of vibration to qualify a building for static analysis should be less than 5 and greater than 1 Hz, respectively. The design pressure p (kpa), for static analysis is given by the equation p = Cp.KaK,Kpqz (2.4) where Cpe: extemal pressure coefficient, Ka: Ki: Kp: qz: area reduction factor for roofs and side walls, local pressure factors for claddings, reduction factor for porous claddings, velocity pressure. The extemal pressure coefficient Cpc accounts for the variation of pressure at various locations on the building surface. Area reduction factors for roofs and side walls are a correction to the peak loads produced on large tributary areas. The local pressure factor accounts for pressures developed on small areas on various locations on the building locations. The standard recommends application of the reduction factor to porous claddings, and to the local negative pressures, when the porosity of the claddings exceeds 0.001 but is less than 0.01. The velocity pressure is given by the equation qz = 0.6 X 10'(M(z.ca.)MMM.V)' (2.5) 13

The constant 0.6 is one half the air mass density of 1.2 kg/m\ The basic wind speed V is a 3second gust wind speed at 10 m height in an open terrain. The Australian Standard divides the basic wind speed in different regions as serviceabihty limit state wind speed V^, permissible stress gust wind speed Vp and ultimate limit state gust wind speed Vu. The ultimate limit state gust wind speed and the serviceability limit state wind speeds are associated with an annual probability of occurrence of 0.001 (1000 year mean recurrence interval) and 0.05 (20 year mean recurrence interval), respectively. The permissible stress gust wind speed is associated with an annual probability of occurrence of 0.02 (50 year mean recuitence interval). The terrain and stmcture height multiplier M(z,cat) modifies the basic wind speed to account for the variation of terrain and height. Wind speed is retarded considerably due to shielding from adjacent buildings. To account for the reduction in wind speed due to obstmctions, a shielding multiplier is used. The shielding multiplier depends on the average height, breadth and distance between the buildings surrounding the site. The topographic multiplier Mt, modifies the basic wind speed for sudden changes occurring in the topography. The structure importance multiplier Mi modifies the basic wind speed based on the structural classification. The values of Mi are tabulated according to the structural classification which is, in tum, based on the importance of the stmcture, and its impact on humans in case of failure. The multiplying factors M(z.cat), Ms, Mt, and Mi, which modify the basic wind speed are the same for static and dynamic analysis. The Australian standard does not use gust effect factor in the calculation of wind loads. 14

2.2.2.2 Dynamic Analysis. Dynamic analysis is applied to buildings and suiictures which are sensitive to wind action. The conditions for the applicabihty of dynamic analysis are (i) Height or length to breadth ratio should be greater than 5 (ii) Structures should have the firstmode of frequency of vibration less than 1 Hz. In the dynamic analysis Ausualian standard calculates the net horizontal force and design peak base overtuming moment. The horizontal force acting on a building or stmcture at height z is calculated from the equation Fz=ZCpcqzAz (2.6) where Cpe: extemal pressure coefficient q^: Az: hourly mean velocity pressure the area of the structure at height z The hourly mean velocity pressure is similar to the velocity pressure discussed in static analysis, the only difference is that the basic wind speed used in the dynamic analysis is hourly mean wind speed instead of 3second gust speed used in static analysis. The summation of moments resulting from the horizontal forces gives the mean overtuming moment Ma. The design peak base overtuming moment is then calculated using the equation M, =GM3 (2.7) where M^: mean overtuming moment G: gust effect factor 15

2.3 British Standard The Part 2. Code of Practice for Wind Loads of British Standard BS6399, describes two methods for calculating the design wind pressures: a standard method and a directional method. The standard method is used to obtain a standard wind speed (standard's nomenclature), without considering wind direction. The standard effective wind speed (standard nomenclature) with standard pressure coefficients is used to evaluate the wind load for winds parallel and wind normal to the faces of the building. In the directional method the effective wind speed and direction pressure coefficients are used for different wind directions to check the critical wind loads. Velocity pressure in the standard includes windstmcture interaction parameters which makes it difficult to explain use of each of the parameter. 2.3.1 Standard Method The wind pressure p (pa) acting on the surface of a building is given by the equation p = qcpca (2.8) where q: velocity pressure, Ca: size effect factor different for extemal and internal pressures, Cp: Cpe for extemal pressure coefficient, : Cpi for internal pressure coefficient. 16

2.3.2 Directional Method The wind pressure on the extemal and intemal surface of the building is given by the equation P = qcp (2.9) where q: velocity pressure, Cp: Cpe for external pressure coefficient, : Cpi for internal pressure coefficient, the velocity pressure q is given by the equation q = 0.613(SaSbSdS..SpVb)' (2.10) where Vb: the basic wind speed, Sa: Sd: Ss: Sp: Sb: altitude factor (elevation above sea level), directional factor, seasonal factor, probabihty factor, terrain and building factor. The constant 0.613 is one half the air mass density of 1.226 kg/m^ The basic wind speed Vb used here is a hourly mean wind speed at height 10 m above flat terrain with uniform roughness at sea level. Basic wind speed is associated with an annual probability 0.02. The factors Sj, Ss, and Sp, are same for standard and directional methods. The factor Sa is employed to harmonize the basic wind speed with the elevation of site above sea level. The computation of Sa differs based on the topography considerations. For the simple procedure, if topography is considered, then Sa is taken as the larger of 17

Sa= 1+0.001 As or (2.11) Sa = 1 + O.OOIAT + 1.2\ /es (2.12) where A.s: site altitude. AT: altitude of the base of significant topography, \ /e: effective slope, s: topographic location factor, if topography is not significant then Sa= 1+0.001 As. (2.13) For the directional method, if topography is considered, Sa= 1+O.OOIAT, (2.14) and, if topography is not considered Sa = 1 + O.OOlAs. (2.15) The basic wind speed is modified by the directional factor Sd to wind speeds with same risk of exceedence in any wind direction. The east wind is taken as a wind direction < ) = 90. Directional factors for wind directions from <) = 0 to (j) = 330 are tabulated with 30 intervals. If the building position is unknown or ignored the directional factor is taken equal to 1.0 for all directions. The probabihty factor Sp is used to modify basic wind speed for probability of occurrence other than 0.02. The seasonal factor Ss is used to modify basic wind speed to wind speeds that a building experiences for a specific period, i.e., temporary works and buildings during construction. Ss is taken equal to 1.0 for permanent structures and structures exposed to wind for a period of more than six months. Sb is the terrain and building factor which accounts for the effective height, the 18

distance of the site from the sea and the site terrain category. Sb is calculated differently for standard method and directional method. In the directional method, a gust peak factor gt is introduced in the calculation of terrain and building factors, which give the appropriate gust speed for structure or its component that produce the maximum loading. Ca is the size effect factor, which accounts for the influence of the wind gusts operating at different time intervals across an extemal surface and for the response of intemal pressures. The size effect factor used in the standard method is determined assuming a gust peak factor gt = 3.44. The factor C, depends on the exposure of the site and the diagonal dimension of the loaded area. Pressure coefficients, which account for the shape and form of the building, depend on the method used to calculate wind loads. It is evident from the above discussion that the British standard is difficult to describe and is just as difficult to interpret. 2.4 Canadian Standard In the Canadian standard the design wind pressure p (kpa) is given by the equation: p = qcecgcp (2.16) where q = reference velocity pressure, Cc = exposure factor, Cg = gust effect factor, Cp = external pressure coefficient. The National Building Code of Canada refers to three different procedures for calculating wind loads on buildings and stmctures. The first procedure is a simplified 19

procedure used for low and medium rise buildings. The second method is a detailed procedure, which is apphcable to tall buildings and slender suiictures. The third procedure is an experimental method or wind tunnel test used for complex shaped buildings, where the details of dynamic response of the stmcture are essential. The reference wind pressure, q, is given by q = 0.5pV^ where V is the reference wind speed and p is the air density. The reference wind speed is a mean houriy wind speed at 10 m above ground in open terrain. The air mass density p is taken as 1.229 kg/m^ The Canadian standard tabulates reference wind pressure q, for three annual probabilities of 0.1,0.033, and 0.01 for specific Canadian locations. The exposure factor Ce accounts for changes in wind speed and height. The exposure factor also takes into account the variations in terrain roughness and topography. In the simple procedure, there is only one value of exposure factor for one reference height and for any terrain roughness. For lowrise buildings reference height is taken as the mean height of the roof or 6m, whichever is greater. For windward walls of tall buildings, the reference height is taken as the total height of the building and for leeward wall the reference height is taken as half the height of the building. In the detailed procedure three exposure categories are specified, which depend on the terrain roughness. The gust effect factor, Cg accounts for the additional load due to the wind gusts and the dynamic properties of the structure. In the simple procedure, Cg is taken as 2.5 for cladding elements and 2.0 for the entire building system. Gust effect factor for the detailed procedure of flexible buildings is evaluated using a technique given in the "Supplement to the National Building Code of Canada, 1990" (NRCC, supplement 1990). The pressure 20

coefficient Cp, accounts for the pressure variations on the surface due to the variation of in shape, direction of wind and wind velocity profile. Values of pressure coefficients for various building shapes are tabulated in the "Supplement to the National Building Code of Canada, 1990" (NRCC, supplement 1990). 2.5 Summary For calculating wind loads the four standards compared in the study consider the parameters reference wind speed, terrain roughness, height above ground, topography factor, gust effect factor and pressure coefficients. In addition to these parameters, Australian standard uses a shielding factor. The American, Australian and Canadian standards specify provisions to obtain wind loads for rigid and flexible buildings. The British standard provides procedures to analyze rigid buildings only. The design pressure equation (2.4) indicates that the Australian standard uses area reduction factor K,, local pressure factor Ki and reduction factor for porous claddings Kp. In order to apply these factors effectively the designer should know the details of the component tributary areas and the porosity of the cladding elements. For calculating the terrain and stmcture height multiplier, the designer should know the terrain conditions within a 2500 m radius from the site, and the wind speed with respect to each direction (northeast, east, southeast, etc.). In addition, for calculating the shielding multiplier Ms the designer should know the average height, breadth, and distance between the buildings surrounding the site. The interpretation and application of these factors is a time consuming process. 21

From the description of British standard (section 2.3), it is evident that the standard includes a windstmcture interaction parameter (factor accounting for elevation of site above sea level) in the velocity pressure. The determination of altitude factor requires the knowledge of the topography surrounding the site. 22

CHAPTER III FORMULATION OF WIND LOAD PARAMETERS The study of the equations and parameters involved in determining the wind pressures in Chapter II indicates that all standards take into account the surrounding terrain, the variation of pressure coefficients at different locations on the building surface, and the effect of sudden changes in topography. It is also seen in Chapter II that the reference wind speed used by the American and Australian standards is a 3second gust wind speed while the reference wind speed used by the British and Canadian standards is a mean hourly wind speed. Even though the American standard uses 3second gust speed the standard applies a gust effect factor (see section 3.4.1) and though the British standard uses mean hourly wind speed the standard does not use gust effect factor (see section 3.4.3). One more parameter worth mentioning is the use of importance factor. The American standard and British standard change wind speeds to probabilities of occurrence other than the common annual probability of 0.02 (50 year mean recurrence interval) by using importance factor and probability factor, respectively. However Canadian standard does not use an importance factor; it specifies wind speeds associated with different annual probabilities of occurrence. The stmctural importance multiplier of the Austrahan standard does not change the annual probabilities of occurrence, since the basic wind speed is itself formulated to account for specific annual probabilities, depending on the designing method. To understand these differences, it is important to review the formulation of these wind load parameters. In the following sections the critical 23

parameters used in the four standards are reviewed. Detail study of each of the parameter is beyond the scope of this thesis. The common parameters which are used in four standards are 1. reference wind speed, 2. probability of occurrence associated with the reference wind speed, 3. height and terrain factor, 4. gust effect factor, 5. pressure coefficients. In addition to these parameters, the Australian standard uses a factor known as shielding factor. As the name implies it accounts for the reduction in wind speed caused by upwind buildings. The shielding factor depends on the height, number of buildings, and the spacing between the buildings in the 45 sector of radius 20h (h is the height of the building being shielded) upwind of the building being shielded. 3.1 Reference Wind Speed Wind speed is measured at an established base plane of reference. The plane of reference for the four standards is wind speed measured at 10 m height above ground in an open terrain. A typical record of the horizontal wind speed measured by a wind measuring instrument is shown in Figure 3.1. Figure 3.1 describes the wind speed at a given point as a function of time. The wind speed recorded can be considered as having a mean component and a fluctuating component. 24

o o oo o o o 6 o o o IT) o 6 o ^ E c E D r; r5 >^ ~D 'J c ;/. N; D o o ro O 6 o N o 6 o»" o d r.4_, c TJ ^^ ^. rs 'J H ^ C". u Ui CO (JU paods puim p.^.^ils pul/^ 25

The American and the Australian standards use 3second wind speed as the reference wind speed. The 3second gust wind speed, which is the peak wind speed is assumed to be averaged over a period of 3seconds, because of the limitations of the response of the anemometer. The 3second gust wind speed is assumed to include the fluctuating component of wind speed. The Canadian standard and the British standard use mean hourly wind speed as the reference wind speed. Mean hourly wind speed is defined as the wind speed averaged over one hour. Mean wind speed is the value of a wind speed recorded over some time interval, hence mean wind speed depends on the averaging time. Mean wind speed increases with the decrease in length of averaging interval. For open terrain conditions Durst (1960), proposed a curve (Figure 3.2) based on the statistical studies, which permits the transformation of wind speed from one averaging time to another. The curve in Figure 3.2 relates the ratio of wind speed (Vt) averaged over t seconds to mean hourly wind speed (V) versus the averaging time (t). 3.2 Annual Probability Basic wind speed is defined as the wind speed corresponding to a specified mean recurrence interval of the cumulative distribution function. The cumulative distribution function of annual maxima, when fitted to Fisher Tippett Type I extreme value disu"ibutions, gives a relationship between wind speed and annual probability of being exceeded. The relationship is V = X + [ln[ln(lpj]] (3.3) a^ 26

1.7 I I II!I]I 1 I I lll l 1 I I lllll 1 I I I Mil 1.6 1.5 1.4 > > 1.3 1.2 1.1 1.0 I I 1 iiini 1 i I mill I I I mil 10 100 1000 / (sec) llahi 10.000 Figure 3.2. Ratio of probable maximum speed averaged over period t to that averaged over one hour (Simiu, 1986). Note: V,: Wind speed averaged over l.seconds V: Mean hourly wind speed t: averaging lime 27

where V: wind speed, X: mode. Pa: annual probabihty, : dispersion, a The four standards use the Fisher Tippett Type I distribution to model the wind speeds. Let Pa be the annual probability of the extreme wind speed V at some given location. Then the probability p that the wind speed V will not occur once in n years ( n trials) is (1 Pa)". The probabihty that the wind speed V will occur once in n trials is Pn=l(1Pa)". (3.4) If the random variable N represents the number of years in which the wind speed V occurs for the first time, then the expected value or the mean recurrence interval of N is equal to 1 / Pa. Hence a wind speed with an annual probability of 0.01 corresponds to mean recurrence interval of 100 years. The value of probability Pn exceeding the reference wind speed are tabulated in Table 3.1 with respect to reference periods. A reference period is the period of time the stmcture is exposed to wind. Table 3.1 indicates that the probability that a wind speed of given magnitude will be equaled or exceeded increases with increase in reference period. The annual probabihties used by the four standards are discussed below. 28

Table 3.1. Probability of Exceeding the Reference Wind Speed During the Reference Period for Various Values of Annual Probabihty Annual Reference Periods, Years Probability Pa 1 5 10 25 50 100 0.04 0.04 0.18 0.34 0.64 0.87 0.98 0.02 0.02 0.10 0.18 0.40 0.64 0.87 0.01 0.01 0.05 0.10 0.22 0.40 0.64 0.005 0.005 0.02 0.05 0.10 0.22 0.39 0.001 0.001 0.005 0.01 0.02 0.05 0.10 29

3.2.1. American Standard The basic wind speed map of the American standard gives 3second gust wind speeds associated with an annual probability of 0.02. To modify the wind speed to other annual probability of occurrences, consistent with the building classification category, an importance factor I is used. The American standard modifies wind speed to mean recurrence intervals other than 50 years based on building and stmcture classification categories. For normal stmctures like the buildings associated with the Case Study, mean recurrence interval of 50 years is used. A mean recurrence interval of 100 years is used for important buildings and stmctures which have special postdisaster functions. For unoccupied buildings mean recurrence interval of 25 years may be used. 3.2.2. Australian Standard The Australian standard provides the designer with the ultimate hmit state gust speed, Vu, permissible stress gust wind speed, Vp and serviceabihty hmit state wind speed, Vs through the basic wind speed map. The ultimate limit state gust wind speed Vu has 0.05 probabihty of being exceeded in a 50 year reference period, which correspond to annual probability of occurrence of 0.001 (1000 year mean recurrence interval). The serviceabihty hmit state wind speed Vs is associated with an annual probability of 0.05 ( 20 year mean recurrence interval). The permissible stress gust wind speed Vp is similar to the basic wind speed used by American standard and is associated with an annual probability of 0.02 (50 year mean recurrence interval). Unlike the American standard, the Australian standard does not modify the basic wind speed based on suuctural classification category. 30

3.2.3. British Standard The British standard also gives basic wind speeds associated with an annual probability of exceedence of 0.02. To change the basic wind speed to other annual probabilities, the basic wind speed Vb is multiplied by a probabihty factor Sp. Probability factor is obtained by using the following expression ^ [5ln[ln(lQ)]] ' ^[5ln[ln(0.98)]] ^^'^^ where Q is the desired annual probability of occurrence. The above equation is deduced from the FisherTipett Type I model for dynamic pressures that has mode / dispersion ratio equal to 5. The probability factor modifies the basic wind speed to account for the design method (limit state or working suess) used. For ultimate limit state a probabihty factor of Sp = 1.18 (annual probability of 5.7 x 10"^) corresponding to mean recurrence interval of 1754 years is used. Bridges and nuclear installations are designed with annual probabilities of 0.0083 (120 year mean recurrence interval) and 10"* (10000 year mean recurrence interval), respectively. For standard design, a probability factor of 1.0 is used. 3.2.4. Canadian Standard The Canadian standard specifies velocity pressures based on annual probabilities of 0.1, 0.033 and 0.01. For the design of components and cladding the standard requires velocity pressures with an annual probability of occurrence of 0.1 (10 year mean recurrence interval). The design of building structural members are based on an annual probabihty of occurrence of 0.033 (30 year mean recurrence interval). Important structures such as 31

buildings which have special postdisaster functions, are designed with an annual probability of 0.01 (100 year mean recurrence interval). The Canadian standard does not provide an importance factor like the American and British standards for changing the velocity pressures to an altemate annual probabihty of occurrence. 3.3 Terrain Factor The wind moving over the ground surface experiences retarding forces due to the ground surface roughness. The layer of air experiencing retardation is referred to as the boundary layer. The wind speed increases from zero at the ground surface to its maximum value, at the gradient height Zg of the boundary layer. The depth or height of the boundary layer depends on the wind intensity, roughness of terrain, and angle of latitude. The wind speed at the top of the boundary layer is referred to as the gradient speed. Above the gradient height the effect of ground roughness is negligible. When determining the wind loads, the frictional force retarding the wind speed near the ground surface is accounted by an exposure coefficient. The change in wind speed due to large natural features of earth such as hills and valleys is accounted for by a topography factor. All four standards define exposure categories based on the surface roughness. The exposure coefficients used in the four standards are defined as the velocity pressure coefficient in the American standard Kz, the terrain and stmcture height multiplier M(z.cat) in the Australian standard, the terrain and building factor Sb in the British standard and the exposure factor Cc in the Canadian standard. The exposure categories used in the four standards are tabulated in Table 3.2. 32

Table 3.2. Exposure categories used in the four standards Exposure Description large city centers American Standard Exposure A Australian Standard Category 4 British Standard Town Terrain Canadian Standard Exposure C urban and suburban areas Exposure B Category 3 Town Terrain Exposure B open terrain Exposure C Category 2 Country Terrain Exposure A wind flowing over water Exposure D Category 1 Sea bodies 33

The variation in wind speed with height, known as a wind speed profile (Figure 3.3 ), can be represented by the logarithmic law or the power law equation. Logarithmic law: 1 z V, =UJn k z (3.6) where Vz: wind speed at height z, Z(,: roughness length, U*: frictional velocity. constant. Power law: V = V * zl ^ i2 _ 2 _ or (3.7) z zg 7^ Z (3.8) where V zg gradient wind speed, height above ground, ^g a Vz gradient height, wind speed at any height Z, exponential coefficient. Meteorologists consider the logarithmic law as the superior representation of wind profiles in the lower atmosphere (Simiu, 1986), but for engineering purposes the power law is used without significant eitor. Davenport (1965) assumed that the power law holds 34

Wind speed Figure 3.3. Wind speed profile 35

with constant exponent a up to the gradient height Zg. The gradient height and the exponential coefficient depend on terrain roughness. Reference wind speeds are usually measured at the airport locations in open terrain. This exposure category is taken as the reference exposure category. The reference exposure categories in the four standards are Exposure C (American standard). Category 2 (Australian standard). Country Terrain (British standard) and Exposure A (Canadian standard). The wind speed at any height and for any exposure category can be determined using equations (3.6), (3.7), or (3.8). 3.3.1. American Standard The velocity pressure exposure coefficient Kz in the American standard is based on the power law. f^, V r ( 900^19.5 ^ v33y V^sy K:Z = V^33y = 2.01 ^Z^ vz.y for 15 ft <Z<Zc /^N0.21 I for open exposure (a = 7) U3. (3.9) K, = 2.01 for Z < 15 ft (3.10) The values of gradient height Zg and the exponential coefficient a used by the American standard are tabulated in Table 3.3. 36

Table 3.3. Gradient heights and the exponential coefficients used in the American standard Terrain Description Exposure Exponential Gradient Category coefficient, a height, Zg (m) large city centers A 5.0 1500 urban and suburban areas B 7.0 1200 open terrain C 9.5 900 wind flowing over water bodies D 11.5 700 37