# Performance-based serviceability design optimization of wind sensitive tall buildings

vi Table of Contents Title…………… ........................................................................................................... i Authorization…. ........................................................................................................ ii Signature……… ....................................................................................................... iii Acknowledgement ..................................................................................................... iv

Table of Contents ...................................................................................................... vi

Nomenclature…......................................................................................................... xi

List of Figures… .................................................................................................... xvii

List of Tables… ....................................................................................................... xxi

Abstract………. .................................................................................................... xxiii

CHAPTER 1 Introduction ...................................................................................... 1

1.1 Background ......................................................................................................... 1

1.2 Scope and objectives ........................................................................................... 4

1.3 Major challenges of the research......................................................................... 6

1.4 Thesis organization ............................................................................................. 9

1.5 List of Publications ........................................................................................... 12

CHAPTER 2 Literature Review........................................................................... 16

2.1 Performance-based engineering and design ...................................................... 16

2.1.1 Performance-based seismic design (PBSD) ........................................... 16

2.1.2 Performance-based wind resistant design (PBWD) ............................... 18

2.1.3 Prediction of typhoon risk ...................................................................... 21

2.1.4

Uncertainty modeling in wind engineering ............................................ 26

2.2 Dynamic response analysis of wind-excited building systems ......................... 29

2.2.1 Analysis method in time domain ............................................................ 29

2.2.2 Analysis method in frequency domain ................................................... 37

vii 2.3 Structural design optimization .......................................................................... 45

2.3.1 Classical optimization method ............................................................... 45

2.3.2 Formulations for structural optimization ............................................... 48

2.3.3

Dynamic response optimization ............................................................. 52

2.4 Reliability-based design optimization ............................................................... 59

2.4.1 Reliability analysis method .................................................................... 59

2.4.2 Reliability index optimization approach ................................................ 66

2.4.3 Performance measure optimization approach ........................................ 68

2.5 Summary ........................................................................................................... 69

CHAPTER 3 Coupled Dynamic Analysis of Wind-excited Tall Buildings ...... 75

3.1 Introduction ....................................................................................................... 75

3.2 Analysis of wind-induced coupled response ..................................................... 78

3.2.1 Equations of motion ............................................................................... 78

3.2.2 Vibration analysis in frequency domain ................................................ 80

3.3 Estimation of intermodal correlation coefficient .............................................. 86

3.4 Illustrative example ........................................................................................... 94

3.5 Summary ......................................................................................................... 101

CHAPTER 4 Wind Load Updating and Drift Design Optimization of Tall Buildings ...................................................................................... 109

4.1 Introduction ..................................................................................................... 109

4.2 Determination of equivalent static wind loads ................................................ 113

4.3 Dependence of wind-induced loads on natural frequency .............................. 120

4.4 Design optimization ........................................................................................ 123

4.4.1 Formulation of lateral drift design problem ......................................... 123

4.4.2 Optimality Criteria method .................................................................. 126

4.4.3

Procedure of design optimization ......................................................... 129

4.5 Illustrative example ......................................................................................... 131

viii 4.5.1 Example 4-1: A 45-story CAARC building ......................................... 131

4.5.2 Example 4-2: A 40-story public housing building ............................... 137

4.6

Summary ......................................................................................................... 143

CHAPTER 5 Wind-induced Drift and Acceleration Performance Optimization of Tall Buildings .......................................................................... 160

5.1 Introduction ..................................................................................................... 160

5.2 Probabilistic analysis of performance-based design wind speed .................... 165

5.2.1 Estimation of design wind speed .......................................................... 165

5.2.2 Uncertainties in the estimation of design wind speeds ........................ 166

5.3 Dynamic response analysis of wind-induced motion...................................... 168

5.4 Acceleration response and occupant comfort criteria ..................................... 174

5.5 Wind-induced performance-based design optimization.................................. 177

5.6 Explicit formulation of acceleration constraints ............................................. 180

5.7 Illustrative example ......................................................................................... 185

5.7.1 The 60-story benchmark building with 4-story height outriggers ....... 186

5.7.2 Site-specific Design Wind Speed Estimation ...................................... 188

5.7.3 Results and discussion .......................................................................... 190

5.8 Summary ......................................................................................................... 194

CHAPTER 6 Peak Response Statistics and Time-variant Reliability Analysis ....................................................................................................... 205

6.1 Introduction ..................................................................................................... 205

6.2 First-passage probability: Poisson models ...................................................... 208

6.2.1 Mean level-crossing rate of stationary random process ....................... 208

6.2.2 Extreme value distribution and probabilistic peak factor..................... 215

6.3 Asymptotic theory of statistical extremes ....................................................... 219

6.3.1 Analytical peak distribution for stationary random process................. 219

6.3.2 Asymptotic extreme value distribution and expected peak factor ....... 226

6.3.3 Time-variant reliability of a scalar response process ........................... 236

ix 6.4 Application: The expected largest wind-induced response of tall buildings .. 239

6.4.1 Wind-induced time history analysis for the 60-story benchmark building and the 45-story CAARC building ....................................................... 239

6.4.2 Results and discussion for peak factors ............................................... 240

6.4.3 Results and discussion for the expected largest component acceleration response ................................................................................................ 243

6.4.4 Results and discussion for the expected largest resultant acceleration response ................................................................................................ 244

6.5 Summary ......................................................................................................... 246

CHAPTER 7 Time History Analysis and Optimal Drift Design of Tall Buildings under Random Wind Excitation ................................................ 258

7.1 Introduction ..................................................................................................... 258

7.2 Wind-induced response analysis in time domain ............................................ 259

7.3 Time-variant reliability approximation and probabilistic constraints for dynamic response optimization ....................................................................... 261

7.4 Dynamic Response Optimization .................................................................... 266

7.4.1 Formulation of dynamic response optimization ................................... 266

7.4.2 Treatment and explicit formulation of time-dependent drift constraints….. ...................................................................................... 268

7.5 Optimality criteria method and design procedure ........................................... 271

7.6 Illustrative example ......................................................................................... 273

7.7 Summary ......................................................................................................... 278

CHAPTER 8 Reliability Performance-based Design Optimization of Wind-excited Tall Buildings ....................................................... 291

8.1 Introduction ..................................................................................................... 291

8.2 Occupant perception performance function .................................................... 292

8.3 Uncertainties in occupant comfort design problems ....................................... 295

8.4 Reliability Performance-based Design Optimization...................................... 298

8.4.1 Formulations of reliability-based structural optimization .................... 298

8.4.2 Decoupling of stiffness optimization and probabilistic constraints ..... 300

x 8.4.3 Reliability index approach and inverse reliability method .................. 303

8.4.4 The stiffness design optimization subject to frequency and drift constraints ............................................................................................ 309

8.4.5 Procedure of reliability performance-based design optimization ........ 311

8.5 Illustrative example ......................................................................................... 313

8.6 Summary ......................................................................................................... 316

CHAPTER 9 Conclusions and Recommendations ........................................... 323

9.1 Conclusions ..................................................................................................... 323

9.2 Recommendations for future work.................................................................. 331

Reference……… ..................................................................................................... 339

xi Nomenclature Latin letters

ˆ a Peak resultant acceleration A i Axial cross sectional area of a structural member b Given boundary level for a particular process B The building width normal to the approaching wind direction B i Breadth of rectangular concrete frame element d U The allowable displacement or interstory drift ratio limit D i Depth dimension of rectangular concrete frame element D f The failure domain D s The safe domain D(·) Mathematical standard deviation operator e ij strain energy coefficient E The axial elastic material modulus E(·) Mathematical expectation operator f Frequency f j Modal frequency of a building structure f(·) A general function Probability density function F Cumulative probability distribution function F External force vector g Peak factor g f Davenport peak factor g e The equivalent peak factor g j Design constraints Performance limit-state functions g p The probabilistic peak factor g W The Weibull peak factor g G The Gamma peak factor G The shear elastic material modulus G j Performance limit-state functions in the standard normal space

xii h(t) The unit impulse response function h k (x) The equality constraints H The building height H j The mechanical admittance function for j-th modal vibration I Moments of inertia of a cross-section J x_u Jacobian matrix of all first-order derivatives of a vector-valued function k j The j-th modal stiffness of a building K Stiffness matrix of a building system L(·) Lagrangian function m(·) Moment function m j The j-th modal mass of a building m(·) Moment vector function M Mass matrix of a building system N Number of crossing events p A specific probability value Distribution parameters of random variables P{·} Probability of a given event q Bandwidth parameter of a random process q j The j-th Modal displacement Q j The j-th Mode generalized force r jk Intermodal correlation coefficient n R Vector space of n-dimension R(·) The correlation function of a random process S M Base moment response spectrum S Q Modal force spectrum t Time parameter i t Thickness of concrete shear wall element T b The first-passage time T R (·) The Rosenblatt transformation u The fluctuating component of wind speed The modal wind speed in a Gumbel distribution u n The characteristic largest peak response value

xiii u Displacement response vector The standard normal vector * u The most probable failure point u(·) The unit step function U The mean component of wind speed v The value of wind speed v b The mean our-crossing rate (level-crossing rate) of a random process from the level b V The annual largest wind speed V R The design wind speed corresponding to a R-year return period x Random vector describing system uncertainties X X-component displacement response vector Y(t) A random response process Y m Peak value of Y(t) Y n Extreme peak value of Y(t) Y Y-component displacement response vector z i Generic element sizing design variables z j j-th component of state space vector Z L i z The lower element sizing bounds for a sizing variable U i z The upper element sizing bounds for a sizing variable Z State space vector

Greek letters

α j Regression constant for the j-th modal force spetrum S Q

β Reliability index in the FORM β j Regression constant for the j-th modal force spetrum S Q

Reliability index related to the occupant comfort performance function of the j-th modal vibration β n A dispersion measure of the distribution of extreme peak response J The Euler constant G (·) Dirac delta function H Bandwith parameter of a random process

xiv I Mode shape N Shape parameter of the Weibull peak distribution j O The Lagrangian multiplier for the j-th design constraint m O m-th order spectral moments of a random process P Mean value of a random variable or a stationary random process j [ Modal damping ratio U Scale parameter of the Weibull peak distribution jk U CQC combination factor V Standard deviation or root mean square (RMS) of a random variable or a stationary random process W Time duration

) Standard normal cumulative distribution function ) ) Mode sha pe matrix of a building system M The joint action factor Y Circular frequency

Other mathematical operation

erf(·) The error function Gradient of a scalar function Euclidean norm 1 N i

Union of N events 1 N i

Intersection of N events * Complex conjugate operator

Abbreviations

3D Three-dimensional ABL Atmospheric boundary layer CA Combined approximation

xv CAARC Commonwealth Advisory Aeronautical Research Council CFD Computational fluid dynamics CMD Computational molecular dynamics CDF Cumulative distribution function CQC Complete quadratic combination ESWLs Equivalent static wind loads EPSD Evolutionary power spectral density FEM Finite element method FORM First-order reliability method FPK Fokker-Planck-Kolmogorov equation GA Genetic algorithm GC Gaussian closure HFFB High-frequency force balance HLRF Hasofer-Lind-Rackwitz-Fiessler algorithm KKT Karush-Kuhn-Tucker necessary conditions LCR Level-crossing rate MCS Monte Carlo simulation MDOF Multi-degree-of-freedom MM5 The 5 th generation of Mesoscale wind climate model MP Mathematical programming MPEC Mathematical programming with equilibrium constraint MPFP Most probable failure point OC Optimality criteria ODEs Ordinary differential equations PBSD Performance-based seismic design PBWD Performance-based wind resistant design PDEs Prtial differential equations PDF Probability density function POT Peak over threshold PSD Power spectral density RBDO Reliability-based design optimization RMS Root-mean-square SDF Single-degree-of-freedom

xvi SL Stochastic linearization SMPSS Synchronous multi-pressure scanning system SORM Second-order reliability method SRSS The square root of sum of square combination XPSD Cross power spectra density

xvii List of Figures Figure 2.1 National earthquake related losses in United States .............................. 73

Figure 2.2 Classification of the dynamic analysis problems of structural systems 73

Figure 2.3 Spectrum of horizontal gustiness ........................................................... 74

Figure 3.1 The traditional CQC factor jk U and the imaginary CQC factor ( )I jk U ..... 104 Figure 3.2 A 60-story hybrid building with 2-story height outriggers .................. 104

Figure 3.3 Power spectral densities of modal forces for the 60-story hybrid under 0 degree wind .............................................................................................................. 105

Figure 3.4 Power spectral densities of modal forces for the 60-story hybrid under 90 degree wind ......................................................................................................... 105

Figure 3.5 3D mode shapes of the 60-story hybrid building................................. 106

Figure 3.6 Intermodal correlations due to the 0 degree wind ............................... 107

Figure 3.7 Intermodal correlations due to the 90 degree wind ............................. 108

Figure 4.1 Wind load spectra of typical square and rectangular tall buildings: (a) alongwind base moment spectra; (b) crosswind base moment spectra; (c) base torque spectra; (d) building cross-sections .......................................................................... 147 Figure 4.2 The wind loads spectra with initial reduced frequency f A and critical reduced frequency f C ................................................................................................ 148

Figure 4.3 Resultant drift at j-th story d j ............................................................... 148

Figure 4.4 Flow chart of integrated design optimization process ......................... 149

Figure 4.5 A 45-story steel framework example ................................................... 150

Figure 4.6 History of the structure weight for the 45-story framework: (a) Wind drift design for Case A; (b) Wind drift design for Case B ....................................... 151

Figure 4.7 History of the alongwind and crosswind base shear for the 45-story framework: (a) utilizing case A initial element sizes; (b) utilizing case B initial element sizes ............................................................................................................ 152

Figure 4.8 History of the base torque for the 45-story framework: (a) utilizing case A initial element sizes; (b) utilizing case B initial element sizes ............................. 153

Figure 4.9 Lateral deflection profile for the 45-story framework: (a) Case A; (b) Case B ...................................................................................................................... 154

xviii Figure 4.10 Interstory drift ratio profile for the 45-story framework: (a) Case A; (b) Case B ...................................................................................................................... 155

Figure 4.11 The 3D view of the 40-story public housing building ....................... 156

Figure 4.12 Typical floor layout plan of with variable shear wall elements of the 40-story public housing building ............................................................................. 156

Figure 4.13 Wind-induced modal force spectra for the 40-story building ............ 157

Figure 4.14 3D mode shapes of the 40-story public housing building ................. 158

Figure 4.15 History of the normalized structure cost for the building .................. 158

Figure 4.16 Lateral deflection profiles at the center and the corner of the building before and after optimization ................................................................................... 159

Figure 5.1 The flow chart of performance-based design optimization of wind sensitive tall buildings .............................................................................................. 199 Figure 5.2 A 60-story benchmark building with 4-story height outriggers .......... 200

Figure 5.3 Coupled 3D mode shapes of the 60-story benchmark building ........... 200

Figure 5.4 Power spectral densities of modal forces of the 60-story benchmark building: (a) 0-degree wind; (b) 90-degree wind ..................................................... 201

Figure 5.5 Design hourly-mean wind speed at the height of 90 m in Hong Kong area (1953-2006) ...................................................................................................... 202

Figure 5.6 The uncertainty in estimation of design wind speeds for 50-year return period........................................................................................................................ 202

Figure 5.7 Design histories of the normalized structure cost of the 60-story building .................................................................................................................... 203

Figure 5.8 Lateral deflection profiles of the 60-story building for case 4 .......... 203

Figure 5.9 Interstory drift ratio profiles of the 60-story building for case 4 ....... 204

Figure 6.1 Peak factors .......................................................................................... 250 Figure 6.2 The PDFs of peaks of Gaussian processes with various bandwidth values........................................................................................................................ 250

Figure 6.3 The PDFs of peaks and the intermediate peak variable for a Rayleigh process ...................................................................................................................... 251

Figure 6.4 The relationship of Davenport’s peak factor to reliability index for the Rayleigh peak distribution ....................................................................................... 251

Figure 6.5 Time histories of 3D wind forces at the top level of the 60-story benchmark building under 90-degree wind: (a) Alongwind force; (b) Crosswind

xix force; (c) Torsional moment..................................................................................... 252

Figure 6.6 Acceleration time histories at the top corner of the 60-story benchmark building under 90-dgree wind: (a) X-component acceleration; (b) Y-component acceleration; (c) Resultant acceleration ................................................................... 253

Figure 6.7 Acceleration histograms of the 60-story building: (a) X-component acceleration; (b) Y-component acceleration; (c) Resultant acceleration ................. 254

Figure 6.8 Fit of the Weibull distribution to peak acceleration responses of the 60-story benchmark building: (a) X-component acceleration; (b) Y-component acceleration; (c) Resultant acceleration ................................................................... 255

Figure 6.9 The Weibull Peak factors and Gamma peak factors for component and resultant accelerations of the 60-story building ....................................................... 256

Figure 6.10 The Weibull distributions of component and resultant accelerations of the 60-story building ................................................................................................ 256

Figure 6.11 Power spectral density curves of acceleration responses for the 60-story benchmark building under 90-degree wind ............................................... 257

Figure 7.1 Possible treatments of a dynamic constraint: (a) Worst-case design optimization; (b) Constraints at grid points adjacent to maximum points ............... 283 Figure 7.2 Flow chart of probabilistic dynamic response optimization ................ 284

Figure 7.3 Locations of pressure taps of the CAARC building ............................ 285

Figure 7.4 Time histories of 3D wind forces at the top level (Layer 6) of the CAARC building: (a) Alongwind force; (b) Crosswind force; (c) Torsional moment .................................................................................................................................. 286

Figure 7.5 Lateral deflection profile for the 45-story CAARC building at the critical time instant ................................................................................................... 287

Figure 7.6 Interstory drift ratio profile for the 45-story CAARC building at the critical time instant ................................................................................................... 287

Figure 7.7 Design history of structure cost for the 45-story CAARC building .... 288

Figure 7.8 Time histories of drift response of the initial 45-story building: (a) Overall top drift ratio; (b) Critical interstory drift ratio at the 29 th story ................. 289

Figure 7.9 Time histories of drift response of the optimized 45-story building: (a) Overall top deflection ratio; (b) Critical interstory drift ratio at the 13 th story ........ 290

Figure 8.1 Two-loop nested configuration of reliability-based structural optimization ............................................................................................................. 320 Figure 8.2 Flow chart of reliability performance-based design optimization process .................................................................................................................................. 321

xx Figure 8.3 Design history of structure cost for the sub-problem 2 of the 60-story benchmark building .................................................................................................. 322

Figure 8.4 Design history of modal frequencies for the sub-problem 2 of the 60-story benchmark Building ................................................................................... 322

xxi List of Tables Table 2.1 Recommended performance-based wind engineering design level ........ 72

Table 3.1 Modal RMS acceleration response of the 60-story hybrid building ..... 103

Table 3.2 Intermodal correlation coefficients for the 60-story hybrid building ... 103

Table 3.3 RMS acceleration response at the top of the 60-story hybrid building . 103

Table 4.1 Initial member sizes of Cases A and B for the 45-story framework ..... 145

Table 4.2 Breakdown of wind-induced structural loads for the framework ......... 145

Table 4.3 Initial wind-induced structural loads for the 45-story framework ........ 145

Table 4.4 Breakdown of maximum wind loads for the 40-story building before optimization ............................................................................................................. 145

Table 4.5 Wind-induced base shears and base moments of the 40-story building before and after optimization ................................................................................... 146

Table 4.6 Original and optimized thickness of variable shear walls ..................... 146

Table 5.1 Initial member sizes for the 60-story benchmark building ................... 196

Table 5.2 Design wind speed at the height of 90 m in Hong Kong area .............. 196

Table 5.3 Modal acceleration and peak resultant acceleration responses of the 60-story building before optimization ...................................................................... 197

Table 5.4 Modal acceleration and peak resultant acceleration responses of the 60-story building after optimization ........................................................................ 197

Table 5.5 Modal frequencies for the optimized 60-story benchmark buildings with different optimization cases ..................................................................................... 198

Table 6.1 Component accelerations at the top corner of the 60-story building under 90-degree wind ......................................................................................................... 249

Table 6.2 Acceleration responses at the top corner of the 60-story building and the 45-story CAARC building ....................................................................................... 249

Table 6.3 Peak factors and reliability index for resultant acceleration responses of the two buildings ...................................................................................................... 249

Table 7.1 Design history of top deflection and critical interstory drift responses for the 45-story CAARC building ................................................................................. 281

xxii Table 7.2 Design history of top deflection performance of the CAARC building 281

Table 7.3 Design history of critical interstory drift performance of the CAARC building .................................................................................................................... 282

Table 8.1 Random variables in wind-induced occupant comfort problem ........... 318

Table 8.2 Performance-based wind hazard design level ....................................... 318

Table 8.3 The reliability index and probability of failure for the initial 60-story benchmark building .................................................................................................. 318

Table 8.4 Iteration history of the results for the sub-problem 1 using inverse reliability method ..................................................................................................... 319

Table 8.5 The reliability index and probability of failure for the optimized 60-story benchmark building .................................................................................................. 319

xxiii Performance-based Serviceability Design Optimization of Wind Sensitive Tall Buildings By Mingfeng Huang

Department of Civil & Environmental Engineering The Hong Kong University of Science and Technology Abstract Recent trends towards developing increasingly taller and irregularly-shaped buildings have led to slender complex structures that are highly sensitive and susceptible to wind-induced deflection and vibration. In the design of this new generation of tall buildings, structural engineers are facing the challenge of striving for the most efficient and economical design solution while ensuring that the final design must be serviceable for its intended function, habitable for its occupants and safe over its design life-time. The emerging performance-based design concept provides a general framework for solving the optimal serviceability design problems. This research aims to develop an innovative computer-based design method for optimal performance-based design of tall buildings achieving a satisfactory and reliable performance in various extreme and hazard wind loading conditions. The outcome of this research will provide a powerful computer-automated design tool for

xxiv optimal performance-based design to deliver cost-effective low-risk design solutions for tall buildings in a typhoon-prone city, such as Hong Kong. This thesis firstly develops a coupled dynamic analysis method for predicting the wind-induced complex motions of buildings. The equivalent static wind load approach is built on the results of dynamic analysis and is integrated into the stiffness design optimization of tall buildings subject to static drift and dynamic acceleration serviceability design criteria. The dynamic optimization problem has also been solved in the time domain with the aid of time history analysis. Furthermore, the uncertainty due to inherent variability in wind-induced random vibrations has been modeled and quantified in terms of peak factors based on statistical analysis of peak responses and the statistics of extremes. The time-variant reliability of wind-induced motions in tall buildings is then analyzed using the peak response distributions. Finally, a general reliability performance-based design optimization framework for the dynamic serviceability design of tall buildings is developed taking into due account of the major uncertainties in both wind loadings and the dynamic characteristics of structural systems. Numerous examples and practical applications are presented in relevant chapters to demonstrate the efficiency and practicality of the proposed automated reliability performance-based design optimization method.

1 CHAPTER 1 Introduction 1.1 Background Tall buildings historically emerged with the development of stronger and lighter construction materials, such as wrought iron and subsequently steel, after the industrial revolution in the nineteenth century. For a dynamic, modern metropolitan city, such as New York, London, Tokyo or Hong Kong, where tall buildings have been an effective way to make use of valuable and limited land. Recent boom in high-rise construction is the continual expansion with this urban form. The reasons for recent trends of constructing skyscrapers involve many aspects, from historical evolution to social development, from technology innovation to cultural recognition, and from economical achievements to civilization. Surely for cities such as Hong Kong and Tokyo, it is a consequence of their insular locations and the exorbitant value of a limited supply of land. In these cities people have become used to population densities almost unthinkable in the West. There has been a long demand for working and living in high-rise buildings. More importantly however, a towering skyscraper is the supreme architectural and corporate gesture. Its height makes it an instantly recognizable entity, it exerts its presence on the city through its defiance of nature, and from within, its views garner an impression of supremacy. Recently, there has been a shift towards the creation of genuinely distinctive, as well as hugely ambitious, more complexly shaped buildings. Of the 10 tallest buildings in the world eight are now in Asia. The tallest, Taipei 101, was the first skyscraper to break through the 500m height barrier. With its extraordinary height of 509m, Taipei

2 101 is a self consciously Asian structure. Its unusual form is inspired by pagodas, the ideal - and only - native Asian paradigm for this typology. Its shape is distinctive and original. It may not be aesthetically most pleasing but it has become a fine and recognizable symbol for Taiwan. Shanghai's 421m Jin Mao Tower in an elegant shape heralds China's extraordinary entry into the height contest helped along of course by Hong Kong's sharp skyline. Shanghai World Financial Center of 492 m and Shanghai Center of 580 m are currently under construction. These two buildings are located at the skyscraper-studded Lujiazui area of Pudong District and constitute a super high-rise building cluster together with Shanghai Jin Mao Tower. It is true that the title of tallest building is about to pass from Asia to the Middle East with the construction of Burj Dubai Tower in 2008. At close to half a mile in height, this particular giant is being built with a new construction speed. In some parts of the world, tall buildings are necessary to house growing urban populations and to accommodate more closely interrelated business activities. However, tall building structures are expensive. Tall buildings consume vast amounts of increasingly expensive energy to construct and maintain; they can be vulnerable to natural and human-made hazards. Such disadvantages have led to new challenges for the design of a new generation of modern tall structures. All tall buildings must be designed to be not only safe over its intended life and serviceable for its intended function, but also resource efficient, environment and people friendly. For most tall buildings, their shape and orientation are mainly driven by architectural

3 inspirations, functional requirements and site limitations. In some cases, however, wind engineering and structural engineering also play significant roles in determining the shape and structural form of the building. This can be particularly the case with supertall buildings where wind controls many aspects of the structural design. In order to reduce the base overturning moments in Taipei 101 tower, a number of building models of the prototype with various corner shapes were conducted in wind tunnels (Irwin 2006). The end result of examining a series of corner modifications was the cross section with stepped corners, which achieved a 25% reduction in the wind-induced base moment. To reduce wind-induced vibrations, a 600-tonne pendulum tuned mass damper was installed at the upper observatory levels. During the conceptual design stage of the Burj Dubai Tower, high frequency force balance studies indicated that wind-induced loads and responses could be reduced significantly by re-orienting the axes of the tower so as to align the most unfavorable aerodynamic directions with the wind directions where strong winds were least likely to occur. The whole tower was rotated through 120 degrees to achieve this. As the design evolved, a series of five force balance tests were undertaken at various stages, with the results being used in the next iterative design cycle (Irwin and Baker 2005). Although the current design practice is capable of delivering feasible designs of tall buildings, but the final design achieved tends to be conservative and by no means optimal in terms of construction cost and serviceable performance. Furthermore, ensuring safety and reliability in the design require a deeper understanding into the risks of hazards threatening buildings. The difficulty of the design problem is also compounded by the inherent uncertainties presented in the environmental loads and

4 in the structural system properties. Therefore, developing an automated design optimization technique to deliver the most cost efficient and reliable structural design while satisfying all specified ultimate safety, serviceability and habitability design performance criteria has appeared to be very challenging to the engineering community. Computer-based design optimization has emerged as a promising design methodology, in which a design problem has been firstly formulated into a mathematical optimization model, and then a theoretically sound and numerically reliable algorithm has been developed to solve the optimal design problems. In the tall building design, the mathematical optimization model is mainly composed of two components. One is the formulation of design optimization problem, which consists of design variables, design objectives, and design constraints. The other is the structural analysis of building system, which is achieved by solving the equation of motions governing the building behavior. Much attention is firstly put to the development of a mathematical optimization model for tall building designs in this research. Numerical algorithms are devised based on the rational mathematical optimization model, which really captures the major design factors and realistically reflects the behavior of the physical building system and the characteristics of its external wind loading conditions. Finally, computational algorithms for design optimization must be properly implemented in a computer program to build a computer-based user friendly platform for practical applications. 1.2 Scope and objectives