Ming-Yi Liu Yu-Jie Li Reliability Analysis of High-Rise Buildings under Wind Loads Department of Civil Engineering, Chung Yuan Christian University, Taiwan

2The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Hurricane Katrina, August 2005 Hurricane Katrina, August 2005 Hyatt Regency New Orleans, USA Hyatt Regency New Orleans, USA Structural Safety Affected by Wind

3The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Taipei 101, Taiwan, Completed in 2004, 508 m High Taipei 101, Taiwan, Completed in 2004, 508 m High Tuned Mass Damper Tuned Mass Damper Occupant Comfort Affected by Wind

4The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Objectives The objective of this paper is to conduct the reliability analysis of high-rise buildings under wind loads. Numerical examples are provided to capture the dynamic effects of structures with eccentricity between the elastic and mass centers. The framework of this research consists of two stages The objective of this paper is to conduct the reliability analysis of high-rise buildings under wind loads. Numerical examples are provided to capture the dynamic effects of structures with eccentricity between the elastic and mass centers. The framework of this research consists of two stages The first stage includes two parts: the deterministic analysis of wind-induced acceleration for a variety of attack angles, i.e., the demand, and the determination of allowable acceleration based on the occupant comfort criteria for wind-excited buildings, i.e., the capacity The first stage includes two parts: the deterministic analysis of wind-induced acceleration for a variety of attack angles, i.e., the demand, and the determination of allowable acceleration based on the occupant comfort criteria for wind-excited buildings, i.e., the capacity According to the results obtained in the first stage, the reliability analysis is conducted in the second stage, which can predict the probability of dissatisfaction with occupant comfort criteria for a variety of probability distributions of the structural eccentricity According to the results obtained in the first stage, the reliability analysis is conducted in the second stage, which can predict the probability of dissatisfaction with occupant comfort criteria for a variety of probability distributions of the structural eccentricity

5The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Framework High-rise building model Wind load model Demand Capacity Reliability analysis

6The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 High-Rise Building Model High-rise building model

7The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 N-Story Torsionally Coupled System Mass center Elastic center Aerodynamic center Three-dimensional configuration Top view of the ith floor Mass center Elastic center Aerodynamic center

8The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Wind Load Model Wind load model

9The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Wind Load Components Drag Lift Torque Attack angle Wind direction Top view of the ith floor

10The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Demand Demand

11The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Frequency Domain Analysis

12The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Capacity Capacity

13The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Occupant Comfort Criteria Melbourne and Palmer (1992) Duration of wind velocity Frequency of structural oscillation Return period of wind velocity Occupant comfort criteria

14The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Reliability Analysis Reliability analysis

15The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Synthetic Method

16The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Limit State Function and Basic Variables Original coordinate system Transformed coordinate system Limit state function Basic variable Limit state function Basic variable Design point Reliability index

17The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Numerical Examples Two numerical examples, i.e., the torsionally uncoupled and coupled systems (40-story buildings), are provided to conduct the reliability analysis of high-rise buildings under wind loads for a variety of attack angles Two numerical examples, i.e., the torsionally uncoupled and coupled systems (40-story buildings), are provided to conduct the reliability analysis of high-rise buildings under wind loads for a variety of attack angles Four types of parameters: the high-rise building model, wind load model, occupant comfort criteria and reliability analysis, are considered in this study Four types of parameters: the high-rise building model, wind load model, occupant comfort criteria and reliability analysis, are considered in this study All parameters of the two numerical examples are the same except the eccentricity between the elastic and mass centers All parameters of the two numerical examples are the same except the eccentricity between the elastic and mass centers Three types of probability distributions: the normal, lognormal and type I extreme value distributions, are used to model the uncertainties of the eccentricity between the elastic and mass centers Three types of probability distributions: the normal, lognormal and type I extreme value distributions, are used to model the uncertainties of the eccentricity between the elastic and mass centers

18The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Cross-Spectral Density Function of Wind Load θθθθθθθθ xxyy xyxyxyxy Attack Angle = 45˚ Attack Angle = 45˚

19The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Cross-Spectral Density Function of Acceleration (1) xxyyθθ xyxyxyxy xθxθxθxθ yθyθyθyθ Torsionally Uncoupled System, Attack Angle = 45˚ Torsionally Uncoupled System, Attack Angle = 45˚

20The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Torsionally Coupled System, Attack Angle = 45˚ Torsionally Coupled System, Attack Angle = 45˚ Cross-Spectral Density Function of Acceleration (2) xxyy θθθθθθθθ xyxyxyxy xθxθxθxθ yθyθyθyθ

21The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Structural and Allowable Responses Allowable peak acceleration Peak acceleration at corner of the 40th floor Torsionally uncoupled system Torsionally coupled system

22The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Probability of Dissatisfaction with Occupant Comfort Criteria Torsionally uncoupled system Torsionally coupled system Normal Lognormal Type I extreme value

23The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Conclusions The objective of this paper is to conduct the reliability analysis of high-rise buildings under wind loads. Two numerical examples, i.e., the torsionally uncoupled and coupled systems, are provided to capture the dynamic effects of structures with eccentricity between the elastic and mass centers. The framework of this research consists of two stages The objective of this paper is to conduct the reliability analysis of high-rise buildings under wind loads. Two numerical examples, i.e., the torsionally uncoupled and coupled systems, are provided to capture the dynamic effects of structures with eccentricity between the elastic and mass centers. The framework of this research consists of two stages In the first stage, the occupant comfort criteria are satisfied in the two numerical examples from the viewpoint of deterministic approaches. The peak acceleration of the torsionally coupled system is relatively higher than that of the torsionally uncoupled system for each attack angle due to the coupled mode effects In the first stage, the occupant comfort criteria are satisfied in the two numerical examples from the viewpoint of deterministic approaches. The peak acceleration of the torsionally coupled system is relatively higher than that of the torsionally uncoupled system for each attack angle due to the coupled mode effects In the second stage, compared to the lognormal and type I extreme value distributions, the normal distribution can be used to more conservatively simulate the uncertainties of the eccentricity between the elastic and mass centers in the two numerical examples from the viewpoint of probabilistic approaches. The probability of the torsionally coupled system is relatively higher than that of the torsionally uncoupled system for each attack angle due to the coupled mode effects In the second stage, compared to the lognormal and type I extreme value distributions, the normal distribution can be used to more conservatively simulate the uncertainties of the eccentricity between the elastic and mass centers in the two numerical examples from the viewpoint of probabilistic approaches. The probability of the torsionally coupled system is relatively higher than that of the torsionally uncoupled system for each attack angle due to the coupled mode effects

24The Fifth International Conference on Reliable Engineering Computing (REC2012), June 13-15, 2012 Thank You Very Much