Wind Hazard Risk Assessment and Management for Structures

Wind Hazard Risk Assessment and Management 

for Structures 

Siu Chung Yau 

A Dissertation 

Presented to the Faculty 

of Princeton University 

in Candidacy for the Degree 

of Doctor of Philosophy 

Recommended for Acceptance 

by the Department of 

Civil and Environmental Engineering 

Advisor: Erik Vanmarcke 

April 2011

c○ Copyright by Siu Chung Yau, 2011. 

All Rights Reserved

Abstract 

Rising hurricane damages over the past half century have served to motivate policy makers 

and insurance industry executives to demand better quantification of risk exposure to ex- 

treme winds. Advances in wind engineering and weather observation have enabled a shift 

away from empirically-based estimates, derived from insurance claim records, to more real- 

istic physically-based structural damage simulations. In this dissertation, the risk and reli- 

ability of low-rise structures under extreme winds are investigated using an advanced prob- 

abilistic scheme, a windborne debris model, and a novel pressure-based structural damage 

model. A review of several loss estimation methodologies, their sensitivities and inter-model 

discrepancies is provided. Specifically, the studies examined structural damage processes 

in three aspects: (1) structural components, (2) low-rise structures in isolation, and (3) 

neighborhoods of residences. Damage to the structural components was found to increase 

if the pressure acting on the components was either highly correlated with wind direction 

or wind direction varied over a larger range over time. The cumulative effect of internal 

pressure on the building envelope was analyzed using three methods: American Society of 

Civil Engineers 7 Standard, Eurocode, and Florida Public Hurricane Loss Projection Model 

(FPHLPM). The percentage damage of the building envelope differed by a few percent to 

a few hundred percent depending on the wind speed, and structural configuration. The 

most striking results came from the application of a novel vulnerability model, which for 

the first time, parameterized the interplay between pressure damage and windborne debris. 

Simulations forced with probabilistic data from FPHLPM as well as wind-tunnel experi- 

ments revealed how a structure may be effected by the resistance of and the proximity to 

neighboring buildings. The vulnerability results were applied in a long-term risk assess- 

ment to illustrate the possible effects of a changing climate on structural life-cycle cost. 

Collectively, the ideas and model improvements presented in this dissertation represent a 

significant contribution to the development of the next generation of wind loss models. 

iii

Acknowledgements 

First of all, I owe my deepest gratitude to my advisor, Professor Erik Vanmarcke, for his 

guidance and support throughout my graduate study at Princeton. This thesis would not 

have been possible without his encouragement, insight and patience. It is truly my honor 

to be his student, learning from him about risk analysis, scientific field, and even different 

global issues. I would also like to thank the other thesis committee members, Professor 

Branko Gliˇsić, Professor Elie Bou-Zeid and Professor Maria Garlock, for their valuable 

suggestions and insightful comments. 

In addition, I gratefully acknowledge financial support for this research, in part through 

a grant to Princeton University from Baseline Management Company and in part under a 

project entitled “Improved Hurricane Risk Assessment with Links to Earth System Models,” 

funded through the Cooperative Institute for Climate Science (CICS) by the U.S. National 

Oceanographic and Atmospheric Administration (NOAA). Thanks are also due to Princeton 

Environmental Institute (PEI) for granting me the Program in Science, Technology, and 

Environmental Policy (PEI-STEP) Fellowship. 

Next, I would like to express my gratitude to Professor Michael Oppenheimer and Pro- 

fessor Gregory van der Vink, who serve as my PEI-STEP fellowship advisors. I also need 

to give special thanks to Professor Henri Gavin at Duke University. Without his inspi- 

ration and guidance during my undergraduate study, I would not have chosen to pursue 

my doctoral degree at Princeton University. I am also thankful to Dr. Ning Lin for her 

collaboration. 

I am very fortunate to have many friends to accompany me throughout my days at 

Princeton. Dr. Craig Ferguson, who was my roommate for more than two years, has in- 

troduced me to American cooking and the exciting outdoor life. Serdar Selamet, my close 

friend since my undergraduate, has been the single person whom I see most and talk most to 

in these four and a half years. Raghav Pant, who shares numerous similar viewpoints with 

iv

me, has given me countless fun time. Yee Lok Wong has provided advice on mathematics 

as well as companionship remotely from Boston. I would also like to thank Joshua Fink, 

Eric Hui, Dr. Chitsomanus Muneepeerakul, Dr. Rachata Muneepeerakul, Zhihua Wang and 

Dr. Yan Zhang for their company and many enjoyable conversations. 

Finally, I express my sincere gratitude to my family. Thanks to my parents, Richard 

and Elaine, and brother, Robee, for their care and encouragement during the preparation 

of this dissertation. Final thanks are due to my girlfriend, Chloe Kung, for her seemingly 

unending patience and support in every difficult moment of mine. 

v

Contents 

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii 

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv 

Chapter 1: 

Introduction 1 

1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 

1.2 Review on Wind-Related Vulnerability Models . . . . . . . . . . . . . . . . 2 

1.2.1 Full-Scale Extreme-Wind Loss Model . . . . . . . . . . . . . . . . . . . 2 

1.2.2 Qualitative Vulnerability Model . . . . . . . . . . . . . . . . . . . . . . 4 

1.2.3 Quantitative Vulnerability Model . . . . . . . . . . . . . . . . . . . . . 6 

1.2.4 Recent Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

1.3 Objectives and Scope of Study . . . . . . . . . . . . . . . . . . . . . . . . . 10 

1.4 Organization of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 

Chapter 2: 

Structural Components and Wind Directionality 13 

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

2.2 Tropical-Cyclone Wind Time Series Model . . . . . . . . . . . . . . . . . . . 16 

2.2.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

2.2.2 Tropical Cyclone Properties . . . . . . . . . . . . . . . . . . . . . . . . 16 

2.2.3 Tropical Cyclone Track . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 

vi

CONTENTS vii 

2.2.4 Mean Boundary Layer Wind . . . . . . . . . . . . . . . . . . . . . . . . 19 

2.2.5 Three-Second Surface Wind . . . . . . . . . . . . . . . . . . . . . . . . 21 

2.2.6 Damage Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 

2.2.7 Sample Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 

2.3 Alternative Approaches to Wind-Load and Reliability Assessment . . . . . 24 

2.3.1 Wind Load and Reliability Calculation . . . . . . . . . . . . . . . . . . 24 

2.3.2 Time-Stepping Method and Point-in-Time Method . . . . . . . . . . . . 25 

2.4 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 

2.4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 

2.4.2 Maximum Wind Pressure . . . . . . . . . . . . . . . . . . . . . . . . . 27 

2.4.3 Probability of Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 

2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 

2.6 Closing Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 

Chapter 3: 

Internal Pressure in Low-Rise Structures 40 

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 

3.2 Structural Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 

3.3 External Wind Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 

3.4 Internal Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 

3.4.1 Florida Public Hurricane Loss Projection (FPHLP) Model . . . . . . . . 47 

3.4.2 ASCE 7 Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 

3.4.3 Eurocode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 

3.5 Windborne Debris Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 

3.6 Damage Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 

3.6.1 Component Failure Probability . . . . . . . . . . . . . . . . . . . . . . 51 

3.6.2 System Failure Probability . . . . . . . . . . . . . . . . . . . . . . . . . 52

CONTENTS viii 

3.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 

3.7.1 Baseline structure B under 150-mph wind . . . . . . . . . . . . . . . . . 54 

3.7.2 Roof Damage over 50–250 mph Wind Speed Range . . . . . . . . . . . . 59 

3.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 


Chapter 4: 

Integrated Multi-Structural Vulnerability Model 69 

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 

4.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 

4.2.1 Wind Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 

4.2.2 Structural Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 72 

4.2.3 Component-Based Pressure Damage Model . . . . . . . . . . . . . . . . 75 

4.2.4 Windborne Debris Model . . . . . . . . . . . . . . . . . . . . . . . . . 77 

4.2.5 Integrated Structural Damage Estimation . . . . . . . . . . . . . . . . . 79 

4.2.6 Approximate Economic Model . . . . . . . . . . . . . . . . . . . . . . . 81 

4.3 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 

4.3.1 A Hip-roof Concrete Residential Structure in Isolation . . . . . . . . . . . 83 

4.3.2 Hypothetical Residential Community . . . . . . . . . . . . . . . . . . . 83 

4.3.3 Two Neighboring Houses . . . . . . . . . . . . . . . . . . . . . . . . . . 88 

4.3.4 Sarasota, Florida . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 


Chapter 5: 

Long-Term Risk Assessment and Management 94 

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 

5.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

CONTENTS ix 

5.3 Hazard model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 

5.3.1 Wind Speed Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 96 

5.3.2 Compound Poisson Process . . . . . . . . . . . . . . . . . . . . . . . . 98 

5.4 Single-Limit-State Vulnerability Model . . . . . . . . . . . . . . . . . . . . . 102 

5.4.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 

5.4.2 Life-cycle Cost Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 

5.4.3 Life-cycle-cost-related Decisions . . . . . . . . . . . . . . . . . . . . . . 109 

5.5 Modified Florida Public Hurricane Loss Projection (FPHLP) Model . . . . 113 

5.5.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 

5.5.2 Expected Repair Cost over the Contiguous United States . . . . . . . . . 116 

5.5.3 Expected Repair Cost for Different Structures . . . . . . . . . . . . . . . 118 


Chapter 6: 

Conclusions and Future Work 123 

6.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 

6.2.1 Structural Components . . . . . . . . . . . . . . . . . . . . . . . . . . 125 

6.2.2 Low-Rise Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 

6.2.3 Multi-Structural Communities . . . . . . . . . . . . . . . . . . . . . . . 127 

6.2.4 Low-Term Risk Assessment . . . . . . . . . . . . . . . . . . . . . . . . 128 

Bibliography 129

List of Figures 

2.1 Flowchart illustrating the tropical cyclone wind time series model and the 

difference between point-in-time and time-stepping methods. . . . . . . . . 15 

2.2 Overview of the tropical cyclone wind time series model. . . . . . . . . . . . 17 

2.3 Sample simulated wind speed time series and wind angle time series. . . . . 21 

2.4 Wind speed and wind angle time records during Hurricane Katrina and Wilma. 23 

2.5 Four selected pressure coefficients with respect to wind angle. . . . . . . . . 27 

2.6 Cumulative distributions of the maximum wind load and the approximated 

maximum wind load generated from the simulated wind time series for cat- 

egory 5 tropical cyclones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 

2.7 Kolmogorov-Smirnov statistics comparing the maximum wind load and the 

approximated maximum wind load. . . . . . . . . . . . . . . . . . . . . . . . 30 

2.8 Percentage differences between the probabilities of failure and the approxi- 

mated probabilities of failure for normally distributed resistances. . . . . . . 35 

2.9 Percentage differences between the probabilities of failure and the approxi- 

mated probabilities of failure for lognormally distributed resistances. . . . . 36 

3.1 Unfolded view of baseline structures. . . . . . . . . . . . . . . . . . . . . . . 42 

3.2 Component and cladding external pressure zones. . . . . . . . . . . . . . . . 46 

3.3 Flowchart of system damage simulation. . . . . . . . . . . . . . . . . . . . . 53 

x

LIST OF FIGURES xi 

3.4 Distributions of internal pressure coefficient and building envelope damage 

of baseline structure B under a 150-mph wind towards the structure’s front 

face. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 

3.5 Distributions of internal pressure coefficient and building envelope damage 

of baseline structure B under a 150-mph wind towards the structure’s front 

face. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 

3.6 Roof panel vulnerability curves. . . . . . . . . . . . . . . . . . . . . . . . . . 61 

3.7 Maximum percentage increase in mean roof damage. . . . . . . . . . . . . . 63 

3.8 Percentage differences between the average roof damages over four cardinal 

wind directions and the average roof damage of baseline structure C without 

windborne debris. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 

4.1 Eight nominal angles of wind incidence. . . . . . . . . . . . . . . . . . . . . 71 

4.2 Three dimensional rendering of residential structure models. . . . . . . . . . 74 

4.3 Flowchart of the component-based pressure damage model. . . . . . . . . . 76 

4.4 Flowchart of the integrated vulnerability model. . . . . . . . . . . . . . . . . 80 

4.5 Vulnerability of a hip-roof concrete house at four different wind speeds. . . 84 

4.6 Vulnerability of a hip-roof concrete house under 200-mph at three different 

wind directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 

4.7 Three-dimensional view of a hypothetical residential development. . . . . . 86 

4.8 Estimated damage condition of each individual house in the hypothetical 

residential development under a wind speed of 65 m/s at a 45-degree angle. 87 

4.9 Comparison of subassembly and overall damage ratios with and without con- 

sideration of windborne debris. . . . . . . . . . . . . . . . . . . . . . . . . . 88 

4.10 (a) Illustration of two neighboring houses. (b) Breakdown of overall damage 

ratio of structure A versus resistance factor of structure B. . . . . . . . . . 89

LIST OF FIGURES xii 

4.11 Study area of a residential development of 358 houses in Sarasota County, 

Florida and simulated storm track of Hurricane Charley of 2004. . . . . . . 90 

4.12 Comparison of the estimated wind damage condition of the residential de- 

velopment in Sarasota County, Florida, under a Hurricane Charley wind 

condition, by time series and maximum wind analyses. . . . . . . . . . . . . 91 

4.13 Comparison of subassembly and overall damage ratios between time-series 

and maximum-wind damage analyses. . . . . . . . . . . . . . . . . . . . . . 92 

5.1 Distribution of Gumbel distribution parameters λ and µ of extreme wind 

speed data in 129 stations over the contiguous United States. . . . . . . . . 100 

5.2 Two sample results of the hazard model. . . . . . . . . . . . . . . . . . . . . 101 

5.3 Vulnerability curves of the single-limit-state deterministic model. . . . . . . 103 

5.4 Mean total discounted repair cost in 36 different climate change scenarios. . 104 

5.5 Percentage difference in mean total discounted repair costs between 36 dif- 

ferent climate change scenarios and the ‘no climate change’ scenario. . . . . 105 

5.6 Mean total discounted repair cost in 36 different climate change scenarios. . 107 

5.7 Percentage difference in mean total discounted repair costs between 36 dif- 

ferent climate change scenarios and the ‘no climate change’ scenario. . . . . 108 

5.8 Ratios of the total mean discounted repair costs attributed to the uncertainty 

in parameters to that attributed to the mean value of parameters. . . . . . 110 

5.9 Ratios of the standard deviations of the discounted repair cost attributed 

to the uncertainty in parameters to that attributed to the mean value of 

parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 

5.10 Four sample simulations showing the effects of resistance deterioration in two 

different climate scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 

5.11 Minimization of life-cycle cost in two different climate scenarios. . . . . . . 114

LIST OF FIGURES xiii 

5.12 Examples of vulnerability curves of the modified Florida Public Hurricane 

Loss Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 

5.13 Expected total repair cost of a one-story hip-roof concrete-block house over 

129 geographic locations in contiguous United States in nine different future 

climate scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 

5.14 Expected total repair cost related to structural damage: (a) hip roof vs. 

gable roof (b) tiles vs. shingles (c) shutters vs. no shutters. . . . . . . . . . 119 

5.15 Vulnerability curves and total expected repair cost related to structural dam- 

age of a concrete-block house at four different geographic locations. . . . . . 120 

5.16 Vulnerability curves and total expected repair cost related to structural dam- 

age of a wood-frame house at four different geographic locations. . . . . . . 121

List of Tables 

1.1 The five costliest U.S. hurricanes, 1900-2006. . . . . . . . . . . . . . . . . . 2 

1.2 Saffir-Simpson hurricane damage potential scale. . . . . . . . . . . . . . . . 4 

1.3 Building classification by Minor and Mehta (1979). . . . . . . . . . . . . . . 5 

2.1 Probability distribution of tropical cyclone parameters. . . . . . . . . . . . . 18 

2.2 Percentage of simulated wind records by track location. . . . . . . . . . . . 32 

2.3 Probabilities of failure of four component limit states . . . . . . . . . . . . . 34 

3.1 Statistics of structural component resistance. . . . . . . . . . . . . . . . . . 44 

3.2 Statistics of external pressure coefficient. . . . . . . . . . . . . . . . . . . . . 46 

4.1 Example parameters of a residential structure’s geometry. . . . . . . . . . . 73 

4.2 Limit states of structural components. . . . . . . . . . . . . . . . . . . . . . 75 

4.3 Properties of debris objects. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 

5.1 Expected total discounted repair costs and maximum maintenance cost in 

two different climate change scenarios. . . . . . . . . . . . . . . . . . . . . . 111 

5.2 Gumbel distribution parameters of four different geographic locations with 

similar 50-year wind speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 

xiv

1.1 Overview 

Chapter 

1 

Introduction 

Death and injuries in windstorms are relatively low compared to the casualty rates in other 

natural disasters, due to the predictability of extreme winds. However, the relative low 

number of casualties does not sufficiently reflect the massive destructiveness of extreme 

winds. Windstorm (including tropical cyclone, tornado and thunderstorm) is the most 

costly type of natural disaster in the United states in recent decades (EM-DAT, 2010). 

Hurricane Andrew, which caused an insured loss of $16.5 billion in 1992, deeply impacted 

the insurance industry. Twelve insurers bankrupted and most of the catastrophe capital 

in the world reinsurance market is depleted (Malmquist and Michaels, 2000). In 2005, 

Hurricane Katrina caused $81 billion of property damage (Blake et al., 2007) and $40.6 

billion of insured loss (Knabb et al., 2005). Table 1.1 (Blake et al., 2007) lists the five 

costliest United States hurricanes. 

In light of the recent massive amounts of damage caused by tropical cyclones, wind- 

related vulnerability of structures has received increasing attention in the research field. 

Traditionally, structural damage caused by extreme winds is approximated by some em- 

1

Chapter 1. Introduction 2 

Table 1.1: The five costliest U.S. hurricanes, 1900-2006 (Blake et al., 2007). 

Hurricane Date Cost of Damage (2006 dollar value) 

Katrina August 2005 $84.6 billion 

Andrew August 1992 $48.1 billion 

Wilma October 2005 $21.5 billion 

Charley August 2005 $16.3 billion 

Ivan September 2004 $15.5 billion 

pirical relationships between wind speed and insurance-claim amounts determined from 

historical data (e.g. Chandler et al., 2001; Huang et al., 2001; Sparks, 2003). However, 

such relationships may be inaccurate because insurance records are strongly influenced by 

human factors (Watson and Johnson, 2004). They also do not predict damage to build- 

ings that have not been subjected to major wind hazards (Watson and Johnson, 2004). 

Therefore, some recent studies have employed structural engineering analysis to simulate 

the actual physical damage processes and hence the economic loss due to structural dam- 

age (e.g. Stubbs and Perry, 1996; Pinelli et al., 2004; Unanwa et al., 2000; Vickery et al., 

2006b). Performance-based design, which is based on the structural damage simulation, was 

proposed to strengthen future residences’ resistance against high winds (e.g. van de Lindt 

and Dao, 2009). By developing a more accurate and in-depth structural risk assessment 

in tropical cyclone-prone areas, engineers can help the actuaries and policymakers better 

prepare for and mitigate the future risk of extreme wind posed to our communities. 

1.2 Review on Wind-Related Vulnerability Models 

1.2.1 Full-Scale Extreme-Wind Loss Model 

A full-scale extreme-wind loss estimation model includes, but not limited to, calculation of 

genesis of extreme winds, evaluation of wind effects on buildings, estimation of insurance 

claim amounts based on building damage, etc ˙ , which require knowledge in a range of pro-


fessions including meteorology, wind engineering, structural engineering, actuarial science. 

In general, the model may be divided into four modules: 

1. Wind Model 

Given the historical storm tracks and a land cover model, a wind model determines 

the occurrence and intensity of wind hazard such as wind speed and wind direction. 

One commonly-used simple model for tropical cyclones is the Rankine Vortex wind 

field model. 

2. Boundary Layer Model 

The wind hazard information generated by the large-scale wind field model is modified 

in a boundary layer model to take into account the effects of land topography. Infor- 

mation about the local wind field, which impacts the buildings and the environment, 

is obtained. 

3. Vulnerability Model 

A vulnerability model relates the extreme wind data to the consequent physical dam- 

age of buildings in a geographic area. The damage is expressed as the failure proba- 

bility of some structural components of the buildings, and may also be represented in 

monetary terms by the cost to repair the damage. 

4. Insurance Loss Model 

The economic losses are approximated based on the structural damage by an insurance 

loss model which considers the economy situation and insurance policy terms such as 

deductibles. 

The wind model and the boundary layer model are usually subjects of meteorology 

and aerodynamics, while the insurance loss model is the study of actuarial science. This 

dissertation, as well as the following literature review, mainly focuses on the vulnerability


model from a structural engineering standpoint. Most vulnerability models are about low- 

rise structures, particularly residential houses, since they are the most commonly damaged 

structural type in extreme wind events. 

1.2.2 Qualitative Vulnerability Model 

Wind damage to a building may be estimated via both qualitative and quantitative meth- 

ods. Qualitative vulnerability models categorize different building types or different wind 

events, and describe the expected damage level of buildings at a range of wind intensities 

(Unanwa et al., 2000). An example of qualitative vulnerability model is the Saffir-Simpson 

hurricane damage potential scale as shown in Table 1.2. Another example is the classifi- 

cation of buildings developed by Minor and Mehta (1979) presented in Table 1.3, which 

categorizes a building as fully engineered, pre-engineered, marginally engineered, or non- 

engineered, with their associated performance in extreme winds. 

Table 1.2: Saffir-Simpson hurricane damage potential scale. 

Category Wind Speed (mph) Damage Level 

1 74-95 Minimal 

2 96-110 Moderate 

3 111-130 Extensive 

4 131-155 Extreme 

5 >155 Catastrophic 

The categorizations used by the qualitative vulnerability models are developed for gen- 

eral purposes only. They may be useful notifying the general public what to expect for 

different building types in various wind scenarios. However, they are not precise enough to 

predict hurricane damage or insurance loss to any specific buildings. Quantitative vulnera- 

bility models are necessary for accurate prediction of losses.


Table 1.3: Building classification by Minor and Mehta (1979). 

Building Description Performance 

Fully-engineered 

buildings 

Pre-engineered 

buildings 

Marginally engineered 

buildings 

Non-engineered 

buildings 

Buildings that receive specific, individualized 

design attention from 

professional architects and engineers 

Buildings of this type receive engineering 

attention in advance of 

a commitment to constmction and 

are subsequently marketed in many 

similar units for a wide variety of 

uses. 

Commercial buildings, light industrial 

buildings, schools, and certain 

types of motels and apartments 

built with some combination of masonry, 

light steel framing, openweb 

joists, wood framing, and wood 

rafters falls under this category. 

Single and multifamily residences, 

one or two story apartment units 

and many small commercial buildings 

receive no engineering attention 

at all and are called non-engineered 

Performance in the face of 

extreme winds is likely to 

be very good. 

Damages can occur at 125 

mph, if care is not exercised 

in design and construction. 

Total destruction may result 

at wind speed of 125 

mph or less. 

Wind speeds of 75 mph 

represent a threshold of 

damage, and total destruction 

may occur when winds 

reach 125 mph.

1.2.3 Quantitative Vulnerability Model 


Generally, there are three different approaches to develope a quantitative vulnerability 

model (Watson and Johnson, 2004): (1) claim-based, (2) engineering judgment, and (3) 

theory-based. Each of the approaches has its own advantages over the others and is improved 

over time. Some vulnerability models employ more than one approach simultaneously. 

1.2.2.1 Claim-based Approach 

Vulnerability models using the claim-based approach estimate the hurricane damage of a 

building without considering the physics or engineering of the building components, and 

usually derive relationships between the historical damage and wind speeds from the past 

insurance claim data. This approach may not predict the damage precisely mainly because 

the insurance loss information, including the amount of claims and the date of claims, is 

largely controlled by human factors. Such factors may include personal view of an individual 

insurance adjuster and aggressiveness of homeowner (Watson and Johnson, 2004). For ex- 

ample, the amount a homeowner claims is affected by the policy details such as deductibles. 

The company policies regarding insurance claims are subjected to administrative and polit- 

ical considerations that differ from storm to storm. Moreover, the insurance claim data in 

a region may not apply to other regions. Factors including environment and construction 

practices vary from region to region. 

Many vulnerability models are developed using the claim-based approach. Studies by 

Leicester et al. (1979) and Leicester (1981) are those of the first studies in the literature that 

established and elaborated the concepts of vulnerability curves. In their models, Leicester 

et al. adopted a linear relationship between the damage index and the gust wind speed 

for different types of housing in Australia based on damage surveys. Contrast to the linear 

relationship between wind speed and damage, Sparks et al. (1994) suggested that significant 

damage begins when the gradient wind speed reaches 40 m/s and rises steadily until 70 m/s.


Between 70 m/s and 80 m/s, there is a sudden rise in damage due to loss of building envelope 

and rain entering the building. Sparks et al. (1994) also observed that housing damage 

is closely related to the performance of the roof and wall building envelope. Similarly, 

Mitsuta et al. (1996) observed a highly correlated relationship between home damage and 

surface wind speed from insurance data of tropical cyclones Mireille and Flo in Japan. Sill 

and Kozlowski (1997) developed an approach for predicting the hurricane damage for a 

population of structures as a function of a wide range of factors including gradient wind 

speed, gust factor, average value of the buildings, and two parameters which govern the 

rate of damage increase with wind speed. The proposed method was intended to move 

away for curve fitting schemes, but its practical value is hampered by insufficient clarity 

and transparency (Pinelli et al., 2004). 

1.2.2.2 Engineering judgment Approach 

The engineering judgment approach is based on the engineering survey of damaged struc- 

tures (Watson and Johnson, 2004). Similar to the claim-based approach, it largely depends 

on individual interpretation. For instance, there are many different versions about the 

definition of a 50% damage of a roof (Watson and Johnson, 2004). 

One example of the engineering judgment approaches is the analysis of data obtained 

from the American Red Cross data on residential damage from hurricanes by Howard et al. 

(1972). Also, engineering judgment often supplements the theory-based approach. For 

example, the Florida public hurricane loss projection model (Gurley et al., 2005b) uses 

engineering judgment to modify the ASCE 7 wind load specification for hurricane loss 

estimation.

1.2.2.3 Theory-based Approach 


In the theory-based approach, the vulnerability of the structure is determined based on the 

physics of behaviors of the structure (Watson and Johnson, 2004). The approach explicitly 

characterizes the resistance of various building components and the wind load effects on 

them. Damage to a component occurs when the load effect is greater than its resistance. 

The vulnerability of a structure at various wind speed can be estimated once the strength 

capacities, load demands and load paths within a structure are identified (Pinelli et al., 

2004). Unlike the claim-based approach, the theory-based approach is able to evaluate the 

hurricane vulnerability of structures without the heavy influence of human judgment. 

Some recent examples of the theory-based vulnerability models are by Chiu (1994), 

Holmes (1996), Stubbs (1996), Unanwa and McDonald (2000) and Unanwa et al. (2000). 

Holmes (1996) presented the vulnerability curve for a fully-engineered building with re- 

sistance of lognormal distribution. It was assumed that the failure of each component is 

independent of each other and is designed to resist the same value of wind load. The study 

indicates that more thorough post-disaster investigations are needed to better define the 

model. Stubbs (1996) proposed a vulnerability model which is based on an analysis of the 

performance of different building components and their corresponding relative importance. 

The damage ratio for the entire structure is weighted in proportion to some constants rep- 

resenting the relative importance of the contribution of the consequence of each damage 

mode. However, as indicated by Unanwa and McDonald (2000), this study is restricted to 

damage prediction of a group of buildings within a given geographic area. Unanwa and 

McDonald (2000) developed a similar approach as Stubbs (1996), but their model is more 

versatile and more capable of predicting wind damage for a large number of different house 

types and building performance parameters.

1.2.4 Recent Developments 


Damage analysis of a building can be very complex, since it involves a lot of issues and 

uncertainties. For example, wind pressure acting on the roof largely depends on the roof 

shape, roof angle and even presence of nearby trees. Internal pressure inside a building is 

affected by overall building leakage, flexibility of the building envelope and compartmental- 

ization within the building. Other related issues range from the surrounding environment of 

the structure to the time effect on the building material’s strength. Many of these complex 

issues have been simplified by design codes and standards for structural design purpose. 

However, for the purpose of accurate loss estimation, currently there are still significant 

uncertainties regarding the wind damage process such as the wind-borne debris impacts 

and the progressive damage, leaving plenty of room for development in the literature. 

Most current models analyze the vulnerability of a structure individually without con- 

sidering the surrounding environment, especially other neighboring structures. Presence 

of neighboring structures not only affects the local wind intensity and direction, but also 

contributes to the hurricane debris that often causes severe structural damages. Hence, 

one of the recent directions is the effect of wind-borne debris on structures during tropical 

cyclones. An example of the recent developments is the work by Lin and Vanmarcke (2010). 

In addition, many vulnerability models estimate losses of buildings as it was during the time 

period when they were constructed. As a result, the hurricane losses of the aging buildings 

may not be estimated accurately. Therefore, some recent research studies focus on modeling 

the time effect on vulnerability by incorporating changes in housing types, new materials, 

age profiles, building code specifications. For example, Stewart et al. (2003) used the vul- 

nerability model developed by Huang et al. (2001) and extended the method to include 

changes in existing residential structural vulnerability due to improvements in building en- 

velope performance. Davidson and Rivera (2003) introduced a quantitative methodology 

to model how the vulnerability of a regions building inventory changes over time due to,


for example, aging, structural upgrading efforts, construction and demolition of buildings. 

Also, Khanduri and Morrow (2003) presented a method to disaggregate a vulnerability curve 

into several curves representing different building types so that a known vulnerability curve 

from one region can be applied to another region of a different building inventory. Pinelli 

et al. (2004) proposed a probabilistic approach for evaluation of hurricane vulnerability of 

residential structures. The model first defines the basic damage modes for components of 

specific building types. Then the damage modes are combined into possible damage states, 

of which the probabilities of occurrence are calculated as functions of wind speeds from 

Monte Carlo simulations conducted on engineering numerical models of typical houses. 

The above recent developments are not realized in practice until they are applied to 

the loss estimation models that are used by the catastrophe modeling industry. While 

a number of proprietary commercial models are available to the insurance industry for 

estimating the potential insurance loss caused by hurricanes, currently there are only a 

very limited number of hurricane loss estimation models accessible in the public domain. 

One of the most well-known public software is the HAZUS-MH model that is developed 

by the Federal Emergency Management Agency (FEMA). However, a lot of details and 

methodologies implemented in the model are not disclosed to the public. Recently a new 

hurricane loss estimation model, namely Florida Public Hurricane Loss Projection (FPHLP) 

Model is approved by the Florida Commission on Hurricane Loss Projection Methodology 

for estimating hurricane insurance rates in the state of Florida. One of its goals is to provide 

a more publicly accessible model. However, he model is confined to analysis of structures 

in Florida, and is not fully open-source. 

1.3 Objectives and Scope of Study 

Very recently, the research field has started full-scale wind tunnel experiments, such as the 

‘Wall of Wind’ (WoW) facility at Florida International University, to simulate the damage


of low-rise structures under tropical cyclone winds. As full-scale experiments may be costly 

in both time and money, it is important to identify the critical issues that can utilize 

the facilities. So far, many research results in the literature are obtained from numerical 

analysis. The first objective of this dissertation is to identify the discrepancies among 

different numerical methodologies in vulnerability analysis, indicating the issues that have 

to be studied in the physical experiments. 

Moreover, presently, the very limited number of open-source hurricane loss estimation 

models impedes the improvement of the methodology. The details and methodologies em- 

bedded in many current models are concealed from the public so that it is difficult to 

examine the difference in loss estimation results of different geographic regions, building 

types and details among different analysis methods. The second objective of this disserta- 

tion is to review the details of the loss estimation methodology and examine the effects of 

the details on the vulnerability analysis results. 

Thirdly, effect of climate change on structural engineering analysis has been addressed 

by very limited literature only. Optimization of structural design requires evaluation of 

long-term structural performance, which is sensitive to any change in future extreme wind 

load. The third objective of this dissertation is to study the potential impact of climate 

change on the long-term risk assessment and management of structures. 

Risk assessment of structures under extreme winds is a complex and sizable topic. As 

specified in the last section, this dissertation focuses on the vulnerability analysis of struc- 

tures, which relates the extreme wind data to the consequent physical damage of buildings. 

The genesis of extreme winds and related aerodynamics such as boundary layer modeling 

are not considered. Also, this dissertation does not look into the details of the economic 

loss estimation, particularly the insurance policies of damaged structures. In addition, the 

structural analysis is very different for high-rise and low-rise structures. Under tropical cy- 

clone winds, high-rise structures are subjected to dynamic loading while low-rise structures


are subjected to quasi-static wind load. A majority of this dissertation is devoted to the 

estimation of the structural damage of one-story residential structure. 

1.4 Organization of Dissertation 

This dissertation is constituted of two parts. The first part studies the vulnerability of resi- 

dential structures in individual wind events, starting from building components to structural 

systems and residential communities. First, the effect of wind directionality on the vulner- 

ability of building components is studied (Chapter 2). Using a numerical tropical cyclone 

wind time series model, the study contrasts the difference in damage predictions between 

time series analysis and point-in-time analysis during a storm passage. Then, the interac- 

tion between different building components is investigated in the risk assessment of low-rise 

structures (Chapter 3). Different internal pressure adjustment methods and their effects 

on the loss estimation are compared. The last module presents an integrated vulnerability 

model that considers the interplay between pressure damage and wind-borne debris impact, 

and applies the model to the damage estimation of a community of residential structures 

(Chapter 4). The second part of the dissertation moves the focus from individual wind 

events to the long term risk assessment of structures. The results of structural vulner- 

ability in individual wind events are applied to estimation of life-cycle cost of structures 

under different climate change scenarios (Chapter 5). A non-stationary stochastic pro- 

cess is developed to simulate the long-term wind climate. The wind results are applied to 

two vulnerability models to illustrate the possible effects of climate change on the mean 

and standard deviation of future repair cost. The end of the dissertation summarizes the 

findings, draws conclusions, and outlines areas of future work (Chapter 6).

Chapter 

2 

Structural Components and 

Wind Directionality 

2.1 Introduction 

This chapter focuses on the effect of varying wind directionality on structural damage in 

individual tropical cyclone events. During a tropical cyclone event, a structure is exposed 

to winds from different directions as the cyclone moves along its track. The greater the 

variation in wind directionality, the wider the structure’s angle of exposure to windward 

wind. (“Windward” is the direction from which the wind is blowing at a given time, while 

“leeward” is the direction downwind from the point of reference.) If windward and leeward 

winds cause different types or levels of structural damage, this may significantly affect the 

damage estimation. For instance, more damage can be caused by wind-borne debris if wind 

directionality changes more, as debris mainly impacts the windward side of the structure 

(Lin and Vanmarcke, 2010). Moreover, failures of structural components are interdependent. 

After the initial structural damage, a change in wind direction can significantly affect the 

subsequent occurrences of damage. This effect of interdependent component failures cannot 

be quantified reliably without considering the change in wind speed and wind direction over 

13

Chapter 2. Structural Components and Wind Directionality 14 

time within individual strong-wind events. 

Currently, two methods are commonly used in different tropical cyclone damage esti- 

mation models. The first considers the effect of varying wind directionality during a strong 

wind event and the second does not. In the first, the time-stepping method, employed in 

damage estimation models such as the HAZUS-MH model, the structural loading is eval- 

uated at a series of time steps, e.g. at 10-minute interval, for both wind speed and wind 

direction (Vickery et al., 2006a,b). The second method, the point-in-time method, used 

in other models, including the Florida Public Hurricane Loss Projection Model, evaluates 

the wind load only at the maximum wind speed during the tropical cyclone event (and 

the corresponding wind direction at the maximum wind speed) (Gurley et al., 2006; Li 

and Ellingwood, 2006). If the two methods are applied to the same quasi-static wind load 

model (used by both HAZUS-MH and the Florida Public Hurricane Loss Projection Model, 

since fatigue and dynamic loading are generally not considered), the difference in results is 

attributable to the variation in wind direction over time. 

The flowchart in Figure 2.1 summarizes the simplified loss estimation framework adopted 

in this study. In what follows, we examine and quantify the effect of varying wind direc- 

tionality on low-rise structural damage estimation, illustrating the methodology through 

numerical examples. In the first part of this chapter, we present an efficient probabilistic 

model to generate wind speed and wind direction time series in tropical cyclones. These 

are used, in the second part, to calculate wind loads and analyze the reliability of some 

representative structural components of low-rise structures.


Maximum Wind Speed (Vmax) 

Approximated Max Wind Load (S*) 

Tropical Cyclone Properties (Vt, !P, Rmax) 

Track Location (s) 

Tropical Cyclone Wind Time Series Model 

Wind Speed Time Series (V(t)) 

Wind Angle Time Series (!(t)) 

Point-in-Time Method Time-Stepping Method 

Pressure Coefficient 

Reliability Analysis 

over all t 


Maximum Wind Load (Smax) 

Reliability Analysis 

Approximated Probability of Failure (Pf*) Probability of Failure (Pf) 

Figure 2.1: Flowchart illustrating the tropical cyclone wind time series model and the 

difference between point-in-time and time-stepping methods.


2.2 Tropical-Cyclone Wind Time Series Model 

2.2.1 Scope 

Due to the lack of historical tropical cyclone records, many advanced meteorological models 

have been developed to simulate wind data for various geographical regions (e.g. Powell 

et al., 2005; Vickery et al., 2000). They tend to be computationally expensive to solve, and 

their solutions, typically in the form of a two-dimensional time-dependent field, provide 

much more information than is needed for the purpose of structural damage estimation, in 

particular in this study. A geographically non-specific parametric model that reasonably 

approximates the results of the wind field equations at a single location is judged most 

suitable for use in this study. Figure 2.2 indicates the methodology involved. 

2.2.2 Tropical Cyclone Properties 

First, the intensity and the spatial scale of the tropical cyclone are sampled. These are 

measured by three parameters: (1) the translational speed of the storm, Vt, namely the 

speed at which the tropical cyclone is moving along the earth surface; (2) the central 

pressure difference, ∆P , being the difference between atmospheric pressures at the center 

of the storm and at the periphery; and (3) the radius of maximum winds, Rmax, which is 

the distance from the storm center to the locations of maximum wind speed. 

Models have been suggested for the probability distributions of these parameters (Geor- 

giou 1985; Vickery and Twisdale 1995a). In this study, we adopt the simple probability 

distributions used by Iman et al. (2002), which are not specific to any geographic region; 

each of the three parameters (Vt, ∆P and Rmax) is characterized by a triangular distri- 

bution and the parameters are assumed to be statistically independent. The distributions 

are defined for each of the Saffir-Simpson hurricane categories 1, 3 and 5 in the study by 

Iman et al. (2002), according to which the parameters of the probability distributions are

(deg) 

V (m/s) 

60 

40 

20 

0 

180 

90 

0 

90 

Storm 

Track 


Structure 

Location 

SETUP 

s d(t) 

t (hr) 

Storm Center 

Position at t 

!(t) 

180 

0 5 10 15 20 

t (hr) 

d (km) 

(deg) 

V env (m/s) 

V tan (m/s) 

V rad (m/s) 

RELATIVE POSITION BETWEEN STORM CENTER 

AND STRUCTURE 

400 

200 

0 

180 

90 

0 

90 

t (hr) 

180 

0 5 10 15 20 

t (hr) 

WIND VELOCITY TIME SERIES WIND COMPONENTS 

50 

0 

50 

50 

0 

50 

50 

0 

5 10 15 

t (hr) 

5 10 15 

t (hr) 

50 

0 5 10 

t (hr) 

15 20 

Figure 2.2: Overview of the tropical cyclone wind time series model. The two upper subfigures 

illustrate the methodology of determining distance d(t) and relative angle φ(t) between 

the structure and the storm center over time. Based on d(t) and φ(t), the three tropical 

cyclone wind components: environmental wind (Venv), storm-scale tangential wind (Vtan) 

and storm-scale radial wind (Vrad) are computed, as shown in the lower right subfigure. The 

sum of these components is the wind velocity timer series in the lower left subfigure.


determined by a professional team in the Florida Commission on Hurricane Loss Projection 

Methodology. For example, the statistical measures (lower limit, mode and upper limit) of 

Vt, ∆P and Rmax for a category 5 hurricane are (4.5, 6.75, 9) (85, 95, 105) and (8, 20, 40), 

respectively. 

Table 2.1: Probability distribution of tropical cyclone parameters. 

Parameter Symbol Unit Category 1 Category 3 Category 5 

Translational velocity Vt m/s 

Central pressure difference ∆P mB 

Radius of maximum wind Rmax km 

2.2.3 Tropical Cyclone Track 

a = 4.5 

b = 6.75 

c = 9 

a = 15 

b = 22.5 

c = 30 

a = 20 

b = 35 

c = 64 

a = 4.5 

b = 6.75 

c = 9 

a = 45 

b = 57.5 

c = 60 

a = 13 

b = 32 

c = 64 

a = 4.5 

b = 6.75 

c = 9 

a = 85 

b = 95 

c = 105 

a = 8 

b = 20 

c = 40 

Two simplifying assumptions are made in modeling the tropical cyclone track. First, for 

the purpose of estimating the wind damage to an individual structure, it is unnecessary 

to track the tropical cyclone from genesis to dissipation. We are only interested in the 

time period when the wind speed is above a certain threshold (below which damage is 

highly unlikely). It is assumed that the tropical cyclone track remains straight during this 

relatively short time period. Second, we are interested in the wind angle relative to the 

structure’s orientation, not the absolute wind angle with respect to the cardinal directions; 

therefore the absolute translational direction of the tropical cyclone does not matter. 

Based on these assumptions, the location of the tropical cyclone track can be fully 

defined by the closest distance between the track and the structure, denoted herein by s. A 

plus or minus sign is assigned to the quantity s to indicate whether the structure is on the


right or the left side with respect to the translational direction of the tropical cyclone. The 

condition s = 0 means that the tropical cyclone center passes directly over the structure. 

Let t = 0 indicate the time when the tropical cyclone track is closest to structure. As 

illustrated in Figure 2.2, at time t the distance between the storm center and the structure 

location is: 

d(t) = 

 

V 2 

t t2 + s 2 , (2.1) 

and the relative angle from the structure location to the storm center at time t is: 

2.2.4 Mean Boundary Layer Wind 

−1 s 

φ(t) = tan . (2.2) 

Vtt 

Given d(t) and φ(t), the wind velocity at the location of the structure can be characterized 

by inserting the sampled tropical cyclone properties into a wind field model. Instead of 

solving the wind field by differential equations based on Navier-Stokes, we calculate the 

wind velocity over time using the framework developed by Jakobsen and Madsen (2004). 

In a tropical cyclone event, the mean boundary layer wind is composed of the environ- 

mental-scale wind and the storm-scale wind. The storm-scale wind can be further broken 

down into tangential and radial wind speed components. This can be expressed by 

Vmbd = Venv + Vtan + Vrad, (2.3) 

where the subscript ‘mbd’ abbreviates ‘mean boundary layer’. The formulation of each 

component, according to Jakobsen and Madsen (2004), is briefly described below. 

The environmental-scale wind, Venv, at the location of the structure has the same direc- 

tion as the translational direction of the storm (see Figure 2.2). Its magnitude is expressed

as: 


 

Venv(d) = Vt · exp − d 

 

, (2.4) 

RG 

where RG, the length scale of the environmental-scale processes, is taken to be 500 km 

(Jakobsen and Madsen, 2004). The tangential wind speed, Vtan, is calculated based on 

the parametric tropical cyclone model developed by Jakobsen and Madsen (2004) and the 

air pressure distribution model described by Holland (1980). The latter expresses the air 

pressure as follows: 

P (r) = Pc + ∆P exp 

 

− 

Rmax 

r 

B 

, (2.5) 

where r is distance from the storm center, Pc is the central pressure, and B is a dimension- 

less scaling parameter (affecting the shape of the pressure profile). A simple empirical 

equation is used to relate B to Pc, expressed in mbar (Hubbert et al., 1991): 

B = 1.5 + 

980 − Pc 

. (2.6) 

120 

This expression, originally derived based on data from Australian tropical cyclones but 

found to be generally applicable, is adopted herein mainly for its simplicity. The magnitude 

of the tangential wind at the structure’s location is (Jakobsen and Madsen, 2004): 

Vtan(d) = 

λd 

P 

· ∂P 

∂r 

+ 1 

4 f 2d2 − 1 

2 

fd, (2.7) 

where β is a parameter relating tangential and radial wind speeds and f is the Coriolis 

parameter. In the Northern hemisphere, the tangential wind is counter-clockwise, so the 

tangential wind angle at the structure location is φ − π/2. The radial wind, Vrad, at the 

structure’s location has a wind angle equal to φ + π. Its magnitude is based on that of the


tangential wind speed (Jakobsen and Madsen, 2004): 

Vrad(d) = Vtan(d) · B(Bd′−2B + (1 − 3B)d ′−B + B − 1)k − 2k − 2d ′ c 

B(d ′−B − 1) + 2 + 2fdV −1 

tan (d) 

, (2.8) 

where d ′ = d/Rmax, k is a diffusion parameter, and c is a drag parameter. 

V (m/s) 

(deg) 

60 

40 

20 

0 

180 

90 

0 

90 

5 10 15 20 

t (hr) 

180 

0 5 10 15 20 

t (hr) 

V (m/s) 

(deg) 

60 

40 

20 

0 

180 

90 

0 

90 

5 10 15 

t (hr) 

180 

0 5 10 15 

t (hr) 

(a) (b) 

Figure 2.3: Sample simulated wind speed time series (V (t)) and wind angle time series 

(θ(t)) using parameters: (a) Vt = 7 m/s, ∆P = 55 mB, Rmax = 50 km, and s = -50 km; 

(b) Vt = 12 m/s, ∆P = 47 mB, Rmax = 80 km, and s = 30 km. 

Figure 2.3 shows a sample of the wind (speed and orientation) profiles at two loca- 

tions during a tropical cyclone. Parameters such as the Coriolis force, diffusion coefficient, 

frictional drag coefficient are assumed to be constant for each sampled tropical cyclone. 

2.2.5 Three-Second Surface Wind 

The mean boundary wind velocity Vmbd at the location of the structure needs to be converted 

to the near-surface (10-meter) wind velocity for wind-load calculation. First, the 0.8 mean 

conversion factor is applied to obtain the best estimate of the surface wind velocity over 

open water (Powell, 1980): 

Vwater = 0.8 Vmbd. (2.9)


It is assumed that represents the mean wind speed over a 1-hour time period (Vickery 

and Twisdale, 1995); it is denoted by , where 3600 is the averaging time in seconds. The 

quantity V water 

3600 can be further converted to a best estimate of the three-second wind speed 

at 10 m over open-terrain exposure (Simiu et al., 2007): 

V land 

3 

= (1.16)(1.07) V water 

3600 . (2.10) 

The three-second wind speed is defined as the highest average speed, when averaging is over 

segments of three-second duration. Note that V land 

3 

is the wind speed used in wind load 

calculation according to the ASCE 7 Standard (American Society of Civil Engineers, 2003). 

Combining all the factors yields a direct relationship between V land 

3 

and Vmbd : 

V land 

3 = 0.993 Vmbd. (2.11) 

This simple approximate expression does of course not consider any specific topographic 

features of the area of interest. It assumes that the structure is located in terrain with open 

exposure. For the sake of clarity, V land 

3 

2.2.6 Damage Threshold 

will be denoted V in what follows. 

As stated earlier, our interest focuses on the parts of wind records when the wind speed 

exceeds a certain damage-related threshold. The level selected is 20 m/s, based on the lowest 

wind speed (50 mph) needing to be considered by the Florida Department of Financial 

Services in their hurricane loss model (Gurley et al., 2006). Hence, when a tropical cyclone 

is approaching the structure, the wind speed and wind angle begin to be re-corded when 

the wind speed exceeds the damage threshold, and the record stops when the cyclone is far 

enough away so that no subsequent wind speed exceeds 20 m/s. In each time series, the 

time when the wind speed first reaches 20 m/s is set at zero.


In situations when the distance s is large and the intensity of the tropical cyclone low, 

it may happen that the wind speed never exceeds the damage threshold. In this case, no 

wind speed or wind angle is recorded. The simulation record is then labeled ‘below damage 

threshold’; the wind loads in these records are assumed to be negligible. 

V (m/s) 

(deg) 

60 

40 

20 

0 

180 

90 

0 

90 

5 10 15 20 

t (hr) 

180 

0 5 10 15 20 

t (hr) 

V (m/s) 

(deg) 

0 

180 

(a) (b) 

60 

40 

20 

90 

0 

90 

5 10 15 

t (hr) 

180 

0 5 10 15 

t (hr) 

Figure 2.4: Wind speed and wind angle time records during Hurricane Katrina and Wilma: 

(a) Data record at Belle Chasse, LA during Hurricane Katrina; (b) Data record at Everglade 

City, FL during Hurricane Wilma (Civil and Coastal Engineering Department of the 

University of Florida, 2009). 

2.2.7 Sample Results 

Two sample sets of time series generated by the probabilistic wind model described above are 

compared with some historical hurricane wind (speed and orientation) records of the Florida 

Coastal Monitoring Program (FCMP) at the University of Florida (Civil and Coastal En- 

gineering Department of the University of Florida, 2009). The three hurricane parameters 

(Vt, ∆P and Rmax) used to generate the two sample sets are obtained from the tropical cy- 

clone reports of the National Hurricane Center (Knabb et al. 2006; Pasch et al. 2006). The 

relative distance between the tropical cyclone track and the record location (s) is obtained 

from the FCMP tower deployment map (Civil and Coastal Engineering Department of the


University of Florida, 2009). The values of the parameters are listed in the caption of Figure 

2.3, which shows the simulated wind records. For comparison, the historical wind records 

(see Figure 2.4) are converted from 15-minute average to 3-second gust. The general trends 

of the simulated wind speed and wind angle time series match the historical record quite 

well. The magnitude of the wind velocity is also close to the historical data. Note that the 

absolute accuracy of this model is not the major focus in this study. Since the objective is 

to look at the effect of changing wind directionality in individual wind events, it is more 

important for the wind time series model to be capable to generate wind time series that 

have trends similar to those of the historical wind records, in terms of both wind speed and 

wind angle. 

2.3 Alternative Approaches to Wind-Load and Reliability 

Assessment 

Given the simulated tropical cyclone wind velocity time series described in the previous 

section, wind loads may be computed and structural reliability analysis may be carried out, 

for the two afore-mentioned approaches, in the way explained below. 

2.3.1 Wind Load and Reliability Calculation 

Damage of envelope components, which is the major factor in insurance claims (Sparks 

et al., 1994), is mainly caused by wind loads during tropical cyclones (National Institute of 

Standards and Technology, 2006b). Given a wind velocity time series over the time domain 

[0, tL] (with wind speed V (t) and θ(t)), from bluff-body aerodynamics, the wind pressure 

acting on a building envelope component at time t ∈ [0, tL] is given by (Holmes, 2007): 

S(t) = 1 

2 ρV (t)2 Cp(θ(t) − γ), (2.12)


where ρ is the air density, and Cp is the non-dimensional pressure coefficient of the compo- 

nent. The pressure coefficient, which depends on the size and orientation of the structure 

and the structural component, is derived from wind tunnel tests. It is generally modeled as 

a function of θ(t) with respect to the component orientation, γ. 

Assume that wind pressure is the only damage source to the structural component. The 

limit state may be defined such that S is the wind pressure acting on the component and R 

is the capacity to resist the wind pressure. It is assumed that dead load is relatively small 

and may be (conservatively) ignored. Since tL is very short compared to the lifetime of the 

structure, deterioration is assumed to be negligible across [0, tL]. Thus, R may be defined 

as a random variable whose value remains constant over time. The probability of failure 

may be written as 

Pf = P {S(t) − R > 0, for any t ∈ [0, tL]}. (2.13) 

Since R is constant over time, the probability of failure may also be expressed as: 

where Smax is the maximum value of S within [0, tL]. 

Pf = P {Smax − R}, (2.14) 

2.3.2 Time-Stepping Method and Point-in-Time Method 

In the time-stepping method, a sample wind load S(t) is evaluated at time steps at which 

the wind time series sample values of V (t) and θ(t) are recorded. It is then compared with 

R at each of those time steps. If S(t) is larger than R at any time step, then the building 

component fails for that specific wind time series sample (equation (2.13)). Alternatively, 

for each sample wind time series, Smax may be found by comparing the values of S(t) at 

every time step, and then compared to R (equation (2.14)). 

The point-in-time method reformulates the problem by evaluating the probability of


failure at a single point in time, t ∗ , within the time domain [0, tL]. (This approach is in a 

sense compatible with the characteristics of wind loads on low-rise structures, when dynamic 

response amplification is insignificant.) The method approximates the probability of failure 

as: 

Pf ≈ P ∗ f = Prob{S(t∗ ) − R < 0}. (2.15) 

The above equation would be equivalent to equation (2.13) if S(t ∗ ) = Smax. However, 

finding t ∗ such that S(t ∗ ) = Smax requires evaluation of S(t) across the time domain [0, tL], 

which is equivalent to the time-stepping method described above. To simplify the problem, 

the effect of wind direction is assumed to be negligible so that t ∗ is selected as the time 

point at which the wind speed is maximum, e.g. V (t ∗ ) = maxt V (t). Therefore, 

2.4 Numerical Examples 

2.4.1 Setup 

Smax ≈ S ∗ = 1 

2 ρV (t∗ ) 2 Cp(θ(t ∗ ) − γ). (2.16) 

This section focuses on the building envelope of low-rise residences, which is the most vul- 

nerable building component in tropical cyclones under wind pressure (National Institute of 

Standards and Technology, 2006b). Four pressure coefficients of building envelope compo- 

nents are selected to illustrate the difference in results between the two analysis methods; 

these coefficients relate to: 

1. Positive Wall Pressure; 

2. Negative Wall Pressure; 

3. External Pressure at Roof Corner; 

4. External Pressure at Near-Edge Roof.



4 

3 

2 

1 

Negative Wall Pressure 

Positive Wall Pressure 

External Pressure 

at Roof Corner 

External 

Pressure 

at Roof 

NearEdge 

0 

0 90 180 

Wind Angle (deg) 

270 360 

Figure 2.5: Four selected pressure coefficients with respect to wind angle. 

The pressure coefficients (see Figure 2.5) are all obtained from the HAZUS-MH3 tech- 

nical manual (Federal Emergency Management Agency, 2006) and the Florida Public Hur- 

ricane Loss Projection Model engineering team report (Gurley et al., 2006). This study 

focuses on the basic cases of evaluating wind pressure using pressure coefficient functions. 

Reliability analysis of structural systems is not explicitly considered in this study, as this 

would involve many more factors, such as load paths, pressure zone distribution, and de- 

pendence among component failures, thereby clouding the focus on comparing the time- 

stepping and point-in-time methods and quantifying the effect of changing wind direction- 

ality. Comparison, as regards structural system reliability, between the time-stepping and 

point-in-time methods is dealt with in the work by Lin et al. (2010) and Yau et al. (in 

press). 

2.4.2 Maximum Wind Pressure 

10,000 wind velocity time series were generated at one-minute intervals for each of the 

hurricane categories 1, 3 and 5 by randomly sampling Vt, ∆P and Rmax using the probability


distribution parameters by Iman et al. (2002) and assuming that s is uniformly distributed 

from -200 km to 200 km. This results in three collections of simulated wind time series 

in which the tropical cyclone track is at most 200 km away from the structure. Note 

that since the entire analytical model involves only algebra, a large number of simulated 

wind time series can be generated with scant computational effort. The three wind time 

series databases are then employed to calculate the wind pressure over time associated with 

each pressure coefficient. Each database, generated with the category 1, 3 or 5 hurricane 

parameters, consists of 10,000 wind time series and represents the scenario in which the 

tropical cyclone track is at most 200 km from the structure. The angle in which the 

tropical cyclone approaches the structure is assumed to be uniformly distributed within 

[0, 2π]. For each wind time series, we fix the absolute wind direction and let the orientation 

of the structure be one of the 24 evenly spaced angles across [0, 2π]. As a result, 240,000 

individual wind velocity time series are considered for each hurricane category. 

Figure 2.6 shows the cumulative distribution functions of maximum wind pressure over 

time using the hurricane-category-5 simulated wind time series database. In each plot, the 

solid line is the cumulative distribution of the maximum wind pressure over time (Smax) 

obtained by the time-stepping method, and the dashed line is the cumulative distribution 

of wind pressure at maximum wind speed (S ∗ ) obtained by the point-in-time approach. 

The mean values of both distributions are shown in the plots. The cumulative distributions 

using hurricane categories 1 and 3 are not shown due to space constraints. 

The difference between Smax and S ∗ , indicating the degree of inaccuracy of the point- 

in-time approach, varies with the pressure coefficient. To compare the two cumulative 

distributions of each wind pressure quantitatively, the Kolmogorov-Smirnov statistic is cal- 

culated. It is defined (Kendall et al., 1999) as the largest absolute difference between two


cumulative distribution functions, F1(x) and F2(x), at the same value of the variable: 

K-S Statistic = max 

−∞

NEGATIVE WALL PRESSURE 

(COV = 0.509) 

POSITIVE WALL PRESSURE 

(COV = 0.977) 


0.5 

0.5 

0.4 

0.4 

0.3 

0.2 

K-S Statistic 

0.3 

0.2 

K-S Statistic 

0.1 

0.1 

0 

All Records |s| – Rmax < 0 |s| – Rmax ! 0 

EXTERNAL PRESSURE AT ROOF NEAR- 

EDGE 

ROOF NEAR-EDGE EXTERNAL (COV PRESSURE = 0.093) 

0.5 (COV = 0.093) 

0 


EXTERNAL PRESSURE AT ROOF CORNER 

(COV = 0.200) 

0.5 

0.5 

LEGEND 

0.4 

0.3 

0.4 

0.4 

Category 1 

Category 3 

0.2 

K-S Statistic 

0.3 

0.2 

K-S Statistic 

0.3 

Category 5 

0.1 

0.2 

0 

K-S Statistic 

|s| – Rmax ! 

0 

All Records |s| – Rmax < 

0 

0.1 

0.1 

0 

0 



Figure 2.7: Kolmogorov-Smirnov statistics comparing the maximum wind load (Smax) (obtained from time-stepping 

method) and the approximated maximum wind load (S∗ ) (obtained from point-in-time method).


A detailed analysis is conducted to examine how the Kolmogorov-Smirnov statistic 

changes under different conditions. The results of the analysis are illustrated in Figure 

2.7. First, we are interested in how the pressure coefficient function affects the results. The 

variation of pressure coefficient with respect to wind angle is quantified by the coefficient of 

variation, which is shown in the title of each plot in Figure 2.7. The plots show a very high 

correlation between the Kolmogorov-Smirnov statistic and the coefficient of variation of the 

pressure coefficients, confirming that the variation in the pressure coefficient, indicative of 

the sensitivity of wind pressure to wind angle, is one of the main sources of inaccuracy of 

the point-in-time approach. 

Second, we are interested in the effect of tropical cyclone track location on the results. 

For here we categorize all the wind time series into two types, depending on whether the 

location of the structure is ever inside the radius of maximum wind Rmax of a tropical 

cyclone. This condition may be indicated by the difference between |s| and Rmax: 

1. |s| − Rmax < 0 

The tropical cyclone track is close enough to the structure, so the latter is within 

Rmax for a period of time. The wind speed series is likely to be M-shaped and the 

change in wind angle is abrupt, as shown in Figure 2.4b. 

2. |s| − Rmax ≥ 0 

The structure is never inside Rmax. The wind speed series is likely to be bell-shaped 

and the change in wind angle is more gradual, as shown in Figure 2.4a. 

Note that |s| − Rmax is not a precise parameter that unambiguously indicates whether 

a wind speed time series has a M-shape, owing to the asymmetry of the tropical cyclone 

structure (higher wind speed on the left side and lower wind speed on the right side in the 

Northern hemisphere). For example, if the structure is to the left of the cyclone path and 

is inside Rmax, the trend of the wind speed time series may not show any M-shape.


From Figure 2.7, the Kolmogorov-Smirnov statistics are significantly larger in the case 

when |s| − Rmax < 0 for each of the four pressure coefficients, indicating that the point-in- 

time approach underestimates the wind pressure more if the structure is ever inside Rmax. 

This shows that the different trends of wind speed and wind angle due to the track location 

affects the accuracy of the point-in-time approach. A more abrupt change in wind speed 

and wind angle tends to yield less accurate results. 

Third, we examine the effect of hurricane intensity on the results. Considering all records 

(without categorizing the data by track location), Kolmogorov-Smirnov statistics de-crease 

as one goes from category 1 to category 5 for all four pressure coefficients. This indicates 

that the point-in-time approach is less accurate in calculating wind pressure for hurricanes 

of lower intensity. However, further breaking down the results by examining how the K-S 

statistics change for each case separately, |s| − Rmax < 0 and |s| − Rmax ≥ 0, one finds that 

the inaccuracy of the point-in-time approach grows with the tropical cyclone intensity for 

|s| − Rmax < 0, and vice versa for |s| − Rmax ≥ 0. Since the |s| − Rmax ≥ 0 records dominate 

for all hurricane categories (see Table 2.2 for the ratio of data in each category), on the 

whole, the inaccuracy of the point-in-time approach decreases as tropical cyclone intensity 

increases. 

Table 2.2: Percentage of simulated wind records by track location. 

|s| − Rmax < 0 |s| − Rmax ≥ 0 

Category 1 36.90% 63.10% 

Category 3 26.31% 73.69% 

Category 5 18.29% 81.71% 

2.4.3 Probability of Failure 

The next step is to apply the calculated wind pressure to reliability analysis. Here we focus 

on single-limit-state failures. We computed two probabilities of failure for each of the four


types of wind pressure by assuming two different probability models for the resistances: 

normal and lognormal. While the normal distribution is widely adopted in current vulner- 

ability models, including the HAZUS-MH model (Vickery et al., 2006b) and the Florida 

Public Hurricane Loss Projection Model (Gurley et al., 2006), the lognormal distribution 

is generally considered a better model for resistance. For comparison, the mean and stan- 

dard deviation is set at the same values in both models. The probability of failure of a 

roof sheathing panel resisting the external pressure at a roof corner or near-edge roof is 

computed, by assuming that the resistance capacity of the panel has mean and standard 

deviation equal to 6,000 Pa and 2,400 Pa, respectively. Similarly, the probability of failure 

of a wall sheathing panel resisting wall pressures is calculated by assuming that the resis- 

tance capacity of the panel has mean and standard deviation equal to 7,000 Pa and 2,800 

Pa, respectively. From equation (2.14), the probability of failure can be expressed as: 

∞ 

Pf = FR(x)fSmax(x)dx (2.18) 

−∞ 

In this case, we have 240,000 random samples of Smax (and S ∗ ) and a complete probabilistic 

description of R, Therefore, the probability of failure can be calculated from: 

Pf ≈ 

n 

i=1 

FR(Smax,i) 

n 

(2.19) 

where n is the total number of samples of Smax (240,000), FR(·) is the cumulative distribu- 

tion of R, and Smax, i is the i-th random sample of Smax. 

For the case of normally distributed resistances, the results of the reliability analysis 

are shown in Table 2.3. The percentage difference in failure probabilities between the 

time-stepping and point-in-time methods is compared, as illustrated in Figure 2.8. For the 

case of lognormally distributed resistances, the results are shown indirectly, as percentage 

differences in failure probabilities relative to the normal-distribution case, in Figure 2.9.


Table 2.3: Probabilities of failure of four component limit states 

Time-Stepping Method Point-in-Time Method 

Category 

All records |s| − Rmax < 0 |s| − Rmax ≥ 0 All records |s| − Rmax < 0 |s| − Rmax ≥ 0 

1 16.88% 51.80% 9.051% 10.40% 28.052% 6.459% 

Positive 

3 6.93% 15.47% 8.951% 9.43% 25.260% 5.885% 

Wall 

5 1.65% 2.20% 9.406% 14.06% 40.268% 8.193% 

Pressure 

1 16.88% 51.80% 9.051% 10.40% 28.052% 6.459% 

Positive 

3 6.93% 15.47% 8.951% 9.43% 25.260% 5.885% 

Wall 

5 1.65% 2.20% 9.406% 14.06% 40.268% 8.193% 

Pressure 

1 16.88% 51.80% 9.051% 10.40% 28.052% 6.459% 

Positive 

3 6.93% 15.47% 8.951% 9.43% 25.260% 5.885% 

Wall 

5 1.65% 2.20% 9.406% 14.06% 40.268% 8.193% 

Pressure 

1 16.88% 51.80% 9.051% 10.40% 28.052% 6.459% 

Positive 

3 6.93% 15.47% 8.951% 9.43% 25.260% 5.885% 

Wall 

5 1.65% 2.20% 9.406% 14.06% 40.268% 8.193% 

Pressure


(COV = 0.509) 


(COV = 0.977) 


-60% 

-60% 

-40% 

-40% 

-20% 

Percentage Difference 

-20% 


0% 



EDGE 

NEAR-EDGE ROOF EXTERNAL (COV PRESSURE = 0.093) 

0.5 (COV = 0.093) 

0% 


ROOF CORNER EXTERNAL PRESSURE 

(COV = 0.200) 

LEGEND 

0.4 

-60% 

-60% 

0.3 

Category 1 

Category 3 

0.2 

K-S Statistic 

-40% 

-40% 

Category 5 

0.1 

0 

-20% 

-20% 

|s| – Rmax ! 

0 


0 



0% 

0% 



Figure 2.8: Percentage differences between the probabilities of failure (Pf ) (obtained from time-stepping method) and the 

approximated probabilities of failure (P ∗ f ) obtained from point-in-time method) for normally distributed resistances.


(COV = 0.509) 


(COV = 0.977) 


-60% 

-60% 

-40% 

-40% 

-20% 


-20% 


0% 



EDGE 

NEAR-EDGE ROOF EXTERNAL (COV PRESSURE = 0.093) 

0.5 (COV = 0.093) 

0% 


ROOF CORNER EXTERNAL PRESSURE 

(COV = 0.200) 

LEGEND 

0.4 

-60% 

-60% 

0.3 

Category 1 

Category 3 

0.2 

K-S Statistic 

-40% 

-40% 

Category 5 

0.1 

0 

-20% 

-20% 

|s| – Rmax ! 

0 


0 



0% 

0% 



Figure 2.9: Percentage differences between the probabilities of failure (Pf ) (obtained from time-stepping method) and the 

approximated probabilities of failure (P ∗ f ) (obtained from point-in-time method) for lognormally distributed resistances.


Overall, all probabilities of failure are underestimated significantly by the point-in-time 

method due to the underestimation of wind load. The degree of underestimation ranges from 

about -5% to -60%. In addition, by comparing Figures 2.8 and 2.9, it shows that the choice 

of probability model for the resistance changes the percentage difference in probability of 

failure substantially. Unlike the Kolmogorov-Smirnov statistics related to wind pressure, 

the percentage differences in probability of failure do not exhibit any obvious trend with the 

variation of the pressure coefficient with respect to wind angle. The relationship between 

hurricane intensity and the percentage difference in probability of failure also differs for each 

wind pressure coefficient. However, it is observed that in almost all instances the percentage 

difference is larger in case the structure is within the radius of maximum wind for some time 

interval (|s| − Rmax < 0) than when the structure is located outside the radius of maximum 

wind (|s| − Rmax ≥ 0). 

2.5 Discussion 

The point-in-time method underestimates the wind load primarily because it neglects the 

effect of changing wind angle during individual wind time series. Maximum wind pressure 

usually does not occur at maximum wind speed if the pressure coefficient varies significantly 

with the wind angle or if the change in wind angle is abrupt over time. In the single-limit- 

state reliability problems, the probabilities of failure are underestimated by up to 60%. If 

the interdependence among failures of structural components is considered, the point-in- 

time approach is expected to become even less accurate. For example, in low-rise structures, 

the breakage of a window, which changes the internal pressure of the structure, would affect 

the subsequent pressure loading on the envelope components and hence significantly change 

their failure probabilities. The point-in-time approach cannot capture the subsequent effect 

of any component’s failure on the other components. In addition, the numerical examples 

consider wind pressure only. If debris impact is included, the effect of wind directionality


on the reliability results probably will be greater, since the chance of debris impact may 

strongly depend on wind direction. The time-stepping method is capable of considering 

the above effects by evaluating the structural loading in a series of time steps, but such 

evaluation can be very computationally intensive. By using approximate methods such as 

FORM or SORM instead of Monte Carlo simulation, the computation time for the time- 

stepping method may be shortened. However, assessing structural reliability under tropical 

cyclone conditions is highly complex and nonlinear and such approximate methods may 

provide inaccurate results. 

The number or pattern of time steps may be modified in the time-stepping method, per- 

haps to save computational effort. One way is to increase the length of all evenly spaced 

time time intervals. However, since maximum wind pressure and component failures are 

more likely to occur at higher wind speeds, optimality (in time stepping) could be pursued 

by making the time intervals shorter at the high wind speeds, and longer at lower wind 

speeds. 

An underlying assumption of the analysis presented is that no information is available 

regarding the orientation of the structure or the direction of the tropical cyclone track. 

When considering a prototype structure, this assumption seems appropriate, and it is com- 

monly adopted in wind-related loss estimation for a large number of buildings (see Gurley 

et al., 2006). However, in light of the significant effect of wind directionality on wind loads 

and on structural reliability, demonstrated in this study, there clearly is merit to analyze 

the prototype building using the time-stepping method. To evaluate a large number of 

individual buildings with specific orientations and locations, computation-time issues may 

be more crucial and the point-in-time method may be more advantageous. 

The analysis of the effect of changing wind direction depends almost entirely on the 

pressure coefficient functions, which provide approximations for the actual wind pressures 

acting on a structure. However, different wind tunnel testing conditions often yield very


different results, implying significant uncertainty in pressure coefficient functions for the 

same structure under the same wind condition (Fritz et al., 2008; Ho et al., 2005; Pierre 

et al., 2005). Further work is needed to determine the impact of these errors (in pressure 

coefficient functions) on the effects of changing wind directionality. 

2.6 Closing Remarks 

This chapter presents a probabilistic model to generate tropical cyclone wind velocity time 

series for use in structural reliability analysis. With the databases of wind time series 

generated by this model, a detailed assessment is made of the differences between the results 

of the time-stepping and point-in-time methods. The study shows that the point-in-time 

approach significantly underestimates the wind load and the probability of failure. The 

degree of underestimation of maximum wind load is more significant when the variation 

of the pressure coefficient with respect to the wind angle is large, or when the structure 

is located inside the radius of maximum wind of a tropical cyclone for some period of 

time. As the tropical cyclone intensity increases, the degree of underestimation of the wind 

load generally decreases. When calculating component failure probabilities, the results are 

found to depend significantly on the choice of probabilistic model (normal vs. lognormal) 

for the resistance. Also, the accuracy of the point-in-time method is reduced in case the 

structure is located, for some period of time, within the radius of maximum wind of a 

tropical cyclone. Although the point-in-time method significantly underestimates both the 

wind load and the failure probability, it is more computationally efficient than the time- 

stepping approach. Future studies might pursue optimization of time-stepping procedures 

to best balance accuracy and computational efficiency.

Chapter 

3 

Internal Pressure in Low-Rise 

Structures 


Design codes and standards, which are based on the results of various wind tunnel ex- 

periments and related research, provide a basis for the wind-related risk assessment of 

structures. However, current codes and standards do not completely cover all the factors 

involved in the complex structural damage process during high winds, such as the random- 

ness of wind pressure loads, quantification of windborne debris impact, progressive damage 

of different structural components, etc. More importantly, the purpose of the design codes 

and standards is to provide guidelines to avoid structural failure. Structural performance 

during and after failure is not the focus. To better assess the wind-related risk, structural 

models are developed to simulate the load paths and the failure sequence of some prototype 

low-rise residences (e.g. Unanwa et al., 2000; Gurley et al., 2005b). However, they require 

more available experimental data to be fully verified (Ellingwood et al., 2004). 

Besides the load paths inside the structural system and the building envelope system, 

internal pressure is the determining factor in the interplay between building components’ 

40

Chapter 3. Internal Pressure in Low-Rise Structures 41 

failures. For example, during major wind events, the presence of a dominant opening 

on a building envelope may result in an increase in internal pressure, which significantly 

intensitifes the wind load on the roof (Holmes, 2007). Failures of the roof can further 

alter the internal pressure and cause more damages in other parts of the building. Past 

research efforts have indicated that internal pressure depends on several factors, including 

geometries of openings, overall building leakage, internal volume of the building, flexibility of 

the building envelope and structure, compartmentalization within the building, etc. (Ginger 

et al., 1997; Ginger, 2000; Kopp et al., 2008). Oh et al. (2007) summarized the recent work 

on internal pressure in houses. 

This chapter examines and discusses the relationship between the damage on building 

envelope and the internal pressure in low-rise structures. The scope of this study is confined 

to building envelope due to two reasons. First, as indicated by past hurricane damage sur- 

veys, hurricane winds primarily cause damage of components and cladding on the building 

envelope, e.g. roofing materials, windows, doors and garage doors (National Institute of 

Standards and Technology, 2006b). The damage of envelope components, which causes rain 

to enter the building, is the major factor of insurance claims (Sparks et al., 1994). Second, 

the wind vulnerability of building envelope is studied extensively in the past literature. For 

example, Ellingwood et al. (2004) illustrated the sensitivity of roof panel and roof-to-wall 

connection fragility to exposure factor and component resistance. Lee and Rosowsky (2005) 

presented the reliability of roof panels given different roof shapes and structural geometry. 

Focusing on the vulnerability of building envelope is a continuation of past studies and 

facilitates comparison with previous results. 

In this study, a structural model is developed to probabilistically simulate the wind load 

acting on roof panels and wall openings according to the modified ASCE 7 standard. Several 

methods of internal pressure adjustment are implemented into the model to formulate a 

progressive damage mechanism, in which internal pressure can cause damage of structural


Figure 3.1: Unfolded view of baseline structures: (a) House A (b) House B (c) House C.


components, and any component failure may change back the internal pressure, causing 

further damages. The mathematical formulation of the damage mechanism is presented. In 

the end, the effects of the different internal pressure adjustment methods on the structural 

vulnerability are closely examined and discussed. The significance of internal pressure in 

different conditions (presence of windborne debris impact, different number of windows, 

etc.) is also discussed. 

3.2 Structural Model 

Three baseline structures (see Figure 3.1) are considered in this study and they are based 

on a model that has been extensively studied in the Wind Load Test Facility at Clemson 

University (Rosowsky and Cheng, 1999a,b). Their roofs have been analyzed under a series 

of numerical fragility assessments (Lee and Rosowsky, 2005; Rosowsky and Cheng, 1999a,b). 

Different from the previous studies, we explicitly model the dimensions and locations of the 

wall openings including doors, windows, and garage doors. All structures are assumed to 

be located at an open-country terrain (exposure type C in ASCE 7 Standard) (American 

Society of Civil Engineers, 2003). 

To access the vulnerability of the building envelope, three limit states are defined: roof 

sheathing uplift, opening pressure failure and opening debris impact failure. Each limit 

state function may be stated as R − (W + D), where R = resistance; W = wind load; D = 

dead load. The dead load is normally distributed with mean = 3.5 psf and COV = 0.1 for 

roof sheathing (Lee and Rosowsky, 2005) and is equal to 0 for opening. The component is 

considered failed if the value of the limit state function is below zero. 

The resistance statistics of roof sheathing and openings are obtained from a previous 

study (Rosowsky and Cheng, 1999b) and the Florida Public Hurricane Loss Projection 

(FPHLP) Model (Gurley et al., 2005b), respectively. According to the studies, all the 

resistances are assumed normally distributed. A summary of resistance statistics is provided

in Table 3.1. 


Table 3.1: Statistics of structural component resistance. 

Component Dimension Limit State Unit Mean COV 

Roof sheathing panel 4’ × 8’ Uplift psf 57.7 0.20 

Roof sheathing panel 4’ × 4’ Uplift psf 73.3 0.20 

Glass window 3’6” × 3’6” Pressure psf 104.4 0.20 

Door 6’10” × 3’2” Pressure psf 100 0.20 

Garage door 6’10” × 12’ Pressure psf 52 0.20 

3.3 External Wind Pressure 

In ASCE 7 Standard (American Society of Civil Engineers, 2003), the design wind pressure 

acting on components and cladding of a low-rise structure is determined from: 

W = qh(GCp − GCpi), (3.1) 

where qh = velocity pressure evaluated at mean roof height (h), G = gust factor; Cp = 

external pressure coefficient; Cpi = internal pressure coefficient. The velocity pressure 

evaluated at h is given by: 

qh = 0.00256KhKztKdV 2 I (units: lb/ft 2 ; V in mph), (3.2) 

where 0.00256 is half of the value of air density in English unit; Kh = velocity pressure 

exposure factor; Kzt = topographic factor; Kd = wind directionality factor; V = 3-second 

gust wind speed at 33 ft (10 m) and in open terrain; and I = importance factor. In 

our model, I is removed from equation (3.2) because it is a safety factor measuring the 

importance level of the structure. By assuming that there is no hill or escarpment around 

the structure, Kzt is also taken as unity. From a Delphi study by Ellingwood and Tekie


(1999), the velocity pressure exposure factor (Kh) is normally distributed (mean = 0.82, 

COV = 0.14) for exposure type C, and the directionality factor (Kd) is a normal random 

variable (mean = 0.89, COV = 0.16). 

External wind pressure varies spatially over the building envelope depending on the 

structural geometry and wind direction. Such spatial variation is represented by multiple 

pressure zones of different external pressure coefficient values (GCp) in ASCE 7 Standard. 

Table 3.2 lists the statistics of pressure coefficient (GCp) of each pressure zone, which are 

obtained from the study by Lee and Rosowsky (2005), the FPHLP model Gurley et al. 

(2005b), and the study by Ellingwood and Tekie (1999). Figure 3.2 shows the distribution 

of pressure zones under two cases of wind directionality: (1) wind perpendicular to ridgeline 

and (2) wind parallel to ridgeline, according to Lee and Rosowsky (2005). By definition, 

the directionality factor (Kd) does not apply to both cases. 

External pressure on individual sheathing panel or wall opening is calculated by a 

weighted-average method. The value of external pressure coefficient on a component is 

the sum of all the external pressure coefficient on different pressure zones multiplied by the 

percentage of component area over which those pressures act on. The external pressure 

coefficient (GCp) values are randomized for each component, according to the statistics in 

Table 3.2. In reality, the external pressure acting on the building envelope may change if 

the roof panels are uplifted. However, there is insufficient research data on such changes in 

external pressure. Thus, similar to many previous studies (e.g. Lee and Rosowsky, 2005), 

we assume that the external pressure is the same before and after the roof and the openings 

are damaged. 

3.4 Internal Pressure 

External pressure is often assumed constant regardless of the damage of the structure. 

However, internal pressure is often based upon the damage of building envelope in the


Figure 3.2: Component and cladding external pressure zones: (a) wind perpendicular to 

ridgeline (b) wind parallel to ridgeline. The wind directions are indicated by the arrows. 

The description of the pressure zones may be referred to Table 3.2. 

Table 3.2: Statistics of external pressure coefficient (GCp). 

Zone Location Nominal Mean COV 

1 Roof -0.9 -0.855 0.12 

2 Roof -1.7 -1.615 0.12 

3 Roof -2.6 -2.470 0.12 

4A Windward wall 1.0 0.950 0.12 

4B Leeward wall -0.8 -0.760 0.12 

4C Sidw wall -1.1 -1.045 0.12 

5 Side wall leading edge -1.4 -1.330 0.12

design guidelines. 


First, to calculate the initial internal pressure value of an intact structure, we employ the 

ASCE 7 Standard (American Society of Civil Engineers, 2003). According to the Standard, 

an intact structure is considered as an ‘enclosed building’, of which the internal pressure 

coefficient (GCpi) is ±0.18. Applying the statistics from Ellingwood and Tekie (1999), GCpi 

is assumed normally distributed (mean = ±0.15, COV = 0.33). Plus or minus value of the 

internal pressure, whichever yields a larger net pressure, is used to evaluate the failure status 

of a component. 

Once any building component fails, we need to adjust the internal pressure value ac- 

cording to the damage condition of the building envelope. Although the subject of internal 

pressure has been extensively studied, most studies consider only a single dominant wall 

opening (e.g. Ginger, 2000; Kopp et al., 2008), which does not fully represent many dam- 

age conditions in reality. Therefore, in the following, we consider several internal pressure 

adjustment mechanisms adopted from different design codes and loss models, which are 

applicable to any envelope damage condition. 

3.4.1 Florida Public Hurricane Loss Projection (FPHLP) Model 

The FPHLP Model (Gurley et al., 2005b) models the internal pressure as a weighted average 

of external wind pressures acting on the failed wall openings. Each failed window and door 

is given an equal weight, while a failed garage door is given a weight four times the others 

due to its large surface area. The adjusted internal pressure coefficient is given by: 

 

GCpi = 

k wkGCp,k 

 

k wk 

, (3.3) 

where GCp,k is the external wind pressure coefficient acting on the k-th failed opening and 

wk is the weight of the k-th failed opening. The weight wk is 4 if the k-th failed opening is 

the garage door, and is equal to 1 otherwise. It is assumed that a roof panel failure does

not affect the internal pressure. 

3.4.2 ASCE 7 Standard 


In ASCE 7 standard (American Society of Civil Engineers, 2003), the value of internal 

pressure depends on the enclosure classification of a structure. A building is classified as a 

‘partially enclosed building’ if both the following conditions are satisfied (American Society 

of Civil Engineers, 2003): 

1. The total area of openings in a wall that receives positive external pressure exceeds 

the sum of the areas of openings in the balance of the building envelope (walls and 

roof) by more than 10 percent. 

2. The total area of openings in a wall that receives positive external pressure exceeds 

4 ft 2 (0.37 m 2 ) or 1 percent of the area of that wall, whichever is smaller, and the 

percentage of openings in the balance of the building envelope does not exceed 20 

percent. 

For a partially enclosed building, the nominal value of GCpi is ±0.55. We employ the 

statistics from Ellingwood and Tekie (1999), assuming that the value of GCpi is normally 

distributed with mean = 0.46 and COV = 0.33. 

According to ASCE 7 standard (American Society of Civil Engineers, 2003), ‘opening 

in a wall’ is defined as any failed window, door, garage door, or roof panel. However, 

as indicated previously, the FPHLP model assumes that internal pressure is a function of 

failed windows, doors and garage doors only. Roof panels do not affect the internal pressure. 

In the results section, we will examine the effect of omitting the failed roof panels in the 

calculation of internal pressure. In addition, we will also examine the effect of an assumption 

made by Lee and Rosowsky (2005), in which a structure becomes partially enclosed once 

there is any damage on roof panels.

3.4.3 Eurocode 


In Eurocode (European Committee for Standardization/Technical committee (CEN/TC 

250), 2004), the value of internal pressure depends on the areas and locations of openings 

on the building envelope. If the area of openings on one face is at least twice the areas 

of openings in the remaining faces, that face is defined as he dominant face. The updated 

internal pressure coefficient is a fraction of the external pressure coefficient acting on the 

openings on the dominant face. If a dominant face does not exist, the internal pressure 

coefficient is a function of (1) the ratio of the height and the depth of the building and 

(2) the opening ratio, which is defined as the sum area of openings subjected to negative 

external pressure divided by the sum areas of all openings. The calculation is much more 

lengthy than the previous two methods and the details are not described here due to space 

constraint. Similar to the ASCE 7 internal pressure determination method, we will also 

examine the effect of omitting the failed roof panels in the calculation of updated internal 

pressure. 

For comparison, the Eurocode pressure internal coefficient (Cpi) has to be converted to 

the equivalent ASCE values (GCpi)eq (Oh et al., 2007): 

(GCpi)eq = 

1/2ρV 2 

10m,10min Ce(z) 

1/2ρV 2 

10m,3gust KztKhKdI Cpi, (3.4) 

where V10m,10min is the 10-min-mean wind velocity at 10 m, V10m,3gust is the 3-second gust 

wind speed, Ce(z) is the exposure factor in Eurocode. For consistency, we assume that 

(GCpi)eq has the same nominal-to-mean ratio and COV as in the ASCE internal pressure 

adjustment mechanism. Note that we are not using the Eurocode to calculate the wind 

load. We are referencing the Eurocode only regarding the internal pressure adjustment 

given the occurrence of building envelope damage.


3.5 Windborne Debris Impact 

In tropical cyclones, windborne debris contributes significantly to the damage of build- 

ing envelope, particularly glass openings (National Institute of Standards and Technology, 

2006b). For simplicity, we assume that glass windows are the only structural components 

vulnerable to windborne debris. Both HAZUS-MH hurricane model (Federal Emergency 

Management Agency, 2006) and the FPHLP Model (Gurley et al., 2005b) formulate the 

probability of debris damage to an opening, PV (D), at a given wind speed (V ) as: 

PV (D) = 1 − exp[−λq(1 − P (ζ − ζ0))], (3.5) 

where λ is the mean number of missile impacts on the building, q is the fraction of the 

building surface covered by the opening, P (ζ − ζ0) is the probability that the momentum 

(ζ) of the debris is less than the damage threshold value (ζ0) given an impact. 

In the FPHLP Model (Gurley et al., 2005b), the parameters λ and P (ζ − ζ0) are some 

functions of wind speed (V ) and are expressed in five different parameters: 

P (a window fails due to impact) = 1 − exp(−ANABCD), (3.6) 

where A is the fraction of potential missile objects in the air, NA is the total number of 

available missle objects, B is the fraction or airborne missiles that hit the house, C is 

the fraction of the impact wall that is glass, and D is the probability that the impacting 

missiles have momentum above damage threshold. As explained in the report of Florida 

public hurricane loss projection model (Gurley et al., 2005b), NA is chosen as 100. A is 

modeled as a Gaussian cumulative density function of wind speed, with a mean value of 

135 mph and a standard deviation of 15 mph. B is a linear function of wind speed, with a 

value of zero at 50 mph and a value of 0.4 at 250 mph. D is a Gaussian cumulative density


function of wind speed with a mean of 70 mph and a standard deviation of 10 mph. While 

other advanced windborne debris models (e.g. Lin and Vanmarcke, 2010; Lin et al., 2010) 

are available, we employ the FPHLP debris model parameters in this study because we are 

considering a standalone structure and do not consider its interaction with the surrounding 

environment. 

3.6 Damage Evaluation 

Given the external pressure model, the internal pressure model, the windborne debris model 

and the resistance model, the damage of building envelope may be evaluated at any wind 

speed and wind direction. The following explains the damage evaluation mechanism math- 

ematically. 

3.6.1 Component Failure Probability 

A binary random variable, Ai, may be defined to indicate the damage condition of the i-th 

roof panel or wall opening: 

⎧ 

⎪⎨ 0 if component i has not failed 

Ai = 

⎪⎩ 1 if component i has failed 

(3.7) 

Hence, a set A = {Ai : Ai = 1, 1 ≤ i ≤ n}, where n is the number of components, can 

be defined to indicate the damage condition of the entire building envelope. A = ∅ means 

an intact builiding envelope. Given A = a, we may define the probability distribution 

of the internal pressure coefficient value (GCpi) using one of the internal pressure models 

introduced previously. Along with the probability distributions of the external pressure 

coefficient (GCp) and other parameters (GCpi, Kh, Kzt and Kd in equations 3.1 and 3.2, 

we can evaluate the conditional probability density function f Li|a(·) of the wind load (Li) 

acting on any structural component i. Therefore, given the cumulative distribution FRi (·)


of the component resistance (Ri), the uplift or pressure failure probability of the component 

is defined as: 

⎧ ∞ 

⎪⎨ FRi 

P (Ai = 1|A = a) = 0 

⎪⎩ 

(x)fLi|a(x)dx if Ai ∈ a 

1 if Ai ∈ a 

. (3.8) 

The above equation only applies to roof panel, door and garage door, which fail due to 

wind pressure only and is not affected by windborne debris impact. For windows, we have 

to consider the windborne debris impact in addition to wind pressure. Assuming that both 

failure modes are independent of each other, the failure probability of a window is: 

P (Ai = 1|A = a) = P (pressure i|A = a) + P (debrisi|A = a) 

−P (pressure i|A = a) · P (debrisi|A = a), 

(3.9) 

where P (pressure i|A = a) is equal to the expression in equation 3.8. P (debrisi|A = a), 

which is the probability that the i-th window is damaged by debris impact given the damage 

condition A = a, may be obtained from the windborne debris model. 

3.6.2 System Failure Probability 

The system damage simulation is graphically illustrated in Figure 3.3, and is explained 

mathematically as follows. Given a damage condition A = ap , the probability that A 

becomes aq is equal to: 

⎧ 

⎪⎨ 

P (A = aq|A = ap) = 

⎪⎩ 

0 if ∃k : Ak ∈ ap, Ak ∈ aq 

n 

i=0 P (Aq,i = 1|A = ap) otherwise 

, (3.10) 

where the formulation of P (Ai = 1|A = a) is given in equations 3.8 and 3.9. The condition 

Ak ∈ ap and Ak ∈ aq means that once a component fails, it is always considered as failed

Wind Speed & 

Wind Direction 


Windows Only 

External 

Pressure 

Internal 

Pressure 

Debris 

Impact 

Roof Panels, Windows, Doors and Garage Doors 

Wind 

Pressure 

if additional envelope damage occurs 

Figure 3.3: Flowchart of system damage simulation. 

and cannot be repaired during the damage simulation in the model. 

Envelope 

Damage 

Given an intact structure, a failure sequence over time can be defined as {∅, a1, a2, . . . , am}, 

where ap ⊂ aq, p < q. The building envelope is intact at the beginning (A = ∅), then it 

becomes a1 and eventually a2 over time because of the change in internal pressure. The 

damage condition stops at am when it achieves the equilibrium between the internal pres- 

sure and the envelope damage. To calculate the occurrence probability that A = am, we 

have to consider all the failure sequences that lead to am: 

P (A = am) = 

 

P (A = a2|A = a1) · · · · 

all {a1,...,am} 

· P (A = am|A = am−1) · P (A = am|A = am). 

(3.11) 

The last term P (A = am|A = am) in the above equation accounts for the probability 

that the failure sequence stops at am, at which an equilibrium has achieved between the 

internal pressure and building envelope damage. To avoid repeated counts of windborne 

debris impact after every change of internal pressure value, we only account for the debris


impact at the beginning when the building envelope is intact (A = ∅): 

P (debrisi|A = a) = 0 if a = ∅. (3.12) 

To quantify the damage condition of the building envelope, we can easily obtain the number 

of failed roof panels and the number of failed wall openings from the set A. The loss ratio is 

obtained by dividing the number of failed components over the total number of components. 

3.7 Results 

3.7.1 Baseline structure B under 150-mph wind 

Baseline structure B under 150-mph wind towards the structure’s front face is served as an 

example to illustrate the damage mechanism that is illustrated earlier in Figure 3.3. For 

simplicity, windborne debris impact is omitted. 10,000 numerical simulations are carried 

out for each of the three internal pressure adjustment methods that are introduced earlier. 

Figure 3.4 presents the interplay between the internal pressure and the building envelope 

damage using each of the three methods. 

In each simulation, two values for the initial internal pressure coefficient are randomly 

selected from two normal distributions (mean = +0.15, COV = 0.33; and mean = -0.15, 

COV = 0.33). With the two initial internal pressure coefficients, two net pressure values are 

calculated for each roof panel and wall opening, and the larger one will be used to estimate 

the failure of the structural components. In Figure 3.4, the histogram labeled ‘internal 

pressure coefficient’ shows the distribution of the internal pressure coefficient which yields 

the larger load. The distribution of the internal pressure coefficient and the loss ratio of roof 

panels and wall openings are the same in every method’s step 1, because internal pressure 

adjustment does not apply until step 2. In most cases of step 1, the garage door, which is 

has the lowest resistance in the model, fail. In some cases, there may be no wall opening

(a) 

STEP 1 

STEP 2 

STEP 3 

(b) 

STEP 1 

STEP 2 

STEP 3 

(c) 

STEP 1 

STEP 2 

STEP 3 

-1.5 

-1.5 

-1.5 

-1.5 

-1.5 

-1.5 

-1.5 

-1.5 

-1.5 


Internal Pressure Coefficient Damaged Roof Panels Damaged Wall Openings 

0 +1.5 

0 +1.5 

0 +1.5 

0% 

0% 

0% 

100% 0% 

100% 0% 

100% 0% 


0 +1.5 

0 +1.5 

0 +1.5 

0% 

0% 

0% 

100% 0% 

100% 0% 

100% 0% 


0 +1.5 

0 +1.5 

0 +1.5 

0% 

0% 

100% 0% 

100% 0% 

100% 0% 

Figure 3.4: Distributions of internal pressure coefficient and building envelope damage 

of baseline structure B under a 150-mph wind towards the structure’s front face using 

(a) FPHLP (b) ASCE 7 Standard (c) Eurocode internal pressure adjustment mechanism. 

Windborne debris impact is not considered in the analysis. Each roof panel has the same 

weight in the calculation of loss ratio regardless of its area. Similarly, each window, door 

and garage door has the same weight. 

0% 

100% 

100% 

100% 

100% 

100% 

100% 

100% 

100% 

100%


failures at all, or there are several broken windows in addition of the failed garage door. At 

least 20% of the roof panels are uplifted in most cases of step 1. Based on the damage in 

step 1, the internal pressure distribution is updated in step 2 using three different internal 

pressure adjustment methods. 

Using the internal pressure adjustment method in the FPHLP model (see Figure 3.4a), 

the internal pressure coefficient becomes around 1.0 in many of the simulations in step 2. It 

is because in this model, the internal pressure coefficient is a weighted average of external 

pressure coefficients acting on the broken wall openings. In most cases, as a result of the 

failed garage door on the front face, the updated internal pressure coefficient becomes ∼1.0, 

which is the value of the external pressure coefficient acting on the front face. The positive 

internal pressure intensifies the uplift load on the roof, causing much more damage on the 

roof panels. It also increases the pressure loads on the walls which experience suction from 

leeward winds, causing more damage on the windows and doors. Based on the damage 

level at step 2, the internal pressure is updated again. But it virtually does not induce 

any further damage. The failure mechanism finishes after step 3, in which each of the 

10,000 simulations has achieved equilibrium between the internal pressure and the building 

envelope damage. 

In the ASCE 7 Standard internal pressure method (see Figure 3.4b), there is no internal 

pressure adjustment in almost all simulations, because it is very rare that the first condition 

of a partially enclosed building is satisfied. When significant roof panels are uplifted, it is 

almost impossible that the sum area of failed windows and doors will exceed the sum area of 

uplifted roof panels. As a result, the total area of openings in a wall that receives positive 

pressure cannot exceed the sum area of openings that receive zero or negative external 

pressure, since the roof is always subjected to uplift (negative) pressure. This may not 

reflect the reality very well since it is difficult to believe that the internal pressure does not 

change even after most roof panels are uplifted, exposing the internal of the structure to the


wind. Therefore, as stated in the previous section, we are modifying the ASCE 7 internal 

pressure mechanism so that the internal pressure depends on the wall openings only. We are 

also modifying the mechanism so that the building becomes partially enclosed immediately 

once any component fails. The results will be shown and discussed later in this chapter. 

In the Eurocode internal pressure method (see Figure 3.4c), the internal pressure is 

based on the area and location of failed wall openings and failed roof panels. The internal 

pressure coefficient becomes around either -1.10 or -0.25 in almost all simulations of step 2. 

In some simulations, the area of uplifted roof panels is at least twice the area of the failed 

windows and doors. According to the Eurocode, the internal pressure coefficient hence 

becomes a fraction of the negative external pressure coefficients that act on the roof panels, 

which is around -1.10. In other simulations, the internal pressure becomes around -0.25, 

because when the roof damage is not severe, the internal pressure is calculated based on the 

opening ratio, which is defined as the sum area of openings subjected to negative external 

pressure divided by the sum areas of all openings. Similar to the FPHLP model in Figure 

3.4a, after step 2, the internal pressure becomes smaller (closer to zero) in many simulations, 

leading to a smaller wind load acting on the structure. It is because in both methods, the 

internal pressure coefficient is some average of the external pressure coefficients acting on 

several damaged components. More damages often mean that the internal pressure is the 

average of more positive and negative values, and has a smaller absolute value. 

The results above do not consider the presence of windborne debris impact. Herein we 

use the same example but include windborne debris impact in the simulations. Figure 3.5 

presents the distributions of internal pressure coefficient and building envelope damage using 

each of the three internal pressure adjustment methods. Compared to the previous results, 

windborne debris impact leads to additional window damage in step 1 (see step 1 in Figure 

3.5). The additional failed windows may or may not affect the internal pressure value or the 

roof panel damage in step 2, depending on the method of internal pressure adjustment. In

(a) 

STEP 1 

STEP 2 

STEP 3 

(b) 

STEP 1 

STEP 2 

STEP 3 

(c) 

STEP 1 

STEP 2 

STEP 3 

-1.5 

-1.5 

-1.5 

-1.5 

-1.5 

-1.5 

-1.5 

-1.5 

-1.5 



0 +1.5 

0 +1.5 

0 +1.5 

0% 

0% 

0% 

100% 0% 

100% 0% 

100% 0% 


0 +1.5 

0 +1.5 

0 +1.5 

0% 

0% 

0% 

100% 0% 

100% 0% 

100% 0% 


0 +1.5 

0 +1.5 

0 +1.5 

0% 

0% 

100% 0% 

100% 0% 

100% 0% 

Figure 3.5: Distributions of internal pressure coefficient and building envelope damage 

of baseline structure B under a 150-mph wind towards the structure’s front face using 

(a) FPHLP (b) ASCE 7 Standard (c) Eurocode internal pressure adjustment mechanism. 

Windborne debris impact is considered in the analysis. Each roof panel has the same weight 

in the calculation of loss ratio regardless of its area. Similarly, each window, door and garage 

door has the same weight. 

0% 

100% 

100% 

100% 

100% 

100% 

100% 

100% 

100% 

100%


the FPHLP model, the internal pressure distribution changes significantly in the presence of 

windborne debris impact, because the internal pressure value is very sensitive to the number 

of failed wall openings (see equation 3.3). This considerably increases the roof panel loss 

ratio. However, in the ASCE 7 internal pressure adjustment method, the additional window 

damage does not make the structure a ‘partially enclosed building’. Therefore, it does not 

affect the internal pressure calculation, leaving the roof panel loss ratio the same as in 

the previous results. In the Eurocode, the windborne debris impact changes the internal 

pressure distribution in certain extent, but such change in internal pressure does not lead 

to much difference in roof panel damage distribution. 

3.7.2 Roof Damage over 50–250 mph Wind Speed Range 

The results above demonstrated the behavior of baseline structure B under a sepcific wind 

speed and wind direction. We can expand the analysis by running the same type of sim- 

ulations using different baseline structures, wind speeds and directions, and more internal 

pressure adjustment mechanisms. The resultant roof vulnerability curves are presented in 

Figure 3.6. Herein, the roof vulnerability is defined as the mean loss ratio of roof panels 

at the last step of the internal pressure adjustment process, which is step 3 in Figures 3.4 

and 3.5. Since the results are the same for both wind directions parallel to ridgeline, we are 

presenting only one of them. Therefore, the figure shows the results of three wind angles, 

instead of the four cardinal wind directions. Also, different assumptions within the ASCE 

7 and Eurocode internal pressure adjustment methods are considered, leading to a total 

of seven different internal pressure adjustment models. In the figure, ‘(instant)’ in ASCE 

7 means that a building becomes ‘partially enclosed’ immediately after occurrence of any 

degree of damage on the building envelope. 

As wind speed increases, mean roof damage increases nonlinearly in almost all cases. 

For each wind direction (presented in each subfigure (a), (b) and (c) in Figure 3.6), if

(a) 

WITHOUT WINDBORNE DEBRIS WITH WINDBORNE DEBRIS 

(b) 

Mean Loss Ratio 




1 

0.8 

0.6 

0.4 

0.2 

1 

0.8 

0.6 

0.4 

0.2 


BASELINE STRUCTURE A BASELINE STRUCTURE B BASELINE STRUCTURE C 

0 

50 100 150 200 250 

Wind Speed (mph) 

0 

50 100 150 200 250 


0.6 

0.6 

BASELINE STRUCTURE B BASELINE 0.8 STRUCTURE C 

0.8 

0.8 



1 

0.8 

0.6 

0.4 



1 

0.8 

0.6 

0.4 

0.2 

0 

50 100 150 200 250 


1 

0.8 

0.6 

0.4 

0.2 

0 

50 100 150 200 250 




1 

0.8 

0.6 

0.4 

0.2 

0 

50 100 150 200 250 


1 

0.8 

0.6 

0.4 

0.2 

0 

50 100 150 200 250 



0.2 

0.2 

0.2 


1 

0 

50 

1 

100 150 200 250 

0 

50 

1 

100 150 200 250 

LINE STRUCTURE A 

0.8 

1 



BASELINE STRUCTURE B BASELINE STRUCTURE C 

0.8 

0.8 

1 

1 

1 



0 

50 100 0.2 150 200 250 


0 

00 250 50 100 150 200 250 




1 

0.8 

0.6 

0.4 

0.8 



1 

0.8 

0.6 

0.4 

0 

50 100 150 200 250 


1 

URE B 

0.4 

1 

BASELINE 0.6 STRUCTURE C 

0.6 

0.4 

0.6 

0.6 

0.4 

0.6 

LEGEND 

.8 

0.2 

0.8 

0.2 

0.2 

1 

0.4 

0.4 

0.4 

0.4 

0.4 

LEGEND 

.6 

0 

0.6 

0 

0 

0.8 50 100 150 200 0.2 250 50 100 150 200 0.2 250 50 100 150 200 0.2 250 

0.2 


0.2 

No internal pressure 



adjustment 

.4 

0.4 

0.6 

0 

LEGEND 0 

FLPHP 

1 

0 

0 

50 

1 

100 1500 200 250 50 

1 

100 150 200 250 50 

150 200 250 50 100 150 200 250 50 100 150 200 250 

ASCE 7 

.2 



ind Speed (mph) 

0.2 

0.4 


Wind Speed 

No internal 

(mph) 

pressure 

(excl. failed roof panels) 

0.8 

0.8 LEGEND 

adjustment 0.8 

ASCE 7 

FLPHP 

(incl. failed roof panels) 

0 

1 

0 

1 

50 100 0.2 150 


0.6 200 250 50LEGEND 100 150 0.6 200 250 

ASCE 7 

ASCE 7 (instant) 

adjustment 

0.6 





0.8 

FLPHP 0.8 

ASCE 7 


0 

00 250 50 0.4 100 150 200 250 0.4 ASCE 7 

(incl. failed roof 

0.4 

panels) 


1 

1 


(excl. failed roof panels) ASCE 7 (instant) 

EUROCODE 

0.6 

ASCE 7 

0.6 



.8 

0.2 

0.8 

0.2 (incl. failed roof panels) ASCE 7 (instant) 0.2 

EUROCODE 

1 




0.4 

0.4 

(excl. failed roof panels) EUROCODE 

.6 

0 

0.6 

0 

0.8 50 100 150 200 250 50ASCE 7 100 (instant) 

(excl. failed roof 0panels) 

150 200 250 50 100 150 200 250 

0.2 


(incl. failed 0.2 


roof 

Speed 

panels) 

(mph) Figure EUROCODE 3.6: To beWind continued. 

Speed (mph) 

.4 

0.4 

EUROCODE 


0.6 


0 

150 200 250 50 100 150 200 EUROCODE 

0 

250 50 100 150 200 250 

.2ind 

Speed (mph) 

0.2 


0.4 




adjustment 

FLPHP 

ASCE 7 


ASCE 7 


100 ASCE 1507 (instant) 200 250 

Wind (excl. Speed failed (mph) roof panels) 



EUROCODE 


EUROCODE 












0 

50 100 150 200 250 




0.6 

1 

0.8 

LEGEND 


adjustment 

FLPHP 

ASCE 7 


ASCE 7 






EUROCODE 


EUROCODE 


LEGEND 


adjustment 

FLPHP 

ASCE 7 


ASCE 7 






EUROCODE 


EUROCODE 

(incl. failed roof panels)



0.6 

0.6 

BASELINE STRUCTURE B BASELINE 0.8 STRUCTURE C 

0.8 

0.8 



1 

0.8 

0.6 

0.4 



0.2 

0.2 

0.2 


1 

0 

50 

1 

100 150 200 250 

0 

50 

1 

100 150 200 250 

LINE STRUCTURE A 

0.8 

1 



BASELINE STRUCTURE B BASELINE STRUCTURE C 

0.8 

0.8 

1 

1 

1 



0 

50 100 0.2 150 200 250 


0 

00 250 50 100 150 200 250 




1 

0.8 

0.6 

0.4 

0.8 



1 

0.8 

0.6 

0.4 

0 

50 100 150 200 250 


1 

URE B 

0.4 

1 

BASELINE 0.6 STRUCTURE C 

0.6 

0.4 

0.6 

0.6 

0.4 

0.6 

LEGEND 

.8 

0.2 

0.8 

0.2 

0.2 

1 

0.4 

0.4 

0.4 

0.4 

0.4 

LEGEND 

.6 

0 

0.6 

0 

0 

0.8 50 100 150 200 0.2 250 50 100 150 200 0.2 250 50 100 150 200 0.2 250 

0.2 


0.2 




adjustment 

.4 

0.4 

0.6 

0 

LEGEND 0 

FLPHP 

1 

0 

0 

50 

1 

100 1500 200 250 50 

1 

100 150 200 250 50 

150 200 250 50 100 150 200 250 50 100 150 200 250 

ASCE 7 

.2 



ind Speed (mph) 

0.2 

0.4 



No internal 

(mph) 

pressure 


0.8 

0.8 LEGEND 

adjustment 0.8 

ASCE 7 

FLPHP 


0 

1 

0 

1 

50 100 0.2 150 


0.6 200 250 50LEGEND 100 150 0.6 200 250 

ASCE 7 


adjustment 

0.6 





0.8 

FLPHP 0.8 

ASCE 7 


0 

00 250 50 0.4 100 150 200 250 0.4 ASCE 7 

(incl. failed roof 

0.4 

panels) 


1 

1 


(excl. failed roof panels) ASCE 7 (instant) 

EUROCODE 

0.6 

ASCE 7 

0.6 



.8 

0.2 

0.8 

0.2 (incl. failed roof panels) ASCE 7 (instant) 0.2 

EUROCODE 

1 




0.4 

0.4 

(excl. failed roof panels) EUROCODE 

.6 

0 

0.6 

0 

0.8 50 100 150 200 250 50ASCE 7 100 (instant) 

(excl. failed roof 0panels) 

150 200 250 50 100 150 200 250 

0.2 


(incl. failed 0.2 


roof 

Speed 

panels) 

(mph) 

EUROCODE 


.4 

0.4 

EUROCODE 


0.6 


0 

150 200 250 50 100 150 200 EUROCODE 

0 

250 50 100 150 200 250 

.2ind 

Speed (mph) 

0.2 


0.4 




adjustment 

FLPHP 

ASCE 7 


ASCE 7 


100 ASCE 1507 (instant) 200 250 

Wind (excl. Speed failed (mph) roof panels) 



EUROCODE 


EUROCODE 








(c) 





0 

50 100 150 200 250 




0.6 

Figure 3.6: Roof panel vulnerability curves: (a) Wind towards the front face of structure 

(b) Wind parallel to ridgeline (c) Wind towards to the back face of structure. In the legend, 

‘excl. failed roof panels’ means that the roof damage condition is not considered in the 

calculation of internal pressure. Similarly, ‘incl. failed roof panels’ means that the roof 

damage condition is included in the calculation of internal pressure. 

1 

0.8 

LEGEND 


adjustment 

FLPHP 

ASCE 7 


ASCE 7 






EUROCODE 


EUROCODE 

(incl. failed roof panels)


there is no internal pressure adjustment, the roof vulnerability curves are exactly the same 

regardless of the choice of baseline structure or the presence of windborne debris, because 

all the baseline structures have the same roof and the windborne debris does not damage 

the roof given the setup of the model. On average, wind parallel to ridgeline is causing a 

smaller roof damage, because about half of the roof is well shielded and is not subjected to 

any load, as shown in Figure 3.2. In all cases, internal pressure adjustment increases or has 

no effect on the mean roof damage. The degree of such increase depends on the wind speed, 

the wind direction, the existence of windborne debris and the number of windows on the 

structure. There is no simple linear relationship between the degree of increase and any of 

the above parameters. The following presents a breakdown of the effect of each parameter 

on the mean roof panel loss ratio in each of the internal pressure adjustment methods. 

3.7.2.1 Percentage increase in mean roof damage ratio 

First, Figure 3.7 shows the range of percentage increase as well as the average percentage 

increase in mean roof damage, using different internal pressure adjustment methods com- 

paring no internal pressure adjustment over all 18 cases in Figure 3.6. The FLPHP internal 

pressure adjustment model has the largest overall impact on the mean roof damage, partic- 

ularly over the 120-130 mph wind speed (>200%). On average it contributes an addittional 

∼50% to the mean roof damage ratio. 

Comparatively, the ASCE 7 method has a relatively small effect on the mean roof 

damage. If we do not consider any failed roof panels in the internal pressure adjustment, 

the maximum percentage increase is about 70%. But the average is less than 20% over all 

wind speeds. There is almost no effect on the mean roof damage if we do consider the failed 

roof panels in the internal pressure adjustment. As explained in last section, the reason is 

because the condition of ‘partially enclosed’ building is difficult to satisfy. However, if it 

is assumed that a building becomes ‘partially enclosed’ immediately after any damage (see

Maximum Percentage 

Increase in 

Mean Roof Damage (%) 

Maximum Percentage Difference (%) 


Increase in 




Increase in 



250 

200 

150 

100 

50 


0 

100 150 200 250 



250 

200 

150 

100 

50 

0 

100 150 200 250 



250 

200 

150 

100 

50 

!"#$" 

%&'()(*%+,-./01+2340-5+6772+839-0: 

%&'()(*%+,49/01+2340-5+6772+839-0: 

0 

100 150 200 250 

Wind Speed (mph) (mph) 


Increase in 




Increase in 




Increase in 

Mean Maximum Roof Percentage Damage Difference (%) (%) 


Increase in 

Mean Maximum Roof Percentage Damage Difference (%) (%) 

250 

200 

150 

100 

50 

0 

100 150 200 250 



250 

200 

150 

100 

50 

0 

100 150 200 



250 

250 

200 

150 

100 

50 

0 

100 150 200 250 

Wind Speed (mph) (mph) 

250 

200 

150 

100 

50 

;


the figures labeled ASCE 7 (instant)), the effect of internal pressure on the roof damage is 

significantly increased. This significant increase is the same no matter whether the failed 

roof panels are taken into account, since in almost every simulation with wind speed over 

100 mph, both roof panels and wall openings almost cannot avoid damage and the building 

turns to ‘partially enclosed’. The internal pressure coefficient hence becomes the prescribed 

value for ‘partially enclosed’ building. The percentage increase is more significant when the 

wind speed is around 100 mph. The increases diminishes as the wind speed increases. 

Lastly, in the Eurocode internal pressure adjustment mechanism, if failed roof panels 

are omitted, the mean roof damage significantly increases in cases in which the wind speed 

is under 160 mph. The effect diminishes when the wind speed increases. If failed roof panels 

are considered in the calculation of internal pressure, the results are opposite. The increase 

in mean roof panel loss ratio is relatively small when the wind speed is under 160 mph, and 

the increase can reach up to 80% as wind speed increases. 

3.7.2.2 Number of windows and windborne debris 

Second, we examine the effects of the number of windows and the windborne debris on the 

roof damage in the presence of internal pressure adjustment. Average roof vulnerability 

curves are first obtained by averaging the respective roof vulnerability curves from the 

four cardinal wind directions. The average roof vulnerability curve of baseline structure C 

without the presence of windborne debris is selected as the control that is to be compared 

with all other average roof vulnerability curves. The percentage differences between all the 

average vulnerability curves and the structure-C-without-debris average vulnerability curve 

are presented in Figure 3.8. 

The left of Figure 3.8 illustrates how the number of windows affects the mean roof 

damage if windborne debris impact is not accounted for. In the figure, the dotted line is 

always at 0%, since it represents the percentage difference between the mean roof damage


baseline structure C and itself. The other two lines which represent baseline structure 

A (which has the most windows) and baseline structure B (which has the second most 

windows) vary with the wind speed and the choice of internal pressure method. As indicated 

in the Figure, more windows do not necessarily imply a ‘worse’ internal pressure, higher 

wind load of the roof and hence a higher damage on roof. For example, when wind speed is 

around 200 mph, baseline structures A and B have a mean roof damage at least 5% lower 

than baseline structure C, which has much fewer windows. Also, at some wind speeds, 

baseline structure B, which has the second least windows, has the highest roof damage. 

It shows that there can be a nonlinear relationship between the number of windows and 

the roof damage. In most of the cases, additional windows do not lead to more than 10% 

change in the average roof damage over the four wind angles if windborne debris impact is 

omitted. 

The right of Figure 3.8 illustrates how the number of windows affects the mean roof 

damage if windborne debris is considered in the model. The windborne debris impact has 

very significant effects on the roof damage since the percentage differences are significantly 

larger in all cases than the left panels, except in the cases of ASCE 7 where the structure 

becomes partially enclosed immediately given any building envelope damage (as indicated 

by ASCE (instant) in the Figure). It is because once the structure becomes partially en- 

closed, the internal pressure coefficient becomes the prescribed values for partially enclosed 

structure. Any additional damage on the building envelope can no longer affect the internal 

pressure. Besides, the effect of the number of windows on the roof damage is more signifi- 

cant in the presence of windborne debris impact, as shown by a larger percentage difference 

between the lines. But similar to the left panel of the figure, additional windows solely does 

not imply an increase or decrease in roof damage.

FPHLP 

ASCE 7 

(excl. failed 

roof panels) 

ASCE 7 

(incl. failed 

roof panels) 

ASCE 7 

(instant) 

(excl. failed 

roof panels) 

ASCE 7 

(instant) 

(incl. failed 

roof panels) 

Eurcode 

(excl. failed 

roof panels) 

Eurocode 

(incl. failed 

roof panels) 

1 

0.8 

0.6 

0.4 

0.2 

10 % 

0 % 


10% 

100 

4 % 

150 200 250 

0 % 

4% 

100 

3 % 

150 200 250 

0 % 

3% 

100 

4 % 

150 200 250 

0 % 

4% 

100 

4 % 

150 200 250 

0 % 

4% 

100 

10 % 

150 200 250 

0 % 

10% 

100 

30 % 

150 200 250 

0 % 

30% 

100 150 200 250 

LEGEND 


150 % 

0 % 

150% 

100 

60 % 

150 200 250 

0 % 

60% 

100 

10 % 

150 200 250 

0 % 

10% 

100 

4 % 

150 200 250 

0 % 

4% 

100 

4 % 

150 200 250 

0 % 

4% 

100 

100 % 

150 200 250 

0 % 

100% 

100 

40 % 

150 200 250 

0 % 

40% 

100 150 200 250 

Wind speed (mph) Wind speed (mph) 

1 

Baseline structure A (15 windows) 

(without windborne debris 

0.8 

impact) 

Baseline structure B (11 windows) 

(without windborne debris impact) 

Baseline structure C (4 

0.6 

windows) 

(without windborne debris impact) 

0.4 

0.2 

0.2 

0.4 

0.6 

0.8 

LEGEND 

Baseline structure A (15 windows) 

(with windborne debris impact) 

Baseline structure B (11 windows) 


Baseline structure C (4 windows) 


Figure 3.8: Percentage differences between the average roof damages over four cardinal wind 

0 directions and the average roof damage of0 baseline structure C without windborne debris. 

0.2 

0.4 

0.6 

0.8 

1 

1 

1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 1 0.8 0.8 1 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1

3.8 Discussion 


As shown in the results, the internal pressure plays a very significant role in the building 

envelope damage over a wide range of wind speed and wind direction. In some cases, the 

number of failed roof panels is increased by a few times if internal pressure adjustment 

is implemented. However, the effect of internal pressure on the building damage very 

much depends on the setup of the internal pressure adjustment model. Unfortunately, 

there are not many design guidelines or experimental data on the simulation of internal 

pressure changes during the structural damage process. In fact, this may be a difficult 

task to introduce a simple model. As shown in past research, internal pressure depends 

on a series of factors including geometries of openings, overall building leakage, internal 

volume, flexibility of building envelope, etc. Damages on building envelope would further 

complicate the problem since it involves complex aerodynamics depending on the details of 

structural failure. But given the large effect of internal pressure on the building envelope as 

shown above, this is important for the wind engineering field to tackle the issue. Also, as 

more research efforts address the problem of windborne debris impact, there is an increasing 

demand for the internal pressure research, since windborne debris impact on the building 

envelope is very closely related to the internal pressure problem. 

In the results, we only demonstrated the structural damage under individual wind direc- 

tions (wind parallel with or perpendicular to ridgeline). However, structural design requires 

an examination of the ‘worst’ structural behavior under a range of wind directions. Con- 

ventionally, some codes and standards (e.g. ASCE 7 Standard) do not take into account 

the effect of different wind directions individually. Instead, they conservatively consider the 

‘worst’ wind angle for each envelope surface, evaluating the maximum wind pressure (in 

both positive and negative signs) over all wind angles acting on each individual structural 

component. The maximum load is then converted to the design wind pressure by some 

factor (e.g. wind directionality factor (Kd) in ASCE 7 Standard), which accounts for the


probability that the maximum wind may not impact the component in its weakest orien- 

tation. However, if progressive damage (e.g. progressive building envelope damage due to 

internal pressure adjustment) is considered, it is necessary to consider the structural behav- 

ior under each individual wind angle in order to accurately model the initial damage and 

hence the failure sequence. Looking at the worst-case scenario of each individual component 

separately and not inspecting all structural components simultaneously under a single wind 

direction, the simplified approach in ASCE 7 Standard is unable to simulate the realistic 

failure sequence. 


A structural model is developed in this study to examine the effect of internal pressure 

on the damage of building envelope. A number of internal pressure adjustment methods 

(FPHLP model, ASCE 7 Standard and Eurocode) are implemented in the model to simulate 

the interplay between the building component failure and the internal pressure, creating a 

progressive damage mechanism. The mechanism is explained in details in mathematics and 

is illustrated through a few numerical examples. The roof damage results using different 

baseline structures, internal pressure adjustment methods and windborne debris parameters 

over a wide range of wind speeds are presented. The effect of internal pressure on the roof 

damage is very significant, but the degree of the effect depends on the setup of the internal 

pressure adjustment model. It is necessary to further examine the internal pressure change 

in various building envelope damage conditions.

Chapter 

4 

Integrated Multi-Structural 

Vulnerability Model 


Wind pressure, a major cause of hurricane-induced damage to structures, has been studied 

extensively through wind tunnel experiments and in situ measurements, and approxima- 

tions of wind pressures acting on (components of) structures are incorporated into current 

vulnerability models, which include the FEMA HAZUS-MH model (Vickery et al., 2006b) 

and the Florida Public Hurricane Loss Projection (FPHLP) model (Gurley et al., 2006). 

Apart from wind pressure, windborne debris is another major cause of wind damage. Often 

generated from building materials damaged by high local wind pressure, windborne debris 

can penetrate building envelopes and induce internal pressurization, which increases wind 

pressure damage, generating more debris and further debris damage, amounting to a chain 

reaction of failures. Most current vulnerability models, including the HAZUS-MH model 

and the FPHLP model, consider only the (one-way) effect of debris damage on pressure 

damage and approximate the debris impact risk to a structure by considering only sim- 

ple, idealized building environments. An integrated vulnerability model is developed to 

69

Chapter 4. Integrated Multi-Structural Vulnerability Model 70 

explicitly account, for the first time, for the interaction between pressure damage and de- 

bris damage by fully coupling a debris risk model (Lin and Vanmarcke, 2008, 2010) and 

a component-based pressure damage model (developed starting from the FPHLP model). 

This integrated methodology can be applied to general site- and storm-specific analyses for 

residential developments consisting of (realistically) large numbers of buildings. 

Using the model by Lin et al. (2010), this chapter (1) illustrates how a structure is af- 

fected by neighboring buildings resistance against high wind; (2) contrasts the difference in 

damage predictions between time series analysis and point-in-time analysis during a storm 

passage; and (3) extends the estimation of wind-induced losses from structural components 

to the entire structural system, the interior system, and the utility system (including elec- 

trical, pluming, heating systems) of buildings. In what follows, the theory underlying the 

integrated pressure-debris risk model is briefly outlined. Additional details about the wind 

characteristics, the internal pressure model and the approximate economic loss model that 

are not covered by Lin et al. (2010) are described. In the end, four numerical examples of 

wind-damage estimation in residential developments are presented and discussed. 

4.2 Methodology 

4.2.1 Wind Characteristics 

An appropriate description of wind conditions is necessary to evaluate the structural damage 

and resultant economic loss for the defined cluster of buildings. Traditionally, though wind 

direction plays an important role in the hurricane damage of a structure, wind damage 

is often expressed as a function of wind speed only. One of the reasons is that there is 

very limited data about the wind direction with respect to the orientation of a residential 

structure in the insurance database. To accurately assess the wind risk of a structure, the 

damage of a structure is analyzed at eight nominal wind directions at 45 degree interval as


shown in Figure 4.1. Damage at any other wind directions may be linear interpolated from 

the damages at the two closest nominal wind directions. 

Figure 4.1: Eight nominal angles of wind incidence. 

During a tropical cyclone event, a structure is exposed to winds from different directions 

as the storm moves along its track. The greater the variation in wind directionality, the 

wider the structures angle of exposure to windward wind. For instance, more damage 

can be caused by wind-borne debris if wind directionality changes more, as debris mainly 

impacts the windward side of the structure. Moreover, failures of structural components 

are interdependent. After the initial structural damage, a change in wind direction can 

significantly affect the subsequent occurrences of damage. This effect of interdependent 

component failures cannot be quantified reliably without considering the change in wind 

speed and wind direction over time within individual strong-wind events. 

Currently, two ways of specifying wind characteristics are commonly adopted in differ- 

ent vulnerability models. In the first method, used in damage estimation models such as 

HAZUS-MH (Vickery et al., 2006b), the structural loading and performance (of individual 

structures) are evaluated at a series of time steps for wind speed and direction; structural


damage at a particular time step depends on the cumulative damage in previous time steps. 

The second method, used in the FPHLP model (Gurley et al., 2006) and some other stud- 

ies (e.g. Li and Ellingwood, 2006), evaluates the structural performance at one given wind 

speed and direction. In some studies such as the FPHLP model, the average performance of 

the structure over all wind directions at a certain wind speed is then calculated. Progressive 

damage due to evolving wind speed/direction during a hurricane event is not accounted for. 

The first method gives a more detailed analysis of the effect of a storm passage on structure. 

The second method uses wind speed as the indicator of storm intensity, allowing easier com- 

putation and construction of vulnerability and fragility curves. Herein, we consider both 

analysis methods to assess damage to a cluster of buildings. 

4.2.2 Structural Characteristics 

This study analyzes hurricane wind damage to structures that are part of a residential 

community, as opposed to individual prototype structures (e.g. Gurley et al., 2006; Vickery 

et al., 2006b). A cluster of buildings is defined by specifying the location, orientation and 

(significant) structural details of each building in a study area. 

A residential structure is composed of the structural system, enclosure system, mechani- 

cal and electrical system, interior system and its contents. The wind loads on the structural 

system and parts of the enclosure system can be calculated using structural engineering 

theories and by identifying their load paths. However, the loads on other systems, the 

interior system in particular, are technically infeasible to be determined accurately in engi- 

neering scale. Therefore, the simulation engine cannot evaluate the hurricane damage on all 

systems, and the residential structure has to be simplified in the vulnerability model. The 

followings are building components on which the wind loadings can be obtained readily in 

engineering scale and are also significantly vulnerable to hurricane damage according to the 

investigation report of the FPHLP model (Gurley et al., 2005a): (1) roof covers, (2) roof


sheathing panels, (3) roof-to-wall connections, (4) gable-end sheathing panels (in gable roof 

only), (5) wall sheathing panels (in wood frame structures only), (6) walls, (7) openings 

(including windows, doors and garage door). A structural model is built by all the above 

components only. 

Currently considered building types include one-story concrete and wood-frame houses 

with gable roof or hip roof, of arbitrary overall dimensions, roof slope, sheathing panel size, 

truss spacing and number of openings. The two structure types above account for more 

than 70% of the residential structures in three of the four regions in Florida (Gurley et al., 

2006). Statistics regarding house types and house geometries within a residential commu- 

nity may be obtained from information about the local building stock (as in many cases 

building-specific data is not available). The statistics of the building components, which are 

inherently random in nature, may be found in many previous studies (e.g. National Asso- 

ciation of Home Builders, 1999; Rosowsky and Cheng, 1999b). Table 4.1 shows an example 

of the parameters of a typical residential structure’s geometry (Gurley et al., 2006). 

Table 4.1: Example parameters of a residential structure’s geometry. 

Parameter Value 

Length of structure 60 ft 

Width of structure 44 ft 

Height of wall 10 ft 

Roof pitch 5/12 

Eave overhang 2 ft 

Space between roof trusses 2 ft 

Roof sheathing panel dimension 8 ft × 4 ft 

Gable-end sheathing panel dimension 8 ft × 4 ft 

Wall sheathing panel 8 ft × 4 ft 

Figures 4.2 show the three dimensional renderings of four types of residential struc- 

ture models in this study. In the figure, the roof sheathing, gable-end sheathing and wall 

sheathing are lifted off in order to show the walls and the roof trusses clearly.


(a) (b) 

(c) (d) 

Figure 4.2: Three dimensional rendering of residential structure models: (a) concrete block 

house with gable roof (b) wood frame house with gable roof (c) concrete block house with 

hip roof (d) wood frame house with hip roof.


4.2.3 Component-Based Pressure Damage Model 

The component-based pressure damage model is developed based on the FPHLP model 

(Gurley et al., 2006). For a given wind speed and direction, wind loads on structural com- 

ponents are calculated based on the specified wind condition and designated load paths. 

All the building components in the models are assumed to fail only in their designated limit 

states listed in Table 4.2. All the failures except the projectile impact of openings may be 

determined in the component-based pressure damage model. 

Table 4.2: Limit states of structural components. 

Structural Component Limit State 

Roof Covers Uplift 

Roof Sheathing panels Uplift 

Roof-to-Wall Connections Uplift 

Gable-end Sheathing Panels Separation 

Wall Sheathing Panels Separation 

Concrete Walls Shear, Uplift, or Bending 

Wood Frame Walls Shear, Lateral Force or Bending 

Openings Pressure Failure or Projectile Impact 

Specification of wind pressure coefficient and wind pressure zone distribution for each 

building component are based on the FPHLP model (Gurley et al., 2006) and the ASCE 

7 Standard (American Society of Civil Engineers, 2003), which is the standard used in the 

United States as a basis for determining structural loads. In the ASCE 7 wind specification, 

wind loads are considered in two different scales: (1) Main wind force resisting system 

(MWFRS), which is a group of structural members working together to resist and transfer 

wind loads acting on the entire structure to the ground; (2) Component and cladding (C&C), 

which is individual building component which receives wind load either directly or from the 

cladding, and transfers the loads to the MWFRS. In general, the C&C components are 

exposed to higher wind pressures than the MWFRS components. Given the configuration


of the structure model in this project, MWFRS coefficients are used only when wall shear 

force is calculated. Wind loadings on all other components adopt the C&C coefficients. 

Figure 4.3 illustrates the framework of loading mechanism using the ASCE 7 standard. In 

the modification of the ASCE 7 specification for hurricane loss estimation, all safety factors 

that are incorporated in the specification are removed for more accurate estimation of wind 

loading. 

Input 

Angle of 


Incidence 

3-second 

Gust Wind 

Speed 

Sampled 

Resistance 

Capacities 

MWFRS 

C&C 

Wall Shear 

Wall Bending 

Moment / " 

Out-of Plane 

Roof Sheathing 

Gable-end 

Sheathing " 

(Gable Roof only) 

Wall Sheathing" 

(Wood Frame House 

only) 

Openings 

Roof Cover 

Wall Failure Check 

Wall Uplift 

Roof-to-Wall 

Connection 

Internal 

Pressure 

Output 

Area % of Failed 

Roof Cover 


Roof Sheathing 


Gable-end 

Sheathing " 

(Gable Roof Only) 


Wall Sheathing (Wood 

Frame House Only) 

% of Failed" 

Roof-to-Wall 

Connections 

Number of 

Damaged Walls 

Number of Failed 

Windows 


Doors 


Garage Door 

Internal Pressure 

Figure 4.3: Flowchart of the component-based pressure damage model. 

By comparing the sample component resistance to the load, the pressure damage model 

assesses the wind-pressure damage to each building component. The levels of damage to 

these building components are highly correlated in most cases. When opening damage (for


instance, to windows, doors, or garage doors) occurs due to pressure or debris damage, the 

internal pressure is adjusted to a weighted-average external pressure acting on the areas 

of the broken components (see Gurley et al., 2006); this affects the damage conditions of 

almost all components. Different from the FPHLP model that adjusts the internal pressure 

once, in this integrated model the interplay between the internal pressure and the damage 

condition continues after the first internal-pressure adjustment. If additional openings are 

damaged due to the change in internal pressure, the internal pressure is updated again. An 

iterative algorithm is applied to obtain the equilibrium between the internal pressure and 

the damage condition. 

4.2.4 Windborne Debris Model 

In tropical cyclones, windborne debris significantly contributes to the damage of building en- 

velope, particularly glass openings (National Institute of Standards and Technology, 2006b). 

For simplicity, we assume that glass windows are the only structural members vulnerable 

to windborne debris. Both HAZUS-MH hurricane model (Federal Emergency Management 

Agency, 2006) and the FPHLP Model (Gurley et al., 2006) formulate the probability of 

debris damage to an opening, PV (D), at a given wind speed (V ) as: 

PV (D) = 1 − exp[−λq(1 − P (ζ < ζ0))], (4.1) 

where λ is the mean number of missile impacts on the building, q is the fraction of the 

building surface covered by the opening, P (ζ − ζ0) is the probability that the momentum 

(ζ) of the debris is less than the damage threshold value (ζ0) given an impact. In the 

FPHLP Model (Gurley et al., 2006), the parameters λ and P (ζ − ζ0) are some functions of 

wind speed (V ) only and are independent of all other factors. 

Alternatively, λ and P (ζ − ζ0) may be simulated based on the potential number of 

debris objects in the environment and the properties of the debris objects. We assume that


the only debris sources are the roof covering and sheathing panel uplifted by wind pressure 

from nearby residences. Post-damage survey by Twisdale et al. (1996) shows that the debris 

either flies less than 1 second (mean = 0.73 sec), or stays in the air for a much longer time 

(mean = 1.58 sec). The parameters λ and P (ζ − ζ0) are calculated independently for each 

flight mode. Their weighted average will be used for equation (4.1) to estimate PV (D). 

Properties of potential windborne debris objects, such as the mass and area of roof cover 

and roof sheathing panels, plus the glass windows resistance against debris impact, are re- 

quired to quantify the windborne debris risk. The properties of common debris objects are 

presented in several studies (e.g. McDonald, 1990; Minor et al., 1978). Table 4.3 lists the 

properties of debris objects from the study by Twisdale et al. (1996). 

Table 4.3: Properties of debris objects. 

Parameter Symbol Description Value 

Flight Time td Mode 1 (P =0.38) 0.73 sec 

Mode 2 (P =0.62) 1.58 sec 

Debris Mass md Roof cover 2.5 lbf 

Sheathing panel 32 lbf 

Debris Area Ad Roof cover 3 ft 2 

Sheathing panel 32 ft 2 

The mean along-wind distance traveled by a debris object, ¯ Xd , is approximated by an 

empirical equation (Lin et al., 2006): 

¯Xd = 2Md 

[ 

Adρa 

1 

2 C(Kt′ ) 2 + c1(Kt ′ ) 3 + c2(Kt ′ ) 4 + c3(Kt ′ ) 5 ], (4.2) 

where C is a debris geometry constant; c1, c2 and c3 = regression coefficients; t ′ = gt/V ; 

and K is the Tachikawa number (Tachikawa, 1983) given by: 

K = ρaV 2Ad , (4.3) 

2mdg


where Ad is debris area; md is debris mass; and ρa is air density. Equation (4.3) applies 

when Kt ′ is between [0, 6.5]. If Kt ′ > 6.5, ¯ Xd is the value approximated by using Kt ′ = 

6.5, plus an additional distance by assuming that the flight speed is equal to 0.98V . The 

along-wind displacement Xd is normally distributed with a COV of 0.35. The across-wind 

distance Yd is normally distributed with a mean of 0 and a COV of 0.35. It is assumed that 

the debris hits the structure if it falls on the plan area of the target structure. 

The debris impact velocity, Vd, is assumed to follow a beta distribution (Lin et al. 2009), 

with probability density function: 

d (1 − vd) b−1 

va−1 

f(vd)vd = 

B(a, b) 

, (4.4) 

where B(·) denotes a Beta function. The parameters a and b are determined by assuming 

the mean of debris velocity and the dispersion parameter are: 

¯Vd = a 

 

CρaAd¯x 

= V 1 − exp − 

, (4.5) 

a + b 

 

1 

η = a + b = max , 

¯Vd 

1 

1 − ¯ Vd 

Md 

 

+ γ, (4.6) 

where γ is assumed to be 3 (Lin et al. 2009), which may be statistically updated when 

new debris data is available. The probability that the momentum, ζ = mdVd, exceeds the 

damage threshold is hence obtained. 

4.2.5 Integrated Structural Damage Estimation 

The Lin et al. (2010) vulnerability model integrates the debris risk model and the component- 

based pressure damage model. Damaged roof cover, roof sheathing, and gable-end sheathing 

are considered as debris sources, and windows and glass doors (or their protective covers) are 

assumed to be debris-impact vulnerable areas. The integrated structural damage estimation


INPUT PRESSURE DAMAGE MODEL DEBRIS DAMAGE MODEL 

OUTPUT 

Structure 1 of N 


Y 

N 

New 

Opening 

Damage 

Debris 

Damage 

Analysis 

Internal 

Pressure 

Adjustment 

Y 

New 

Opening 

Damage 

Pressure 

Damage 

Analysis 

Any Roof 

Cover or 

Sheathing 

Damage 

from Any 

Structure 

= 

Available 

Debris 

Objects 


Speed 

N 

Final 

Damage 

Condition 

of 


1 - N 




Direction 

... 

... 

Structure N-1 of N 

Structure N-1 of N 

Structure N of N 

Structure N of N 

Y 

Initial 

Damage 

Condition 

of 


1 - N 

N 

New 

Opening 

Damage 

Debris 

Damage 

Analysis 

Internal 

Pressure 

Adjustment 

Y 

New 

Opening 

Damage 

Pressure 

Damage 

Analysis 

N 

If it is a time series analysis, the final damage condition in each structure 

becomes the initial damage condition in the next step. 

Figure 4.4: Flowchart of the integrated vulnerability model.


model is summarized in a flowchart in Figure 4.4. The model implements Monte Carlo 

simulation, with structural resistance randomly assigned to every building component in 

each simulation run, in accordance with the specified (joint) probability distributions. In 

most cases, the structural parameters are assumed independent of each other. However, 

the roof-to-wall connection strength in each structure is batch-selected to simulate the 

consistency in quality of material and installation within a single structure (see Gurley 

et al., 2006). 

In each simulation, for a given wind speed and direction, wind loads and damages 

of structural components are first calculated using the component-based pressure damage 

model. After that, the information about roof covers and roof sheathing panels damaged by 

wind pressure is passed along to the debris risk model, which estimates the probability of 

debris damage to each window and glass door of each house. If there is any debris damage, 

the internal pressure of the damaged house is updated, and the damage to structural com- 

ponents is recalculated in the pressure damage model. The information about any newly 

damaged roof covers and roof-sheathing panels are again sent to the debris risk model to 

estimate their damage risk, starting a loop of pressure-debris damage interaction, until no 

more debris is generated from any house. The damage condition of each building is thus 

obtained for the given wind speed and direction. In the case of time-series damage analysis, 

similar analysis is conducted for the wind speed and direction at each analysis step of the 

wind time history; the damage condition of each structure from one analysis step is carried 

to the next step, until the end of the hurricane wind time series. 

4.2.6 Approximate Economic Model 

Based on the percentage damage to each structural component, the damage ratio of a 

building is approximated, following (e.g. Leicester et al., 1979), as a ratio of total repair 

cost to the initial (or replacement) cost of the structural system. To calculate the damage


ratio, the breakdown of the initial cost of the building is obtained from construction cost 

databases such as R.S. Means Residential Cost Data (R.S. Means., 2009). The damage 

ratio of the structural system is the weighted average of the damage percentages of all 

structural components considered in the integrated vulnerability model (roof cover, roof 

sheathing panels, etc.), with the weights proportional to the repair cost of the corresponding 

component. 

Similarly, damage ratios may be defined for the interior system and the utility system, 

which, combined with the structural system, constitute an entire residential structure. How- 

ever, unlike for the structural system, the damages on interior system and utility system are 

not readily analyzable using (structural) engineering models. Therefore, loss models such 

as HAZUS-MH (Vickery et al. 2006) and FPHLP (Gurley et al., 2006) formulate sets of 

empirical equations to relate the interior damage to the percentage damage of each struc- 

tural component. Similar equations are also applied to modeling utility-system damage. 

The total damage ratio of a building, which is a measure of insurance loss, is the weighted- 

average of the damage ratios of each subassembly, with the weights proportional to the 

respective repair costs. (Content loss, additional living expenses, and business interruption 

are usually also counted in economic loss estimation in the insurance industry. They are not 

included in this study, however, since they greatly depend on building function, occupancy, 

and details of insurance policies.) Since the pressure damage module of the integrated vul- 

nerability model is based on the FPHLP model, for consistency, this study employs the 

FPHLP method to evaluate the damage ratios for the interior system and utility system.


4.3 Numerical Examples 

4.3.1 A Hip-roof Concrete Residential Structure in Isolation 

Before showing the results of the integrated vulnerability model, a hip-roof concrete house 

is used as an example to illustrate the component-based pressure damage model. In this 

example, there is no windborne debris impact on the structure. 

Figure 4.5 illustrates the vulnerability of a hip-roof concrete house at four different wind 

speeds from 100 mph to 250 mph. 1,000 simulations were carried out at each of the eight 

nominal wind directions at each wind speed. The results are the average vulnerability of 

the house over the eight wind directions. In the figure, the color indicates the probability 

of failure of each structural component. As wind speed increases, the probability of failure 

increases for every component. Virtually all the roof covers are damage when wind speed 

reaches 250 mph. If this is combined with the windborne debris model, the failed roof 

panels will serve as a considerable amount of debris objects that impact the other nearby 

structures. Figure 4.6 illustrates the vulnerability of the same hip-roof concrete house under 

a 200-mph wind in three different directions. 

4.3.2 Hypothetical Residential Community 

This second numerical example is to illustrate the effect of windborne debris on the neigh- 

boring structures. Consider a residential development of 16 identical single-story concrete 

block gable roof houses having the same characteristics and orientation, as shown in Figure 

4.7. Vulnerability analysis of the hypothetical houses is conducted for a wind speed of 65 

m/s at 45-degree angle, based on 500 Monte Carlo simulations. Since all the houses in this 

hypothetical development are identical, the difference in damage to each house is mainly 

caused by the debris impact and the subsequent internal pressure change. 

Figure 4.8 presents the breakdown of estimated structural damage to each house. Note


(a) 100 mph (b) 150 mph 

(c) 200 mph (d) 250 mph 

Figure 4.5: Vulnerability of a hip-roof concrete house at four different wind speeds.


(a) 0 ◦ wind angle (b) 45 ◦ wind angle 

(c) 90 ◦ wind angle 

Figure 4.6: Vulnerability of a hip-roof concrete house under 200-mph at three different wind 

directions.


Figure 4.7: Three-dimensional view of a hypothetical residential development. The arrows 

indicate wind direction. 

that the house at the upper right corner is hardly impacted by debris, while all houses at 

the lower left are affected by debris impact. There is a trend indicating that the further the 

house is from the upper right, the more damage it suffers. Among all structural components, 

the window and door are the two most damaged components, as both are debris-vulnerable 

according to the model. The damage to other structural components on suction zones, such 

as garage doors, roof sheathings, and roof covers, are also increased due to the internal 

pressurization resulting from debris damage. 

The information about structural damage presented in Figure 4.8 is converted to sub- 

assembly damage ratios and an overall damage ratio. The average damage ratios of all 

houses are shown in Figure 4.9 as bars labeled debris. The vulnerability analysis is then 

repeated for the same residential development under the same wind condition, but without 

accounting for any debris effects. The resulting damage ratios are also shown in Figure 

4.9, as bars labeled no debris. Notice significant differences between the damage ratios from 

the two analysis methods. If debris is not considered, the average overall damage ratio is

LEGEND 

Roof sheathing 

onnection 

indow 

Door 

Connection 

1% Damage 

indow 

Damage 

Garage door 

Roof cover 

12.5% 

25% 

37.5% Wall 

50% 

EXAMPLE 


7% Damage 

Door 

3% Damage Garage door 

15% Damage 

Roof cover 

21% Damage 

Wall 

1% Damage 


Longitude (m) 

90 

60 

30 

0 

DAMAGE ESTIMATON OF HYPOTHETICAL RESIDENTIAL DEVELOPMENT 

LEGEND 


Connection 

Roof cover 

Window 

0 30 60 

Latitude (m) 

12.5% 

25% 

37.5% Wall 

60 

DAMAGE ESTIMATON 50% OF HYPOTHETICAL RESIDENTIAL DE 

Door 90 

Garage door 

LEGEND 


Connection 


Door 

Roof cover 

12.5% 

25% 

37.5% Wall 

50% 

Garage door 

EXAMPLE 

Longitude (m) 

90 

60 

0 

Connection 

11% Damage 


41% Damage 

EXAMPLE 


7% Damage 

Door 


15% Damage 

Roof cover 

21% Damage 

Wall 

1% Damage 

Figure 4.8: Estimated damage condition of each individual house in the hypothetical residential 

development under a wind speed of 65 m/s at a 45-degree angle. Each radar 

30 


diagram represents the mean damage percentage of the structural components of an indi- 

7% Damage 

Connection 

vidual house. The 11% arrows Damage indicate wind direction. On the left panel are the legend and an 

Roof cover 

example illustrating the meaning21% ofDamage the radar diagram. 


41% Damage 

Door 


15% Damage 

Wall 

1% Damage 

Longitude (m) 

90 

30 

0 

DAMAGE ES 

0 30 60 9 

0


Damage Ratio 

0.16 

0.14 

0.12 

0.1 

0.08 

0.06 

0.04 

0.02 

Debris 

No debris 

0 

Structural System Interior Utility System Overall 

Figure 4.9: Comparison of subassembly and overall damage ratios with and without consideration 

of windborne debris. The bars labeled debris indicate the average damage ratios 

of all houses in the hypothetical residential development if windborne debris is considered. 

The bars labeled no debris indicate the same variables without considering debris. 

underestimated, in this case, by as much as 29%. 

4.3.3 Two Neighboring Houses 

The previous numerical example demonstrated the effect of neighboring buildings on a 

structures wind damage on account of the locations of the buildings. This second example 

further illustrates how a deteriorated neighboring building may increase damage through 

windborne debris. Consider two houses separated by 30 m (see Figure 4.10a). Both are 

the same as the houses in the previous example, except that the resistance of all building 

components in House B is multiplied by a resistance factor. 

Figure 4.10b shows the overall damage ratio (and its breakdown) for structure A versus 

the resistance factor of structure B. While structure As resistance is always the same, an 

increase in structure Bs resistance lowers the windborne debris risk faced by structure A, 

resulting in a lower damage ratio of structure A. In this particular example, if the resistance 

of a neighboring house deteriorates and becomes half of that of another house, it can cause


Structure A 

Structure B 

30m 

Wind Direction 

Damage Ratio of Structure A 

0.35 

0.3 

0.25 

0.2 

0.15 

0.1 

0.05 

Structural System 

Utility System 

Interior System 

0 

0.5 1 

Resistance Factor of Structure B 

1.5 

(a) (b) 

Figure 4.10: (a) Illustration of two neighboring houses. (b) Breakdown of overall damage 

ratio of structure A versus resistance factor of structure B. 

about 90% more damage to the other house. 

4.3.4 Sarasota, Florida 

This last numerical example demonstrates the difference in damage estimation results be- 

tween time series analysis and point-in-time analysis during a storm passage. Consider a 

residential development of 358 single-story houses in Sarasota County, Florida (Figure 4.11). 

The locations of the residential houses are known, while the orientation of each house is 

modeled as a Gaussian random variable with as its mean the direction perpendicular to the 

main street of the house and as its standard deviation 15 degrees. The structural character- 

istics of each house are estimated based on information about the building stock in central 

Florida (Gurley et al., 2006). We estimate wind damage to the study area from Hurricane 

Charley (2004), which passed to the left of the study area. Hurricane Charley is numerically 

simulated using the Weather Research and Forecasting (WRF) model (Skamarock et al., 

2005); this yields a simulated wind-velocity time history at a representative location within 

the study region.


Figure 4.11: Study area of a residential development of 358 houses in Sarasota County, 

Florida (left) and simulated storm track of Hurricane Charley of 2004 (right). The circle 

(in both panels) represents the recording location of the wind time history during the 

passage of the simulated storm. 

Unlike most other vulnerability models (Gurley et al., 2006; Vickery et al., 2006b) that 

evaluate individual prototype buildings, the integrated vulnerability model analyzes a clus- 

ter of buildings as a whole, seeking to account for the (time-varying) interaction between 

building damage levels due to windborne debris. In this case of a 358-residence community, 

computation time for estimating the damage condition can be significant. Evaluation of 

building performance only at the maximum wind speed (and the corresponding direction), 

has the advantage, compared to the cumulative damage analysis, of reduced computational 

effort. The results of both methods of representing the wind conditions are compared in 

Figure 4.12.

DAMAGE ANALYIS 

USING MAXIMUM WIND VELOCITY 


DAMAGE ANALYSIS USING A TIME SERIES OF WIND VELOCITY 

Only Step 

Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 

150 

100 

50 

Wind speed 

(mph) 

0 

360 5 10 15 20 

240 

120 

0 

0 5 10 15 20 

Time (hour) 

Wind direction 

(deg) 

Roof cover 

2.4% 

150 

100 

50 

0 

360 

5 10 15 20 

240 

120 

0 

0 5 10 15 20 

Time (hour) 



LEGEND 

EXAMPLE Connection 0.2% 

Connection 

0.0% damage 

Roof cover 


3.7% damage 


Wall 

0.0% 

Wall 

1.25% 

2.5% 

3.75% 

5% 

Door 

3.3% damage Garage door 

0.1% damage 

Door Garage door 

Figure 4.12: Comparison of the estimated wind damage condition of the residential development in Sarasota County, 

Florida, under a Hurricane Charley wind condition, by time series (left) and maximum wind analyses (right), respectively. 

The radar diagrams represent the overall average damage percentage of the building components of all houses, under the 

simulated wind time history of Hurricane Charley of 2004. The red dots indicate the analysis wind series of the maximum 

wind velocity in each 15-degree direction segment. The legend with an example illustrates the meaning of the radar 

diagram.


In the time-series damage analysis, structural damage is estimated over a time series of 

wind speed and wind direction. Figure 4.12 (left) shows the analysis result using a sequence 

of maximum wind speeds (and corresponding wind directions) during consecutive 15-degree 

wind-direction segments of the wind time history. Note that the analysis steps are unevenly 

distributed, being more concentrated where the wind direction varies significantly. Analysis 

using a 15-min interval time series was also conducted, but the results are not shown because 

they are very similar to those based on the 15-degree wind-direction segmentation (for which 

computational effort is considerably reduced (see Lin et al., 2010). As Figure 4.12 (left) 

shows, significant damage starts to occur, in this case, when the wind speed approaches its 

peak. Due to the relatively low wind speeds (compared to 65 m/s in the previous numerical 

example), only the most vulnerable building components, including roof covers, windows 

and doors, sustain damage. 

Damage Ratio 

0.01 

0.009 

0.008 

0.007 

0.006 

0.005 

0.004 

0.003 

0.002 

0.001 

Progressive 

Max Wind 

0 

Structural System Interior Utility System Overall 

Figure 4.13: Comparison of subassembly and overall damage ratios between time-series 

and maximum-wind damage analyses. The bars labeled as progressive indicate the average 

damage ratios of all houses in Sarasota County, Florida using the analysis wind series of 

the maximum wind velocity in each 15-degree direction segment of the wind time history. 

The bars labeled as max wind indicate the same variables using only the maximum wind 

speed and the corresponding wind direction. 

Alternatively, the damage condition is estimated using the maximum wind speed (and


corresponding direction) for the entire wind time history. Computationally faster since it 

involves a one-step analysis compared to multiple steps in the time-series damage analysis, 

this method predicts significantly lower damage. As shown in Figure 4.13, the predicted 

overall average damage ratio can differ by about 25% for the different methods. 


We presented and illustrated improved methodology to assess structural vulnerability and 

wind-related economic losses in residential neighborhoods during hurricanes. Involving the 

interplay between a pressure damage model and a debris risk model, the method is capable of 

estimating cumulative damage to the overall structural system, the interior, and the utility 

system of buildings in a residential development. By means of four numerical examples, it is 

shown that windborne debris tends to contribute significantly to total damage and economic 

loss, and that the cumulative wind-related damage during the passage of a storm may be 

much greater than would be estimated by considering only the maximum wind speed during 

the storm. Future field studies are needed to collect damage data to validate this (and other) 

damage assessment methodology. The integrated vulnerability model will be applied to 

develop vulnerability and fragility curves for building categories within generic communities 

in hurricane-prone regions. To further improve wind damage estimation for residential 

communities, in addition to debris effects, more complex and detailed aerodynamic effects 

may have to be incorporated into the models.

Chapter 

5 

Long-Term Risk Assessment and 

Management 


Effects of climate change have been extensively studied in various scientific fields. How- 

ever, the potential impact of climate change on structural engineering analysis has been 

addressed by very limited literature only (Kasperski, 1998; Steenbergen et al., 2009). In 

current practice of civil engineering, environmental loads are usually calculated based on 

data collected over the past decades, assuming that they have the same trend in the future. 

This omission of climate change may underestimate the future structural loads, which may 

particularly concern new infrastructure projects which are expected to service for more than 

50-100 years as well as existing buildings which will continue to be in use for decades. 

Buildings are impacted by climate change in many forms including wind load, rain 

load, snow load and temperature load (Steenbergen et al., 2009). This study focuses on 

extreme wind load, which is one of the most common types of load causing structural 

failures. Given that the trends of future wind hazards are still uncertain, we present a non- 

stationary compound Poisson process to simulate future wind conditions under the effect 

94

Chapter 5. Long-Term Risk Assessment and Management 95 

of climate change. The simulated wind conditions are applied to two different vulnerability 

models: a single-limit-state vulnerability model and the modified Florida Public Hurricane 

Loss Projection (FPHLP) model, to illustrate the effect of climate change on a structure’s 

life-cycle cost and the decisions regarding the structural design. 

5.2 Methodology 

In the insurance literature, stochastic processes (e.g. Poisson process) are commonly em- 

ployed to simulate economic damage associated with extreme weather as a function of 

time (Embrechts et al., 1997; Katz, 2002). In order to more accurately assess the poten- 

tial effect of climate change, the simulation process is divided into two parts. First, a 

stochastic process, which is referred as the hazard model, is used to simulate the wind 

hazard events. Parameters describing the climate change scenarios are implemented in this 

stochastic process. Then, the simulated wind conditions are translated into the damage 

level (and associated economic cost) of an individual structure using vulnerability models 

that are developed using reliability engineering theories. Combining the hazard model and 

the vulnerability model, of which the details are described in the following sections, we can 

obtain projections of future economic cost of a structure due to wind hazard in different 

climate change scenarios. 

Given the projections of future economic cost, the change in risk and reliability as a 

result of climate change may be quantified by a number of metrics. Life-cycle cost, which 

is the overall discounted cost in a structure’s design life, serves as an indicator of the 

cost-effectiveness of a structure and governs the objective function in the optimization of 

structural design (Frangopol and Maute, 2003; Chang and Shinozuka, 1996). Let [0, tL] be a 

structure’s life cycle and N(tL) be the total number of wind hazard events occurred within 

[0, tL]. Let Ti denote the time that the i-th wind event occurs. A structure’s total life-cycle


cost, C, may be expressed as: 

N(tL) 

C = C0 + δ(Ti)Cr,i, (5.1) 

i=1 

where C0 is the initial construction cost; Cr,i the repair cost associated with the i-th hazard 

event. The discount factor, δ(t), is used to to convert the future Cr,i into the present value. 

This study adopts the most common exponential discounting: 

δ(t) = exp(−γt), (5.2) 

where γ is the discount rate. Typical discount rates range from 5% to 20% (e.g. Coffelt 

et al., 2010), and a 5% discount rate will be used throughout this study. We are going 

to investigate the change in expected value and probability distribution of life-cycle cost, 

particularly the total discounted repair cost, in different scenarios of wind event frequency 

and intensity. 

5.3 Hazard model 

5.3.1 Wind Speed Distribution 

Severe winds, which originate from normal weather or different types of wind hazards (i.e. 

thunderstorms, tropical cyclones, tornadoes, etc.), may be characterized by wind speed, 

wind direction, duration, etc. Wind speed is conventionally used as the metric to measure 

a wind hazard’s intensity. For example, the Saffir-Simpson hurricane scale is based on 

maximum sustained wind speed. This study will also use wind speed as the parameter 

linking the hazard model and the vulnerability model. 

Wind speed is the governing factor of a structure’s resistance against lateral and uplift 

forces in structural design. In the United States, the design wind speed is specified by the


50-year return period, which means the wind speed with a probability of being exceeded 

per year of 1 in 50. Probability distribution of wind speed may be obtained by best fitting 

observed data. While strong frontal depressions and thunderstorms may be adequately 

captured in the collected data over the past decades, the tropical cyclones may not be so 

due to their infrequent occurrence. Monte Carlo simulations are often employed to decide 

the design wind speed in hurricane-prone regions. 

Generalized extreme value (GEV) distribution is generally adopted to represent the 

annual maximum wind, Vmax: 

F (vmax) = exp 

 

− 

 

1 + ξ 

 

−1/ξ 

vmax − ψ 

, (5.3) 

σ 

where F (·) is the cumulative distribution function, and ψ, σ and ξ are the location, scale 

and shape parameters, respectively. If ξ → 0, the distribution is referred as Gumbel distri- 

bution (type I extreme value distribution), and if ξ < 0, it is refered as Weibull distribution 

(type III extreme value distribution). (ξ > 0 defines the Fréchet distribution (type II ex- 

treme value distribution), but it is not discussed here.) In meteorology and wind energy 

analysis, Weibull distribution is commonly used as the extreme wind speed distribution, 

since it has an upper limit, which is appropriate for physical grounds (Simiu and Heckert, 

1996). The use of Gumbel distribution for extreme wind distribution has a long history and 

is still being extensively used (Galambos and Macri, 1999; Holmes, 2007; Naess and Gaidai, 

2009). Though it does not impose any upper limit on the wind speed like Weibull distri- 

bution, it is suitable for the purpose of engineering design codes and standards (Holmes, 

2007). In addition, Gumbel distribution describes the distribution of the maxima of a series 

of identical and independently distributed exponential random variables. This allows us 

to interpret the distribution as a compound Poisson process, which is useful in this risk 

assessment study because it allows simulation of the number of failure events as well as the 

time of each occurrence of failure event.


5.3.2 Compound Poisson Process 

Assume that the occurrence of wind event is a Poisson process with rate of occurrence λ. 

The probability mass function of the number of wind hazards, n, occurring in the time 

interval [0, t) is: 

P(N = n) = e−λt (λt) n 

, n ≥ 0. (5.4) 

n! 

Furthermore, let the intensity (wind speed) of each wind event (V1, . . . , Vn) be an identical 

exponential random variable which is independent of each other and has a mean of µ: 

F (vn) = 1 − e −vn/µ . (5.5) 

Based on the assumptions on the frequency and intensity of wind hazards, the cumulative 

distribution function of the maximum wind speed within the time interval [0, t), which is 

defined as Vmax = max(V1, . . . , Vn), is equal to: 

 

F (vmax) = exp −λt exp − vmax 

 

. (5.6) 

µ 

This is equivalent to the Gumbel cumulative distribution function, which is usually ex- 

pressed as: 

 

F (vmax) = exp − exp 

α − vmax 

β 

 

, (5.7) 

where α = µ ln(λt) is the location parameter and β = µ is the scale parameter. The return 

period, which is the inverse of the non-exceedence probability, is directly related to the 

cumulative probability distribution F (vmax) as follows: 

Return Period = 

1 

. (5.8) 

1 − F (vmax) 

The above stationary compound Poisson process may be converted to a non-stationary


process by introducing time-varying parameters λ(t) and µ(t) to replace λ and µ in equa- 

tions (5.4) and (5.5). This is similar to the non-stationary analysis of extreme wind speed 

distribution (e.g. Hundecha et al., 2008), in which the distribution parameters are fit to 

some functions of time, except that both parameters λ and µ have physically meanings in 

addition to statistical meanings in this study. Based the assumptions of the trends of mean 

frequency (λ) and mean intensity (µ) of wind events, we may explicitly simulate future 

wind conditions. Unfortunately, the scientific community is still uncertain about the fu- 

ture trends of tropical cyclones and other wind activities (American Meteorological Society, 

2007). There have been studies suggesting that tropical cyclones have become more intense 

over the last several decades and the trends may continue in the future (e.g. Knutson and 

Tuleya, 2004; Elsner, 2008). The storm tracks are also projected to move, influencing the 

wind pattern (Intergovernmental Panel on Climate Change, 2007). However, there has not 

been a consensus about the degree of future changes in the intensity or frequency of wind 

hazards under the effect of climate change (Pielke et al., 2005). Therefore, instead of look- 

ing at some projected climate change scenarios, we investigate a number of hypothetical 

scenarios in which the mean frequency (λ) and the mean intensity (µ) of wind events change 

linearly or exponentially over time: 

⎧ 

⎪⎨ λ(t) = λ0 ± ∆λt, 

⎪⎩ µ(t) = µ0 ± ∆µt, 

⎧ 

⎪⎨ λ(t) = λ0 exp(kλt), 

⎪⎩ µ(t) = µ0 ± exp(kµt), 

(5.9) 

where {λ0, ∆λ, kλ} and {µ0, ∆µ, kµ} are the initial value, yearly constant change and rate 

of change for the mean frequency and mean intensity, respectively. 

Reasonable and realistic ranges of the parameters λ and µ may be found in a study by 

National Institute of Standards and Technology (NIST), which has exported the extreme 

wind speed data in 129 stations over the contiguous United States from another study by


Mean Intensity (!) 

14 

12 

10 

8 

6 

4 

2 

10 1 

Greenville, SC 

Greensboro, NC 

10 2 

Portland, OR 

Memphis, TN 

10 3 

Block Island, RI 

Evansville, IN 

Columbus, OH 

10 4 

Mean Frequency () 

North Platte, NE 

Denver, CO 

10 5 

10 6 

Elkins, WV 

Figure 5.1: Distribution of Gumbel distribution parameters λ and µ of extreme wind speed 

data in 129 stations over the contiguous United States (National Institute of Standards and 

Technology, 2006). Some geographic locations of the stations are labeled. 

Simiu et al. (1979), and fitted the data into Gumbel distributions using Gumbel’s method 

(National Institute of Standards and Technology, 2006a). The Gumbel distribution param- 

eters are converted into λ and µ and are shown in a scatter plot in Figure 5.1. Despite the 

wide range of values of both parameters, the 50-year-return-period wind speed only ranges 

from 45.4 mph to 97.2 mph fastest-mile wind. Note that the values of the parameters do not 

represent the actual frequency or intensity of wind hazards. For example, Figure 5.1 does 

not mean that Greensville, SC has much less wind events than Denver, CO. It is because the 

parameters are based on best-fit of the extreme wind data and do not distinguish different 

types of wind events. However, the underlying physical meanings of both parameters are 

still valid means to interpret the fitted Gumbel distribution, if we view the occurrence of 

wind events as a stochastic process and treat the parameters as general representations of 

the parameters of all types of wind events. 

Based on the range of parameters shown in Figure 5.1, two sets of parameters, {λ0 = 

10 7


Figure 5.2: Two sample results of the hazard model using (a) λ0 = 100, µ0 = 6, ∆λ = 

0.01λ0, ∆µ = 0.01µ0 (b) λ0 = 10, 000, µ0 = 6, ∆λ = 0.01λ0, ∆µ = 0.01µ0. Below each 

sample result are the wind speed distributions at the beginning and the end of the 50-year 

time interval.


100, µ0 = 6} and {λ0 = 10, 000, µ0 = 6}, are selected to demonstrate two sample results 

of the non-stationary compound Poisson process. Both sample results assume that the 

parameters are changing linearly with time. Comparing Figure 5.2a and 5.2b, a higher λ 

yields a larger extreme wind speed given the same µ. 

5.4 Single-Limit-State Vulnerability Model 

5.4.1 Model Description 

In structural engineering, a limit state may be defined as a set of performance criteria that 

has to be satisfied during the design process. An ultimate limit state is met if all the 

structural forces are below the resistance, ensuring that the structure does not collapse in 

a load event. In general, a limit state may be expressed as L − R, where L is the load and 

R is the resistance. If the limit state is smaller than zero, the structure is considered failed. 

Conservatively, in a hazard event, the normalized repair cost, CR, may be expressed as: 

⎧ 

⎪⎨ 1, L ≥ R 

CR = 

⎪⎩ 0, L < R 

, (5.10) 

in which the structure requires full repair once the limit state is exceeded. 

The building code in the United States specifies that a structure has to withstand min- 

imally a 50-year return period wind speed. Depending on the factor of safety embedded 

in the structural design, a structure would normally sustain a wind speed higher than the 

50-year wind speed. Figure 5.3 shows three example vulnerability curves of three different 

factors of safety. The repair cost is a function of the factor of safety against 50-year return 

period wind only, and does not depend on the actual values of the 50-year wind speed or the 

resistance, which varies largely from region to region and from structure to structure. The 

simplicity of this model will allow us to illustrate the effect of climate change on structural


design without ambiguity arising from the complexity of the vulnerability model, before we 

move on to the next more complex vulnerability model. 

C R 

1 

0.8 

0.6 

0.4 

0.2 

0 

FS = 1 

FS = 1.5 

FS = 2 

0 50 100 150 


Figure 5.3: Vulnerability curves of the single-limit-state deterministic model, in which the 

structure is designed to resist against the 50-year return period load calculated using parameters 

λ = 100 and µ = 6. FS denotes the factor of safety. 

5.4.2 Life-cycle Cost Results 

Consider a newly constructed structure with a 50-year design life, which is typical for general 

structures. The design load of the structure is calculated based on the Gumbel distribution 

parameters, mean intensity (µ) and mean frequency (λ) of wind events, assuming that both 

parameters are stationary with time throughout the design life. The factor of safety against 

50-year wind speed ranges from 1.5 to 3 in the following analysis, since 2 is the mean factor 

of safety for the ultimate limit state (Christian and Urzua, 2009), and we are interested in 

a higher factor of safety for adaptation to climate change. The ranges of λ and µ are [100, 

100,000] and [4, 10], respectively, based on the NIST Gumbel distribution parameters in 

Figure 5.1. 

Figure 5.4 shows the mean total discounted repair cost over the structure’s design life 

as a function of initial mean wind event frequency (λ0) and factor of safety against 50-year

(a) 

Change in Mean Frequency / Year 

(as a percentage of µ0) 

(b) 

Percentage Change in Mean Frequency / Year 

1.0% 

0.8% 

0.6% 

0.4% 

0.2% 

0% 

1.0% 

0.8% 

0.6% 

0.4% 

0.2% 

0% 


0% 

0% 

0.2% 0.4% 0.6% 0.8% 1.0% 

Change in Mean Intensity / Year 

(as a percentage of !0) 

0.2% 0.4% 0.6% 0.8% 1.0% 

Percentage Change in Mean Intensity / Year 

Initial Frequency ( 0 ) 

10 5 

10 4 

10 3 

10 2 

LEGEND 

10 

1.5 2 2.5 3 

1 

Factor of Safety 

10 5 

10 4 

10 3 

10 2 

LEGEND 

10 

1.5 2 2.5 3 

1 


Figure 5.4: Mean total discounted repair cost as a function of initial frequency and safety 

factor in 36 different climate change scenarios with (a) linearly increasing parameters (b) 

exponentially increasing parameters. The total discounted repair cost is denoted by the 

color. 


0.1 

0.01 

0.001 

0.0001 

1e05 

1e06 

1e07 

1e08 

1e09 

0.1 

0.01 

0.001 

0.0001 

1e05 

1e06 

1e07 

1e08 

1e09

(a) 



(b) 


1.0% 

0.8% 

0.6% 

0.4% 

0.2% 

0% 

1.0% 

0.8% 

0.6% 

0.4% 

0.2% 

0% 


0% 

0% 

0.2% 0.4% 0.6% 0.8% 1.0% 



0.2% 0.4% 0.6% 0.8% 1.0% 


Initial 

Initial 

Frequency 

Frequency 

( 

( 

) 

) 

0 

0 


10 5 10 5 

10 4 10 4 

10 3 10 3 

10 2 10 2 

LEGEND 

10 

1.5 2 2.5 3 

1 10 

1.5 2 2.5 3 


1 


10 5 

10 4 

10 3 

10 2 

LEGEND 

10 

1.5 2 2.5 3 

1 


1,000,000% 1,000,000 

10,000% 

100,000% 100,000% 

1,000% 

10,000% 

1,000% 

100% 

100% 

10% 

10% 

1% 

1% 

1,000,000% 1,000,000 

100,000% 

10,000% 

Figure 5.5: Percentage difference in mean total discounted repair costs between 36 different 

climate change scenarios and the ‘no climate change’ scenario. Parameters are linearly 

increasing with time in (a) and exponentially increasing in (b). The percentage difference 

is denoted by the color. 

1,000% 

100% 

10% 

1%


wind in 72 different climate change scenarios, in which λ and µ changes from 0 to 1.0% per 

year linearly or exponentially. Given the same value of µ, a higher λ yields a higher 50-year 

return-period wind speed, and hence requires a more resistant structure. Each subplot in 

Figure 5.4 indicates that a lower λ in fact leads to a higher expected life-cycle cost, implying 

that a historically safe region can have a larger expected damage than the disaster-prone 

regions due to the much lower resistance of structures. Also, as expected, the total repair 

cost is higher if the safety factor is low. These relationships are consistent throughout all 

the 72 scenarios. 

Figure 5.5 presents the percentage difference in mean total discounted repair costs be- 

tween the 72 different climate change scenarios and the ‘no climate change’ scenario. The 

life-cycle cost is much more sensitive to the change in µ than the change in λ. The mean 

total discounted repair costs can increase drastically if µ increases by more than 0.2% per 

year, despite the fact that future repair costs are being discounted by 5 % per year. 

In addition to the minimization of the mean life-cycle cost, a small variation of the 

life-cycle cost is desired in structural design optimization because it implies consistency 

of structural performance through time. Figure 5.6 shows the standard deviation of the 

total discounted repair cost in the 72 climate change scenarios. Within each scenario, the 

standard deviation decreases with λ0 and the factor of safety, which is the same as the mean 

in previous results. However, in all scenarios, the standard deviation remains within the 

range between 0 and 0.2, which is much smaller than that of the mean shown earlier in Figure 

5.4. Figure 5.7 shows the percentage difference in the coefficient of variation (ratio of the 

standard deviation to the mean) of the total repair costs between different climate change 

scenarios and the ‘no climate change’ scenario. In each scenario, the percentage difference 

in the coefficient of variation is negative, and increases (in absolute value) with λ0 and the 

factor of safety. Comparing different scenarios, the change in coefficient of variation is much 

more sensitive to the change in µ than to the change in λ. Also, the coefficient of variation

(a) 



(b) 


1.0% 

0.8% 

0.6% 

0.4% 

0.2% 

0% 

1.0% 

0.8% 

0.6% 

0.4% 

0.2% 

0% 


0% 

0% 

0.2% 0.4% 0.6% 0.8% 1.0% 



0.2% 0.4% 0.6% 0.8% 1.0% 



10 5 

10 4 

10 3 

10 2 

LEGEND 

10 

1.5 2 2.5 3 

1 


LEGEND 

10 

1.5 2 2.5 3 

1 


Figure 5.6: Standard deviation of total discounted repair cost as a function of initial frequency 

and safety factor in 36 different climate change scenarios with (a) linearly increasing 

parameters (b) exponentially increasing parameters. The total discounted repair cost is indicated 

by the color. 


10 5 

10 4 

10 3 

10 2 

0.2 

0.18 

0.16 

0.14 

0.12 

0.1 

0.08 

0.06 

0.04 

0.02 

0 

0.2 

0.18 

0.16 

0.14 

0.12 

0.1 

0.08 

0.06 

0.04 

0.02 

0

(a) 



(b) 


1.0% 

0.8% 

0.6% 

0.4% 

0.2% 

0% 

1.0% 

0.8% 

0.6% 

0.4% 

0.2% 

0% 


0% 

0% 

0.2% 0.4% 0.6% 0.8% 1.0% 



0.2% 0.4% 0.6% 0.8% 1.0% 


Initial Frequency ( ( ) 

0 


10 5 

10 5 

10 4 

10 4 

10 3 

10 3 

10 2 

10 2 

LEGEND 

10 

1.5 2 2.5 3 

1 

10 

1.5 2 2.5 3 


1 


10 5 

10 4 

10 3 

10 2 

LEGEND 

10 

1.5 2 2.5 3 

1 


10,000% 0% 

10% 

20% 

1,000% 

30% 

40% 

100% 50% 

60% 

70% 

10% 

80% 

90% 

1% 100% 

1,000,000% 

0% 

10% 

100,000% 

20% 

Figure 5.7: Percentage difference in coefficient of variation of total discounted repair costs 

between 36 different climate change scenarios and the ‘no climate change’ scenario. Parameters 

are linearly increasing with time in (a) and exponentially increasing in (b). The 

percentage difference is indicated by the color. 

30% 

40% 

50% 

60% 

70% 

80% 

90% 

100%


decreases as the mean total discounted repair cost increases, implying that the mean of 

life-cycle cost increases more rapidly than the standard deviation when the structure is 

subjected to more intense loads. This indicates that the significant increase in structural 

life-cycle cost, but not the uncertainty about the life-cycle cost, may be the major problem 

in climate change. 

Each climate change scenario above assumes that the changes in mean intensity (µ) or 

mean frequency (λ) are deterministic. However, as discussed above in the hazard model, 

currently the trends of future wind hazards are still uncertain. The mean and the standard 

deviation of the total discounted repair cost are recalculated, assuming that the yearly 

changes in λ and µ are constant and are uniformly distributed between 0% and 0.1% of 

the initial values. The results are compared with the scenario in which the yearly changes 

are deterministically 0.05% of the initial values of parameters. The uniformly distributed 

parameters yield a larger mean and a larger standard deviation of the total discounted 

repair cost, and the differences are attributed to the uncertainty in parameters. Figures 

5.8 and 5.9 illustrate the ratios of the total mean discounted repair cost attributed to the 

uncertainty in parameters with respect to that attributed to the mean value of parameters. 

In the most extreme case, the uncertainty in parameters can contribute additional 61% of 

the mean repair cost and additional 82% of the standard deviation of the repair cost. The 

contribution diminishes as the factor of safety or the initial mean wind event frequency (λ0) 

increases, and the degree of sensitivity to both parameters is similar. 

5.4.3 Life-cycle-cost-related Decisions 

Previous results have demonstrated different degrees of changes in total discounted repair 

costs in various scenarios. The followings will demonstrate how the changes in cost may 

impact different decisions regarding the management and design of a structure.

Initial Mean Frequency 


100 

1,000 

10,000 

100,000 

58% 

39% 

84% 

74% 

42% 

80% 

61% 62% 


1.5 2.0 2.5 3.0 

16% 

26% 

90% 

5% 

95% 

10% 

20% 

38% 

92% 

79% 

1% 

99% 

3% 

97% 

9% 

21% 

0% 

100% 

1% 

99% 

97% 

89% 

4% 

11% 

89% 

89% of 

the mean repair cost 

attributed to mean 

value of parameters 

11% of the mean 

repair cost attributed 

to uncertainty in 

parameters 

Figure 5.8: Ratios of the total mean discounted repair costs attributed to the uncertainty 

in parameters to that attributed to the mean value of parameters. 

Initial Mean Frequency 

100 

1,000 

10,000 

100,000 

58% 

45% 

31% 

18% 

69% 

82% 

42% 

75% 

55% 63% 

46% 

28% 


1.5 2.0 2.5 3.0 

25% 

37% 

54% 65% 

72% 

79% 

45% 

87% 

13% 

21% 

35% 

78% 

55% 60% 

94% 

88% 

6% 

12% 

22% 

40% 

60% 

11% 

60% of 

the standard 

deviation in repair cost 

attributed to mean value 

of parameters 

40% of the standard 

deviation in repair cost 

attributed to uncertainty 

in parameters 

Figure 5.9: Ratios of the standard deviations of the discounted repair costs attributed to 

the uncertainty in parameters to that attributed to the mean value of parameters. 

40%


5.3.3.1 Maintenance cost 

Structure deteriorates over time and hence requires maintenance. With resistance deterio- 

ration, a structure is more vulnerable to wind hazards and its life-cycle cost is expected to 

increase. An exponential deterioration model is applied to the study: 

R(t) = R0 exp(−αt), (5.11) 

where R0 is the initial resistance value, and α is the deterioration rate, to illustrate the 

maintenance-related analysis. A 0.5% deterioration rate is used, and it is assumed that 

after each failure, the structure is fully repaired so that the resistance is restored to the 

initial value in a short amount of time. 

Four sample simulations are shown in Figure 5.10 explaining the effect of resistance 

deterioration. In the simulations, the factor of safety against 50-year wind speed is 1.0. 

The initial mean wind event frequency (λ0) is 100 and the initial mean wind event intensity 

(µ0) is 6. The figure illustrates that the resistance deterioration can significantly increase 

the number of structural failures across the 50-year design life. If there is no change in 

wind event parameters over time, resistance deterioration increases the number of failures 

from 2 to 8. If λ and µ increase by 1% of the initial values every year over time, resistance 

deterioration increases the number of failures from 6 to 13. 100,000 additional simulations 

Table 5.1: Expected total discounted repair costs and maximum maintenance cost in two 

different climate change scenarios. 

No change in mean frequency ↑ 1% of initial frequency/yr 

No change in mean intensity ↑ 1% of initial intensity/yr 

No deterioration 0.0080 0.0333 

5% deterioration 0.3885 0.5746 

Max maintenance cost 0.3805 0.5414

No resistance 

deterioration 

5% resistance 

deterioration / year 


(relative to 50year speed) 

Resistance 


Resistance 



2 

1.5 

1 

0.5 

0 

0 10 20 30 40 50 

Time (year) 

2 

1.5 

1 

0.5 

0 

0 10 20 30 40 50 

Time 

2 

1.5 

1 

0.5 

No change in mean frequency 

No change in mean intensity 

0 

0 10 20 30 40 50 

Time 



Resistance 


Resistance 


"1% of initial mean frequency / year 

"1% of initial mean intensity / year 

2 

1.5 

1 

0.5 

0 

0 10 20 30 40 50 

Time (year) 

2 

1.5 

1 

0.5 

0 

0 10 20 30 40 50 

Time 

2 

1.5 

1 

0.5 

0 

0 10 20 30 40 50 

Time 

Figure 5.10: Four sample simulations showing the effects of resistance deterioration in two 

different climate scenarios. The circles indicate failure of structure.


are carried out and the resultant mean total discounted repair costs are listed in Table 5.1. 

The difference in life-cycle cost between the case with deterioration and the case without 

deterioration is the maximum maintenance cost that the owner is willing to pay over the 

50-year design life from the economic sense. The climate change scenario can increase the 

repair cost significantly and encourage maintenance of structure against deterioration. 

5.3.3.2 Structural Design 

In life-cycle-cost design, a structural design is optimized for the lowest life-cycle cost, which 

comprises initial construction cost, C0, and the repair cost (see equation 5.1). For simplicity, 

we assume that C0 is a linear function of factor safety. Figure 5.11 illustrates the total life- 

cycle cost as a function of factor of safety in two different climate change scenarios using 

λ0 = 100 and µ0 = 6. If λ and µ increase by 1% of the initial values every year over time, 

due to the increase in expected repair cost, a higher factor of safety is required to achieve 

the minimum total life-cycle cost. In this example, future climate change encourages the 

design of a more costly but safer structure. 

5.5 Modified Florida Public Hurricane Loss Projection 

(FPHLP) Model 

5.5.1 Model Description 

Traditionally, vulnerability models of structures are deduced from empirical relationship 

between wind speed and insurance claims from historical insurance loss databases. Recent 

developments have employed engineering theories to simulate the physical damage process 

when severe winds impacts a structure. Design codes and standards are used to calculate 

the wind loads during a wind hazard. Comparing the load with the resistance data of 

different components collected in test experiments, a building’s damage condition may be

Expected Total 

Discounted Repair 

Cost 

Initial Construction 

Cost 

Expected Total 

Life-Cycle Cost 

0.04 

0.03 

0.02 

0.01 

0.04 

0.02 

0.06 

0.04 

0.02 


No change in mean frequency 

No change in mean intensity 

0 

2 2.5 3 3.5 4 

0 

2 2.5 3 3.5 4 

Min 

0 

2 2.5 3 3.5 4 

0.04 

0.03 

0.02 

0.01 

0.04 

0.02 

0.06 

0.04 

0.02 

!1% of initial mean frequency / year 

!1% of initial mean intensity / year 

0 

2 2.5 3 3.5 4 

Factor of Safety Factor of Safety 

+ + 


0 

2 2.5 3 3.5 4 

= = 



Min 

0 

2 2.5 3 3.5 4 


Figure 5.11: Minimization of life-cycle cost in two different climate scenarios. The circle 

indicates the minimum life-cycle cost and the associated factor of safety.

simulated. 


Florida Public Hurricane Loss Projection (FPHLP) Model, which is developed by a 

multi-disciplinary team of experts from various universities and research institutions at 

Florida International University, is one of the actuarial models that were approved by the 

Florida Commission on Hurricane Loss Projection Methodology for estimating hurricane 

insurance rates in the state of Florida. Though its source code is not open, it is the most 

transparent model compared to the other approved models, which are proprietary and 

commercial. Using a structural engineering approach, FPHLP model calculates the wind 

loads acting on a single-story house based on ASCE 7 Standard and checks a series of limit 

states including the uplift force on roof covers and roof sheathing panels, tension of roof-to- 

wall connections, shear force on walls, and pressure on windows, doors and garage doors. 

The probability distribution of both the wind loads and building component resistance are 

explicitly specified. Using Monte Carlo simulation, the probability of various structural 

damage conditions under a given wind speed is calculated. 

We have developed a vulnerability model based on the engineering component of FPHLP 

model, and modified some of the mechanisms inside the model including internal pressure 

and wind-borne debris. The model is capable of estimating damage ratios of a range of 

building components (e.g. roof covers, roof panels, roof-to-wall connections, walls, windows, 

doors and garage doors) and the damage ratio of the structural system, which is the weighted 

average of the damage ratio of the building components, with the weights proportional to the 

repair cost of the corresponding component. Figure 5.12 shows four example vulnerability 

curves of different structures from the modified FPHLP model. Note that only damage of the 

structural system is considered in the vulnerability curves, as content damage or additional 

living expenses are out of the scope of an engineering model and are not considered here.

Structural Damage Ratio 

1 

0.8 

0.6 

0.4 

0.2 


Hip roof with tiles (no shutters) 

Gable roof with tiles (no shutters) 

Hip roof with tiles (with shutters) 

Hip roof with shingles (with shutters) 

0 

0 50 100 150 200 250 


Figure 5.12: Examples of vulnerability curves of the modified Florida Public Hurricane 

Loss Model. All the curves are related to a one-story concrete-block house with normal 

resistance commonly found in South Florida. 

5.5.2 Expected Repair Cost over the Contiguous United States 

Consider an one-story hip-roof concrete-block house with tiles and no shutters that is com- 

monly found in South Florida. Assume that the structure has a 50-year design life. Figure 

5.13 shows the expected total discounted repair cost of the structure in 129 geographic lo- 

cations over nine different combinations of percentage changes in mean intensity and mean 

frequency. The Gumbel distribution parameters from the extreme wind data at the 129 lo- 

cations are from Figure 5.1, and the wind speed data is converted from fastest mile wind to 

3-second gust wind, on which the modified FPHLP model is based. As observed in the last 

section, the results of the life-cycle costs are similar regardless of whether the parameters 

λ and µ are changing linearly or exponentially with time. Therefore, only results of expo- 

nentially changing parameters are presented here due to space constraint. The expected 

total discounted repair costs, which are indicated by the size and the color of the markers 

in Figure 5.13, may be interpreted as the ratio of the repair cost due to structural damage 

with respect to the construction cost of the structure in the 50-year design period. 

In each subplot of Figure 5.13, the mean total discounted repair cost increases with 

initial mean frequency (λ0) and initial mean intensity (µ0). Comparing subplot to subplot,

Percentage Change in Mean Frequency / Year (k!) 

0.05% 

0% 

Initial Mean Intensity (! ) 


0 0 

0.1% 


0 

14 

12 

10 

8 

6 

4 

2 

14 

12 

10 

10 0 

8 

6 

4 

2 

14 

12 

10 

10 0 

8 

6 

4 

2 

10 0 


10 5 

Initial Mean Frequency ( 0 ) 

10 5 


10 5 


Percentage Change in Mean Intensity / Year (kµ) 

0% 0.05% 0.1% 

Average: 

0.080 

Average: 

0.087 

Average: 

0.095 

10 10 

10 10 

10 10 

Initial Mean Intensity (! 0 ) 



14 

12 

10 

8 

6 

4 

2 

14 

12 

10 

10 0 

8 

6 

4 

2 

14 

12 

10 

10 0 

8 

6 

4 

2 

10 0 

10 5 


10 5 


10 5 

Average: 

0.215 

Average: 

0.244 

Average: 

0.278 


10 10 

10 10 

10 10 


1 

0.9 

0.8 


0.7 

0.6 

0.5 

0.4 


0.3 

0.2 

0.1 

14 

12 

10 

8 

6 

4 

2 

14 

12 

10 

10 0 

8 

6 

4 

2 

14 

12 

10 

10 0 

8 

6 

4 

2 

10 0 

10 5 


10 5 


10 5 

Average: 

0.792 

Average: 

0.929 

Average: 

1.091 

10 10 

10 10 

10 10 

Initial Mean Frequency () 0 

0 

0 0.2 0.4 0.6 0.8 1 

Figure 5.13: Expected total repair cost of a one-story hip-roof concrete-block house over 129 

geographic locations in contiguous United States in nine different future climate scenarios. 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0


the costs are more sensitive to the yearly percentage change in mean intensity (kµ) than 

the change in mean frequency (kλ), similar to the results in the last section. Also, when 

there is no change in mean intensity over time, the wind climate with smallest λ0 yields the 

largest expected repair cost. However, when kµ reaches 0.1%, the result is opposite. The 

wind climate with largest λ0 yields the largest expected repair cost. This indicates that a 

structure in a wind climate of larger µ0 is more sensitive to an increase in mean intensity 

of wind hazards. Overall, given a 0.1% increase in both mean intensity, the expected repair 

cost may increase by more than 10 times. 

5.5.3 Expected Repair Cost for Different Structures 

The wind condition in Greensboro, NC (λ0 = 689.29, µ0 = 5.9743) is applied to the four 

vulnerability curves of different structures shown in Figure 5.12 to find out the impact of 

structural details on the total expected repair cost related to structural damage. The re- 

sults are presented in Figure 5.15 as a function of the percentage change in mean wind event 

intensity (kµ) only, since previous results have indicated that the repair cost’s sensitivity to 

kµ is significantly larger than that to the mean wind event frequency (kλ). Three compar- 

isons are made in the three subfigures: (a) hip roof vs. gable roof; (b) tiles vs. shingles; and 

(c) shutters vs. no shutters. They show that the expected total repair cost may differ very 

significantly, from ∼20% to ∼100%, although the vulnerability looks relatively similar. A 

larger increase in future µ always leads to a larger difference in expected repair cost between 

two structures, which makes a safer structural design more financially justifiable. 

As mentioned above, the design codes and standards in the United States require build- 

ings to be capable to resist minimally a 50-year-return-period wind speed. However, as 

shown in all previous results, each parameter of the wind speed distribution does have dis- 

tinctive effects on a structure’s life-cycle cost in various climate scenarios. Based on the 

study by NIST (National Institute of Standards and Technology, 2006a), four set of Gumbel

Expected Total Structural Damage Cost 

0.1 

0.05 

Hip 

Gable 


0 

0 0.2 0.4 0.6 0.8 1 

Percentage Change in Mean Intensity (k ) (%) 

µ 


0.1 

0.05 

No shutters 

Shutters 

0 

0 0.2 0.4 0.6 0.8 1 


µ 

0 

0 0.2 0.4 0.6 0.8 1 


µ 

(a) (b) (c) 


0.1 

0.05 

Tile 

Shingle 

Figure 5.14: Expected total repair cost related to structural damage: (a) hip roof vs. gable 

roof (b) tiles vs. shingles (c) shutters vs. no shutters. 

distribution parameters from four different stations (see Table 5.2) are selected and applied 

to two set of vulnerability curves, which represent wood-frame houses and concrete-block 

houses at different ages. 

The left of Figure 5.15 shows the vulnerability curves of three concrete-block houses 

that are commonly found in North Florida and are built before 1970, between 1970 - 1993, 

and after 1994. They are labeled as ‘weak’, ‘medium’, and ‘strong’, respectively. The right 

of the figure shows the expected total repair cost as a function of the percentage change 

in mean wind event intensity (kµ) in the four geographic locations. The mean frequency λ 

is assumed to have no change over time. Although the 50-year wind speed is almost the 

Table 5.2: Gumbel distribution parameters of four different geographic locations with similar 

50-year wind speed. 

Location Mean frequency (λ0) Mean intensity (µ0) 50-year wind speed (mph) 

Evansviille, IN 11108.1 4.699 62.11 

Denver, CO 244592.5 3.815 62.23 

Greensboro, NC 689.3 5.974 62.36 

Memphis, TN 4169.6 5.103 62.44


same in the four locations, the structure can have four significantly different expected total 

discounted repair costs over its design life. And such difference increases as kµ increases. 

The same applies to wood-frame houses in Figure 5.16, except that the expected total 

discounted repair costs are less sensitive to the age of the structure. 


1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

Vulnerability Curves 

Weak 

Medium 

Strong 

0 

0 50 100 150 200 250 


Mean Total 

Mean Structural Total Structural Damage Damage Cost Cos 

Mean Total 


0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 0.2 0.4 0.6 0.8 1 


µ 

0.5 

0.4 

0.3 

0.2 

0.1 

Evansville, IN Denver, CO 

0 

0 0.2 0.4 0.6 0.8 1 


µ 

Mean Total 


Mean Total 


0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 0.2 0.4 0.6 0.8 1 


µ 

Greensboro, NC Memphis TN 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 0.2 0.4 0.6 0.8 1 


µ 

Figure 5.15: Vulnerability curves and total expected repair cost related to structural damage 

of a concrete-block house at four different geographic locations. 


This study has examined some of the possible effects of climate change on the life-cycle 

cost of structures from a wind engineering aspect. A hazard model was developed by 

converting the Gumbel distribution into a compound Poisson process to simulate future 

wind conditions. The hypothetical climate assumptions are made to calculate the life-cycle 

cost of structures using two vulnerability models: a single-limit-state vulnerability model 

and the modified FPHLP model. 

The results in this study have illustrated that future trends in wind hazards can affect


1 

0.9 

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Vulnerability Curves 

0 

0 50 100 150 200 250 


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0 0.2 0.4 0.6 0.8 1 


µ 

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Evansville, IN Denver, CO 

0 

0 0.2 0.4 0.6 0.8 1 


µ 

Mean Total 


Mean Total 


0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 0.2 0.4 0.6 0.8 1 


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Greensboro, NC Memphis TN 

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0 0.2 0.4 0.6 0.8 1 


µ 

Figure 5.16: Vulnerability curves and total expected repair cost related to structural damage 

of a wood-frame house at four different geographic locations. 

the expected future repair cost of structures very significantly. Given the uncertainty of 

future climate trends, the future risk of structural failures remain ambiguous. This can 

remarkably affect the insurance market, since insurers would charge 25% higher premiums 

for ambiguous risks than for risks with probabilities that were well specified (Kunreuther 

and Michel-Kerjan, 2009). 

As illustrated in the results of the modified FPHLP model, different types of structural 

design can have very different life-cycle cost in long-term, particularly if the future wind 

hazards intensify, although they may have similar vulnerability curves. Currently, insurance 

companies have only limited economic incentive to set individual insurance rates based on 

the risk characteristics of each property. More information on each property can help reduce 

the ambiguity of risk and hence the insurance premium. 

In addition, the life-cycle cost depends significantly on the wind speed distribution pa- 

rameters rather than the design wind speed. If the effects of climate change are considered,


a life-cycle cost design should investigate the actual wind speed distribution as well as its 

possible changes in the future. Traditional design only considers the 50-year wind speed 

based on the wind map in design codes and standards and assumes that the environmental 

loads are stationarity with time in long term.

Chapter 

6 

Conclusions and Future Work 

6.1 Summary and Conclusions 

This research first investigates the wind vulnerability of structural components. The method- 

ology is then extended to the analysis of entire residential structures and hence communities 

of residential structures. The last part of the dissertation extends the analysis to the long- 

term risk assessment and management of structures under the effect of climate change. The 

following highlights the findings and concludes each of the chapters: 

Chapter 2 compares two prevalent methodologies to specify loads and estimate damage 

for low-rise structures due to tropical cyclones. One method, the time-stepping method, 

evaluates structural loads and performance at consecutive time steps, accounting for evolv- 

ing wind direction during an individual wind event. The other, commonly known as point- 

in-time reliability analysis, approximates structural performance in an event by referencing 

to the events maximum wind speed only. To compare the two approaches, a database of 

synthetic tropical-cyclone wind velocity time series is generated based on a probabilistic 

model. A test set of reliability analyses indicates that the point-in-time method, by ignor- 

ing information about directionality, underestimates the maximum wind load on structures. 

123

Chapter 6. Conclusions and Future Work 124 

The differences tend to grow (1) the greater the variability of the pressure coefficient with 

respect to wind direction; or (2) when the structure is within the tropical cyclones radius of 

maximum wind for some time period; or (3) when events intensity is relatively low. The re- 

sults also show that the probability of failure approximated using the point-in-time method 

may be underestimated by up to 60%. 

Chapter 3 compares three different internal pressure adjustment methods (FPHLP 

model, ASCE 7 Standard, and Eurocode), and examines each of their significance in the 

structural vulnerability analysis. During major wind events, the presence of an opening 

on a building envelope may result in high internal pressure and hence a critical increase in 

the wind load on the roof. Due to the complexity of aerodynamics, there has not been a 

consensus on how to determine the value of internal pressure numerically given the damage 

of the building envelope. This study illustrates the interplay between internal pressure and 

building envelope damage through several numerical examples, and presents the roof dam- 

age results of three baseline structures using different internal pressure adjustment methods 

and wind-borne debris parameters over a wide range of wind speeds. It is found that the 

internal pressure significantly alters the roof damage, but the degree of effect depends on 

the details of the internal pressure adjustment model. Additional windows, presence of 

wind-borne debris, and increase in wind speed does not necessarily exacerbate the roof 

damage in every internal pressure model. Depending on the wind speed and the structural 

configuration, the damage results may differ by a few percent to a few hundred percent. 

Chapter 4 presents an integrated vulnerability model to estimate structural damage and 

related economic losses in clusters of residential buildings due to tropical cyclone winds. The 

model couples a component-based pressure damage model, which is based on the FPHLP 

model, and a wind-borne debris model by Lin and Vanmarcke (2008, 2010), accounting for 

the occurrence of a possible ‘chain reaction’ of events involving wind pressure damage and 

wind-borne debris damage, amplifying overall losses. The first part of the chapter presents


the details of the methodology. The second part (1) illustrates how a structure is affected by 

neighboring buildings resistance against high wind; (2) contrasts the difference in damage 

predictions between time series analysis and point-in-time analysis during a storm passage; 

and (3) extends the estimation of wind-induced losses from structural components to the 

entire structural system, the interior system, and the utility system (including electrical, 

pluming, heating systems) of buildings. Different approximate damage and loss prediction 

methods are compared, and four numerical examples are provided. 

Chapter 5 studies the potential impact of climate change on structural engineering 

analysis, particularly the life-cycle cost of structures. A non-stationary stochastic process 

is developed based on the assumption that extreme wind speed is Gumbel distributed. The 

process simulates the long-term wind climate assuming that the mean frequency and/or 

the mean intensity of future wind events change linearly or exponentially with time. The 

wind event simulation results are applied to two vulnerability models: a single-limit-state 

vulnerability model and the modified FPHLP model. The life-cycle cost of a structure 

over its design life is calculated over a range of wind climate and a number of hypothetical 

climate change scenarios. The results show that future trends in wind hazards may affect 

the expected repair cost of a structure very significantly: a 0.1% or 0.2% yearly increase 

in mean intensity of wind hazards may double or triple the expected repair cost. Also, 

uncertainty in future wind intensity and frequency can almost double the mean and the 

standard deviation of the future repair cost. 

6.2 Future Work 

6.2.1 Structural Components 

The results in Chapter 2 show that the damage level of structural components is signifi- 

cantly affected by the trend and variability of the tropical cyclone wind time history. The


effect of such trend and variability may be quantified, so that general guidelines can be 

developed regarding how much damage should be expected given certain characteristics of 

the tropical cyclone wind (besides maximum wind speed). First, one or several measures 

may be developed to quantify the shape or trend of the wind time history. Examples are 

the total change in wind angle, the weighted change in wind angle (weights proportional to 

wind speed), etc. Relationships between such measures and the structural damage may be 

obtained through numerical simulations. The goal is to express wind damage as a function 

of not only the maximum wind speed over time, but also other measures which describes 

the wind time history. 

Another potential future work is regarding the uncertainty of the pressure coefficient, 

which is a critical component of the wind load equation (see Equation 2.12). Chapter 2 

obtains the pressure coefficient functions from the wind tunnel experiments and other vul- 

nerability models, and does not take into account the uncertainty of the pressure coefficient 

itself. Depending on the wind speed, wind directionality and the building component, the 

degree of uncertainty of the pressure coefficient may change. An uncertainty analysis may 

be carried out to examine the effect of changing wind directionality over time on the uncer- 

tainty of the damage level of building components. Any change in uncertainty may affect 

the probability of failure of the building components. 

6.2.2 Low-Rise Structures 

Chapter 3 has shown that the details of the internal pressure adjustment mechanisms may 

completely change the results of the roof damage estimation. Such analysis may be extended 

to other parts of the structure and hence the economic loss estimation, further illustrating 

the importance of the internal pressure adjustment mechanism. Similarly, different internal 

pressure adjustment mechanisms may be applied to the vulnerability analysis of multi- 

structural community. This may further highlight the importance of the interplay between


change in internal pressure and wind-borne debris risk. Furthermore, by comparing the 

damage surveys with the results of different internal pressure adjustment methods, one 

may conclude which internal pressure adjustment method better reflects the reality. 

More importantly, the study presented in Chapter 3 indicates the need of wind tunnel 

experiments regarding internal pressure changes inside a damaged structure. While the 

internal pressure determination method differs very much in different design specifications 

and loss models, there is no consensus in the field regarding the how to determine the inter- 

nal pressure value numerically based on the damage on building envelope. Also, there are no 

publicly available results of wind tunnel experiments regarding this issue. Further investi- 

gations using wind tunnel and and full-scale wind experiments are necessary before deriving 

an accurate numerical method to determine internal pressure changes due to openings on 

the building envelope. 

6.2.3 Multi-Structural Communities 

Chapter 4 presents the integrated vulnerability model which couples the debris risk model 

and the pressure damage model, and applies the model to communities of residential struc- 

tures. In the wind vulnerability analysis of a multi-structural community, wind load may 

be significantly affected by the shielding effect due to the presence of nearby buildings and 

trees. A more complete analysis should consider the shielding effect as well as possible effect 

of topography on the wind load acting on each structure. Such analysis may reveal a better 

layout of the residences in order to minimize the wind loads, which is similar to finding out 

the best layout of wind turbines in order to maximize the energy output of a wind farm. 

The third numerical example in Chapter 4 has shown the effects of a house’s strength 

on the other house’s wind vulnerability. The analysis may be extended to further analyze 

the effect of a weak house on the entire neighborhood. A more detailed analysis which 

reveals the economic cost of the presence of a deteriorated house will be very useful to the


insurance industry and the homeowners in identifying the potential sources of danger in a 

residential community. 

6.2.4 Low-Term Risk Assessment 

The analysis in Chapter 5 may be enhanced and extended in a number of areas. For example, 

Chapter 5 develops a compound Poisson process to simulate future wind events. Instead, 

more sophisticated and complex stochastic processes may be developed. Different wind 

hazards may be considered individually and the stochastic processes may reflect periodic 

environments like those forming tropical cyclones (Cook et al., 2003; Lu and Garrido, 2005). 

Furthermore, in Chapter 5, the hypothetical climate change scenarios are limited to linear 

and exponential increase in wind hazard intensity and frequency of occurrence. A more 

complex assumption may be made, i.e. only certain levels of wind hazard events increase in 

frequency in the future. 

Also, a more detailed analysis on the life-cycle cost may be conducted. For instance, 

the tails of the probability distribution of repair costs, in addition to the mean and the 

standard deviation, may be analyzed in details, since they are essential in catastrophe 

management. An uncertainty analysis that attributes the sources of uncertainty in life- 

cycle cost to different origins, including hazard model, vulnerability model and life-cycle 

cost formulations, will be very insightful in guiding the future developments of the risk 

assessment related to wind hazards.

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