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Development of a Hurricane Loss Projection Model for Commercial Residential Buildings

Permanent Link: http://ufdc.ufl.edu/UFE0041010/00001

Material Information

Title: Development of a Hurricane Loss Projection Model for Commercial Residential Buildings
Physical Description: 1 online resource (154 p.)
Language: english
Creator: Balderrama, Juan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: commercial, debris, engineering, hurricane, impact, loss, low, mid, model, projection, residential, rise, wind, windborne
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.E.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract: DEVELOPMENT OF A HURRICANE LOSS PROJECTION MODEL FOR COMMERCIAL RESIDENTIAL BUILDINGS Candidate's name: Juan Antonio Balderrama Garcia Mendez Phone number: 574-344-3133 Department: Civil and Coastal Engineering Supervisory chair: Kurtis R. Gurley Degree: Master of Engineering Month and year of graduation: December 2009 This thesis contributes to the development of a hurricane loss projection model for commercial residential buildings. The results of the completed model will allow engineers to project hurricane damage and develop more effective hurricane damage mitigation measures. The results of this model will also aid insurance companies in the assessment of their insurance rates.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Juan Balderrama.
Thesis: Thesis (M.E.)--University of Florida, 2009.
Local: Adviser: Gurley, Kurtis R.
Local: Co-adviser: Masters, Forrest.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041010:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041010/00001

Material Information

Title: Development of a Hurricane Loss Projection Model for Commercial Residential Buildings
Physical Description: 1 online resource (154 p.)
Language: english
Creator: Balderrama, Juan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: commercial, debris, engineering, hurricane, impact, loss, low, mid, model, projection, residential, rise, wind, windborne
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.E.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: DEVELOPMENT OF A HURRICANE LOSS PROJECTION MODEL FOR COMMERCIAL RESIDENTIAL BUILDINGS Candidate's name: Juan Antonio Balderrama Garcia Mendez Phone number: 574-344-3133 Department: Civil and Coastal Engineering Supervisory chair: Kurtis R. Gurley Degree: Master of Engineering Month and year of graduation: December 2009 This thesis contributes to the development of a hurricane loss projection model for commercial residential buildings. The results of the completed model will allow engineers to project hurricane damage and develop more effective hurricane damage mitigation measures. The results of this model will also aid insurance companies in the assessment of their insurance rates.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Juan Balderrama.
Thesis: Thesis (M.E.)--University of Florida, 2009.
Local: Adviser: Gurley, Kurtis R.
Local: Co-adviser: Masters, Forrest.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041010:00001


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1 DEVELOPMENT OF A HURRICANE LOSS PROJECTION MODEL FOR COMMERCIAL RESIDENTIAL BUILDINGS By JUAN ANTONIO BALDERRAMA GARCIA MENDEZ A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2009

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2 2009 Juan Antonio Balderrama Garcia Mendez

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3 ACKNOWLEDGMENTS I am grateful for the ongoing support and guidance that Dr. Kurtis Gurley gave me, for the patience that he had, and for his challenges during the development of this thesis; without his mentoring the completion of this project would not have been possible. I a m also grateful for the support and suggestions given to me by Dr. Masters and Dr. Prevatt. Johann Weekes also deserves my gratitude; the work that we completed for Dr. Gurley was always the result of our valuable teamwork. I also thank Katherine Alva for her ongoing support and motivation.

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4 TABLE OF CONTENTS ACKNOWLEDGMENTS ...............................................................................................................3 page LIST OF TABLES ...........................................................................................................................7 LIST OF FIGURES .........................................................................................................................9 ABSTRACT ...................................................................................................................................14 CHAPTER 1 INTRODUCTION ..................................................................................................................16 Community Development in Disaster Prone Areas ................................................................16 The Need to Predict Hurricane Losses ...................................................................................18 Regulatory Oversight of Insurance Premiums at the State Level ...........................................18 Existing Loss Models .............................................................................................................19 Scope of Research ...................................................................................................................20 2 LOSS MODELING BACKGROUND ...................................................................................22 The Sources of Damage ..........................................................................................................22 Earthquakes .....................................................................................................................22 Tornadoes ........................................................................................................................26 Hurricanes ........................................................................................................................28 Terrorism .........................................................................................................................32 Loss Models ............................................................................................................................32 HAZUS Multi Hazard Model ..........................................................................................33 Florida Public Hurricane Loss Model .............................................................................35 Commercial Residential Public Hurricane Loss Model ..................................................37 3 COMMERCIAL RESIDENTIAL BUILDINGS: FUNDAMENTAL CONSIDERATIONS IN THE MODEL ................................................................................38 Conceptual Representation of a Wide Array of Building Types ............................................38 The Florida Commercial R esidential Buildings Survey ..................................................38 The Monte Carlo Concept ...............................................................................................43 Low Rise Commercial Residential Building ..........................................................................45 General Descriptions .......................................................................................................45 Major Contributors to Insured Losses .............................................................................46 Components within the Model ........................................................................................48 Basic Model Descriptors .................................................................................................50 Mid High Rise Commercial Residential Building ..................................................................51 General Descriptions .......................................................................................................51 Major Contributors to Insured Losses .............................................................................53

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5 Components within the Model ........................................................................................54 Basi c Model Descriptors .................................................................................................55 4 LOW RISE COMMERCIAL RESIDENTIAL MODEL PERFORMANCE .........................56 Overview .................................................................................................................................56 Program Architecture and Solution Process ...........................................................................56 Model and Analysis Definition Phase ....................................................................................56 Options for Model Descriptors ........................................................................................57 Restrictions ......................................................................................................................58 Modeling the Building, its Components, and Wind Loads ....................................................59 Mapping of Components .................................................................................................60 Capacity Modeling ..........................................................................................................63 Wind Pressure Load Modeling ........................................................................................64 Debris Impact Load Modeling .........................................................................................69 Anal yzing the Building and Determining and Processing the Damage .................................79 Examples of Simulation Results .............................................................................................82 Sample of Preliminary Results for Gabled Roof Building .....................................................83 Preliminary Verification .........................................................................................................89 5 MID HI GH RISE COMMERCIAL RESIDENTIAL MODEL PERFORMANCE ...............91 Overview .................................................................................................................................91 Program Architecture and Solution Process ...........................................................................92 Model and Analysis Definition Phase ....................................................................................92 Options for Model Descriptors ........................................................................................92 Restrictions ......................................................................................................................93 Modeling the Building, its Components, and Wind Loads ....................................................94 Mapping of Components .................................................................................................95 Capacity Modeling ..........................................................................................................96 Loading Model ................................................................................................................98 Damage Quantification and Process and Verification of Results .........................................101 Examples of Simulation Results ...........................................................................................102 Sample of Preliminary Results .............................................................................................103 Preliminary Verification .......................................................................................................111 6 CONCLUSIONS AND RECOMMENDATIONS ...............................................................113 Delegation of Responsibilities ..............................................................................................113 Potential Uses for the Output ................................................................................................114 User Input of Generic Parameters .........................................................................................114 Recommendations to Improve the Current Model ...............................................................115 APPENDIX A PRELIMINARY RESULTS FOR LOW RISE BUILDINGS ..............................................117 Low Rise Model with a Gable Roof .....................................................................................117

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6 Low Rise Model with a Hip Roof .........................................................................................122 B PRELIMINARY RESULTS FOR MID HIGH RISE BUILDINGS ....................................127 Middle Unit in a Building with an Exterior Corridor ...........................................................127 Corner Unit in a Building with an Exterior Corridor ...........................................................131 Middle Unit in a Building with an Interior Corridor ............................................................135 Corner Unit in a Building with an Interior Corridor .............................................................139 C MISSILE MODEL PARAMETERS AND CHECKS ..........................................................143 Missile Model Parameters ....................................................................................................143 Missile Model Check ............................................................................................................145 LIST OF REFERENCES .............................................................................................................149 BIOGRAPHICAL SKETCH .......................................................................................................154

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7 LIST OF TABLES Table page 21 Earthquake intensity and magnitude scales (adapted from Federal Emergency Management Agency, 2006) ..............................................................................................24 22 The Saffir Simpson hurricane scale (adapted from National Weather Service, 2004) ......30 23 Examples of acts of terrorism ............................................................................................32 31 Roof characteristics for low rise buildings (adapted from Pita et al. 2008) ......................39 32 Roof characteristics for mid high rise buildings (adapted from Pita et al. 2008) ..............40 33 Exterior wall material for low rise and mid high rise buildings (adapted from Pita et al. 2008) .............................................................................................................................40 34 Prevalent plan dimensions (adapted from Pita et al. 2008) ...............................................41 35 Number of stories for low rise buildings (adapted from Pita et al. 2008) .........................41 36 Number of stories for mid high rise buildings (adapted from Pita et al. 2008) .................41 37 Distribution by construction date (adapted from Pita et al. 2008) .....................................42 38 Conceptual commercial residential building models .........................................................43 41 Low rise building model descriptors ..................................................................................57 42 Gable end mapping matrices ..............................................................................................62 43 Pressure capacities (psf) and coefficients of variation for components in the building envelope .............................................................................................................................64 44 Impact capacity correction factors .....................................................................................64 45 Sample model analyzed .....................................................................................................83 51 Mi d high rise model descriptors ........................................................................................93 52 Pressure capacities and coefficients of variation for glazing components ........................97 53 Manufacturer data for capacities of glazing components commonly used in mid high rise commercial residential buildings (PGT Industries) ....................................................97 54 Pressure vulnerability matrix for a building with an interior stairway ............................100 55 Impact vulnerability matrix for a building with an interior stairway ...............................100

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8 56 Pressure vulnerability matrix for a building with an exterior stairway ...........................100 57 Impact vulnerability matrix for a building with an exterior stairway ..............................101 58 Mid high rise sample models analyzed ............................................................................103 59 Pressure and impact capacities in model .........................................................................110 510 Pressure and impact capacities from a manufacturer (www.pgtindustries.com/) ............110 A 1 MatLAB generated header describing the gable roofed low rise building analyzed ........117 A 2 MatLAB generated header describing the hip roofed low rise building analyzed ...........122 B 1 MatLAB generated header describing the exterior corridor buildings middle unit analyzed ...........................................................................................................................127 B 2 MatLAB generated header describing the exterior corridor buildings corner unit analyzed ...........................................................................................................................131 B 3 MatLAB generated header describing the interior corridor buildings middle unit analyzed ...........................................................................................................................135 B 4 MatLAB generated header describing the interior corridor buildings corner unit analyzed ...........................................................................................................................139 C 1 MatLAB generated header describing the unit analyzed ..................................................145

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9 LIST OF FIGURES Figure page 21 Plate boundaries (Credit: U.S. Geological Survey/Lisa Wald) ..........................................23 22 Mexico City (1985) Earthquake .........................................................................................25 23 Northridge (1994) Earthquake (Credit: U.S. Geological Survey/Lisa Wald) ....................25 24 Tornado development (By courtesy of Encyclopdia Britannica, Inc., copyright 1999; used with permission) ..............................................................................................27 25 Locations favorable for development and intensification of tropical cyclones (Gutro, 2009) ..................................................................................................................................29 26 Effects of Hurricane Katrina (2005) in Mississippi ...........................................................31 27 Effects of Hurricane Katrina (2005) in Louisiana .............................................................31 28 HAZUS Wind model framework (Federal Emergency Management Agency, 2008) .......35 31 Layout types modeled for mid high commercial residential model ..................................53 41 Low rise commercial residential model algorithm ............................................................60 42 Gable end sheathing layout and areas (3 story building) ...................................................62 43 ASCE 7 05 (2005) roof and wall pressure zones (With permission from ASCE) ............66 44 Copes (2004) modified roof pressure zones .....................................................................67 45 Urban and suburban missile exposure layouts ...................................................................72 46 Open missile exposure layout ............................................................................................72 47 Directions of wi nd approach in the missile model .............................................................73 48 Value of parameter A versus wind speed (strong shingles) ...............................................74 49 Value of parameter B versus wind speed (strong shingles) ...............................................77 410 Value of parameter D versus wind speed (strong shingles) ...............................................78 411 Frequency distribution of load effect and resistance for a general system ........................80 412 Roof sheathing and roof cover damage for a 3 story, gable roofed, medium quality building ..............................................................................................................................85

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10 413 Roof and wall sheathing damage for a 3 story, gable roofed, medium quality building ...85 414 ASCE 7 05 (2005) wall pressure zones 4 and 5 (With permission from ASCE) ..............86 415 Wall sheathing and cover damage for a 3 story, gable roofed, medium quality building ..............................................................................................................................86 416 Window damage for a 3 story, gable roofed, medium quality building ............................87 417 Sliding door damage for a 3 story, gable roofed, medium quality building ......................88 418 Entry door damage for a 3 story, gable roofed, medium quality building .........................88 51 Mid high rise commercial residential model algorithm .....................................................95 52 Simulated wind approach direction for a building with an exterior corridor ....................98 53 Simulated wind approach direction for a building with an interior corridor .....................99 54 Comparative window damage for a middle unit in a building with an exterior corridor .............................................................................................................................104 55 Comparative window damage for a middle unit in a building with an interior corridor .104 56 Comparative window damage for a corner unit in a building with an exterior corridor .105 57 Comparative window damage for a corner unit in a building with an interior corri dor ..105 58 Comparative entry door damage for a middle unit in a building with an exterior corridor .............................................................................................................................106 59 Comparative entry door damage for a middle unit in a building with an interior corridor .............................................................................................................................106 510 Comparative entry door damage for a corner unit in a building with an exterior corridor .............................................................................................................................107 511 Comparative entry door damage for a corner unit in a building with an interior corridor .............................................................................................................................107 512 Comparative sliding door damage for a middle unit in a building with an exterior corridor .............................................................................................................................108 513 Comparative sliding door damage for a middle unit in a building with an interior corridor .............................................................................................................................108 514 Comparative sliding door damage for a corner unit in a building with an exterior corridor .............................................................................................................................109

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11 515 Comparative sliding door damage for a corner unit in a building with an interior corridor .............................................................................................................................109 516 Reliability and damage probability for a missile check analysis .....................................112 A 1 Gable end/truss damage for a 3 story gable roofed medium quality building .................118 A 2 Roof to wall connection damage for a 3 story gable roofed medium quality building ...118 A 3 Roof sheathing/cover damage for a 3 story gable roofed medium quality building ........119 A 4 Roof/wall sheathing damage for a 3 story gable roofed medium quality building ..........119 A 5 Wall sheathing/cover damage for a 3 story gable roofed medium quality building ........120 A 6 Window damage for a 3 story gable roofed medium quality building ............................120 A 7 Sliding door damage for a 3 story gable roofed medium quality building ......................121 A 8 Entry door damage for a 3 story gable roofed medium quality building .........................121 A 9 Gable end/truss damage for a 3 story hip roofed medium quality building .....................122 A 10 Roof to wall connection damage for a 3 story hip roofed medium quality building .......123 A 11 Roof sheathing/cover damage for a 3 story hip roofed medium quality building ...........123 A 12 Roof/wall sheathing damage for a 3 story hip roofed medium quality building .............124 A 13 Wall sheathing/cover damage for a 3 story hip roofed medium quality building ...........124 A 14 Window damage for a 3 story hip roofed medium quality building ................................125 A 15 Sliding door damage for a 3 story hip roofed medium quality building ..........................125 A 16 Entry door da mage for a 3 story hip roofed medium quality building ............................126 B 1 Comparative window damage for a middle unit in a building with an exterior corridor .............................................................................................................................127 B 2 Comparative entry door damage for a middle unit in a building with an exterior corridor .............................................................................................................................128 B 3 Comparative sliding door damage for a middle unit in a building with an exterior corridor .............................................................................................................................128 B 4 Combined reliability/damage probability from impact for all windows in a middle unit in a building with an exterior corridor ......................................................................129

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12 B 5 Combined reliability/damage probability from impact for one window in a middle unit in a building with an exterior corridor ......................................................................129 B 6 Combined reliability/damage probability from impact for the entry door in a middle unit in a building with an exterior corridor ......................................................................130 B 7 Combined reliability/damage probability from impact for the sliding door in a middle unit in a building with an exterior corridor ......................................................................130 B 8 Comparative window damage for a corner unit in a building with an exterior corridor .131 B 9 Comparative entry door damage for a corner unit in a building with an exterior corridor .............................................................................................................................132 B 10 Comparative sliding door damage for a corner unit in a building with an exterior corridor .............................................................................................................................132 B 11 Combined reliability/damage probability from impact for all windows in a corner unit in a building with an exterior corridor ......................................................................133 B 12 Combined reliability/damage probability from impact for one window in a corner unit in a building with an exterior corridor ......................................................................133 B 13 Combined reliability/damage probability from impact for the entry door in a corner unit in a building with an exterior corridor ......................................................................134 B 14 Combined reliability/damage probability from impact for the sliding door in a corner unit in a building with an exterior corridor ......................................................................134 B 15 Comparative window damage for a middle unit in a building with an interior corridor .135 B 16 Comparative entry door damage for a middle unit in a building with an interior corridor .............................................................................................................................136 B 17 Comparative sliding door damage for a middle unit in a building with an interior corridor .............................................................................................................................136 B 18 Combined reliability/damage probability from impact for all windows in a middle unit in a building with an interior corridor .......................................................................137 B 19 Combined reliability/damage probability from impact for one window in a middle unit in a building with an interior corridor .......................................................................137 B 20 Combined reliability/damage probability from impact for the entry door in a middle unit in a building with an interior corridor .......................................................................138 B 21 Combined reliability/damage probability from impact for the sliding door in a middle unit in a building with an interior corridor .......................................................................138

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13 B 22 Comparative window damage for a corner unit in a building with an interior corridor ..139 B 23 Comparative entry door damage for a corner unit in a building with an interior corridor .............................................................................................................................140 B 24 Comparative sliding door damage for a corner unit in a building with an interior corridor .............................................................................................................................140 B 25 Combined reliability/damage probability from impact for all windows in a corner unit in a building with an interior corridor .......................................................................141 B 26 Combined reliability/damage probability from impact for o ne window in a corner unit in a building with an interior corridor .......................................................................141 B 27 Combined reliability/damage probability from impact for the entry door in a corner unit in a building with an interior corridor .......................................................................142 B 28 Combined reliability/damage probability from impa ct for the sliding door in a corner unit in a building with an interior corridor .......................................................................142 C 1 Value of parameter A versus wind speed (strong shingles) .............................................143 C 2 Value of parameter B versus wind speed (strong shingles) .............................................144 C 3 Value of parameter D versus wind speed (strong shingles) .............................................144 C 4 Comparative window damage for the missile model check ............................................145 C 5 Comparative entry door damage for the missile model check .........................................146 C 6 Comparative sliding door damage for the missile model check ......................................146 C 7 Combined reliability/damage pr obability from impact for all windows for the missile model check .....................................................................................................................147 C 8 Combined reliability/damage probability from impact for one window for the missile model check .....................................................................................................................147 C 9 Combined reliability/damage probability from impact for the entry door for the missi le model check .........................................................................................................148 C 10 Combined reliability/damage probability from impact for the sliding door for the missile model check .........................................................................................................148

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14 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering DEVELOPMENT OF A HURRICANE LOSS PROJECTION MODEL FOR COMMERCIAL RESIDENTIAL BUILDINGS By Juan Antonio Balderrama Garcia Mendez December 2009 Chair: Kurtis R. Gurley Major: Civil Engineering Natural d isasters and other hazards inflict considerable losses to our society. Predicting t hese losses is crucial for both the development of techniques for physical damage mit igation and the reduction of economic losses produced after a disaster. Hurricane inflic ted damage is the main contributor to insurance losses in the State of Florida; thus, years ago the Florida Department of Financial Services sponsored the development of the Florida Public Hurricane Loss Model. The purpose of the model was to predict hurri cane wind induced insurance losses for residential structures in Florida. The University of Florida was responsible for the engineering component of this multiuniversity project. A considerable portion of the hurricane induced insured losses in the s tate of Florid a result s from damage inflicted to low rise and mid high rise commercial residential construction; thus, the current Florida Public Hurricane Loss Model is under expansion to incorporate modules that will enable the prediction of losses for these types of buildings. Modules currently under development at the University of Florida are the engineering components of the Low Rise and Mid High Rise Commercial Resid ential Hurricane Loss Models. The goal of these components is to relate wind speeds to pre dicted physical exterior damage in low rise and mid high rise buildings. The research presented in this thesis contributes to the development of a probabilistic

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15 model that fulfills this goal. The main component of the model is a Monte Carlo Simulation engi ne that samples component capacities, the loads they sustain, and predicts their probability of damage. The damage estimates calculated by these models will be used to predict interior building damage and finally monetary losses.

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16 CHAPTER 1 INTRODUCTION Community Development in Disaster Prone Areas Natural disaster prone areas have been historically attractive locations for rising communities. Even though developed in areas subject to earthquakes, windstorms, or other nat ural disasters, cities such as San Francisco, New York, New Orleans, Miami, or Tampa, continue to grow and have become important urban and economic centers. The first settlers of these cities were certainly not attracted to these areas because they were di saster prone; instead they found appeal either in their easy access due to the proximity of large bodies of water their copious supply of resources, or their pleasant climate. Abundance of resources or easily accessible means of transportation i.e., wate r ways have been usually coincident with a higher rate of occurrence of natural hazards. Consider as evidence the rich farmlands of the Mississippi Valley, seasonal floods deposit rich nutrients in the ground; however, in 1993 the Great Midwest Flood, amon g the most devastating disasters in the United States history, produced catastrophic losses valued between $12 and $16 billion in property damage (Federal Emergency Management Agency, 2003) The Port of San Francisco is one the three great natural harbors of the world, while the port system of New Orleans and South Louisiana has one of the longest wharfs in the world. Property damage in the San Francisco area surpassed $6 billion after the 1989 Loma Prieta Earthquake and the New Orleans area has not yet recovered from the damage caused by Hurricane Katrina (Stover & Coffman, 1993) The continued growth of large concentrated population centers simultaneously increases their economic importance and elevates the impact of natural disasters. Population growth demands development of infrastructure, resulting in higher risks of private/public property damage and economic losses in a given area during a hazard event.

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17 The most heavily populated regions in the United States are the Northeast, the Pacific, and the Great Lakes, with 34%, 26%, and 18%, respectively, of the total population of the country. The coastal regions in the Southeast and the Gulf of Mexico are less populated areas (9% and 13% respectively) ; nevertheless, all of these areas are vulnerable to some type of natural hazard. The Southeast and the Gulf of Mexico are among the coastal areas that have had the largest increase in the potential damage due to an extreme event during the last two decades (Aponte, 2006) As of 2007, the U.S. Census Bureau estimated a population of 35.3 million in the hurricane prone coastal region stretching from North Carolina to Texas 12% of the total population of the United States. Flori das coastal population, 17.8 million, makes up more than 50% of the population living in the Southeast and Gulf of Mexico coastal regions (U.S. Department of Commerce, 2008) Metropolitan areas such as Houston, Miami, and Tampa have become among the 20 most populous in the United States elevating the potential for catastrophe in the event of a hurricane (U.S. Department of Commerce, 2008) Hurricane related damage is a major contributor to the overa ll property damage of the Southeast and the Gulf of Mexico; therefore, the main focus of this document will be related to tropical cyclones and the prediction of hurricane wind induced damage. The damage caused by landfalling hurricanes in recent seasons h as been greater than in previous seasons. The 2004 and 2005 seasons became the costliest hurricane seasons producing $79.1 billion in insured losses. In 2005, Hurricane Katrina surpassed Hurricane Andrew as the costliest natural disaster in the United States history. Hurricane Katrina estimated damage totaled $40.6 billion, most of it in Louisiana and Mississippi, in comparison to Hurricane Andrews $26.1 billion, most of it in South Florida (U.S. Department of Commerce, 2008) The increasing activity of tropical

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18 cyclones and the increased potential for catastrophic economic losses due to rising coastal populations lead to the creation of models to predict hurricane losses. The Need to Predict Hurricane Losses The insured losses sustained during the 14 months from August 2004 to October 2005 amassed $79.1 billion; the Insurance Information Institute also reported that during this time frame Hurricanes Katrina, Rita, Wilma, Charley, Ivan, Frances, and Jeanne became seven of the ten costliest hurricanes in insurance history for the United States. The damage induced by Hurricane Katrina produced $40.6 billion on 1.7 million claims for home, businesses, and vehicle damage. There were 1.1 million home claims; commercial claims accounted for more than 50% of the total insured losses. While the 2005 season was the costliest year for insured disaster losses, the continuing growth of insured coastal exposure in the United States and the warming trend in the Atlantic could lead to increased l osses. The total insured coastal exposure for New York, Florida, and Massachusetts is valued at $1.9 trillion for the first two and $662 billion for the latter (Insurance Information Institute, 2007) Although hurricane mitigat ion and prediction research is ongoing, the prediction of annualized losses remains a difficult task. Regulatory Oversight of Insurance Premiums at the State Level Regulation of insurance is currently the responsibility of the individual State oversight ag encies. States monitor insurance companies solvency and regulate rate changes. A rate is the price of a given unit of insurance, while a premium is the cost of the total units of insurance purchased (Premium = Rate x Number of Units). Rates are calculated based on the price necessary to cover the future cost of insurance claims and expenses, allowing for a profit margin. The process of determining rates involves using historical data and development trends to predict future losses. States oversee rates for premiums; adequate rates will maintain the insurers solvency and prevent excessive profits or losses.

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19 Existing Loss Models The regulation of rates by individual states usually establishes prior approval or competitive ceiling rates, but officials are more commonly relying on the market to create competitive rates among insurance companies (Insura nce Information Institute, 2008) Thus, in order to aid insurance companies in predicting hurricane damage and prevent them from emerging insolvent after an event, loss models have been developed. Loss models enhance the insurers or the states ability to predict the physical and financial vulnerability of the insured good and aids them in accurately determining insurance rates. Several loss models currently exist. These are either proprietary or public models. The HAZUS MH Hurricane Model, a private mod el contracted by FEMA, produces loss estimates used by government authorities when planning for hurricane risk mitigation, emergency preparedness, response, and recovery. The HAZUS MH model, based on scientific and engineering principles, contains national databases for the built environment and specific properties of a given region and uses experimental data to produce realistic loss estimates for that region (Federal Emergency Management Agency, 2008) Other important proprie tary models have been developed by catastrophe modeling firms such as AIR Worldwide Solutions, Risk Management Solutions, EQECAT, Applied Research Associates, and Karen Clark & Co.; insurance companies usually license models from these firms or develop the ir own models (Wilkinson, 2008) The details and assumptions used in the development of these private models are not fully released to the public, although in some cases portions of the model are published in peer reviewed jour nals (Cope, 2004) There are very few public studies that predict aggregate hurricane damage; most of them use regression techniques and post disaster data. The multiuniversity Florida Public Hurricane Loss Model (FPHL M) is a component based public model. The component approach

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20 incorporates information pertaining to the resistance of particular components and the effects of mitigation procedures such as the installation of shutters. Currently the FPHL M addresses the vulnerabili ty of single family residential construction only (Cope, 2004) However, a large portion of the overall residential infrastructure at risk is comprised of commercial residential construction. Commercial residential includes apa rtments and condominiums, both low rise (three stories and less) and mid high rise (above three stories). Scope of Research Low rise and midhigh rise commercial residential construction comprises a large amount of the insured coastal exposure, thus models predicting physical and economic damage to these types of construction are important for preparedness, planning and rate setting. The focus of the research in this document is the development of component based simulation engines that calculate the probab ility of damage for low rise and mid high rise commercial residential construction during extreme wind events. While based in part on the single family FPHL M, unique concepts and new assumptions are required to properly reflect construction differences tha t affect vulnerability. Development of the Low Rise and MidHigh Rise Commercial Residential Hurricane Loss Projection Model involves multiple major components, including meteorology, engineering (vulnerability), actuarial/financial, and computer science t o tie the components together. This is a multiuniversity effort, including the University of Florida and Florida Institute of Technology (engineering), the University of Miami and Florida State University (meteorology), and Florida International Universit y (actuarial, financial, computer science). This document describes the contributions of UF to the development of the engineering component of the commercial residential model.

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21 This document explains the theory, assumptions and concepts used to develop the simulation engines that project the physical damage to structures. The algorithm and procedure are summarized, and sample results are provided. Chapter 2 presents loss modeling background and explores existing hurricane loss models. Chapter 3 explores the fundamental considerations in the model currently under development; more specifically the conceptual representation of a wide array of building types and the component based Monte Carlo simulation concept are explained in this chapter. Chapters 4 and 5 f ocus on the performance of the low rise and midhigh rise commercial residential models, respectively. The programs architecture, solution process, individual component modeling procedure, and processing and analysis of the damage generated in the output are outlined in these chapters. Sample results are al so provided in Chapters 4 and 5 and the preliminary verification process is discussed. Conclusions about the models, modeling process, and the use for the output are given in Chapter 6. R ecommendations a nd suggestions for improving the current models in the future are also presented in Chapter 6.

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22 CHAPTER 2 LOSS MODELING BACKGR OUND The Sources of Damage Progress and development of civilization are inevitable. Nat ural disasters or hazard events provoke severe damage to our societies economic, intellectual, and material. The repertoire of events threatening society is immense; included in this group are earthquakes, terrorism, hurricanes, floods, fires, and tornadoes. The recurrence of hurricanes floods, and tornadoes is seasonal and through the use of Doppler radars and imaging systems on satellites, the National Weather Service monitors unstable atmospheric conditions and issues warnings that help minimize the loss of life. Major earthquakes an d terrorism are less predictable events. Predicting the precise location and occurrence of a major earthquake and issuin g warnings is not possible yet. This chapter briefly reviews several hazards and discusses loss models for hurricane damages Earthquake s The Federal Emergency Management Agency defines an earthquake as the sudden slipping or movement of a portion of the earths crust accompanied by a series of vibrations (Federal Emergency Management Agency, 2006) During an earthquake ground displacements and vibrations are generated as energy suddenly released in the earths crust due to plate tectonic motion propagates to the surface in the form of seismic waves. The stress build up and subsequent abrupt slipping/rupturin g along faults or near inter plate boundaries result in the sudden release of stored strain energy that produces the static and dynamic seismic deformations exhibited during earthquakes (Louie, Seismic Deformation, 1996) The conditions of plate motion at inter plate boundaries affects the types of geological faults and the types of earthquakes exhibited; these boundaries, depicted in Figure 21, can be

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23 divergent (extensional), convergent (compressive), or transform (Wald, 2007) Shallow earthquakes are common at all plate boundaries, while the larger and stronger deep earthquakes mostly occur at convergent boundaries. Figure 21. Plate b oundaries (Credit: U.S. Geological Survey/Lisa Wald) The amount of energy released during an earthquake determines its magnitude in the Moment Magnitude Scale The amount of seismic energy, ES, radiated by an earthquake as seismic waves is a function of the seismic moment, M. The seismic moment corresponds to the moment developed during an earthquake as a result of the forces acting at a fault with a moment arm equal to the slip distance (Louie, What is Richter Magnitude, 1996) Thus, the magnitude of an earthquake increases for larger faults. Earthquake intensity or qualitative effects at specific locations are measured by the Mod ified Mercalli Index where I denotes that the earthquake was barely felt and XII denotes total destruction (Kijewski Correa, The Nature of Seismic Loads, 2006) The Modified Mercalli Index and the original Richter Magnitude Sca les are shown in Table 2 1, along with typical effects of earthquakes for different magnitude ranges.

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24 Table 21. Earthquake intensity and magnitude s cales (adapted from Federal Emergency Management Agency, 2006) Earthquake Intensity and Magnitude Scales The Modified Mercalli Scale Level Of Damage The Richter Scale I IV Instrumental to Moderate No damage. 8.1 Societal conditions, geologic characteristics of a specific location, and the type of the motion affect the intensity of an earthquake. Wide spread damage and tremendous losses can result from an earthquake or from any of its secondary effects landslides, liquefaction, tsunamis, etc. Catastrophic earthquake damage observed in the Mexico City (1985) and in the Northridge, California (1994) earthquakes is exhibited by Figure 22 and Figure 2 3, respectively. Thus, research continues in order to attempt to reduce the extent of the losses sustained, speed up the recovery process after an event, and predict major earthquakes.

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25 Figure 22. Mexico City (1985) Earthquake Figure 23. Northridge (1994) Earthquake ( Credit: U.S. Geological Survey/Lisa Wald)

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26 Although the accurate prediction of major earthquakes is not possible yet, other tools have been developed to address the preparedness and response to these hazards. Earthquake hazard models, such as the HAZUS MH e arthquake model, forecast damage and losses resulting from an earthquake. Estimates of losses to buildings, lifelines, and essential facilities from scenario and probabilistic earthquakes, produced by the HAZUS MH earthquake model, are particularly useful to government authorities for earthquake response planning and disaster preparedness (Federal Emergency Management Agency, 2008) Emergency managers, state hazard mitigation officials, shelter managers, and utility companies enhance their capabilities to prepare and respond to an earthquake event by using damage estimates produced by such loss models. Recent examples of uses of the HAZUS MH model include re evaluation of hospitals in California by the California Building Standards Commission and scenario development by the New Madrid Seismic Zone Catastrophic Planning Initiative (Federal Emergency Managem ent Agency, 2008) Tornadoes The American Meteorological Society defines a tornado as a small diameter rotating column of air that extends from a cumuliform cloud to make contact with the ground (American Meteorological Societ y, 2000) Tornadoes usually develop as a result of the escalation of chaotic atmospheric conditions present during thunderstorms. Solar energy destabilizing near surface air by heating the surrounding ground area or a steep temperature gradient between t wo colliding air masses can supply the required energy to trigger the initiation of the convective cycle vital for thunderstorm formation (Brain & Lamb, 2000) Sharp contrasts among the two air masses will produce chaotic/unst able atmospheric conditions favorable for the development of air vortices. The wind speed and direction variations through a vertical cross section of an air mass resulting from vertical wind shear cause the air to spin horizontally while, a strong updraft tilts this column of spinning air upward and creates a mesocyclone. The spinning mesocyclone develops a

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27 dynamic pipe, or tornado core, which becomes a tornado once its concentrated rotating core extends to the surface as depicted in Figure 24. The conical shape of the condensation cloud is maintained by the pressure differential between the tornados centerline and sections offset from the centerline (Encyclopdia Britannica, 2009) Figure 24. Tornado development (By courtesy of Encyclopdia Britannica, Inc., copyright 1999; used with permission) Tremendous wind speeds can be sustained throughout the duration of a tornado resulting in severe damage once the storm makes contact with the ground and travels in a path controlled by its parent storm. The scope of tornado inflicted damage ranges from cas ualties and injuries to

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28 infrastructure damage due to wind induced forces. Windborne debris generated during the storm is one of the main sources of building damage. Large storms can remain on the ground for hours and travel more than 90 miles causing consi derable damage. A tornados severity and potential damage along its path are the main criteria utilized to classify a storms intensity into one of the six categories (EF0 to EF5) in the Enhanced Fujita Scale. The damage caused during a storm can be extens ive and although predicting a tornado with enough time for safety preparations is feasible, tornadoes develop so rapidly that advance warning is barely possible (Federal Emergency Management Agency, 2009) The uses of Doppler radars and imaging systems on satellites allow the National Weather Service to monitor unstable atmospheric conditions increasing warning times prior to the development of a tornado. Tornado damage can potentially be catastrophic as observed in the Tri Sta te Tornado of March 18, 1925. This tornado has been the deadliest in the United States history. Tornados can occur on every continent and their potential for disaster is tremendous; thus, the necessity to predict tornadoes and allow for longer preparation times is indispensable and as such research continues (Brain & Lamb, 2000) Hurricanes A tropical cyclone is defined as a non frontal synoptic scale low pressure system over tropical or subtropical waters with organized convection and definite cyclonic surface wind circulation (Holland, 1993) A combination of warm ocean temperatures and sufficient atmospheric instability creates a gradient that promotes the strengthening of convection in an existing atmospheric disturbance through the release of heat energy stored in the water. Existing atmospheric disturbanc es i.e. thunderstorms subjected to these conditions could develop into tropical cyclones if the magnitude of the Coriolis force is sufficient to deflect the winds and induce a cyclonic rotation in the disturbance (counterclockwise in the Northern Hemispher e and

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29 clockwise in the Southern Hemisphere). High wind shear hinders the organization of convection in the cyclones center and weakens the disturbance. Thus, low vertical shear is favorable for the intensification of the storm ( Gray, 1979) Tropical cyclones with sustained winds of 74 miles per hour or greater are referred to as hurricanes in the North Atlantic Ocean, the Northeast Pacific Ocean, and the Southeast Pacific Ocean and typhoons Figure 2 5 in the Northwest Pacific Ocean west o f the dateline (Neumann, 1993) Locations most favorable to the development and intensification of tropical cyclones are depicted in Figure 25. Locations favorable for development and intensification of tropical cyclones (Gutro, 2009) High sustained winds can cause structural damage to infrastructure and rain and storm surge can lead to flooding. The potential damage and flooding in a coastal area due to a hurricane can be estimated with the guidance of the Saffir Simpson Hurricane Intensity Scale which rates a hurricane based on the peak sustained (one minute averaged) winds and/or the peak coastal storm surge The five categories of intensity, described in Table 22, are related to expected leve ls of damage based on past observations. However, these damage descriptions are not

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30 absolute, and serve as a guide in an aggregate sense only for the regions impacted by the most intense portions of the land falling cyclone. Table 22. The Saffir Simpson hurricane s cale (adapted from National Weather Service, 2004) The Saffir Simpson Scale Category Description Level of Damage 1 Wind Speed: 74 95 mph Primary damaged to unanchored mobile homes, shrubbery, and trees. Some coastal road flooding and minor pier damage. Little damage to building structures. Storm Surge: 4 5 ft. above normal 2 Wind Speed: 96 110 mph Considerable damage to mobile homes, piers, and vegetation. Coastal and low lying escape routes flood 2 4 hours before arrival of hurricane center. Buildings sustain roofing material, door, and window damage. Small craft in unprotected moorings break moorings. Storm Surge: 6 8 ft. above normal 3 Wind Speed: 111 130 mph Mobile homes destroyed. Some structural damage to small homes and utility buildings. Flooding near coast destroys smaller structures; larger structures damaged by floating debris. Terrain continuously lower than 5 feet. ASL may be flooded up to 6 miles inland. Storm Surge: 9 12 ft. above normal 4 Wind Speed: 131 155 mph Extensive curtain wall failures with s ome complete roof structure fail ure on small residences. Major erosion of beaches. Major damage to lower floors of structures near the shore. Terrain continuously lower than 10 feet. ASL may flood (and require mass evacuations) up to 6 miles inland. Storm Surge: 13 18 ft. above normal 5 Wind Speed: Over 155 mph Complete road failure on many homes and industrial buildings. Some complete building failures. Major damage to lower floors of all structures located less than 15 feet ASL and within 500 yards of the shoreline. Massive evacuation of low ground residential areas may be required. Storm Surge: Over 18 ft. above normal The effects of a hurricane can vary depending on the societal and geographic conditions of the area affected. Hurricane damage can be catastrophic as observed in Louisiana and Mississippi during Hurricane Katrina in 2005. Figure 26 and Figure 2 7, respectively, display surge and flood damage sustained in Long Beach, Mississippi and in New Orleans, Louisiana. Katrina is a prime example of the limitations of a single intensity scale that lumps surge and wind speed into common categories. Katrina was a severe Category 5 storm by storm surge intensity, but the highest ove rland winds are estimated in the low mid Category 3 range.

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31 Figure 26. Effects of Hurricane Katrina (2005) in Mississippi Figure 27. Effects of Hurrica ne Katrina (2005) in Louisiana

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32 Terrorism Severe damage to our societies can result from alternate forms of hazards such as terrorism. The United Nations Security Council refers to terrorism as criminal acts committed with the purpose to provoke a state of terror in the general public, a group of people, or particular persons, to intimidate a population, or to compel a government or an international organization to do or to abstain from doing any act (United Nations Security Council, 2004) Acts of terrorism, such as those listed in Table 23, seek intimidation, coercion, or propaganda and could result in large scale losses of life, destruction of property, and staggering economi c losses (Federal Emergency Management Agency, 2006) Table 23. Examples of acts of t errorism Examples of Acts of Terrorism Threats of Terrorism Assassinations Kidnappings Hijackings Bomb Scares Bombings Cyber Attacks Use of Weapons of Mass Destruction Military and civilian government facilities, international airports, large cities, and high profile landmarks have been targeted by terrorists. In September 11, 2001 terrorist attacks targeting the World Trade Center Towers resulted in their collapse, catastrophic loss of life, and considerable economic losses. Due to the potential damage and detrimental effects of terrorism, its prevention has become a priority for th e international community. Loss Models The occurrence of hazards is inevitable; and the continued development of infrastructure in hazard prone regions must be conducted in a manner that appropriately balances hazard risk and its associated costs with the cost of preparedness. For example, the construction of residential

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33 and commercial infrastructure to resist hurricane wind loads is guided in Florida by codes and standards that stress prevention of loss of life, but do not seek to completely prevent the oc currence of damage. Loss models are playing a more prominent role in both preparedness (mitigation policy) and insurance regulation and rate setting Loss models produce damage predictions for various structural types Typically the prediction is presented in an aggregate average sense on an annualized basis, i.e. the average residential home of type X, located in Y, will incur an annualized loss of Z % of its value. The other prediction mode is scenariobased, where a specific hurricane and structural expos ure is input to project losses, i.e. Hurricane Wilma produced an average loss per home of X% of value. Damage predictions are commonly expressed using vulnerability and fragility curves (Cope, 2004) Some models use post disas ter observed damage and insured claims data to fit the vulnerability and fragility curves that relate wind speed to damage, while other models create a probabilistic model of a typical building and the loads it sustains (component based models) The latter model type uses Monte Carlo Simulations to generate the loss curves; subsequently, post disaster data is used to validate the results and calibrate the model as necessary. Several loss models currently exist. Most of these are proprietary models developed by private companies that lease the predictive products to insurers and re insurers to help guide rate setting and develop incentives for homeowners to mitigate against wind damage HAZUS Multi Hazard Model The HAZUS MH Model was developed in 1997 by the Federal Emergency Management Agency (FEMA) under contract with the National Institute of Building Sciences (NISB). This model initially estimated losses due to earthquakes; however, a module that estimates wind and flood hazard induced losses, developed by Applied Research Associates (ARA), was recently incorporated to the original model. The model provides government authorities with information

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34 useful in the planning and simulation of hazard and preparedness efforts. Potential benefits include the reducti on of physical damage and disaster payments and a more efficient use of available emergency management resources. This tool also aids government authorities in the preparation for emergency response and recovery by planning for displaced persons, shelterin g requirements, and post disaster debris removal (Federal Emergency Management Agency, 2008) The HAZUS Hurricane model is one of the components of the HAZUS Wind Model; its approach consists of a hurricane risk model, a surface roughness model, a wind load model, a missile (debris) model, physical damage models, and a loss model. The approach of t he HAZUS Hurricane model, within the Wind Model, is summarized in Figure 2 8. The wind load model is based on the UK building code; the roof and wall coefficients required to obtain pressure loads depend on the direction of approaching wind and are estimated based on wind tunnel tests. The missile model exposes buildings within a modeled subdivision to the impact of roof components that failed on other buildings within the subdivision and determines the risk of damage to an opening from flying debris The physical damage model calculates the resistance capacity of each building component and determines the physical damage resulting from the sustained loa ds (thus HAZUS is referred to as a component based model) Finally, monetary losses are calculated based on the physical damage to the structure. Validation of each component and incorporation of newly available data and knowledge can be accomplished by up dating the appropriate module(s) (Federal Emergency Management Agency, 2008) The HAZUS Model is considered to be the state of the art in damage prediction. Most of the framework for the model has been well defined in its technical manual; however, many of the basic assumptions regarding the missile and pressure load models remain undis closed. Another component based loss model is the Florida Public Hurricane Loss Model (FPHLM)

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35 Figure 28. HAZUS W ind model framework (Federal Emergency Management Agency, 2008) Florida Public Hurricane Loss Model The Florida Public Hurricane Loss Model was sponsored by the Florida Department of Financial Services and coordinated by the International Hurricane Research Center. Developers include faculty and staff from NOAA, Florida State University, University of Florida, Florida Institute of Technology, Florida International University, and the University of Miami. The model predicts hurricane wind induced insurance losses for residential structures by zip code in Florida, on both an annualized basis and for predefined scenarios i.e. specific hurricanes (Cope, 2004) The model is comprised of t he meteorology, engineering, financial/actuarial and computer science components. Annualized probabilistic peak wind speeds for each Florida zip code are generated in the meteorological component. Physical damage to the struct ure resulting from peak 3second gust wind speeds is estimated in the engineering component. The insur ed

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36 losses are projected from the physical building damage and the computer science team creates one computational unit from the various contributors com ponents The engineering (vulnerability) model determines the probability of physical damage to the structure and building envelope through the use of a Monte Carlo Simulation engine. Interior damage to the building is determined based on the damage to the building envelope. To predict physical damage to the building as a function of gust wind speeds, a series of residential models were created and defined in the form of the wind resistance (pressure capacity) of the various components of the structure (roo f, windows, walls, doors, connections). The Monte Carlo Simulation engine assigns the se probabilistic capacities and the wind loads acting on the building components and the status of the various components (damaged or undamaged) after applying a wind loa d. Wind load calculations are based on the Minimum Design Loads for Buildings and Other Structures (ASCE 7 05) wind loading standard; the roof and wall coefficients required to obtain pressure loads have been adapted to reflect actual loads sustained by th e structure instead of design loads. The probabilistic capacities of the various structural components are based on laboratory studies and other sources of capacity information. The storm is modeled by subjecting the structure to pressure loads resulting f rom wind approaching the structure from eight different directions. Comparisons of predicted physical damage and insur ed losses against insurance claims data and hurricane damage assessment reports are used to validate the F PHL M. Currently the FPHL M addres ses the vulnerability of single family residential construction only (Cope, 2004) That is, the engineering vulnerability module has only developed probabilistic structural component capacities and wind load representations for single family one and two story structures. However, a large portion of the overall residential infrastructure at risk is comprised of commercialresidential construction (apartments, condominiums)

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37 Commercial Residential Public Hurricane Loss Model The F PHLM is currently being extended to include commercial residential construction. This includes low rise (three stories or less), and mid high rise (greater than three stories). This requires additional work on the meteorological module (to include wind spe ed probabilities with height), the engineering module (developing probabilistic component capacities and the wind load representations), and the actuarial model (insurance structuring differs from single family). Subsequent chapters discuss the fundamental considerations, assumptions, and strategies that are currently employed in the development of the engineering vulnerability component.

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38 CHAPTER 3 COMMERCIAL RESIDENTI AL BUILDINGS: FUNDAM ENTAL CONSIDERATIONS IN THE MODEL C onceptual Representation of a Wide Array of Building Types The development of a commercial residential hurricane loss projection model is only feasible if several simplifying assumptions and probabilistic procedures are adopted. The tremendous size and variability of the building stock and the inherent uncertainty of the individual building component capacities and of the environmental loads they sustain make the development of a model that projects losses sustained by each building in the building stock uneconomical. The implementation of a generalized conceptual representation of a wide array of building types and the Monte Carlo concept into the model reduces its production cost and enables its development; this chapter discusses these fundamental considerations. The building stock can vary si gnificantly with location. Common construction practices, predominant materials, and building types vary greatly across the state of Florida. Modeling every type of building that exists in Florida would be an unreasonable task, thus representations of only the most prevalent types of buildings were modeled. The use of a model structure that does not represent a specific exist ing structure is key in the fulfillment of the projects goalthe prediction of losses in an aggregate sense, rather than to an indivi dual building. Versatile model structures that encompass the most prevalent features of the building stock in Florida were created based on data obtained by the Florida Commercial Residential Buildings Survey. The Florida Commercial Residential Buildings S urvey The Florida Commercial Residential Buildings Survey conducted by partner researchers at the Florida Institute of Technology identified the characteristics and distribution of the most prevalent buildings comprising the building stock in the State of Florida. The basic model vulnerabilities were developed from the results of the exposure study. The major building

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39 features comprising the scope of the model are structural material and roof type for low rise buildings and exposure of stairway/corridor for mid high rise. Construction quality, mitigation practices, and environmental exposure are secondary features in the scope of the model. The features impleme nted in the models are flexible in order to enable analysis of, for example, buildings with similar construction features but significant differences in geometric features (square footage, roof slope, etc). The survey concluded that low rise buildings account for 96% of commercial residential buildings (76% of the dollar exposure) while the mid high ris e buildings totaled 4% (24% of the dollar exposure). Pita et al (2008) concluded that gable/hip roofs account in average for 90% of the total low rise building stock in Florida and that flat roofs are the more predominant roof type for mid high rise buildings. Shingles were identified as the most common roof cover (75% of the roofs) for low rise buildings; roof characteristics for low rise and mid high rise buildings are summarized in Table 3 1 and Table 3 2, respectively. Table 31. Roof characteristics for low rise buildings (adapted from Pita et al 2008) Roof Type and Cover for Low Rise Buildings County Roof Types Roof Cover Material Gable/Hip Flat Other Shingle Tiles Gravel Other Alachua NA NA Bay 95% 2% 3% 81% 0% 0% 19% Brevard 85% 11% 4% 72% 8% 0% 20% Duval 91% 8% 1% 75% 0% 15% 10% Lake NA 63% 3% 0% 34% Lee 91% 2% 7% 70% 17% 10% 3% Leon 94% 1% 5% 91% 0% 0% 9% Marion 95% 0% 5% 95% 2% 1% 2% Monroe 68% 18% 14% 28% 3% 9% 60% Orange 95% 2% 3% 82% 8% 8% 2% Osceola 97% 0% 3% 91% 2% 0% 7% Palm Beach NA NA Pasco 97% 2% 1% 88% 0% 6% 6% Pinellas 91% 0% 9% 83% 4% 11% 2% Saint Johns 85% 3% 12% 87% 5% 0% 8% Saint Lucie 88% 0% 12% 75% 2% 16% 7% Volusia 94% 6% 0% 83% 8% 0% 9%

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40 Table 32. Roof characteristics for mid high rise buildings (adapted from Pita et al. 2008) Roof Type and Cover for Mid High Rise Buildings County Roof Types Roof Cover Material Gable/Hip Flat Shingle Tiles Membrane Brevard 24% 76% 8% 11% 78% Lee 43% 56% NA Pinellas NA NA Timber and masonry exterior walls were the most prevalent in low rise buildings and concrete block exterior walls were most common in mid high rise buildings. The detailed distribution for exterior wall material in both types of buildings is summarized in Table 3 3. Table 33. Exterior wall material for low rise and mid high rise buildings (adapted from Pita et al. 2008) Exterior Wall Material Low Rise Buildings County Wood CB Other Alachua 30% 52% 18% Bay 48% 36% 16% Brevard 35% 64% 1% Duval 51% 49% 0% Lake 44% 55% 1% Lee 16% 84% 0% Leon 56% 40% 4% Marion 27% 73% 0% Monroe NA Orange 35% 60% 5% Osceola 51% 49% 0% Palm Beach 25% 71% 4% Pasco 16% 84% 0% Pinellas 28% 72% 0% Saint Johns 78% 22% 0% Saint Lucie 23% 75% 2% Volusia 56% 41% 3% Mid High Rise Buildings County Wood CB Other Brevard 1% 98% 1% Lee 0% 99% 1% Pinellas 2% 98% 0% The Florida Hurricane Loss Projection Model for Commercial Residential Buildings enables flexibility for modeling building and unit sizes with certain restrictions. Data regarding

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41 average areas per floor and per unit and the total number of stories for bot h types of buildings, summarized in Table 3 4 Table 3 5, and Table 3 6, was used to develop the standard, or most representative model as a starting point to develop the damage prediction algorithms. Table 34. Prevalent plan dimensi ons (adapted from Pita et al. 2008) Prevalent Plan Dimensions Mid High Rise Buildings Area per Floor Area per Unit 17000 ft. 2 1500 ft. 2 Low Rise Buildings Units per Floor Area per Unit 3 to 4 800 ft.2 to 1000 ft.2 Table 35. Number of stories for low rise buildings (adapted from Pita et al. 2008) Number of Stories for Low Rise Buildings County Stories 1 2 3 Alachua 51% 33% 16% Bay 59% 38% 3% Brevard 35% 50% 9% Collier 57% 26% 17% Duval 53% 47% 0% Lake 46% 2% 0% Lee 64% 34% 1% Marion 92% 8% 0% Orange 56% 33% 11% Osceola 50% 43% 7% Palm Beach 53% 35% 5% Pasco 89% 7% 4% Pinellas 69% 24% 3% Polk 91% 9% 0% Saint Lucie 77% 21% 2% Volusia 63% 34% 3% Table 36. Number of stories for mid high rise buildings (adapted from Pita et al. 2008) Number of Stories for Mid High Rise Buildings County Stories 4 5 6 7 8 9 >9 Brevard 25% 40% 10% 10% 10% 3% 2% Lee 30% 16% 10% 9% 7% 3% 25% Palm Beach 55% 15% 8% 8% 12% 2% 0% Pinellas 27% 15% 21% 8% 6% 6% 17%

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42 Construction quality can be determined by analyzing the dates in which the buildings were initially built. The evolution of building codes, specifically in the adoption of more stringent requirements and enforcement policies, has lead to an increase in con struction quality during recent decades. Pita et al. (2008) identified key dates in which construction practices or building codes had important changes; the distribution of the year built for low rise and mid high rise buildings within the identified cuto ff dates is shown in Table 3 7. The model reflects construction quality by offering weak, medium, or strong versions of any given selected geometry. A ssignment of these classes to any given region of Florida will be based on the age as provided in Table 3 7. Table 37. Distribution by construction date (adapted from Pita et al. 2008) Year Built Building Type County Pre 1970 19711983 19841992 19932002 20032007 Low Rise Alachua 17% 48% 18% 13% 3% Bay 16% 37% 27% 15% 6% Brevard 25% 27% 35% 10% 4% Collier 14% 9% 21% 49% 7% Duval 85% 8% 7% 0% 0% Hillsborough 27% 36% 22% 10% 5% Lee 12% 30% 19% 13% 25% Marion 4% 33% 41% 13% 8% Monroe 62% 24% 8% 5% 2% Orange 20% 29% 38% 10% 3% Osceola 12% 24% 38% 18% 8% Palm Beach 31% 35% 24% 7% 1% Pasco 24% 57% 12% 1% 7% Pinellas 58% 29% 9% 2% 2% Polk 33% 43% 18% 3% 3% Saint Johns 13% 11% 25% 9% 43% Saint Lucie 46% 30% 11% 9% 4% Seminole 13% 35% 32% 18% 2% Volusia 19% 31% 34% 8% 9% Building Type County Pre 1970 19711983 19841992 19932002 20032007 Mid High Rise Brevard 2% 34% 31% 22% 10% Lee 3% 42% 15% 24% 17% Palm Beach 6% 46% 40% 7% 1% Pinellas 9% 54% 14% 12% 11%

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43 The conceptual model buildings developed from the statistical averages identified by Pita et al. (2008) are summarized in Table 38. There exist nume rous uncertainties as to the vulnerability of the various components that make up any selected building type. Thus, the components are represented probabilistically, and Monte Carlo concepts are adopted to create a representation of building vulnerability. Table 38. Conceptual commercial residential building models Low Rise Model Building Exterior Wall = Wood or Concrete Block Roof Type = Gable or Hip Roof Roof Cover = Shingle or Tile Building Plan Size = 80 ft. x 40 ft. or 80 ft. x 50 ft. Construction Quality = Weak, Medium, or Strong Number of Stories = 1, 2, and 3 Mid High Rise Model Building Building Types = Exterior Stairway (3 units per floor) or Interior Stairway (8 units per floor) Unit Locations = Corner or Middle Unit Size = 30 x 60 The Monte Carlo Concept The Monte Carlo concept application to the Florida Hurricane Loss Projection Commercial/Residential Model involves the probabilistic representation of both wind loads and capacities of key building components. Regarding wind loads, wind velocity fluctuates as does the resultant pressure experienced by building components, in a wa y that cannot be precisely (deterministically) assigned. Implementation of the Monte Carlo concept to the wind load calculation provides a framework in which the various sources of wind loading uncertainty can be represented. If future developments alter a given source of uncertainty, it is straightforward to change the model to reflect this. In this model, wind speed uncertainty is represented by selecting a random number based on a mean (specified) value, and coefficient of variation that represents the u ncertainty of wind speed. That is, if the assigned wind speed is 100 mph, the actual value used for a given simulation would be a

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44 random value close to 100 mph, with a deviation reflective of the assigned coefficient of variation. Likewise, the pressure co efficient that translates wind speed to wind pressure is also randomly assigned, based on ASCE 7 values as the mean. Regarding building capacities, the model considers the capacities for all components in the building that are critical to physical exterior damage. As in the case of the loads, the capacity of all components are represented by a random value assigned based on a probabilistic model of the capacity of the given component. For example, each shingle on a roof will have its own randomly assigned c apacity against uplift pressure based on research describing the probability of failure of shingles. This approach is classified as Component Based vulnerability model. The Monte Carlo component based approach is a method that permits the model to account for different sources of uncertainties such as construction quality or simplifying assumptions. As new laboratory tests refine the probabilistic failure models of various building components, this information can be directly inserted into the vulnerability model. Likewise, the inclusion of vulnerability reducing features can be easily represented. For example, a building without window protection (storm shutters), and a building with window protection can be analyzed by a simple change of the model describi ng the window component vulnerability to wind and debris. The Monte Carlo procedure incorporated in the model creates a probabilistic building i.e. a collection of randomized capacities, load paths, and their interactionand subjects it to probabilistic lo ads referenced to a mean value for the peak wind gust for every simulation. Creating a probabilistic building and determining the probabilistic loads require mean values and coefficients of variations for capacities, wind velocities, and pressure coefficients. Physical exterior damage is determined by analyzing the limit state of every element in the system. Aggregate statistics of physical exterior damage are produced by combining exterior damage

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45 from many simulations each including a full randomization pr ocess. For example, the same building type is constructed (capacities randomly assigned) several thousand times, each subjected to one (randomized) wind speed, and resultant (randomized) loads from one wind direction. This is repeated over a range of wind speeds and directions, ultimately producing for any wind speed many thousands of experimental outcomes that are aggregated to show, for example, that 100 mph winds produce (on average) 20% roof shingle loss, 5% broken windows, etc. The resulting output, aggregate physical exterior damage, is processed by modelers from the engineering team at the Florida Institute of Technology to estimate internal damage in the building. Subsequently, the actuarial and financial model team uses the physical internal and exterior damage in the low and mid high rise commercial residential buildings to project monetary losses and factor in various insurance issues (deductibles, etc.). Low Rise Commercial Residential Building General Descriptions Commerci al residential buildings are defined by the County Property Tax Appraisers ( CPTA ) as a broad classification of condominiums and multi family residential buildings. The only feature considered in this classification system is the type of ownership; building physical characteristics number of stories, number of units, floor size, etc.are disregarded. For the purpose of the Florida Public Hurricane Loss Commercial/Residential Model, low rise commercial residential buildings are those that are 1, 2, or 3 stori es tall. According to Pita et al. (2008) most of the multi family residential buildings are low rise, hence low rise c ondominium buildings are combined with multifamily residential buildings into the same classification. The units of a multifamily residential building are occupied by tenants and the building is owned by

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46 a single landlord, therefore low rise commercial residential buildings are analyzed as single entities and aggregate losses are calculated for the whole building. The variation of the layouts, floor plans, number of units, and other characteristics in low rise commercial residential buildings can be considerably widespread. Possi ble layout types for low rise commercial residential buildings are exterior or interior access corridor, exterior stairways with interior opened corridors, among others. Floor plans the number of units and their distribution within a floor are closely related to the layout type, thus the variability of the floor plans among the low rise commercial residential building stock is also considerable. Since the goal of the model is to predict aggregate losses, the Florida Public Hurricane Loss Commercial/Resident ial Model will initially only model one type of layout for the low rise model building. While the characteristics for the rest of the building remain flexible, its layout is established as an exterior corridor type. In an exterior corridor building the ent ry way for each unit is located along one of the long sides of the building, sliding (balcony access) doors are located along the other long side of the building, and windows are present on every wall exposed to the outside. Although the calculation of individual unit losses is not the scope of the low rise model building, the relevance of the number of units per floor towards the calculation of the overall physical damage to the building lies in the fact that the number of openings windows and entry and sl iding doors affect the buildings vulnerability. Major Contributors to Insured Losses Complete loss of single family residential homes by a hurricane has been observed in the past and has resulted in significant insured losses. As common construction pract ices evolve and the building codes become more stringent the probability that single family residential homes sustain complete failure decreases. Furthermore, enhanced standards of construction practices for

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47 multifamily low rise commercial residential bui ldings, with basis on the increased occupancy of these buildings and the greater hazard they pose to society in the case of complete failure, result in the reduction of their vulnerabilities to total collapse. Failure of components and cladding, water intr usion, and internal pressurization and breaches have displaced structural damage as the main sources of low rise commercial residential building insured losses. Although less probable than in the past, progressive collapse of low rise commercial residentia l buildings is still possible if critical components are severely damaged. Wind loads are transferred from the building envelope to the foundation through the structural system. External and internal pressures act on the roof and exterior walls, subsequent ly the loads are transferred to structural elements i.e. roof trusses, columns, floor diaphragms, studs which transport these forces to the foundation. Failure of a critical component within this load path could lead to the progressive collapse of the structure, i.e. roof pullout resulting from failed roof to wall connections. Failure of the building envelope either at the roof or the exterior walls resulting from wind overloads, could occur throughout the duration of the hurricane. Wind induced roof suct ion pressures, due to the diversion of fluid flow by sudden changes in the geometry of obstacles in the wind pathi.e. the roof ridge can overcome roof cover restraining forces and result in pullout of that component. The loss of roof cover allows a means of rain water ingress. The combination of internal pressures in the attic and exterior roof pressures result in uplift forces that can pull off sheathing panels. Loss of sheathing panels can escalate quickly if uplift forces intensify as a result of a su dden change in attic internal pressure. Pulled out sheathing panels leave openings through which roof trusses become exposed to environmental forces and subject to damage; contact with the environmental conditions rain and wind, as well as the loads

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48 trans ferred to trusses, can provoke the failure of their connections roof to wall connections potentially triggering domino truss collapse mechanisms. The lack of diaphragm action at the top story level due to complete roof failure could trigger instability. D amage sustained by the components in the exterior wall is similar to that sustained by the roof components. In timber frames wind induced pressures pull the wall cover (e.g., vinyl siding) off the walls, exposing wall sheathing panels and increasing their vulnerability. Panels can be damaged or lost during the storm. In masonry buildings wind induced pressures can lead to excessive cracking of the exterior walls. Glazing, i.e. entry doors, sliding doors, windows, can sustain damage resulting from pressure overloads or from windborne debris impact. The breach of the building envelope through panel losses or glazing damage results in floor area internal pressure changes and water intrusion. Internal damage sustained by a building as a result of water intrusion can be considerable. Wind forces water through the breaches in the building envelope and through the tiny seeps present at window sills and other components; carpeting, furniture, and other belongings will be damaged. Breaches and sudden internal pressur ization can lead to rapid changes in the loads sustained by the structure. Wind flow through breaches on the windward side of the attic intensifies the loads acting on the leeward side and on the roof, potentially resulting in gable end collapse or complet e roof failure. Components within the Model Major insurance losses are triggered by damage of the building envelope; thus, the low rise commercial residential model specifically simulates components comprising the building envelope and components essential to the transmission of loads through the structure. Components modeled for low rise buildings can be grouped in the following categories: roof

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49 components, exterior wall components, and transfer elements. Roof and exterior wall components are subject to environmental load conditions directly, while transfer elements transmit the loads sustained by the building to the foundations. Roof components modeled include roof cover and roof sheathing. Shingles and tile are modeled for roof cover; their layouts on the roof are determined by distributing the total number of entities uniformly over the roof. Roof cover varies among buildings, thus the model was designed to allow variability and flexibility as it evolves in the future. Shingles or tiles can be replaced by other types of roof cover by simply changing the mean dimensions and capacities and the coefficients of variation of the individual entities and adapting the model as required. Roof sheathing is modeled with plywood sheathing panels; although assumptions simplified the procedure, placement of the panels in the model emulates common construction practices accurately. Although currently plywood is the only sheathing panel material modeled, characteristics of the panels i.e. the material and dimensions can e asily be modified in the code. Exterior wall components modeled include wall cover, wall sheathing, and glazing. The algorithms used to model roof cover and sheathing and wall cover and sheathing are nearly identical. Sources for the variations between the procedures are differences in material and in common construction practices. Wall sheathing panel layout types can vary greatly, thus the modeled layout was simplified to a single type. Wall cover was modeled as vinyl siding section. The types of layout f or these components are fixed, but the materials, entity sizes, and capacities are flexible. Components covering openings in the model buildings i.e. entry doors, sliding doors, and windows are defined as glazing, regardless of their material (glass or woo d). The number of sliding doors and entry doors are direct functions of the number of units present at a

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50 given floor, w hile the number of windows is directly dependent on the percentage that the total glazing area occupies of the entire wind exposed buildi ng surface area. Low rise building complexes offer a wide variety of floor plan distributions resulting in multiple possibilities for glazing component locations; therefore, glazing placement in the model was assumed to be nearly uniform along the perimete r of the building. Transfer elements modeled include roof to wall connections and roof trusses. Roof trussesincluding gable end trusses support the roof components and the loads they sustain, while roof to wall connections tie the roof and wall together e nabling the transfer of loads to the foundation. Common construction practices were the main consideration controlling the assembly of these components into the low rise building model. Roof to wall connections and trusses were uniformly spaced along the l onger sided of the building. Chapter 4 discusses in detail the algorithm and reasoning used to determine the capacities, loads, and placement of the components present in the low rise commercial residential model. Basic Model Descriptors A building model c an be constructed from different options for key features of the basic building descriptors. Key flexible features in the model are the number of stories, the footprint size per floor and unit, the roof type, material, and slope, the exterior wall type, and the percentage of glazing occupying the buildings surface area. Multiple combinations of these features can be analyzed by the model. There is no limit to the number of stories, however, according to the definition of low rise commercial residential bui ldings only one to three story buildings need to be analyzed. Roof properties identifying the building model are its type, gable or hip, its material, shingles or tiles, and its slope, usually 6/12. Exterior walls can be either timber or masonry, while one sliding door and one entry door is assigned to each unit. Windows are distributed uniformly throughout the building envelop.

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51 The quality of construction is also flexible, allowing the user to select various combinations of component strengths (weak, medium, strong) as desired to reflect a specific age or geographic location in Florida. This flexibility in component strength also allows the modeling of older buildings of weak construction that have had certain components upgraded, such as a newly shingle (m ore resistant) roof cover, or the use of storm shutters. The units in this type of building are either middle or corner units; a unit based loss analysis is not conducted by the low rise model, since low rise buildings have single owners and estimates of unit losses are not as relevant as overall building losses. The model predicting losses for mid high rise commercial residential buildings, characterized by individual unit ownership, does perform a unit based loss analysis. Mid High Rise Commercial Residential Building General Descriptions The Florida Hurricane Loss Projection Commercial/Residential Model considers any commercial residential building having four or more stories a mid high rise building. The CPTA groups multi family and condominium building s in the commercial residential buildings category. The creation of a condominium regime, i.e. establishing individual unit ownerships, usually results in an increase in the residential density approved in a given area during the planning phases of future developments. Residential density refers to the number of people living in an area of residential land. Efficient exploitation of increased allowable residential densities is manifested through the addition of units to the building by raising its total num ber of stories; considering the models definition of mid high rise buildings, a greater presence of condominium mid high rise buildings over multifamily residential buildings can be assumed. The mid high rise building stock exhibits more heterogeneity t han the low rise building stock. In many cases, the uniqueness of the architecture/ layout of the taller residential buildings

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52 is a selling feature. Thus there is no one or two or three standard models capable of representing a typical mid high rise building, and creating enough model buildings to represent a wide array of building types is prohibitive. However, most condominium mid high rise commercial residential buildings have corner and middle units (two and one exposed walls, respectively); this commo n feature can be used to define simplified models of individual units rather than the structure as a whole. A condominium is legally defined as the absolute ownership of a unit based on a legal description of the airspace the unit actually occupies, plus an undivided interest in the ownership of the common elements, which are owned jointly with the other condominium unit owners (Hejl, 2006) The condominium association holds an insurance policy to cover the joint areas, whil e individual owners hold insurance policies for the areas within their units. The arrangement of insurance policies, the type of ownership, and unit location as a common feature of condominium mid high rise commercial residential buildings led to prioritiz ation of the prediction of unit aggregate losses in the model. Nevertheless, individual unit losses can be projected to building losses. Layout types for mid high rise commercial residential buildings can be very widespread, they can resemble those for lof ts, apartments, duplexes, townhomes, etc. Therefore the only layout types modeled are exterior corridor and interior corridor; these layouts are illustrated in Figure 31. In an exterior corridor building the entry way for each unit is along one of the long sides of the building; sliding doors are located along the other long side and windows are present at every exterior exposed side of the building. In exterior corri dor buildings middle units and corner units have two and three walls exposed to the environment, respectively, and in each case the entry door is on an outside wall and subject to damage from wind and debris. An interior

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53 corridor building has by definition an inner core that isolates the stairway and unit entry doors from the outside environment. Units in an interior corridor building have exposed windows and sliding balcony doors only, while the entry door is protected. Middle units in interior corridor buildings only have one wall exposed, while corner units have two walls exposed. Figure 31. Lay out types modeled for mid high commercial residential model Major Contributors to Insured Losses Significant structural type failure due to hurricane winds is an extremely rare event for mid high rise commercial residential buildings, by nature of their engineered design. O ften this type of failure is due to erosion of the supporting foundation, which is not considered in this windinduced damage only model. Although very resistant to structural failure, mid high rise buildings can still sustain considerable insured losses during a hurricane via damage to components and cladding (openings) and water intrusion. The failure of glazing elements in the building envelope rarely compromises the structural system. Glazing components tend to have greater load to capacity ratios making them the weak links in the load transfer chain.

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54 Openings, i.e. entry doors, s liding balcony doors, windows, can sustain damage resulting from pressure overloads and from windborne debris impact. The puncturing of the building envelope through glazing damage results in unit area internal pressure changes and in water intrusion. The influence of water ingress on neighboring units (i.e., the neighboring units below the unit with the breach) is accounted for in the model developed by Florida Institute of Technology, based on the exterior damage results generated by the UF model (subject of this Thesis). Components within the Model Major insurance losses are triggered by damage of the building envelope; thus, the mid high rise commercial residential model specifically simulates components comprising the building envelope and components es sential to the isolation of the interior of the building. Components modeled for mid high rise buildings can be grouped in the following categories: glazing and mitigation focused components. Windows, entry doors, and sliding doors are glazing components; glazing protection, such as steel or plywood shutters, and type of glass, such as normal or laminated, are components focused in the mitigation of glazing damage. The algorithm used to model windows for units in buildings with either exterior or interior c orridors is based on a flexible architectural feature, the fraction of glazing area per exterior wall area. The number of windows allocated to each unit wall exposed to the environment is based on the window size and on the glazing area per exterior wall area ratio; the location of the window closest to the corner is determined from a pre established corner to window distance. In an exterior corridor building the entry way for each unit is along one of the long sides of the building and sliding doors are located along the other long side. An interior corridor building isolates the unit entry doors from the outside environment and places the sliding door at one of

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55 its exposed walls. The modeling of components intended to mitigate damage (shutter protection) i s accomplished through the correction of impact resistance of glazed component. Basic Model Descriptors Key flexible features in the model are the type of building layout (interior or exterior corridor), the location of the unit within the building (middl e or corner unit), the footprint size per floor, the percentage of glazing occupying the buildings surface area, common dimensions for glazing components, and types of mitigation measures (shutters and glass type). Multiple combinations of these features can be analyzed by the model. The basic model descriptors identified in this chapter for low rise and mid high rise buildings will be used in their corresponding models to develop building models and determine their vulnerability. Chapter 4 and Chapter 5 discuss this procedure in detail for low rise buildings and mid high rise buildings, respectively. Monte Carlo Simulation engines, also described in Chapters 4 and 5, will model the building components identified in this chapter and assess their performance.

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56 CHAPTER 4 LOW RISE COMMERCIAL RESIDENTIAL MODEL PE RFORMANCE Overview This chapter discusses the probability based engineering vulnerability model developed to predict damage for low rise commercial residential buildings. Details regarding the programs architecture, solution process, key features, assumptions, modeling algorithm for the different variables, analysis, results, and preliminary verification are provided in this chapter. Program Architecture and Solution Process The low rise commercial residential damage model is a Monte Carlo Simulation engine that calculates wind loads and building component resistance values and simulates the performance and interaction of structural and cladding components in typical low rise commercial residential buildings dur ing hurricane winds (Cope, 2004) The components of the algorithm used by the Low Rise Commercial Residential Model can be grouped in four distinct phases: 1) model and analysis definition, 2) modeling the building, its compone nts, and wind loads, 3) analyzing the building and determining the damage, and 4) processing the damage to verify the results. Model and Analysis Definition Phase The interface between the programs user and the simulation engine occurs through the model a nd analysis definition. Two alternatives exist for running this component, the batching mode or the default mode. The batching mode performs damage analysis on multiple models during a single run, and is typically used to produce final results. The default mode performs only one model analysis per run and is usually used by the model developer to evaluate performance prior to finalizing the model(s) and producing results. In the default mode the user is prompt to define the various analysis parameters that determine the building being modeled

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57 and the extent of the analysis. Variables identifying the range of wind speeds and the number of simulations performed for each wind speed define the extent of the analysis; for example 1000 simulations and a range of w ind speeds of 50 mph to 250 mph with 5 mph increments. In the batching mode the user must code the analysis parameters directly in the model control function. The extent of the analysis, the physical characteristics of the building, the environmental expos ure, and the damage mitigation strategies are all defined by the user at this stage. Options for Model Descriptors The low rise commercial residential model was designed to be flexible and user friendly. The main objectives were to: a) allow the user (deve loper) to analyze different types of buildings (shapes, number of stories, etc.), b) provid e the developer with an easy route within the code for updating as modeling concepts evolve Flexibility regarding building physical characteristics, mitigation stra tegies, environmental exp osure, and extent of analysis are key features offered by the model in the input definition stage. The alternatives the program offers for the different input variables are shown in Table 4 1. Table 41. Low rise building model descriptors Low Rise Commerci al Residential Model Alternatives Low Rise Building Physical Characteristics Roof Cover = Shingle or Tile Roof Type = Gable or Hip Roof Exterior Wall Type = Wood or Concrete Block Number of Stories = Any Building Plan Size = Any Rectangular Shape Construction Quality = Weak, Medium, or Strong Mitigation Strategies Shutter Protection = None, Plywood, Steel, or Engineered Glazing Type = Normal, Laminated, or Impact Resistant Glass Environmental Exposure Missile Exposure Type = Urban, Suburban, or Open Extent of Analysis Number of Simulations = Depends on Computer Capacity

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58 Restrictions Assumptions and simplifications made during the development of the model result in restrictions to the variability of some of the model descriptor parameters outlined in Table 4 1. The current model offers flexible roof types, gable or hip, at the input definition stage; although the roof slope is also flexible, it is not currently a variable model descriptor parameter i.e. the program does not prompt the user to input the roof slope. The Minimum Design Loads for Buildings and Other Structures (ASCE 705) was used as guidance to calculate the roof loads, thus, the roof slope is restricted to a range between 7 to 45 for gable roofs and 7 to 27 for hip roofs. Roof cover is also flexible to a certain degree; the building can be constructed with either asphalt shingles or tile. There exist a variety of roof cover materials besides asphalt shingles and tiles; thus the program contains a section that enables modelers to enter properties i.e. dimensions and density of any type of roof cover directly into the code. The current model can theoretically analyze a building with any number of stories; however, by model definiti on low rise commercial residential buildings are restricted to three or less stories. The user is allowed to input any building plan dimensions, yet the program is only capable of analyzing building sizes with four foot increments. Common commercially avai lable wall sheathing panels are 4 ft. by 8 ft.; in order to simplify modeling the roof and wall sheathing panels it was established that only full panels and half panels would be available, thus the dimensions input by the user are re assigned by rounding up to the nearest dimensions divisible by four. Modeling the layout of sheathing panels for the exterior wall is also versatile in nature the dimensions of the sheathing panel can be user defined and the material can be simulated by entering the panels resistance data directly into the code. The only restriction when defining the exterior wall sheathing panels is that the horizontal dimension must be 4 feet.

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59 The definition of the building physical characteristics, mitigation strategies, environmental expos ure, and extent of analysis with the alternatives outlined in Table 41 concludes the extent of analysis and model definition phase. The basic parameters defined durin g this stage are loaded into the next component of the program in order to create and analyze the building. Modeling the Building, its Components, and Wind Loads This phase of the program creates low rise commercial residential building models, determines their component capacities, the loads resulting from hurricane winds, and analyzes the damage resulting from their interaction. This phase of the program consists of three nested loops. The two outer loops simulate the hurricane conditions i.e. the approac h direction of the wind and the maximum 3 second gust wind speeds, respectively. The wind approach directions loop iterates through eight angles of incidence and the wind speeds loop can iterate through any range of wind speeds currently the range is set f rom 50 mph to 250 mph peak 3 second gusts in 5 mph increments. The inner loop reconstructs an individual building (assigning randomized component capacity values), assigns loads, and documents damage multiple times. Thus one pass through the inner loop pr oduces the resulting damage to a single realization of the building being modeled, from one wind direction and at one wind speed. An iterative solution for damage to a single model realization occurs within the inner loop to account for internal pressure c hanges resulting from breaching of the building envelope. The enclosure condition and internal pressure coefficients are updated within each iteration to obtain the resultant pressure coefficients ( CP = Cp ext + Cpi nt). During an iterative solution for dama ge to a single model realization wind speed and resultant pressure coefficients are rerandomized to assess damage resulting from loads that reflect the current condition of the building. A flowchart depicting the modeling and analysis components of the pr ogram is shown in Figure 4 1.

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60 Figure 41. Low rise commercial residential model algorithm Mapping of Components Upon loading the analysis parameters and prior to the simulation of the storm, the program maps the location of the modeled building components to matrix spaces For example, each roof sheathing panel must be mapped to its physical location on the roof to allow proper determination of the wind load. This mapping task provides the necessary framework to analyze the interaction between wind loads and building components using matrix operations. Common construction practices and sizes of commercial ly available materials are the main factors influencing the mapping and modeling of the building components. Locations in the building are associated with particular entries in the mapping matrices. These matrices simplify

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61 the capacity and wind loading modeling procedures Components such as roof and wall sheathing panels, roof trusses, roof to wall connections, and glazing components are mapped to matrices in order to determine the wind loads and resultant damage Roof sheathing panels are mapped by mimick ing the common construction practice of staggering the panels, while wall sheathing panels are mapped assuming that all panels are placed vertically side by side. In order to create a realistic model, panels should be limited to sizes commercially availabl e, thus, more than one panel may be required to cover the full wall height of an individual story. The model assumes that construction techniques usually place a ring beam below the joists supporting the floor slab; the space between the ring beam and the bottom of the floor slab is defined as the inter story space, while the space spanning from the top of the floor slab to the bottom of the ring beam is defined as the main story space. Wall sheathing panels are mapped into main story and inter story spaces throughout the perimeter of the building. Glazing components are then mapped to their corresponding locations in the walls. Windows are spaced evenly among all four walls, while entry doors and sliding doors are placed at the center of each unit in their corresponding side. Glazing and wall sheathing panels may coincide in a location; in this event, a section of the wall sheathing panel is removed to allow the installation of the window, entry door, or sliding door. These matrices are used to locate the co mponent, to assign and to keep track of its capacity and wind loads, facilitating the damage calculation process through their interaction. Sample mapping matrices for wall sheathing on the gable end of a model building (see Figure 42) are shown in Table 42. The following sections describe the details of the representation of com ponent capacities, wind loading on components, and the ability of those components to resist these loads.

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62 Figure 42. Gable end sheathing layout and a reas (3 story building) Table 42. Gable end mapping m atrices Gable End Mapping Matrix: Wall Sheathing Area per Panel ( ft. 2 ) 4 12 20 28 32 32 32 32 32 32 32 32 32 32 32 32 32 28 20 12 4 0 0 0 0 4 12 20 28 32 32 32 32 32 28 20 12 4 0 0 0 0 0 0 0 0 0 0 0 0 4 12 18 12 4 0 0 0 0 0 0 0 0 Gable End Mapping Matrix: Original Sheathing Panel Identification (Before the Storm) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 Gable End Mapping Matrix: Centroid Heights for the Sheat h ing Panels ( ft. ) 36.67 37.56 38.53 39.52 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 39.52 38.53 37.56 36.67 0.00 0.00 0.00 0.00 44.67 45.56 46.53 47.52 48.00 48.00 48.00 48.00 48.00 47.52 46.53 45.56 44.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 52.67 53.56 54.26 53.56 52.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

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63 Capacity Modeling The capacities of the various exterior building components are represented within a probabilistic framework and require a mean and coefficient of variation for the component capacities. Mean component capacities and their coefficients of variation are assigned based on the buildings construction quality. Improvements in the construction quality lead to larger mean resistances and less variation from the mean. The actual resistance assigned to a given component in a single simulation, e.g. a single piece of roof sheathing, is randomly assigned based on the mean and coefficient of variation, and stored in a matrix entry mapping the physical location of the component. The Gaussian distribution is the default probability model for all components. To alleviate the occurrence of negative capacity values and unrealistic outliers the normal distribution is truncated at two standard deviations from the mean. Mean component capacity values and their coefficients of variation a re based on the Florida Public Loss Hurricane Model for Single Family Residential Construction and on manufacturer data (PGT Industries) for non impact resistant vinyl products commonly used in low rise commercial residential construction Engineering judgment was used to modify these values and test the performance of the model. Thus, further investigations regarding the actual mean capacities and coefficients of variation for components of low rise commercial residential buildings are required to obtain more accurate results. Current capacities and coefficients of variation for components in the building envelope are summarized in Table 43. The resistance to impact of a glazing component is modeled as the likelihood that the component will be impacted and damaged by windborne debris. Correction factors account ing for mitigation measures are applied to the impact capacity obtained. Table 4 4 depicts the correction factors used to account for the presence of opening protecti on and the type of glass of

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64 the component The procedure for assigning the resistance to impact of glazing components is illustrated in the section describing the debris impact loads. Table 43. Pressure c apacities (psf) and coefficients of variation for components in the building e nvelope Pressure Capacities (psf) and Coefficients of Variation for Components in the Building Envelope Component Weak Construction Medium Construction Strong Construction Mean, C v Mean, C v Mean, C v Shingles 50 0.4 70 0.25 90 0.15 Vinyl Siding 25 0.4 72 0.25 88 0.15 Wall Sheathing Panels 70 0.4 90 0.25 110 0.15 Roof Sheathing Panels 55 0.4 80 0.25 130 0.15 Windows 37 0.4 71 0.25 104 0.15 Sliding Doors 5 0 0.4 9 0 0.25 1 13 0.15 Entry Doors 55 0.4 97.5 0.25 12 0 0.15 Table 44. Impact capacity correction f actors Impact Capacity Correction Factors Protection Correction Factor Material Correction Factor Shutter Type Factor Glass Type Factor None 1 Normal 1 Plywood 1.15 Laminated 1.5 Steel 1.25 Impact Resistant 2 Engineered 1.5 Wind Pressure Load Modeling Exterior c omponents on low rise commercial residential buildings are subjected to wind induced loads either direct ly or indirect ly Direct loads are those transferred directly from the environment to components in the building envelope i.e. sheathing panels subjected to wind pressure, or glazing subjected to pressure or flying debris. I ndirect loads are those transferred by components in the building envelope to other components that are not directly exposed to the environment such as roof sheathing transferring loads to roof trusses and roof to wall connections. Wind loads are determined by modifying the curr ent wind load design provisions

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65 (ASCE 7 05) and impact loads are determined by calculating the probability of debris impact ing glazing and doors The loads calculated by the model are not intended to represent design levels; rather, load values are selected to best represent pressure or uplift acting on each building component during a wind storm (Cope, 2004) The current wind load design standard was used as a framework for the models wind load calculation, and the pressure coefficients and the various loading zones were modified. Instead of using the maximum resultant pressure coefficients for the various combinations of positive or negative internal and external pressures ( Cp ext Cpi nt) to determine the design loads for the components at a given location, the model determines the actual resultant pressure coefficients for each zone in the walls and roof for each of the eight angles of incidence represented in the wind model. The pressure zones suggested by the ASCE 705 components and cladding wind loading standard are meant to represent worst case scenarios for the structure. According to the standard the distribution of these zones on the roof and walls is independent of the wind approach direction. The ASCE 705 pressure zones for the design of roof and wall components and cladding are depicted in Figure 43. Corner zones (zone 3) are subjected to the largest suctions. End zones (zones 2 and 5) are applied to locations of discontinuity in the roof and wall surfaces. Interior zones (zones 1 and 4), all other areas in the roof and walls, are subjected to the lowest magnitude pressure loads. For the current task of modeling the component damage due to wind approaching from a specified direction, the ASCE enveloped approach must be modified to account for specific wind directions. That is, the location of the zones shifts over the building envelope as the wind approaches the building from different directions. Cope ( 2004) manipulated the location of these

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66 zones to represent observed damage patterns and knowledge of directionally controlled wind tunnel and full scale pressure investigations. The modified components and cladding roof pressure zones for various directions of wind approach are shown in Figure 44. The characteristic a dimension shown in Figure 43 is still used to determine the size of each zone, but the zone locations now reflect the influence of wind approach direction. The concept developed by Cope (2004) regarding the modified roof pressure zones is used in the low rise commercial residential model wind load algorithm. A feature that can calculate the a dimension and the sizes of the roof zones for buildings of any dimension was added to accommodate for the dimensional flexibility of the model. In addition, Cope (2004) also modified the ASCE 705 wall pressure zones by re moving the edge zones on the windward and leeward walls and the trailing zone on the side walls; however, this concept was not used in the low rise commercial residential model. The trailing zones on the side walls were not removed because the location on the side walls at which reattachment of wind vortices occurs, if any, depends on the buildings dimensions. Removal of the trailing zones on the side walls would lead to an inaccurate representation of the pressure loads in those zones. Figure 43. ASCE 705 (2005) roof and wall pressure zones (With permission from ASCE)

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67 Figure 44. Co pes (2004) modified roof pressure zones The computation of wind loads on the surface of the structural model is a simple process once the pressure coefficient maps have been developed. Weighted external pressure coefficients are mapped to every component on the building envelope based on the percentage of the components area occupied by each pressure zone. Once these weighted external pressure coefficient maps have been determined for the wall and roof surfaces, they are superimposed with the internal pre ssure coefficient to obtain the resultant pressure coefficients for every structural component. The internal pressure coefficient is determined in accordance with ASCE 705 based on the current buildings enclosure condition. This resultant overall wind pr essure coefficient building surface map is then randomized by using the assigned values as the mean of a Gaussian distribution with a coefficient of variation of 0.05. This reflects the natural variability of pressure loading as observed in wind tunnel and full scale experiments. Wind velocity is not constant throughout the height of the building; it increases at higher elevations. In order to accurately calculate the pressure loads acting on components at each story,

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68 the reference peak 3 second gust wind s peed, vpeak_3s@10mts (at a height of 10 meters 33 feet), must be converted to a reference peak 3 second gust wind speed, vpeak_3s, applicable to the particular height of the centroid of each component. A gust factor, GF is used in Equation 41 to convert the reference peak 3 second gust wind speed, vpeak_3s@10mts, to the 10minute averaged mean wind speed, vmean_10min@10mts (at a height of 10 meters 33 feet). 10 @ 10 ( 0) = 3 @ 10 ( ) ( 0) < 0 ( 41) In Equation 41, T0 is the duration of the data record ( T0 = 10 minutes) and is the gust duration ( = 3 seconds). The value for GF ( = 3 sec., T0 = 10 min.) is taken as 1.38, only applies to inland open exposures at 10 meter heights, and was calculated using the Durst met hodology with data recorded by the Florida Coastal Monitoring Program (Masters, 2004) Variations in mean wind velocity with height from the ground are modeled using Equation 42 the wind shear formula (Danish Wind Industry Association, 2003) The wind speed conversion is shown in Equation 42, where z0 is the roughness length and h is the height of the components centroid. 10 @ 10 @ 10 = 0 10 0 10 @ 10 ( 42) Since the gust factor, GF used in Equation 41 applies only to heights of 10 meters, a different gust factor, G must be used in Equation 43 to convert the 10minute averaged mean wind speed, vmean _10min@h, to the peak 3 second gust wind speed at the height of each components centroid, vpeak_3s. The gust factor, G used in Equation 43 is calculated in accordance with ASCE 705 section 6.5.8.1. 3 = 10 @ ( 43)

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69 The converted applied peak 3second gust wind speeds, vpeak_3s, are then randomized and mapped to every component in the building envelope. The resulting pressure loads are calculated using Equation 44. ( ) = 0 00256 2 ( 44) In Equation 44, P is the pressure load (in lb/ft.2), vwind is the randomized peak 3second gust wind speed (in miles per hour), GCPResultant is the randomized resultant pressure coefficient, and red is a reduction factor that accounts for the reduced density of air during a hurricane. The current value for red is 0.94 as suggested by Dr. Mark Powell on the team developing the meteorological component of the model (Hamid, 2007) Debris Impact Load Modeling The component maps are also useful in the determination of impact loads. Windows and doors are assumed as susceptible to impact loads, whereas roof systems and walls are not. The loads acting on the components vulnerable to impact are modeled as the probability of damage of those components, PD (vwind) Damage to a glazing component is determined by comparing the loads acting on these components (i.e. the ir probability of damage, PD (vwind) ) with their resistance to impac t (i.e. the likelihood that they will withstand impact). For instance, the value denoting the resistance to impact of a particular component could be assi gned 0.5 (randomly drawn from a uniform distribution over a possible range [0, 1] ) Mitigation measure s such as the presence of shutter s and higher qualities of glass increase a components likelihood to withstand impact. Therefore, if the component consists of laminated glass, its resistance is increased by a factor of 1.5; if the component is additionally protected by shutters (such as plywood shutters) its resistance to impact is again increased, this time by factor of 1.1 5 (see Table 44). Thus, the resis tance to impact for the laminated glass component protected by plywood shutters would be 0.8625 (0.5.5.15 = 0.8625). The specific value for its probability of damage is a combination

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70 of wind speed, location of the opening, surroundings, and materials. If the components probability of damage is less than 0.8625 the component is undamaged, otherwise the component failed. The public Commercial/Residential Construction Impact Model assumes that missile impacts on glazed components of the building envelope are rar e and unrelated discrete events. The fundamental equation for the missile model is based on the cumulative exponential distribution. Equation 45 models the pr obability of damage of a component covering an opening ( PD( vwind) ) given a 3 second gust wind speed ( vwind): ( ) = 1 ( ) ( ) ( ) ( 45) where A ( vwind) is the fraction of potential missile objects that are in the air at a given 3 second gust wind speed ( vwind), B ( vwind) is the fraction of airborne missiles that hit the building at a given 3second gust wind speed ( vwind), C is the fraction of the impact wall tha t covers a given opening, D ( vwind) is the probability that the impacting missiles have enough momentum to damage the component impacted, and NA is the total number of available missile objects in the area upwind. This development is a simplified version of the missile impact model developed by Applied Research Associates and documented in the FEMA HAZUS MH manual (Federal Emergency Management Agency, 2008) A missile is defined as an object that has become airborne. If airborne, a broken tree branch, a roof shingle, a stud, and a sheathing panel are all examples of missiles or windborne debris. If these objects are stil l on the ground they are referred to as debris. The Commercial/Residential missile model currently assu mes that roof cover is the dominant source of windborne debris.

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71 The number of available missile objects in the area upwind of a building ( NA) is related to the exposure category of the area in which the building is located and the winds direction of approach. The exposure category of the area (a user input) in which the building is located can be U rban Suburban or O pen depending on the density of the area. The exposure categories and subdivision layouts are illustrated in Fig ure 45 for urban and suburban densities and in Figure 4 6 for open density. The missile model assum es that the layout for the surrounding buildings is similar to that of the targeted building for the three exposure categories. Inter building distances are the only variables for the different exposure categories. Engineering judgment was used to define t he general inter building distances: a) 45 ft. between the targeted building and its directly adjacent neighboring buildings, i.e. buildings A and B in Figure 45, and b) 45 ft. between the targeted building and buildings in the corners of the subdivision, i.e. buildings C Note that open exposure subdivisions do not have buildings directly adjace nt to each other (see Figure 46) Distance multipliers 1.0 for urban, 2.0 for suburban, and 5.0 for open exposures factor the inter building distances shown in Figure 45. For example, the distances between the targeted building and its directly adjacent neighboring buildings would be 45 ft. (45 ft. = 45 ft.) and 90 ft. (45 ft. 2 = 90 ft.) respectively, for urban and suburban exposures. The number of available missile objects ( NA) is obtained by adding the total number of shingles of all the neighboring buildings in the area upwind of the target. As the winds direction of appro ach changes during a storm, the number of buildings in the path of approach and their distances to the target building also change affecting the number of available missile objects in the area upwind of a building ( NA) and the distance each missile must travel to impact the target. Eight directions of wind approach, including cornering winds, winds parallel to the

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72 roof ridge, and winds perpendicular to the ridge line, were modeled; Figure 47 illustrates and labels these eight directions. Figure 45. Urban and suburban missile exposure layouts Figure 46. Open missile exposure layout

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73 Figure 47. Directions of wind approach in the missile model Referring back to Equation 45, the fraction of potential missile objects ( A ) that are in the air at a given 3 second gust wind speed is related to the resistance of the upwind potential missile objects (shingles), since those that fail may become windborne debris and potentially i mpact the subject building. Thus, A is a function of the 3second gust wind speed. A loose shingle becomes airborne when the instantaneous wind speed, vwind, exceeds the flight initiation or threshold velocity, U for that shingle. The threshold velocity, U a function of the missiles density ( missile), thickness ( tmissile), fixing strength ( I ), gravity (g), air density ( air), and a generalized force coefficient ( CF) is shown in Equation 46 (Willis, Lee, & Wyatt, 2002) = 2 ( 46) The procedure for calculating the parameter A ( Equation 45) involves the following steps: 1) randomizing the properties (capacity, thickness, and density) of all available missile objects (shingles) in the area u pwind of a target building ( NA) 2) randomizing the current 3 second gust wind speed at the mean roof height and calculating the resulting pressure at each shingle, 3)

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74 determining the total number of shingles that failed in the area upwind, 4) calculating the threshold velocity for each failed shingle using Equation 46 and comparing it to the randomized wind speed acting at every failed shingle, 5) determining the tota l number of airborne shingles, and finally, 6) dividing the total number of airborne shingles by the total number of available missile objects in the area upwind to obtain the value of A for the current 3second gust wind speed. Plots of the values of parameter A versus wind speeds for the eight directions modeled (defined in Figure 47 ) are depicted in Figure 48. These values were obtained from a sample simulation with strong shingles in a suburban missile exposure. The fraction of potential missile objects in the air is less at low gust wind speeds, and increases at higher wind speeds as more upwind building roof components fail and become airborne. Figure 48. Value of parameter A versus wind speed (strong shi ngles) Among the variables required to calculate parameter A the number of available missile objects in the area upwind of a target building ( NA) is the only one affected by wind direction. Since parameter A is a ratio airborne missiles to available missile objects, NA, changes in the number of 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Variable A (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Value of A 17-Jul-2009 Output 1000 simulations Direction 1 Direction 2 Direction 3 Direction 4 Direction 5 Direction 6 Direction 7 Direction 8

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75 airborne missiles are proportional to changes in NA (i.e. the sample size) and parameter A results unaffected by wind direction. Out of the total number of upwind miss iles that are airborne ( NAA ) only a fraction of these will impact the subject building. The fraction of airborne missiles that strike the building at a given 3second gust wind speed ( vwind), described by parameter B depends on the wind speed and the dis tance between the subject building and the source of debris (e.g. see Figure 45 and Figure 46 ). A missile colliding with the building is modeled as one which travels a minimum distance equal to the distance between the source and the target. The source to target distance depends on the exposure category and the distance that each missile travels and its velocity at impact are determined by simulating its flight trajectory. Motion of a generic missile object moving in a uniform flow is described by Equation 47, Equation 48, and Equation 49 for the horizontal, vertical, and rotational degrees of freedom, respectively (Baker, 2007) 2 2 =1 2 [ ( )2+ 2] [cos ( + ) sin ]( 47) 2 2 =1 2 [ ( )2+ 2] [sin + ( + ) cos ]( 48) 2 2 =1 2 [( )2+ 2] ( + ) ( 49) Variables introduced in the previous equations are defined as follows: l is the missiles reference length (i.e. the width of the shingle) I is its moment of inertia and Amissile is its plan area x y and are the missiles horizontal, vertical, and angular positions, respectively umissile and vmissile are the missiles horizontal and vertical velocities, respectively t denotes time is the relative angle of attack, measured between the wind direction and the debris direction of travel CD, CL, and CM are the quasi steady drag, lift, and moment force coefficients CLA and CMA are the autorotation lift and moment force coefficients

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76 The quasi steady aerodynamic force coefficients are functions of the total angle of attack, me asured between the wind direction and the debris axis (see Equation 410, Equation 411, and Equation 412), wh ereas the autorotation force coefficients are functions of the missiles angular velocity ( ) and the steady state angular velocity i.e. the maximum value that the angular velocity can achieve ( MAX ) (see Equation 413, Equation 414, and Equation 415). Determination of these coefficients is based on the model suggested by Baker (2007) for flat plates. = 0 75 [1 + 0 65 2 2 ] ( 410) = 1 2 ( 2 ) ( 411) = 0 2 ( + ) ( 412) =0 64 ( 413) = ( 414) = ( 1 ) ( 415) Values for the autorotation lift and pitching moment constants ( kLA and kMA) are taken as 0.4 and 0.12, respectively (Baker, 2007) A time stepping algorithm is used to model the flight trajectories; accelerations (2 2 2 2 and 2 2 ) are calculated at time t ( i) by solving Equation 47, Equation 48, and Equation 49, while positions ( x y and ) and velocities ( umissile, vmissile, and missile) at time t(i+1) are obtained by substituting acceleration, velocity, and position values at time t(i) into Equations 416 through Equations 421 (Lin, Holmes, & Letchford, 2007) + 1= +1 2 [( +2 2 ) + ] ( 416) + 1= +1 2 [( +2 2 ) + ] ( 417)

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77 + 1= +1 2 [( +2 2 ) + ] ( 418) + 1= +2 2 ( 419) + 1= +2 2 ( 420) + 1= +2 2 ( 421) Missile trajectories are simulated until the missile collides with the ground or a building; parameter B can then be obtained from the total number of missiles that collide with the building. Plots of the values of parameter B versus wind speeds for the eight directions modeled are illustrated in Figure 4 9. These values were obtained from the same sample simulation as the values of parameter A As the gust wind speed increases the missiles travel distance increases. The figure reflects that the number of missiles striking the bu ilding grows with increas es in the wind speeds. Figure 49. Value of parameter B versus wind speed (strong shingles) 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Variable B (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Value of B 17-Jul-2009 Output 1000 simulations Direction 1 Direction 2 Direction 3 Direction 4 Direction 5 Direction 6 Direction 7 Direction 8

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78 Given that a piece of debris does impact a glazing or door component, the probability tha t the missile has enough momentum to damage the impacted component is described by parameter D and is a function of the wind speed. Equation 422 models the transfer of momentum fr om the shingle to the component during a collision assuming conservation of momentum. In Equation 422 Lmissile and Wmissile are the length and width of the missile object, while uimpactcos is the component of the missiles velocity perpendicular to the surface of the impacted object during the collision. The angle of i ncidence, is 0 for a head on impact and 45 for an impact at an angle, respectively. The missiles velocity at impact is equal to the missiles horizontal velocity obtained from the last time step of the missiles trajectory ( Equa tion 419). = cos ( 422) Plots of the values of parameter D versus wind speeds for the eight directions modeled are depicted in Figure 410. These values wer e obtained from the same sample simulation as the values of parameter s A and B The figure reflects that the number of missiles causing the damage grows with increasing gust wind speeds. Figure 410. Value of parameter D versus wind speed (strong shingles) 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Variable D (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Value of D 17-Jul-2009 Output 1000 simulations Direction 1 Direction 2 Direction 3 Direction 4 Direction 5 Direction 6 Direction 7 Direction 8

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79 Models for calculating trajectories of platetype windborne debris are rare; Tachikawa (1983), Holmes et al. (2006), Lin et al. (2007), and Baker (2007) have proposed models based on Newtons Second Law and the fundamental equations of motion. Wind tunnel studies have also been performed to investigate flight trajectories of flat plates and validate these models (Tachikawa, 1983 and Lin et al, 2006). These studies have shown that while the flight tra jectories of flat plates are very widespread and dependent on the characteristics of the missile and its initial angle of release, the modeled trajectories are in accordance with experimental data (Tachikawa, 1983) The flight trajectory model presented in this section contains features from the different models developed by these authors. The last variable required to calculate the probability of damage is the parameter C which is the fraction of the wall that is made up of components vulnerable to impact (windows and doors). Once this fraction is mapped to the openings location in the building, the probability of damage ( PD) from Equation 45 can be determined for each glazing component. This concludes the calculation of wind pressure and debris impact l oads for the low rise commercial residential model. In order to calculate the damage sustained by individual components the model must analyze the interaction of the components capacities and loads. Analyzing the Building and Determining and Processing the Damage Failure of a system or component can be defined through its limit sta te ( G = Resistance Load). Failure occurs when the loads on the system exceed its capacity. The limit state, loads, resistance and failure for a component are illustrated in Figure 411. The model determines the damage to building components, resulting from the interaction of their capacities and loads, by analyzing their limit states. Matrix operations are used to compare the mapped loads against the mapped capacities of the various components and create a preliminary map of component damage. Every simulated building goes through two phases of loading for each wind speed and direction, thus

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80 these preliminary maps of component damage are crucial for updating the component mapping matrices and the enclosure condition of the building. Figure 411. Frequency distribution of load effect and resistance for a general system The enclosure condition of the building analyzed is e nclosed throughout the first phase of loading. The internal pressure coefficients based on the enclosure condition, are determined in accordance with ASCE 7 05 and the pressure loads are modeled as described in the wind pressure load modeling section. Breaches in the building envelope resulting from loss of sheathing panels or failure of glazing components during the f irst phase of loading, lead to changes in the enclosure condition and internal pressure of the building. In order to update the enclosure condition of the building (i.e. the internal pressure coefficients) the model assumes that the individual stories and the attic are isolated from each other so that breaches in a given level will only affect the internal pressure of that level. For example, a breach in the second story will lead to internal pressurization and result in changes in the internal loading of s heathing panels and glazing components only in that level; this breach will not affect the enclosure condition or

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81 internal pressure of the third story. In reality the floor slab of the third story would be subjected to uplift forces in the event of a second story breach; however, slab modeling is not within the scope of this model, thus, the original assumption is reasonable. Preliminary maps of component damage are used to compute the total open wall/roof area for each level after the first phase of loadin g and thus, to update the levels enclosure condition (based on open area requirements described in ASCE 7) for the second loading phase. Wind pressure loads resulting from the second loading phase are calculated based on the updated enclosure condition a nd in accordance with the procedure discussed in the wind pressure load modeling section. Damage resulting from the second phase of loading is added to the preliminary maps of component damage to obtain final damage maps. This process is repeated by reass igning random capacities to the model building n times, producing n samples of damage for every combination of 41 wind speeds and 8 wind directions. Multidimensional damage matrices containing the losses (for each component for each simulation for each wi nd speedfor each wind direction) are the output of the nested loops. The analysis output damage matrix file consists of a header containing all metadata (building dimensions, etc.) and a multi dimensional array containing the physical exterior damage of every component in every simulated building for every wind speed and every angle of incidence. The information included in the outputs damage matrix is summarized in the following: Percent roof cover (shingles or tiles) failed Percent field roof sheathing failed Percent edge (overhang) roof sheathing failed Percent roof to wall connections failed Number of collapsed gable end trusses side 1 Number of collapsed gable end trusses side 2 Percent gable end wall covering failed Percent gable end sheathing failed

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82 Percent wall covering failed for every floor Percent wall sheathing failed for every floor Number of windows failed from wind pressure for every floor Number of windows failed from debris impact for every floor Number of sliding glass doors failed from w ind pressure for every floor Number of sliding glass doors failed from debris impact for every floor Number of entry doors failed from wind pressure for every floor Number of entry doors failed from debris impact for every floor The damage information contained in this matrix is the data used by engineering vulnerability modelers at FIT to predict interior losses. This information needs to be processed if the user desires to interpret or check the results for model refinement. For example, the average dama ge to roof shingles for peak winds of 120 mph can be determined from this output matrix b y averaging all roof shingle damage results at that wind speed. That is, averag ing the results of the n simulations at each of the eight wind directions, fixing the pe ak wind to 120 mph. The last component of the program, a plotting function, processes the output and produces graphical representations of statistical averages of the damage obtained in the analysis; this feature allows the user to represent, interpret, an d validate the results of the analysis. Examples of Simulation Results Results presented in this section represent the vulnerability of a sample low rise commercial residential building using the Monte Carlo Simulation engine described in this chapter. The sample model analyzed is described in Table 45; capacities for glazing components and roof/wall sheathing panels were modified in order to verify the results in terms of expected trends M ean pr essure capacities of 80 psf and 70 psf wer e used for roof/wall sheathing panels and windows, respectively; entry and sliding doors were assigned mean pressure capacit ies of 100 psf

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83 Table 45. Sample model analyzed Model 1 No. of Simulations ( n ) : 1000 Construction Quality : Medium No. of Stories : 3 Dimensions : 80 ft x 40 ft Roof Cover : Shingles Roof Type : Gable Roof Slope : 6/12 Wall Type : Wood Protection : None Glass Type : Normal Exposure : Suburban Comparative graphs of mean damage summarizing the results are presented in this section. Mean levels of damage compare the overall damages to the building components for varying wind speeds. Damage is presented as percentages of total component damage for roof cover, wall cover, roof sheathing, and wall sheathing; window, entry door, and sliding door damage is expressed as the total number of components failing. Preliminary verification of the results based on engineering judgment is accomplished in this section. Sample of Preliminary Results for Gabled Roof Building Average quantities of damage for components of the Model 1 building described in Table 45 are presented in the following figures. Roof sheathing and roof cover damage are illustrated in Figure 412, showing the average percentage of component damage (across all n s imulations for each of eight wind directions) as a function of peak 3 second wind speed. Edge roof sheathing refers to the sheathing on the overhang portion of the roof, and field roof sheathing is elsewhere. As expected, the general shape of the curves resembles sigmoid functions, with less average damage occurring at lower wind speeds than at higher wind speeds. Sheathing in e dge roof zones experience greater suction pressures than field roof zones i.e. the external pressure coefficients for field zones are 2. 0, 1.2, and 0.8 for zones 3, 2, and 1,

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84 respectively, while for the overhangs (after accounting for the pressure from underneath the overhang) they are 2.5 and 2.2, respectively for zone s 3 and 2. This is due to the differential in loading from underneath the overhang vs. internal pressure. Thus, the damage levels represented in Figure 412 are logical; i.e. the damage of field roof sheathing is less than that of edge roof sheathing. E dge and field roof sheathing are expressed as percentages of total edge and field roof sheathing, respectively Roof cover damage (shingle loss) is not delineated by edge and fie ld regions, and simply relates the percentage of shingles damaged over the entire roof. Roof and wall sheathing damage is illustrated in Figure 4 13, where results ar e shown for sheathing on the walls for multiple stories, wall sheathing on the gable end (vertical face on gable ends above the top floor ceiling), and roof sheathing. A comparison of sheathing panel damage sustained by the individual stories reveals that the percent damage increases with height; thus, the results are as expected, higher wind speeds at higher elevations result in greater pressure loads as discussed in the wind pressure load modeling section The proportion of area located in pressure zone 5 for the 3rd story is greater than that for the gable end, thus at lower wind speeds the percentage of sheathing panel damage is less for the gable end than for the 3rd story ( wall pressure zones 4 and 5 are illustrated in Figure 414 ) However, at higher wind speeds the percentage of sheathing panel damage for the gable end is greater than that for the 3rd story; this phenomenon is explained by the hig her elevations of panels in zone 4 for the gable end than those of their counterparts for the 3rd story. Greater proportion of areas in the individual stories and the gable end sustain larger pressure magnitudes than areas in the roof, resulting in greater percent damage of sheathing panels in the upper stories and the gable end compared to the roof. The results shown in Figure 413 were obtained from a simulation in which roof and wall sheathing had equal mean capacities and coefficients of variation. Roof and wall sheathing mean

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85 capacities and coefficients of variation are not necessarily equal, however, producing preliminary results with equal values a llows the modelers to check the program Figure 412. Roof sheathing and roof cover damage for a 3 story, gable roofed, medium quality building Figure 413. Roof and wall sheathing damage for a 3 story, gable roofed, medium quality building 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Roof Sheathing/Cover Damage for a 3 Story Gable Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 22-Jul-2009 Output 1000 simulations Roof Cover Edge Roof Sheathing Field Roof Sheathing 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Roof/Wall Sheathing Damage for a 3 Story Gable Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 22-Jul-2009 Output 1000 simulations 1s t Floor Wall Sheathing 2n d Floor Wall Sheathing 3r d Floor Wall Sheathing Gable End Wall Sheathing Edge Roof Sheathing Field Roof Sheathing

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86 Figure 414. ASCE 7 05 (2005) w all pressure zones 4 and 5 ( With permission from ASCE ) Figure 415 depicts wall sheathing and cover damage for every story and for the gable end. Loss of a sheathing panel results in the loss of the roof or wall cover attached to that panel, thus, it is ex pected that the percent damage of wall and roof cover are greater than that of wall and roof sheathing. The curves shown in Figure 4 15 illustrate this concept. Figu re 415. Wall sheathing and cover damage for a 3 story, gable roofed, medium quality building 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Wall Sheathing/Cover Damage for a 3 Story Gable Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 22-Jul-2009 Output 1000 simulations 1s t Floor Wall Cover 1s t Floor Wall Sheathing 2n d Floor Wall Cover 2n d Floor Wall Sheathing 3r d Floor Wall Cover 3r d Floor Wall Sheathing Gable End Wall Cover Gable End Wall Sheathing

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87 Figure 416, Figure 417, and Figure 418 compare the number of windows, entry doors, and sliding doors, respectively, damaged by pressure and debris impact. The modeled building has 22 windows, 3 entry doors, and 3 sliding doors per floor (three units per floor). The model checks for damage due to pressure before damage due to impact. At low wind speeds, the damage due to pressure for these components is very low. However, missile impacts at even low wind speeds can cause damage. Thus, damage due to impact resembles a sigmoid function when damage due to pressure is negligible, i.e. at low wind speeds. At higher wind speeds, damage due to pressure begins to increase. Since the program checks for damage due to pressure before damage due to impact, a gradual drop in impact damage accompanies the incr ease in pressure damage (a window already damaged from pressure is not evaluated for damage from debris). As expected due to the height dependent wind speed, pressure damage is greater at higher elevations. Figure 416. Window damage for a 3 story, gable roofed, medium quality building 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 20 22 Window Damage for a 3 Story Gable Roofed Medium Building (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Windows Damaged 22-Jul-2009 Output 1000 simulations Normal Windows Shutters = None 1s t Floor Pressure 1s t Floor Impact 1s t Floor Total 2n d Floor Pressure 2n d Floor Impact 2n d Floor Total 3r d Floor Pressure 3r d Floor Impact 3r d Floor Total

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88 Figure 417. Sliding door damage for a 3 story, gable roofed, medium quality building Figure 418. Entry door damage for a 3 story, gable roofed, medium quality building The current missile model does not account for the height of the individual window and door components, it only accounts for the distance the missile must travel to strike the building. Thus, the model does not distinguish between a missile impact to the first floor or to the third floor. Further research is necessary to incorporate a more accurate missile trajectory into the 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3 Sliding Door Damage for a 3 Story Gable Roofed Medium Building (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Sliding Doors Damaged 22-Jul-2009 Output 1000 simulations Normal Windows Shutters = None 1s t Floor Pressure 1s t Floor Impact 1s t Floor Total 2n d Floor Pressure 2n d Floor Impact 2n d Floor Total 3r d Floor Pressure 3r d Floor Impact 3r d Floor Total 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3 Entry Door Damage for a 3 Story Gable Roofed Medium Building (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Entry Doors Damaged 22-Jul-2009 Output 1000 simulations 1s t Floor Pressure 1s t Floor Impact 1s t Floor Total 2n d Floor Pressure 2n d Floor Impact 2n d Floor Total 3r d Floor Pressure 3r d Floor Impact 3r d Floor Total

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89 model. The trajectory modeled would ne ed to accurately distinguish the elevation of the missile throughout its path. As a result, there is no distinguishable difference in number of windows broken among the different stories for low wind speeds. At higher wind speeds, the pressure loading incr ease with height causes the observed divergence of results with building story. The results summarized in this section appear to be in accordance with good engineering judgment; however, a full verification process is required in order to validate the simulation engine developed. The data is not available for this verification, and thus detailed verification is not within the scope of this thesis. Preliminary Verification The prediction of hurricane damage using a component based approach, such as the Low R ise Commercial Residential Hurricane Loss Projection Model, is a viable and flexible method that allows new data (e.g. laboratory test results on capacities) to be easily incorporated. The scope of the work in this thesis is to develop the logic and algori thms that incorporate varying building geometries, surrounding terrain effects, load scenarios, and interactions among various building components. However, the algorithm and the results must be validated with available damage data. This data can be obtain ed from hurricane damage reports or from insurance claims. Goals of the Florida Public Hurricane Loss Model are to compare the models output to insurance claims data as soon as it becomes available and to calibrate the model as necessary. Comparison of the models monetary losses to insured losses from insurance claims will contribute to the validation of the model. The physical damage obtained by the component based approach must be compared with the damage reports that provide detailed damage to complete the validation process. Thus, so far engineering judgment has been applied to verify that the shape and location of the damage curves are reasonable, as di scussed in the previous section.

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90 The next chapter discusses the Mid High Rise Commercial Residential Hurricane Loss Projection Model.

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91 CHAPTER 5 MID HIGH RISE COMMER CIAL RESIDENTIAL MOD EL PERFORMANCE Overview Various similarities exist between the mid high rise and low rise commercial residential model s. The main differences are the use of a modular approach, the components within the model, and the use of two basic floor plans in the mid high rise model. As mentioned in Chapter 3, the high level of variability among mid high rise buildings (due to the com bination of the number of stories, number of units per floor, intentionally unique geometries, and exterior materials) renders the application of a standard model unfeasible. As a result the mid high rise model uses a modular approach and models individual units instead of the structure as a whole. Middle and corner units are modeled in the two basic floor plans (i.e. interior and exterior stairway) described in Chapter 3. The construction techniques and materials used in mid high rise buildings result in relatively low damage to the superstructure and exterior surfaces during hurricanes. The majority of damage occurs as a result of water penetration and loss of openings, thus, only glazing components (windows and doors) are modeled (Weekes, Balderrama, Gurley, Pinelli, Pita, & Hamid, 2009) This chapter discusses the probability based engineering vulnerability model developed to predict damage for mid high rise commercial residential buildings. Details regarding the programs a rchitecture, solution process, key features, assumptions, modeling algorithm for the different variables, analysis, results, and preliminary verification are provided in this chapter. Concepts common to the low rise and mid high rise models that have been discussed in Chapter 4 will not be repeated in this chapter

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92 Program Architecture and Solution Process The mid high rise commercial residential damage model is a Monte Carlo Simulation engine that calculates wind loads, impact loads, and glazing component resistance values and simulates the performance and interaction of these components in mid high rise commercial residential buildings during hurricane winds. The components of the algorithm used by the Mid High Rise Commercial Residential Model can be grou p ed in four distinct categories: 1) model and analysis definition, 2) modeling the building, its components, and wind loads 3) analyzing the building and determining the damage and 4) processing the damage to verify the results These four phases, origin ally comprising the core of the Low Rise Commercial Residential Model, underwent the necessary modific ations to ensure their applicability to the Mid High Rise Commercial Residential Model. Model and Analysis Definition Phase The interface between the program user and the simulation engine occurs through the model and analysis definition. The same alternatives available for execution of the Low Rise Model (the batching mode and the default mode) are also featured in the Mid Hig h Rise Model. The features of each alternative have been discussed in Chapter 4. Inputs pertaining to the extent of the analysis, the physical characteristics of the building, the environmental exposure, and the damage mitigation strategies are all defined by the user at this stage. Options for Model Descriptors The mid high rise commercial residential model was developed as a flexible computer tool that would allow the user to analyze different types of buildings and would provide the developer with an eas y route within the code for updating as modeling concepts evolve Flexible features available in the program allow the user to define the buildings physical characteristics,

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93 mitigation strategies environmental exposure, and extent of analysis. The altern atives the program offers for the different input variables are summarize d in Table 5 1 Table 51. Mid high rise model descriptors Mid High Rise Commercial Residential Model Alternatives Mid High Rise Building Physical Characteristics Building Type = Exterior Stairway or Interior Stairway Unit Type = Middle or Corner Unit Exterior Length = Any Unit Interior Width = Any Mitigation Strategies Shutter Protection = None, Plywood, Steel, or Engineered Glazing Type = Normal, Laminated, or Impact Resistant Glass Environmental Exposure Missile Exposure Type = Urban, Suburban, or Open Extent of Analysis Number of Simulations = Depends on Computer Capacity Restrictions Assumptions and simplifications made throughout the development of the model restrict, to a certain degree, the variability of some of th e model descriptor parameters i dentified in Table 51. Layouts currently offered in the model are exterior stairway and interior stairway. Each building type is composed of several individual units and common areas. Two types of individual units ( middle and corner units) exist for each type of building. Details regar ding the characteristics of the building and unit types were described in Chapter 3. The model permits any unit sizes, provided that the building remains rectangular in shape. However, t he total number of units per story is restricted to three in exterior stairway buildings and to eight in interior stairw ay buildings. Unlike the low rise model, the mid high rise model does not currently offer variable construction qualities Construction quality is not a basic model descriptor for the mid high rise model However, the user c an mo dify the sizes of the individual glazing/opening components,

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94 their capacities and coefficients of variation, and the percentage of the surface area covered by glazing for the exter ior walls of each floor. The definition of the building physical characteristics, mitigation strategie s, environmental exposure, and extent of analysis with the alternatives outlined in Table 51 concludes the extent of analysis and model definition phase. The basic pa rameters defined during this stage are loaded into the next component of the program in order to create and analyze the building. These parameters are also used to organize and identify the output files upon conclusion of the analyses. Model ing the Building, its Components, and Wind Loads This phase of the program creates different types of units for mid high rise commercial residential building models, determines their glazing component capacities, the loads resulting from hurricane winds and debris impact and analyzes the damage resulting from their interaction. This phase of the algorithm is describ ed by the same three nested loops that comprise this phase in the low rise model ( See Figure 41) The approach direction of the wind and the maximum 3 second gust wind speeds are simulated by the two outer loops, while multiple reconstructions of the unit model assignation of loads, and documentation of damage occur within the inner loop. The inner loop simulates individual units defined by the parameters loaded from the model and analysis definition phase The wind approach directions loop iterates through eight angles of incidence and the wind speeds loop can iterat e through any range of wind speeds currently the range is set from 50 mph to 250 mph peak 3 second gusts in 5 mph increments. A flowchart depicting the model ing and analysis components of the program is shown in Fig ure 5 1.

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95 Figure 51. Mid high rise commercial residential model algorithm Mapping of Components Upon loading the analysis parameters and prior to the simulation of the loads the program maps the location of the modeled glaz ing components to matrix spaces providing the necessary framework to analyze the interaction between wind and impact loads and glazing components. The main factor affect ing the mapping matrices for glazing components is the percentage of exterior wall area covered by glazing. The number of windows in the exterior wall faces of each unit is a function of the amount of available glaz ing area for each unit after the entry and

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96 sliding doors have been installed on their corresponding walls. Entry doors and sliding doors are located far from the units corners they occupy the area defined as pressure zone 4 by the ASCE 7 05 standard. A mi nimum clear distance between the corner of the building and the closest windows, currently set to 6 feet, defines the location of the windows closest to the buildings corner. The remaining windows on each side are spaced evenly. Locations of windows in the exterior wall faces are associated to particular entries of mapping matrices. The model uses these locations to determine the proportions of window area occupying the ASCE 705 pressure zones 4 and 5. These mapping matrices are also used to locate the gl azing components, assign and keep track of their capacities and loads, and identify the damage resulting from their interaction. Capacity Modeling The resistances of glazing components are represented within a probabilistic framework, and require a mean an d coefficient of variation for the component pressure capacities. Mean pressure capacities for glazing components and their coefficients of variation are predefined inputs. The current values ( Table 52) were assigned with the purpose of verifying the performance of the program and are based on engineering judgment, on values obtained from manufacturer data (PGT Industries), and on values used in the si ngle family residential and low rise commercial residential models. The values shown in Table 52 can be modified by any user or modeler to simulate di fferent qualities of construction. The actual resistance to a given component in a single simulation is randomly assigned based on the mean and coefficient of variation, and stored in a matrix entry mapping the physical location of the component. This proc edure is identical to that explained in Chapter 4; the truncated Gaussian distributionat two standard deviations from the meanis also the default probability model for glazing components.

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97 Table 52. Pressure capacities and coefficients of variation for glazing components Pressure Capacities (psf) and Coefficients of Variation for Glazing Components in the Building Envelope Component Mean, C v Windows 100 0.2 Sliding Doors 150 0.2 Entry Doors 150 0.2 Mid high rise commercial residential buildings commonly use impact resistant glazing components with aluminum frames (sample capacities from PGT Industries are shown in Table 53). However, glazing components vary in shape, size, and material; thus, manufacturer data for capacity values is considerably widespread. Therefore, further investigation regarding mean capaci ties and coefficients of variation for windows, sliding doors, and entry doors representative of those used in mid high rise commercial residential buildings in Florida is required to obtain more accurate results. Table 53. Manufacturer data for capacities of glazing components commonly used in mid high rise commercial residential buildings (PGT Industries) Sample Glazing Capacities (psf) Type Model Test Pressure (psf) Window PW820 135 Sliding Door SGD3030 180 Entry Door ST3550 150 The procedure for modeling glazing components resistance to impact of the mid high rise model is the algorithm used by the low rise model. The same correction factors that account for mitigation measures in the low rise model are also applied to the impact capacity of mid high rise buildings. In order to calculate the damage sustained by individual components, the model must analyze the interaction of the co mponents capacities and loads.

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98 Loading Model Glazing co mponents modeled for mid high rise commercial residential buildings are subjected to wind loads and debris impact loads. The procedures for determining the wind and impact loads for the glazing components are identical to those outlined in Chapter 4 for th e low rise model. In the mid high rise model loads are calculated for glazing components on each face of the individual units, thus vulnerability matrices for the components on each unit face are defined based on the direction of the approaching wind. Figure 5 2 and Figure 53 illustrate the different directions of wind approach modeled for buildings with exterior and interior stairways, respectively. Wind approach directions 2, 4, 6, and 8 simulate quartering winds, directions 1 and 5 model head and tail winds, respectively, and directions 3 and 7 simulate flank winds. Figure 52. Simulated wind approach direction for a building with an exterior corridor

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99 Figure 53. Simulated wind approach direc tion for a building with an interior corridor Components located on the windward walls are vulnerable to positive external pressures and debris impact, while components on the side and leeward walls are only vulnerable to suction pressures. Table 54, Table 55, Table 56 and Table 57 summarize the vulnerability of components on each of the units exterior wall faces. A 1 denotes vulnerability to suction pressures, a 0 denotes no vulnerability, and a 1 denotes vulnerabili ty to d ebris impact or pressure loads. A value of zero in the vulnerability matrix of a particular component zeros out the corresponding loads for that component and wind direction; thus the component will not be affected by those loads.

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100 Table 54. Pressure vulnerability matrix for a building with an interior stairway Interior Stairway Pressure Vulnerability Wind Direction Corner Unit Middle Unit Entry Door Sliding Door Windward Windows Side Windows Entry Door Sliding Door Windward Windows 1 0 1 1 1 0 1 1 2 0 1 1 1 0 1 1 3 0 1 1 1 0 1 1 4 0 1 1 1 0 1 1 5 0 1 1 1 0 1 1 6 0 1 1 1 0 1 1 7 0 1 1 1 0 1 1 8 0 1 1 1 0 1 1 Table 55. Impact vulnerability matrix for a building with an interior stairway Interior Stairway Impact Vulnerability Wind Direction Corner Unit Middle Unit Entry Door Sliding Door Windward Windows Side Windows Entry Door Sliding Door Windward Windows 1 0 1 1 0 0 1 1 2 0 1 1 1 0 1 1 3 0 0 0 1 0 0 0 4 0 0 0 1 0 0 0 5 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 8 0 1 1 0 0 1 1 Table 56. Pressure vulnerability matrix for a building with an exterior stairway Exterior Stairway Pressure Vulnerability Wind Direction Corner Unit Middle Unit Entry Door Sliding Door Windward Windows Side Windows Leeward Windows Entry Door Sliding Door Windward Windows Leeward Windows 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1 1

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101 Table 57. Impact vulnerability matrix for a building with an exterior stairway Exterior Stairway Impact Vulnerability Wind Direction Corner Unit Middle Unit Entry Door Sliding Door Windward Windows Side Windows Leeward Windows Entry Door Sliding Door Windward Windows Leeward Windows 1 1 0 1 0 0 1 0 1 0 2 1 0 1 1 0 1 0 1 0 3 0 0 0 1 0 0 0 0 0 4 0 1 0 1 1 0 1 0 1 5 0 1 0 0 1 0 1 0 1 6 0 1 0 0 1 0 1 0 1 7 0 0 0 0 0 0 0 0 0 8 1 0 1 0 0 1 0 1 0 D amage Q uantification and P rocess and V erification of Re sults Damage to building components, resulting from the interaction of their capacities and the loads they sustain, is dete rmined by analyzing their limit states. Matrix operations are used to calculate the total damage sustained by glazing components in each of the different faces of the unit. The total damage sustained by the unit is then calculat ed by adding the damage sust ained by each face for each direction of wind approach. Unlike the low rise model, simulated mid high rise buildings are only subjected to one phase of loading for each wind speed. A single loading phase consists of subjecting all the glazing components in the unit modeled to pressure loads and exposing any component that withstood the applied pressures to potential debris impact. Limit state matrices are analyzed and damage matrices are obtained for each component. This process is repeated by reassigning r andom capacities to the unit modeled n times, producing n samples of damage for every combination of 41 wind speeds and 8 wind directions. Multidimensional damage matrices containing the total losses (for each glazing component for each simulation for each wind speedfor each wind direction) are the output of the nested loops. The damage matrices differentiate between damage due to pressure loads and damage resulting from debris impact. This informatio n is useful for the preliminary verification of the algorithm.

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102 The analysis output damage matrix file consists of a header containing metadata (building type, unit type, dimensions, etc.) and a multidimensional array containing the physical exterior damag e of every glazing component in every simulated unit for every wind speed and every angle of incidence. The information included in the outputs damage matrix is summarized in the following: Number of w indow s damage d due to pressure loading Number of entry doors damaged due to pressure loading Number of sliding doors damaged due to pressure loading Number of windows damaged due to debris impact Number of entry doors damaged due to debris impact Number of sliding doors damaged due to debris impact The damage information contained in this matrix is the data used by engineering vulnerability modelers at FIT to predict interior losses due to water intrusion T his information needs to be processed if the user desires to interpret or check the individual results of this module for model refinement The last component of the program, a plotting function, processes the output and produces graphical representations of statistical averages of the damage obtained in the analysis. This component also analyzes t he data generated by the missile model; it provides graphs for the missile models parameters and for the reliability and vulnerability of the glazing components. The following section presents preliminary results focusing on the damage for the glazing com ponents; full results including reliability and damage probabi lity graphs are presented in Appendix B and Appendix C Examples of Simulation Results Results presented in this section represent the vulnerability of four basic sample mid high rise commercial residential building models obtained using the Monte Carlo Simulation engine described in this chapter The sample model s analyzed are described in Table 58. All models

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103 have 30% of their exposed wall areas covered by glazing components. Comparative graphs of mean damage summarize the results in this section. Damage is presented as the total number of components dama ged for all glazing components. Table 58. Mid high rise sample models analyzed Characteristic Model 1 Model 2 Model 3 Model 4 Density Suburban Suburban Suburban Suburban Building type Exterior Stairway Interior Stairway Exterior Stairway Interior Stairway Unit location Middle Middle Corner Corner Shutter protection None None None None Glass type Normal Glass Normal Glass Normal Glass Normal Glass Unit interior width 30 ft 30 ft 30 ft 30 ft Unit exterior length 60 ft 60 ft 60 ft 60 ft No. of windows 21 8 29 16 Window dimensions 4 ft. x 3 ft. 4 ft. x 3 ft. 4 ft. x 3 ft. 4 ft. x 3 ft. Entry door dimensions 4 ft. x 7 ft. 4 ft. x 7 ft. 4 ft. x 7 ft. 4 ft. x 7 ft. Sliding door dimensions 12 ft. x 7 ft. 12 ft. x 7 ft. 12 ft. x 7 ft. 12 ft. x 7 ft. Sample of Preliminary Results Mean levels of damage for glazing components of all the models analyzed ( Table 58 ) are presented and compared in this section. Figure 5 4, Figure 5 5, Figure 5 6, and Figure 5 7 illustrate the damage sustained by wind ows for the models defined in Table 58. Figure 5 8, Figure 5 9, Figure 5 10, and Figure 5 11 depict the damage sustained by entry doors, and the curves illustrated in Figure 5 12, Figure 5 13, Figure 514, and Figure 5 15 represent the damage sustained by sliding doors. The shapes of all damage curves are as expected, i.e. sigmoid shapes for total damage and pressure damage, and bell shapes for impact damage. Pressure damage has a higher hierarchical order of operations in the damage assessment process; thus, at high wind speeds when pressures are strong enough to cause damage, glazing components that could potentially have been damaged by debris impact are instead assigned a causation of pressure. A decrease in the damage due to impact, reflected by the bell shape of the debris impact damage curve, is the outcome of the higher hierarchical order of pressure over impact damage. The

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104 damage curves depicted in Figure 5 4, Figure 5 5, Figure 5 6, and Figure 5 7 reflect the vulnerability of the windows to impact and pressure loads as delineated in Table 54, Table 55, Table 56, and Table 57. Pressure damage is sustained for all directions of the wind approach, while impact damage is only experienced when the windows lie directly in the winds path. Figure 54. Comparative window damage for a middle unit in a building with an exterior corridor Figure 55. Comparative window damage for a middle unit in a building with an interior cor ridor 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 20 Window Damage Comparisson for a Middle Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Windows Damaged 14-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 1 2 3 4 5 6 7 8 Window Damage Comparisson for a Middle Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Windows Damaged 15-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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105 Figure 56. Comparative window damage for a corner unit in a building with an exterior corridor Figure 57. Comparative window damage for a corner unit in a building with an interior corridor The entry door damage curves depicted in Figure 58, Figure 5 9, Figure 510, and Figure 511 reflect the vulnerability of entry doors to impact and pressure loads expected; the curves are in accordance with the vulnerability matrices defined in Table 54, Table 5 5, Table 56, and Table 57. Entry doors for units in buildings with interior stairways are not exposed to the outside environment, thus, they do not experience any load; these components are expected to 50 100 150 200 250 0 5 10 15 20 25 Window Damage Comparisson for a Corner Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Windows Damaged 14-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 2 4 6 8 10 12 14 16 Window Damage Comparisson for a Corner Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Windows Damaged 15-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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106 sustain zer o damage. Entry doors for middle and corner units of buildings with exterior stairway are equally vulnerable to pressure loads and debris impact, thus they are expected to portray similar results. Pressure damage is sustained for all directions of the wind approach by entry doors in buildings with exterior stairways. Figure 58. Comparative entry door damage for a middle unit in a building with an exterior corridor Figure 59. Comparative entry door damage for a middle unit in a building with an interior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entry Door Damage Comparisson for a Middle Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Entry Doors Damaged 14-Jul-2009 Output 1000 simulations Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entry Door Damage Comparisson for a Middle Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Entry Doors Damaged 15-Jul-2009 Output 1000 simulations Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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107 Figure 510. Comparative entry door damage for a corner unit in a building with an exterior corrido r Figure 511. Comparative entry door damage for a corner unit in a building with an interior corridor The susceptibility of sliding doors to debris impact is greater than that of entry doors simply due to the larger size of sliding doors. Thus, sliding doors are expected to sustain more damage due to impact than entry doors. The damage to sliding doors, il lustrated in Figure 512, 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entry Door Damage Comparisson for a Corner Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Entry Doors Damaged 14-Jul-2009 Output 1000 simulations Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entry Door Damage Comparisson for a Corner Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Entry Doors Damaged 15-Jul-2009 Output 1000 simulations Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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108 Figure 513, Figure 514, and Figure 515, is in accordance with the vulnerability of sliding door s to impact and pressure loads. Figure 512. Comparative sliding door damage for a middle unit in a building with an exterior corridor Figure 513. Comparative sliding door damage for a m iddle unit in a building with an interior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sliding Door Damage Comparisson for a Middle Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Sliding Doors Damaged 14-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sliding Door Damage Comparisson for a Middle Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Sliding Doors Damaged 15-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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109 Figure 514. Comparative sliding door damage for a corner unit in a building with an exterior corridor Figure 515. Comparative sliding door damage for a corner unit in a building with an interior corridor A comparison between the damage levels sustained by units in buildings with interior and exterior corridors reveals a higher vulnerabi lity of windows and sliding doors for units in buildings with interior corridors. When calculating the total number of available missile objects 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sliding Door Damage Comparisson for a Corner Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Sliding Doors Damaged 14-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sliding Door Damage Comparisson for a Corner Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Sliding Doors Damaged 15-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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110 (roof shingles), the model assumes that the buildings in the surrounding areas are identical to the analyzed bu ilding. The interior corridor building modeled is larger than the exterior corridor building, thus the total number of available missile objects affecting the unit is larger for interior corridor buildings than for exterior corridor buildings This result s in a higher vulnerability of windows and sliding doors in exterior corridor buildings. In terms of trends the results summarized in this section appear to be in accordance with good engineering judgment; however, in terms of nominal results the damage to entry and sliding doors due to impact is too high at low wind speeds. The missile model assumes that windborne debris is just as likely to break an entry or sliding door as a window; that is, the threshold momentum used to determine the missile model para meter D for all components is the same. This is not necessarily true; more energy is required to break entry and sliding doors because they are usually made of stronger materials, such as tempered glass. Furthermore, the glazing pressure capacity values sh own in Table 5 2 and used to obtain the results summarized in this section were selected merely to verify expected trends. Table 59 and Table 510 compare the models current pressure and impact capacity values to those obtained from PGT Industries (a window and door manufacturer). Table 59. Pressure and impact capacities in m odel Glazing Capacities (psf) Currently in Mid High Rise Model Type Size Pressure (psf) Momentum Threshold Window 4' x 3' 100 62 kg m/sec Sliding Door 12' x 7' 150 62 kg m/sec Entry Door 4' x 7' 150 62 kg m/sec Table 510. Pressure and impact cap acities from a manufacturer ( www.pgtindustries.com/ ) Manufacturer (PGT Industries) Sample Glazing Capacities (psf) Type Model Test Pressure (psf) Missile Test Momentum Threshold Window PW820 135 9 lb @ 50 ft/s 450 lb ft./sec = 62 kg m/sec Sliding Door SGD3030 180 9 lb @ 50 ft/s 450 lb ft./sec = 62 kg m/sec Entry Door ST3550 150 9 lb @ 50 ft/s 450 lb ft./sec = 62 kg m/sec

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111 The high vulnerability of doors to debris and the discrepancy between glazing capacity values currently in the model and those of commercially available windows and doors render necessary a detailed study to determine realistic capacity values for these compon ents. The next section provides preliminary verification for the missile model and delineates the steps required to achieve full verification of the complete model. Preliminary Verification The procedures used to predict hurricane damage for low rise and mid high rise commercial residential buildings are very similar. Thus, the steps required to verify the models are very similar. Damage reports and insurance claims data are also necessary to validate the mid high rise model; neither is currently available. Most hurricane damage prediction models are proprietary models and results may not necessarily be released to the public, thus comparison of results with other models is not always possible However, other steps can be taken to partially verify the model, such as verification of results based on good engineering judgment. Simple checks can be incorporated into the model to determine if the results are logical. The mid high rise model has a f eature that zeros the pressure loads in order to check the missile model results. The reliability and damage probability for a single window in the front side of a middle unit in a building with an exterior stairway are depicted in Fi gure 516. These curves were obtained executing the mid high rise model with the missile check feature enabled. A front side window is only vulnerable to impact for three directions of wind approach, as illustrated. The models algorithm and the results obtained appear to be reasonable. Further validation of the model can be accomplished through comparison of the results with actual hurricane damage reports and insurance claims data analysis (not within the scope of this thesis) The release of a fully verified and validated public model could lead to constructive criticism that would help improve the model. Moreover, the release of the model might reveal many potential

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112 uses that had not been initially considered by the developers. C oncluding remarks and recommendations for future research are discussed in the next chapter. Figure 516. Reliability and damage probability for a missile check analysis 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for a Front Side Window for a Middle Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Only Missile Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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113 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS The multiuniversity Florida Public Hurricane Loss Model (FPHLM) is a component based public model that predicts aggregate hurricane damage. The Lo w Rise and Mid High Rise Commercial Residential Hurricane Loss Projection Models are two of the components of the FPHLM. This thesis presented the contributions of the engineering team at the University of Florida to the development of the engineering component of the commercial residential models. Concluding remarks regarding the delegation of different work to different students during the development of the model, potent ial uses for the output, and recommendations to improve the model are discussed in th is chapter. Delegation of Responsibilities The completion of the major components of the FPHLM was assigned to different universities. The engineering team at the University of Florida divided the project in two phases (the low rise model and the mid high rise model) and delegated its responsibilities to the different students involved. The development of the low rise model was initially accomplished through group work and as the project developed, responsibilities were defined for the different students. D efinition of a general solution process, a main driver, and the hierarchical order of operations for the building components, as well as the establishment of the necessary inputs and outputs for individual modules were completed through group work. Individual modules executed by functions within the main driver were developed by different students. A well defined general solution process was imperative to the functionality of the end product because it ensured compatibility of the individual modules compris ing the model.

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114 The prior exposure to the low rise model eased the development of the mid high rise model. This phase was completed through group work, for the most part; very few of the responsibilities were delegated to individual students. Constant communication between the students through daily meetings enabled the solution of any compatibility issues within the codes. Compatibility between the engineering model completed at UF and those developed at other universities must also exist in order for the w hole FPHLM to function. Uses for the resulting output are discussed in the next section. Potential Uses for the Output The main goal of the Florida Public Hurricane Loss Model (FPHLM) is to predict aggregate hurricane wind damage to collections of similar structures The final output of this model and the intermediate results of its components are applicable in several scenarios. Data generated by the FPHLM and its components could be useful for insurance companies, independent contractors, landlords and homeowners, students, etc. Physical damage results obtained from the engineering component could be used to assess the integrity of commercial/residential buildings and to determine what kind of retrofits would reduce the building vulnerability most effectively during an extreme wind event Replacement costs generated by the cost estimate model under development at FIT could be used by homeowners or contractors. Insurance companies could use the results to predict insurance risk on an annualized basis and asses their insurance rates. User Input of Generic Parameters The most common features of the building stock in the state of Florida are used to create a flexible model that will be able to predict aggr egate hurricane losses. A flexible model would al low the users to input any kind of building and the results would predict losses for that building. Efforts were made to create a flexible commercial residential model and the goals

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115 defined throughout the project were fulfilled; however the model contains many constraining assumptions Generic user defined parameters include the total number of stories, the building dimensions, and the construction quality. Assumptions for the development of the model create further restrictions to the building, such as a r ectangular floor plan. As the current understanding of wind structure interaction increases along with computing power, developing a model with less geometric constraints is feasible Ideally, the engineering component of this model would simulate the inte raction of both structural and nonstructural elements with different types of environmental loads for any given user input building. The complication of modeling any kind of building could be resolved by developing a graphical input window through which t he user could draw every component of the structure and enter material properties, similar to those used by commercial structural analysis programs. The range of applicability of such a model would be very widespread, including structural and architectural design aids and damage predictions to particular types of buildings or to the general building stock. Recommendations to Improve the Current Model I mprovements to the model could improve its overall performance. The addition of a graphical user interface would increase the user friendliness of the program and allow anyone to use the model. Implementation of a simple graphical user interface can be realized through MatLA B Removal of the wind speeds loop would result in a more efficient computer code and co uld be followed by the addition of the time stepping model. Three dimensionalizing the capacity and load matrices so that the first and second dimensions map the component to its physical location and the third dimension models the current velocity, would render the wind speeds loop obsolete. A simple form of time stepping, in which a predefined input determined the number of times the building would be subjected to the same mean wind speed, was

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116 implemented to the current low rise model; however, an accurat e time stepping model would need to account for the duration of the storm and its sustained winds. Studies to validate the results currently produced by the commercial residential models are the highest priority. However, the field data (observed damage fr om real hurricanes) and claims data (monetary losses on a per building le vel) required for such a validation study are not easily accessible. This is an ongoing effort.

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117 APPENDIX A PRELIMINARY RESULTS FOR LOW RISE BUILDIN GS This appendix contains figures representing simulated damage to building components modeled by the Low Rise Commercial Residential Construction Loss Projection Model. Development of this model is not complete yet; thus, the results presented are preliminar y. Two models were analyzed, a gabled roof building and a hipped roof building; details regarding the models are outlined in each section. Low Rise Model with a Gable Roof Table A 1. MatLAB generated h eader describing the gable roofed low rise building analyzed Header = 'LengthFLR' '80 ft' 'WidthFLR' '40 ft' 'Units Per Floor' '3' 'Number of Windows' '66' 'Slope of Roof' '6/12' 'Roof Type' 'Gable' 'Shutter Protection' 'None' 'No. of Stories' '3' 'Con. Quality' 'Medium' 'Window Dim.' '4 ft x5 ft' 'Entry Door Dim.' '4 ft x8 ft' 'SL Door Dim.' '8 ft x8 ft' 'Overhang Length' '2 ft' 'Truss Spacing' '2 ft' 'Overhang Sheathing' '42' 'Overhang Sheathing' '90'

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118 Figure A 1. Gable end/truss damage for a 3 story gable roofed medium quality building Figure A 2. Roof to wall connection damage for a 3 story gable roofed medium quality building 50 100 150 200 250 0 2 4 6 8 10 12 Gable End/Truss Damage for a 3 Story Gable Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Trusses Damaged 25-Jul-2009 Output 1000 simulations Side 1 Gable End/Trusses Side 2 Gable End/Trusses 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Roof to Wall Connection Damage for a 3 Story Gable Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 25-Jul-2009 Output 1000 simulations Roof to Wall Connections

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119 Figur e A 3. Roof sheathing/cover damage for a 3 story gable roofed medium quality building Figure A 4. Roof/wall sheathing damage for a 3 story gable roofed medium quality building 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Roof Sheathing/Cover Damage for a 3 Story Gable Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 25-Jul-2009 Output 1000 simulations Roof Cover Edge Roof Sheathing Field Roof Sheathing 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Roof/Wall Sheathing Damage for a 3 Story Gable Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 25-Jul-2009 Output 1000 simulations 1s t Floor Wall Sheathing 2n d Floor Wall Sheathing 3r d Floor Wall Sheathing Gable End Wall Sheathing Edge Roof Sheathing Field Roof Sheathing

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120 Figure A 5. Wall sheathing/cover damage for a 3 story gable roofed medium quality building Figure A 6. Window damage for a 3 story gable roofed medium quality building 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Wall Sheathing/Cover Damage for a 3 Story Gable Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 25-Jul-2009 Output 1000 simulations 1s t Floor Wall Cover 1s t Floor Wall Sheathing 2n d Floor Wall Cover 2n d Floor Wall Sheathing 3r d Floor Wall Cover 3r d Floor Wall Sheathing Gable End Wall Cover Gable End Wall Sheathing 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 20 22 Window Damage for a 3 Story Gable Roofed Medium Building (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Windows Damaged 25-Jul-2009 Output 1000 simulations Normal Windows Shutters = None 1s t Floor Pressure 1s t Floor Impact 1s t Floor Total 2n d Floor Pressure 2n d Floor Impact 2n d Floor Total 3r d Floor Pressure 3r d Floor Impact 3r d Floor Total

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121 Figure A 7. Sliding door damage for a 3 story gable roofed medium quality building Figure A 8. Entry door damage for a 3 story gable roofed medium quality building 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3 Sliding Door Damage for a 3 Story Gable Roofed Medium Building (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Sliding Doors Damaged 25-Jul-2009 Output 1000 simulations Normal Windows Shutters = None 1s t Floor Pressure 1s t Floor Impact 1s t Floor Total 2n d Floor Pressure 2n d Floor Impact 2n d Floor Total 3r d Floor Pressure 3r d Floor Impact 3r d Floor Total 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3 Entry Door Damage for a 3 Story Gable Roofed Medium Building (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Entry Doors Damaged 25-Jul-2009 Output 1000 simulations 1s t Floor Pressure 1s t Floor Impact 1s t Floor Total 2n d Floor Pressure 2n d Floor Impact 2n d Floor Total 3r d Floor Pressure 3r d Floor Impact 3r d Floor Total

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122 Low Rise Model with a Hip Roof Table A 2. MatLAB generated h eader describing the hip roofed low rise building analyzed Header = 'LengthFLR' '80 ft' 'WidthFLR' '40 ft' 'Units Per Floor' '3' 'Number of Windows' '66' 'Slope of Roof' '6/12' 'Roof Type' 'Hip' 'Shutter Protection' 'None' 'No. of Stories' '3' 'Con. Quality' 'Medium' 'Window Dim.' '4 ft x5 ft' 'Entry Door Dim.' '4 ft x8 ft' 'SL Door Dim.' '8 ft x8 ft' 'Overhang Length' '2 ft' 'Truss Spacing' '2 ft' 'Overhang Sheathing' '34' 'Overhang Sheathing' '110' Figure A 9. Gable end/truss damage for a 3 story hip roofed medium quality building 50 100 150 200 250 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Gable End/Truss Damage for a 3 Story Hip Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Trusses Damaged 25-Jul-2009 Output 1000 simulations Side 1 Gable End/Trusses Side 2 Gable End/Trusses

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123 Figure A 10. Roof to wall connection damage for a 3 story hip roofed medium quality building Figure A 11. Roof sheathing/cover damage for a 3 story hip roofed medium quality building 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Roof to Wall Connection Damage for a 3 Story Hip Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 25-Jul-2009 Output 1000 simulations Roof to Wall Connections 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Roof Sheathing/Cover Damage for a 3 Story Hip Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 25-Jul-2009 Output 1000 simulations Roof Cover Edge Roof Sheathing Field Roof Sheathing

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124 Figure A 12. Roof/wall sheathing damage for a 3 story hip roofed medium quality building Figure A 13. Wall sheathing/cover damage for a 3 story hip roofed medium quality building 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Roof/Wall Sheathing Damage for a 3 Story Hip Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 25-Jul-2009 Output 1000 simulations 1s t Floor Wall Sheathing 2n d Floor Wall Sheathing 3r d Floor Wall Sheathing Gable End Wall Sheathing Edge Roof Sheathing Field Roof Sheathing 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 Wall Sheathing/Cover Damage for a 3 Story Hip Roofed Medium Building. Average 3-second Gust Wind Speed at a 10 meter height (mph)Percent Damage (%) 25-Jul-2009 Output 1000 simulations 1s t Floor Wall Cover 1s t Floor Wall Sheathing 2n d Floor Wall Cover 2n d Floor Wall Sheathing 3r d Floor Wall Cover 3r d Floor Wall Sheathing Gable End Wall Cover Gable End Wall Sheathing

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125 Figure A 14. Window damage for a 3 story hip roofed medium quality building Figure A 15. Sliding door damage for a 3 story hip roofed medium quality building 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 20 22 Window Damage for a 3 Story Hip Roofed Medium Building (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Windows Damaged 25-Jul-2009 Output 1000 simulations Normal Windows Shutters = None 1s t Floor Pressure 1s t Floor Impact 1s t Floor Total 2n d Floor Pressure 2n d Floor Impact 2n d Floor Total 3r d Floor Pressure 3r d Floor Impact 3r d Floor Total 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3 Sliding Door Damage for a 3 Story Hip Roofed Medium Building (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Sliding Doors Damaged 25-Jul-2009 Output 1000 simulations Normal Windows Shutters = None 1s t Floor Pressure 1s t Floor Impact 1s t Floor Total 2n d Floor Pressure 2n d Floor Impact 2n d Floor Total 3r d Floor Pressure 3r d Floor Impact 3r d Floor Total

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126 Figure A 16. Entry door damage for a 3 story hip roofed medium quality building 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3 Entry Door Damage for a 3 Story Hip Roofed Medium Building (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Number of Entry Doors Damaged 25-Jul-2009 Output 1000 simulations 1s t Floor Pressure 1s t Floor Impact 1s t Floor Total 2n d Floor Pressure 2n d Floor Impact 2n d Floor Total 3r d Floor Pressure 3r d Floor Impact 3r d Floor Total

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127 APPENDIX B PRELIMINARY RESULTS FOR MID HIGH RISE BU ILDINGS This appendix contains figures representing simulated damage to building components modeled by the Mid High Rise Commercial Res idential Construction Loss Projection Model. Development of this model is not complete yet; thus, the results presented are preliminary. Middle Unit in a Building with an Exterior Corridor Table B 1. MatLAB ge nerated h eader describing the exterior corridor buildings middle unit analyzed Header = 'Density' 'Suburban' 'Bu i lding Type' 'Exterior Stairway' 'Unit Location' 'Middle' 'Shutter Protection' None 'Glass Type' 'Normal Glass' 'Unit interior width' '30 ft' 'Unit ext. length' '60 ft' '# of Windows' '21' 'Window Dim.' '4 ft. x 3 ft.' 'Entry Door Dim.' '4 ft. x 7 ft.' 'Sliding Door Dim.' '12 ft. x 7 ft.' Figure B 1. Comparative window damage for a middle unit in a building with an exterior corridor 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 20 Window Damage Comparisson for a Middle Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Windows Damaged 17-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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128 Figure B 2. Comparative entry door damage for a middle unit in a building with an exterior corridor Figure B 3. Comparative sliding door damage for a middle unit in a building with an exterior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entry Door Damage Comparisson for a Middle Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Entry Doors Damaged 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sliding Door Damage Comparisson for a Middle Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Sliding Doors Damaged 17-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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129 Figure B 4. Combined reliability/damage probability from impact for all windows in a middle unit in a building with an exterior corridor Figure B 5. Combined reliability/damage probability from impact for one window i n a middle unit in a building with an exterior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for All Windows for a Middle Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for a Front Side Window for a Middle Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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130 Figure B 6. Combined reliability/damage probability from impact for the entry door in a middle unit in a building with an exterior corridor Figure B 7. Combined reliability/damage probability from impact for the sliding door in a middle unit in a building with an exterior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for Entry Door for a Middle Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for Sliding Door for a Middle Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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131 Corner Unit in a Building with an Exterior Corridor Table B 2. MatLAB generated h eader describing the exterior corridor buildings corner unit analyzed Header = 'Density' 'Suburban' 'Bu i lding Type' 'Exterior Stairway' 'Unit Location' 'Corner' 'Shutter Protection' None 'Glass Type' 'Normal Glass' 'Unit interior width' '30 ft' 'Unit ext. length' '60 ft' '# of Windows' '29' 'Window Dim.' '4 ft. x 3 ft.' 'Entry Door Dim.' '4 ft. x 7 ft.' 'Sliding Door Dim.' '12 ft. x 7 ft.' Figure B 8. Comparative window damage for a corner unit in a building with an exterior corridor 50 100 150 200 250 0 5 10 15 20 25 Window Damage Comparisson for a Corner Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Windows Damaged 17-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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132 Figure B 9. Comparative entry door damage for a corner unit in a building with an exterior corridor Figure B 10. Comparative sliding door damage for a corner unit in a building with an exterior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entry Door Damage Comparisson for a Corner Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Entry Doors Damaged 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sliding Door Damage Comparisson for a Corner Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Sliding Doors Damaged 17-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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133 Figure B 11. Combined reliability/damage probability from impact for all windows in a corner unit in a building with an exterior corridor Figure B 12. Combined reliability/damage probability from impact for one window in a corner unit in a building with an exterior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for All Windows for a Corner Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for a Front Side Window for a Corner Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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134 Figure B 13. Combined reliability/damage probability from impact for the entry door in a corner unit in a building with an exterior corridor Figure B 14. Combined reliability/damage probability from impact for the sliding door in a corner unit in a building with an exterior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for Entry Door for a Corner Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for Sliding Door for a Corner Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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135 Middle Unit in a Building with an Interior Corridor Table B 3. MatLAB generated h eader describing the interior corridor buildings middle unit analyzed Header = 'Density' 'Suburban' 'Bu i lding Type' 'Interior Stairway' 'Unit Location' 'Middle' 'Shutter Protection' None 'Glass Type' 'Normal Glass' 'Unit interior width' '30 ft' 'Unit ext. length' '60 ft' '# of Windows' '8' 'Window Dim.' '4 ft. x 3 ft.' 'Entry Door Dim.' '4 ft. x 7 ft.' 'Sliding Door Dim.' '12 ft. x 7 ft.' Figure B 15. Comparative window damage for a middle unit in a building with an interior corridor 50 100 150 200 250 0 1 2 3 4 5 6 7 8 Window Damage Comparisson for a Middle Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Windows Damaged 17-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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136 Figure B 16. Comparative entry door damage for a middle unit in a building with an interior corridor Figure B 17. Comparative sliding door damage for a middle unit in a building with an interior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entry Door Damage Comparisson for a Middle Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Entry Doors Damaged 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sliding Door Damage Comparisson for a Middle Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Sliding Doors Damaged 17-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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137 Figure B 18. Combined reliability/damage probability from impact for all windows in a middle unit in a building with an interior corridor Figure B 19. Combined reliabilit y/damage probability from impact for one window in a middle unit in a building with an interior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for All Windows for a Middle Unit in a Building with an Interior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for a Front Side Window for a Middle Unit in a Building with an Interior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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138 Figure B 20. Combined reliability/damage probability from impact for the entry door in a middle unit in a building with an interior corridor Figure B 21. Combined reliability/damage probability from impact for the sliding door in a middle unit in a building with an interior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for Entry Door for a Middle Unit in a Building with an Interior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for Sliding Door for a Middle Unit in a Building with an Interior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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139 Corner Unit in a Building with an Interior Corridor Table B 4. MatLAB generated h eader describing the interior corridor buildings corner unit analyzed Header = 'Density' 'Suburban' 'Bu i lding Type' 'Interior Stairway' 'Unit Location' 'Corner' 'Shutter Protection' None 'Glass Type' 'Normal Glass' 'Unit interior width' '30 ft' 'Unit ext. length' '60 ft' '# of Windows' '16' 'Window Dim.' '4 ft. x 3 ft.' 'Entry Door Dim.' '4 ft. x 7 ft.' 'Sliding Door Dim.' '12 ft. x 7 ft.' Figure B 22. Comparative window damage for a corner unit in a building with an interior corridor 50 100 150 200 250 0 2 4 6 8 10 12 14 16 Window Damage Comparisson for a Corner Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Windows Damaged 17-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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140 Figure B 23. Comparative entry door damage for a corner unit in a building with an interior corridor Figure B 24. Comparative sliding door damage for a corner unit in a building with an interior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entry Door Damage Comparisson for a Corner Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Entry Doors Damaged 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sliding Door Damage Comparisson for a Corner Unit in a Building with an Interior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Sliding Doors Damaged 17-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Pressure/Impact Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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141 Figure B 25. Combined reliability/damage probability from impact for all windows in a corner unit in a building with an interior corridor Figure B 26. Combined reliabilit y/damage probability from impact for one window in a corner unit in a building with an interior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for All Windows for a Corner Unit in a Building with an Interior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for a Front Side Window for a Corner Unit in a Building with an Interior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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142 Figure B 27. Combined reliability/damage probability from impact for the entry door in a corner unit in a building with an interior corridor Figure B 28. Combined reliability/damage probability from impact for the sliding door in a corner unit in a building with an interior corridor 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for Entry Door for a Corner Unit in a Building with an Interior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for Sliding Door for a Corner Unit in a Building with an Interior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Pressure/Impact Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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143 APPENDIX C MISSILE MODEL PARAME TERS AND CHECKS This appendix contains figures representing the missile model parameters described in Chapter 4 and results for a mid high rise building vulnerable only to debris impact. The missile model parameters can vary for each analysis. Although the plots shown apply to a building analyzed in a suburban area, they still illus trate the general shape of the model parameters curves. The purpose of the results shown for a building vulnerable only to debris impact is to verify that the missile model is working appropriately. Missile Model Parameters Figure C 1. Value of parameter A versus wind speed (strong shingles) 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Variable A (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Value of A 17-Jul-2009 Output 1000 simulations Direction 1 Direction 2 Direction 3 Direction 4 Direction 5 Direction 6 Direction 7 Direction 8

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144 Figure C 2. Value of parameter B versus wind speed (strong shingles) Figure C 3. Value of parameter D versus wind speed (strong shingles) 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Variable B (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Value of B 17-Jul-2009 Output 1000 simulations Direction 1 Direction 2 Direction 3 Direction 4 Direction 5 Direction 6 Direction 7 Direction 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Variable D (Suburban Area). Average 3-second Gust Wind Speed at a 10 meter height (mph)Value of D 17-Jul-2009 Output 1000 simulations Direction 1 Direction 2 Direction 3 Direction 4 Direction 5 Direction 6 Direction 7 Direction 8

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145 Missile Model Check Table C 1. MatLAB generated h eader describing the unit analyzed Header = 'Density' 'Suburban' 'Bu i lding Type' 'Exterior Stairway' 'Unit Location' 'Corner' 'Shutter Protection' None 'Glass Type' 'Normal Glass' 'Unit interior width' '30 ft' 'Unit ext. length' '60 ft' '# of Windows' '29' 'Window Dim.' '4 ft. x 3 ft.' 'Entry Door Dim.' '4 ft. x 7 ft.' 'Sliding Door Dim.' '12 ft. x 7 ft.' Figure C 4. Comparative window damage for the missile model check 50 100 150 200 250 0 5 10 15 20 25 Window Damage Comparisson for a Corner Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Windows Damaged 17-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Only Missile Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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146 Figure C 5. Comparative entry door damage for the missile model check Figure C 6. Comparative sliding door damage for the missile model check 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entry Door Damage Comparisson for a Corner Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Entry Doors Damaged 17-Jul-2009 Output 1000 simulations Only Missile Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sliding Door Damage Comparisson for a Corner Unit in a Building with an Exterior Stairway (Suburban Area). Average 3-second Gust Wind Speed at height of unit (mph)Number of Sliding Doors Damaged 17-Jul-2009 Output 1000 simulations Normal Glass Shutters = None Only Missile Model Pressure Dir. 1 Pressure Dir. 2 Pressure Dir. 3 Pressure Dir. 4 Pressure Dir. 5 Pressure Dir. 6 Pressure Dir. 7 Pressure Dir. 8 Impact Dir. 1 Impact Dir. 2 Impact Dir. 3 Impact Dir. 4 Impact Dir. 5 Impact Dir. 6 Impact Dir. 7 Impact Dir. 8 Total Dir. 1 Total Dir. 2 Total Dir. 3 Total Dir. 4 Total Dir. 5 Total Dir. 6 Total Dir. 7 Total Dir. 8

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147 Figure C 7. Combined reliability/damage probability from impact for all windows for the missile model check Figure C 8. Combined reliability/damage probability from impact for one window for the missile model check 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for All Windows for a Corner Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Only Missile Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for a Front Side Window for a Corner Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Only Missile Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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148 Figure C 9. Combined reliability/damage probability from impact for the entry door for the missile model check Figure C 10. Combined reliability/damage probab ility from impact for the sliding door for the missile model check 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for Entry Door for a Corner Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Only Missile Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reliability/Damage Probability from Impact for Sliding Door for a Corner Unit in a Building with an Exterior Stairway (Suburban Area).Average 3-second Gust Wind Speed at height of unit (mph)Probability 17-Jul-2009 Output 1000 simulations Only Missile Model Reliability Dir. 1 Reliability Dir. 2 Reliability Dir. 3 Reliability Dir. 4 Reliability Dir. 5 Reliability Dir. 6 Reliability Dir. 7 Reliability Dir. 8 Damage Probability Dir. 1 Damage Probability Dir. 2 Damage Probability Dir. 3 Damage Probability Dir. 4 Damage Probability Dir. 5 Damage Probability Dir. 6 Damage Probability Dir. 7 Damage Probability Dir. 8

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149 LIST OF REFERENCES 1. American Meteorological Society. (2000). Tornado. Retrieved February 27, 2009, from Glossary of Meteorology: http://amsglossary.allenpress.com/glossary/search?id=tornado1 2. Aponte, L. (2006). Measured Hurricane Wind Pressure On Full Scale Residential Structures: Analysis and Comparison to Wind Tunnel Studi es and ASCE 7. PhD dissertation Department of Civil and Coastal Engineering, University of Florida, Gainesville, Florida. 3. ASCE 7 05. (2005). Minimum Design Loads for Buildings and Other Structures. Reston, VA: American Society of Civil Engineers. 4. Baker, C. J. (2007). The debris flight equations. Journal of Wind Engineering and Industrial Aerodynamics 329353. 5. Brain, M., & Lamb, R. (2000, April 1). How Tornadoes Work. Retrieved February 27, 2009, from How Stuff Works: http://science.howstuffworks.com/tor nado.htm 6. Cope, A. (2004). Predicting the Vulnerability of Typical Residential Buildings to Hurricane Damage. PhD dissertation Department of Civil and Coastal Engineering, University of Florida, Gainesville, Florida. 7. Danish Wind Industry Association. (2003, June 1). Roughness and Wind Shear. Retrieved March 2, 2009, from Danish Wind Industry Association: http://www.windpower.org/en/tour/wres/shear.htm 8. Encyclopdia Britannica. (2009). Tornado. Retrieved February 27, 2009, from Encyclopdia Britannica Online : http://www.britannica.com/EBchecked/topic/599941/tornado 9. ESDU. (2002). Strong Winds in the Atmospheric Boundary Layer. Part 2: Discrete Gust Speeds. London: Engineering Science Data Unit. 10. Federal Emergency Management Agency. (2008, August 20). HAZUS. Ret rieved March 27, 2009, from Federal Emergency Management Agency: http://www.fema.gov/plan/prevent/hazus/index.shtm 11. Federal Emergency Management Agency. (2006, April 12). Know Your Earthquake Terms. Retrieved February 26, 2009, from Federal Emergency Manage ment Agency: http://www.fema.gov/hazard/earthquake/eq_terms.shtm 12. Federal Emergency Management Agency. (2008). Multihazard Loss Estimation Methodology Hurricane Model: HAZUS MH MR4 User Manual. Washington, D.C.: Federal Emergency Management Agency.

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150 13. Federal Emergency Management Agency. (2006, April 26). Terrorism. Retrieved March 1, 2009, from Federal Emergency Management Agency: http://www.fema.gov/hazard/terrorism/index.shtm 14. Federal Emergency Management Agency. (2003, May). The 1993 Great Midwest Flood: Vo ices 10 Years Later. Retrieved February 8, 2009, from Federal Emergency Management Agency: http://www.fema.gov/ 15. Federal Emergency Management Agency. (2009, March 1). Tornado. Retrieved March 18, 2009, from Federal Emergency Management Agency: http://www.fema.gov/hazard/tornado/index.shtm 16. Gray, W. (1979). Hurricanes: Their formation, structure and likely role in the tropical circulation. Journal of the Royal Meteorological Soci ety 155218. 17. Gutro, R. (2009, February 17). Theres Always Something Brewing All Year Round. Retrieved March 3, 2009, from NASA: http://www.nasa.gov/mission_pages/hurricanes/features/hurricane_brew.html 18. Hamid, S. S. (2007). Florida Public Hurricane Loss Model. Miami: Florida International University. 19. Harper, B., Kepert, J., & Ginger, J. (2008). Wind Speed Time Averaging Conversions for Tropical Cyclone Conditions. AMS 28th Conference on Hurricanes and Tropical Meteorology. Orlando, FL. 20. Hejl, R. (2006, Ma rch 23). Real Estate Ownership: Condominium or Fee Simple? Retrieved March 1, 2009, from Article Alley: http://www.articlealley.com/article_38207_33.html 21. Holland, G. (1993). Chapter 9, Ready Reckoner. In Global Guide to Tropical Cyclone Forecasting. Geneva: World Meteorological Organization. 22. Holmes, J. D. (2001). Wind Loading of Structures. New York: Spon Press. 23. Holmes, J. D., Letchford, C. W., & Lin, N. (2006). Investigations of plate type windborne debris Part II: Computed trajectories. Journal of Wind Engineering and Industrial Aerodynamics 2139. 24. Insurance Information Institute. (2008, August). Florida Hurricane Insurance Fact File. Retrieved February 8, 2009, from Insurance Information Institute: http://server.iii.org/yy_obj_data/binary/794975_1_0/Florida%20Hurricane%20Fact%20F ile.pdf 25. Insurance Information Institute. (2008, December). Regulation Modernization. Retrieved February 8, 2009, from Insurance Information Institute: http://www.iii.org/media/hottopics/insurance/ratereg/

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151 26. Insurance Information Institute. (2007). Research and Analysis. Retrieved February 8, 2009, from Inurance Information Institute: http://www.iii.org/media/rese arch/katrinafacts07/ 27. Jesteadt, J. (2006). Wind Data Collection, Wind Resistance of Florida Residential Structures, and Simulation of Hurricane Force Winds: 2003 to 2006 Florida Coastal Monitoring Program (FCMP). Master Thesis Department of Civil and COas tal Engineering, University of Florida, Gainesville, Florida. 28. Kijewski Correa, T. (2006, Fall). Introduction to Wind Effects. CE 60240 Structural Systems Notre Dame, Indiana, United States of America: University of Notre Dame. 29. Kijewski Correa, T. (2006, Fall). The Nature of Seismic Loads. CE 60240 Structural Systems Notre Dame, Indiana, United States of America: University of Notre Dame. 30. Kijewski Correa, T. (2006, Fall). Treatment of Wind Effects in Codes and Standards. CE 60240 Structural Systems Not re Dame, Indiana, United States of America: University of Notre Dame. 31. Lin, N., Holmes, J. D., & Letchford, C. W. (2007). Trajectories of WindBorne Debris in Horizontal Winds and Applications to Impact Testing. Journal of Structural Engineering 274282. 32. Lin, N., Letchford, C. W., & Holmes, J. D. (2006). Investigations of plate type windborne debris. Part I. Experiments in wind tunnel and full scale. Journal of Wind Engineering and Industrial Aerodynamics 5176. 33. Louie, J. (1996, October 10). Earths Inte rior. Retrieved February 25, 2009, from Geology 100: Earthquakes, Volcanoes, and other Natural Disasters: http://www.seismo.unr.edu/ftp/pub/louie/class/100/interior.html 34. Louie, J. (1996, October 9). Earthquake Effects. Retrieved February 25, 2009, from Geo logy 100: Earthquakes, Volcanoes, and other Natural Disasters: http://www.seismo.unr.edu/ftp/pub/louie/class/100/effects kobe.html 35. Louie, J. (2001, May 11). Plate Tectonics, the Cause of Earthquakes. Retrieved February 25, 2009, from Geology 100: Earthquakes, Volcanoes, and other Natural Disasters: http://www.seismo.unr.edu/ftp/pub/louie/class/100/plate tectonics.html 36. Louie, J. (1996, October 7). Seismic Deformation. Retrieved February 26, 2009, from Geology 100: Earthquakes Volcanoes, and other Natural Dis asters: http://www.seismo.unr.edu/ftp/pub/louie/class/100/seismic waves.html 37. Louie, J. (1996, October 9). The Modified Mercalli Scale of Earthquake Intensity. Retrieved February 25, 2009, from Geology 100: Earthquakes, Volcanoes, and other Natural Disaster s: http://www.seismo.unr.edu/ftp/pub/louie/class/100/mercalli.html

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152 38. Louie, J. (1996, October 9). What is Richter Magnitude. Retrieved February 25, 2009, from Geology 100: Earthquakes, Volcanoes, and other Natural Disasters: http://www.seismo.unr.edu/ftp/pub/louie/class/100/magnitude.html 39. Masters, F. (2004). Measurement, Modeling and Simulation of GroundLevel Tropical Cyclone Winds. Phd Dissertation Department of Civil and Coastal Engineering, University of Florida, Gainesville, Florida. 40. Mc Donald, J., & M ehta, K. C. (2006, October 10). A Recommendation for an Enhanced Fujita Scale (EF Scale). Retrieved March 1, 2009, from Wind Science and Engineering Center: http://www.wind.ttu.edu/EFScale.pdf 41. Mogil, H. M. (2007). Extreme Weather: Understanding the Science of Hurricanes, Tornadoes, Floods, Heat Waves, Snow Storms, Global Warming and Other Atmospheric Disturbances. New York: Publisher: Black Dog & Leventhal Publishers, Inc. 42. National Hurricane Center. (2008, November 26). The Saffir Simpson Hurricane Scale. R etrieved February 28, 2009, from National Hurricane Center: http://www.nhc.noaa.gov/aboutsshs.shtml 43. National Weather Service. (2004, July 21). Saffir Simpson Hurricane Scale Retrieved February 21, 2009, from National Oceanic and Atmospheric Administration: http://www.srh.noaa.gov/srh/tropicalwx/s s_scale.php 44. Neumann, C. (1993). Chapter 1, Global Overview. In Global Guide to Tropical Cyclone Forecasting. Geneva: World Meteorological Organization. 45. Peterka, J. A., Cermak, J. E., Cochran, L. S., Cochran, B. C., Hosoya, N., Derickson, R. G., et al. (1997). Wind uplift model for asphalt shingles. Journal of Architectural Engineering 147155. 46. PGT Industries. (2008). PGT Industries Retrieved May 20, 2009, from PGT Industries: http://www.pgtindustries.com/Pages/Main.aspx 47. Pita, G. L. (2008). Survey of Commercial Residential Buildings in Florida: Final Report. Melbourne: Florida Institute of Technology. 48. Rodriguez, F. (2007). Hurricane Damage Mitigation: Field Deployment Strategies and Residential Vulnerability Modeling. Master Thesis Department of Civil and Coastal Engineering, University of Florida, Gainesville, Florida: University of Florida. 49. Stover, C. W., & Coffman, J. L. (1993). Seismicity of the United States, 15681989 (Revised), U.S. Geological Survey Professional Paper 1527. Washington: United States Government Printing Office. 50. Tachikawa, M. (1983). Trajectories of flat plates in uniform flow wi th application to wind generated missiles. Journal of Wind Engineering and Industrial Aerodynamics 443453.

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153 51. Toothman, J. (2008, May 12). 5 Most Destructive Storms. Retrieved February 11, 2009, from How Stuff Works: http://science.howstuffworks.com/most destructive storms.htm 52. Twisdale, L. A., & Vickery, P. J. (2003). The Classification of Commercial Residential Buildings for Hurricane Damage and Loss. Eleventh International Conference on Wind Engineering. Lubbock, Texas. 53. Twisdale, L. A., & Vickery, P. J. ( 2003). The Classification of Single Family Residential Buildings for Hurricane Damage and Loss. Eleventh International Conference on Wind Engineering. Lubbock, Texas. 54. U.S. Department of Commerce. (2008). 2008 Hurricane Season Begins. Washington, D.C.: U.S. Census Bureau. 55. United Nations Security Council. (2004, October 8). Resolution 1566. Retrieved March 16, 2009, from United Nations Security Council: http://www.undemocracy.com/S RES 1566(2004).pdf 56. Wald, L. (2007, November 13). USGS Earthquake Hazards Progr am. Retrieved February 25, 2009, from U.S. Geological Survey: http://earthquake.usgs.gov/learning/eq101/EQ101.htm 57. Watts, H. M. (1889, July). Tornado, Hurricane, and Cyclone. Monthly Weather Review 58. Weekes, J., Balderrama, J., Gurley, K., Pinelli, J.P., P ita, G., & Hamid, S. (2009). Predicting the Vulnerability of Typical Commercial and Mid/High Rise Buildings to Hurricane Damage. Eleventh Americas Conference on Wind Engineering. San Juan, Puerto Rico. 59. Wilkinson, C. (2008, February). Research and Analysis. Retrieved February 8, 2009, from Insurance Information Institute: http://www.iii.org/media/research/catmodeling/ 60. Willis, J., Lee, B., & Wyatt, T. (2002). A model of windborne debris damage. Journal of Wind Engineering and Industrial Aerodynamics 555565.

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BIOGRAPHICAL SKETCH Juan Antonio Balderrama Garcia Mendez was born in Mexico in 1984.