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PREDICTING THE VULNERABILITY OF TYPICAL COMMERCIAL AND SINGLE FAMILY RESIDENTIAL BUILDINGS TO HURRICANE DAMAGE By JOHANN EVERTON CHRISTOPHER WEEKES A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORI DA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014
Â© 2014 Johann Everton Christopher Weekes
To my family and my friends that have given me th e strength, support and motivation to strive for my best.
4 ACKNOWLEDGMENTS I would never have been able to finish my dissertation without the guidance of my committee members, help from friends, and support from my family. I am grateful for the time, s upport, patience and assistance that Dr. Kurtis Gurley has shown me. He gave me the ability to grow on my own while always being there to give a helping hand. Because of him, many doors were opened. Without his guidance my completion of this project would not have possible. I am also thankful to Dr. Masters, Dr. Prevatt and Dr. Shankar for their help as my committee members. Special gratitude is given to Juan Antonio Balderrama for the teamwork we shared while developing the program. Family and friends are important parts of ones growth and maturation process. My parents (Judy and Rev. Canon Jonathan Weekes) and sister (Dr. Juelle Weekes) have provided me with strong foundation upon which I could build upon. Special thanks to all my friends who have been the re throughout the process, encouraging me to strive for my goals and keeping me well grounded. Finally, I would like to thank God for the many blessings he has bestowed upon me.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................... 15 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 16 Research Hypo thesis ................................ ................................ .............................. 18 Goals and Objectives ................................ ................................ .............................. 19 2 PREVIOUS RESEARCH ................................ ................................ ........................ 22 Hazard Model Assessment and Variabi lity ................................ .............................. 22 Loss Models Using Claims Data ................................ ................................ ............. 24 Probabilistic Engineering Loss Models: HAZUS ................................ ..................... 30 Florida Public Hurricane Loss Model Overview ................................ .................... 33 Status of the FPHLM ................................ ................................ ............................... 36 3 NEW COMMERCIAL RESIDENTIAL STRUCTURE CODE ................................ ... 42 Methodology: low rise commercial residential ................................ ........................ 42 Survey of the Florida building stock (exposure study) ................................ ...... 43 Monte Carlo simulation process ................................ ................................ ....... 44 Mapping of the individual components ................................ ............................. 46 Resistance capacities of components ................................ .............................. 48 Structural loads: low rise commercial residential ................................ .............. 50 Pressure loading ................................ ................................ ........................ 50 Debris impact damage ................................ ................................ ............... 58 Roof Components: Roof Sheathing ................................ ................................ .. 61 Roof to wall connections ................................ ................................ ............ 65 Roof cover ................................ ................................ ................................ .. 67 Gable End and Truss Collapse ................................ ................................ .. 69 Soffits ................................ ................................ ................................ ......... 70 Wal l Components ................................ ................................ ............................. 71 Wall sheathing ................................ ................................ ........................... 72 Wall cover ................................ ................................ ................................ .. 73 Masonry wall ................................ ................................ .............................. 73 3 openings (windows, sliding doors and entry doors) ................................ 76 Garage doors ................................ ................................ ............................. 76
6 Damage Matrices and Vulnerability Curves ................................ ...................... 76 Examples of S imulation Results ................................ ................................ ............. 78 Validation of the Low Rise Commercial Residential Model ................................ ..... 83 Methodology: Mid High Rise Commercial Residential ................................ ............ 84 Survey of building stock ................................ ................................ .................... 85 Monte Carlo Simulation Proces s ................................ ................................ ...... 86 Mapping of openings ................................ ................................ ........................ 87 Capacities of components ................................ ................................ ................ 88 Structural loads on openings: mid high rise commercial residential ................. 90 Pressure loading ................................ ................................ ........................ 90 Debris impact damage ................................ ................................ ............... 91 Damage Matrices and Vulnerability Curves ................................ ...................... 92 4 ACQUISITION OF PERTINENT BUILDING SHAPES ................................ .......... 144 5 REASSESSING STRUCTURAL LOADS ................................ .............................. 148 6 INCORPORATION OF THE SINGLE FAMILY RESIDENTIAL CODE AND COMPARISON TO THE CURRENT SINGLE FAMILY RESIDENTIAL CODE ..... 157 7 MITIGATION STUDIES ................................ ................................ ........................ 170 Determining the Average Loss Ratio ................................ ................................ .... 172 Comparison of Average Loss Ratios for Different Models and Mitigation Options 174 Models and Mitigations Analyzed ................................ ................................ ......... 174 Roof cover, roof to wall connection and gable end bracing ............................ 176 Roof deck replacement ................................ ................................ .................. 176 Engineered shutters ................................ ................................ ....................... 177 Roof deck replacement and enginee red shutter combination ......................... 177 Comparison to the Saffir Simpson Scale ................................ .............................. 178 8 CONCLUSIONS ................................ ................................ ................................ ... 196 LIST OF REFERENCES ................................ ................................ ............................. 199 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 204
7 LIST OF TABLES Table page 1 1 Institutions that are working on the FPHLM and their individual tasks ................ 21 3 1 Roof and Wall characteristics for low rise commercial residential structures (Pita G. L., 2008) ................................ ................................ ................................ 98 3 2 The distribution of 1, 2 and 3 story low rise commercial residential buildings by county ................................ ................................ ................................ ............ 99 3 3 Distribution of low rise commercial residential structure by year built (adapted from Pita et al. 2008) ................................ ................................ ........................ 100 3 4 List of User Defined Inputs ................................ ................................ ............... 100 3 5 Pressure capacities (psf) and coefficients of variation for components in the building envelope ................................ ................................ .............................. 101 3 6 Protection Correction Factors for Glazing Component Resistances ................. 101 3 7 Material Correction Factors for Glazing Component Resistances .................... 101 3 8 Internal Pressure Coefficients ................................ ................................ ........... 102 3 9 R2w Load shearing distribution implemented in the LRCR model .................... 102 3 10 The final output column designation for low rise commercial residential structures ................................ ................................ ................................ .......... 103 3 11 Low rise commercial residential sample models analyzed ............................... 104 3 12 Ro of characteristics for mid high rise buildings (adapted from Pita et al. 2008) 104 3 13 Number of stories for mid high rise buildings (adapted from Pita et al. 2008) .. 104 3 14 Distribution of low ri se commercial residential structure by year built (adapted from Pita et al. 2008) ................................ ................................ ........................ 104 3 15 Desc riptor for the mid high rise residential model ................................ ............. 105 3 16 Mean pressure capacities and coefficient of variation for opening components ................................ ................................ ................................ ...... 105 3 17 Glazing material factors for openings ................................ ............................... 106 3 18 Shutter protection factors for openings ................................ ............................. 106
8 3 19 high rise buildings ................................ ................................ ............................. 106 3 20 Sign of wind pressure loading on components per wind direction for ................................ ................ 107 3 21 Th e final output column designation for mid high rise commercial residential structures ................................ ................................ ................................ .......... 107 3 22 Mid high rise commercial residential sample models analyzed ........................ 108 4 1 Results of the building shape study ................................ ................................ .. 147 6 1 Damages compared between the Existing SFR model and Modified LRCR Model ................................ ................................ ................................ ................ 163 7 1 Range of Reductions for Different Mitigation (Division of Emergency Management) ................................ ................................ ................................ ... 181 7 2 New and repair costs for exterior building components ................................ .... 182 7 3 List of identified mitigation options used in the study ................................ ........ 183 7 4 List of the different mitigation options and combinations compared in the study ................................ ................................ ................................ ................. 183 7 5 Nationa l Hurricane Center Saffir Simpson Hurricane Wind Scale (National Oceanic and Atmospheric Administration(NOAA), 2013) ................................ . 184 7 6 National Hurricane Center Saffir Simpson Hurricane Wind Scale w/ modified wind speeds ................................ ................................ ................................ ...... 184
9 LIST OF FIGURES Figure page 2 1 Loss Costs for Florida model Submission ................................ .......................... 37 2 2 Lost Costs in Florida ................................ ................................ ........................... 38 2 3 ........................... 38 2 4 Bhinderwala's Relationship between wind speeds and loss ratio ....................... 39 2 5 HAZUS Individual Storm Simulation Methodology ................................ .............. 40 2 6 Plan view of a roof depicting the eight wind directions considered ..................... 41 3 1 Flow Chart of Low Rise Commercial Residential Simulation Algorithm ............ 109 3 2 Matrix relationship of sheathing panel dimension ................................ ............. 109 3 3 Matrix relationship of sheathing panel capacities ................................ ............. 110 3 4 Matrix relationship of sheathing panel pressure loads ................................ ...... 111 3 5 Sample distribution for component capacities with two standard deviation truncation ................................ ................................ ................................ .......... 111 3 6 Comparison of ASCE 7 05 Pressure Coefficient Zones and the Modified Directional Mapping in the SFR model ................................ ............................. 112 3 7 Wind profile by terrain ................................ ................................ ....................... 112 3 8 ASCE 7 05 external pressure coefficients for roof components (Components and Cladding Method) ................................ ................................ ...................... 113 3 9 ASCE 7 05 external pressure coefficients for wal l components (Components and Cladding Method) ................................ ................................ ...................... 113 3 10 Effects on interior pressure due to openings on the windward and leeward walls of the building ................................ ................................ .......................... 114 3 11 Mean internal pressure coefficient as a function windward/leeward opening area ratio ................................ ................................ ................................ .......... 114 3 12 Urban missile exposure layout assuming a base clearance of 45ft .................. 115 3 13 Open missile exposure layout assuming a base clearance of 45ft ................... 115 3 14 Directions of wind approach in the missile model ................................ ............. 116
10 3 15 Sample of the A(vwind) variable against wind speeds ................................ ...... 116 3 16 Calculation of C values for various openings ................................ .................... 117 3 17 Photo of Roof Sheathing Damage ................................ ................................ .... 117 3 18 Hip roof comparison of the unprojected vs. projected roof areas ..................... 118 3 19 Orientation of wind pressure loads on roof components ................................ ... 118 3 20 Roof Sheathing Layout and Mapping ................................ ............................... 118 3 21 Photo of R2W Connection Failure ................................ ................................ .... 119 3 22 Tributary Area R2W Connection Theory. Depiction of the sheathing uplift relationship with r2w connection ................................ ................................ ....... 119 3 23 Load Distribution with the application of a singular load at a truss connection . 120 3 24 Photo of Roof Cover Damage ................................ ................................ ........... 120 3 25 Outward Gable end Wall Collapse ................................ ................................ .... 121 3 26 Gable End Collapse Damage Threshold ................................ .......................... 121 3 27 Post Hurricane Soffit Damages ................................ ................................ ........ 122 3 28 Photo of Wall Cover and Sheathing Damage ................................ ................... 122 3 29 Photo of Wall Cover Damage with no Sheathing Damage ............................... 123 3 30 Photo of a masonry wall crack after a hurricane ................................ ............... 123 3 31 Out of Plane bending loads for a masonry wall ................................ ................ 124 3 32 Shear loading of masonry walls due to external pressures .............................. 125 3 33 Photo of Window, Sliding Door and Entry Door Damage ................................ . 125 3 34 Sample Vulnerability Curve for Roof Cover ................................ ...................... 126 3 35 Roof, wall and opening component vulnerability curves for a 1 story weak gable roof timber frame building ................................ ................................ ....... 127 3 36 Roof, wall and opening component vulnerability curves for a 1 story medium gable roof timber frame building ................................ ................................ ....... 128 3 37 Roof, wall and opening component vulnerability curves for a 1 story strong gable roof timber frame building ................................ ................................ ....... 129
11 3 38 Roof, wall and opening component vulner ability curves for a 2 story weak gable roof timber frame building ................................ ................................ ....... 130 3 39 Roof, wall and opening component vulnerability curves for a 3 story weak gable roof timber frame building ................................ ................................ ....... 131 3 40 Roof, wall and opening component vulnerability curves for a 1 story weak gable roof masonry wall building ................................ ................................ ...... 132 3 41 Roof, wall and opening component vulnerability curves for a 1 story medium gable roof masonry wall building ................................ ................................ ...... 1 33 3 42 Roof, wall and opening component vulnerability curves for a 1 story strong gable roof mas onry wall building ................................ ................................ ...... 134 3 43 Roof, wall and opening component vulnerability curves for a 3 story weak gable roof masonry wall building ................................ ................................ ...... 135 3 44 Roof, wall and opening component vulnerability curves for a 1 story weak gable roof timber frame building w/ engineered shutters ................................ .. 136 3 45 Roof, wall and opening component vulner ability curves for a 1 story weak hip roof timber frame building ................................ ................................ ................. 137 3 46 Flow Chart of Mid High Rise Commercial Residential Simulation Algorithm .... 138 3 47 Mid high rise building models: Closed building (left), and open building (right) 139 3 48 irway mid high rise buildings ................................ ................................ ...................... 139 3 49 mid high rise buildings ................................ ................................ ...................... 140 3 50 Linear relationships for opening breaching due to debris impact for window, and entry and sliding doors ................................ ................................ .............. 140 3 51 Comparative opening damage for a corner unit in a buildi ng with an interior corridor. Unit is in a high impact zone ................................ ............................... 141 3 52 Comparative opening damage for a middle unit in a building with an interior corridor. Unit is in a high impact zone ................................ ............................... 141 3 53 Comparative opening damage for a corner unit in a building with an exterior corridor. Unit is in a high impact zone ................................ ............................... 142 3 54 C omparative opening damage for a middle unit in a building with an exterior corridor. Unit is in a high impact zone ................................ .............................. 142
12 3 55 Comparative opening damage for a middle unit in a building with an exterior corridor. Unit is in a high impact zone with shutter protection on windows and sliding doors ................................ ................................ .............................. 143 3 56 Comparative opening damage for a middle unit in a building with an exterior corr idor. Unit is in a low impact zone ................................ ............................... 143 4 1 Photo of Residential Neighborhood Being Surveyed For Building Shapes ....... 147 5 1 Contour of Coefficient of Pressure with winds running vertically along the length of the building ................................ ................................ ........................ 152 5 2 Procedure used to determine the limits for the pressure coefficients extracted from the NIST database and plotted on the contour maps. The color bar corresponds with the pressure coefficient ranges found on the contour maps. 153 5 3 Sample mapping of roof zone ................................ ................................ ........... 154 5 4 Comparison of the Zone Layouts for NIST, Clemson and ASCE 7 Modification Models. The relative size of the models is depicted in the figure. . 154 5 5 Contours for a hip roof building ................................ ................................ ......... 155 5 7 The determined zone delineation for a hip roof. ................................ ............... 156 6 1 Comparison of the previous single family and the modified low rise commercial residential models. For a 1 story weak timber frame structure. ..... 164 6 2 Comparison of the previous single family and the modified low rise com mercial residential models. For a 1 story weak masonry structure. ........... 165 6 3 Comparison of the previous single family and the modified low rise commercial residential models. For a 1 story medium timber frame structure .. 166 6 4 Comparison of the previous single family and the modified low rise commercial residential models. For a 1 story medium masonry frame structure ................................ ................................ ................................ ........... 167 6 5 Comparison of the previous single family and the modified low rise commercial residential models. For a 1 story strong timber frame structure .... 168 6 6 Comparison of the previous single family and the modified low rise commercial residential models. For a 1 story strong masonry wall structure .... 169 7 1 Loss mitigation features cons idered in the ARA 2008 Florida Residential Wind Loss Mitigation Study ................................ ................................ .............. 185 7 2 Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with strong roof cover ................................ ................................ ................................ ......... 185
13 7 3 Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with strong roof cover ................................ ................................ ............................... 186 7 4 Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with str ong r2w connection ................................ ................................ ................................ . 186 7 5 Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with strong r2w connections ................................ ................................ ..................... 187 7 6 Avera ge Loss Ratio comparison of Weak LRCR vs Weak LRCR with braced gable end ................................ ................................ ................................ .......... 187 7 7 Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with braced gable end ................................ ................................ .............................. 188 7 8 Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with strong roof cover and roof sheathing ................................ ................................ ........... 188 7 9 Average Loss Ratio comparison of Medium LRC R vs Medium LRCR with strong roof cover ................................ ................................ ............................... 189 7 10 Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with strong roof cover and sheathing w/ braced gable ends ................................ ............... 189 7 11 Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with strong roof cover and sheathing w/ braced gable ends ................................ .... 190 7 12 Average Loss Ratio co mparison of Weak LRCR vs Weak LRCR with engineered shutter protection ................................ ................................ ........... 190 7 13 Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with engineered shutter protection ................................ ................................ ........... 191 7 14 Average Loss Ratio comparison of Strong LRCR vs Strong LRCR with engineered shutter protection ................................ ................................ ........... 191 7 15 Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with strong roof cover, roof sheathing and engineered shutters ................................ ......... 192 7 16 Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with strong roof cover, roof sheathin g and engineered shutters .............................. 192 7 17 Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with strong roof cover, roof sheathing, braced gable ends and engineered shutters .......... 193 7 18 Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with strong roof cover, roof sheathing, braced gable ends and engineered shutters ................................ ................................ ................................ ............. 193
14 7 19 Comparative graph of all Weak mitigation option with respect to the modified Saffir Simpson Wind Scale ................................ ................................ ............... 194 7 20 Comparative graph of all Medium mitigation option with respect to t he modified Saffir Simpson Wind Scale ................................ ................................ 194 7 21 Comparative graph of all Strong mitigation option with respect to the modified Saffir Simpson Wind Scale ................................ ................................ ............... 195
15 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PREDICTING THE VULNERABILITY OF TYPICAL COMMERCIAL AND SINGLE FAMILY R ESIDENTIAL BUILDINGS TO HURRICANE DAMAGE By Johann Everton Christopher Weekes August 2014 Chair: Kurtis Gurley Major: Civil Engineering Hurricane impacts have caused significant damage to residential and commercial structures, producing billions of dol lars in insured losses. Numerical models are widely used by insurance companies in the prediction of loss cost. Several such loss projection models have been developed by privat e industry and the State of Florida sponsored development of a non proprietary hurricane loss model, known as the Florida Public Hurricane Loss Model (FPHLM). This model resulted from a multi university effort t o quantify the damages and cost of repairs for structures that have been subjected to hurricane force winds. The ori ginal F PHLM focused on single family residential housing. The model is now extended to cover commercial residential buildings ranging from multi story apartments to the high rise condominiums typically found lining the beaches of South Florida. Th is paper proposa l focuses on the development of the exterior vulnerability component of t he commercial residential model and provides a description of the strategies to probabilistically quantify physical exterior damage for two models: low rise and mid/high rise commerci al residential structures.
16 CHAPTER 1 INTRODUCTION Over the 20 year period, 1990 to 2009, hurricanes and tropical storms made up 45.2 percent of total catastrophe losses, followed by tornado losses (29.0 percent), winter storms (7.4 percent), terrorism (7.0 percent), earthquakes and other geologic events (5.2 percent), wind/hail/flood (3.3 percent) and fire (2.4 percent) (Catastrophes: Insurance Issues, 2011) . A recent study normalized the cost of hurricane damages from 1900 to 2005 into 2005 dollars (Pielke, 2006) . The research has suggested that the average annual normalized damage in the continental United States is about $10 billion. Over one half of related hurricane damages in the United States occur in the State of Florida (Pinelli, et al., 2004) . The State of Florida has $1.5 trillion dollars worth of existing structures, with 85 percent 1200 miles of coastline. Damage in Florida will contin ue to escalate as the population density continues to rise. One catastr ophe modeling company predicts the losses will approximately double every decade due to the growth of residential and commercial structures and the increasing expenses of buildings (Catastrophes: Insurance Issues, 2011) . Recently, computer simulation models have been developed that integrate long term disaster information with current demographic data to produce potential insurance losses for any given geogra phical location under various conditions . This information allows insurers and insurance regulatory bodies to better differentiate between high and low risk areas in states such as Florida. In addition, computer programs designed to help underwriters eval uate a building's potential damage from windstorms allow insurers to price property insurance more accurately. The ability to generate such
17 information has also led insurers to reassess their business strategies (Catastrophes: In surance Issues, 2011) . There are several proprietary commercial hurricane loss projection models which used by the insurance industry for setting actuarial rates . The State of Florida has developed a public model as an accessible par allel to the propriet ary models (Powell, 2005) . The Florida Department of Financial Services (FDFS) sponsored the development of the FPHLM to assess the annualized risk of insured losses to the residential infrastructure in Florida. This model, along with several proprietary r isk models, has been certified by the Florida Commission on Hurricane Loss Projection M ethodology (FCHLPM) . Created in 1995 during a legislative session, the FCHLPM is a panel of experts that evaluates computer models or other form of actuarial methodology used to predict hurricane damages (Florida State Board of Administration, 2014) . The FPHLM combines the fields of meteorology, engineering, actuarial, statistics and computer science. It was developed by faculty at the Florida International University (FIU), the University of Florida (UF), the Florida Institute of Technology (FIT), the Florida State University (FSU), the University of Miami (UM), and the National Oceanographic and Atmospheric Administration (NOAA). A breakdown o f the participating institutions and their respective duties can be found in Table 1 1. The focus of this project was the development of the engineering (vulnerability) component of a commercial residential extension to the original single family residenti al FPHLM. This extension include s low rise and mid/high rise structures. Low rise commercial r esidential (LRCR) structures include 1, 2 and 3 story multi dwelling structures, such as town homes and apartment buildings. Mid High Rise structures are
18 4 storie s and higher. The ability to analyze single family residential structures will also be incorporated into the new code, utilizing many of the theories and advancements used in the development of the commercial residential structures. Further enhancements we re made to single family residential model and modifications to the structural loads acting on the building. Additional research was done to assess the expansion of the building stock shapes for single family residential structures. A Monte Carlo simulatio n approach was utilized. Probabilistic wind loads were applied to the i ndividual structural components and component capacities were assigned from random distributions determined from labora tory experiments, field surveys and other sources. Component failu res may result in load redistributions, thus the probabilistic structural model is analyzed via iteration. The application of such models extends beyond ratemaking processes of insurance companies, but can also be used in the mitigation of buildings and po tentially influence the current building codes. Research Hypothesis During extreme wind events , structures are susceptible to damage. The damages accumulated by the structure are dependent on four main factors: the wind field existing in the vicinity of t he structure, the loads that are that are created by the wind field , the resistance capacity of the individual building components ; and the interaction between the components. All these factors play important roles in determining the vulnerability of the b uilding. The problem of quantifying the risk of wind damage can be addressed by applying a probabilistic framework to the structural loading and the resistance of the building component, while preserving component interaction.
19 Significant information on pr obabilistic wind loading is available through wind tunnel and full scale test results, building codes and wind design load standards. Laboratory testing by researchers and product manufacturers and post storm damage reports provide valuable information on structural resistance. Using this information to simulate the occurrence of hurricane events on typical residential and commercial residential buildings provide a measure of the ability of constructed commercial residential buildings to withstand hurricane force winds. Incorporating new construction practices and retrofits can be implemented by adjust ing load paths and the resistance of the components, and provides a means of calculating the savings that homeowners will gain by adding hurricane damage mitig ation features to their homes. This approach was applied by modifying and expanding the capabilities of the existing single family residential (SFR) construction vulnerability model, and developing a companion commercial residential model for both low ris e and mid high rise building s . Goals and Objectives The goal of the research was to expand, update, and develop new components for the engineering / vulnerability module of the hurricane wind damage prediction model. These goals were represented by the fo llowing five research objectives: 1. Create a probability based system response model which simulates wind load and component interaction for low (1 3 Story) and mid/hi gh rise (Condominium Style) commercial residential structure. 2. Make the necessary changes t o the commercial residential model to accommodate damage predictions for single family residential structure with the goal of supplanting the existing FPHLM . 3. Develop an improved wind load model for low rise residential models through the incorporation of w ind tunnel data and full scale studies . 4. Produce vulnerability results for various combinations of wind damage mitigation features, identifying reductions in structural vulnerability to hurricane force winds.
20 The research objectives described above are deta iled in Chapters 3 through 8, following a brief summary of previous work in the field of hurricane damage prediction in Chapter 2. Chapter 3 present s the methodology used in producing the Monte Carlo engine for both the low rise and mid high rise commercia l residential models. Chapter 4 provides the method used to integrate the single family residential model into the low rise commercial residential model. Chapter 5 describes the efforts made for defining the different wind zones for gable and hip roofs. Ch apter 6 illustrates a study conducted to determine the need for an expansion of building shape options. Chapter 7 presents the results of a mitigation study that compares the benefits of multiple mitigation options. Con clusions about the model, model ing pr ocess, and potential future work are discussed in Chapter 8 .
21 Table 1 1. Institutions that are working on the FPHLM and their individual tasks Institution Module Component Functionalities Florida State University, University of Miami and National Oceanographic and Atmospheric Administration (NOAA) Wind Field Model Storm Track Model Generate the storm tracks for simulated storms based on random historical initial conditions (from HURDAT database) and stochastic a lgorithms Wind Field Model Calculate wind speed time series for each of the zip codes affected by the storms Wind Speed Correction Refine open terrain wind speed produced by the Wind Field Model with respect to the actual terrain (based on land u se/land cover) Wind Speed Probability Calculate the probabilities of the 3 second gust wind speeds affecting each of the targeted zip codes University of Florida and Florida Institute of Technology Damage Estimation Module Engineering Model Deve lop the exposures and vulnerability model to estimate the physical damage for different exposures and wind speeds Florida International University Loss Estimation Module Scenario Based Insurance Loss Model Calculate the expected losses of a certain insu rance portfolio caused by a Loss Estimation specific hurricane Probabilistic Based Insurance Loss Model Calculate the annual expected loss of a certain insurance portfolio
22 CHAPTER 2 PREVIOUS RESEARCH Hazard Model Assessment and Variability The St ate of Florida faced an insurance crisis after Hurricane Andrew impacted South Florida in 1992 . This prompted the raising of rates and in some case s the complete w ithdrawal of hurricane coverage from the state. These occurrences inc reased attention on meth ods insurance companies use to determine rates, especially the use of proprietary computer models that could not be fully evaluated by the State Department of Insurance (Watson, Johnson, & Simons, 2004) . In 1995 the state of Florida established the Florida Commission on Hurricane Loss Projection Methodology (FCHLPM), whose task is to evaluate models through the adoption of standard s that the models must meet . With an understanding of the technology, users of lost costs data would benefit greatly in their ab ility to establish the limitations and performance of thes e models in an objective manner . Moreover, the sheer complexity of the models makes it difficult for even a sophisticated user to accomplish a proper evaluation (Watson, Johnson, & Simons, 2004) . Th e standards that are developed are reviewed and modified on a recurring basis. Watson and Johnson reviewed the processes of selecting appropriate proprietary models for use in the State of Florida. Their approach was to amass an array of modeling methods from the published literature (meteorology, engineering and actuarial sciences). Nine wind models, four surface friction models and nine damage models were identified as being suitable for use in the prediction models. Every combination of the three types of models was investigated, leading to a total of 324 potential combinations . Annual loss costs were computed for each of the combinations and
23 compared to hurricane losses that were reported by a major insurance company. The results that are produced by pr oprietary models were then compared to the 324 combinations. In 2002, four proprietary models, including those produced by Applied Insurance Research (AIR), Applied Research Associates (ARA), EQECAT (EQE) and Risk Management Solutions (RMS), were submitte d for evaluation under 2002 standards and were approved by the Commission in 2003. Average loss costs were computed for every county in the state of Florida for a typical wood frame structure . Figure 2 1 depicts the variability in results, highlighting a s ubstantial amount of uncertainty in the modeling process among the four proprietary models. O n the ratemaking level, this difference allows the insurer the opportunity to select the model that will yield the highest loss cost. A n insurer can also select th e model which produces the lowest values, undercutting its competitors, but possibly leaving them in a position where if a major hurricane occurs t hey will not be able to compensate for the losses . Because testing and analysis of proprietary models is not an option, models based on public domain sources can be used by the regulatory and research communities to assess methods for both improving hurricane loss modeling and the methods used to evaluate these models (Watson, Johnson, & Simons, 2004) . All combin ations of the publically sourced data were run putting the proprietary model results into perspective and comparing how well they reflect one another . Figure 2 2 shows a county by county analysis of the models. The maximum, minimum and median values are ca lculated for the 324 public domain model combinations, creating a range for which the proprietary results can be superimposed with. The public domain
24 r esults effectively brackets the results of the proprietary results . In other words, the range of variatio n of the proprietary results is not dissimilar to the differences found in the public domain. As seen in Figure 2 2 , the variation of the results can be drastic and is hinged on three combined factors. From the 324 model combinations a variability chart w as created to identify the most sensitive parameters . For example, for each combination of damage function s and wind field s , there are four separate friction functions. A very small spread among the friction factors indicated that friction factors do not s trongly influence the loss cost. Further investigation revealed that the damage function was the primary source of variation in loss cost. The wind field had the second highest influence. Both functions are correlated with one another as the highly non lin ear damage function grows exponentially as the wind speed increase. Therefore the uncertainties in the wind field dramatically influence the damage calculations . Because of this interaction, making improvements to damage function s will also require signifi cant improvements to the wind field s that create the loads (Watson, Johnson, & Simons, 2004) . Loss Models U sing Claims Data Damage prediction utilize of the current knowledge base to predict damage in future extreme wind events. While post damage reports e xist in the public domain, damage prediction models are proprietary, with varying degrees of detail published in the literature depending on the model developer (eg. HURLOSS developed by ARA and HAZUS developed by ARA for FEMA ). These models are created by using insurance claims data as a basis for curve fitting vulnerability curves (the model output), or the development of probabilistic model within an engineering based framework.
25 C urve fitting techniques use available claims data to produce vulnerability curves without relying on engineering concepts of structural load and resistance/capacity of structural systems. The probabilistic approach uses Monte Carlo Simulations, engineering calculations and probability modeling concepts to produce the vulnerabi li ty curves. This approach uses the claims data as a source of validation and calibration of the model assumptions. 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. The use of claims data for hurricane damage prediction purposes has been ongoing for the past five decades. One of the first significant studies in which the risk of property damage associated with hurr icanes were quantified by studying residential insurance files of hurricane damages was conducted by Don Friedman. In 1960, he studied approximately 1,300 insurance claims from Hurricane Donna in Florida, and later compared the data with claims data collec ted in New England from the same storm. He also analyzed 175,000 insurance claims after Hurricane Carol hit New England in 1954. Through analysis of the best available information on peak wind speeds and the claims data representation of damage in terms of dollars, Friedman identified a non linear relationship between wind speed and damage. The relationship is depicted in Figure 2 3, where the vertical axis represents the average loss ratios combined from the three events and the maximum peak gusts is on th e horizontal axis. The loss ratio is defined as the total claim paid divided by the insured value of the structure and its contents.
26 in 1989 by Hurricane Hugo in North Carolina (Wat ford, 1991) . Her study showed that in 95 percent of the homes considered , more than 95 percent of the direct wind damage to the structure were to the roof system. It was also determined that damage due to direct wind interaction averaged a 6.5 percent loss ratio. Rickborn et al. (1992) used aerial photographs of the islands near Charleston, SC to study the damage caused by Hurricane Hugo. On these islands the average loss ratio was 17 percent and the peak gust was projected at 108 mph . Of the 3194 houses s urveyed, 26 percent had less than 15 percent of the roof coverings removed, 18 percent had between 15 percent and 40 percent removed, and 7 percent had more than 40 percent removed. In addition to these, 2 percent lost roof sheathing and 3 percent had more serious struc tural damage caused by the wind (Rickborn, 1992) . A ground survey of 466 houses in South Florida following Hurricane Andrew found that the average loss ratio was approximately 75 percent . Seventy seven percent of the homes sustained significa nt damage to roof coverings and 25 percent experienced the loss of one or more panels of roof sheathing. Loss of roof sheathing and subsequent collapse of trusses appeared to be a problem associated with gable roofs. Thirty three percent of those roofs had severe roof damage compared to 6 percent of houses with hip roofs in that category. Sixty five percent of homes had severe rain damage and 64 percent had at least one broken window. Only 2 percent of the walls sustained moderate to severe damage. Homes ta ken into consideration for the survey were located in regions of varying max wind speeds ranging from 130 to 150 mph (U.S. Department of Housing and Urban Development, 1993) .
27 More recently, Shiraj Bhinderwala produced a M asters thesis providing an analysis of the relationship between wind speeds and hurricane induced damages to single family residential structures. Insurance files were obtained for homes in Dade County after Hurricane Andrew in 1992 (Bhinderwala, 1995) . Da ta was provided by two separate insurers. The first insurer provided the Clemson group with data for 731 properties. The data consisted of the address of each claim, the insured value of the building, the insured value of th e contents, the amount paid for debris removal and the amount paid for additional living expenses. Of the 731 homes, 250 of the claims incorporated additional data, including estimates of repair and replacement, photographs of the damaged structures and written reports. Information such as roof types, exterior construction, number of broken doors, number of broken door s , number of broken sliding doors, missing roof sheathing etc. were extracted. Because many people were involved in the assembly of the data, the quality and quantity of the data varied. The files with insufficient data information were removed from the database, leaving 222 buildings available for a detailed analysis of the damages. A rating system from 0 3 (No Damage Extensive Damage) was created in order to identify the severity of particular components, such as roof, walls, doors and window and external facilities. The region was separated into a 20 street interval grid with an initial origin northeast of all the houses. An average loss ratio was determined for each grid . An analysis was made initially comparing the loss ratio as distance increased in a northerly direction from the path of Andrew, which was traveling virtually East West within that vicinity. Bhinderwala also developed a loss magnifier, which is defined as the overall total loss, minus the cost of damage to the external facilities, divided by the sum of the cost of the
28 damage to the roof, doors, windows and walls. This is used to study the effects of rain entering the house and damaging the interior of the building and its contents. The 20 street grid was then assigned a wind speed, determined using flight level reconnaissance data published by Powell and Houston (1996) and a surface wind speed map published by Powell, Houston and Reinhold ( 1996 ). Analyses w ere made to compare the loss ratios to the wind speeds and the severity of damages to components at that location. Plotting of the loss ratios vs. the wind speeds yielded a similar trend to grew exponentially and was non linear. The second insurer provided a larger sampling of 189,399 houses, which were separated into 158 zip code areas. Information for zip code s where the amount of losses were less than $100,000, or where there were less than 10 buildings within in the zip code area were discounted. Upon elimination of zip codes meeting either of these criteria, the sample size shrank to 72,796 houses in 71 zip codes. Data for each zip code only included the total value of the policies, the total amount of claims, the total number of policies and the number of claims data for which the claims were filed. From this data, the loss ratios and claims ratios were extrapolated. As previously defined, the loss ratio is defined as the total claim paid divided by the insur ed value of the structure and its contents . The claims ratio is equal to the number of policies for which claims were filed divided by the total number of policies. In order to properly compare e second insurer was used because the land mass area of 2500 km 2 , a larger county akin to Dade County, was used . The two ratios were also plotted against the maximum gust wind speed in
29 us work (Bhinderwala, 1995) . From the results in Figure 2 4 , one can deduce that this method is consistent when comparing loss ratios of exist ing structures that form part of the region or are comparable to structures within the region for which the data w as originally collected. However, this data is a snapshot in time, capturing only the damage on structural types that existed when the extreme wind event took place. The data cannot take into consideration improvements in building construction over time, n or can it be readily applied to areas where the terrain and type of construction is notably different (Cope 2004). The most important limitation of this claims curve fitting method is the lack of consistent quality and quantity of detailed claims informat ion. Generally, the information that is maintained by insurance companies does not contain thorough content for a proper analysis to determine the performan ce of various system components and the combinations of different component and structural features. With improvements in the quality and consistency of data, it would ability to evaluate the method is li mited by the information available to the engineer. T he influence of various wind damage mitigation features (such as hurricane window shutters) cannot be delineated from this approach unless a high volume of claims data (with such features identified) is available. Thus , the curve fitting modeling technique is not a robust tool for performing comparative vulnerability analysis of a variety of construction types and mitigation features.
30 Last , the estimation of the wind speeds at a given location can drastically influence loss model results. The actual wind sp eed that is responsible for the damages to the house at that particular location is always uncertain . Comprehensive ground wind measurements with consistent recordings in local areas , which closely match the reconnaissance aircraft measurements , could impr ove the understanding of the damage wind speed relationship. Probabilistic Engineering Loss Models: HAZUS HAZUS is a methodology and software program for estimating potential losses from earthquakes, floods, and hurricane winds. HAZUS was developed by the Federal Emergency Management Agency (FEMA) under contract with the National Institute of Building Sciences (NIBS), who maintains a committee of engineering experts to provide technical oversight and guidance to the wind model development project. Applied R esearch Associates, Inc., is the technical subcontractor developing the model. The HAZUS MH Hurricane (HM) was developed using wind engineering principles to enable detailed estimates of possible damage and loss to buildings and their content due to high v elocity wind storms. The program is comprised of five major model components, including the hurricane hazard, terrain, wind load, physical damage and loss models (Vickery, Lin, Skerlj, Twisdale, & Huang, 2006) . The hurricane hazard model is based on the mo del described in the pa per written by Vickery et al (Vickery, Sperlj, & Twisdale, 2000) . The model determin es the entire track, wind field and associated rainfall of the hurricane being simulated . Also incorporated into the mode l are the rain fall rates that are based on the hurricanes wind field . The rates are not used for calculation of structural damages to the building, but are important for determining the amount of interior damage that is caused by the water intrusion throu gh damaged windows and
31 doors. Validations of the model were conducted through comparisons of simulated and observed wind speeds at over a 140 anemometer stations. Wind speed and directional time history data are produced at 15 minute intervals throughout t he duration of the storm and recorded in the database. As the ground roughness of the terrain becomes rougher around structures, the ground level wind speeds can become dramatically reduced, but with increased turbulence. Therefore , a proper terrain model must be created to correctly interpret the wind speeds that are acting on the structure itself. Surface roughnesses were mapped by assigning roughness values to existing land use land cover (LULC) databases. The methods used to estimate the vulnerability of buildings for the HAZUS model are similar to those in the research proposed in this dissertation, utilizing a component based simulation approach to evaluate the risk to individual components that make up the structure. The general approach taken by AR A for the development of HAZUS was to build a component model to run Monte Carlo simulations of hurricane events striking particular building types, producing a probabilistic load model for comparison against structural resistances. Figure 2 5 is a flow chart detailing the steps taken in the HAZUS simulation process for the component model. The first step in the component model algorithm is to generate an individual probabilistic realization of a building by random ly sampling the component re sistances, building orientation and shielding factor f rom pre assigned probability models. The probabilistic nature of building component resistances are developed from laboratory testing results in the literature and from engin eering judgment in the case of missing information. The wind loading on the structure is then determined in a time stepping
32 fashion using wind intensities and direction in 15 minute increments. The wind induced loadings acting on the structural components are calculated by pressure coefficients based on an empirical modeling approach and the applied winds. The structural loads are compared to the previously sampled resistance values to determine if any components are loaded beyond capacity. If a component is overloaded, then it is removed from the structure and the damage is recorded. Pressure loading is not the only failure mechanism accounted for in the analysis. Windborne debris can contribute a major portion of the total damages to the structure. Two de bris models were created: one accounting for debris from other residential structures and another for debris originating from gravel roof tops. A probabilistic model is used to determine if missile strikes occur and damage openings. If an opening fails as a result of either wind pressure or impact from windborne debris, then the program has the capability of adjusting the internal pressure and recalculating the structural loads to check for failure again. This process is continued for each 15 minute interva l throughout the length of the storm. The damage information obtained for thousands of iterations of each type of building in the model is used to generate vulnerability curves. These are used in conjunction with knowledge o n th e number of each type of bu ilding in a specific area, and the likelihood that a hurricane of a specific intensity will strike the area to determine the amount of damage likely to occur. The HAZUS m odel also defines the damage state of the structure governed the performance of the bu ilding envelope and is separated into 5 states, varying from 0 (representing no damage) to 4 (complete destruction). Losses are estimated from the building damage states using empirical cost estimation
33 techniques for building repair and replacement. The lo ad resistance damage loss methodology used in the HAZUS MH provides the framework needed to examine the effect of miti gation in a quantitative manner by the modeling of building components with increased resistances, and assessing the reduction in the hurr icane induced damage and loss (Vickery, Skerlj, Lin, Twisdale, Young, & Lavelle, 2006) . The fundamental concept of modeling aggregate probabilistic damage to structures as a sum of various individual components provides tremend ous flexibility. It allows for the inclusion of new code provisions, retrofit measures, construction methodologies and materials directly into the framework to determine structural vulnerability to wind. The assignment of appropriate failure probability d istributions for the various structural components separates the model dependency on existing claims data to estimate future storm damage in regions for which claims data is not available . Claims data from various sources are used for validation of the mod el rather than determining the shape of the vulnerability curves as previously seen in the curve fitting methods. Given these advantages, the current multi university public domain loss model project is using the probabilistic component approach to determi ne structural vulnerability to wind. While there are significant departures from the HAZUS methodology, the ability to generate vulnerability curves from simulation is the key commonality. Florida Public Hurricane Loss Model Overview As mentioned, the FD FS sponsored the development of the FPHLM to assess the annualized risk of insured losses to the residential infrastructure in Florida. The model is coordinated by the I nternational Hurricane Research Center at FIU . The FPHLM combines the fields of meteoro logy, engineering, actuarial science, and
34 computer science, and includes faculty at FIU , UF , FIT, FSU , UM , and NOAA . The goal of the project is to develop a model to predict the annualized hurricane wind induced insured losses to residential buildings in v arious regions in Florida (Cope, 2004) . The meteorological team consists of students and faculty from FSU, UM and NOAA. Their role is to develop a wind field model that projects a probabilistic descriptor of annualized 3 second peak wind speed for each Flo rida zip code. The method uses computer simulations based on historical hurricane tracking and intensity (Powell, et al., 2005) . The wind field model is based on the slab boundary layer concept originally conceived by Ooyama (1 969) and implemented by Shapiro (1983) . The engineering group includes students and faculty from the UF and FIT . Their role is to develop probabilistic relationships between wind speeds and the physical damage from wind pressure, debris and water intrusion , referred to as the vulnerability model. The actuarial team (FIU) aggregates and translates this physical building damage into insured losses. Finally , the comput er science team ( also FIU) combines all components into one program and performs the task of generating outcomes of loss risk for insurance portfolios provided by the State of Florida. The development of the vulnerability model is based on a component approach, similar to that used in the HAZUS MH model developed by ARA , combining engineering mod eling and simulations with engineering judgment and observed data. The determination of the probability of external (envelope) damage to a modeled building is based on structural calculations, physical tests of the capacity of various building components a nd Monte Carlo Simulations. Interior damage to the building is determined
35 based on the damage to the building envelope. The basic model is a rectangular shaped building with a footprint , representative of an average square footage , for different regions in Florida. The modeled exterior components include windows, doors, walls, roof cover, roof decking, and roof to wall connections. The capacities of these components are assigned using random number generation based on a probabilistic description which diffe rs from component to component. The probabilistic capacities are based on laboratory studies, the interpretation of post damage surveys and manufacturer test data (e.g. Simpson Strong Tie High Wind Resistant Construction Guide). Many simulations are genera ted in which wind loads are compared to the capacities of each exterior component to produce a total damage output. The results of these many simulations are analyzed to determine vulnerability. For each simulation of a model, a unique realization of the s tructure and wind load is created. The wind load is also randomized based on a probabilistic description of wind speed as well as pressure coefficients. Wind load calculations are based on the Minimum Design Loads for Buildings and Other Structures (ASCE 7 05). The structure is subjected to pressure loads from winds approaching it from eight different directions (Figure 2 6). The resultant wind loading on the building is thus directionally dependent. Modifications were made to the delineations of the pres sure zones in the ASCE Wind Load Provision based on analysis of wind tunnel data conducted in the initial development of the model. Damages to the building envelope are then used in the prediction of water intrusion. It has been estimated that, once water enters the structure, insured losses can reach 80 percent of the total insured value of the house (Spark et. al.
36 1994, Rosowsky). Once damage to both the building envelope and interior spaces has been assessed, the cost of repair or replacement is estimate d to determine the total losses. In conclusion , the component approach represents the subject structure as a probability of damage to individual building components conditioned upon wind speed, this translates an approach wind field into pressure loads on the building exterior , and quantifies resultant damage to components whose randomly assigned capacities are exceeded. After many such simulations the likelihoo d of failure (vulnerability) of the various components is assessed and presented as a function of wind speed. Validation for the vulnerability model is conducted by comparing predicted physical damage vulnerability against observed field data following land falling hurricanes. Validation for the FPHLM final output of projected insured losses is condu cted by comparing modeled loss projections with portfolios of actual insured losses. Status of the FPHLM Until recently, the FPHLM model only addressed the vulnerability of SFR construction (Cope, 2004) . However, a large portion of the overall residential infrastructure at risk is comprised of commercial residential construction (apartments and condominiums). The purpose of the proposed research was to expand the capabilities of the vulnera bility model in three ways: 1) d evelop ing a commercial residential vulnerability model (multi family units less than four stories ), 2) by creat ing a updated version of the single family residential vulnerability model by increasing flexibility with regard to footprint shape and size and improving component cap acity and wi nd load assumptions and 3) develop a mid high rise model (multi family units greater than three stories).
37 Figure 2 1. Loss Costs for Florida model Submission (Watson, Johnson, & Simons, 2004)
38 Figure 2 2. Lost Costs in Florida (Watson, Johnson, & Simons, 2004) Figure 2
39 Figure 2 4. Bhinderwala's Relationship between wind speeds and loss ratio (Bhinderwala, 1995)
40 Figure 2 5. HAZUS Individual Storm Simulation Methodology (Vic kery, Lin, Skerlj, Twisdale, & Huang, 2006).
41 Figure 2 6. Plan view of a roof depicting the eight wind directions considered
42 CHAPTER 3 NEW COMMERCIAL RESIDENTIAL STRUCTURE CODE Methodology: low rise commercial residential The LRCR model was develop e d to represent apartment and town house style structures of three stories or lower. The development of the hurricane loss projection model is only feasible by making simplifications to various assumptions. The wide variety of individual structures that ma ke up the building stock, along with the uncertainty of component capacities and wind loading for each structure makes the development of loss projection model for separate building economically impractical. Hence, the implementation of the Monte Carlo con cept which provides a general representation of the building stock aggregate . The components in the damage model include roof cover, roof sheathing, roof to wall connections, walls, wall cover and wall sheathing, windows, entry doors, sliding glass doors, soffits, and gable end truss integrity. Given the large array of sizes and geometries for low rise commercial residential structures, the program is developed to provide the user with flexibility in choosing a building layout and dimensioning details (foot print, overhang length, roof slope, roof and wall type, etc.). The changes in construction practice over decades also require flexibility when choosing construction quality with regard to hurricane wind resistance. The model allows the selection of buildin g components with a variety of strength options to represent a range from poor to high wind resistance (braced or unbraced gable ends, old or new roof cover, sheathing nailing schedules, etc.). A standard (default) model was developed based on a building e xposure study that quantified the average square footage per story and other
43 descriptors. Default settings were also developed to represent weak, medium, and strong construction practices. Typical construction practices, building types and material usage varies across the state of Florida. One of the important stages of the project was to identify the most prevalent variables in order to define a scope of work which will allow the loss projection model to encompass as much of the building stock as possibl e. These variables were isolated by the exposure study conducted at FIT . Survey of the Florida b uilding s tock (exposure study) FIT conducted a survey of commercial residential structures in various counties in Florida in order to identify the most common b uilding features that make up the building stock. The survey was done using the Florida property appraiser s database from different counties. Of the 31 counties contacted, 23 provided commercial residential data. Of th ose 23, 19 had partially useable data , while 13 of those had complete information on the features being investigate d . These features became the primary variables used in generalizing the model and covering the majority of various structures in Florida. The survey revealed that, among the comm ercial residential inventory, low rise structures accounted for 96 percent of building stock , with the remaining 4 percent mid high rise (Pita G. L., 2008) . Within the low rise category , it was determined that over 90 percent of the roof types consisted of either gable or hips roofs. Flat and other roofs (including shed, mansard, gambrel roof , etc . ) made up a small portion of the buildings and were not considered for the low rise commercial residential model. The most frequently encountered roof cover type was shingles at 75 percent , except in Monroe County which was predominantly metal roof. The exterior wall materials were distributed
44 between wood and concrete block option depending on the county. By adding both wall materials to the model, roughly 80 to 1 00 percent of structures were accounted for in any county . Table 3 1 below, summarizes information gathered by FIT on the roof type, roof cover and exterior wall materials from the property appraisers database. Ave rage square footages and layouts were determined for the low rise commercial residential structures. The average square footage for a unit in a commercial residential building was between 800 to1000 square feet with a total of at least 3 to 5 units per flo or. These were used in the determination of the square footage and partitioning for the units. The total number of stories was also sampled for the different counties. The distribution of the total number of stories (1 3) varies drastically from one county to another, as seen in Table 3 2. The construction quality of the structures can be associated with the time period it was constructed in. Building codes and standards evolve as new research and experience uncover the necessity for improvements in buildi ngs. Pita et al. (2008) identified important changes in building code requirements and the years that they were implemented. Table 3 3 reflects the distribution of the low rise commercial building that was constructed in each county during their respective time periods. The LRCR code separates the building into 3 categories of strength; weak, medium and strong. The buildings from the different time periods is related to one the aforementioned construction qualities. Monte Carlo s imulation p rocess Probabilistic damage assessment is conducted by creating an individual building realization . Random capacity values are assigned to the variou s components based on application of a truncated Gaussian distribution. This realization is subjected to a peak
45 3 second gust wind speed from a particular direction. Directional loads are calculated using randomized pressure coefficients based on directional modifications to ASCE 7, and a comparison of surface and internal loads to component capacities. Damage occurs when the assigned capacity of a component is exceeded by its loading. Once the openings are checked for pressure failure , any impact of airborne debris is also evaluated. Damaged components are removed and a series of checks are p erformed to determine if lost components redistribute d loading to adjacent components or if they change d the overall loading. For example, loss of a roof to wall connection places additional load on adjacent connections, while an envelope breach can potent ially alter internal loading by changing the overall loading on many components. Iterative convergence is used to produce the final damage state for that building realization. The results of this single simulation are documented based on the final iteratio n . A nother realization of that building is constructed by assigning new random capacities to each component, and the process repeats for the same base 3 second gust, same wind direction, and newly randomized pressure coefficients. The process is repeated f or eight wind directions and a series of wind speeds between 50 a nd 250 mph in 5 mph increments. Figure 3 1 describes the iterative simulation process for the LRCR . The damage to the building envelope is then used to project internal damage using algorithm s developed by the FIT engineering vulnerabi lity team, most significantly from water penetration from wind driven rain. T he interior damage projection accounts for a significant portion of the overall lo ss and presents additional modeling challenges. A sig nificant challenge in the expansion from SFR to LRCR was the need to incorporate dimensional flexibility in the representation of building shape. In the single -
46 family version of this program, the user was required to select from a small population of avail able structural dimensions. The layout of each component for the model was hard coded into the program. The new commercial residential model takes a dimensional variability approach. For example, t he user input s the desired dimensions of the building and u nits per floor, and the algorithm will assign the layout of all of the components of the building, i.e. roof sheathing, roof to wall connections, windows, doors etc. Sizes of components such as the roof and wall sheathing are assigned based on typical cons truction practice. As a user selects, for example, a desired building width, height and roof slope, the algorithm will appropriately determine the roof and wall sheathing layout, opening locations in each unit (windows, doors), wind load pressure zones, lo ad paths, etc. Table 3 4 lists the variable parameters. Exposure studies conducted by FIT produced the default settings most representative of typical Florida construction. These defaul t settings were used to produce the results shown later. Mapping of th e individual components Once the specified parameters of the structure are defined by the user, the first task is the mapping of the different building components. Data, including dimensions, the height of the centroids from the floor, the capacities and t he loading for the components are placed in a matrix format. The matrix is populated with information in a way that the cells represent the physical location on a particular surface of or around a building. Component interactions are also established. The use of typical construction layouts of components are used to determine the location and dimension of the individual components. Other variables such as the number of units also define the location of building openings.
47 The mapping of components is a vital part of programming. It is the basis that determines the makeup of the building, the dimensions of components, the assignment of capacities, the allocation of loads, the interaction of components and the recording of damage. Mapping is used for the majori ty of the larger components which determined breaches to the building envelope. Roof sheathing, roof to wall connections, wall sheathing and openings are components mapped using this matrix format. Components damages such as roof cover, wall cover and soff its are not individually mapped in matrices due to their smaller sizes and the fact that their exact locations do not directly affect other aspects of the model, including internal pressurization or water intrusion. Roof sheathing panels are positioned on the roof using common roofing techniques. Based on the dimensions of the building an appropriate sheathing pattern is selected. The first row of sheathing is placed at the eave of the roof and the subsequent rows are staggered by 4ft (half the length of th e 4ft by 8ft panels). Matrices determining the dimensions of the panels are also created (Figure 3 2). Randomized capacities are assigned to each panel (Figure 3 3) and r andomized loads based on the zone delineations, coefficient of pressure a nd wind speed s are calculated too (Figure 3 4). Because of the consistency between the matrices, all data can be tracked for the individual panels and comparisons between capacities and load can be used to determine panel fail ure . Roof to wall connections, wall sheath ing and building openings utilize similar matrices. Roof to wall connections are placed 2ft on center along the length of the building for gable roofs. Then, a two row matrix is created where each row represents a particular side of the roof and each colum n is the position along the length of the wall.
48 Hip roof buildings have two matrices . O ne matrix is for the connections along the length of the building and other for those placed along the width. Wall sheathing panels are oriented vertically at a height o f 8ft for the main story and an additional 2ft above to accommodate for inner story spaces ( the support and utility housing space between floors). In addition, a separate matrix is made for each wall face. Because they lie within the same space, locations of openings are mapped within identical matrices to the wall components. The entry and sliding doors are placed at the center of the each unit on their appropriate sides of the building. An offset window is added adjacent to each entry doors and evenly spa ced windows are placed along the width of the building. In order to accommodate the addition of the openings, an equivalent wall sheathing panel is removed from the corresponding location of the wall sheathing matrix. Other advantages of this mapping schem e are the ability to establish component relationships and to identify breached locations. One example is the relationship bet ween roof sheathing and roof to wall con nections. The loads on the roof to wall connections are dependent on the uplift acting on the sheathing. Therefore a roof to wall connection must be appropriately identified with the sheathi ng attached to its truss. Last , the matrices identify the wall face and location of the breaches to the building loads to assess internal pressurization of the building as well as water intrusion. R esistance capacities of components The capacities of the various exterior building components are represented within a probabilistic framework, requiring distribution and shape parameters which vary with constructi on type and quality. The Gaussian distribution is the default probability model for all components, truncated at two standard deviations from the mean. The component capacities are resampled if they fall outside of the two standard deviations in
49 order to n egate the possibility of a negative capacity or an unrealistically high capacity being assigned . The shape parameters needed are the mean and standard deviation of the failure capacity of a given component ( Figure 5) . The actual resistance assigned to a given component in a single simulation, e.g. a single roof sheathing panel , is randomly assigned based on the chosen distribution and stored in a matrix entry mapping the physical location of the component. Thus , the entire structure is represented by a series of matrices whose cell locations and values represent physical locat ion s and capacity. The capacities assigned to the different structural components have a significant effect on the final damage output projecti ons. Acquisition of appropriate probabilistic capacity models includes many different sources: codes and standards, laboratory research both at UF and in the literature, product manufacturers, and post hurricane field observations. Here are a few examples: Wind Resistance capacity was found in ASTM 1300 for annealed glass plates. Window sizes were selected to represent typical residential construction. The safety factors were removed and values between 60 and 90 psf were calculated. An average value then as sumed for medium stren gth windows. The ACI Masonry Design Manual was used in determining failure of masonry walls. By using the equations and methods from the design code, the program is capable of calculating the maximum bending moment of the wall induced by the applied wind pressures. Failure is determined when the cracking moment of the concrete is exceeded. Both out of plane (bending) and in plane (shear and torsion) are taken into consideration for the loading of the walls of each story. Laboratory tes ting quantifying the capacity of sheathing panels with different connections, nailing schedules and of varying ages. Testing has yielded mean capacities and their statistical information (Prevatt, Hill, Datin, & Kopp, 2009) Th e manufacturer Simpson Strong Ties provide s design capacities for their connections. The factor of safety was also obtained in order to gain the mean resistance capacities they had found through their private testing. Laboratory testing has been conducted to help quantify the degree of protection offered to windows via typical metal shutter systems.
50 The selection of resistance capacities used in the model is not static; it evolves as more data becomes available. Values change as more information is compile d about the components. The specific values (mean, standard deviation) for the various component capacities may be updated as additional information becomes available. Table 3 5 , defines the current capacities for the individual components. The resistance to impact of a glazing component is modeled so the component is impacted and it possesses the required force to actually damage the window. Window capacity is au gmented by mitigations measures such as different forms of window protection (plywood, steel or engineered shutters) and stronger window materials (laminated or impact resistant). To account for mitigation measures in the impact capacity of the windows, correction factors (values greater than 1) are appoi nted to each improvement and are directly multiplied to the window capacity ( Tables 3 6 and 3 7) . These values are also applied to the mean pressure capacity of the window and sliding doors, essentially increasing the capacity of the glazing to wind loadin g by acting as buffer. A probability of impact factor was also assigned for each shutter type. These values are not quantifiable and were arbitrarily chosen in order to produce the desired relationship between the different protections. The procedure for a ssigning the resistance to impact of glazing components is illustrated in the section describing the debris impact loads. Structural loads: low rise commercial residential Pressure l oading During a wind event, external components of the building are subjec ted to wind loads. The majority of component failures occur through direct wind surface interaction.
5 1 These components include the roof/wall sheathing and covers, masonry walls, openings and soffits. Roof to wall connection damages incur through load transf er from the uplift of roof sheathing, while gable end collapse are a result of damages to other exterior components (gable end sheathing and roof sheathing . The algorithm to assign wind pressure loads was based on the ASCE 7 05 Wind Load Provisions after m odificati ons were made to account for wind direction. Since the model explicitly considers the direction of the approach wind to determine the pressure loads, it is important the load mapping strategy reflect s this. The ASCE 7 wind load maps cannot be appl ied a s is to the model, since these maps are an envelope of results from all approach wind directions rather than direction specific. C omponent and cladding pressure coefficients were used because of the focus on the performance of the individual exterior components . The mapped zones for the pressure coefficients were modified to reflect the direction of the wind relative to the structure orientation. For example, Figure 6 depicts the zone delineation given by ASC E 7 05 (left) and the modified delineation of the roof pressure zones assuming the winds are normal to the left side of the building (right) . Such a modified layout was developed and applied for eight wind directions in the SFR model developed by Cope (20 04). The LRCR vulnerability model adopted this approach. However, the specific assignment of modified zones with direction was re evaluated based upon wind tunnel data available for a gable roof model with rectangular plan (NIST Aerodynamic Database) . Figure 6 shows the delineation of the pressure co efficient developed from this wind tunnel data for wind parallel to the ridge line. The original (Cope 2004)
52 configuration of the modified wind zones is superimposed on to the zone location on the left figure, the right figure shows the update to the assignment of directional wind zones based on the wind tunnel contour results. This approach was applied to each of the wind directions considered in the model, including win ds parallel, perpendicular, and cornering with respect to the ridge line. The velocity pressures are determined from a modified version of Equation 6 15 of ASCE 7 05. q h = red * 0 . 00256* K z *K zt *K d *V^ 2* I ( 3 1 ) red = Ai r density reduction factor q h = velocity pressure evaluated at height z = h , in lb/ft2 K z = velocity pressure exposure coefficient evaluated at height z K zt = topographic factor K d = wind directionality factor V = basic wind speed I = importance factor r ed 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 , a member of the team developing the meteorological component of the model (Hamid, 2007) . The veloc ity pressure exposure coeffient (Kz), topographic (K zt ), directionality (K d ), and importance (I) factors were removed from the equation. The directionality factor reduces the design pressures to account for the design loads having less than 100 percent pro babilit y of approaching from the worst case direction used to generate the ASCE 7 enveloped map. Since the program takes direction into consideration this factor is excluded from the calculation. In Florida the Topographic factor is rarely allowed to be gr eater than 1.0, therefore factor can also be ignored. T he importance factor is used for
53 design purposes to increase design loads based on its level of importance. T he velocity pressure exposure coefficient (K z ) is also set to 1.0 . The meteorological team p rovides the geographic location dependent probability distribution of 10 meter 3 second gust wind speeds from the hurricane prediction model. T he LRCR code modifies this value to determine wind speeds at different heights. The heights at which the wind spe eds are determined are dependent on the number of stories of the building. The velocity is calculated at the center of every floor for analyzing wall components and openings, and at the mean roof height for roof related components. Following the method pre sented in Simiu and Scanlan (1996) , E quation ( 3 2 is used to convert the 3 second gust wind speed to an hourly average wind speed. The mean wind speed is required for the elevati on adjustment using the log law ( ( 3 3 ). The wind speed is then taken from the 10 m elevation to the gradient wind speed and back down to the desired elevation, yielding the average wind speed ( ). This is done by combining the log law equations going from 10m to gradient height and from the gradient height to the final elevation, thus creating Equation ( 3 4 . Once again , Equation ( 3 2 from Simui and Scanlan is used to convert from the 1 hour mean wind speed to the 3 second gust wind speed, where t = 3s. In this manner the conditional 3 second wind speed at 10 m is converted to 3 second gust at the desired height of interest on the building. Thus a one story building has a lower wind speed at mean roof height than a two or three story building, referenced to the 10 m gust probability distribution. ( 3 2 )
54 ( 3 3 ) k = is the (~0.41) u * = the friction (or shear) velocity (m s 1 ) z = desired height of analysis z o = surface roughness ( 3 4 ) U 2 = 3 second gust at desire height z U 10 = 3 second gust at 10m z = desired height of analysis z o = surface roughness The 3 second gust wind speed is then applied in Equation ( 3 4 to find the velocity pressure at the desired heights. Pressure Equation 6 18 from the ASCE wind provisions ( Equation 3 5 ) is used to determine the pressure loads applied to the component being analyzed. The values for pressure coefficients are determined using the tables found in the ASCE wind load provisions ( Figure 3 8 and 3 9 ) . The appropriate applied pressures were determined for the individual components based on their effective area. p = q h [( GCpf GCpi )] ( 3 5 ) The internal pressure is dependent on how much of the building envelope has been breached. Internal pressure coefficients are 0.18, 0.55 and 0 for enclosed, partially enclosed buildings and open, respect ively. The direction/sign of the internal pressure is determined by the ratio of the volume of air coming into the building versus that of the air being expelled from the building. This is determined by multiplying the size of the damaged wall area by thei r respective wall pressures (positive pressures for windward
55 walls and negative pressures for leeward walls) for each and summing the values. If the net value is positive the internal pressure forces the components outwards ( Figure 3 10 A), further increasi ng the loads applied to components in exterior suction zones and vice versa for negative net values ( Figure 3 10 B) . The internal pressure between the floors of the building are kept independent of one another. Due to the wide array of possible internal set ups of individual buildings it is very difficult to model for the different possibilities . T herefore , it is assumed that there is no transfer of pressure between any of the stories. The internal pressure for each floor is solely determined by the damages t o the openings and walls of that particular floor. A floor with no damage to the wall components or openings is considered to be fully enclosed and the ASCE 7 05 identified internal pressure of 0.18 is assigned. According to ASCE 7 05 Chapter 6.2, for a s tructure to be consider ed partially enclosed structure the total area of openings in a wall that is subjected to positive pressure must exceed 4ft 2 or 1 percent of the area of the wall (whichever is smaller). The same theory was also applied for walls that are placed under negative loads, but the sign of the internal pressure is switched to positive accordingly. For structures where opening are greater than the opening requirements the internal pressure increases to a value of +/ .55, depending on the whet her or not the damage is under negative or positive pressure. In instances where there are openings on both the windward and balance of the building (all side s placed in suction ) a balance must be determined. The mean positive pressure and negative pressur es are used to analyze the flow in and out of the building to solve the internal pressure coefficient. Because it is assumed that the external pressure at the damaged wall components is uniform for both the positive and negative zones, an
56 analysis of there being a single opening on the windward and leeward walls is valid. From Holmes (2001) ( 3 6 ) Rearranging the equation and solving for the internal pressure coefficient, the following equation is obtained. ( 3 7 ) C pi = coefficient of internal pressure C pW = coefficient of pressure on the windward wall C pL = coefficient of pressure on the leeward wall A W = area of the opening on t he windward wall A L = area of the opening on the leeward wall Holmes compared the curvature of the equation to measurements of the mean internal pressure coefficients of a building model with various opening ratios (area of windward opening/area of leeward opening). The measured data agreed very well with the curvature of the lines, as seen in Figure 3 11. Because the limits of +/ 0.18 and +/ .55 were initially used to define the fully enclosed and partially enclosed limit states, the values generated by the model were also limited by the same values. Therefore an internal pressure of 0.65 is reduced to 0.55 for the internal pressure of the building. The internal pressure coefficients for the different opening states are identified in Table 3 8. The inte rnal pressure of the attic space is determined by the aggregate effects of the external pressure acting at the location of the damaged sheathing. The external pressure at each damaged component is multiplied by the ratio of the area of the components divid ed by the total area of the components enclosing the attic space
57 (Equation 3 8) . The final value is also limited by the same internal pressure coefficients as the floor by floor analysis (+/ 0.18 and +/ .55). ( 3 8 ) a i = area of component i A tota l = total area of components enclosing the attic space. p i = pressure acting on component i As previously discussed, the damages to opening and wall components allow ai r to travel into structure resulting in higher internal pressures. Combined with the external wind loads, significantly larg er wind loads could be achieved (Holmes J. D., 1979) . The existence of openings (attic doors etc) betwe en the attic and living spaces provides a pathway for wind to travel from one area to the other. Because of this the internal pressure of the inner story area below the attic can affect the internal pressure of the attic space itself. Kopp conducted wind t unnel tests on models with different sized openings in the ceiling between the attic space and the story below it (Kopp, Oh, & Inculet, 2008) . It was found that buildings with opening area ratios (ratio of the area of the openin g and the total area of the ceiling) greater than 0.4 percent , 80 percent of the peak pressure in the living space can be transmitted to the attic space affecting the pressure applied to the roof components. It is assumed that all structures have an attic door that connects the living space on the top floor into the attic. The damages for the walls and roof are determined assuming an initial fully enclosed condition with the corresponding internal pressure. Once damages have been assigned the openings the i nternal pressure is adjusted. Once these values are determined, 80 percent of the internal pressure to the top story is added to the internal pressure of the attic space to adjust for the new internal pr essure ( Equation 3 9). The
58 new loadings are applied t o the building components and any new damages are recorded. ( 3 9 ) The aggregate pressure of the internal and external pressures can either increase th e potential damage of components or decrease it, depending on the location of the breach. Debris i mpact d amage In addition to wind pressure, failure can also occur due to the impact of windborne debris, which is separately modeled and evaluated for each o pening (window , entry and sliding doors). The LRCR missile model currently assumes that roof cover is the dominant source of windborne debris. The fundamental equation for the missile model is based on the cumulative exponential distribution. Equation 3 10 models the probability of damage of a component covering an opening ( P D ( v wind )) given a 3 second gust wind speed ( v wind ): ( 3 10 ) Where: N A is the total number of available missile objects in the area upwind of the structure being an alyzed. A ( v wind ) is the fraction of potential missile objects that are in the air at a given 3 second gust wind speed ( v wind ). B ( v wind ) is probability of the missile hitting the structure
59 C is the fraction of the total area of a particular opening catego ry (window, entry door or sliding door) to area of the impact wall in which it exists. D ( v wind ) is the probability that the impacting missiles have enough momentum to damage the component impacted. N A is the total number of potential missiles that are upw ind of the target structure. It is assumed that surrounding buildings are similar to that of the target building and therefore have approximately the s ame number of total roof cover. The total number of potential missiles is dependent on the exposure categ ory of the area and the wind direction. The particular exposure category chosen by the user determines the location of the surrounding buildings. There are eight building surrounding the structure in Figure 3 12) while the re are only four buildings Figure 3 13 ). Multipliers of 1.0, 2.0 and 5.0 are factored into building separations for urban, suburban and open exposures, respectively. Assuming a base clearance of 45ft, the target building will be 45 x ft (where x is the exposure multiplier) away from the adjacent buildings A and B, and (45 x) ft away from cornering building C. The variable N A is evaluated for each of 8 directions as seen below in Figure 3 14. Directions of wind approach in the missile model For wind directions that are perpendicular or parallel to ridgeline of the buildings, it is assumed that N A is equal to the number of shingles from the adjacent buildings. For wind directions diagonal to the ridgeline of the building it is assumed that there is full contributions from the building diagonal to ridgeline and a partial contribution from the
60 adjacent structures (25 percent contribution). Therefore there is a 50 percent increase in potential airborne debris from the four diagonally approaching wind directions. The A ( v wind ) variable is dependent on the percentage of shingles that are damaged and have sufficient velocity to take flight. The variable was determined b y r u n ning the model for a building similar to the one being analyzed and the roof cover damages recorded for all the wind speeds. In order to isolate the roof cover damage that is due to wind failure of the cover and not the sheathing, the sheathing panels were given capacities that were much greater than any potential load that was applied. A matrix of percent roof cover damages was created and used as the inputs of the A ( v wind ) variable. Depending on the current model and wind speeds being analyzed , the a pp ropriate percentage is selected and randomized. A sample output is presented in Figure 3 15. B( v wind ) is the probability of the missile hitting the structure and is dependent on wind debris studies performed by Sylvia Laboy at the UF (Laboy, Gurley, & Master, 2012) . The trajectory model tracks the flight of the roof cover fragment from its rest on a sloped roof. It utilizes a Monte Carlo simulation methodology, where 100,000 trajectory experiments are conducted for a debris s ize and the probability of the debris fragment hitting a particular floor is recorded. Variables such as debris size and density, and building clearance distance and heights were modified to depict the necessary need of the loss model. Outputs were arrange d into a matrix that can then be loaded into the program and appropriate corresponding probabilities are extracted (Laboy, Gurley, & Master, 2012).
61 C is the fraction of the total area of a particular opening category (window, entry door or sliding door) t o the total area of impact wall in which it exists. Now that the probability of a floor being hit has been determined, the probability of the debris hitting the opening of interest has to be assessed. This is simply the area of the opening divided by the t otal wall area of the floor. The C value for a 4ft by 4ft window on a wall with dimensions 10ft by 40ft is equal to .04. Based on this value, if a projectile was to strike this wall, there is 4 percent chance of it actually hitting the window itself. The v ariable is dependent on the weight of the shingle (calculated from the density and physical dimensions of missile), the velocity at the end of the time step used in the trajectory calculations for Variable B, and the angle of incidence. The angle of incide surface of the impacted opening during the collision. A recent study evaluated the momentum threshold required for shingles to break unprotected residential window glass. It co ncluded that the wind speeds necessary to remove and transport shingles convey sufficient momentum t o break impacted annealed glass (Masters et al. , 2010) . This is incorporated in the current model by assigning a value of 1.0 (100 percent ) to the D paramet er. For each opening, the probability of damage due to missile impact is simulated. Failure of the openings is analyzed first by pressure application. If the window is not initially broken by the pressure, missile impact damage is assessed. Component failu res are then summed to yield the total damage of the opening. Roof Components: Roof Sheathing Roof sheathing damage, as seen in
62 Figure 3 1 7 , are due to wind uplift pressure. Internal pressurization due to breaches in the building envelope exacerbates or reduces the probability of damage. It is assumed that the pressures acting on the sh ingles are transmitted directly through the shingles and evenly distributed to the sheathing. Before determining any of the loadin g on the structure, the code must first appropriately determine the layout of the roof. The roof dimensions are determined by the roof pitch and the plan view dimension of the roof. The roof pitch is variable, but a standard 4/12 pitch was selected to repr esent the slope of a typical roof in Florida. As previously discussed, the dimensions of the foundation of the building are user defined for each model. In order to simplify the algorithm for component placement, the foundation of the building is rounded t o multiples of two and the overhangs are restricted to whole numbers. For example, a 49ft x 61ft rectangular roof (total area of 2,989 sqft) is rounded up and represented by a 50ft x 62ft roof (3,100 sqft). This yields only a 3.7 percent difference in tota l area. This simplifies the programming process by minimizing the total number of possible sheathing layouts that the loading zones will have to be applied to. A simplification was also applied to the generation of the hip roof layouts. From the plan view position the hip regions of the roof extends the length of the width of the roof and tapers in to where it meets the ridgeline of the roof (distance is equal to the width of the roof). The plan view depicts a 45 45 90 triangle as seen in the Figure 3 18 be low. Due to the pitch of the roof, the length of the hip roof is no longer equal to width of the roof. Instead the distance from the eave to the ridge is equal to half the variable called Width_Slope in Equation 3 10. Because the value of the width along t he eave of
63 the roof is static and does not increase uniformly with the length Width_Slope, the angles at the corners of the triangle also increase. This underestimates the area of both hip and main roof areas. ( 3 1 1 ) Assuming a pitch of 4/12 (18.43 degree) and the width of the building is 30 ft, the value for Width_Slope is 31.6 ft. This provides a difference of 225 sqft and 249.6 sqft, and a total area difference of 9.87 percent . Due to the small discrepancy in areas, the unprojected layout was used . The main advantage is the uniformity from one row of sheathing to another. Each whole sheathing panel is 4ftx 8ft. With a 45 degree angle at ea ch end and 4ft wide rows, there is a decrease of one panel per row beginning from the bottom row and going to the top. Therefore, one sheathing panel is removed for every row while the dimensions of the sheathing panels on the end stay the same. This drast ically simplifies the layout by not having to create an algorithm that has to calculate the areas of the sheathing on the ends which would typically be cut to fit. The external pressure acting on each sheathing member is determined using the modified mappi ng previously discussed. The component and cladding pressures are normal to both the roof cover and sheathing panels and directly applied to the resisting capacities of the component (Figure 3 19). The load on the roof sheathing is a combination of both th e ex terior pressure and the internal pressure of the building (enclosed or partially enclosed after possible breaches and internal pressure modifications have been assessed ) . An aggregate pressure is calculated for each panel based on its location in relat ion to the pressure zones mapped for a given approach
64 wind direction. The delineation of the different zones (1 3) is made for each panel (Figure 3 20 ). Components and cladding pressure coefficients from ASCE 7 are selected for Zones 1 3. An overhang lengt h is assigned for all of the low rise structures. The program accounts for the increased uplift pressure acting on the sheathing over the overhang due to the combination of the external pressure on the top of the sheathing and the pressure created by the w ind pushing up on the sheathing from the bottom. Results of testing conducted by Vickery shows the high correlation between the soffit pressures and nearby wall pressures (Vickery, 2008) . Therefore the overhang pressures for each zone are a summation of th e external pressure and the adjacent wall pressure. For a given single sheathing panel, the area weighted average of all of the zones it lies in is used to find the final external pressure coefficient and summed with the current internal pressure coefficie nt. The pressure coefficients are randomized for each panel and the loads are determined using Equations 3 1 and 3 5. Randomization is conducted for each component in order to reflect the uncertainty of the peak pressure coefficients that will be perceived during the course of a wind event . These values are compared to the capacit ies of the sheathing panel to determine failure. Values for capacities, loading pressures and failure identifications are placed in two dimensional matrices of identical sizes, wh ere entries are representative of particular panels and its location on the roof. Total sheathing failures are calculated using methods previously discussed in the pressure loading section.
65 Roof to w all c onnections The load applied to the individual roof to wall connections is dependent on the vertical load caused by the uplift on the sheathing . Damage occurs upon separation of the roof truss from the wall ( Figure 3 21 ). Uplift loads on the roof sh eathing are transferred through the nails to the trusses that they are fastened to. These loads culminate at the interfacing connection between the trusses and the top of the wall. The roof to wall connection is what fastens the entire roof system to the w alls of the building. Roof to wall connections may be toe nail fasteners, or clips or straps. The roof to wall connections support the uplift of the roof by restricting it with a vertical load that is parallel to the wall that it is attached to . The loads on the sheathing are perpendicular to the plane of the sheathing and the direction it is acting in is dependent on the pitch of the roof. For each roof to wall connection that is analyzed, a tributary area one half of the distance between trusses (2 ft) to the left and right is assumed with a length one half of the roof width. The uplift within that region is combined and oriented parallel to the wall. As discussed in the previous section, coefficients pertaining to the components and cladding were used to attain the applied pressures acting on the sheathing. Once the roof sheathing damage has been assessed, the average pressures of the surviving sheathing within the trusses 2ft tributary width is combined accordingly. Therefore, the vertical load acting on r2w connection is directly related to the uplift created by the attached sheathing within its 2 ft tributary width. Failure to sheathing panels reduces the vertical loading on the r2w connections that is associated with. It is assumed that each r2w connect ion only bares the force from its corresponding half of the building (Figure 3 22 ).
66 As the wind speeds increase so does the damages to the roof sheathing. By fully negating the load of the damaged sheathing from the uplift on the respective connection the effects on the connection is relieved by the damages to the roof sheathing, producing a decline in r2w damage at higher wind speeds. The model takes a snapshot of damages from an instantaneously applied wind speed on the structure from a designated direct ion, unlike time stepping models which track the damage through the progression of a storm. In order to attempt to account for the uplift of a possibly damaged sheathing panel, a relationship between the capacity and the theoretical load on the panel at th at particular wind speed is made. By multiplying the capacity of the sheathing panel by the ratio of the capacity over the load, a new load representing a possible contribution to the uplift is created. As the load increases, the ratio becomes smaller, mea ning that there is a less likely chance that the panels load will be attributed to the roof to wall connection at that wind speed. A typical wood frame roof consists of trusses which are nailed to the top plates of the wall assembly. On a roof, the trusses and sheathing act as a rigid frame, acting as one unit. Testing done at the University of Western Ontario shows that the estimated wind load on each roof to wall connection may be different than the actual reaction load due to load sharing between multipl e connections through the roof elements (Kahn, 2012). In 1991 Wolfe and LaBissoniere published their work where a load was applied to single truss connections at multiple locations along an 8 truss test assembly (Wolfe & LaBissoniere, 1991) . The distributi on of the load was recorded for each connection as a percentage of the applied load. Figure 3 23 below displays a sample of their results. A similar approach was applied in the LRCR model . Each resolved connection load will be
67 distributed to the adjacent c onnections. The sum of the distributions at each connection will represent the shared uplift of the connection and used for failure analysis. Modifications were made to some of the values found within the distribution illustrated in Figure 3 23. The effect s of the load sharing were extended no more than 2 to 3 trusses away from the loaded connection; therefore distributions were altered to meet this constraint. Table 3 9 presents the distributions assigned for the different loaded truss locations. If truss 1 `was loaded with 200 lbs and trusses 2 and 3 were both loaded with 100 lbs, the resultant load at truss 1 would be equal to 146 lbs (200lb *0.58 + 100lb *0.20 + 100b *0.1). The load is much lower than the original 200 lb, while the loads at trusses 2 and 3 will increase in order to compensate. Research conducted by Dr. Peter Datin of the UF was also taken into consideration for the distribution of uplift loads. The research evaluated the vertical structural load paths due to wind loading. The loads at the roof to wall connections were analyzed to find the influence of the uplift at different locations across the surface of the roof (Datin, 2010) . The method used by Wolfe and LaBissoniere correlated directly with the many of the assumptions already implemented and was therefore selected to adequately represent the load sharing between the trusses. However, this can be easily modified in future model versions if warranted. Roof c over When compared to roof sheathin g and other impermeable components on the building, the wind induced uplift on shingles is due to a different mechanism. A positive pressure stagnation region is found at the leading edge of the shingle as the wind flows up roof. A positive pressure is imp osed under the shingle from edge to underlying seal
68 that attaches to the sheathing or asphalt shingle tab below producing uplift on the bottom surface. Flow accelerates over the upper shingle surface as over an airfoil, separating from the surface. Local n egative pressures relative to the ambient air is created on the upper surface of the shingle by the accelerated air flowing up and over the shingle (Peterka, et al., 1997). It is known that the specific mechanisms and their relative magnitudes on the shing le are dependent upon very sight specific features such as shingle material, age, size, installation method, neighboring structures, nearby trees, etc. In the current LRCR model, the shingle pressure load is based only on the component and cladding uplift loads. These other mechanisms are accounted for via calibration of the shingle capacity based on field observations of damage and the associated wind speeds. Modifications are being pursued for future model versions. Component and c ladding pressure coeffic ients are used to determine the uplift on the roof cover. Only external pressures are applied to the loading of the roof covering, as the internal pressures acts solely on the sheathing panels that they are attached to. Damage evaluation is ordered so tha t the loss of sheathing analyzed prior to that of the roof covering. I t is assumed that once the sheathing has been damaged, 100 percent of the roof cover that was attached to the damaged sheathing area is also damaged. Once the loss of roof cover due to roof sheathing has been assessed, t he remaining roof cover on intact sheathing is evaluated against the wind pressure loads to determine the total roof cover loss. The areas of undamaged roof sheathing are determined and are separated into the three wind c oefficient zones. Each area is
69 divided by the size of an individual roof cover component to determine the number of shingles or tiles in the respective zones. Randomized pressure coefficients are assigned to each and compared to their respective capacities . Failure is determined for each shingle. The total roof cover loss is determined by summing the area of roof cover loss due to sheathing damage and the area lost due to direct wind interaction. The values are divided by the total area of the roof cover t o find the percent cover damage. Because damages to roof cover do not affect other components or internal pressure, the location of the damage is not of great importance. Therefore the damage is reported solely as percentages lost, with no location mapping employed. Gable End and Truss Collapse Gable end roofs are more susceptible to damage than hip roofs due to the presence of a large flat surface to rec eive the full force of the wind (FEMA, 2011) . If not properly braced to interior trusses, a gable end wa ll is susceptible to collapse in high wind, either away from the house (Figure 3 25 ) or inward. Inward collapse can produce toppling of adjacent trusses. Both scenarios produce high losses due to repair costs and water ingress. The gable end failure model is dependent on two variables, the loss of roof sheathing along the gable edge and the lo ss of wall sheathing on the face of the gable end. Intact wall sheathing provides a large surface for the wind to act on (positive or negative pressure). L oss of edge roof sheathing essentially removes the bracing of the end roof truss with inter ior trusses. I ncreased damage to gable end wall sheathing reduces vulnerability to gable end collapse, while loss of gable end roof sheathing increase s the vulnerability. A piec e wise failure threshold (Figure 3 26 ) was created to
70 balance these factors. The specific boundaries can be adjusted to reflect the use of gable end bracing, and to include additional knowledge as it becomes available. If the wall sheathing of a gable end is under suction upon gable end failure, it is assumed that the gable end will fall away from the house, leaving the adjacent internal trusses in tact. If the wall sheathing is under positive pressure upon failure, the gable end will bear against the adjace nt internal trusses, causing possible truss toppling. The model trigger for interior truss collapse is the failure of additional roof sheathing that serves as a brace. If less than 50 percent of the roof sheathing remains on the first adjacent internal tru ss, it is considered failed and then bears against the next adjacent internal truss. The same failure check is made for each subsequent internal truss until failure is not triggered. Secondary damage is calculated for roof sheathing , roof cover and r2w c onnections as a result of truss collapse. If a truss member collapses all roof sheathing and r2w connections attached to it are considered to have failed. Soffits Wind induced failure of soffits on low rise commercial structures have been a commonly obser ved in post hurricane damage investigations. The damages to soffits are usually followed by intrusion of significant amounts of water. Therefore damages to the soffits on the underside of the roof overhang are also taken into consideration. Soffits most of ten refers to the material forming a ceiling from the top of an exterior house wall to the outer edge of the roof separating the attic area while producing a means of ventilations. Soffits are usually found in vinyl/aluminum and timber material forms, whic h is highly dependent on the age of the building. The use of different materials also yields a variation in product capacities, where the older timber soffits are
71 stronger than the more recent vinyl and aluminum ones. As previously discussed , the soffit lo ads are highly correlated with the wall load (Vickery, 2008) . ASCE pressure coefficients were used to assess the external pressures while the internal pressure is coupled with and dependent on the internal pressure of the attic space. Damages to soffits ca n be created through application of positive and negative pressures causing ( Figure 3 27 ) Wall Components The model considers timber frame and masonry wall construction . Previously discussed post storm damage studies show a very low rate of occurrence of wall collapse, and those occur only in extreme winds (e.g. hurricane Andrew). Therefore wall collapse is not explicitly modeled. With regard to the final outcome of the overall loss model (insured dollar loss), the lack of explicit wall collapse modeling is not consequential, as the accumulated damage of other components prior to wall collapse renders the structure a near total loss in any case. The modeling of wall crack s in masonry and loss of wall covering and sheathing for timber frame is significant in terms of both direct repair costs and the resultant rain water ingress and internal damage , modeled by the FIT vulnerability modeling team (Pita, et al., 2012) . Analysi s for timber frame construction consists of damage to both wall covering and wal l sheathing underneath. The masonry walls were modeled in bending and shear, with failure defined as cracking. C omponents and cladding pressure values were used for wall press ure coefficients for determining the loads for both wall materials. Wind speeds var y by height. Though the wind speed varies with the height from the ground, the wind speed at each floor is determined at the midpoint of its respective floor using the wind profile
72 calculations discussed in the Pressure Loading section. Pressure loads are calculated and randomized for each component on the floor and applied uniformly across each surface per elevation. Mapping and damage analysis of components are made for eac h wall face and floor. This was done to provide enough information for the application of the water intrusion model that is being developed by Florida Institute of Technology. The routine takes into consideration the damages from all sides of the building envelope and the directionality and rain intensity to determine how much water enters the building. Damages to the interior parts of the building are then assessed. Wall s heathing Wall and gable end sheathing are susceptible to the sum of both the internal and external pressures . The applied internal pressures can either be positive or negative depending on the ratio of the air flow, into and out of the space that they are enclosing . The sign of the wall pressures are dependent on the orientation of the win ds. Windward walls will be placed under positive pressure while the leeward walls will be subjected to negative pressures. Failure to wall sheathing ( Figure 3 28 ) is only considered through suction pull off . W e assume that the sheathing will not break thr ough flexure as the sheathing bears on the 2 ft o.c. stud supports. Damage will only occur on the leeward side of structures. When winds are perpendicular to one of the wall faces of the building, the other three walls are placed in suction and can be pote ntially be damaged due to sheathing removal. Winds that approach the building diagonally to the ridgeline exert positive pressures on two of the walls while subjecting the remaining walls to suction.
73 Wall c over Wall cover failure is induced by wind pressu re suction. Like roof cover, the wall cover is not affected by the internal pressure of the building but solely by the external pressures created by the wind flowing around the building. Additional damage can be accrued if the wall sheathing it is attache d to fails. Due to the wide variety of different wall covers it is impractical to model the exact siz e and layout of the covering. It is assumed that when a sheathing panel fails, an equivalent area of wall cover fails. Total damages to wall cover is a sum mation of wall covers failure due to direct wind interaction and to the underlying sheathing. Masonry w all Common masonry buildings are built with concrete blocks which are adhered to one another using a mortar material. These types of walls are durable an d resistant to high winds. For this program, hollow/unreinforced walls are assigned for the weak models. These structures are most suitable for light transverse loadings. The medium and high strength buildings are modeled using reinforced concrete walls. I ntermittent cores are filled with concrete that are tied to the steel reinforcement. This provides much greater tensile and lateral strength for the building. Since masonry walls are a common type of wall construction in Florida, pertinent modes of failur e must be identified. Post event survey observations have illustrated full wall collapse. But total wall collapse is not a frequent occurrence and does not need to be explicitly modele d . An important source of damage for the interior of the structure is th e proliferation of water from the exterior of the building. Cracks in the masonry walls provide an entrance for rain water into the building. The water then damages the interior walls and floors as it travels through the structure. Cracks developed through bending
74 and shear forces caused by the wind loads are analyzed for the concrete block buildings in the model. ( Figure 3 30) The m asonry wall load calculations were developed using the ACI Building Code Requirements (2008) to back calculate the required wind pressures to induce cracking within unreinforced and reinforced masonry walls. The calculated uniform loads were then compared to the applied wind loads to determine damage. To calculat e out of plane bending for a wal l (Figure 3 31), a n effective length eff for reinforced walls. The minimum net cross sectional area of the blocks was used, essentially negating the effects of the web from analysis. The transformed area concept was used for members with different materials. The compressive and tensile moments were set equal to one another to determine the depth of the neutral axis. The moment of inertia and section modulus were calculated from the cross sectional area and the location of the neutral axis. The flexural compressive strength of the masonry and tensile strength of the steel, if reinforced, were compute the Allowable moment. A uniformly distri buted load w is applied to a simply supported beam. Assuming that the maximum allowable moment occurs at the center of the beam, the uniform load required to cause that moment is determined using the simple beam equation. The combined interior and exterior wall pressures from the ensuing winds are compared to the allowable pressure to determine the failure for each wall on a per floor interval. The model also takes into consideration failure due to shear loads (Figure 3 32) . As the building is loaded by th e pressures created by the wind flowing around the
75 building envelope, in plane stresses are developed in the walls. The shear force required for cracking is determined from equations found within ACI Concrete Design Manual. The Behavior of Masonry Structur es (Drysdale & Hamid, 2008) text book was used in the calculating the shear loads being created by the external pressure d with the Deep Beam Theory. T he relative stiffness of each wall, dependent on the height of the wall / lengt h of the wall and size of openings , can be calculated. The relative stiffness of shear walls is important since in an assemblage of shear walls and rigid diaphragms the lateral forces are distributed to individual shear walls according to th eir relative st iffness. Relative stiffness is also critical when determining the center of rigidity of shear wall systems, which is determined by the relative stiffness of the walls (Neuenhofer, 2006) The direct shear, which in plan view is the summation of the forces in the x and y direction, and the torsional shear forces that are produced by the unbalanced loading around the center of rigidity of the building . Once this load is calculated, it can be compared to the shear load at cracking to determine wall failure. Outp uts for both shear and bending induced damage are reported in terms of load to capacity ratios. The ratios dictate the levels of failure for both damage states. A ratio less than 1.0 signifies a wall whose capacity is greater than that of the applied wind pressures and is therefore undamaged. Values greater than 1.0 signifies a wall that has been damaged. The number not only identifies whether or not the wall has been damaged but is also used to define the magnitude of damage (cracking and wall collapse). T his is interpreted by the FIT team for the analysis of water intrusion through openings caused by wind damages.
76 3 o penings ( w indows, s liding d oors and e ntry d oors) The openings in the building include windows, sliding and entry doors, susceptible to two f orms of damage: pressure and debris impact. The pressure loading is identical to the loading of the walls at their respective floor heights. Unlike the wall cover and sheathing, the openings are capable of failing by both the positive and suction pressures caused by the combined exterior and interior pressures. The order of operation for the opening analysis begins with the impact damage assessment prior to that of pressure. The interior pressure is adjusted based on possible breaches to the building envelo pe. Openings that have been damage from impact are excluded from the pressure analysis. Garage d oors For SFR , garage doors are common. The pressure loading is similar to that of the other openings to the building. The difference is the assumption that the garage space is isolated from the living area of the building and is therefore not affected by fluctuations of internal pressure due to breaches to windows, entry doors and sliding doors. Hence, loading on the garage door is the combined pressure of the e xterior wind pressure and the internal pressure associated with a closed room. Damage Matrices and Vulnerability Curves The outcome of a Monte Carlo simulation of a chosen model (e.g. 3 story building, timber frame, old construction, no window protection, gable end roof) includes many simulations of the model for a se ries of wind speeds and wind directions. By default the simulations are conducted at 41 wind speeds (50 to 250 mph 3 second gusts in 5 mph increments) at each of eight wind directions. The numb er of simulations at a given wind speed and direction is user defined, with a typical value of several thousand,
77 and depends upon whether the run is intended for intermediate model development purposes (fewer simulations) or the production of final results (more simulations). Each simulation at a given wind speed and direction differs from the previous in that a new set of randomly assigned capacities and pressure coefficients are used. Results are collected in a four dimensional array. The columns represen t the state of the various damaged components (Percent of Roof Cover Loss, Percent of Roof Sheathing Loss, Number of Windows Broken by wall, Number of Doors Broken etc.), the row s represent the results of a given simulation, the third dimension represents wind speed, and the fourth represents wind direction. The number of columns is a constant 75 . Table 3 1 0 identifies the modes of failure recorded in each column. Damages not applicable to a particular model are populated with zeroes. For example, damages t o wall sheathing on the third story of a 2 story building. The column still exists but will be filled with only zeroes. T he output damage matrix dimensions would be 2000x75x41x8 for a m odel run using 2000 simulations , 41 wind speeds and 8 wind directions. The damage matrix can be averaged over various stratifications. Typically this includes the percent roof cover loss averaged over all simulations and wind directions for a given wind speed. Repeating this for every wind speed then produces a curve that pre sents the average roof cover loss as a function of wind speed. Figure 3 3 4 represent s the loss of roof cover relative to peak 3 second gust wind speed. Specifications include: 80ftx40ft building footprint, 3 story, Gable End roof, with 6/12 roof pitch. Such vulnerability curves are produced for each exterior component in the model. The following section includes a sample set of some of the various models. The
78 aggregate damage at a given wind speed is then used to pr oject internal damage , dollar loss and loss ratio . Examples of Simulation Results With a large array of variables that characterize a building, the total number of possible models is vast. Looking at only the major variables, including roof shape (gable or hip), story height (1, 2 or 3 story), window protection (none, plywood and engineered), wall type (timber or masonry) and strength of construction (weak, medium or strong), there is a total of 324 different models. T he following sample set of models found in Table 3 1 1 presents 1 1 models designated for the LRCR model. Sample of Results Figures 3 35 through 3 45 present results for the models that were identified in Table 3 1 1 . 2000 simulation runs were made for each model and the data from the outputted m atrices were averaged at each wind speed across all 8 wind directions. The individual columns were combined to provide the desired output variables. Only the most pertinent limit states will be displayed in the graphs. Three graphs were generated for each model, associating component damages into three groups of vulnerabilities: roof, wall and openings. The graph for the roof vulnerabilities depict the mean percent damages to the roof cover, roof sheathing, r2w connections and the number trusses that have toppled from a given side of the building due to gable end collapse. The wall vulnerability identifies the damages to wall cover and wall sheathing for timber frame building. Bending and shear damages are presented in lieu of wall sheathing and wall cover for masonry wall structure. Damage ratios for both failure modes are also identified. Variable wind speeds with reference to height produce greater loads on higher floors. Therefore all wall damages are reported
79 separately for their individual elevations. The same approach is also taken for the openings (windows, entry doors and sliding doors). Except for the masonry models, the weak gable model can be considered the base model for most of the comparisons made within this section. The construction quality h as the largest influence on the vulnerability curves. Models of similar sizes had similar loads applied to the individual components. Though the wind loading values were randomized , the values remain ed within certain limits. The capacities of the building components increase from weak to medium to strong buildings. As the loads stay ed virtually fixed and the ir capacities increase d, the damage outputs for the components began to decrease. Such behavior is exhibited in the Figures 3 35 to 3 37 as the vulnerab ility curves shift to the right as construction quality increases, indicating a reduction in vulnerability. With the implementation of the power law to calculate the wind speed at various heights, the velocity pressure acting on a component increases with respect to its position from the floor. Wind speeds are calculated at the mean roof height and at the centroid of each story. Components within these respective regions are all submitted to a uniform load based off of the determined wind speed. Because of this multistory buildings accrue increased damages due to their growing height from the floor. Comparing Figure 3 35, Figure 3 38 and Figure 3 39, the trend is quite noticeable. With increases in mean roof height, the damages to the roof components for two story buildings were greater than the one story building . S ubsequently the three story building displayed greater damage than either of the lower story buildings. The difference between roof damages for a one and two story building is much greater than
80 th e comparison between two and three story buildings. The wind profile is parabolic in shape, therefore the rate of increase of the wind speed decreases as the observed height from the floor increases. Keeping the wind profile characteristics in mind, the re sults for wall and opening component damages demonstrate a similar relationship. Upper level stories experiencing greater loads resulted in increased component damages. Opening components were susceptible to a combination of both wind pressure and debris i mpact damages. The results were much more convoluted as the impact damages to the openings were not uniform for components on different floors. The debris impact model determines the vulnerability of an opening for a given floor. Based on the assumption th at buildings surrounding the target building are identical to in dimension and the distance between structures, the trajectory model deems that only a small fraction of the debris originating from an adjacent building would hit the target building. The maj ority of the windborne debris was projected to travel above the top story of the building. For the debris that did impact the windward face of the target building, the distribution was inversely related to the floor height as the highest floor were the mos t prone to impact. The higher the building the lower the debris impact will have on the lowest floor. Pressure damages stay constant as the influence from debris impact decreases. Comparing the 1 st floor opening damages from Figure 3 35 , Figure 3 38 and Fi gure 3 39 , the damages decrease d as overall building heights increase d . Of the two wall type options, masonry walls are considered to be the more wind resistant choice over timber frame. The capacity of the weaker unreinforced masonry wall exceeds the cap acity of the strongest timber frame option.
81 The masonry wall damages reported in Figures 3 40 to 3 42 illustrate the vulnerability for both bending and shear wall failure. Each curve is accompanied by a load/capacity ratio, where the capacity represents t he required load to ensue cracking. A value of one represents the onset of cracking. The extent of the cracking damage is dependent on the damage ratio, the higher the ratio , the greater the cracking. This data is used by FIT to also determine not only dam age but water intrusion. Complete wall failures are much more uncommon and occur in the most catastrophic of condition s , therefore it is not explicitly modeled. Damages to other components in a masonry wall structure are fairly consistent with those of ti mber framed structures. Component damages dependent on interior pressure loads may be slightly larger due to the larger internal pressures. Larger internal pressures can occur because there are less possible leeward openings than timber frame structures wh ich can exhibit sheathing withdrawals within the suction zone. These openings help vent out and prevent the build up of internal pressure which can result in higher component damages. A reduction in r2w vulnerabilities is displayed due to a higher capacity tha n comparable timber frame structures. Reinforced masonry walls are far superior to all other wall types. It is assumed that both medium and strong masonry wall structures are built with reinforced walls. Subsequently their wall damages are very compara ble. Lower damages are observed for other components as their capacities are expectedly higher. The total height of the building is also influential on the damages of the masonry structures. The wind pressures increases with height , producing higher vulner abilities for the upper stories. Wind pressures impose higher bending stresses in the upper story
82 walls , increasing vulnerability as height increase s . The shear stresses in a wall are a combination of the torsional forces created on not only the current fl oor but those from the stories above. Therefore the highest shear stress is seen on the bottom story. (Figure 3 43) The installation of shutter systems a commonly used forms of hurricane protection. By installing these protective covers over the openings o f house, the vulnerability of openings and other components are also reduced. In Figure 3 44, engineering shutters were installed on a 1 story weak timber frame building. Shutters are installed at every window and sliding door. To allow occupants movement to and from the interior of the building, the entry doors remain ed unprotected. Shutters protect the windows and sliding doors from impact and also acts as a buffer for the wind pressure loads. Substantial reductions can be seen in the opening vulnerabilit y result. The reduction in damages to openings also affected other building components. Internal pressurization due to opening damages was minimized by the protection, reducing the possibility of overpressuriztion caused by windward breaches of the buildin g envelope. Reductions in damages are exhibited in all components whose loads are directly or indirectly dependent on internal pressure, including roof sheathing, r2w connections and wall sheathing. Therefore opening protection is not only a key mitigation for the vulnerability of the openings but for the entire structure as a whole. Wall and opening component damages for hip roof structures were identical to the gable end roof counterparts. The only difference was the damage outputs are found within the ro of components. As previously discussed, the hip roof system design is more resilient than that of the gable roofs. Lower damages are demonstrated in Figure 3 45.
83 Validation of the Low Rise Commercial Residential Model The validation study of the model is p erformed with the aid of FIT and FIU. Citizens is a not for profit, tax exempt government corporation whose public purpose is to provide insurance protection to Florida property owners throughout the state. The corporation insures hundreds of thousands of homes, businesses and condominiums wh ose owners otherwise might not be able to find coverage. The Citizens report provides a unique dataset of structural damages resulting from hurricane landfall, and it is a significant source of data with which to compar e simulated structural damages for the purpose of validation. The information reported must be considered within an appropriate framework; however, for use as a method of validating damage predicted by the simulation engine. Specifically, the wind speeds, angles of approach, and types of homes represented by the data in the Citizens report impose limits on the use of reported damages to validate simulated damages. In addition to these limitations, the Citizens data does not include a component breakdown of the structural damages. Most insurance claims data is recorded on an aggregated bases per unit. Information that delineates the amount of damage that occurred to individual components of a commercial residential structure is rare and anecdotal. Due to limi ted data the final validation was conducted by the actuarial team that who combine d all facets of the model to determine the average loss costs for the structure. Those lost cost s were compared to the available databases to test for model agreement. This p rocedure is conducted for every submission to the Florida Commission for approval.
84 The LRCR model was designed to predict the component damages in a probabilistic framework while retaining the flexibility required modeling the various building characterist ics. A separate approach was employed for building over three stories. Chapter 4 will discuss the methodology that was developed for mid high rise commercial residential structure, Methodology: Mid High Rise Commercial Residential The parameters of the LRC R model were outlined in the previous section. This section discusses the probability based vulnerability model was developed to assess the damages for mid high rise commercial buildings. LRCR structures are defined by the FPHLM as commercial residential b uilding that are between 1 to 3 stories. Therefore the classification of mid high rise commercial residential buildings comprise of structures that are 4 stories or greater. The mid/high rise model utilizes the Monte Carlo simulation concept, but differs from the low rise model in significant ways. There is a high level of variability among mid hi gh rise buildings due to the combination of the number of stories, number of units per floor, intentionally unique geometries, and the materials used for the exte rior. This u nfeasible . Due to the construction methods and materials used in these structures, damage to the superstructure and exterior surfaces of the buildings are relatively low. The majority of da mage accumulation in mid/high rise structures is due to water penetration and loss of openings. The model reflects this by focusing on the failure of windows and doors, the ingress of rain water, and the proliferation of water from the source of the ingres s to adjacent living units (Weekes, Balderrama, Gurley, Pinelli, Pita, & Hamid, 2009) . The structure in whole is not modeled. Rather, individual units are modeled in isolation. That
85 is, the vulnerability of a single unit was ex plicitly modeled, and damage was assessed to openings as a function of wind speed. A follow up analysis of these simulation results were conducted at FIT to project interior water damage. Another reason for the modular approach is due to the way that insur ance policies are handled processed . Insurance policies for condominiums style structures are sold to the owners of the individual units. The insurance only covers all that exists within their area alone, while the common areas of the structure are actuall y covered by the condominiums association. The vulnerability of each unit varies from one location to another within the building and different elevations. Survey of b uilding s tock The survey conducted by FIT concluded that the mid high rise structures onl y comprise 4 percent of the commercial residential building stock in Florida. Th is seems like a small amount when compared to the other 96 percent of the low rise residential structures. Though there are fewer buildings constructed, the size of the buildin gs are much bigger and contain more units account ing for 24 percent of the total dollar exposure (Pita, 2008) . Survey data was retrieved from four counties, including Brevard, Lee, Palm Beach and Pinellas Counties. Table 3 1 2 p ortrays the standard roof and wall materials for the mid high rise buildings in three of the counties. The predominant form of the roof style was the flat roof, and membrane covers dominat ing the roof cover material. Concrete block walls were constructed f or at least 98 percent of the buildings. The average area of a unit was 1500 sqft, while the average footprint area of the floor was 17000 sqft.
86 The majority of the buildings were within the 4 6 story range for the four counties ( Table 3 1 3 ) . Table 3 1 4 i llustrates the distribution of dates constructed in the four counties. In all of the counties, at least 60 percent of the mid high rise building were constructed prior to Hurricane Andrew in 1992. While combining to form only a small portion of the buildin g stock, the high variability of structure heights and dimensions, and materials used in construction supports the use of the modular approach that is used for the mid high rise model. In order to provide the user with enough flexibility to analyze the vul nerability of the buildings, the descriptors in Table 3 1 5 were used to define the buildings physical parameters, mitigation options and environmental exposure for the model. Monte Carlo Simulation Process A Monte Carlo simulation approach was utilized to determine the vulnerability of a unit in the mid high commercial residential building under hurricane conditions. The basis is a nested three loop set up. Moving from the outside in, there are 8 wind directions, 41 wind speeds with 3 sec gust ranging from 50 250 mph in 5 mph increments and a user defined number of simulations at the center of the loop. A realization of the unit is created, mapping all of the openings appropriately for the unit being analyzed in reference to its position on the building and the current wind direction. Randomized capacities were assigned to the components. Randomized pressures for the current wind speed are loaded for each component for pressure damage analysis and the probability of debris impact damages is also assessed. Onc e completed, the damages are recorded and the program continues to the next iteration of the unit type. A flowchart depicting the modelling and analysis of this process is shown in Figure 3 46 .
87 Mapping of openings Once the parameters of the unit are entere d for model, the first task of the program is to properly map the locations of the unit openings. The locations of the openings determine the vulnerability of the unit for a particular direction and wind speed. It is very important that each opening correl ates with the correct orientation, as the exposure to both wind loads and debris impact are dependent on their location. Two different mid hi gh rise classifications were s are characterized by the location of the unit entry doors at the interior of the building. The sliding glass doors and windows are located on the exterior walls of the unit. For the Open Building model there is exterior corridor access to each unit entry door on one side of the building, while the patio areas are situated on the opposite side of the building ( Figure 3 47 ). The type of building chosen can increase or decrease the vulnerability of a selected unit du e to the exposure of the exterior openings. units are between the corner units. Divi sions between the two units were made due to the increased vulnerability of the corner units. Middle Units have one and two exterior walls in a closed and open building, respectively. While the corner units are exposed have two and three exterior doors for the closed and open building formats. Because the damage assessment for these models is based on the failure of openings, the vulnerability curves are heavily affected by the total number of exterior walls. The number of windows per wall is determined by the total area of a wall. A ratio of glazing to wall area is used to determine the number of windows based on the area of
88 wall, the area of the windows that will be placed and the existence of other opening types (entry or sliding doors). Assume 4ft x 5ft windows were to be installed on a 40ft x 8ft wall. With a glazing ratio of .3, the area of glazing is equal to 96 ft 2 (.3 * (40ft * 8ft)). Therefore the total number windows would be equal to 4.8 windows (96 ft 2/ /(4ft * 5ft)). Rounding up to the nearest w hole value determines the number of windows. Assuming there is either an entry door or a sliding door existing on that wall face, the area of the opening is subtracted from the area of the glazing before the number of windows is determined. A sliding door of 8ft x 8ft, 64 ft 2 will be removed from the calculated glazing area leaving a remainder of the 32ft 2 . An area of 32ft 2 is equivalent to 2 windows (32ft 2/ /(4ft * 5ft) = 1.6 windows). For the LRCR model, wall components were mapped by placing them into lar ge arrays where each column identified the location of either a sheathing panel or an opening. For the mid high rise model there is no need for robust matrices since only the openings are being analyzed. Instead the proper pressure loads and debris impact damages for the current conditions (direction and wind speed) are associated with the correct windows. Capacities of components Per the LRCR program, the capacities of the opening components are randomly selected using the mean and coefficient of variation for the individual components ( Table 3 1 6 ). Capacity data was obtained from manufacturer specifications (PGT Industries). These values were used as a starting point for the capacities and then altered to produce desired outputs that were a suitable repres entation for a wide assortment of buildings. Capacities of the windows fluctuate depending on the size of the opening. Therefore a larger coefficient of variation is used in order to take into
89 consideration such uncertainties. A feature commonly found in m id high rise building s are impact resistant windows with aluminum frames. The pressure capacities are selected from a Gaussian distribution and assigned to each opening, placing them within a matrix format. Values are once again restricted to two standard deviations away from the mean. Outlying values are resampled in order that extremely low or overly strong capacities are not selected. According to the data from the PGT Industries website, the window s will not only have an increased protection against de bris impact but also have an increase in pressure capacity. The pressure capacities of the glazing components were all increased using an identical factor (MFactor) multiplication method found in the low rise residential program. Corresponding MFactor valu e are identified in Table 3 1 7 . Mitigations such as the addition of opening protection were also implemented. Two different factors were used for reducing the vulnerability of the components, PFactor and POIFactor. The PFactor increases the pressure capaci ty resistance of the windows. It is assumed that the opening protection acts as a buffer between the wind and the opening. It was decided that the resilience of the opening is increased instead of decreasing the load. The POIFactor is a variable that reduc es the probability of the opening being impacted by the windborne debris. The PFactors and POIFactors found in Table 3 18 are multiplied directly to respective damage limit state. The capacity of the opening is multiplied by the MFactor and PFactors decrea sing its vulnerability to pressure loads. The probability of impact damage is multiplied by the POIFactor reducing the damages due to windborne debris.
90 The factors described above were chosen through engineering judgment as to produce a desired behavior d ue to the differences in opening material and protections. The mean capacities of the openings are multiplied by both the PFactor and MFactor. The pressure capacity of the entry door is not multiplied by the protection factor because the entry door is typi cally left unprotected as the means for accessing the unit. Structural loads on openings: mid high rise commercial residential The opening components are susceptible to 2 forms of damage: pressure and debris. The pressure loads and debris impact are determ ined as discussed in Chapter 3 of the LRCR model . Pressure loading The application of the pressure loads are determined by orientation of the building relative to the wind, the ASCE 7 05 designated zones (Zone 4 or Zone 5) that the opening lies within and the wind speed. The orientation of the building within the wind field governs whether the openings are subjected to positive or negative pressures. This information is also very important for the FIT team responsible for water penetration. To calculate t he randomized pressure loads the code simply follows the ASCE 7 05 procedure, it multiples as follows: 0.00256*GC p *WindSpeed 2 . The GC p for wall Zones 4 and 5 values are taken from ASCE 7 05. The appropriate GC p values are associated with the openings depen ding on where the location compared to the edge of the building. Components that are very close to the corner of the building can be affected by the higher pressures that are exhibited in Zone 5. These loads are much higher than Zone 4. Weighted pressures are taken for components that lie within more than one zone. The pressure coefficients determined from ASCE 7 05 (for building
91 heights greater than 60 ft) are randomized about the mean values and applied to each component. Failed components are determined by load exceedance of capacity. Damages to components due to pressure failure produces breaches into the building envelope and subsequently water intrusion. Figure 3 48 and 3 49 below depicts the orientation of the eight wind directions. The figu res are ac companied by Tables 3 19 and 3 20 which depict the location of the unit components in comparison to the wind direction. Components on the windward side of the building are placed under positive loading while the leeward facing components are negative. Debr is i mpact d amage Components that are located on the windward side of the building are susceptible to damage from windborne debris . Upstream airborne debris from the target building has the potential of hitting a component on the windward surface of a unit . The probability of damage is determined in a similar manner to a LRCR building. Assuming that the surrounding buildings are of similar construction, the total roof area is also assumed to be the same. Therefore, the number of available missiles (NA) is d etermined by calculating the area and dividing that value by the area of a shingle. Randomized capacities are assigned to each shingle and damages are determined based on the wind pressures calculated using the current wind speed (A Variable). Trajectories of the shingles are calculated to determine whether the flight of the roof cover will span the distance between the two buildings (B Variable). A percentage of wall area is determined as the division of the opening area and the total area of the wall (C v ariable). Finally, the probability of damage due to impact at the current wind speed is determined. From this the probability of opening damage is calculated.
92 Though the debris impact model for the mid/high rise buildings is very similar to that of the low rise buildings, there are two main modifications: Delineation of three zones for debris impact with respect to height Separation of damaged but unbreached from damaged and breached openings As the height of the unit with respect to the ground increases, it is assumed that the availability of possible projectiles reduces. The model is separated into 3 zones: 1st 3rd story (Zone 1), 4 th 7 th story (Zone 2) and finally 8 th story and up (Zone 3), decreasing the debris intensity from Zone 1 to 3. Multipliers of 1.0, 0.5 and 0.25 were used respectively of Zones 1, 2 and 3. This decreases the debris impact vulnerability of openings at higher stories. It is assumed that opening damage due to pressurization will cause a breach to the interior of the structure. In th e case of the impact damages, there is a differentiation between damaged and breached openings. An opening may be struck by airborne debris, damaging the opening and requiring either repair or replacement, but still stay intact while protecting the interio r from water intrusion and internal pressurization. Breaches to the openings are determined based on the exceedence of a randomized value to the predetermined linear relationship s in Figure 3 5 0 . There are two relationships, one for the windows and the oth er for the entry and sliding doors. The difference in the linear relationships reflects the increased resilience of entry and sliding door to breaching due to impact when compared to windows, particularly at the lower wind speeds. Damage Matrices and Vu lnerability Curves The mid hi gh rise model presents output in the same manner as the low rise model, in the form of damage matrices. The difference is the number of failure types.
93 The mid high rise model only analyzes the damages to the opening, which incl ude the windows, sliding doors and entry doors. Each of the components can fail in two possible ways, through pressure failure and debris impact. T he damage matrix has a total of 9 failure states. The total number of damaged openings will be the sum of th e windows damaged due to pressure and impact. A model run at 2 000 simulations would produce a 2 000x9 x 41x8 matrix. As depicted in the low rise section ( Damage Matrices and Vulnerability Curves ), the vulnerability curves can be produced for each one of the f ailure states by averaging the output over the number of simulations and wind directions. Damage values stored within the matrices are used by the engineering team at FIT to determine the damages due to water intrusion. The combination of both the external damage and water intrusion models is required to define the overall damages of the unit . A plotting function is used to graphically display the statistical averages of the damage data obtained in the analysis. The following section presents outputs of som e of the base models for the mid high rise program. Examples of Simulation Results Table 3 2 2 below presents a sam ple of the four base models that are designated for the mid high rise commercial residential model. For comparative purposes a base model was also analyzed with shutter protection within lower level debris zones. The sample models analyzed are described in Table 3 22 . Comparative graphs of mean damage summarize the results in this section. Damages to each component are presented as a percentage of damage. The total number of components is identified on each figure. Depending on the unit the total number of window will vary from 3 to 6, while the number of entry doors and sliding doors are typically 1. There is also an option
94 to negate the sl iding door to represent units without a balcony . By doing so, an additional window replaces the sliding door. Sample of Results Figures 3 51 through 3 56 present the averaged damages for the three building openings of each of the models identified in Table 3 24 . 2000 simulations were used for each model. The average damages are a result of the mean across the 2000 simulations and all 8 wind directions for graphical depictions. Pressure damages to all of the components are sigmoid in shape. Exponential growth is expected at higher wind speeds and damages begin to plateau as damages reach 100 percent. On the other hand, impact damages are bell curved in shape. This is due to the order of operation and architect ure of the code. The pressure damage analysis is conduc ted prior to the impact damage assessment. Therefore the number of openings that are evaluated for impact damage decreases with increasing wind speed. Damages to all opening types were combined into single plots for each model. Units that have an interior stairway have the entry doors facing the interior stairwell of the building. Because of this the entry doors are not susceptible to the effect of direct wind pressures or windborne debris. T he pressure damages to both windows and sliding door increase with increasing wind speed. The debris impact damages also increase, but begin to plateau as the number of available window for analysis are reduced due to the initial pressure damages to the openings. This can be seen by comparing the pressure damages of the sliding doors and the windows. Sliding doors have a higher pressure capacity than that of the windows. Therefore the rate of pressure damage is lower. Conversely, the damages due to debris impact are much higher due to its higher availability after pressur e damages. The windows are placed
95 within 5 ft of the corner of the unit. corners of the corner units are partially located within Zone 5 of ASCE 7 05. The corresponding pressure coefficients (GCp) acting on th e windows are higher than the windows lying further away from the corners and are subsequently more vulnerable. Lastly, the pressure damages for the corner unit are slightly higher than that of the middle unit because of the internal pressurization of the unit during opening failure . Corner units have openings on 2 adjacent side of the building. When an opening is damaged normal to the windward side of the building, the internal pressure of the unit increases. Openings on the windward side have opposing pre ssures acting on the interior and exterior of the undamaged openings. The internal pressure amplifies the net pressure acting on the openings found on the windward side of the building, increasing the probability of damage. The middle unit exhibit opposing net pressures in both windward and leeward cases. The internal pressure reduces the overall load on the opening . ( Figures 3 51 and 3 52) Structures with exterior stairways have entry doors that are subjected to both wind pressure loading and debris impact . Unlike the analysis of interior stairway buildings, the outputs for these buildings include damages to the entry doors as well. The entry door has a higher pressure ca pacity than both the windows and sliding doors, leading to lower pressure damages. Base d on previous discussion, the lower the damages due to wind pressure the more openings that are available for debris impact analysis. 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 vulnerability of middle and corner units for
96 buildings with exterior stairways to pressure and debris are similar, therefore the damage outputs also coincide with one another. ( Figures 3 53 and 3 54) Of all of the shutter options, engineered shutters provide the highest degree of opening protection. Engineered shutter systems were added to the middle unit located in an exterior stairway building. The s hutters are typically installed over the windows and sliding doors of units. The entry door remains unprotected to allow occupant ingress and egress. The shutters provide not only protection from debris impact but also exists as a buffer for wind pressure loading, reducing the effective load that is being transmitted to the opening. Taking these into consideration, in Figure 3 55 below the window and sliding door damages are much lower than that of the entry door whose damage is virtually unchanged compared to the unprotected model. As previously discussed, there are 3 designated debris impact zones that a unit can be identified with. The different zones separate high, medium and low debris impact zones. Z ones are subdivided by the number of available missil es that are used for the debris impact analysis. The total number of available missiles is initially calculated based on the number of missiles (roof shingles) on the current b uilding being modeled. It is assumed that the buildings surrounding the target s tructure are identical in size, therefore having an equivalent roof cover count. 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 inte rior corridor buildings than for exterior corridor buildings. This results in a higher vulnerability of openings in exterior corridor buildings. The designation of the debris impact zones facilitates a means for manipulating the effects of debris impact da mages at different locations on the building. Figure 3 56
97 depicts an exterior stairway middle unit that is located in a low impact zone. As expected the vulnerability to debris impact is much lower than that of the high impact zones. Based on engineering j udgment, the results found for the various models are realistic. The degrees of damage seem fitting for the various wind speeds within ranges modeled. In summary, logical relationships have been established between the various models. The corner unit of th e both building types is more vulnerable than units in the middle of the building. The extra wall possessed by corner units over middle units, 2 walls vs 1 wall for interior stairway and 3 walls vs 2 walls for exterior, allow for a higher interaction with pressure loadings and debris impact throughout the analysis of the 8 wind directions. Shutter protection decreases the vulnerability of those components installed over, while also affecting the vulnerability of the unprotected entry doors due to the r eduction of possible internal pressurization. Lower debris impact zones display an expected higher influence of damage due to pressure loads as the influence of debris impact is lessened. These are all desired trends that manifest in the model comparisons. A lack of information on component damages to individual units combined with e fforts from UF (development of the external damage model), FIT (development of the water intrusion model) and FIU (actuarial science teams) must be used to produce data that can be compared to insurance claim date that are available. Validations are dependent on the final outputs from actuarial science team.
98 Table 3 1 . Roof and Wall characteristics for low rise commercial residential structures (Pi ta G. L., 2008) C ounty Roof Types Roof Cover Material Exterior Wall Material Gable/Hip Flat Other Shingle Tiles Gravel Other Wood CB Other Alachua NA NA 30% 52% 18% Bay 95% 2% 3% 81% 0% 0% 19% 48% 36% 16% Brevard 85% 11% 4% 72% 8% 0% 20% 35% 64% 1% Duval 91% 8% 1% 75% 0% 15% 10% 51% 49% 0% Lake NA 63% 3% 0% 34% 44% 55% 1% Lee 91% 2% 7% 70% 17% 10% 3% 16% 84% 0% Leon 94% 1% 5% 91% 0% 0% 9% 56% 40% 4% Marion 95% 0% 5% 95% 2% 1% 2% 27% 73% 0% Monroe 68% 18% 14% 28% 3% 9% 60% NA Orange 95% 2% 3% 82% 8% 8% 2% 35% 60% 5% Osceola 97% 0% 3% 91% 2% 0% 7% 51% 49% 0% Palm Beach NA NA 25% 71% 4% Pasco 97% 2% 1% 88% 0% 6% 6% 16% 84% 0% Pinellas 91% 0% 9% 83% 4% 11% 2% 28% 72% 0% Saint Johns 85% 3% 12% 87% 5% 0% 8% 78% 22% 0% Saint Lucie 88% 0% 12% 75% 2% 16% 7% 23% 75% 2% Volusia 94% 6% 0% 83% 8% 0% 9% 56% 41% 3%
99 Table 3 2. The distribution of 1, 2 and 3 story low rise commercial residential bui ldings by county County Number of 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%
100 Table 3 3. Distribution of low rise commercial residential structure by year built (adapted from Pita et al. 2008) Table 3 4. List of User Defined Inputs Input Entry Number of Stories 1,2 or 3 Story Foundation Dimension Variable Roof Pitch Variable Roof Type Hip or Gable End Roof Cover Type Shingle or Tile Wall Type Timber Frame or Masonry Window Type Normal, Laminated or Impact Resistant Shutter Protection None, Plywood, Steel or Engineered Construction Quality Weak, Medium or Strong Year Built County Pre 1970 1971 1983 1984 1992 1993 2002 2003 2007 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% M onroe 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%
101 Table 3 5. 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 Roof Cover 51 0.2 51 0.2 70 0.2 Roof Sheathing Panels 55 0.25 80 0.25 130 0.25 Soffit 25 0.25 40 0.25 75 0.25 Roof to wall Connections (lb) Wood Wall 460 0.2 690 0.2 1240 0.2 Masonry Wall 700 0.2 1065 0.2 1400 0.2 Wall Cover 38 0.4 68 0.4 88 0.4 Wall Sheathing Panels 46 0.4 67.2 0.4 109 0.4 Windows 60 0.4 60 0.4 90 0.4 Sliding Doors 50 0.2 50 0.2 120 0.2 Entry Doors 75 0.2 75 0.2 129 0.2 Garage Door 30 0.2 30 0.2 52 0.2 Table 3 6. Protection Co rrection Factors for Glazing Component Resistances Shutter Type Factor Probability of Impact None 1.00 1 Plywood 1.15 1/2 Steel 1.25 1/6 Engineered 1.50 1/100 Table 3 7. Material Correction Factors for Glazing Component Resistances Glass Type Factor Normal 1.00 Laminated 1.50 Impact Resistant 2.00
102 Table 3 8. Internal Pressure Coefficients Condition Internal Pressure Coefficient Fully Enclosed Floor 0.18 Opening on Windward Side ONLY < 4 ft 2 0.18 Opening on Windward Side ONLY > 4 ft 2 0 .55 Opening on Suction Side ONLY < 4 ft 2 +0.18 Opening on Suction Side ONLY > 4 ft 2 +0.55 Openings on both Windward and Suction Sides of the Building Equation 3 7 Table 3 9. R2w Load shearing distribution implemented in the LRCR model Truss Identi fication Truss Identification Number 1 2 3 4 5 End Truss 58% 26% 12% 4% 1 st Interior Truss 20% 60% 15% 10% 6% 2 nd Interior Truss* 10% 20% 40% 20% 10% * The same values would be used for all other interior trusses. Values will slide accordingly pop ulating the identified truss and adjacent trusses as described.
103 Table 3 10. The final output column designation for low rise commercial residential structures Column # Timber Models Masonry Models Col 1 Percent roof cover (shingles or tiles) failed C ol 2 Percent field roof sheathing lost (field roof sheathing is all but overhang) Col 3 Percent edge (overhang) roof sheathing failed Col 4 Percent roof to wall connections failed Col 5 Collapse of gable end trusses (0 = no collapse, 1 to 20) starting f rom side 1 Col 6 Collapse of gable end trusses (0 = no collapse, 1 to 20) starting from side 2 Col 7 8 Percent gable end wall covering failed (side 1 and 2, positive for windward, negative for leeward) Col 9 10 Percent gable end sheathing failed (side 1 and 2, positive for windward, negative for leeward) Col 11 14 Percent wall covering failed 1st floor (walls 1 4, positive for windward, negative for Leeward) Damage ratio due to shear forces (walls 1 4) Col 15 18 Percent wall sheathing failed 1st f loor (walls 1 4, positive for windward, negative for leeward) Damage ratio due to bending forces (walls 1 4, positive for windward, negative for leeward) Col 19 22 Number of windows failed from wind pressure 1st floor (walls 1 4, positive for windward , negative for leeward) Col 23 26 Number of windows failed from wind Debris 1st floor (walls 1 4) Col 27 Number of sliding glass doors failed from wind pressure 1st floor (+ for windward for leeward) Col 28 Number of sliding glass doors failed fr om debris impact 1st floor Col 29 Number of entry doors failed from wind pressure 1st floor (+ for windward for leeward) Col 30 Number of entry doors failed from debris impact 1st floor Col 31 50 Repeat Col 11 Col 30 for 2nd Floor Col 51 70 R epeat Col 11 Col 30 for 3nd Floor Col 71 Garage Door Damage (positive for windward, negative for leeward) Col 72 75 Percent Soffit Damage (walls 1 4)
104 Table 3 11. Low rise commercial residential sample models analyzed Sample of Low Rise Commercial R esidential Model Number of Stories Roof Type Construction Quality Wall Type Window Protection 1 Gable Weak Timber None 2 Gable Weak Timber None 3 Gable Weak Timber None 1 Gable Medium Timber None 1 Gable Strong Timber None 1 Gable Weak Masonry None 1 Gable Medium Masonry None 1 Gable Strong Masonry None 3 Gable Weak Masonry None 1 Hip Weak Timber None 1 Gable Weak Timber Engineered Shutter Table 3 12. Roof characteristics for mid high rise buildings (adapted from Pita et al. 2008) County Roof Types Roof Cover Material Exterior Wall Material Gable/Hip Flat Shingle Tiles Membrane Wood CB Other Brevard 24% 76% 8% 11% 78% 1% 98% 1% Lee 43% 56% NA 0% 99% 0% Pinellas NA NA NA Table 3 13. Number of stories for mid high rise buildings (adapted from Pita et al. 2008) 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% Table 3 14. Distribution of low rise commercial residential structure by year built (adapted from Pita et al. 2008) Year Built County Pre 1970 1971 1983 1984 1992 1993 2002 2003 2007 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%
105 Table 3 15. Desc riptor for the mid high rise residential model Variable for Mid High Rise Building Building Type Exterior Stairway or Interior Stairway Unit Type Middle or Corner Unit Exterior Length Any Unit Interior Width Any Shutter Protection None, Plywood, S teel, or Engineered Glazing Type Normal, Laminated, or Impact Resistant Glass Missile Exposure Type Urban, Suburban, or Open Number of Simulations User defined (within range of computers capabilities) Table 3 16. Mean pressure capacities and coeff icient of variation for opening components Component Mean, C v Windows 81 0.3 Sliding Doors 107 0.25 Entry Doors 116 0.25
106 Table 3 17. Glazing material factors for openings Opening Material Type Mfactor Normal Glass 1.0 Laminated Glass 1.2 Impact Resistant 1.33 Table 3 18. Shutter protection factors for openings Shutter Protection Pfactor POIFactor None 1 1.00 Plywood 1.15 0.50 Steel 1.25 0.17 Engineered 1.5 0.01 Table 3 19. Location of component high rise buildings Wind Direction Sign of applied pressure Middle Unit Corner Unit Entry Door Sliding Door Windward Windows Entry Door Sliding Door Windward Windows Side Windows 1 NA Windward Wi ndward NA Windward Windward Leeward 2 NA Windward Windward NA Windward Windward Windward 3 NA Leeward Leeward NA Leeward Leeward Windward 4 NA Leeward Leeward NA Leeward Leeward Windward 5 NA Leeward Leeward NA Leeward Leeward Leeward 6 NA Leeward Lee ward NA Leeward Leeward Leeward 7 NA Leeward Leeward NA Leeward Leeward Leeward 8 NA Windward Windward NA Windward Windward Leeward
107 Table 3 e buildings Wind Direction Sign of applied pressure Middle Unit Corner Unit Entry Door Sliding Door Front Window Rear Windows Entry Door Sliding Door Front Windows Side Windows Rear Windows 1 Windward Leeward Windward Leeward Windward Leeward Windward Leeward Leeward 2 Windward Leeward Windward Leeward Windward Leeward Windward Windward Leeward 3 Leeward Leeward Leeward Leeward Leeward Leeward Leeward Windward Leeward 4 Leeward Windward Leeward Windward Leeward Windward Leeward Windward Windward 5 Leeward Windward Leeward Windward Leeward Windward Leeward Leeward Windward 6 Leeward Windward Leeward Windward Leeward Windward Leeward Leeward Windward 7 Leeward Leeward Leeward Leeward Leeward Leeward Leeward Leeward Leeward 8 Windward Leeward Windwa rd Leeward Windward Leeward Windward Leeward Leeward Table 3 21. The final output column designation for mid high rise commercial residential structures Column # Output Variables 1 Window failure due to pressure 2 Entry door failure due to pressure 3 Sliding door failure due to pressure 4 Window failure due to impact (damaged) 5 Entry door failure due to impact (damaged) 6 Sliding door failure due to impact (damaged) 7 Window failure due to impact (breached) 8 Entry door failure due to impact (b reached) 9 Sliding door failure due to impact (breached)
108 Table 3 22. Mid high rise commercial residential sample models analyzed Characteristic Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Density Suburban Suburban Suburban Suburban Suburban Subur ban Building type Interior Stairway Interior Stairway Exterior Stairway Exterior Stairway Exterior Stairway Exterior Stairway Unit location Corner Middle Corner Middle Middle Middle Shutter protection None None None None None Engineered Glass type Norm al Glass Normal Glass Normal Glass Normal Glass Normal Glass Normal Glass Debris zone 1 (High) 1 (High) 1 (High) 1 (High) 3 (Low) 1 (High) Unit dimension (w x l) 30 ft x 60ft 30 ft x 60ft 30 ft x 60ft 30 ft x 60ft 30 ft x 60ft 30 ft x 60ft No. of window s 3 3 5 3 6 3 Window dimensions 4 ft. x 5 ft. 4 ft. x 5 ft. 4 ft. x 5 ft. 4 ft. x 5 ft. 4 ft. x 5 ft. 4 ft. x 5 ft. Entry door dimensions 3 ft. x 7 ft. 3 ft. x 7 ft. 3 ft. x 7 ft. 3 ft. x 7 ft. 3 ft. x 7 ft. 3 ft. x 7 ft. Sliding door dimensions 8 ft. x 7 ft. 8 ft. x 7 ft. 8 ft. x 7 ft. 8 ft. x 7 ft. 8 ft. x 7 ft. 8 ft. x 7 ft.
109 Figure 3 1. Flow Chart of Low Rise Commercial Residential Simulation Algorithm Figure 3 2. Matrix relationship of sheathing panel dimension
110 Figure 3 3. Matrix relatio nship of sheathing panel capacities
111 Figure 3 4. Matrix relationship of sheathing panel pressure loads Figure 3 5. Sample distribution for component capacities with two standard deviation truncation
112 Figure 3 6. Comparison of ASCE 7 05 Pressu re Coefficient Zones and the Modified Directional Mapping in the SFR model (Cope, 2004) Figure 3 7. Wind profile by terrain ( http://www.stadtentwicklung.berlin.de/umwe lt/umweltatlas/ed403_01.htm )
113 Figure 3 8. ASCE 7 05 external pressure coefficients for roof components (Components and Cladding Method) Figure 3 9. ASCE 7 05 external pressure coefficients for wall components (Components and Cladding Method)
114 A B Figure 3 10. Effects on interior pressure due to openings on the windward and leeward walls of the building (from Smith, 2012) Figure 3 11. Mean internal pressure coefficient as a function windward/leeward opening area ratio (from Holmes, 2001)
115 F igure 3 12. Urban missile exposure layout assuming a base clearance of 45ft Figure 3 13. Open missile exposure layout assuming a base clearance of 45ft
116 Figure 3 14. Directions of wind approach in the missile model Figure 3 15. Sample of the A( vwind) variable against wind speeds
117 Figure 3 16. Calculation of C values for various openings Figure 3 1 7. Photo of Roof Sheathing Damage (Division of Emergency Management, 2010)
118 Figure 3 18. Hip roof comparison o f the unprojected vs. projected roof areas Figure 3 19. Orientation of wind pressure loads on roof components Figure 3 20. Roof Sheathing Layout and Mapping
119 Figure 3 21. Photo of R2W Connection Failure (Toe Nail, 2006 ) Figure 3 22. Tributary Area R2W Connection Theory. Depiction of the sheathing uplift relationship with r2w connection
120 Figure 3 23. Load Distribution with the application of a singular load at a truss connection (Wolfe and LaBissoniere, 1991) Figure 3 24. Photo of Roof Cover Damage (Division of Emergency Management, 2010)
121 Figure 3 25. Outward Gable end Wall Collapse (Division of Emergency Management, 2010) Figure 3 26. Gable End Collapse Damage Threshold
122 Figure 3 27. Post Hurricane Soffit Damages (Division of Emergency Management, 2010) Figure 3 28. Photo of Wall Cover and Sheathing Damage (The Engineered Wood Association, 2014)
123 Figure 3 29. Photo of Wall Cover Damage with no Sheathing Damage (The Engineered Wood Association, 2014) Figure 3 30. Photo of a masonry wall crack after a hurricane (Marshall)
124 Figure 3 31. Out of Plane bending loads for a masonry wall
125 Figure 3 32. Shear loading of masonry walls due to external pressures Figure 3 33. Photo of Window, Sliding Door and Entry Door Damage
126 Figure 3 34. Sample Vulnerability Curve for Roof Cover
127 Fi gure 3 35. Roof, wall and opening component vulnerability curves for a 1 story weak gable roof timber frame building
128 Figure 3 36. Roof, wall and opening component vulnerability curves for a 1 story medium gable roof timber frame building
129 Fi gure 3 37. Roof, wall and opening component vulnerability curves for a 1 story strong gable roof timber frame building
130 Figure 3 38. Roof, wall and opening component vulnerability curves for a 2 story weak gable roof timber frame building
131 Fi gure 3 39. Roof, wall and opening component vulnerability curves for a 3 story weak gable roof timber frame building
132 Figure 3 40. Roof, wall and opening component vulnerability curves for a 1 story weak gable roof masonry wall building
133 Figu re 3 41. Roof, wall and opening component vulnerability curves for a 1 story medium gable roof masonry wall building
134 Figure 3 42. Roof, wall and opening component vulnerability cu rves for a 1 story strong gable roof masonry wall building
135 Fig ure 3 43. Roof, wall and opening component vulnerability curves for a 3 story weak gable roof masonry wall building
136 Figure 3 44. Roof, wall and opening component vulnerability curves for a 1 story weak gable roof timber frame building w/ engineered shutters
137 Figure 3 45. Roof, wall and opening component vulnerability curves for a 1 story weak hip roof timber frame building
138 Figure 3 46. Flow Chart of Mid High Rise Commercial Residential Simulation Algorithm
139 Figure 3 47. Mid high rise building models: Closed building (left), and open building (right) Figure 3 mid high rise buildings
140 Figure 3 49. Orientation of wind directions to unit location f mid high rise buildings Figure 3 50. Linear relationships for opening breaching due to debris impact for window, and entry and sliding doors
141 Figure 3 51. Comparative opening damage for a corner unit in a building with an interior corridor. Unit is in a high impact zone Figure 3 52. Comparative opening damage for a middle unit in a building with an interior corridor. Unit is in a high impact zone
142 Figure 3 53. Comparative opening damage for a corner unit in a b uilding with an exterior corridor. Unit is in a high impact zone Figure 3 54. Comparative opening damage for a middle unit in a building with an exterior corridor. Unit is in a high impact zone
143 Figure 3 55. Comparative opening damage for a middl e unit in a building with an exterior corridor. Unit is in a high impact zone with shutter protection on windows and sliding doors Figure 3 56. Comparative opening damage for a middle unit in a building with an exterior corridor. Unit is in a low im pact zone
144 CHAPTER 4 ACQUISITION OF PERTINENT BUILDING SHAPES Currently the SFR model (originally developed by Cope, 2004) is limited to analyzing rectangular shaped residential buildings. This simple approach is chosen as a representation of many reside ntial structures constructed in the US. The actual Florida building stock has a large variety of shapes. While it is not possible to provide detailed modeling for every shape, additional shapes will improve the ability to extrapolate the damage simulation results to the actual building stock. The relative benefit of various mitigation measures is dependent upon the distribution of wind loads on the structure being analyzed. The wind loads are dependent on a number of factors, including the shape of the bui lding plan. For example, the same wind speed and approach direction result ed in different roof uplift loads on rectangular vs. L shaped buildings. Thus the relative effectiveness of improved roof cover vs. window protection was also be a function of buildi ng shape. The explicit modeling of additional building shapes was greatly assist any mitigation effectiveness study. At least one additional building shape (L shape) was investigated as an addition to the existing residential model. A sampling of the build ing stock in Florida was made to determine which building shapes are the most prevalent. across the State of Florida. Insurance and County databases rarely incorporate the shap es of the structure into their surveys. Even with access to archives for some of the counties in Florida, a high level of resolution and uniformity across the state would not be attainable. Because of this limitation, a more direct and systematic approach was chosen. A study was conducted by Aashlesh Emandi and Dr. Kurt Gurley to provide
145 statistical assessment of particular structural feature of SFR construct ion of in the State of Florida. Using Google Earth, neighborhoods were selected within individual co unties in Florida. Each neighborhood was assigned an identification number and given a designated boundary as seen in Figure 4 1 below. Once a neighborhood was selected, were identified. Buildings whose shape s were not readily identifiable as one of the most common structures was considered building is categorized based on their shape and recorded in an Excel Spreadsheet. The individual buildings shapes were summed and a statistical analysis of the collected data was made in order to identify the more prevalent structural shapes. The study was conducted for three counties located in the high wind region of South Florida, inclu ding Charlotte, Monroe (Key West) and Miami Dade Counties. Neighborhoods were selected at random and different building shapes were identified and summed. The results from the neighborhoods combined for each county and the percent distribution of each shap e. As seen in Table 4 1 below, the L Shaped building is the consistently the second most dominant building shape being constructed, excluding the possibility of modeling complex building shapes. Summing the percentages for both the Rectangular and L shaped buildings for each county, an approximate 75 percent of all the single family structures sampled were identified as one or the other. Based on this analysis, the code was expanded to include L Shaped structures which encompass a reasonable portion of the building stock. An increased selection allow s the user to considerably improve the programs ability to accurately predict
146 hurricane damages, instead of strictly supplanting data used for a rectangular structure rther wind tunnel testing to characterize the pressure variations across the building envelope will also be necessary in the development of future models. An important caveat to the utility of additional building shapes is the lack of availability of the shapes of the specific homes that are submitted for analysis by the FPHLM. An insurance portfolio of properties may contain structural age and location, and region and age may be used as a proxy for wall type and roof shape, respectively. However, the assi gnment of the shape of the properties may not be feasible based on the lack of direct or proxy information in the portfolio of records.
147 Table 4 1. Results of the building shape study County Rectangular L Shaped T Shaped C Shaped Square Complex Charlott e 47.30% 28.50% 14.30% 1.80% 1.20% 6.40% Key West, Monroe 70.60% 5.55% 2.40% NA NA 19.80% Miami Dade 47.26% 28.50% 6.80% 4.45% NA 15.07% Figure 4 1. Photo of Residential Neighborhood Being Surveyed For Building Shapes
148 CHAPTER 5 REASSESSING STRUC TURAL LOADS T he structur al loading and resistance of the building are important factors in the prediction of hurricane damages to residential structures. Accurate interpretation of both factors and their interaction with one another is necessary in the dev elopment of an acceptable model. Therefore, updates must be made to the different variables as new in formation becomes available. The SFR model utilized a modified version of the ASCE 7 to incorporate wind directionality. The locations of the different lo ading zones were assigned based on modifications to ASCE 7 Provisions (American Society of Civil Engineers, 2006) and engineering judgment. Wind tunnel data was procured for both gable end and hip roof styles to update the loading scheme applied in the Co pe model. Recent wind tunnel testing performed by the University of Western Ontario and Clemson University provided time histories of wind pressure coefficient around the building envelope. efforts provided the wind tunn el data for the NIST Aerodynamic Database (National Institute of Standards and Technology, 2005) . NIST developed the w indPRESSURE Database Assisted Design software using the aforementioned data set. The graphical interface enables the display of pressure t ime series, pressure tap locations, and model photos for gable end buildings. The program utilizes aerodynamic data sets contributed by The Boundary Layer Wind Tunnel Laboratory at The University of Western Ontario (UWO).The aerodynamic data were obtained for low rise, gable roofed building models. Among the available options in the
149 database, the 125ft x 80 ft was the only footprint whose size was indicative of a commercial residential structure, while having corresponding typical roof slopes. A MATLAB Â® pr ogram was written to extract tap data and their respective pressure coefficient time histories. The data was then converted from model to full scale. Additional conversions were made to convert from hourly wind duration to a 3 second gust to coincide with the conditions found in ASCE 7 Wind Provisions. For the generic model tests, pressure measurements were sampled at 500 samples per second for 100 seconds. In order to find an appropriate Cp value for each tap, the Best Linear Unbiased Estimation (BLUE) met hod for extreme value analysis was used. C ontours of the peak pressure coefficients across the roof area were produced for the different wind orientation as seen in Figure 5 1 . UWO conducted 94 tests with varying eave heights, building footprints and roof slopes. Open and Suburban exposures were performed for all combinations. The number of options for the current study was reduced by removing roof slopes not typical of residential construction . Five different roof slopes were tested, including 1.19, 2.39, 4.76, 14.0 and 26.6 degrees. O nly the 14.0 and 26.6 degree sloped models are of significance to either commercial or SFR structures. Of the eight building footprints that were tested, the 80ft x 125ft model analyzed with those roof slopes . The contoured d iagrams are employed with two goals : mapping of the different wind zones and the estimation of model multipliers. Using the contours the boundaries between the different zones were identified at wind angles corresponding to the eight used in the LRCR model . The Cp values are back calculated from GCp values found on Figure 6 11b in the ASCE 7 by removing the gust factor of .85 from the GCp value.
150 Based on these values, appropriate ranges for each zone were determined ( Figure 5 2) . Since the new residential p rogram is structured to accommodate varying building dimensions, the boundaries of the zones cannot be fixed based on the nominal dimensions identified from the wind tunnel studies. Therefore the measurements of the boundaries are based on the physical dim ensions (Length of the building, width of the proportionally with the structure, as seen in Figure 5 3 function of the building geometry. Additi onal data was also acquired from wind tunnel data from Clemson University. The dimensions of the model were typical of a SFR s tructure (60ft x 30ft). Comparing the contours of the NIST and Clemson models, there are a few differences in zone locations and d imensions. But both layouts are drastically different than the currently used ASCE 7 modified layout (that employed within the Cope model), as seen in Figure 5 4 . Through further investigation a suitable choice for the zone layouts was determine for all wi nd orientations, and multipliers were developed to map between The majority of wind tunnel testing has focused on gable end roof buildings. Hand drawings of the pressure coefficient co ntours on hip roofs ( Figure 5 5 ) were found in papers written by Meecham ( 1992 ) and Xu & Reardon ( 1998) . The contours in these pictures represent the mean pressure coefficients from the wind tunnel testing. Compari ng contours of the mean pressure coefficients generated for the gable roofs found in the NIST data set, a correlation between the mean and extreme negative pressure coefficients was developed . This ratio was used as a conversion from mean to
151 extreme negati ve pressure coefficients for hip roof structures. Without access to extreme negative pressure coefficient data for hip roofs, this method can be used to produce useable data. The pictures are imported into Autocad, scaled, and a similar analysis as what wa s performed for the gable ended roof can be made to identify the limits of the different zones. Figures 5 6 and 5 7 illustrate the final zone delineations for gable and hip roofs implemented in the LRCR model. The NIST database allowed for the development of a directionally dependent roof pressure coefficients layout which is suitable for allocating roof pressure to the various roofing components. The distribution of the pressure coefficients was mapped using the methods discussed in Chapter 3. These techni ques were employed to improve the directional wind loading algorithm used in the SFR model (Cope, 2004) . T here are two main components that are directly affected by the changes in the distribution of the pressure coefficients. The physical damage to the ro of cover, roof sheathing and roof to wall connections are all dependent on the directional roof pressure distribution . Damage due to water intrusion is a result of openings in the building envelope, of which roof sheathing and roof cover are critical compo nents. As more information becomes readily available, the capabilities of the program should be updated as warranted .
152 Figure 5 1. Contour of Coefficient of Pressure with winds running vertically along the length of the building
153 Figure 5 2. Proce dure used to determine the limits for the pressure coefficients extracted from the NIST database and plotted on the contour maps. The color bar corresponds with the pressure coefficient ranges found on the contour maps.
154 Figure 5 3. Sample mapping of r oof z one Figure 5 4. Comparison of the Zone Layouts for NIST, Clemson and ASCE 7 Modification Models. The relative size of the models is depicted in the figure.
155 Figure 5 5. Contours for a hip roof building (Meecham, 1992) Figure 5 6. The deter mined zone delineation for a gable roof
156 Figure 5 7. The determined zone delineation for a hip roof.
157 CHAPTER 6 INCORPORATION OF THE SINGLE FAMILY RESIDENTIAL CODE AND COMPARISON TO THE CURRENT SINGLE FAMILY RESIDENTIAL CODE The 1 st generation SFR mode l was created by Dr. Anne Cope and was approved by the Florida Commission on Hurricane Loss Projection Methodology in 2005. The LRCR model was developed after 2005, as a separate code rather than an add on to the existing SFR code. This allowed the impleme ntation of more complex assumptions regarding wind loads, load sharing, component capacities, modes of failure, and differences in construction between single and multi family dwellings. Although it was advantageous from a development standpoint to create the LRCR code as a separate entity from the SFR code, the long term maintenance and operation of the FPHLM would benefit from the creation of a single low rise vulnerability model that encompasses both single and multi family dwellings. Given that the LRC R code contains the implementation of a more up to data knowledge base regarding wind loading and structural performance modeling, the most straightforward means of merging the SFR and LRCR codes into a single entity is to expand the flexibility of the LRC R code to include modeling features specific to single family dwellings (e.g. attached garage). Thus, the merger of the LRCR and SFR is intended to be a replacement of the SFR code with a modified version of the LRCR code. The Commission certification req uirements include an assessment of model stability from one certification cycle to the next. Model assumptions may evolve, new information may be incorporated, and model outputs may change from one version to the next. However, drastic changes in model out put receive special scrutiny, and may trigger a violation of the stability requirement. Therefore, the merger of the SFR and LRCR must be conducted with stability of outputs as an important goal. That is, when
158 the vulnerability projections for single famil y dwellings transition from the SFR to its intended modified LRCR replacement, care must be taken to validate that the output vulnerabilities are not drastically different. It is not required that the outputs be identical, but rather represent a reasonable evolution of results. Th e comparison between SFR and LRCR outputs is the main subject of this chapter. The LRCR model was developed to be a flexible code that can analyze buildings of varying sizes. Because of its capabilities, it is an ideal tool to repl ace the SFR model. The building layout of a SFR structure is very similar to that of the LRCR structures. The main differences include the size of the building, number of units per floor and the addition of a garage door. The size of the building and numbe r of units per floor are variables currently employed in the LRCR code and may be adjusted to replicate a SFR structure (i.e. smaller building footprint with a single unit and a gar a ge). In addition to this, a garage door was also added to the front of the structure. The necessary adjustments were made to the corresponding wall and opening components on the front of the building to accommodate the placement of the garage. With these changes made to the code, LRCR model is capable of generating outputs that can replace the SFR model. Continuing additional efforts to expand the model capabilities will broaden the building stock it represents. Comparison to the current single family residential code : Though there are differences in the architecture of the SFR a nd LRCR models, the fundamental probabilistic framework that compares randomized loads and component capacities to identify failure is the same. The magnitude of the pressure coefficients is the same, although the distribution of these coefficients over th e building surface is slightly
159 different (Chapter 5 ). The capacities of the components among the SFR and LRCR are also similar, although the LRCR has updated some components based on knowledge that was available after the development of the SFR model, incl uding: The reassessment of the pressure coefficient zone delineation based on wind tunnel database The load reduction theory for damaged roof sheathing within the tributary area of truss to determine r2w connection loads The load sharing between adjacent r2w connections The introduction of gable and interior truss collapse The internal pressurization of living spaces when breaches in the building envelope occur and its interaction with the attic areas The incorporation of the power law to determine the win d speed affecting the different components at the respective elevations The addition of a new debris impact model The computation of bending and shear capacities for unreinforced and reinforced masonry walls. Inclusion of the masonry wall cracking ratio (l oad/capacity) E tc . Given the differences enumerated above, it is not expected that damage results will be identical between SFR and LRCR for a given common wind speed reference. The comparisons provide a view of the influence of the improvements to the mod el, and a means to evaluate threats to the model stability as a result of the merge. Simulations were conducted and vulnerability curves produced for SFR and LRCR models of the same structures . The number of components that are explicitly modeled in the LR CR model is much more extensive than the SFR model (e.g. soffits, edge and field roof sheathing delineated). Only common component damages identified in Table 6 1 were used for the comparisons.
160 Figure s 6 1 through 6 6 depicts comparison s of vulnerability c urves for the 1 st Generation SFR model and the proposed currently assimilated version of the LRCR model. A combination of the 3 construction qualities (weak, medium and strong) and 2 wall types (timber and masonry) were compared. All comparisons are conduc ted for single story structures. Comparisons of component vulnerabilities between the SFR (Cope) and LRCR (Weekes) models indicate that each component is less vulnerable in the LRLC model. Roofing components such as roof cover, roof sheathing and opening ( Windows, Entry Doors and Sliding Doors) exhibit the most significant decreases in losses. R2w connections were the only components that exhibited an increase in vulnerability. Roof sheathing vulnerability has an inverse relationship with r2w connection vul nerability, since intact sheathing contributes to the uplift on the connections. The r2w connection behavior is therefore consistent with the less vulnerable sheathing on the LRCR. With identical capacities for both models, the difference in the building v ulnerabilities is attributed to the loading of the components. There are significant differences between SFR and LRCR in how external loading is transmitted to the components (load sharing, truss toppling mechanisms, internal pressurization upon breach, de bris impact model, etc). In addition, the conversion of the reference wind speed to the surface pressure loading of the structure can globally affect the vulnerability of all components. The calculation and utilization of the velocity pressure differs betw een models. Researching a uniformly distributed pressure acting on all component on the structure with respect to
161 elevation. The value was independent of the height of the component relative to the wind field . The velocity pressure was calculated using Equation 6 1. q h = 0 . 00256 * K h * V 2 ( 6 1 ) K h = terrain exposure coefficient V = basic wind speed The prescribed value for the terrain exposure coefficient K h is 0.85 in SFR. The v ariable V is the basic 3 sec gust wind speed at 10 m. As previously discussed in Chapter 4, in the LRCR model the wind velocity is calculated at the various heights of the different components. Within this calculation the effects of the surrounding terrain is taken into consideration, negating the need for terrain exposure coefficient. Applying the 0.85 reduction within the square of the velocity would determine the reduction in wind speed associated with the velocity pressure reduction. In order to do so, the square root of terrain exposure coefficient was taken. By doing so a factor of .92 was calculated, providing an 8 percent decrease in the basic wind speed. Using Equation 4 4 with a corresponding surface roughness of 0.9842 ft (suburban exposure) and a target height of 10.33ft (mean roof height of a 1 story building) a factor of .67 was calculated as a reduction to the wind speed for the LRCR model. Rearranging the equation and pulling the value out of the squared function and applying it to the veloci ty pressure produces a much higher effect as the factor is equal to 0.45. Dividing this value by the SFR terrain exposure coefficient (0.45/0.85 = 0.53) it is determined that there is 47 percent difference in the pressure loads on the roof of the building between the two models. Even higher reductions would be observed for components at lower heights such as the wall and opening components. This supports that the SFR model estimates of vulnerability are more severe than those of the LRCR.
162 This study focuse d on the physical exterior damage to the building envelope. Water intrusion through damaged or faulty components is an important contributor to the overall vulnerability of residential structures. This component of the model is addressed by the FIT modelin g team. As was the case for the physical damage model, the water intrusion model was developed first for the SFR model, and then subsequently for the LRCR model updating methodologies. Prior to drawing conclusions regarding the implications of the results presented herein upon model stability, the influence of water intrusion on overall building vulnerability must be evaluated. In conclusion, the LRCR model has been modified to include the behavior of SFR structures. This was done to allow the replacement of the SFR model with the LRCR model. Comparisons of the vulnerability of individual building components between these models were conducted, and it was found that the SFR model consistently produced higher vulnerability with respect to reference wind spee d. The determination of the implications of these findings is pending a comparative analysis of the contribution of the water intrusion component to the overall building vulnerability. The current results provide a benchmark for further studies of the repl acement of the SFR with the LRCR model, within the context of the stability requirements of the FCHLPM .
163 Table 6 1. Damages compared between the Existing SFR model and Modified LRCR Model Component Descriptors Roof Components Roof Cover Percent d amage of roof cover due to wind pressure Roof Sheathing Percent damage of roof sheathing due to fastener withdrawal R2w Connection Percent damage r2w connections due to uplift loads on attached roof sheathing Wall Components Timber Fra me Wall Cope Timber frame damage due to bending loads Wall Cover Percent damage of wall cover due to wind pressure Wall Sheathing Percent damage of wall sheathing due to fastener withdrawal Masonry Wall Wall Percent maso nry wall damage due to bending Bending Wall Failure Percent masonry wall damage due to bending Shear Wall Failure Percent masonry wall damage due to shear Opening Components Windows Percent damage of windows due to wind pressure and debris impact Doors Cope Percent damage of doors due to wind pressure and debris impact (includes both the entry and sliding doors) Sliding Door Percent damage of sliding doors due to wind pressure and debris impact Entry Door Percen t damage of entry doors due to wind pressure and debris impact
164 Figure 6 1. Comparison of the previous single family and the modified low rise commercial residential models. For a 1 story weak timber frame structure.
165 Figure 6 2. Compariso n of the previous single family and the modified low rise commercial residential models. For a 1 story weak masonry structure.
166 Figure 6 3. Comparison of the previous single family and the modified low rise commercial residential models. For a 1 sto ry medium timber frame structure
167 Figure 6 4. Comparison of the previous single family and the modified low rise commercial residential models. For a 1 story medium masonry frame structure
168 Figure 6 5. Comparison of the previous single family and the modified low rise commercial residential models. For a 1 story strong timber frame structure
169 Figure 6 6. Comparison of the previous single family and the modified low rise commercial residential models. For a 1 story strong masonry wall s tructure
170 CHAPTER 7 MITIGATION STUDIES Mitigation is the application of various vulnerability reducing strategies to limit potential damage to both existing and future structures. In the context of this research, mitigation specifically refers to physical modifications to structures to increase their capacity to resist wind damage. For example, the installation of debris impact protection systems over building openings, or the retrofit of existing structural member connections (e.g. roof to wall ) with conne ctions of a higher load capacity. Mitigation features can be utilized singly or in combination. The net effect on vulnerability reduction is typically nonlinear rather than simply additive. ARA conducted a wind loss mitigation study for residential str uct ures in the State of Florida (Applied Research Associates, 2008) . The goal is to estimate the effects of wind resistive building features in reducing hurricane damages and loss to both single family and multi family residential structures in Florida. The r esearch focused on comparing structures that were built prior to the Florida Building Code 2001 (FBC) and those built post FBC period. The research w as conducted in 2002 with select loss mitigation features and in 2008 with additional features, see Figure 7 1 below. A major task in this project included the analysis of insurance and damage data from the 2004 and 2005 Florida hurricanes and engineering data from laboratory tests and wind tunnel experiments. One of th e conclusions from the analysis of the data was that Post FBC (permitted after March 1, 2002) homes ha d losses 75 to 90 percent lower than pre FBC homes. An additional factor is the evaluation of cost effectiveness. Is the cost of the mitigation offset by the reduction in projected losses over a given time frame? The State of Florida requires insurance rate reductions to incentivize
171 homeowners to install mitigation features. Insurance premium reductions provide a motivation for homeowners to install retrofi tting measure s . Table 7 1 provides a description of both the types of typical retrofits along with the typical range of hurricane related premium reductions. However, the science behind appropriate rate reductions is not settled, and is highly dependent up on structural type and location. Thus there is uncertainty regarding the appropriateness of rate reductions in Table 7 1 . In 2006, state lawmakers took action and appropriated $250 million to create the My Safe Florida Home program. The program was create d to help Floridians identify and make improvements to strengthen their homes against hurricanes through free w ind inspections and grant funds (Mitigation Education) . Mitigation studies that are made publicly available allow the homeowner and insurer make an engineering based cost benefit evaluation of various mitigation measures. The aim is to articulate the relationship between property owners, insurance companies, financial institutions, and regulatory agencies, to devise the most effective mitigation s trategies. A mitigation study is the investigation of the effectiveness of various features, alone and in combination, within the context of both vulnerability reduction and cost effectiveness. Such a study was conducted using the LRCR vulnerability model by determining the impact of various mitigation features upon the projected losses. The model is applied to test mitigation strategies in various combinations, and project a likely dollar vulnerability reduction as a result of these measures. The effective ness of an array of mitigation measures for a broad population of buildings can be evaluated through comparisons of the predicted damage/losses with and without the
172 mitigation measures. The quantified reductions in risk can be contrasted with the added cos t of the various mitigation measures (less the reductions in wind insurance premiums) to provide a cost benefit view of the various measures. For example, the model will project the likely insurable loss for portfolio of houses constructed in 1985 with no hurricane protection as compared to portfolios of identical houses with a wind rated garage door and hurricane shutters. The proposed improvements to the FPHLM will reduce the uncertainty in such a projection, based on the inclusion of the most recent data available within the model. In order to appropriately conduct a mitigation study that fully incorporates cost implications , a combination of results stemming from the engineering team (external building vulnerability and water intrusion) and actuarial sci ence teams is needed. For this study only external damage to the building was analy zed, and cost is isolated to that of replacement of these components . Building components consider ed include: roof cover, roof sheathing, wall cover, wall sheathing, roof to wall connections, soffits, windows, entry doors and sliding doors. The purpose of the study is to evaluate the relative reductions in physical exterior damage resulting from single and combined mitigation measures. This provides a means of validating mode l assumptions and methods by demonstrating logical relationships between construction methods and damage. Determining the Average Loss Ratio The average loss ratio, ranging from 0 to 1.0, i s the cost of repairing damage in ratio with the original cost of t he structure. This normalized presentation of damage allows a relative comparison of the effectiveness of individual mitigation methods. The cost of repairing components and cost of initial construction must be identified. A
173 combination RS Means references (Mewis, 2008) , contractor estimates and engineering judgment were used to determine the cost of new construction and repair for the structures. These values were investigated and decided upon by the team at FIT. Table 7 2 belo w illustrates the costs of repair and new construction for the individual external structural components. For some components the unit cost of repair for many of the components eclipse the unit costs of first construction. Therefore, hypothetically the cos t of repair could possibly exceed the initial cost of the structure, but is not seen in any of the models that are presented. In instances where only the repair cost of the component is available, the values were duplicated for new costs. The cost of repai r and new installation of the components are multiplied by the quantified damages and totals of each component, respectively . The costs of components vary between timber frame and masonry wall, as the wall material differs between the two models. Costs can also vary based on other dependencies such as story height. The cost of installing wall sheathing varies from floor to floor, as material prices stay the same but the labor cost increases when installing on higher floor. The component costs are then summe d to determine total cost of repair and the cost of the structure. Dividing the cost of repair by the initial cost of construction produces the average loss ratio. ( 7 1 ) ( 7 2 )
174 ( 7 3 ) Comparison of Average Loss Ratios for D ifferent M odels and M itigation O ptions The average loss ratio is calculated at wind speeds from 50 to 250 mph. Average loss ratio curves can be plot ted from this data, in a similar manner as the vulnerability expected to produce a reduction in damage which can be quantified in the average loss ratio. Models and Mitigations Analyzed For this analysis standard 1 story weak, medium and strong structures were used prior to the addition of mitigation options to serve as the base cases. These base models were used as a point of reference upon which the effects of the mitigation options can be compared. Several mitigations were considered, chosen based on the mitigations that are usually available and typically employed by homeowners (Tab le 7 3). In order to implement these mitigations, the capacities of the individual components were replaced with the higher performance equivalences from the strong model. This was done for all three construction qualities (weak, medium and strong). Becaus e the mitigations were improved based on the strong model, the only mitigation that can be applied to the strong model is the addition of shutters to the windows. Table 7 4 below encompasses the list of all the mitigation options and combinations that were analyzed for this study. Each option will impart various levels of protection to the base
175 structure. The reductions in damages are not equal and affect the structure differently due to their varying capacities and interaction with the structure as a whole . To generate each model, the capacities of the components were manually increased or the effects of the mitigation was added (addition of shutter protection or bracing) within the code. A simulation count of 500 was used to produce the damage matrices. T he damaged matrices were sent through a post processing algorithm that contained the cost profile presented in Table 7 2, above. Initial building costs, cost of repair for each component and the aggregate average loss ratios for all the models are created and stored, and graphs were assembled. The purpose of mitigating a structure is the desire to improve its overall resilience to the hurricane force winds. With that in mind, the addition of any of these options should reduce the damages expected for the ba se structure. The accuracy of this reduction is dependent on the accuracy of the model that it is based upon. The point of this project is to produce as accurate a model as possible with the given knowledge base. As new techniques and methods are incorpora ted into the model, the evolution of the model will take another step towards representing the reality that we are trying to predict. Some of the options have a minimal impact on the overall damages. Mitigations such as braced gable ends, roof to wall repl acement and roof cover replacement are three of the examples of such occurrences. This is a result of the individual cost of repair of the component relative to the building value. However, these results do not consider the additional significant damage th at result from water ingress, as the study is isolated to physical exterior damage. The FPHLM does account for water ingress. Figures 7 2 to 7 18 illustrate the relationship between wind speeds and average
176 loss ratios for the base weak, medium and strong s tructures and the mitigations features identified in Table 7 4. Each option was plotted on a separate graph and includes a curve that depicts the difference between the base model and the corresponding mitigation. Roof c over, r oof to wall c onnection and g a ble e nd b racing Roof cover (RC) and roof to wall (r2w) connections are considered to be discontinuous components, as there are no other components that are affected by their losses based on the way that the code is structured. Savings found due to their up grades are self compounding as the only savings are due to those components not failing. ( Figures 7 2 to 7 5 ) Gable end bracing prevents the toppling of the gable ends of the roof which can also lead to the subsequent collapse of the interior trusses. This toppling is initiated by a lack of adequate sheathing support along the end of the roof to hold the gable end in place. As a result of the collapse the roof sheathing, RC and r2w connection are damaged in the process. However, the effects of the bracing a re not seen until the higher wind speeds when most of the lateral support of the roof sheathing has been removed and r2w connections have been detached due wind uplift. Small reductions can be observed in Figures 7 6 and 7 7. Roof d eck r eplacement The repl acement of the roof decking in most instances typically includes an upgrade to the roof cover that is installed afterwards. For this analysis it is assumed that roof cover mitigation coincides with that of the roof sheathing. The damages to these component s weigh heavily on the average loss ratio. Mitigation of roof cover and sheathing becomes one of the more impactful damage components for a structure as
177 seen in Figures 7 8 and 7 9. Factoring in the effects of water intrusion through openings in the roof i ntensifies its influence. Minimal damages to the sheathing along the edge of a gable roof provides the lateral support required to prevent the toppling of the gable end and the interior trusses. The prevention of this toppling effect through stronger decki ng essentially negates the influence of the gable end bracing as there average loss ratios are very sim ilar for both figures ( Figure 7 10 and Figure 7 11). Engin eered s hutters Shutter systems protect the openings from damages due to windborne debris. Damag es to the windward opening produce an increase in internal positive pressure. This increase in internal pressure increases the damages to all components whose wind loads are contingent on it, which include roof sheathing, roof cover, wall sheathing and wal l cover. These components were identified as most impactful on the average loss ratio, and the improvements to their resilience shows in Figure 7 12 to 7 14. Roof d eck r eplacement and e ngineered s hutter c ombination A new roof deck and shutters individuall y produce notable improvements to the resilience of the structure in comparison to the other options. The combination of these mitigation measures produces decreased damage values that exceed what either of the options could provide individually (Figures 8 15 and 8 16 ) . A gain, the addition of bracing to an already mitigated roof yields minimal improvements for a structure whose roof sheathing has previously been mitigated. With a lower frequency of gable end collapse due to lack of the necessary sheathing damage, bracing has negligible impact until extreme wind speeds (greater than 170
178 mph). The braced models in Figures 7 17 and 7 18 compared to the previously unbraced models in Figures 7 15 and 7 16 illustrate virtually no improvement in average loss rati o as a result of gable end bracing. Comparison to the Saffir Simpson Scale In order to give a greater frame of reference for the potential damages, the plots are separated into the different hurricane categories of the Saffir Simpson Hurricane Wind Scale. According to the NOAA , the Saffir Simpson (SS) Hurricane Scale is a 1 5 to estimate the potential property damage and flooding expected along the coast due to a hurricane land fall (National Oceanic and Atmospheric Administration(NOAA), 2013) . Table 7 5 delineates the five categories by their wind speeds and observed damage level. The SS scale is based on sustained wind speed (1 min average wind s peed) at a height of 10 m over marine exposure. In order to properly integrate the SS scale into average loss cost ratio curves, the wind speeds were converted to 3 sec gust at 10m over open terrain. According to an article by Vickery, Simiu and Kareem a s imple conversion multiplier between the values1.03 and 1.12 can be utilized (Simiu, Vickery, & Kareem, 2007) . A multiplier of 1.1 was employed for this conversion and the modified SS Scale is depicted in Table 7 6, below. The base models and all of the mitigation options are plotted in Figures 7 19 through 7 20. The delineations for the 5 wind categories designated for the SS scale were also plotted on the figures. From each figure, a progression of vulnerability reduction due to the different mitigations and mitigation combinations can be discerned. The individual upgrades to the roof cover, r2w connection and addition of bracing
179 returned minor improvements to the resistance of the building envelope . T he replacement of the roof deck and installment of engineered shutters produced more significant reductions. The combination of the two mitigations provided the most drastic reduction. The incorporation of the SS scale provides a framework to identify the benefits of a mitiga tion option. For example, at the transition speed from a category 3 to a category 4 hurricane, a weak base model accrues approximately 20 percent in average loss ratio while a structure with a new roof deck and installed shutters might experience less than 5 percent in losses. It must be reiterated that this analysis only considers the damages caused to the external components of the building and does not consider the damages due the infiltration and proliferation of water through the structure. Damages ar e intensified by the addition of water damages. It is also significant that the analysis only considers the nominal value of physical damage, and does not incorporate the reality of insurance adjusting that employs damage thresholds to classify components or structures a total loss. For example, this analysis uses a 40 percent shingle loss at face value when calculating the damage ratio, and does not consider that 20 percent shingle loss may result in total roof cover replacement. The FPHLM does consider th ese issues in its loss projections. The primary goal of this mitigation analysis is to provide a framework by which the relative influence of various mitigation measures and their combinations can be evaluated within the assumptions and limitations of the physical damage module of the FPHLM. The nominal results are of little weight, but the relative comparisons are useful
180 for gaging the efficacy of the assumptions, as well as determining where future modeling efforts should be focused.
181 Table 7 1. Range of Reductions for Different Mitigation (Division of Emergency Management) Action ID Mitigation Action Description Discount Range 1 Re roof 0% to 6% 2 Re roof and Re nail Roof Sheathing 0% to 19% 3 Re roof, Re nail Roof Sheat hing, and Add Secondary Water Resistance 0% to 20% 4 Protect Windows 6% to 7% 5 Protect Windows and Doors 7% to 10% 6 Mitigation Actions 1 and 4 7% to 14% 7 Mitigation Actions 3 and 4 7% to 22% 8 Mitigation Actions 3 and 5 12% to 22%
182 Table 7 2. N ew and repair costs for exterior building components Component Cat 2 Cat 3 Source UNITS Cost New Cost Repair Roof Cover 1 Story Shingle Contractor $/ft2 roof 5.00 6.00 2 Story Shingle " " 5.5 6.6 3 Story Shingle " " 5.75 6.9 Roof Sheathing 1 Story " " 2.50 3.50 2 Story " " 2.75 3.85 3 Story " " 2.88 4.03 R2W Connections 1 Story Engineering Judgement each 50.00 2 Story " " 50.00 3 Story " " 50.00 Exterior Wall Cover 1st Story WD Contractor $/ft2 wall 4.00 2nd Story WD " " 5.60 3rd Story WD " " 6.40 1st Story CB " " 4.00 2nd Story CB " " 5.60 3rd Story CB " " 6.40 Exterior wall 1st Story WD " " 8.50 8.00 2nd Story WD " " 11.90 11.20 3rd Story WD " " 16.66 17.10 1st Story CB " " 8.50 8.00 2nd Story CB " " 11.90 11.20 3rd Story CB " " 16.66 17.10 Windows/ Doors and sliding doors windows " each 179.00 429.00 doors " " 651.00 901.00 slider " " 1283.00 1533.00 Soffits 1 Story " ft2/soffits 2 3.00 2 Story " " 2.8 4.20 3 Story " " 3.2 4 .80
183 Table 7 3. List of identified mitigation options used in the study Mi ti gation Option Description Roof Cover Replacement of current shingles with high velocity wind rated shingles Roof Cover & Sheathing Reroof: The renailing of the roof deck and replacement of current shingles with high velocity wind rated shingles R2W Connection Replacement of current R2W connections with hurricane straps Shutter Protection Installation of engineered metal shutters Bracing Bracing of the gable end for truss c ollapse prevention Table 7 4. List of the different mitigation options and combinations compared in the study Construction Quality Mitigation Weak Base Braced Roof to Wall Roof Cover Roof Cover and Sheathing Shuttered Roof Cover, Sheathing and Braced Shuttered, Roof Cover and Roof Sheathing Shuttered, Roof Cover, Braced and Roof Sheathing Medium Base Braced Roof to Wall Roof Cover Roof Cover and Sheathing Shuttered Roof Cover, Sheathing and Braced Shuttered, Roof Cover an d Roof Sheathing Shuttered, Roof Cover, Braced and Roof Sheathing Strong Base Shuttered
184 Table 7 5 . National Hurricane Center Saffir Simpson Hurricane Wind Scale (National Oceanic and Atmospheric Administration(NOAA), 20 13) Category Winds Effects One 74 95 mph No real damage to building structures. Damage primarily to unanchored mobile homes, shrubbery, and trees. Two 96 110 mph Some roofing material, door, and window damage to buildings. Three 111 130 mph Some stru ctural damage to small residences and utility buildings with a minor amount of curtainwall failures. Mobile homes are destroyed. Four 131 155 mph More extensive curtainwall failures with some complete roof structure r failure on small residences. Five gr eater than 155 mph Complete roof failure on many residences and industrial buildings. Some complete building failures with small utility buildings blown over or away. Table 7 6. National Hurricane Center Saffir Simpson Hurricane Wind Scale w/ modified wind speeds Category Winds Effects One mph No real damage to building structures. Damage primar i ly to unanchored mobile homes, shrubbery, and trees. Two 104.5 mph Some roofing material, door, and window damage to buildings. Three 121 mph Some s tructural damage to small residences and utility buildings with a minor amount of curtainwall failures. Mobile homes are destroyed. Four 143 mph More extensive curtainwall failures w ith some complete roof structural failure on small resid ences. Five greater than 170.5 mph Complete roof failure on many residences and industrial buildings. Some complete building failures with small utility buildings blown over or away.
185 Figure 7 1. Loss mitigation features considered in the ARA 2008 Fl orida Residential Wind Loss Mitigation Study (Applied Research Associates, 2008) Figure 7 2. Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with strong roof cover 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Weak vs Weak Mitigation (RC) Average Loss Ratio Weak Weak RC % Diff Weak RC
186 Figure 7 3. Average Loss Ratio comparison of Medium LRCR vs Medium LRCR wit h strong roof cover Figure 7 4. Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with strong r2w connection 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Medium vs Medium Mitigation (RC) Average Loss Ratio Medium Medium RC % Diff Medium RC 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph Weak vs Weak Mitigation (R2W) Average Loss Cost Weak Weak R2W % Diff Weak R2W
187 Figure 7 5. Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with strong r2w connections Figure 7 6. Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with braced gable end 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Medium vs Medium Mitigation (R2W) Average Loss Ratio Medium Medium R2W % Diff Medium R2W 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph Weak vs Weak Mitigation (Braced) Average Loss Ratio Weak Weak Braced % Diff Weak Braced
188 Figure 7 7. Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with braced gable end Figure 7 8. Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with strong roof cover and r oof sheathing 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Medium vs Medium Mitigation (Braced) Average Loss Ratio Medium Medium Braced % Diff Medium Braced 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Weak vs Weak Mitigation (RC + RS) Average Loss Ratio Weak Weak RC + RS % Diff Weak RC+RS
189 Figure 7 9. Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with strong roof cover Figure 7 10. Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with strong roof cover and sheathing w/ braced gable ends 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Medium vs Medium Mitigation (RC + RS) Average Loss Ratio Medium Medium RC + RS + Braced % Diff Medium RC + RS + Braced 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Weak vs Weak Mitigation (RC + RS + Braced) Average Loss Ratio Weak Weak RC RS Braced % Diff Weak RC RS Braced
190 Figure 7 11. Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with strong roof cover and sheathing w/ braced gable ends Figure 7 12. Average Loss Ratio comparison of Weak LRCR vs Weak LRCR with engineered shutter protection 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Medium vs Medium Mitigation (RC + RS + Braced) Average Loss Ratio Medium Medium RC + RS + Braced % Diff Medium RC + RS + Braced 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Weak vs Weak Mitigation (Shutt) Average Loss Ratio Weak Weak Shutter % Diff Weak Shutt
191 Figure 7 13. Averag e Loss Ratio comparison of Medium LRCR vs Medium LRCR with engineered shutter protection Figure 7 14. Average Loss Ratio comparison of Strong LRCR vs Strong LRCR with engineered shutter protection 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Medium vs Medium Mitigation (Shutt) Average Loss Ratio Medium Medium Shutter % Diff Medium Shutt 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Strong vs Strong Mitigation (Shutt) Average Loss Ratio Strong Strong Shuttered % Diff Strong Shuttered
192 Figure 7 15. Average Loss Ratio comparison of Wea k LRCR vs Weak LRCR with strong roof cover, roof sheathing and engineered shutters Figure 7 16. Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with strong roof cover, roof sheathing and engineered shutters 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Weak vs Weak Mitigation (Shutt + RC + RS) Average Loss Cost Weak Weak Shutt RC + RS % Diff Weak Shutt RC + RS 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Medium vs Medium Mitigation (Shutt + RC + RS ) Average Loss Ratio Medium Medium Shutt RC + RS % Diff Medium Shutt RC + RS
193 Figure 7 17. Average Loss Rat io comparison of Weak LRCR vs Weak LRCR with strong roof cover, roof sheathing, braced gable ends and engineered shutters Figure 7 18. Average Loss Ratio comparison of Medium LRCR vs Medium LRCR with strong roof cover, roof sheathing, braced gable ends and engineered shutters 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Weak vs Weak Mitigation (Shutt + RC + RS + Braced) Average Loss Cost Weak Weak Shutt RC RS Braced % Diff Weak Shutt RC RS Braced 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 50 100 150 200 250 Average Loss Ratio 3 sec Gust Wind Speed (mph) Medium vs Medium Mitigation (Shutt + RC + RS +Braced) Average Loss Ratio Medium Medium Shutt + RC + RS + Braced % Diff Medium Shutt + RC + RS + Braced
194 Figure 7 19. Comparative graph of all Weak mitigation option with respect to the modified Saffir Simpson Wind Scale Figure 7 20. Comparative graph of all Medium mitigation option with respect to the modified Saffir Simpson W ind Scale
195 Figure 7 21. Comparative graph of all Strong mitigation option with respect to the modified Saffir Simpson Wind Scale
196 CHAPTER 8 CONCLUSIONS The FPHLM is a component based public model that predicts the damages due to hurricane events. As a multi university effort, the main goal of the research at the UF was to produce the engineering component of a damage prediction model for both low and mid high rise commercial residential structures, while improving the existing model for SFR structures . The model will need refinement as our understanding of the hurricane wind structure interaction increases, but it will be capable of determining a baseline for the vulnerability of current construction to high wind damage. This knowledge will further th e development of future damage mitigation tools and schemes for typical residential structures in Florida. Availability of the methodology used in the model will allow other engineers the opportunity to review the model and provide insight. Completion of a damage prediction model for commercial residential structures and improvements to the residential model will provide insurers and gover nment officials the tools necessary to predict insurable loss due to hurricane wind loads for a multitude of the residen tial structures in the State of Florida. Utilizing the programs capabilities, government officials can more effectively evaluate and regulate the insurance ratemaking process within the state and increase the preparedness of insurance companies for possibl e catastrophic events. The program can also be used as a tool for assessing the performance of varying mitigation components in conjunction with one another. This knowledge base can better evaluate the potential costs and benefits of adding hurricane damag e mitigation components to an existing house or purchasing a house with added hurricane
197 protection. The education and awareness of the populous on such matters is important for the protection of both life and property. Recommendations to improve the curre nt model Currently the model takes an approach of instantaneous load application and acquisition of damage results. This is done for one realization of the building, with a single wind speed coming from one direction. By doing this, there is no history of accumulated damage. Discontinuities can be found in the results of components that are dependent on internal pressure or dependent on damage to other components. By assimilating a time stepping routine, a single structure will be constructed (set component and capacities) by the program and analysis will begin at the lowest wind speed. Damages to the structure would be recorded and enclosure conditions are updated. The program would then move to the next wind speed and once again assess the damages and encl osure conditions. This would be repeated for the duration of the desired wind speeds. The analysis of the final wind speed would signal the end of one simulation. The introduction of a simple graphical user interface for the model would also be beneficial to all users. Ease of use is important in maximizing the potential of model by the results presented is equally important. A virtual representation of the modeled struc ture based on the output data would help convey the results in a manner that exceeds the capabilities of the vulnerability curves, a results would be comparable to assessing post storm damage surveys. Also taking the suggestion of moving towards a time ste pping model, animations replicating the damages as wind speeds increases can
198 be made for a single realization of a structure. This form of demonstration could prove to be highly effective in possibly presenting the structural damage response throughout the history of the intensifying winds. It would also give a clearer view of the inside workings of the program as an opportunity to learn or identify any abnormalities. Acquisition of field data (observed damages from real hurricanes) and claims data (monetar y losses on a per building level) would significantly improve the development of the commercial residential models. However, such data is not easily accessible. An ongoing effort will continue to collect such data for validation studies.
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204 BIOGRAPHICAL SKETCH Johann Weekes earned his Bachelor of Science in civil e ngineering from the University of Florida in 2004. He receive d his Master of Engineering in c ivil e ngineering in 2006. In 2007 he joined the doctoral program in civil e ngineering at the University of Florida. Dr. Weekes has presented his research at international conference meetings and workshops including the American Association for Wind Engineering and Interna tional Conference on Wind Engineering. Dr. Weekes dissertation, Predicting the Vulnerability of Typical Commercial and Single Family Residential Buildings to Hurricane Damage, was supervied by Dr. Kurtis Gurley.