# A Framework to Model the Wind-Induced Losses in Buildings during Hurricanes

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Building Model

#### 2.1.1. Variables in the Building Model

#### Mean Resistance Capacity for Wind Uplift

_{0}). This mean capcity can be related to nominal load using the following approach. Let us say P is the prescribed nominal load obtained from the relevant ASCE 7 using the design wind speed at the location of the building Then, factor φ, which will be referred to as Factor of Safety (in general, $\phi $ is the ratio of load factor to resistance factor), can be used to determine P

_{0}. The estimated mean capacity is

#### Roof Aging and Condition

_{n}is the normalized condition factor of the roof. For example, for a roof with a lifespan of 50 years, after 10 years of use (please refer Figure 4a), C

_{n}will be 3.3/7 = 0.47.

_{mean}is the mean roof capacity for the particular building simulation, obtained after multiplying the RF

_{age}(the reduction associated with the age of the roof) to P

_{0}(as described in Equations (2) and (3)). The resistance capacities for the discretized elements of the roof are sampled from a Gaussian distribution based on [13,40]. The capacity of an ith element on the roof can then be assigned a capacity as shown below.

#### Interior Value

#### 2.2. Demand Model

#### 2.2.1. Wind Pressure Load

#### 2.2.2. Debris Impact

#### 2.2.3. Rain Intrusion

#### Impinging Rain

#### Distribution of Rain across the Surface of a Building

#### Area of Envelope Failure

#### Deficiency in Windows and Doors

#### 2.3. Damage Evaluation

- Initial failure check: each component of the building is checked for failure for a given wind speed and wind direction. Any component that is failed is recorded. Dependency of the roof cover on the roof deck is considered in this check along with the dependency of the roof sheathing on roof-to-wall connections.
- Recalculate the loads on the components and check for equilibrium: the loads on the components are recalculated, using the new internal pressure. Using the new loads, each component is checked for failure. Since the internal pressure depends on the area and location of failure of the envelope, we need to recalculate load, internal pressure and area of failure until there is an equilibrium, which means there is no more failure of any components. At this point, the maximum damage that can happen to the building due to wind pressure and debris will be obtained. This amount of damage for all the components that are modeled is recorded for the particular wind speed. These values will be further used in the next steps to estimate dollar losses.

#### 2.4. Consequence Evaluation

#### 2.4.1. Quantity of Water Entering the Building

#### 2.4.2. Dollar Loss

#### 2.5. Damage Ratio Calculation

## 3. Results

#### 3.1. Convergence of Simulations

#### 3.2. Case Study 1: Residential Building

#### 3.3. Case Study 2: Commercial Buildings Based on HAZUS Models

#### 3.4. Case Study 3: Influence of Primary and Secondary Modifiers

## 4. Discussion

- A framework for generating vulnerability functions to assist insurance loss modeling has been proposed, which, unlike conventional models, does not rely on the fragility of components. Results were validated using the residential building examples from FPHLM and a commercial building example from HAZUS. The influence of primary modifiers (story and construction) and secondary modifiers (window protection, roof age, and debris composition) on overall loss was also explored.
- A Markovian approach-based roof aging model is introduced, which is able to predict the increase in vulnerability with aging. Further study based on claims data is necessary to validate the results of the model or to calibrate the model as necessary. The state transition probabilities used in the analysis can also be modified if new data are available from in-service roofs.
- Damage ratio was found to decrease with an increase in the number of stories by about 50% for Cat1 hurricanes for each added story. Floor area does not influence losses significantly.
- Reinforced concrete buildings are about twice as resilient as masonry for Cat1 hurricanes.
- The model also shows that window protection can help to mitigate losses induced by debris impact in different debris environments. It can reduce losses for Cat2 hurricanes by 100% and Cat3 by 66%.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Attribute Name | Residential (Case Study 1) | Strong (Case Study 2) | Weak (Case Study 2) |
---|---|---|---|

Occupancy | Single Family | Office | Office |

Construction | Wood | Concrete | Concrete |

Year | 1997 | 1997 | 1997 |

Number of Stories | 1 | 3,5 | 3,5 |

Floor Area | 2464 | 10,000 | 10,000 |

Aspect Ratio | 1.64 | 3 | 3 |

Roof Geometry | Gable | Flat, with basic slope | Flat, with basic slope |

Roof Slope | 5/12 | 1/12 | 1/12 |

Roof Maintenance | Excellent | Excellent | Excellent |

Hurricane Bracing | Adequate | Adequate | Adequate |

Opening Protection | No | Large Debris | No |

Height Ground | 10 | 12 | 12 |

Height Typical | 0 | 10 | 10 |

Height Top | 0 | 10 | 10 |

Exposure Category for Design | C | C | C |

Exposure Category for Load | C | C | C |

Design Speed | 100 | 100 | 100 |

Debris Percentage Small | 90 | 90 | 90 |

Debris Percentage Medium | 5 | 5 | 5 |

Debris Percentage Large | 5 | 5 | 5 |

Wall Cladding Type | Vinyl Siding | Brick Veneer | Brick Veneer |

Percentage Window Area First Floor | 10 | 20 | 20 |

Percentage Window Area Typical Floor | 0 | 20 | 20 |

Percentage Window Area Top Floor | 0 | 20 | 20 |

Roof Factor of Safety in Main region | 1.5 | 1.5 | 1.0 |

Roof Factor of Safety in Corner region | 1.2 | 1.5 | 1.0 |

Roof Factor of Safety in Edge region | 1.2 | 1.5 | 1.0 |

Roof Cover Capacity Distribution | Lognormal | Gaussian | Gaussian |

Roof Insulation Capacity Distribution | NA | Gaussian | Gaussian |

Roof Deck Capacity Distribution | Lognormal | Gaussian | Gaussian |

Roof cover COV | 0.4 | 0.1 | 0.1 |

Roof Sheathing COV | 0.4 | 0.1 | 0.1 |

Wall FS Main | 1.2 | 2 | 1.5 |

Wall FS Corner | 1.2 | 2 | 1.5 |

Wall Capacity Distribution | Gaussian | Gaussian | Gaussian |

Wall COV | 0.4 | 0.1 | 0.1 |

Window Capacity Distribution | Gaussian | Gaussian | Gaussian |

Window COV | 0.2 | 0.1 | 0.1 |

Window FS | 1.16 | 2 | 1.5 |

Attribute Description | Numerical Values | Units |
---|---|---|

Distance to source of debris | [10,35] | feet |

Debris uplift wind speed limits | Small [80,110] Medium [130,160] Large [140,170] | mph |

Debris C value | 0.8, 0.496, 0.9 | |

Momentum capacity of unprotected window | 0.025 | kgm/s |

Momentum capacity of protected window | 62.37 | kgm/s |

**Table A3.**Selected Normative quantities of selected items and their unit rates from RSMeans shown as an example. More details can be found in FEMA (2012) and RSMeans 2013.

Item | Unit of Measurement | Normative Quantity (50th Percentile) | Unit Rate as Per RSMeans 2013 ($) |
---|---|---|---|

Interior partition length | 100 LF per 1 gsf | 1 E-3 | 10/ft |

Ceramic Tile floors | SF per 1 gsf | 0.042 | 4.3/sf |

Ceiling Lay in Tile | % | 95 | 1.8/sf |

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**Figure 4.**(

**a**) Mean roof condition for various service life durations. Fifty-year model compared with Coffelt et al. 2008 model (

**b**) capacity reduction factor from the condition state obtained using the proposed model.

**Figure 5.**Mean Reduction Factor for capacity with respect to age in years for commercial roof cover with lifespan of 30 years. Distribution across the mean is shown at ages 10, 15 and 20 years.

**Figure 6.**Normalized distribution of (

**a**) interior and (

**b**) exterior value for a three-story commercial office building with 10,000 sq ft footprint.

**Figure 7.**Subdivided zones of a building—each zone is assigned a mean pressure coefficient for a given wind direction. The width of corner zones “a” is determined using ASCE 07-10. Arrows of wind 0° and 45° wind direction are also shown. Angles of attack used in the analysis are 0° through 315° in the increments of 45° moving counterclockwise. The zones are numbered from 1 to 14 for the walls, A to H and 1′ to 6′ for the roof.

**Figure 8.**Probability of 3.5ft x5 ft unprotected window failure on a 44ftx10ft wall. Validated using the results of Cope, 2004. Also shown are the probability of failure of protected window in small missile and large missile environment. UPW—Unprotected window, PW—Protected Window, SM—Small-Missile Environment and LM—Large-Missile Environment.

**Figure 9.**Convergence of simulations as observed from the (

**a**) mean and (

**b**) standard deviation of DR for a commercial building at various wind speeds.

**Figure 11.**Roof Cover (RC) and Roof Sheathing (RS) vulnerability at different wind speeds. Model results show component vulnerability using the proposed model. Results are compared with Cope, 2004.

**Figure 12.**Model results for mid-rise vs. HAZUS mid-rise vulnerability functions database. 3S—3-story strong, 3W—3-story weak, 5S—5-story strong, 5W—5-story weak. Attributes for the examples are given in Table A1.

**Figure 13.**Influence of number of stories on the DRs in strong concrete office buildings designed for 100 mph winds and average losses for each hurricane category. (

**a**) Vulnerability functions for buildings with 1, 2 and 3 stories (

**b**) average damage ratio for buildings with 1, 2, and 3 stories.

**Figure 14.**Comparison of vulnerability functions for single-story strong, concrete and masonry office buildings. (

**a**) Vulnerability functions for concrete and engineered masonry construction types; (

**b**) average damage ratio for concrete and engineered masonry construction types.

**Figure 15.**Model results for 3-story concrete office building with impact-rated windows and non-impact-rated windows. Additional example with no window protection in large debris environment is also presented. Design speed is 130 mph for all buildings. (

**a**) Vulnerability functions (

**b**) average damage ratio for different hurricane categories.

**Figure 16.**Roof aging effects on single story concrete office buildings with single ply membrane roof with a 100 mph design wind speed. Results for a 1-, 10-, 20- and 30-year-old roof are presented in this study. (

**a**) Vulnerability functions for 1-, 10-, 20- and 30-year-old (

**b**) Average loss for different hurricane categories for 1-, 10-, 20- and 30-year-old roof.

**Figure 17.**Comparison of DR for different floor areas for single-story concrete strong office buildings; (

**a**) vulnerability functions; (

**b**) average loss for different hurricane categories.

Variable | Description | Units |
---|---|---|

DR | Damage Ratio | - |

P_{0} | Estimated mean capacity of the component | psf |

$\phi $ | Factor of Safety of a component | - |

P | Nominal load on the component determined based on ASCE 7 | psf or lb |

RF_{age} | Reduction factor for age of the component | - |

C_{n} | Normalized Condition for age | - |

$\sigma $ | Standard deviation of capacity | psf |

$q$ | Wind pressure | psf |

k_{z} | Topographic factor from ASCE 7 | - |

$w$ | Wind speed | mph |

GCp_{e} | External pressure coefficient | - |

GCp_{i} | Internal pressure coefficient | - |

z | Height to the location where wind speed is calculated | ft |

z_{g} | Nominal Height to the atmospheric boundary layer | ft |

α | Power law exponent based on ASCE 7 | - |

$K$ | Tachikawa number | - |

$\rho $ | Air density | lb/ft^{3} |

$g$ | Acceleration due to gravity | ft/s^{2} |

h_{m} | Thickness of the debris | ft |

ρ_{m} | Density of the debris | lb/ft^{3} |

${x}^{*}$ | Dimensionless horizontal displacement | - |

$x$ | Debris flight distance | - |

w_{d} | Speed of debris | ft/s |

$C$ | Coefficient based on shape of debris | - |

RAF | Rain Admittance Factor | - |

V_{i} | Volume of rain water | ft^{3} |

$IR$ | Intensity of rain | - |

A_{fw} | Area of failed window | ft^{2} |

d_{i} | Deficiency in window | - |

F_{ij} | Factor for rain water calculation | - |

$\theta $ | Angle of attack of wind | deg. |

A_{rc} | Actual failed area of roof cover | ft^{2} |

A_{rs} | Actual failed area of roof sheathing | ft^{2} |

A_{pfrc} | Area of failed roof cover projected in the vertical plane | ft^{2} |

A_{pfrs} | Area of failed roof sheathing projected in the vertical plane | ft^{2} |

R_{rc} | Factor to address secondary rainwater penetration for roof | - |

D_{i} | Quantity of Damage to the ith component | ft^{2} or number |

Q_{i} | Quantity of the ith component in the building | ft^{2} or number |

C_{i} | Cost of repair of the ith component in the building | Dollar |

N_{c} | Total number of components in the building | - |

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## Share and Cite

**MDPI and ACS Style**

Alduse, B.; Pang, W.; Tadinada, S.K.; Khan, S.
A Framework to Model the Wind-Induced Losses in Buildings during Hurricanes. *Wind* **2022**, *2*, 87-112.
https://doi.org/10.3390/wind2010006

**AMA Style**

Alduse B, Pang W, Tadinada SK, Khan S.
A Framework to Model the Wind-Induced Losses in Buildings during Hurricanes. *Wind*. 2022; 2(1):87-112.
https://doi.org/10.3390/wind2010006

**Chicago/Turabian Style**

Alduse, Bejoy, Weichiang Pang, Sashi Kanth Tadinada, and Shiraj Khan.
2022. "A Framework to Model the Wind-Induced Losses in Buildings during Hurricanes" *Wind* 2, no. 1: 87-112.
https://doi.org/10.3390/wind2010006