Citation
Alternate determinations of wind design sruface roughness coefficient, Kz, using geographic information systems (GIS) modeling

Material Information

Title:
Alternate determinations of wind design sruface roughness coefficient, Kz, using geographic information systems (GIS) modeling
Creator:
Ellison, Nicole ( author )
Place of Publication:
Denver, Colo.
Publisher:
University of Colorado Denver
Language:
English
Physical Description:
1 electronic file (255 pages) : ;

Thesis/Dissertation Information

Degree:
Master's ( Master of Science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Civil Engineering, CU Denver
Degree Disciplines:
Civil Engineering
Committee Chair:
Rutz, Frederick
Committee Members:
Marshall, Wesley
Rens, Kevin

Subjects

Subjects / Keywords:
Winds -- Speed ( lcsh )
Wind-pressure ( lcsh )
Civil engineering -- Geographic Information System ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Review:
The surface roughness of the earth has a significant effect on wind speed. Surface roughness of the earth is defined by the terrain, landscaping and man-built environment. The American Society of Civil Engineers Standard 7 (ASCE7-10) Minimum Design Loads for Buildings and Other Structures, gives general guidelines for classifying the terrain upwind of a structure in order to determine a structure’s design wind pressures. ASCE7-10 method for determining the surface roughness at a building, as it relates to wind load, identifies three primary exposure categories to cover the earth’s terrain. ASCE7-10 provides velocity pressure exposure coefficients that affect the wind pressure for each of these categories. By using a geographic information system (GIS), or aerial mapping program, the surface roughness surrounding a structure can be mapped and analyzed to accurately define the surface roughness values. These values can then be used to refine the velocity pressure exposure coefficients utilized in determining the wind load on a structure. This mapping and analysis removes the uncertainty and ambiguity in of selecting an appropriate Exposure Category while accounting for changes in roughness. This modeling and analysis caters to use in practical design of structures.
Thesis:
Thesis (MS) - University of Colorado Denver.
Bibliography:
Includes bibliographic references
System Details:
System requirements: Adobe Reader.
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Nicole Ellison

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
|Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
944455390 ( OCLC )
ocn944455390
Classification:
LD1193.E53 2015 E55 ( lcc )

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Full Text
ALTERNATE DETERMINATIONS OF WIND DESIGN SURFACE ROUGHNESS
COEFFICIENT, Kz, USING GEOGRAPHIC INFORMATION
SYSTEMS (GIS) MODELING
by
NICOLE ELLISON, P. E.
B.S.C.E., Florida State University, 1995
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Masters of Science
Civil Engineering
2015


This thesis for the Masters of Science degree by
Nicole Ellison
has been approved for the
Civil Engineering Program
by
Frederick R. Rutz, Chair
Wesley Marshall
Kevin Rens


Ellison, Nicole (M.S., Civil Engineering)
Surface Roughness and Its Effect on Wind Speed
Thesis directed by Professor Frederick Rutz.
ABSTRACT
The surface roughness of the earth has a significant effect on wind speed. Surface
roughness of the earth is defined by the terrain, landscaping and built environment. The
American Society of Civil Engineers Standard 7 (ASCE7-10), Minimum Design Loads
for Buildings and Other Structures, gives general guidelines for classifying the terrain
upwind of a structure in order to determine a structures design wind pressures. ASCE7-
10 method for determining the surface roughness at a building, as it relates to wind load,
identifies three primary exposure categories to cover the earths terrain. ASCE7-10
provides velocity pressure exposure coefficients that affect the wind pressure for each of
these categories. By using a geographic information system (GIS) or aerial mapping
program, the surface roughness surrounding a structure can be mapped and analyzed to
accurately define the surface roughness values. These values can then be used to refine
the velocity pressure exposure coefficients utilized in determining the wind load on a
structure. This mapping and analysis removes the uncertainty and ambiguity in of
selecting an appropriate Exposure Category while accounting for changes in roughness.
This modeling and analysis caters to use in practical design of structures.
The form and content of this abstract are approved. I recommend its publication.
m
Approved: Fredrick R. Rutz


ACKNOWLEDGMENTS
I would like to thank my dad who inspired me to be an engineer and remains just
as excited today to discuss my thesis as he was when I took my first engineering class
over twenty years ago. I would also like to thank my husband who now refuses to
discuss my thesis but is my biggest supporter and best friend. Lastly, I would like to
thank Dr. Fredrick Rutz who inspired me to pursue this thesis. His dedication and
enthusiasm are unparalleled to any teacher or professor that I have ever known.
IV


TABLE OF CONTENTS
Chapter
1 OVERVIEW........................................................1
El Introduction..............................................1
1.2 Purpose...................................................3
1.3 Scope.....................................................3
1.4 Outline...................................................4
2 BACKGROUND......................................................5
2.1 Atmospheric Boundary Layer................................5
2.2 Estimating Surface Roughness..............................6
2.3 Power Law.................................................7
2.4 Harris and Deaves Model...................................8
3 CODE WIND REQUIREMENTS FOR DESIGN OF STRUCTURES................10
3.1 ASCE7-10 Wind Load Equations.............................10
3.2 Wind Speed...............................................10
3.3 ASCE7-10 Wind Load Adjustment Factors....................13
4 TERRAIN SURFACE ROUGNESS.......................................15
4.1 Wind Exposure Category...................................15
4.2 ASCE7-10 Equations for Kz................................21
4.3 Surface Roughness Parameter z0...........................22
5 CHANGE IN TERRAIN ROUGNESS.....................................28
5.1 ASCE7-10 Equations for Changes in Roughness..............28
5.2 Multiple Roughness Changes...............................33
5.3 Small Scale Roughness Changes............................43
v


6 USING GEOGRAPHIC INFORAMTION SYSTEMS (GIS) TO DETERMINE
SURFACE ROUGHNESS CHANGE IN TERRAIN ROUGNESS......................39
6.1 ArcGIS 10.1.................................................39
6.2 GIS Data Models.............................................40
6.3 GIS Data Sources............................................41
6.4 Methodology.................................................42
7 GIS SPATIAL MODELS.............................................47
7.1 Site 1 Denver...............................................47
7.2 Site 2 Loveland.............................................51
7.3 Site 3 Utah Building Model..................................55
8 SYNOPSIS.......................................................61
8.1 Summary.....................................................61
8.2 Conclusions.................................................61
8.3 Possible Sources of Error...................................62
8.4 Recommendations for Further Research........................63
REFERENCES..............................................................64
APPENDIX................................................................67
A. Single Roughness Changes in Terrains........................67
B. Vertical Frontal Area, Sob..................................72
C. Single Roughness Calculations Using GIS Data for Each Model.75
D. Data from ArcMap 10.1.......................................78
vi


LIST OF TABLES
Table
4.1: ASCE7-10 Velocity Exposure Coefficient Kz Values.......................21
4.2: ASCE7-10 Table C26.7-2 Davenport Classification of Terrain Roughness...23
4.3: ASCE7-10 Table C26.7-1 Range of z0 by Exposure Category................24
4.4: Kz Values Corresponding to ASCE7-10 Ranges for z0......................25
5.1: ASCE7-10 Table C27.3-1 Tabulated Exposure Coefficients for Example on Multiple
Roughness Changes...........................................................34
7.1: Site 1 Denver Building Data Summary....................................49
7.2: Site 1 Denver Comparison between GIS Calculated Data and ASCE7-10 Design
Values......................................................................50
7.3: Site 1 Denver Comparison between GIS Calculated Data and ASCE7-10 Design
Values......................................................................51
7.4: Site 2 Loveland Building Data Summary..................................54
7.5: Site 1 Loveland Building Comparison between GIS Calculated Data and ASCE7-10
Design Values...............................................................54
7.6: Site 1 Loveland Comparison between GIS Calculated Data and ASCE7-10 Design
Values......................................................................55
7.7: Site 3 Utah Building Data Summary......................................59
7.8: Utah Comparison between GIS Calculated Data and ASCE7-10 Design Values.59
7.9: Site 3 Utah Comparison between GIS Calculated Data and ASCE7-10 Design
Values......................................................................60
A.l: Comparison of Tabulated Values for Kz with Single Roughness Change to ASCE7-
10 Kz Values Related to Exposure Category with Exposure B Terrain adjacent the
Building Site...............................................................69
A. 2: Comparison of Tabulated Values for Kz with Single Roughness Change to ASCE7-
10 Kz Values Related to Exposure Category with Exposure C Terrain adjacent the
Building Site...............................................................71
B. 1: Comparison of footprint to Sob using Nicholas Method.................73
vii


B. 2: Comparison of Sob of Rectangular Buildings vs Square Buildings of the Same
Footprint..........................................................................74
C. 1: Denver Transitions between outer and inner areas............................76
C.2: Loveland Transitions between outer and inner areas............................76
C. 3: Utah Transitions between outer and inner areas..............................77
D. 4: Denver GIS Building Model Data..............................................79
viii


List of Figures
Figure
Figure 2.1 Typical Wind Profile..............................................7
Figure 2.2 Comparison of the ASCE7-02 Gust Profiles with those Predicted by the
Harris Deaves Model (Irwin 2006 with permission from ASCE)....................9
Figure 3.1 Larimer County Wind Speed Map (Larimer 2015)......................11
Figure 4.1 ASCE7-10 Photo of Typical Exposure Category B Terrain. (ASCE 2010 with
permission from ASCE)........................................................16
Figure 4.2 ASCE7-10 Photo of Typical Exposure Category B Terrain (ASCE 2010 with
permission from ASCE)........................................................17
Figure 4.3 ASCE7-10 Photo of Typical Exposure Category B Terrain (ASCE 2010 with
permission from ASCE)........................................................17
Figure 4.4 ASCE7-10 Photo of Typical Exposure Category C Terrain (ASCE 2010 with
permission from ASCE)........................................................18
Figure 4.5 ASCE7-10 Photo of Typical Exposure Category C Terrain (ASCE 2010 with
permission from ASCE)........................................................19
Figure 4.6 ASCE7-10 Photo of Typical Exposure Category D Terrain (ASCE 2010 with
permission from ASCE)........................................................20
Figure 5.1 Google Earth map of Highlands Ranch in Douglas County, Colorado (Google
2015)........................................................................29
Figure 5.2 Google Earth map of Area in Northwest Jefferson County (Google 2015)... 29
Figure 5.3 ASCE7-10 Figure C27.3-2 Transition from Terrain Roughness C to Terrain
Roughness B (ASCE 7-2010 with permission from ASCE).........................32
Figure 5.4 ASCE7-10 Figure C27.3-1 Multiple Roughness Changes Due to Coastal
Waterway (ASCE 2010 with permission from ASCE)...............................34
Figure 5.5 ASCE7-10 Figure C26.7-3 Exposure B with Upwind Open Patches (ASCE
2010 with permission from ASCE)..............................................35
Figure 5.6 ASCE7-10 Figure C26.7-4 Exposure B with Upwind Open Patches (ASCE
2010 with permission from ASCE)..............................................36
Figure 6.1 ArcGIS Screenshot Showing Eight Sections..........................44
IX


Figure 7.1 Google Map Showing Site 1 Denver (Google 2014).
47
Figure 7.2 ArcGIS Screenshot Showing Eight New Shapefiles Merged with Building
Shapefile.......................................................................48
Figure 7.3 Google Map Showing Site 2 Loveland Location (Google 2015)............51
Figure 7.4 Screenshot from ArcGIS Building Model for Site 2 Loveland............52
Figure 7.5 Close up Screenshot from ArcGIS Building Model adjacent Site 2 Loveland.
............................................................................53
Figure 7.6 Google Map of Site 3 Utah (Google 2015)..........................56
Figure 7.7 Screenshot from ArcGIS Building Model adjacent Site 3 Utah.......57
Figure 7.8 Screenshot from ArcGIS Building Model adjacent Site 3 Utah.......58
Figure A.l Single Roughness Change 1 with Exposure B Terrain adjacent the Building
Site........................................................................69
Figure A.2 Single Roughness Change 1 with Exposure C Terrain adjacent the Building
Site........................................................................71
x


1
Overview
1.1 Introduction
Scientists and engineers have been studying the effects of wind for centuries and
have found that wind behavior is not only complex, but that storms further complicate the
nature of wind loading. Because wind has a profound effect on everything in which it
interacts with, understanding and quantifying the effects of wind is critical to the design
of structures and the components used in structures. Wind tunnels and other equipment
have been used to develop tools to empirically estimate wind forces on structures, and
these estimates incorporate many variables including the structure's shape and height and
the nature of the surrounding area. The surrounding environment influences the
structures response because the surrounding terrain topography, including hills,
escarpments, vegetation and surrounding structures can redirect the winds and intensify
turbulence that often increases the effective wind shear and pressures.
In common design practice, structural engineers in the United States use the
requirements of the International Building Code (IBC 2012) as the minimum standard
when designing structures. The IBC gives minimum requirements for the design and
construction of building structures, including the minimum loading to be used for the
design of structures. The IBC defers to many material specific codes and standards, such
as the American Institute of Steel Construction Manual 14th Edition (AITC 2011), and the
American Concrete Institute Building Code Requirements for Structural Concrete (ACI
318-11 2011). The IBC states that wind loading shall be determined in accordance with
the American Society of Civil Engineers Standard 7 (ASCE7-10 2010).
Equations for wind behavior near the earths surface and its effect on structures
provided in ASCE7-10 are based on research and equations derived by physicists,
1


meteorologists and wind engineers. The methods prescribed in ASCE7-10 and equations
used, attempt to take into account the many significant variables that affect the wind
pressure on a structure. Specifically, the equations have factors that take into account the
following: wind speed, terrain roughness, structure height, topographic effects, and a
wind directionality factor. It is terrain roughness that is the focus of this project.
For ease of analysis, ASCE7-10 generalizes roughness variables into three
categories known as Exposure B, C and D. ASCE7-10 provides general parameters to
determine the roughness category for a structure based on the roughness of the terrain
surrounding the structure.
Traditionally in the design practice of a mid to low level structure, the design
begins with investigation of the local jurisdictions design criteria. The local jurisdiction
is often the city or county building department. The local building department dictates
the minimum design and submittal requirements required to receive a building permit for
a structure. The local jurisdiction sets the applicable codes used for design parameters
that must be followed. For the structural design, these include the minimum snow loads
and wind loading. Prior to 2010, local jurisdictions in Colorado would specify the wind
speed and the Exposure Category for an entire county. Today, Colorado building
departments require the design engineer to determine the Exposure Category based on the
specific site and surrounding terrain. As noted by Dr. Peter Irwin, One of the greatest
sources of uncertainty in the calculation of wind loads occurs in the selection of the wind
exposure. (Irwin, 2006). Because of changes in the surface roughness such as a
combination of open fields and man built environments mixed with lakes; the exposure
category can be difficult to select.
2


1.2 Purpose
The focus of this thesis is the study of the current methods for calculating surface
roughness and development of a more accurate way to determine the velocity pressure
coefficient used in practical design of structures for wind load. This study applies the
geographic information systems (GIS) aerial mapping tools to address open patches,
obstacles and changes in roughness, and calculates the surface roughness and
corresponding velocity pressure coefficient for a structure based on the structures
surroundings.
The purpose of the study is to use GIS to improve the calculation of surface
roughness and to refine the calculation of wind pressure. The study expands ASCE7-10
code values for the velocity pressure coefficient to account for a wider range of surface
roughness characteristics and transitions between exposure categories. Expanding the
range of code values for the velocity pressure coefficient will provide designers the
ability to better quantify the wind pressures on a structure.
1.3 Scope
While there are many variables and building codes used in estimating wind
pressures on structures throughout the world, the scope of the study is focused on the
methods and equations used in the most current version of ASCE7-10 issued in 2010 and
sometimes referred to as ASCE7-10. A limitation on the scope of the study is that terrain
model will be used that is distinctively limited to the urban areas in the United States,
specifically to three locations, two in Colorado and one in Utah. To provide comparison
for the analysis and calculations, the subject structure for each area will be a low rise
building with a specific height of 33 feet.
3


1.4 Outline
There are 8 chapters in this thesis. The first chapter gives an overview of the project
and describes the purpose and scope.
Chapter 2 is a literature review that includes the previous studies and research that
have led to the development of the equations used in ASCE7-10 that are currently being
used to design buildings in current engineering practice.
Chapter 3 summarizes the code wind requirements for the design of structures
provided in ASCE7-10.
Chapter 4 presents the terrain surface roughness and wind exposure category.
Chapter 5 delves into the ASCE equations for changes in terrain roughness and
analyzes the impact of varying terrain changes on wind loading.
Chapter 6 discusses the capabilities of GIS aerial mapping and analysis methods
used to create GIS models for three sites and their use in determining surface roughness
and wind velocity pressure exposure coefficients.
Chapter 7 presents the results of the three GIS models.
Chapter 8 presents a summary of this research along with conclusions and
recommendations for future research.
4


2 Background
2.1 Atmospheric Boundary Layer
The Earths surface exerts a horizontal drag force on the wind flow that retards
the flow of air. Wind speeds start from zero in direct contact with the ground and
increase with height above the ground. Wind flow near the surface also encounters
obstacles such as trees and buildings that reduce wind speed. Generally, rough terrain
will create more turbulence than that of smooth terrain and may act to slow the wind,
resulting in a lesser wind pressure on the upwind surface of a structure. Wind flowing
over smooth terrain, such as ponds, lakes or oceans will be unimpeded as the surface is
relatively smooth. Rough terrain, such as a forest with dense trees or a suburban area
with buildings located in close proximity, may provide significant roughness, thus
creating turbulence and disrupting the winds flow. In the levels where the wind is
influenced by the Earth's topography, the layer is referred to as the Atmospheric
Boundary Layer (ABL). This is the area of interest, herein. Paramount to this discussion
is that wind speed is influenced by the surface friction. Equally important is that
turbulence results in vertical movements of the air that induce shear stresses and pressure
changes on any obstacles, such as buildings, in the path, Simiu wrote:
The retardation offlow by surface friction will be more effective over the
rougher terrain: therefore, if the geostrophic speed is the same over both sites, at
equal elevations the mean wind speeds will be lower over a rougher site. (Simiu,
1986)
Mathematical and engineering principals are used to create a profile, velocity and
pressure of the wind. Bernoullis Equations, the Power Law, Log Law and The Harris
and Deaves Model are the basis for the equations in ASCE7-10. Each of these will be
explored more fully in the following discussion.
5


2.2 Estimating Surface Roughness
In 1967, Heinz Lettau was invited to Davis California by a U.S. Army sponsored
micrometeorological cooperative field experiment. The grassy field was littered with
equipment including masts and towers brought by various participating groups. Lettau
began to ask how the different sizes of equipment were affecting the roughness and
ultimately the wind speed. He began studying previous work done by Kutzbacks
(Kutzback 1961) pilot experiments using 30 cm bushel baskets placed on an ice lake to
modify the surface roughness. Lettau performed similar experiments using anemometers
to measure the wind speed where he had placed obstructions 50 meters upwind of the
anemometer. In 1969, Lettau proposed the following question to estimate the
aerodynamic roughness parameter z0:
zo=0.5hb s /S (2.1)
where:
hb = the effective obstacle height.
5 = silhouette area of the average obstacle.
S =the specific areas, or site.
Lettau found that the surface roughness within 50 meters affects the wind speed at
a given target point. The obstacles height and area affected the roughness parameter or
surface roughness. He also found that as he increased the anemometer height, the effect
of the obstacle on the wind speed changed. The higher the anemometer height off the
ground, the less the wind speed was affected by the surface roughness. ASCE7-10 uses a
similar equation to determine the roughness parameter. ASCE7-10 also recommends that
effects of open patches or openings of 50 meters (165 feet) in size be considered when
using Exposure B, to be defined later in this thesis.
6


2.3 Power Law
The Power Law is a mathematical equation used in many applications, including
statistics, economics and physics to describe the relationship between two variables. The
Power Law has traditionally been for the study of wind loading on structures which exist
within the lowest portion of the atmospheric boundary layer. The vertical distribution of
horizontal mean wind speeds is modeled as a simple shear with a vertical velocity profile
varying according to a power law with a constant exponential coefficient based on
surface type. The equation is used to estimate the wind speed at a certain height z, within
the gradient height, zg. Where the gradient height is the nominal top of the boundary
layer based on an engineering simplification proposed in 1935 by Pagon (Simiu 1986)
The Power Law assumes the terrain is homogenous. Figure 2.1 shows the typical
mean wind profile.
i
Building
Height, H
Figure 2.1 Typical Wind Profile.
A wind profile Power Law relationship is:
Vz/Vg = (z/zg)a (Irwin 2006) (2.2)
Where:
/
7


z = height above ground of the structure.
zg= gradient height or height of the boundary wind layer
Vz = mean wind velocity at height z.
Vg = mean velocity at gradient height.
a = empirically derived exponent/coeflficient that varies dependent on the roughness of
the terrain.
2.4 Harris and Deaves Model
The Power Law does not account for changes in the roughness of the surface.
The Earths surface is made up of multitudes of terrain that is constantly varying. The
Harris and Deaves model includes the effects of surface friction and accounts for Coriolis
forces (Irwin 2006). The Harris and Deaves model is a semi-empirical relationship also
used to describe the vertical distribution of horizontal mean wind speeds within the
lowest portion of the atmospheric boundary layer. This wind is considered to be a more
reliable method of determining wind speeds in the lower portion of the ABL, with heights
less than 100 meters (328 feet).
The Harris and Deaves model is as follows (Harris 1981):
Vz = 2.5u In (z/z0) (2.3)
Where:
V= mean velocity,
z = height above ground.
u* = velocity of flow which is dependent on the surface shear, density of the air and the
roughness length.
8


z0= roughness parameter used as a corrective measure to account for the effect of the
roughness of a surface on wind flow.
There has been uncertainty with regards to the exact values of the constants for
the Power Law, the Log Law and the Harris and Deaves Model. However, wind research
and studies have shown that all three models produce similar results for homogenous
terrain with errors that are of little consequence especially considering the uncertainties in
wind speed and terrain. Figure 2.2 below is a graph comparing the gust profiles as
computed by the ASCE7-02 method and Harris and Deaves Model method.
Figure 2.2 Comparison of the ASCE7-02 Gust Profiles with those Predicted by the
Harris Deaves Model (Irwin 2006 with permission from ASCE).
9


3 Code Wind Requirements for Design of Structures
3.1 ASCE7-10 Wind Load Equations
This chapter presents the methodology and equations used by structural engineers
for the design of structures in common design practice. When designing a structure,
design engineers must account for multiple factors as they relate to the specific
structures site.
ASCE7-10 provides the designer equations for finding the vertical and horizontal
wind pressures on a structure for both the Main Wind Force Resisting Systems (MWFRS)
and the structures Components and Cladding (C&C). The MWFRS consists of the
structures primary structural braces, frames or walls that resist the out-of-plane lateral
forces caused by wind or seismic events for the entire structure. The C&C consist of the
individual framing components that are subject to wind or seismic load but do not serve
as lateral systems for the entire structure. For example, roof joists and wall studs are
subject to wind and seismic forces but are typically not part of the MWFRS.
3.2 Wind Speed
Basic wind speed data is calculated by statistically evaluating the regions climate
data over a minimum period of 50 years. The highest wind occurrences in that period
will then become the established design wind load, with an annual probability of the
occurrence ranging based on the building type. The current method in determining wind
speed is based on a three second gust wind speed.
The basic wind speed for the majority of the United States is 90 miles per hour
(mph) service or an equivalent factored wind speed of 115 miles per hour based on 3-
second gust criteria as presented in ASCE7-10. However, the Gulf of Mexico and
Atlantic coastal regions have much higher wind speeds because of the high winds
10


generated by hurricanes. The service wind loads on the hurricane coast range from 100
mph to 190 mph. There are also special wind regions to account for inland areas that
have higher wind loads. For example, the Front Range of Colorado sits in a special wind
region and the predetermined service wind loads for building design can vary from 90
mph to 180 mph. From the following Wind Speed Chart, shown in Figure 3.1, obtained
from the Larimer County Building Department, illustrates the wide variation over a small
area.
Larimer County Wind Speed Map
R 78 W R 77 W R76W R75W R74W R73W R72W R71W R70W R 69 W R 68 W
Legend
Wind Speed 3-Second Gust
WIND_SPEED_MPH
I 190 Plateau
90 To 100 Contours
100 To 110 Contours
I 1110 To 120 Contours
M 120 To 130 Contours
H 130 To 140 Contours
I 1140 Plateau
1^1 180 Plateau
Incorporated Areas
Cities and Towns
I I Berthoud
l l Estes Park
Fori Collins
l l Johnstown
Loveland
l l Timnath
I I Wellington
f I Windsor
---Major Roads
NOTE
Basic Wind Speeds
Colorado Front Range
Peak Gust, mph
Contours Except for
plateau regions at
90,140,180 mph
Figure 3.1 Larimer County Wind Speed Map (Larimer 2015).
The wind pressure formula incorporates adjustments for gust effects, and
aerodynamic effects.
p=qzGCp
(3.1)
Where:
11


qz = velocity pressure at height z in pounds per square foot.
p = the design wind pressure in pounds per square foot.
G = gust factor.
Cp = external pressure coefficient.
ASCE7-10 adds adjustments for wind directionality, velocity exposure and
topographic effects. The wind velocity pressure qz, evaluated at height z is calculated
using the following equation:
qz=0.00256KzKztKdV2Iw (ASCE7-10 equation 27.3-1) (3.2)
Where:
qz = velocity pressure at height z in pounds per square foot.
Kz = velocity pressure exposure coefficient evaluated at height z for
Exposure Category B, C or D.
Kd = wind directionality factor.
Kzt = topographic factor.
V= basic wind speed in MPH for 3-second gust.
Iw = Importance factor for wind design.
Gustiness in wind introduces dynamic loading effects on the system, which can be
examined in terms of a gust loading factor. The aerodynamic effects are represented by
ASCE7-10 external and internal pressure coefficient. The aerodynamic effects account
for the increased effects of wind as it flows over and around a bluff body such as a
building. A building will experience greater forces at the edges of the structure due to the
wind flow. This greatly affects the C&C pressures of a building.
12


3.3 ASCE7-10 Wind Load Adjustment Factors
The wind directionality factor, Ka, is used in ASCE7-10 wind load provisions as a
load reduction factor intended to take into account the less than 100% probability that the
design wind event wind direction aligns with the worst case building aerodynamics.
Typically Ka is 0.85 for enclosed rectangular buildings and can be upwards of 0.95 for
chimneys, tanks and other circular structures.
The topographic factor, Kzt, is used in ASCE7-10 wind load provisions to account
for abrupt changes in the general topography such as hills, ridges and escarpments within
a two mile radius of the structure. Wind speeds up when it goes over these terrain
features resulting in higher wind pressures on the adjacent structures. Studies by Ho,
Surry and Davenport (Ho 1991) on urban areas have shown that a similar effect can be
seen from adjacent buildings, causing increased dynamic and increased turbulence in
cluttered city environments.
Ironically, attempts to determine wind loads on low buildings have been
hampered by the random nature of these surface elements and researchers have
been forced to simply deal with the complex problem. As a result, almost all low
building research to date has been carried out on simple rectangular block-like
buildings in homogeneous surroundings(Ho, et all 1991)
The Importance Factor, Iw, is used in ASCE7-10 wind load provisions to adjust
the structural reliability of a structure for the buildings classification. Importance factor
values range from 0.87 to 1.15 for wind load. A building with a higher potential for loss
of life or a building critical in an emergency, such as a hospital or police station will have
a higher importance factor than a single family residential structure. Barns and
unoccupied structures have a lower importance factor. This factor adjusts the design
wind pressure and is not related to the actual wind pressures.
13


The Velocity Pressure Exposure Coefficient, Kz, is used in ASCE7-10 wind load
provisions to account for ground surface roughness and height of the structure above
ground. Kz is determined by the height of the structure and exposure category of the
structures surrounding terrain. The exposure category is based upon terrain surface
roughness as discussed in the following chapter.
14


4 Terrain Surface Roughness
4.1 Wind Exposure Category
ASCE7-10 provides the adjustment factor Kz for three Exposure Categories, B, C
and D. The upwind distance affecting the Exposure Category is often referred to as the
fetch. While meteorological studies use fetch distances upwards of 100 kilometers
(km) or 62 miles, investigations by Tamura done in 2001 suggest that a buildings fetch is
dependent on the building height. Tamuras studies show that fetches of one to four
kilometers are applicable to buildings with heights less than 50 meters (164) and that a
1 km upstream fetch may be important for exposure classification (Tamura, 2001). The
fetch distances provided by ASCE7-10, as noted below, vary with the roughness of the
terrain and building height.
In previous versions of ASCE7-10, Exposure A was used in densely populated
urban areas with tall and closely spaced buildings. In the ASCE7-02 (ASCE7 2002)
Exposure A was deleted because areas in close proximity to tall buildings have higher
wind loads due to the effect of local channeling and wake buffeting effects. As noted by
Ho, Surry and Davenport after their research on wind load effects near a densely built
city center in Canada:
Another observation is that while high pressures or suctions are often reduced in
complex surroundings, the lower loads increase. This reduction of mean loads and
increase of dynamic loads due to increase in turbulence in the cluttered
environment result in an increase of the lower peak loads for the Random City
results(Ho, et all 1991)
Therefore Exposure A was deleted in the current edition of ASCE7-10 and is only
applicable where wind tunnel testing is performed.
Exposure B is defined as urban and suburban areas, wooded areas, or other
terrain with numerous, closely spaced obstructions having the size of single-family
15


dwellings or larger. Exposure B is applicable when the structures surrounding terrain
meets these criteria for a distance of 1500 feet or more for structures with heights 30 feet
or less. For buildings with heights greater than 30 feet, the fetch distance is increased to
2600 feet or 20 times the building height, whichever is greater. The distance of 1500 feet
has been reduced from the 2005 version of ASCE7-10 from 2600 feet. Figures 4.1 4.3
depict areas categorized by Exposure B.
Figure 4.1 ASCE7-10 Photo of Typical Exposure Category B Terrain. (ASCE 2010
with permission from ASCE)
16


Figure 4.3 ASCE7-10 Photo of Typical Exposure Category B Terrain (ASCE 2010
with permission from ASCE).
17


Exposure C is defined as open terrain with scattered obstructions having heights
less than 30 feet. This category includes flat open country and grasslands a depiction of
Exposure C is shown in Figure 4.4 and 4.5. Exposure D is defined as flat, unobstructed
areas and water surfaces. This category includes smooth mudflats, salt flats, and
unbroken ice as shown in Figure 4.6. ASCE7-10 states that Exposure C is to be used
when Exposure B and D do not apply. ASCE7-10 sets up Exposure C to be the default
exposure category for areas of uncertainty.
Figure 4.4 ASCE7-10 Photo of Typical Exposure Category C Terrain (ASCE 2010
with permission from ASCE).
18


Figure 4.5 ASCE7-10 Photo of Typical Exposure Category C Terrain (ASCE 2010
with permission from ASCE).
The sites in Figures 4.3 and 4.5 each have classic changes in roughness. In Figure
4.3, there are large buildings in what appears to be a city environment and what might
have been considered Exposure Ain earlier versions of the ASCE7 defined as heavily
built-up city centers with tall buildings'" (ASCE7-02 2002). However there are open
spaces and wooded areas at the top of the photo that represent a different surface
roughness. In Figure 4.5, there are clusters of homes present in the foreground and on the
left side of the photo that appear to meet ASCE7-10 criteria for Exposure B terrain. It is
easy to see the uncertainty and ambuiguity in selecting an exposure category for a site.
ASCE7-10 defines Exposure D as flat, unobstructed areas and water surfaces.
This category includes smooth mudflats, salt flats and unbroken ice. Exposure D
prevails in the upwind direction for a distance of5000feet or 20 times the building
height, whichever is greater (ASCE7 2010) and is shown below in Figure 4.6. ASCE7-
10 states that Exposure D shall also apply where the ground surface roughness
19


immediately upwind of the site is B or C, and the site is within a distance of 600feet or
20 times the building height, whichever is greater, from an Exposure D condition
(ASCE7 2010).

Figure 4.6 ASCE7-10 Photo of Typical Exposure Category D Terrain (ASCE 2010
with permission from ASCE).
After the exposure category is selected for the site, the Kz value can be found from
ASCE7-10 Table 27.3-1 based on the exposure category and building height. These
values have been reproduced in Table 4.1 for building heights up to 50 feet. The velocity
pressure coefficient, Kz which is multiplied directly to the wind velocity, can vary by as
much as 49% between Exposure Categories. As such, the wind pressures used in design
are significantly affected by the selection of the Exposure Category.
20


Table 4.1: ASCE7-10 Velocity Exposure Coefficient iC Values (Adapted from
ASCE7-10, Table 26.7-1)).
height above Kz % difference Kz % difference Kz
ground in Exposure btw B and Exposure btw C and Exposure
feet B C C D D
0-15 0.57 33 0.85 21 1.03
20 0.62 31 0.9 20 1.08
25 0.66 30 0.94 19 1.12
30 0.7 29 0.98 18 1.16
40 0.76 27 1.04 17 1.22
50 0.81 26 1.09 17 Ml
60 0.85 25 1.13 16 1.31
As indicated in Table 4.1, for a building 15 feet in height, the design wind
pressure is almost 50% higher for Exposure C than for Exposure B. As the height of the
structure increases, the effect of the terrain roughness becomes less significant.
4.2 ASCE7-10 Equations for Kz
The equations in ASCE7-10 for the Velocity Pressure Coefficient, Kz are based on
the Power Law. The equation allows the Exposure type and height above the ground to
be applied to the wind gust loads. The 2.01 factor is the ratio of the gust speed at
gradient height to that in standard open terrain at 10 meters (33 feet). As shown in the
Power Law equations, the coefficient, a, is an empirically derived exponent/coefficient
that varies dependent on the roughness of the terrain. These values are shown in Table
4.2. The equation is as follows:
21


K:=2.Q\ (z zg)2 u for 15 ft < z < zg (ASCE7-10 equation C27.3-1)
Kz=2.0\(\5/zg)2/a for 15 ft > z (ASCE7-10 equation C27.3-2)
(4.1)
(4.2)
a=cizo0m (4.3)
and
zg=C2Zo0-125 (4.4)
Where:
ci and C2 are constants. ci=6.62 and C2= 1,273 ASCE7-10 page 547
zg = ASCE7-10 gradient height or nominal height of the atmospheric boundary layer as
discussed in Chapter 2.
z0 = surface roughness parameter.
4.3 Surface Roughness Parameter Zo
ASCE7-10 uses a similar equation to determine the roughness parameter that was
developed by Lettau in 1969. ASCE7-10 uses the ground roughness length parameter, z0,
to determine the ground surface roughness which is directly related to ASCE7-10
Exposure Category, B, C or D. The ground surface roughness, z0, is measured for a lot or
area, using the structures or projections on that lot.
ASCE7-10 equation for z0 is as follows:
zo=0.5Hob(&fc/Aofc ) ASCE7-10 equation C26.7-1. (4.5)
Where:
Hob = the average height of the roughness in the upwind terrain in ft.
Ajfc=the average vertical frontal area per obstruction.
A0b=the average area of ground occupied by each obstruction, including open area
surrounding it in ft2.
22


ASCE7-10 Zo values are taken directly from the Davenport studies. However,
ASCE7-10 classifies roughness into three grades, where Davenport had an eight-grade
roughness classification. The Davenport classification is shown in Table 4.2 with the z0,
a, and zg corresponding directly with ASCE7-10 and zd is an adjustment factor to
accurately depict the boundary layer wind flow.
Table 4.2: ASCE7-10 Table C26.7-2 Davenport Classification of Terrain Roughness
(ASCE 2010 with permission from ASCE).
Tabic C26.7-2 Davenport Classification of Effective Terrain Roughness
Class z,,, ft (m) [note 1 ] a [note 2] zg. ft (m) [note 2] Zj (ft or m) [note 3] Wind flow and landscape description4
1 (). 2 0.016 (0.005) 11.4 760 (232) Zd o Smooth: Featureless land surface without any noticeable obstacles and with negligible vegetation; e.g. beaches, pack ice without large ridges, marsh and snow-covered or fallow open country.
3 0.1 (0.03) 9.0 952 (290) Zd = o "Open": Level country with low vegetation (e.g. grass) and isolated obstacles with separations of at least 50 obstacle heights; e.g, grazing land without windbreaks, heather, moor and tundra, runway area of airports, ice with ridges across-wind.
4 0.33 (0.10) 7.7 1,107 (337) Zni = 0 "Roughly open ": Cultivated or natural area with low crops or plant covers, or moderately open country' with occasional obstacles (e.g. low' hedges, isolated low buildings or trees) at relative horizontal distances of at least 20 obstacle heights.
5 0.82 (0.25) 6.8 1,241 (378) z., = 0.2zh Rough : Cultivated or natural area with high crops or crops of varying height, and scattered obstacles at relative distances of 12 to 15 obstacle heights for porous objects (e.g. sheltcrbclts) or 8 to 12 obstacle heights for low solid objects (e.g. buildings).
6 1.64 (0.5) 6.2 1,354 (413) Zj = 0.5zn "Veiy Rough": Intensely cultivated landscape with many rather large obstacle groups (large farms, clumps of forest) separated by open spaces of about 8 obstacle heights. Low densely-planted major vegetation like bushland, orchards, young forest. Also, area moderately covered by low buildings with interspaces of 3 to 7 building heights and no high trees.
7 3.3 (1.0) 5.7 1,476 (450) zd = 0.7zH Skimming": Landscape regularly covered with similar-size large obstacles, with open spaces of tile same order of magnitude as obstacle heights; e.g. mature regular forests, densely built-up area without much building height variation.
8 >6.6 <>2) 5.2 1,610 (490) Analysis by wind tunnel advised Chaotic": City centers with mixture of low-rise and high-rise buildings, or large forests of irregular height with many clearings. (Analysis by wind tunnel advised)
Below, Table 4.3 shows the ranges of typical values for zD listed by ASCE7-10
Exposure Category and the corresponding values used for each exposure category. The z0
23


values used in the code correlating with Exposure Category B and C are conservatively
on the lower end of the ASCE range.
Table 4.3: ASCE7-10 Table C26.7-1 Range of Zo by Exposure Category (ASCE 2010
with permission from ASCE).
Table C26.7-1 Range of z by Exposure Category
Exposure Category Lower Limit of z& ft itm Typical Value of ft (m) Upper Limit of z.2, ft A 2.3 {(}.'!)< Zv 6.6 (2)
B 115 (0.15) C 0.033 (0.01) < / 0.066 (0.02) 2,<0.5 (0.15) 0.066(0.02)
D 0.016 (0005) /< 0.033 (0.01) 0.016 (0,005)
Refer to Table 4.4 for the resulting range of the Kz values for the full range of z0
values from ASCE7-10 Table C26.7-1. As depicted in Table 4.4, the variations in z0
relate directly to the variations in Kz.
24


Table 4.4: Kz Values Corresponding to ASCE7-10 Ranges for z0.(Adapted from
ASCE7-10 Table 26.7-1)
Exposure Zo( ft) Kz at 15' ht Kz at 30' ht Kz at 33 ht K: at 66
A 2.300 0.433 0.548 0.566 0.715
A/B 2.200 0.438 0.553 0.571 0.720
B 1.800 0.460 0.577 0.595 0.746
B 1.400 0.488 0.607 0.626 0.779
B 1.000 0.525 0.648 0.667 0.822
B 0.750 0.558 0.683 0.702 0.859
B 0.660 0.573 0.699 0.718 0.875
B/C 0.500 0.606 0.733 0.753 0.911
C 0.400 0.632 0.761 0.780 0.939
C 0.200 0.715 0.846 0.866 1.026
c 0.066 0.848 0.981 1.001 1.158
C/D 0.033 0.930 1.063 1.082 1.236
D 0.032 0.934 1.066 1.086 1.239
D 0.016 1.014 1.144 1.164 1.313
Notes:
1. Bold entries relate to the values by ASCE7-10.for.Kz
It should be noted that ASCE7-10 ranges of z factor are significantly less than the
Davenport Classification which has a z0 value of 3.3 for landscape regularly covered
with similar-size large obstacles, with open spaces of the same order of magnitude as the
obstacles heights; e.g. mature regular forests, densely built-up areas without much
building height variation (Wieringa 2001). In addition, the values for z0 that are used in
the code for Exposure B and C fall on the low end of the ASCE ranges. ASCE7-10 notes
that the lower values are used to account for suburban terrain that contains open patches,
such as highways, parking lots, and playing fields. ASCE7-10 Exposure D values are on
the low end of ASCE7-10 range and are significantly lower than the Davenport value of
0.0007 for open sea or lake (irrespective of wave size), tidal flat, snow-coveredflat
plain, featureless desert, tarmac and concrete with a smooth fetch of several kilometers
25


(Wieringa 2001). ASCE7-10 allows the use of Exposure C without any adjustments for
Exposure D terrain provided the Exposure D terrain is not within 600 feet of the site. The
Florida Building Code takes exception to this and requires Exposure Category D applies
where the building or structure is exposed to wind over open water that extends 5000ft
or 20 times the height of the building in the upwind direction (Florida 2010).
A substantial amount of research has been performed on surface roughness and
the corresponding roughness parameter. Lettaus 1969 research found values for z0 in the
range of 4.1 to 0.41 for houses of city in dense versus loose array. (Lettau 1969)
To demonstrate the calculation of z0, ASCE7-10 has an example of a typical
suburban neighborhood using the following data:
Hob = the average height of the roughness in the upwind terrain is typical home height of
20 ft.
Ajfc=the average vertical frontal area per obstruction of 1,000 ft.
A0b=the average area of ground occupied is 10,000 ft.
The z0 obtained from ASCE7-10 example is 1.0.
Using statistical data from the Denver Colorado Market Report (Trulia 2013) and
the US Census (US Census 2013), the z0 for a typical suburban neighborhood in Denver,
Colorado will be calculated. The average lot size is 8000 ft2.
Hob = the average height of the roughness in the upwind terrain is typical home height of
20 ft.
Using the same Sob as in ASCE7-10 of 1000 ft2.
A0b=the average area of ground occupied is 8,000 ft2.
The z0 obtained from equation C26.7-1 is 1.25.
26


Both the values of z0 calculated by the ASCE in the example calculation and the z0
calculated above fall within the range of 0.5 to 2.3, but well above the value of z0 of 0.66
given in ASCE7-10 for Exposure B. This shows the Exposure B values in the ASCE7-10
are conservative for the Denver area.
27


5 Change in Terrain Roughness
5.1 ASCE7-10 Equations for Changes in Roughness
As wind moves over terrain it typically encounters many change in roughness
and the boundary layer is most typically in a state of transition from one
roughness to another. (Irwin, 2006)
Prior to the development of computer accessible aerial mapping now available on
the internet, many structural engineers relied on the local building official to provide the
exposure category applicable in their city/county. There are cities/counties in Colorado
currently prescribing one exposure category to be used throughout their area of
jurisdiction and thus do not take into account site specific conditions. These
cities/counties include both densely populated areas and open areas. For example,
Douglas County, Colorado prescribes Exposure C for the entire County (Douglas 2013).
As may be seen from Figure 5.1, the neighborhoods of Highlands Ranch are located in
Douglas County and are located in densely populated suburban areas. Through 2013,
Jefferson County prescribed Exposure B for the entire county with a note saying except
in designated areas (Jefferson 2013). However, the Jefferson County Code
Amendments do not define these areas. In 2014, the language was changed to except in
designated areas included but not limited to Rocky Mountain Airport Rocky Mountain
Metropolitan Airport area between Simms St. and Wadsworth Blvd. and north of 108th
Ave. 120 mph Exposure C (Jefferson 2013). As may be seen in Figure 5.2, there are
large open spaces that are consistent with Exposure C terrain. As discussed previously,
Figure 4.3, the landscape contains terrain consistent with both Exposure B and C
categories. Today most jurisdictions in Colorado require the designer to assess and
define the exposure category based on site specific conditions. Based on my experience,
traditionally a designer will choose the most conservative Exposure Category for the site
28


and not take into account the changes in roughness. This need not always be the case and
what follows are the alternatives.
Figure 5.1 Google Earth map of Highlands Ranch in Douglas County, Colorado
(Google 2015).
Figure 5.2 Google Earth map of Area in Northwest Jefferson County (Google 2015).
ASCE7-10 acknowledges that there are sites that will be located where there is a
combination of terrain. In areas of transition, ASCE7-10 allows an intermediate
29


exposure between Exposures B, C and D to be determined in a transition zone provided
that it is determined by a rational analysis method.The commentary of ASCE7-10
gives empirical formulas to calculate the velocity pressure coefficient, Kz, for single and
multiple roughness changes so that the Kz factor can be determined for buildings that fall
between exposure categories. Equation C27-9 can be used for the most common
condition of a single roughness change, for example from Exposure B to Exposure C:
Change in roughness is calculated using incremental adding to the Kz factor as
shown in the equation below:
Kz=Kzd + AK (ASCE7-10 equation C27.3-5) (5.1)
AX=(A33u-K33d) x (K/d !K\dd) x AFak(x) (ASCE7-10 equation C27.3-6) (5.2)
|A^| = |Azu-Azd| (5.3)
Eak(x) = logio(xi/x)/ logio(xi/x0) (ASCE7-10 equation C27.3-7) (5.4)
Where:
Kz = Velocity pressure coefficient
Kzd = Kz value downwind at the design building
Kdu = Kz value downwind at the height of 33 feet.
Kzu = Kz value upwind of the design building.
x = distance from site to terrain change in miles.
xi = 6.21 miles (10 km) for AAvCAVu (wind from smoother terrain upwind to rougher
terrain downwind).
xi = 62.1 miles (100 km) for K33d>K33u (wind from rougher terrain upwind to smoother
terrain downwind).
X^C3Xl0[-(K33d-K33u)A21A-2'3
30


C3 = 0.621 miles (1.0 km)
ASCE7-10 has one example of a single roughness change for a building 66 feet in
height and its local surroundings are suburban. However the site is o// the edge of the
suburbs and is 0.37 miles (1953 feet) from open terrain. The formulas are reproduced
below:
Equations and values for the upwind open country terrain are as follows:
a=ciz00133 = 6.62 x 0.0660133 = 9.5
zg =c2 zo0125 = 1,273 x 0.0660125 = 906
Using ASCE7-10 equation C27.3-1
AzM=2.01(66/906)2/9 5 = 1.16
K33u=2.01(33/906)2/9-5 = 1.0
Equations and values for the downwind suburban terrain are as follows:
oc= CiZo 0 133 = 6.62 X 1.00133 = 6.62
zg=c2zo0 125= 1,273 x 1.00 125= 1,273
AzM=2.01(66/906)2/6-19 = 0.82
K33u=2.01(33/906)2/9'5 =0.67
X0 = C3X 10 K33d-K33u)r'2-23 = 0 621 x -(0.62-1.0^2-2.3 = Q.00241 miles
Fak(x) = logio(6.21/0.36)/ logio(6.21/.00241) = 0.36
AK = (1.0 -0.67) 0.82 /0.67 x 0.36
Kz=KzA + AK = 0.82 + 0.15 = 0.97
ASCE7-10 calculated value falls between ASCE7-10 prescribed Kz values of 0.88
and 1.16 for Exposure B and Exposure C, see Table 4.4.
31


In this example a roughness factor z0 of 1.0 is used in lieu of the z0 of 0.66 that is
used for the typical ASCE7-10 values to find Kz. ASCE7-10 states that it is acceptable
to use the typical z0 rather than the lower limit for Exposure B in deriving this formula
because of the rate of transition of the wind profiles is dependent on average roughness
over significant distances, not local roughness anomalies'".
Figure 5.3 shows the transitions from Terrain Roughness C to Terrain Roughness
B corresponding to the equations in ASCE7-10.
Figure 5.3 ASCE7-10 Figure C27.3-2 Transition from Terrain Roughness C to
Terrain Roughness B (ASCE 7-2010 with permission from ASCE).
As part of this study, the values for buildings with building height of 33 feet were
tabulated for transitions from Exposure B to C and C to B based on ASCE7-10 equations
for change in roughness using single terrain change upwind of the site beginning with
164 feet, ASCE7-10 length identified as an open patch up to a distance of six miles.
The tables in Appendix A calculate Kz values based on ASCE7-10 equation C27.3-5 also
shown in Equation 5.1. These tables show the effect of small to larger terrain changes on
32


Kz, used to determine wind load on a structure. These tables are presented in Appendix A
with a more detailed discussion of the tabulated values.
Based on the preliminary analysis of the Kz calculated in the tables above implies
the following:
1. Openings of 164 or 50 meters located adjacent to the building site have a
significant impact on Kz and wind velocity.
2. Wind roughness up to 6 miles from a site has a significant effect on wind velocity.
An Exposure B classification may not adequately account for the surrounding
Exposure C roughness within 6 miles.
3. Exposure C values are conservative for areas with Exposure B type rough terrain
as far away as 6 miles.
5.2 Multiple Roughness Changes
ASCE7-10 offers one example of multiple roughness changes for a building 50
feet in height that is located inland and the wind travels over both suburban and sea
surroundings before it reaches the site. Refer to Figure 5.4 below that describes the sites
terrain. The distances are defined as:
di= 1 mile, d.2 = 2 miles, 0.1 miles (528 feet)
The example uses a z0 = 1 feet for the suburban terrain defined as Exposure B and
a z0 = 0.01 feet for the sea terrain defined as Exposure D.
33


wind

Roughness
b
l dt 4 J
i T T*-^
-rLTU-LTUIn
Roughness Roughness Roughnes
B D B
Building
Site
ij%^JtJTruTinnurLri
Figure 5.4 ASCE7-10 Figure C27.3-1 Multiple Roughness Changes Due to Coastal
Waterway (ASCE 2010 with permission from ASCE).
At the site the Kz factor is found to be 1.067 which is similar to that for Exposure
C but well below the value of 1.27, ASCE7-10 Kz factor for Exposure D.
Table 5.1: ASCE7-10 Table C27.3-1 Tabulated Exposure Coefficients for Example
on Multiple Roughness Changes (ASCE 2010 with permission from ASCE).
CHAPTER C27 WIND LOADS ON BUILDINGSMWFRS DIRECTIONAL PROCEDURE
Table (. 27.3-1 Tabulated Exposure Coefficients
Transition from sea to station 1 J Ksqj Fsm 8!
1.215 0.667 0.758 0.220 0.137 0.895
Transition from station 1 to station 2 K F.uc AKs) m
0.667 1.215 1.301 0.324 -0.190 mi
Transition from station 2 to station 3 Fm K
1.215 0.667 0.758 0,498 0.310 1.067
Note: The equilibrium values of the exposure coefficients, XJV, Knz and (downwind value of K, at 50 ft), were calculated from Kq. C27-1
using cc and zg values obtained from Eqs, C27-3 and C27-4 with the roughness values given. Then is calculated using Lqs. C27-7 and C27-8,
and then the value of AK at 50 ft height, M, is calculated from Eq. 27-6. Finally, the exposure coefficient at 50 ft at station i, K$, is obtained
front Eq. C27-5.
5.3 Small Scale Roughness Changes
Small scale roughness changes, such as openings for parks and roadways are
often present adjacent to buildings. In the commentary of ASCE7-10, ASCE7-10
recommends that effects of open patches or openings of 50 meters (164 feet) in size be
considered when using Exposure B. ASCE7-10 offer Figures C26.7-3 and C26.7-4,
shown in Figures 5.5 and 5.6 respectively below, to aid the designer in addressing open
patch equal to or larger than 164 feet (50 meters).
34


-OHHMTCte* W0WQ5 £ tHmiUff |ittn 1r a,,-,*, 5 IWFItfqpQ
d( d4 _. A ( < HIFT^BtoiJ
TOHL LENGTH OF SURFACE RGUttfESBS £3KKFTpOnf
IWTtM BH FT ftdHDaiJ OF UPMD FETCH DISTANCE.
FKiURK CJfrJ-3 l Figure 5.5 ASCE7-10 Figure C26.7-3 Exposure B with Upwind Open Patches
(ASCE 2010 with permission from ASCE).
35


uu*Qiw<7iHaiirmuCTUK
Figure 5.6 ASCE7-10 Figure C26.7-4 Exposure B with Upwind Open Patches
(ASCE 2010 with permission from ASCE).
As shown in Figure 5.6, ASCE7-10 C26.7-4, if the open patches total less than
656 feet, then Exposure B is still applicable. It should be noted that the upwind distances
defined for Exposure B for a building 30 feet or less in height is 1500 feet. If there are
36


significant openings, based on the ASCE7-10 the upwind fetch is increased to 3280 feet
(1 km) and if there are significant open patches, then a more conservative exposure
category, such as Exposure C, would be used. In Tables 5.1 through 5.13, distances or
open patches of 50 meters (164 feet) adjacent to the structure were included so the effect
of these changes in roughness on the Kz factor could be calculated.
In both these figures the fetch distance for Exposure B appears to be increased to
3280 feet (1 km), which is more consistent with studies than the 1500 feet or 2600 feet
given for the Exposure Categories in the body of ASCE7-10. This implies that using a
greater fetch distance for Exposure B is acceptable when performing a more detailed
assessment of the structures surroundings.
The 2007 study by Wang and Stathopoulos performed a wind tunnel and
numerical analysis on 61 fetch cases using different size open-patches. They stipulate
that inhomogeneous fetches can be regarded as composed ofpatches of different
roughness, where a patch is a finite piece of homogenous terrain (Wang 2007). They
developed a series of equations referred to as the Speed Model where the number of open
patches and characteristics of the open patches within 4 km of the site are taken into
account to find the wind profile. These formulas may be more easily applied to data from
a mapping software. Wind profiles, calculated using the Speed Model are more
consistent with the experimental wind tunnel data than the Harris and Deaves model
(Wang 2007).
5.4 Recap
As discussed in Chapter 4.3, the ASCE7-10 surface roughness factors for
Exposure B and C are conservative. While the surface roughness factors for Exposure D,
37


in combination with the ASCE7-10 provision that Exposure D only applies within 600
feet of Exposure D terrain, underestimate the surface roughness values.
When there is varying terrain including open spaces, the selection of one
appropriate exposure classification becomes more complex. ASCE7-10 states an
intermediate exposure category between preceding categories is permitted in a transition
zone provided that it is determined by a rational analysis method defined in the
recognized literature. ASCE7-10 also provides a series of equations for calculating the
velocity pressure coefficient for changes or transitions in terrain. However, these
equations do not take into account surface roughness values that fall between the ASCE7-
10 exposure categories.
38


6 Using Geographic Information Systems (GIS) to Determine Surface Roughness
Change in Terrain Roughness
6.1 ArcGIS 10.1
This thesis research explores methods to use Geographic Information Systems
(GIS) topographical data and building data to map and calculate the roughness surface
coefficient Kz as an alternate to selecting one of three limited ASCE exposure categories
and corresponding Kz factor.
A GIS is a computer-based system to aid in the collection, maintenance, storage,
analysis, output, and distribution of spatial data and information (Bolstad 2012). With
todays computer and mapping technology, GIS has made it possible to turn what used to
be paper maps into spatial computer models that contain sophisticated data and objects that
can be analyzed and manipulated in a myriad of different ways. With the right data, you
can see whatever you want to see land features, elevation, weather and climate zones,
forests, political boundaries, population density, per capita income, land use, energy
consumption, mineral resources, and a thousand other things in whatever part of the
world that interests you. (Law 2013)
Environmental Systems Research Institute (ESRI) ArcGIS 10.1 software (ESRI,
2012) is a geographic information system and one of the computer software programs used
to solve complex problems that involve data, maps and geographic information. In this
program, spatial topographic data obtained from a variety of sources such as surface
surveys can be merged with attribute data obtained from sources such as city and county
property databases. This program allows the processing of the data using tabulated tables,
graphs and visual representations of the data.
39


6.2 GIS Data Models
There are two commonly used types of data models used in GIS, vector data models
and raster data models. Both contain vector data that is linked to a coordinate system. A
spatial data model often consists of layers or collections of geographic objects represented
by points, lines or polygons and associated data. The layers might include states, counties,
roads, rivers and buildings. Each geographic object is called a feature. Each feature has
an associated shape and size and is represented by a polygon, line or point. Each feature
has a location that is related to a coordinate system which allows the data to be in the proper
place on the map. The GIS map features are commonly linked to information beyond the
physical shape or locations. For example a state feature might also contain the population
and could contain information about yearly rainfall, registered voters or a plethora of other
information. This information is contained in a table format referred to as an attribute table.
The files that contain this data are often referred to as shapefiles. The entities are related
to essential characteristics subjectively chosen by the developer based on the purpose of
the model. The data developed for the city of Denver might include address, property size
and property value where data developed for the census might include population and not
property value. Many city municipalities have land use data that includes property size,
land use and some include building footprint size.
Raster data models contain their spatial data and associated information about the
data itself organized in a regular set of cells in a grid pattern. Raster data models are utilized
in continuous spatial features, such as land use, elevation or slope that can have significant
changes over broad areas. The United States Geological Survey Land Cover Institute
(USLCI2013) has developed land use data files for the United States. This data is available
to the public at no cost (LCI 2014). As part of this study, the use of this data was
40


investigated. However, due to the size of the files and difficulties in manipulating the data,
raster data was not utilized in the final models analyzed as part of this thesis project.
6.3 GIS Data Sources
There is an abundant amount of topographical data for the United States. This data
includes maps by Google Earth that show buildings, trees and streets and state and
government geographic mapping data including roads, land use, topography and buildings.
My research indicates that bigger and more sophisticated municipalities, such as Denver,
Dallas, Chicago and Boston, have more geographic data.
The available GIS data contains a variety of information ranging from land use to
building footprints. The data varies greatly. For example the City of Loveland has data
on building footprint but not building height. The City of Denver has extensive building
data, including year built, property value, and type of structure; however, the files do not
include polygons for the buildings, so data on the width and length of the structures is not
available.
Two primary types of GIS shapefile data were reviewed for their suitability for use
with determining the site's terrain surface roughness. The first is the GIS land use
shapefiles where lots are assigned a land use such as vacant lot, commercial, single family,
high density residential or low density residential. The second type of GIS shapefile data
is data that contains information about the buildings on the site including the building
footprint area size and the footprint width, length and height. Investigation was made into
correlating land use to a z surface roughness factor. However, the building shapefile data
provided the more detail about the surface roughness and was used in each model.
41


6.4 Methodology
Three sites with varying terrain were selected. The term terrain refers to the
both landscaping and the built environment including buildings. The three sites will be
referred to as Site 1 Denver, Site 2 Loveland, and Site 3 Utah. Each of these three sites
will be discussed in detail in the following chapter. Each of the sites was chosen based
on the following criteria:
1. GIS data containing building footprints was readily available for the site. The
GIS data was free. The available data sizes were not so large as to require a large
or sophisticated computer system to analyze the data.
2. The site was not located within one mile of a large city center and therefore
falling into ASCE7-10 Exposure A classification.
3. The site was not located near an ocean coastal area or hurricane region.
4. The first two sites were chosen based on my first hand familiarity with these
areas.
5. Each of the locations contained a combination of surface roughness including
open terrain and urban and suburban areas consisting primarily of residential
neighborhood buildings/houses and small commercial buildings.
GIS spatial data models were built in ArcMap 10.1 for each of the three sites using
the available GIS data including geographic data for addresses, buildings, lakes and roads.
The GIS data was obtained from the following sites:
For Site 1 Denver: http://data.denvergov.org/dataset/citv-and-countv-of-denver-
parcels (Denver 2014) and http://data.denvergov.org/dataset/citv-and-countv-of-denver-
building-outlines (Denver 2015)
42


For Site 2 Loveland: http://www.ci.loveland.co.us/index.aspx?page=434
(Loveland 2015)
For Site 3 Utah: http://gis.utah.gov/data/ (Utah 2015)
When developing the GIS map model to determine the surface roughness, two
questions were tackled: what is the best way to use these GIS data and maps to quantify
the surface roughness surrounding a site" and what is the best way to capture, quantify
and analyze surface roughness variations surrounding a site? To address these questions
the follow method was used.
In ArcMap 10.1, the terrain surrounding one kilometer of each of the three sites
was divided into eight sections; Outer North, Inner North, Outer South, Inner South,
Outer West, Inner West, Outer East and Inner East. The terrain was divided in ArcMap
by creating eight new polygon shapes for each section and using the ArcGIS interest tool,
the terrain was divided into these sections. The 1 km circle was divided into both inner
and outer so that the surface roughness closest to the site could be divided from the
terrain one half a kilometer from the site. Then the surface roughness for each section
could be calculated and the surface roughness directly adjacent the site could be
considered separately. See Figure 6.3 below for each of the eight sections.
43


E
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Figure 6.1 ArcGIS Screenshot Showing Eight Sections.
After the terrain surrounding the site was divided into eight sections, the
geographic data for the building structures was then extracted from the model. Two
components of the surface roughness were calculated for a low-rise fictional structure
located at the center of the site; the surface roughness factor, z0, and the Kz factor
including consideration of a single roughness change for each of the four directions.
Critical to determining the z0 surface roughness factor was determining the
average vertical frontal area, Sob. Because the data for Denver did not contain the width
or length of the buildings, investigation into the relationship between the footprint and
area using the Site 2 Loveland model was performed to determine an appropriate method
of calculating the Sob for all the sites. The following method was used to determine the
vertical frontal area. An average building height of 20 feet was assumed for all buildings.
44


The average building size was used to calculate an average length and width, both equal
and determined based on the average footprint. Then Nicholass equation was used to
determine Sob by multiplying the number of buildings by an average Sob (Nicholas 1980).
A discussion of the Nicholas method and calculations can be found in Appendix B.
Average L = Average W = Average footprint (6.1)
where:
L = average building length in feet.
W= average building width in feet.
Average footprint = in square feet extracted from GIS spatial data model.
Average Sob = 2 x (0.7 x L) x H (6.2)
where:
H = average building height in feet.
To determine the surface roughness factor z0 for each of the eight sections, the
average Sob for each section was multiplied by the number of buildings in each section
using equation 4.5.
Average z0 = 0.5Hoh(Ave S0b/A0b) (6.3)
Where:
Hob = 20 ft average height.
Ave Njfc=the total of the average vertical frontal area, see equation 6.2 above.
A0b=the total area of the section in ft2.
The z0 factor was then used to determine velocity pressure coefficient, Kz for each
section using equation 4.2. These calculations are summarized in Chapter 7 for each site.
45


To complete the calculations, one velocity pressure coefficient was calculated for
each of the four directions; North, South, East and West using equation 5.1, ASCE7-10
equation C27.3-5 (ASCE 2010). The Kz for the inner and outer sections in each direction
were used in these equations to take into consideration one terrain change per direction
occurring at 1/2 km where the sections have been divided in the GIS data models. .
46


7 GIS Spatial Models
7.1 Site 1 Denver
Site 1 Denver is located at 898 South Vine Street in Denver Colorado. The first
site was primarily selected based on my familiarity of this area, the abundance of free GIS
data available for the City of Denver (City and County of Denver, 2014) and the terrain
surrounding the specific property, which contains terrain consistent with both Exposure
Category B and Exposure Category C topography. This site can be seen in Figure 7.1.
Figure 7.1 Google Map Showing Site 1 Denver (Google 2014).
This residential site is located approximately one-half kilometer from Washington
Park in Denver Colorado. The surrounding terrain consists of primarily residential
neighborhoods. In traditional design, this site might conservatively be classified as
Exposure Category C based on the large open space located on the west side of the site.
47


The Denver building data shapefile contains an abundance of data including the
buildings footprint sizes, building types, and number of stories of each building.
The available Denver data, used in this model, does not contain the footprint
dimensions or heights of the buildings. The shapefile contains points to represent each
building. These points can be seen in Figure 7.2, a screenshot of the Site 1 Denver
building model. This building data does contain the number of stories and the use of the
structure, i.e. residential, commercial. This data was used to determine an average
building height of 20 feet.
^ Drawing- OB' A- ^ia,
j Customize Windows Help Editor- = --li I j
Figure 7.2 ArcGIS Screenshot Showing Eight New Shapefiles Merged with Building
Shapefile.
48


Of interest is the density of the typical neighborhoods in the middle section of the
1 km area. The neighborhood in the northwest section contains houses that are much less
densely spaced.
The data for each of the eight sections are extracted from the model. Refer to
Appendix D for this data. The sum of the buildings footprints is used with the number
of buildings to determine an average Sob and average z for each section. While the
terrain does consist of large mature landscaping with large shrubs and trees, these were
not included in the calculation of z0. The calculation of z does include an additional
0.066 to be added to the value calculated for the buildings to account for low vegetation
such as grazing land.
Table 7.1: Site 1 Denver Building Data Summary.
Section Total area of section (ft2) Bldg ftprint sum (ft2) Ave bldg ftprint (ft2) Total bdgs Sob total Zo Ave
Outer North 6334010 1072675 1898 565 689215 1.15
Inner North 2111335 503158 1778 283 334126 1.65
Outer South 6334010 1198148 2017 594 746960 1.25
Inner South 2111335 553415 2065 268 340999 1.68
Outer West 6334010 295857 2618 113 161890 0.32
Inner West 2111335 498505 1940 257 316951 1.57
Outer East 6334010 1052053 1996 527 659248 1.11
Inner East 2111335 389072 1826.7 213 254901 Ml
From this data, as represented by the Google Map and GIS building map the
Outer West Section, with the large open space, has a significantly lower surface
roughness factor, z0, in comparison to the other sections, which have larger surface
roughness factors. Table 7.2 below shows the Kz coefficient calculated for each section
and compares both the Kz and z values calculated using the GIS data model with the
values used in ASCE7-10 for Exposure Category B and Exposure Category C. ASCE7-
49


10 Exposure B values were used for comparison for all sections except the West Outer
Section, where ASCE7-10 Exposure Category C values were used. The last column has
the reduction in design wind load based on the GIS model calculated surface roughness
values.
Table 7.2: Site 1 Denver Comparison between GIS Calculated Data and ASCE7-10
Design Values.
Section GIS calc Zo ASCE Exp ASCE Zo GIS calc Kz at 30 ht ASCE Kz % reduction in Wind Loading
Outer North 1.15 B 0.66 0.63 0.70 10
Inner North 1.65 B 0.66 0.59 0.70 16
Outer South 1.25 B 0.66 0.62 0.70 11
Inner South 1.68 B 0.66 0.58 0.70 16
Outer West 0.32 C 0.07 0.79 0.98 20
Inner West 1.57 B 0.66 0.59 0.70 15
Outer East 1.11 B 0.66 0.64 0.70 9
Inner East Ml B 0.66 0.62 0.70 12
The GIS calculated values are lower than the values in the ASCE7-10. This
percentage reduction is shown in the last column.
Finally, one singe velocity pressure coefficient is calculated for each of the four
directions; North, South, East and West using equation 5.1. This equation accounts for a
single roughness change between the two sections in each direction. These calculations
are summarized in Table 7.3. The spreadsheets of the data can be found in Appendix C.
This table also compares both the calculated Kz value for each direction with the values
used in ASCE7-10 for Exposure Category B and Exposure Category C.
50


Table 7.3: Site 1 Denver Comparison between GIS Calculated Data and ASCE7-10
Design Values.
Section ASCE Exp ASCE Kz GIS calc Kz % reduction
North B 0.7 0.63 11
South B 0.7 0.62 11
West C 0.98 0.70 28
East B 0.7 0.63 10
There is a significant decrease in the Kz and z0 values between ASCE7-10 values
and the GIS calculated values which would result in a corresponding lower design wind
load.
7.2 Site 2 Loveland
Site 2 Loveland is located at 2860 Mountain Lion Drive in Loveland Colorado. The
site was selected because the terrain was similar to the terrain shown in ASCE7-10 photo
representing Exposure Category C terrain, referred to in Figure 4.5. The City of Loveland
has an abundance of free GIS data available including building data that includes building
footprint. The specific site terrain is shown in Figure 7.3.
51


This commercial site is located on the south side of Loveland Colorado. The
surrounding terrain consists of a combination of open spaces, residential neighborhoods
and commercial buildings. Based on ASCE7-10 representative photo, this site would be
classified as Exposure Category C based on the large open spaces surrounding the site.
Below in Figure 7.4 a screenshot of the GIS data model is shown.
P Slitifi& ~ Drawing-1 ft 3 AAriai
1_;Editor-| ' £J- : ^ IS0B|
Selection Geoprocessing Customize Windows Help
Figure 7.4 Screenshot from ArcGIS Building Model for Site 2 Loveland.
The Loveland GIS shapefile data for the buildings consists of polygon shapes
with the building outline for each structure. Figure 7.5 shows a screenshot of the GIS
data with a closer view of the site. In this figure, the building polygon shapes can be
seen. This data was especially useful for determining an appropriate method to finding
Sob, because the length and width of the building can be measured in the model.
52


lovelandsitel ArcMap
Drawing-O'1 D-A-' 4Arial v r v_ b i si.*.-*-
l^|B5IEiian3 Editor -A- ! Ulc-h v ? >! E:
action Geoprocessing Customize Windows Help
Figure 7.5 Close up Screenshot from ArcGIS Building Model adjacent Site 2
Loveland.
The data for each of the eight sections was extracted from the model. This data
can be found in Appendix D. The sum of the buildings footprints is used with the
number of buildings to determine an average Sob and average z0 for each section. Shrubs
and trees were not included in the calculation of za. The calculation of z does include an
additional 0.066 to be added to the value calculated for the buildings to account for low
vegetation. This data is summarized in Table 7.4 below.
53


Table 7.4: Site 2 Loveland Building Data Summary.
Section Total area of section (ft2) Bldg ftprint sum (ft2) Ave bldg ftprint (ft2) Total bdgs Sob total Zototal
Outer North 640455 14265 47 565 157178 0.31
Inner North 18760 4042 10 283 17801 0.15
Outer South 410422 2072 198 594 252359 0.46
Inner South 218949 1972 111 268 138018 0.72
Outer West 866700 3494 248 113 410460 0.71
Inner West 234174 1984 18 257 22449 0.17
Outer East 117359 6903 17 527 39548 0.13
Inner East 3395 1698 2 213 2308 0.08
As represented by the Google Map and GIS building model, there are large
sections of open space and the surface roughness factor, z0, factors are correspondingly
lower than the values in the Site 1 Denver model. Table 7.5 below shows the Kz
coefficients calculated for each section and compares both the Kz and z values calculated
using the GIS data model with the values used in ASCE7-10 for Exposure Category C.
The last column has the reduction in design wind load based on the GIS model calculated
surface roughness values.
Table 7.5: Site 1 Loveland Building Comparison between GIS Calculated Data and
ASCE7-10 Design Values.
Section GIS calc Zo ASCE Exp ASCE Zo GIS calc Kz at 30' ht ASCE Kz % reduction in Wind Loading
Outer North 0.31 C 0.07 0.79 0.98 19
Inner North 0.15 C 0.07 0.88 0.98 10
Outer South 0.46 c 0.07 0.74 0.98 24
Inner South 0.72 c 0.07 0.69 0.98 30
Outer West 0.71 c 0.07 0.69 0.98 30
Inner West 0.17 c 0.07 0.86 0.98 12
Outer East 0.13 c 0.07 0.90 0.98 8
Inner East 0.08 c 0.07 0.96 0.98 2
54


Finally, one single velocity pressure coefficient is calculated for each of the four
directions; North, South, East and West using equation 5.1. This equation accounts for a
single roughness change between the two sections in each direction. These calculations
are summarized in Table 7.6. The spreadsheets of the data can be found in Appendix C.
This table also compares both the calculated Kz value for each direction with the values
used in ASCE7-10 for Exposure Category C values.
Table 7.6: Site 1 Loveland Comparison between GIS Calculated Data and ASCE7-
10 Design Values.
Section ASCE Exp ASCE Kz GIS calc Kz % reduction
North C 0.98 0.79 19
South C 0.98 0.70 29
West C 0.98 0.69 30
East C 0.98 0.90 8
As seen in the summary tables for Site 2 Loveland there is a significant decrease
in the Kz and z0 values between ASCE7-10 values and the GIS calculated values which
would result in a corresponding lower design wind load.
7.3 Site 3 Utah Building Model
Site 3 Utah is located at 593 Lakeview Drive in Lehi, Utah. The site was selected
because of its proximity to a relatively large body of water, Utah Lake, and because the
Utah State government has an abundance of free GIS data available including building
data that includes building footprints. The specific site terrain is shown in Figure 7.6.
55


Figure 7.6 Google Map of Site 3 Utah (Google 2015).
This residential site is located 1000 feet north of Utah Lake in Lehi, Utah. The
surrounding terrain consists of a combination of residential neighborhoods on the north
side of the site and Utah Lake on the south side of the site. Utah Lake extends
approximately 20 miles south of the site and is approximately 8 miles wide. Based on
ASCE7-10 exposure category definitions, this site would be classified as Exposure C
because it is located more than 600 feet from the lake or body of water. Below in Figure
7.7, a screenshot of the GIS data model is shown.
56


Figure 7.7 Screenshot from ArcGIS Building Model adjacent Site 3 Utah.
The Utah GIS shapefile data includes polygon shapes for the outlines of the
buildings and polygons representing the bodies of water. Figure 7.8 shows a screenshot
of the GIS Data with a closer view of the site. In this figure, the building polygon shapes
can be seen as well as the lake body of water shown in blue.
57


Figure 7.8 Screenshot from ArcGIS Building Model adjacent Site 3 Utah.
The data for each of the eight sections was extracted from the model. This data
can be found in Appendix D. The sum of the buildings footprints is used with the
number of buildings to determine an average Sob and average z0 for each section. Shrubs
and trees were not included in the calculation of z0. The lake was assigned a z0 value of
0.016 based on ASCE7-10 recommended value for Exposure Category D. The land areas
include an additional 0.066 to be added to the z0 value calculated for the buildings to
account for low vegetation. This data is summarized in Table 7.7 below.
58


Table 7.7: Site 3 Utah Building Data Summary.
Section Total area of section Outer North 6334010 220201 1643 134 152083 0.306
Inner North 2111335 301277 1594 189 211283 1.067
Outer South 6334010 0 0 0 0 0.016
Inner South 2111335 0 0 0 0 0.040
Outer West 6334010 129368 1470 88 94471 0.199
Inner West 2111335 265434 1324 202 205804 1.039
Outer East 6334010 42494 2023.5 23 28969 0.105
Inner East 2111335 107534 1558.5 69 76271 0.427
As represented by the Google Map and GIS building model, there is a large
variation in terrain surrounding the site and the surface roughness factors. The z factors
correspondingly have a large variation between the sections. Table 7.8 below shows the
Kz coefficient calculated for each section and compares both the Kz and z0 values
calculated using the GIS data model with the values used in ASCE7-10 for Exposure
Category C.
Table 7.8: Utah Comparison between GIS Calculated Data and ASCE7-10 Design
Values.
Section GIS calc Zo ASCE Exp ASCE Zo GIS calc Kz at 30' ht ASCE Kz % reduction in Wind Loading
Outer North 0.31 C 0.07 0.79 0.98 19
Inner North 1.07 C 0.07 0.64 0.98 35
Outer South 0.02 c 0.07 1.14 0.98 -17
Inner South 0.04 c 0.07 1.04 0.98 -6
Outer West 0.20 c 0.07 0.85 0.98 14
Inner West 1.04 c 0.07 0.64 0.98 34
Outer East 0.10 c 0.07 0.93 0.98 6
Inner East 0.43 c 0.07 0.75 0.98 23
59


Finally, one single velocity pressure coefficient is calculated for each of the four
directions; North, South, East and West using equation 5.1. This equation accounts for a
single roughness change between the two sections in each direction. These calculations
are summarized in Table 7.9. The spreadsheets of the data can be found in Appendix C.
This table also compares both the calculated Kz value for each direction with the values
used in ASCE7-10 for Exposure Category C values.
Table 7.9: Site 3 Utah Comparison between GIS Calculated Data and ASCE7-10
Design Values.
Section ASCE Exp ASCE Kz GIS calc Kz % reduction
North C 0.98 0.73 25
South C 0.98 1.11 -13
West C 0.98 0.76 23
East C 0.98 0.85 13
While there is a significant decrease in the Kz and z0 values between ASCE7-10
values and the GIS calculated values for the North, West and East sections, there is an
increase in values for the south section, where the body of water is accounted for in the
roughness calculations. The negative numbers indicate that there is an increase in the
design wind load and not a reduction. These calculations indicate that ASCE7-10 design
loads may be unconservatively low when there is a large body of water near the site.
The ASCE7-10 does not account for surface roughness values that fall between
exposure categories. As shown above, alternate methodology utilizing GIS can improve
the determination of the velocity pressure coefficient used in design.
60


8 Synopsis
8.1 Summary
ArcGIS 10.1 was used to create mapping models for three sites with varying
terrain surrounding a subject low rise structure. GIS Building shapefile data was used in
modeling each of the three sites. The building sizes and open spaces surrounding the
subject structure were used to calculate a specific surface roughness, z0, using the
equations provided in ASCE7-10. The surface roughness factor, z0 was then used to
calculate a velocity pressure coefficient, Kz specific to the site for four directions, North,
South, East and West. To account for varying terrain adjacent the site, each of these four
quadrants was divided into two sections to allow the terrain closer to the site to be
considered separately. This allowed the use of the ASCE 7-10 equations for transitions in
roughness to further refine the Rvalues ultimately used in the determination of design
wind load.
This research provides an alternate method for determining the velocity pressure
coefficient used in the determination of design wind loads. This thesis study suggests
removing the three ASCE7-10 exposure categories and associated values as a method to
determining surface roughness surrounding a site.
8.2 Conclusions
Because of the variable nature of the topography, selecting one Exposure
Category often does not represent the actual surface roughness conditions adjacent to the
design structure. By using mapping software, such as ArcGIS, the surface roughness
surrounding a site can be determined by the surrounding terrain including buildings and
open spaces. This research provides an alternate method to replace the exposure
classification method provided in the ASCE7-10 typically used today. This will provide
61


designers the opportunity to refine the design wind pressures on a structure. This method
allows for the review of the roughness in multiple directions, similar to the techniques
used by wind tunnel studies. By using GIS to map the terrain, a more precise surface
roughness can be calculated, eliminating uncertainty and ambiguity from selecting one
exposure category.
The typical design practice today includes detailed 3D modeling of structures. As
technology has become more sophisticated, modeling the surface terrain around a structure
using GIS could represent the future for wind exposure determination.
8.3 Possible Sources of Error
The surface roughness calculations are based primarily on the surface roughness
of buildings. While a surface roughness of z0=.066 was included to account for low
vegetation, no attempt was made to account for landscaping such as grasses and trees.
On the opposite end, no attempt was made to account for terrain that is fully covered in
snow, i.e. a snow-covered flat plain with a roughness value of z,,= 0.007 (Wieringa
2001). In addition no consideration was given for variability in the size of the buildings
and variability of open patches sizes and varying locations and their effect on the surface
roughness.
This study did not take into account the topographic effects of the terrain such as
changes in elevation surrounding a site and mountainous terrain that is subject to
meteorological conditions such as downslope or Chinook winds. In current design
practice the effects of these are addressed by using a higher or increased wind speed
(Peterka 2005).
62


8.4 Recommendations for Further Research
There are a number of areas that this research could be further investigated and
tested.
To review the validity of the calculations of surface roughness determined from
the GIS models, testing could be performed in a boundary layer wind tunnel.
The models utilized a fetch distance of 3280 feet (1 km) to capture the terrain
surrounding the site. This is consistent with ASCE7-10 for Exposure Category C terrain.
ASCE7-10 specifies 5000 feet (1.5 km) fetch for Exposure D terrain. Generally
researchers consider 1 km to be appropriate (Wang 2007), but it could be useful to begin
increasing the fetch and study the results both in a computer model and in a boundary
layer wind tunnel.
Currently large hills and escarpments are addressed in the ASCE7-10 standards,
however ASCE7-10 does not address changes in elevation over larger distances. It could
be useful to use wind tunnel testing to understand the effects of these longer range
elevation changes. GIS modeling could be advanced to include a study of elevation
changes and hills and escarpments.
This study was isolated to three sites. Additional studies could include more sites.
Housing density and low rise commercial areas in different parts of the country could be
studied and correlated to surface roughness factors to building density.
With corresponding GIS topographic data, a program could be developed to run
the analysis and provide specific data that could include wind loading for a structure of
varying height for different directions and could be formatted so the output is consistent
with the design load requirements.
63


REFERENCES
1. American Society of Civil Engineers (2010), Minimum Design Loads for
Buildings and Other Structures ASCE7-10.
2. American Society of Civil Engineers (2002), Minimum Design Loads for
Buildings and Other Structures ASCE7-02.
3. American Concrete Institute (2011), Building Code Reqirirements for Structural
Concrete. (ACI 318-11) and Commentary (ACI 318R-11).
4. American Institute of Steel Construction (2011), Steel Construction Manual 14th
Edition, AITC 2011.
5. ArcGIS 10.1 for Desktop Advanced Student Edition Software (2012),
Environmental Systems Research Institute.
6. Bolstad, Paul, GIS Fundamentals, A First Test on Geographic Information
Systems, Fourth Edition, Eider Press, White Bear Lake Minnesota, 2012.
7. Douglas County. Building Department Website
http://www.douglas.co.us/land/building/design-informationA (downloaded March
2013).
8. City and County of Denver. Open Data Catalog, Parcels within the City and
County of Denver, http://data.denvergov.org/dataset/citv-and-countv-of-denver-
parcels (downloaded September 2014), Denver.
9. City and County of Denver. Open Data Catalog, Buildings data within the City
and County of Denver http://data.denvergov.org/dataset/citv-and-countv-of-
denver-building-outlines (downloaded March 2015) Denver.
10. City and County of Loveland, Map and Data Downloads,
http://www.ci.loveland.co.us/index,aspx?page=434. (downloaded January 2015)
Loveland.
11. Florida Government. Building Department,
http://www.floridabuilding.org/fbc/Wind 2010/Flyer Wind Januarv2012.pdf
(downloaded February 2015).
12. Google Maps for Denver,CO, https://www.google.com/maps (downloaded
September 2014).
13. Google Maps for Loveland, CO, https://www.google.com/maps (downloaded
January 2015).
14. Google Maps for Utah, CO, https://www.google.com/maps (downloaded January
2015).
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15. Harris, R. I. and Deaves, D.M. (1981). The Structure of Strong Winds,
Proceedings of he CIRIA Conference on Wind Engineering in the Eighties,
CIRCIA, London, Paper 4.
16. Ho, E., (1991), Variability of Low Building Wind Loads., Doctoral
Dissertation, University of Western Ontario, Canada.
17. International Code Council (2012). International Building Code, IBC 2012
18. Irwin, Peter A.(2006), Exposure Categories and Transitions for Design Wind
Loads, Journal of Structural Engineering ASCE.
19. Jefferson County. Building Department, http://ieffco.us/building-
safetv/documentsA (downloaded September 2013).
20. Kutzbach, J. (1961), Investigations of the Modifications ofWindProfdes by
Artifically Controlled Surface RoughnessAnnual Report, 1961, Deptarment of
Meteorology, University of Wisconsin, Madison.
21. Larimer County. The official website of Larimer County
http://www.larimer.org/building/wind speed.pdf
22. Law, M. and Collins, Getting to Know ArcGIS for Desktop Third Edition, Esri
Press Redlands, California 2013.
23. Lettau, H. (1969). Note on aerodynamic roughness element description.Journal
of Applied Meteorology, 8, 828-832.
24. Nicholas, F, et al, (1980) Relationship between Aerodynamic Roughness on
Land Use and Land Cover in Baltimore, Maryland, Geological Professional
Paper1099-C.
25. Peterka, Jon (2005) Colorado Front Range Gust Map http://seacolorado.org/wp-
content/uploads/2010/01/FINAL-C OLORADO-FRONT-RANGE-GUST-MAP-
2013.pdf (downloaded January 2013).
26. Simiu E. and Scanlan, R. H. (1986). Wind Effects on Structures:An Introduction
to Wind Engineering 2nd Edition, Wiley, New York.
27. Truilia. Denver Colorado Market Report,
http://activerain.com/blogsview/3426502/denver-colorado-market-report-as-of-
august-29-2012. (downloaded January 2013).
28. United States Census Bureau (2012),
http://www.census.gov/construction/chars/highlights.html (downloaded January
2013), US Census.
65


29. United States Geological Survey Land Cover Institute. Land Cover Data,
http://landcover.usgs.gov/ (downloaded September 2014), USLCI.
30. Utah Automated Geographic Reference Center (AGRC) http://gis.utah.gov/data/
(downloaded January 2015).
31. Wang, K. and Stathopoulos, (2007), Exposure Model for Wind Loading of
Buildings, Journal of Wind Engineering and Industrial Aerodynamics 95.
32. Wieringa, et. A1 (2001) New Revision of Davenport Roughness Classification, 3rd
European &African Conference on Wind Engineering, Eindhoven, Netherlands,
July 2001.
66


Appendix
Introduction
The following Appendix includes calculations and data that provides a pathway to my
methods, assumptions and conclusions. This information can be used by future
researchers to independently verify my conclusions.
A. Appendix A: Single Roughness Changes in Terrains
As part of this study, a single roughness change adjacent a fictional building with
roof height of 33 feet is tabulated for varying roughness lengths beginning with 164 feet,
up to a distance of six miles. The value of 164 feet was borrowed from the ASCE7-10 as
a starting point as this is identified as an opening in the surface roughness B large
enough to have a significant impact on the exposure category determination and is
defined as an open patch (ASCE7 2010) and shall be considered in the determination
of exposure category. The distance of six miles was selected because this is consistent
with the constant xi used in Equation 5.4, ASCE7-10 Equation C27.3-8.
ASCE7-10 identifies the terrain adjacent the site as the downwind terrain and
the wind further from the site as the upwind terrain. This is depicted in Figure A. 1 with
the wind hitting the upwind terrain before it reaches the downwind terrain that is located
closest to the site. This terminology will be used throughout the Appendix.
The first single roughness change calculated is for a site that has Exposure
Category B terrain downwind, or directly adjacent to the site. The terrain experiences a
single roughness change to Exposure Category C. Refer to Figure A. 1 for graphical
representation.
67


Table A. 1 has columns for the distance D1 adjacent, the upwind and downwind Kz
values prescribed by ASCE7-10, the calculated Kz for a single roughness change per the
equation 5.4, the traditional ASCE7-10 exposure category classification and associated Kz
and the percentage difference between the traditional ASCE7-10 value of Kz and the
calculated single roughness change Kz.
As shown in Table A.l, when the Exposure Category B terrain adjacent the site is
less than 2600 feet in length, the site is classified as Exposure C. When the Exposure
Category B terrain adjacent the sites exceeds 2600 feet, it is then defined by ASCE7-10
as Exposure B terrain.
Based on this table, small distances of Exposure Category B terrain will lower the
Kz value and therefore lower the design wind loading, represented in the table by positive
differences in percentages. However, if large distances of Exposure Category C terrain
are downwind of Exposure Category B terrain, the Kz values are increased indicating that
there are higher design wind loadings, represented in the table by positive differences in
percentages.
68


WIND---->
BUILDING
SITE
jiJ¥Liiririi¥iJ¥¥¥mivmjTim
D2
ROUGHNESS C UPWIND ROUGNESS B DOWNWIND
InnnnrL
Figure A.l Single Roughness Change 1 with Exposure B Terrain adjacent the
Building Site.
Table A.l: Comparison of Tabulated Values for Kz with Single Roughness Change
to ASCE7-10 Kz Values Related to Exposure Category with Exposure B Terrain
adjacent the Building Site.
D2 feet D2 miles downwind Kzd upwind Kzu Calc Kz ASCE Exp Cat ASCE Kz % diff
164 0.03 0.62 1.00 0.87 C 1.00 13
528 0.10 0.62 1.00 0.82 C 1.00 18
655 0.12 0.62 1.00 0.81 c 1.00 19
1056 0.20 0.62 1.00 0.78 c 1.00 22
1320 0.25 0.62 1.00 0.77 c 1.00 23
1584 0.30 0.62 1.00 0.76 c 1.00 24
2112 0.40 0.62 1.00 0.75 c 1.00 25
2640 0.50 0.62 1.00 0.74 B 0.70 -6
3168 0.60 0.62 1.00 0.73 B 0.70 -4
3696 0.70 0.62 1.00 0.72 B 0.70 -3
5280 1.00 0.62 1.00 0.71 B 0.70 -1
10560 2.00 0.62 1.00 0.67 B 0.70 4
15840 3.00 0.62 1.00 0.65 B 0.70 7
21120 4.00 0.62 1.00 0.64 B 0.70 9
26400 5.00 0.62 1.00 0.63 B 0.70 10
69


31680 6.00 0.62 1.00 0.62 B 0.70 12
The second single roughness change calculated is for a site that has Exposure
Category C terrain downwind, or directly adjacent to the site. The terrain experiences a
single roughness change to Exposure Category B. Refer to Figure A.2 for graphical
representation. The columns in the tables correspond to the columns used in Table A. 1.
Based on this table, there is a significant decrease in the design wind loading
when the Exposure B terrain is incorporated into the wind calculations. The ASCE
values can be reduced significantly. However in both tables, as discussed above, for a
low- rise building the terrain affecting the wind loading is one to four km and not
upwards of four to six miles.
70


WIND---->
BUILDING
SITE
mnnart
Figure A.2 Single Roughness Change 1 with Exposure C Terrain adjacent the
Building Site.
Table A.2: Comparison of Tabulated Values for Kz with Single Roughness Change
to ASCE7-10 Kz Values Related to Exposure Category with Exposure C Terrain
adjacent the Building Site.
D2 feet D2 miles downwind Kzd upwind Kzu Calc Kz ASCE Exp Cat ASCE Kz % diff
164 0.03 1.00 0.62 0.618 B 0.70 12
528 0.10 1.00 0.62 0.707 B 0.70 -1
655 0.12 1.00 0.62 0.752 B 0.70 -7
1056 0.20 1.00 0.62 0.760 C 1.00 24
1320 0.25 1.00 0.62 0.779 C 1.00 22
1584 0.30 1.00 0.62 0.787 C 1.00 21
2112 0.40 1.00 0.62 0.794 C 1.00 21
2640 0.50 1.00 0.62 0.805 C 1.00 19
3168 0.60 1.00 0.62 0.814 C 1.00 19
3696 0.70 1.00 0.62 0.821 C 1.00 18
5280 1.00 1.00 0.62 0.827 C 1.00 17
10560 2.00 1.00 0.62 0.841 C 1.00 16
15840 3.00 1.00 0.62 0.868 C 1.00 13
21120 4.00 1.00 0.62 0.883 C 1.00 12
26400 5.00 1.00 0.62 0.894 C 1.00 11
31680 6.00 1.00 0.62 0.903 C 1.00 10
71


B. Appendix B: Vertical Frontal Area, S0b
ASCE7-10 defines the vertical frontal area as the area of the projection of the
obstruction onto a vertical plane normal to the wind directionWhile ASCE7-10 states
that this factor can be determined by summing the vertical frontal areas of the
obstructions in the area, it does not provide a detailed example of how this can be
calculated. Studies by Nicholas of surface roughness, suggests Sob can be calculated by
summing the two adjacent elevation surface areas of a building and multiplying this by
0.707 (Nicholas 1980). This method takes into account front and side frontal areas
suggesting the wind will rarely hit one face head on, but will typically hit the building at
an angle.
Because the GIS data for Denver did not contain the width or length of the
buildings, and the GIS tabulated data tables for the Loveland and Utah sites did not
contain the width or length of the buildings, alternative methods were reviewed to
determine an appropriate Sob. Investigation into the relationship between the footprint
and area using the Site 2 Loveland model was performed using Excel. As seen in Table
B.3, the relationship between footprint and Sob cannot be used as these values do not have
a consistent relationship.
72


Table B.l: Comparison of footprint to S0b using Nicholas Method
Bldg Height(ft) width(ft) length(ft) Footprint Area (ft2) Sob
10 40 40 1600 560
20 40 40 1600 1120
30 40 40 1600 1680
40 40 40 1600 2240

10 30 60 1800 630
20 30 60 1800 1260
30 30 60 1800 1890
40 30 60 1800 2520

10 50 50 2500 700
20 50 50 2500 1400
30 50 50 2500 2100
40 50 50 2500 2800
The next method utilized the fact that the square root of the GIS footprint data
could be used to determine a width and length for a square shape. The Sob was calculated
for a set of randomly selected buildings, measured from the Loveland building model and
compared the calculated Sob for a square building with the same footprint. As seen in
Table B.4, the Sob values for a square building are within 5% of the values of a
rectangular building with the same footprint. Therefore, using the square root of the
footprint to create an equivalent square building to calculate Sob is an acceptable method.
73


Table B.2: Comparison of S0b of Rectangular Buildings vs Square Buildings of the
Same Footprint
Rectangular Bldg from model Equivlnt Square Bldg
ht width length Bldg Area Sob w/1 Sob
20 30 45 1350 1050 37 1029
20 50 80 4000 1820 63 1771
20 30 60 1800 1260 42 1188
20 34 61 2074 1330 46 1275
20 90 160 14400 3500 120 3360
20 30 65 1950 1330 44 1236
20 36 55 1980 1274 44 1246
74


C. Appendix C: Single Roughness Calculations Using GIS Data for Each Model
For each model, one velocity pressure coefficient was calculated for each of the
four directions; North, South, East and West using equation 5.1, ASCE7-10 equation
C27.3-5 (ASCE 2010). The Kz for the inner and outer sections in each direction were
used in these equations to take into consideration one terrain change per direction
occurring at 1/2 km where the sections have been divided in the GIS data models. These
calculations are shown in Table C.5 below for the Denver model, Table C.6 for the
Loveland model and Table C.7 for the Utah model.
75


Table C.l: Denver Transitions between outer and inner areas
Section terrain change (miles) a inner upwind K:u a outer dnwind K: d Xl xo Faa(x) Km- K:,l A K controll ing A K Calc Kz
North 0.31 6.19 0.61 6.49 0.65 62.1 0.003 0.54 -0.04 -0.02 -0.02 0.63
South 0.31 6.18 0.60 6.43 0.64 62.1 0.003 0.54 -0.04 -0.02 -0.02 0.62
West 0.31 6.24 0.61 7.70 0.81 62.1 0.003 0.53 -0.20 -0.10 -0.10 0.70
East 0.31 6.41 0.64 6.53 0.65 62.1 0.003 0.54 -0.02 -0.01 -0.01 0.65
Table C.l: Loveland Transitions between outer and inner areas
Section terrain change (miles) oc inner upwind K:u 0C outer dnwind K:d Xl xo Faatx) Km- K:,l A K controll ing AK Calc Kz
North 0.31 8.52 0.79 7.72 0.88 0.621 0.003 0.13 0.09 0.01 0.01 0.79
South 0.31 6.92 0.74 7.33 0.69 62.1 0.003 0.53 -0.05 -0.03 -0.05 0.70
West 0.31 8.36 0.69 6.92 0.86 0.621 0.003 0.13 0.18 0.02 0.02 0.69
East 0.31 9.31 0.90 8.70 0.96 0.621 0.003 0.13 0.06 0.01 0.01 0.90
On


Table C.3: Utah Transitions between outer and inner areas
Section terrain change (miles) a inner upwind K:u a outer dnwind K:d Xl xo Fak(x) Kzu-Kzd AK Controlli ng AK Calc Kz
North 0.31 6.56 0.66 7.75 0.81 62.1 0.003 0.53 -0.15 -0.08 -0.15 0.66
South 0.31 10.16 1.06 11.47 1.16 62.1 0.003 0.53 -0.10 -0.06 -0.10 1.06
West 0.31 6.59 0.66 8.21 0.87 62.1 0.003 0.53 -0.20 -0.11 -0.20 0.66
East 0.31 7.41 0.77 8.94 0.95 62.1 0.003 0.53 -0.17 -0.09 -0.17 0.77


D. Appendix D: GIS Data for Each Model
Provided for reference are ArcMap 10.1 reports showing the building addresses
and footprints for each of the eight sections of each model. Table D.8 contains the
Denver building data. Table D.9 contains the Loveland building data. Table D. 10
contains the Utah building data. At the bottom of each table is a summary showing the
number of buildings, the minimum footprint size, the maximum footprint size and the
average footprint size.
78


Table D.l Denver GIS Building Model Data
Denver_buildings_innerN
address footprint
890 S VINE ST 1620
884 S VINE ST 1683
878 S VINE ST 1704
872 S VINE ST 1612
867 S GAYLORD ST 1474
863 S VINE ST 1746
866 S VINE ST 1617
859 S GAYLORD ST 1247
857 S VINE ST 1525
860 S VINE ST 1658
853 S GAYLORD ST 1349
851 S VINE ST 1458
850 S VINE ST 1454
845 S GAYLORD ST 1982
845 S VINE ST 2213
844 S VINE ST 1617
840 S GAYLORD ST 2107
840 S RACE ST 1259
839 S VINE ST 1553
Page 1 of 14
Page 79


address
footprint
838 S VINE ST
837 S GAYLORD ST
834 S RACE ST
834 S GAYLORD ST
833 S VINE ST
832 S VINE ST
831 S GAYLORD ST
828 S RACE ST
828 S GAYLORD ST
821 SYORK ST
827 S VINE ST
826 S VINE ST
825 S GAYLORD ST
822 S RACE ST
821 S VINE ST
820 S VINE ST
819 S GAYLORD ST
820 S GAYLORD ST
819 SYORK ST
816 S RACE ST
817 S RACE ST
813 S VINE ST
1802
1554
1238
2523
1788
1764
1713
1588
1229
967
1812
1661
1722
1579
1709
1796
1846
1457
2047
1293
1582
1844
Page 2 of 14
Page 80


address
footprint
814 S VINE ST
815 S GAYLORD ST
812 S GAYLORD ST
809 S YORK ST
810 S RACE ST
809 S RACE ST
807 S VINE ST
808 S VINE ST
807 S GAYLORD ST
800 S GAYLORD ST
802 S RACE ST
801 S RACE ST
801 SYORK ST
802 S YORK ST
801 S VINE ST
802 S VINE ST
801 S GAYLORD ST
793 S RACE ST
792 S HIGH ST
790 S RACE ST
795 S VINE ST
1842
1795
1497
1554
1610
1546
1959
1599
1580
2036
2113
1580
1497
1536
1593
1695
1624
1401
1331
1677
1203
Page 3 of 14
Page 81


address
footprint
790 S VINE ST
789 S GAYLORD ST
790 S GAYLORD ST
791 S YORK ST
794 S YORK ST
785 S RACE ST
786 S HIGH ST
784 S RACE ST
791 S VINE ST
782 S VINE ST
785 S GAYLORD ST
780 S GAYLORD ST
783 S YORK ST
786 S YORK ST
779 S RACE ST
778 S HIGH ST
774 S RACE ST
775 S VINE ST
774 S VINE ST
777 S GAYLORD ST
776 S GAYLORD ST
775 S YORK ST
1445
1838
1784
2079
1759
1206
1114
1360
1640
2518
1795
1518
1735
1714
1633
1193
1462
1978
1814
1712
1345
1774
Page 4 of 14
Page 82


address
footprint
776 S YORK ST 1540
785 S UNIVERSITY BLVD 5629
773 S RACE ST 1815
772 S HIGH ST 2434
771 SHIGH ST 1242
766 S RACE ST 1550
765 S VINE ST 2026
764 S VINE ST 1258
767 S GAYLORD ST 1711
764 S GAYLORD ST 1379
767 S YORK ST 2130
765 S RACE ST 2630
764 S YORK ST 1389
766 S HIGH ST 2281
765 S HIGH ST 1959
759 S RACE ST 1725
758 S RACE ST 1507
757 S VINE ST 2166
758 S VINE ST 1790
759 S GAYLORD ST 1444
758 S GAYLORD ST 1850
Page 5 of 14
Page 83


address
footprint
759 S YORK ST 2888
756 S HIGH ST 2124
754 S YORK ST 1781
757 S UNIVERSITY BLVD 4089
751 S RACE ST 1564
751 S HIGH ST 2003
750 S RACE ST 1807
748 S HIGH ST 1811
749 S VINE ST 2977
750 S VINE ST 1553
751 S GAYLORD ST 1288
750 S GAYLORD ST 1434
751 S YORK ST 1757
750 S YORK ST 1413
747 S UNIVERSITY BLVD 4125
728 S UNIVERSITY BLVD 2363
728 S UNIVERSITY BLVD 3940
748 S WILLIAMS ST 3153
743 S RAGE ST 1926
743 S HIGH ST 2201
740 S HIGH ST 1600
744 S RACE ST 1326
Page 6 of 14
Page 84


address
footprint
745 S GAYLORD ST 1415
744 S GAYLORD ST 1266
745 S YORK ST 1683
744 S YORK ST 1174
741 S VINE ST 1613
742 S VINE ST 1917
741 S UNIVERSITY BLVD 3165
744 S WILLIAMS ST 2360
739 S RACE ST 1869
715 BONNIE BRAE BLVD 1455
739 S HIGH ST 2002
736 S HIGH ST 1973
734 S RACE ST 1347
735 S GAYLORD ST 1446
738 S GAYLORD ST 1549
739 S YORK ST 1620
738 S YORK ST 1117
735 S VINE ST 1606
734 S VINE ST 1755
731 S RACE ST 1583
730 S HIGH ST 1772
Page 7 of 14
Page 85


address
footprint
732 S RACE ST 1227
736 S WILLIAMS ST 1973
733 S GAYLORD ST 1362
732 S GAYLORD ST 1646
733 S YORK ST 1589
732 S YORK ST 1309
715 S UNIVERSITY BLVD 8573
725 S HIGH ST 2015
725 S VINE ST 1230
726 S HIGH ST 1681
726 S VINE ST 1862
725 S RAGE ST 1643
726 S RACE ST 1485
724 S UNIVERSITY BLVD 2947
727 S GAYLORD ST 1364
726 S GAYLORD ST 1832
727 S YORK ST 1629
726 S YORK ST 1496
724 S WILLIAMS ST 1493
720 S HIGH ST 1730
719 S RACE ST 1670
722 S RACE ST 1526
Page 8 of 14
Page 86


address
footprint
719 S WILLIAMS ST 1700
720 S VINE ST 1598
720 S GAYLORD ST 1373
715 S HIGH ST 1955
721 S YORK ST 1506
719 S VINE ST 1391
720 S YORK ST 893
720 S WILLIAMS ST 1592
723 S GAYLORD ST 1691
714 S HIGH ST 1683
713 S RACE ST 1511
716 S RACE ST 1294
709 S UNIVERSITY BLVD 2066
712 S VINE ST 1281
712 S GAYLORD ST 1657
715 S YORK ST 1544
700 BONNIE BRAE BLVD 8020
712 S YORK ST 1308
713 S WILLIAMS ST 1892
706 S WILLIAMS ST 3499
711 S HIGH ST 1869
Page 9 of 14
Page 87


address
footprint
711 S VINE ST 1668
711 S GAYLORD ST 1543
708 S HIGH ST 1650
707 S RAGE ST 1665
710 S RACE ST 1060
708 S VINE ST 1104
704 S GAYLORD ST 1422
709 S YORK ST 1456
706 S YORK ST 1106
705 S WILLIAMS ST 1864
700 S WILLIAMS ST 2811
701 S HIGH ST 2104
703 S VINE ST 1529
700 S HIGH ST 1988
701 S GAYLORD ST 1393
701 S RACE ST 1607
700 S RACE ST 1578
701 S UNIVERSITY BLVD 5089
700 S VINE ST 1527
700 S GAYLORD ST 1360
701 S YORK ST 1516
700 S YORK ST 1500
Page 10 of 14
Page 88


address
footprint
689 S HIGH ST 1506
698 S HIGH ST 1785
691 S VINE ST 1343
690 S WILLIAMS ST 2130
690 S VINE ST 1411
1937 E EXPOSITION AVE 1837
690 S RACE ST 1737
695 S GAYLORD ST 1769
690 S YORK ST 1435
694 S GAYLORD ST 1230
691 S YORK ST 1863
683 S HIGH ST 1266
692 S HIGH ST 1654
685 S VINE ST 1450
684 S VINE ST 1787
684 S WILLIAMS ST 2229
684 S RACE ST 1704
683 S RACE ST 1818
681 S GAYLORD ST 1515
683 S YORK ST 2368
682 S YORK ST 1508
Page 11 of 14
Page 89


address
footprint
680 S GAYLORD ST
679 S HIGH ST
686 S HIGH ST
679 S VINE ST
678 S VINE ST
678 S RACE ST
681 S RACE ST
673 S HIGH ST
673 S GAYLORD ST
675 S YORK ST
672 S GAYLORD ST
674 S YORK ST
673 S VINE ST
680 S HIGH ST
672 S VINE ST
670 S RACE ST
673 S RACE ST
668 S VINE ST
670 S GAYLORD ST
667 S VINE ST
670 S HIGH ST
665 S GAYLORD ST
1203
1442
1670
1573
1680
1593
976
1425
1508
2914
2506
1732
1421
1926
1596
1714
888
1709
1195
1277
2505
2425
Page 12 of 14
Page 90


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trbt tr.t tnt tnnrtt t,rf-nft tb-t tnft bb.f tnnft tnnrtt tnt t,rf-nft trbt tb-t tr.t tfntn trbt tnft tnnrtt tnt tr.t tnnft !!"#$$ %&&'(")*' +#&%

PAGE 125

tnft tb-t tnnft tnnrtt tnt tr.t trbt tnnrtt tnt tr.t trbt tb-t tnft tfntn tnft tnnft tb-t tnnft tnnrtt tnnrtt tnt !!"#$$ %&&'(")*' +#&%

PAGE 126

tnt tr.t tr.t tnft trbt trbt tb-t tfntn tnft tb-t tnnft tnnrtt tnnrtt tnt tnt trbt tr.t tr.t tnft trbt tb-t tfntn !!"#$$ %&&'(")*' +#&%

PAGE 127

tnnft tnnrtt tb-t trbt tnnrtt trbt tnt tnt tr.t tr.t tnft tnft tb-t tfntn tnnrtt tb-t trbt trbt tnft tnft tnt !!"#$$ %&&'(")*' +#&%

PAGE 128

tr.t tr.t tb-t tfntn tnt tb-t trbt trbt tnft tnft tnt tr.t tr.t tb-t tfntn tnft tb-t trbt tnt tnft trbt tnft !!"#$$ %&&'(")*' +#&%

PAGE 129

tnt tr.t tr.t tb-t tnft trbt tfntn tb-t r0#" +#%&&'(")*'1.&2*'%&&'(")*' 3%&&'(")*' )*%&&'(")*'t24%&&'(")*' !!"#$$ %&&'(")*' +#&%

PAGE 130

btntfrt bt nff bt r ft nt n nbt n nbt r nbt nft n nt f nt r bt nrf fbt f nbt nn rt nt nt n nbt ff nt ff bt r !!"#$%" &'!

PAGE 131

bt bt r t n ft nn t f t r (bt) n bt nff bt nr bt nnb*&&b ++t r t t nnn nt (bt) n r,*t nf r++t nn rbt rbt nnf nb*&&b nf r(bt) r !!"#$%" &'n!

PAGE 132

rbt n r++t nr rt f rt f t fn nrb*&&b nfb*&&b nn ,*t rn n++t n(bt) bt r bt bt nf bt rf ++t rn t f t n ft n t f,*t fr fr++t fn !!"#$%" &'!

PAGE 133

fn(bt) f f++t nr ft r f-b&+bt fbt nf fnbt n fbt n f(bt) nf fbt fn ft nn t ft f ft f r,*t ff t ,*t f ++t f (bt) -b&+bt ++t bt n bt !!"#$%" &'!

PAGE 134

bt rn (bt) nf bt n t f t n t nff ,*t f ,*t bt r r++t t rnn (bt) n r-b&+bt r ++t f(bt) rn bt fr bt rbt nr ft nn ,*t n t rn !!"#$%" &'!

PAGE 135

rt n bt f,*t f ,*t ++t f (bt) n -b&+bt n++t n (bt) nn rbt r bt nn bt t nt rr ft f t n ,*t bt n n,*t n ++t n n(bt) n++t f !!"#$%" &'!

PAGE 136

fbt n bt bt f t t r t n t n f(bt) bt f,*t nn ,*t (bt) ++t nr nt ++t rrr bt r bt n bt f t f nt t fff !!"#$%" &'f!

PAGE 137

bt nr (bt) bt rn nf++t t f n(bt) nf n,*t f n++t n nbt r nt rrf nbt nt nfn nt n nbt nn bt rn nf(bt) f n++t ,*t t n ++t f fbt nn nfbt f !!"#$%" &'!

PAGE 138

bt f ft n rt nfr bt f ++t nrf (bt) fn bt n++t f t ff bt n bt fr nbt fn t n t n t fbt f ++t nfn ++t nnf bt nr bt nrn bt !!"#$%" &'r!

PAGE 139

t n t n (bt) r t n bt r rr++t rn rrbt nn rrbt nn rrbt rrbt n rrt rrt rrft n rrt r r++t nr rbt nfr rft fn rbt fn rbt fr rbt nff rt rt !!"#$%" &'!

PAGE 140

rnt rf++t nf rt f rfbt n rbt f rfbt n rfbt nr rfft f rft f rfft rfbt rbt n rbt nf rrbt nn rrt f rt n rft rr rnbt rnn rt rrbt rf rt f !!"#$%" &'!

PAGE 141

rbt rf rrbt rf rrt n rbt n rt r rrt rnbt f rbt f rbt nf rft rn rt f rbt rft n rnbt fn rbt rnt rbt nn rrt f rt fr rbt rn rbt nfr rbt nrrn !!"#$%" &'n!

PAGE 142

rt rnrbt nf rnt f rnbt n rnbt nf rrt r rbt nf rbt r rt rf rbt rbt rn rbt rn.' !!"#$%"n/r!0%" !!"#$%"n*1 !!"#$%"ff *$% !!"#$%"n02 !!"#$%" !!"#$%" &'!

PAGE 143

btntfrb btnfr fb btnfr tf btnfr fb btnfr tf tf ftnr btnfr fb tf !! "##$%&'$ () #"

PAGE 144

btnfr tf ftnr ftnr btnfr fb tf btnfr tf ftnr ftnr *(+ btnfr fb ftnr tf tf btnfr ftnr !! "##$%&'$ () #"

PAGE 145

*(+ btnfr *(+ fb ftnr tf tf ftnr *(+ btnfr btnfr *(+ fb ftnr tf tf ftnr !! "##$%&'$ () #"

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*(+ n, btnfr btnfr *(+ fb ftnr tf tf ftnr *(+ n, btnfr btnfr *(+ fb ftnr tf !! "##$%&'$ () #"

PAGE 147

tf ftnr *(+ n, n, btnfr *(+ btnfr fb ftnr tf tf ftnr *(+ n, n, btnfr *(+ !! "##$%&'$ () #"

PAGE 148

nbbb n-b+ fb btnfr tf nbbb tf nbbb *(+ btnfr n, n, *(+ n( .nnb, .nnb, ++ ++ fb !! "##$%&'$ () #"

PAGE 149

nbbb btnfr n, n, btnfr tf nbbb n-b+ n-b+ fb ftnr *(+ *(+ n( .nnb, .nnb, ++ ++ fb !! "##$%&'$ () #"

PAGE 150

ftnr n, btnfr n, btnfr n-b+ tf tf n-b+ ftnr fb *(+ *(+ n( .nnb, nbt ++ ++ fb !! "##$%&'$ () #"

PAGE 151

ftnr btnfr n, n, btnfr tf tf n-b+ n-b+ ftnr .nnb, fb *(+ nbt .nnb, ++ ++ fb ftnr !! "##$%&'$ () #"

PAGE 152

*(+ btnfr n, btnfr n, fb n( n-b+ tf tf n-b+ ftnr *(+ .nnb, fb .nnb, nbt ftnr ++ ++ fb !! "##$%&'$ () #"

PAGE 153

btnfr *(+ n, n, btnfr tf tf n-b+ ftnr *(+ fb n( fb .nnb, ftnr ++ ++ .nnb, !! "##$%&'$ () #"

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n, btnfr *(+ btnfr tf tf n-b+ ftnr nbt nbt n, n-b+ *(+ fb fb n( .nnb, n, ++ ++ !! "##$%&'$ () #"

PAGE 155

ftnr btnfr *(+ btnfr tf tf n-b+ ftnr nbt *(+ .nnb, nbt fb fb n, n-b+ n, .nnb, ++ ++ !! "##$%&'$ () #"

PAGE 156

ftnr *(+ btnfr *(+ fb fb btnfr tf n( tf n-b+ nbt ftnr .nnb, nbt n, n-b+ n, .nnb, ++ !! "##$%&'$ () #"

PAGE 157

++ fb fb ftnr *(+ btnfr *(+ btnfr tf tf n-b+ nbt ftnr /nn,f .nnb, n, n, n( n-b+ !! "##$%&'$ () #"

PAGE 158

nbt .nnb, ++ ++ fb fb tf ftnr btnfr *(+ *(+ btnfr tf n-b+ nbt ftnr n, n, n-b+ tf !! "##$%&'$ () #"

PAGE 159

.nnb, .nnb, ++ ++ fb fb nbt ftnr btnfr *(+ *(+ btnfr tf n-b+ nbt ftnr n, n, n( !! "##$%&'$ () #"

PAGE 160

n-b+ tf .nnb, bf-bb ++ ++ fb fb ftnr *(+ btnfr *(+ btnfr tf nbt ftnr n, n, n-b+ n( !! "##$%&'$ () #"

PAGE 161

/fbn .nnb, .nnb, ++ btnfr n-b+ btnfr tf bf-bb fb n-b+ nbt bf-bb tf n-b+ .nnb, .nnb, ++ !! "##$%&'$ () #"

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btnfr btnfr bf-bb tf ftnr fb n-b+ nbt n( n-b+ *(+ *(+ /fbn ++ .nnb, .nnb, fb n-b+ tf !! "##$%&'$ () #"

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btnfr bf-bb btnfr tf ftnr n( n-b+ ++ n-b+ n( .nnb, .nnb, fb n-b+ tf btnfr btnfr tf ftnr !! "##$%&'$ () #"

PAGE 164

++ n-b+ ++ /fbn n-b+ n( fb n( fb .nnb, .nnb, tf btnfr btnfr tf ftnr ++ n, n, ++ !! "##$%&'$ () #"

PAGE 165

fb n-b+ *(+ *(+ .nnb, .nnb, tf btnfr btnfr /fbn tf n( ftnr ++ ++ fb n( n, ftnr !! "##$%&'$ () #"

PAGE 166

n-b+ *(+ *(+ n, .nnb, .nnb, tf btnfr btnfr ++ fb tf ftnr n( ++ ftnr n( n, /fbn *(+ !! "##$%&'$ () #"

PAGE 167

n-b+ n, *(+ fb .nnb, .nnb, ++ ftnr tf ++ tf ftnr *(+ n( n( n, n, /fbn *(+ ftnr ++ !! "##$%&'$ () #"

PAGE 168

.nnb, .nnb, ++ *(+ ftnr tf n, n( n, ftnr *(+ ++ n( *(+ ftnr .nnb, .nnb, n, n, /fbn n( ftnr !! "##$%&'$ () #"

PAGE 169

*(+ ++ ftnr *(+ n, n( .nnb, .nnb, ftnr n( *(+ ++ n, /fbn *(+ ftnr n( .nnb, .nnb, n( *(+ !! "##$%&'$ () #"

PAGE 170

n, ftnr *(+ n( n( *(+ *(+ .nnb, n( *(+ *(+ .nnb, n( *(+ n( n( b0 ) "##$%&'$1#2'$"##$%&'$,3"##$%&'$ ,&'"##$%&'$24"##$%&'$ !! "##$%&'$ () #"

PAGE 171

btntfrt btn ff rbtn f btn f bb btn fbb fr fbtn r bb btn btn bb fr bb f btn fr btn bb r bb f f btn ff btn r t"

PAGE 172

bb f bb f btn bb f btn bb f r fbtn fr bb r btn rbb fff f r btn f btn ff bb bb frr r f f btn fr t"f

PAGE 173

btn fr bb frr bb f r btn r #$n%bn fbb f btn bb r $&' f rbtn rrr rr frr rrbb f rf#$n%bn rbtn rr rbb r fff r$&' r btn ffr t"

PAGE 174

r r bb ff f#$n%bn r rbtn f rbb f f $&' fbtn f fbb ff#$n%bn fbtn bb f f f f f f$&' f fr$&' r fbtn fbb #$n%bn f f fbtn bb f t"r

PAGE 175

f$&' ff $&' btn bb rf #$n%bn f fbtn r f bb f $&' $&' fr btn bb #$n%bn f '%'n(&%)*' r bb ff btn f $&' r t"

PAGE 176

f$&' rf *n' btn rf btn rf #$n%bn ffr r'%'n(&%)*' rr *n' fbb f r $&' ff btn r btn f $&' f *n' r bb #$n%bn f bb r rr $&' fr btn t"

PAGE 177

btn *n' bb #$n%bn ff $&' bb r btn rr rbtn $&' f *n' r bb $&' f btn r btn r f $&' r fbb f t"

PAGE 178

*n' rf #$n%bn rr bb $&' fbtn r r $&' f bb r btn fr rbb f r#$n%bn r $&' f btn f rf $&' r bb ff btn fr rf#$n%bn f$&' fbb r t"

PAGE 179

r btn $&' r bb r r$&' rr rrbtn r#$n%bn fr rbtn r rfbb f r$&' ff rbb btn r r r frr f#$n%bn r btn fbb rr $&' t"

PAGE 180

bb fbtn f f f f$&' bb rf fr#$n%bn f fbtn fff fbb fff fbtn f f fbb f$&' f btn f f f fbtn ff fbb f #$n%bn f bb f fbtn r t"

PAGE 181

r btn fr bb ff bb r btn r r btn r'++*' f bb ff btn ff f f r'++*' r bb f fbtn bb bb ff t"

PAGE 182

btn ff fbb bb btn f fbb f bb f rbb r btn f bb frr bb fbtn bb fbb btn r bb ffr rbtn rbb btn rbb fbtn bb t"f

PAGE 183

fbtn r," !-&.! !f/ ! !.0 !r t"

PAGE 184

btntfrb bbbbttn ffr rbnb r rbtb rr bnb btb fff bnb btb ff bb f bnb btb fr bb frf bnb btb bb bnb f btb f bb bnb r fbtb r !! "##$%&'$ t( #"

PAGE 185

bb bnb fbb r fbnb rr btb rr bb bnb fr bb ff bnb f bb rbb r rbnb rr rb)nb f bb rr bnb fr b)nb f bb r bnb f b)nb r bb b)nb f rbnb f !! "##$%&'$ t( f#"

PAGE 186

bb b)nb fr bb f b)nb bb rf b)nb f bb fbb fb)nb bb f fb)nb fr bb fb)nb f bb f fb)nb bnb f bnb bnb ff bnb bnb bnb rf !! "##$%&'$ t( #"

PAGE 187

f*)+n rbb rb)nb f rrbb rf rb)nb f rbb r rb)nb r rbb rb)nb f rbb rfb)nb rrb)nb rbb f rbb rb)nb rbb rb)nb f rbb rfbb f rfb)nb f rbb rrb)nb fr !! "##$%&'$ t( #"

PAGE 188

rbb rb)nb f rbb rbnb f rb)nb rbb bb f rbb ff bb ff bb bb bb ff bb bnb f bb fr bb r bb r bb r fbb fbtb f btb ffr !! "##$%&'$ t( #"

PAGE 189

btb f bnb rbtb rfbnb fff bnb bnb r rnn rnn fn, ( "##$%&'$fr-f)#.'$"##$%&'$/"##$%&'$f &'"##$%&'$rrb.0"##$%&'$fr !! "##$%&'$ t( #"

PAGE 190

btntfrt btnfrt btnfrt btnfrt btnfrt btnfrt btnfrt rftf btnfrt btnfrt rftf btnfrt btnfrt bfrt rftf btnfrt btnfrt bfrt rftf btnfrt !"" #$$%& '(% n)!$#

PAGE 191

btnfrt bfrt ttrrttt*t rftf btnfrt btnfrt bfrt b+ rftf btnfrt rftf btnfrt bfrt b+ rftf btnfrt rftf btnfrt bfrt b+ rftf btnfrt !"" #$$%& '(% n)!$#

PAGE 192

rftf btnfrt bfrt b+ btnfrt rftf rftf btnfrt bfrt b+ b+ b+ btnfrt rftf rftf btnfrt bfrt bfrt b+ b+ b+ !"" #$$%& '(% n)!$#

PAGE 193

btnfrt rftf rftf btnfrt bfrt bfrt ,*b b+ b+ btnfrt rftf rftf bfrt bfrt btnfrt ,*b b+ b+ btnfrt rftf rftf bfrt !"" #$$%& '(% n)!$#

PAGE 194

bfrt ,*b b+ b+ btnfrt ,*b btnfrt rftf rftf bfrt bfrt b+ b+ ,*b ,*b btnfrt b+ rftf btnfrt rftf bfrt !"" #$$%& '(% n)!$#

PAGE 195

bfrt b+ ,*b t+tr+*t ,*b b+ b+ btnfrt t+tr+*t rftf t+tr+*t t+tr+*t t+tr+*t ,*b t+tr+*t ,*b bfrt b+ b+ rftf btnfrt btnfrt !"" #$$%& '(% n)!$#

PAGE 196

,*b rftf ,*b b+ b+ rftf btnfrt bfrt ,*b btnfrt ,*b b+ b+ rftf rftf btnfrt bfrt bfrt btnfrt bfrt ,*b !"" #$$%& '(% n)!$#

PAGE 197

b+ b+ rftf rftf btnfrt bfrt btnfrt ,*b b+ b+ rftf rftf bfrt btnfrt b+ b+ rftf bfrt btnfrt bfrt rftf btnfrt !"" #$$%& '(% n)!$#

PAGE 198

b+ b+ rftf btnfrt btnfrt rftf b+ rftf btnfrt btnfrt btnfrt btnfrt b+ rftf btnfrt btnfrt btnfrt btnfrt b+ rftf rftf !"" #$$%& '(% n)!$#

PAGE 199

btnfrt rftf btnfrt tbfb*t btnfrt btnfrt btnfrt tbfb*t tbfb*t tbfb*t rftf tbfb*t tbfb*t brrft*t rftf brrft*t brrft*t brrft*t brrft*t brrft*t brrft*t brrft*t !"" #$$%& '(% n)!$#

PAGE 200

!"" #$$%& '(% *-! )!#$$%& '(%.$/(%#$$%& '(%0#$$%& '(% '(#$$%& '(%/1#$$%& '(% n)!$#

PAGE 201

btntfrb btnf r btnf r ftf btnf r ftf nt btnf r ftf r btnf btnf r ftf ftf btnf btnf r ftf ftf rbtnf btnf r bf r !"" #$$%& '(% )*!$#

PAGE 202

ftf ftf rbtnf btnf bf +f,f ftf rbtnf r btnf bf r +f,f rftf rr+f,f rftf btnf rbtnf rbf ftf r r+f,f r ftf r rbtnf btnf !"" #$$%& '(% )*!$#

PAGE 203

bf +f,f ftf +f,f ftf btnf r btnf r bf +f,f ftf +f,f +f,f r ftf btnf btnf bf bf r rtb+f ftf r +f,f +f,f r !"" #$$%& '(% )*!$#

PAGE 204

ftf btnf btnf bf bf tb+f r tb+f r +f,f ftf r +f,f ftf b)) rr btnf bf r b)) tb+f tb+f +f,f +f,f r rb)) btn btn !"" #$$%& '(% )*!r$#

PAGE 205

b ft b)) rr b)) r b)) tb+f tb+f rr +f,f +f,f rrr ft btn btn r b ft tb+f tb+f +f,f r +f,f ft r btn r btn r !"" #$$%& '(% )*!$#

PAGE 206

rb r -t),f tb+f rtb+f r +f,f r +f,f b ft ft rbtn rb r btn -t),f tb+f tb+f +f,f r +f,f r ft b r ft r rbtn r b !"" #$$%& '(% )*!$#

PAGE 207

btn r btn r -t),f tb+f tb+f ft +f,f r +f,f r ft b r btn r btn b r rrft btn r rtb+f rtb+f r r+f,f r+f,f f btn !"" #$$%& '(% )*!$#

PAGE 208

rft rbtn rbtn tb+f tb+f r +f,f +f,f f ft r btn btn f ft btn tb+f rtb+f +f,f +f,f rf rr +t+n+. rft ft !"" #$$%& '(% )*!$#

PAGE 209

tb+f tb+f r +f,f +f,f r f r +t+n+. +t+n+. r f ft ft tb+f +f,f +f,f r r+t+n+. ft ft t r +t+n+. ft rb f !"" #$$%& '(% )*!$#

PAGE 210

tb+f +f,f ft r ft r b r +t+n+. rt btn rr t r +t+n+. r rt +t+n+. b t f rtb+f r btn rrr +f,f f t +f,f r +t+n+. !"" #$$%& '(% )*!$#

PAGE 211

b btn r btn t r +t+n+. r rt rtb+f r+f,f t btn t btn tb+f +f,f t rr +t+n+. r +f,f r rrbtn ft btn r t !"" #$$%& '(% )*!$#

PAGE 212

+t+n+. r rtb+f r +f,f r rbtn t btn btn ft +t+n+. +f,f t tb+f ft btn rr +t+n+. rr+f,f r rft r+t+n+. tb+f !"" #$$%& '(% )*!$#

PAGE 213

+f,f r ft btn r ft +f,f btn ft r. rr btn ft +f,f btn rt ) rr rr. ft rft r btn !"" #$$%& '(% )*!$#

PAGE 214

+f,f r r+t+n+. ft r rft r r. ) rt ft ft r t r +t+n+. r ) r ft r ft t r ft t ) !"" #$$%& '(% )*!r$#

PAGE 215

ft r t ft r +t+n+. f rr r ) t ft r t f r f)f f)f r) rf t +t+n+. f rf r !"" #$$%& '(% )*!$#

PAGE 216

f f f)f r f)f t ) b. r f)f t f)f ) b. t r f)f b. t r tb+f rr rrtb+f f)f ) rtb+f rb. !"" #$$%& '(% )*!$#

PAGE 217

+t+n+. rt tb+f ) r b. f)f t rb. rr +t+n+. ) tb+f r f)f rb. b. t +t+n+. rb. b. r t tb+f tb+f !"" #$$%& '(% )*!$#

PAGE 218

b. b. tb+f r tb+f b. b. tb+f +t+n+. t rb. rb. f)f bf r r+t+n+. rb. r tb+f r b. r+t+n+. rbf b. -t),f b. r !"" #$$%& '(% )*!$#

PAGE 219

bf +t+n+. b. +t+n+. rrbf bf b. r+t+n+. b. t,t rr rbf b. bf r bf +t+n+. b. bf btnf bf rr b. bf !"" #$$%& '(% )*!$#

PAGE 220

+t+n+. bf btnf r +f,f r btnf r bf +t+n+. bf +t+n+. r btnf t,t bf rt,t t,t r+f,f rtb+f rr t,t bf rbtnf +f,f t,t r rtb+f !"" #$$%& '(% )*!$#

PAGE 221

bf r btnf +f,f r btnf r bf btnf t,t r +f,f r tb+f btnf r +f,f ftf t,b r t,b t,b btnf r tb+f +f,f tb+f r t,b btnf !"" #$$%& '(% )*!$#

PAGE 222

t,b bf t,t ftf r tb+f r+f,f tb+f ftf +f,f t,t btnf rftf rtb+f r +f,f rtb+f t,t rftf r +f,f t,t rr t,b rr ftf +f,f rr !"" #$$%& '(% )*!$#

PAGE 223

tb+f tb+f btnf t,t rr bf t,b rt,b ftf +f,f ftf +f,f r tb+f tb+f btnf r ftf bf ftf bf r r+f,f +f,f tb+f r !"" #$$%& '(% )*!$#

PAGE 224

btnf r tb+f rbtnf r ftf ftf +f,f r +f,f tb+f btnf tb+f r r/)tft btnf /)tft bf r ftf r ftf +f,f +f,f /)tft btnf tb+f r btnf !"" #$$%& '(% )*!r$#

PAGE 225

/)tft )tt+.n /)tft r /)tft )tt+.n r /)tft r r)tt+n r)tt+n )tt+.n )tt+.n )tt+.n r )tt+.n )tt+.n 0! *!#$$%& '(%1$2(%#$$%& '(%b3#$$%& '(% b'(#$$%& '(% 24#$$%& '(% !"" #$$%& '(% )*!$#