Whole Hurricane Protection, Jason Barrocas, Kevin Hernandez

Transcription

EML 4905 Senior Design Project
A SENIOR DESIGN PROJECT
PREPARED IN PARTIAL FULFILLMENT OF THE
REQUIREMENT FOR THE DEGREE OF
BACHELOR OF SCIENCE
IN
MECHANICAL ENGINEERING
Whole Hurricane Protection
Final Report
Jason Barrocas
Kevin Hernandez
Tanisha Richard
Advisor: Dr. Kuang-Hsi Wu
April 5, 2010
This report is written in partial fulfillment of the requirements in EML 4905. The
contents represent the opinion of the authors and not the Department of
Mechanical and Materials Engineering.
Ethics Statements and Signatures
The work submitted in this project is solely prepared by a team consisting of Jason Barrocas,
Kevin Hernandez, and Tanisha Richard and it is original. Excerpts from others’ work have been
clearly identified, their work acknowledged within the text and listed in the list of references. All
of the engineering drawings, computer programs, formulations, design work, prototype
development and testing reported in this document are also original and prepared by the same
team of students.
Jason Barrocas
Team Member
Kevin Hernandez
Team Member
Dr. Kuang-Hsi Wu
Faculty Advisor
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Tanisha Richard
Team Member
Table of Contents
Ethics Statements and Signatures ................................................................................................... 1
List of Figures ................................................................................................................................. 5
List of Tables .................................................................................................................................. 9
Abstract ......................................................................................................................................... 13
1.
Introduction ........................................................................................................................... 14
1.1
Problem Statement ......................................................................................................... 14
1.2
Motivation ...................................................................................................................... 15
1.3
Literature Survey ............................................................................................................ 17
1.3.1
Introduction to Hurricanes ...................................................................................... 17
1.3.2
Hurricane Wind Testing .......................................................................................... 18
1.3.3
Hurricane Protection Methods ................................................................................ 22
1.3.4
Rail Road Couplers ................................................................................................. 28
1.3.5
Retractable Roof Structures .................................................................................... 30
1.3.6
Mesh Materials and Fabrics .................................................................................... 33
1.3.7
Introduction to Gears .............................................................................................. 39
1.4
2.
3.
Discussion ...................................................................................................................... 41
Project Formulation .............................................................................................................. 42
2.1
Overview ........................................................................................................................ 42
2.2
Project Objectives .......................................................................................................... 43
Design Alternatives ............................................................................................................... 44
3.1
Overview of Conceptual Designs Developed ................................................................ 44
3.2
Design 1.......................................................................................................................... 44
3.3
Design 2.......................................................................................................................... 46
3.4
Design 3.......................................................................................................................... 48
3.5
Design 4.......................................................................................................................... 50
3.6
Design 5.......................................................................................................................... 52
3.7
Final Design ................................................................................................................... 53
3.8
Comparison of Different Design Alternatives ............................................................... 56
3.9
Power Requirements ...................................................................................................... 57
3.10
Deploying/Retracting Mechanism .............................................................................. 58
3.10.1
4.
Revision to Deploying/Retracting Mechanism ....................................................... 83
Project Management ............................................................................................................. 85
4.1
Overview ........................................................................................................................ 85
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4.2 Organization of Work and Timeline (Timeline for Senior Design Organization and
Senior Design Time Frame) ...................................................................................................... 86
5.
6
4.2.1
Month of November 2009 ....................................................................................... 86
4.2.2
Month of December 2009 ....................................................................................... 87
4.2.3
Month of January 2010 ........................................................................................... 87
4.2.4
Month of February/March 2010.............................................................................. 87
4.2.5
Month of April 2010 ............................................................................................... 88
Engineering Design and Analysis ......................................................................................... 89
5.1
Analytical Analysis and Structural Design of Design 4 ................................................. 89
5.2
Major Components of Design 4 ..................................................................................... 94
5.3
Simulations of Design 5 ................................................................................................. 95
5.4
Analytical Analysis and Structural Design of Final Design .......................................... 99
5.4.1
Wind Loads Calculation ......................................................................................... 99
5.4.2
Simulations of Final Design.................................................................................. 104
5.4.3
Cost Analysis of Final Design .............................................................................. 111
Prototype Construction ....................................................................................................... 113
6.1
Description of Prototype .............................................................................................. 113
6.2
Visual Prototype ........................................................................................................... 113
6.2.1
Visual Prototype – Process for Construction ........................................................ 114
6.2.2
Hours Put In for Visual Prototype ........................................................................ 118
6.2.3
Visual Prototype Cost Analysis ............................................................................ 124
6.3
7
Functional Prototype .................................................................................................... 124
6.3.1
Testing on Functional Prototype ........................................................................... 125
6.3.2
Results from Testing on Functional Prototype ..................................................... 126
Conclusion .......................................................................................................................... 129
7.1
Conclusion and Discussion .......................................................................................... 129
References ................................................................................................................................... 131
Appendices .................................................................................................................................. 133
Appendix A: Detailed Raw Design Calculations and Analysis .............................................. 133
A.1
Design 1 Calculations ............................................................................................... 133
A.2
Design 4 Calculations ............................................................................................... 137
A.3
Final Design Calculation .......................................................................................... 144
Appendix B: Engineering Drawings ....................................................................................... 154
Piecewise Truss Drawing .................................................................................................... 154
21 ft Aluminum Tube Drawing........................................................................................... 155
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20 ft Aluminum Tube Drawing........................................................................................... 156
Top Joint Drawing .............................................................................................................. 157
Middle Joint Drawing ......................................................................................................... 158
End Joint Drawing .............................................................................................................. 159
Appendix C: Wind Loads ....................................................................................................... 160
Appendix D: Transmission Design ......................................................................................... 167
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List of Figures
Figure 1: Wind Pressure Effects on a Residential Home [18] ...................................................... 14
Figure 2: Saffir-Simpson Hurricane Scale - Graphic [13] ............................................................ 18
Figure 3: Wall of Wind at Florida International University [1].................................................... 20
Figure 4: Shingle Damage Caused by Intense Wind [17]............................................................. 23
Figure 5: Accordion Shutters [16] ................................................................................................ 26
Figure 6: Colonial Hurricane Shutters [16] .................................................................................. 27
Figure 7: Electric Roll Down Shutters [16] .................................................................................. 27
Figure 8: Fractured Coupler [19] .................................................................................................. 30
Figure 9: Mesh Sizes Provided By Incord [6] .............................................................................. 35
Figure 10: Hajj terminal at Jeddah International Airport in Saudi Arabia [5] .............................. 37
Figure 11: Taoguan County Stadium [2] ...................................................................................... 39
Figure 12: Spur Gear Set [11] ....................................................................................................... 40
Figure 13 : Bevel Gears [11]......................................................................................................... 41
Figure 14: Dome Roofed Structure ............................................................................................... 45
Figure 15: Ribbed Structure of Protective Dome ......................................................................... 45
Figure 16: Displacement of Middle Truss .................................................................................... 46
Figure 17: Alternate Design of Ribbed Structure – Retracted ...................................................... 47
Figure 18: Alternate Design of Ribbed Structure – Being Deployed ........................................... 47
Figure 19: Alternate Design of Ribbed Structure – Deployed ...................................................... 48
Figure 20: Piecewise Truss Formed from I-Beams ...................................................................... 49
Figure 21: Side Profile of Piecewise Dome – Retracted............................................................... 50
Figure 22: Side Profile of Piecewise Dome - Being Deployed .................................................... 50
Figure 23: Simulation of Design 4 - Fully Deployed ................................................................... 51
Figure 24: Side Profile of Design 4 - Fully Deployed .................................................................. 52
Figure 25: Piecewise Truss Formed from Circular Tubes ............................................................ 53
Figure 26: I-Beam Truss for Final Design .................................................................................... 53
Figure 27: Side Profile of Final Design ........................................................................................ 54
Figure 28: Central Hub ................................................................................................................. 55
Figure 29: Simulation of Final Design.......................................................................................... 56
Figure 30: Scissor Mechanism – Retracted .................................................................................. 59
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Figure 31: Scissor Mechanism - Deployed ................................................................................... 60
Figure 32: Scissor Nomenclature – Retracted .............................................................................. 61
Figure 33: Scissor Nomenclature - Deployed ............................................................................... 61
Figure 34: Retracted Dimensions of Scissor Mechanism ............................................................. 65
Figure 35: Deployed Dimensions of the Scissor Mechanism ....................................................... 65
Figure 36: Procedure for Spur Gear Bending Analysis ................................................................ 68
Figure 37: Procedure for Spur Gear Wear Analysis ..................................................................... 71
Figure 38: Procedure for Bevel Gear Bending Analysis .............................................................. 73
Figure 39: Procedure for Bevel Gear Wear Analysis ................................................................... 76
Figure 40: Simulation of Transmission - Isometric View ............................................................ 82
Figure 41: Simulation of Transmission - Rear View .................................................................... 83
Figure 42: Displacement of Simply Supported Pipe..................................................................... 96
Figure 43: Factor of Safety of Simply Supported Pipe ................................................................. 96
Figure 44: von Mises Stress of Tube Truss .................................................................................. 97
Figure 45: Displacement of Tube Truss........................................................................................ 98
Figure 46: Factor of Safety of Tube Truss .................................................................................... 99
Figure 47: Joint of Final Design ................................................................................................. 105
Figure 48: Deformation of Truss #2 in Final Design .................................................................. 105
Figure 49: Factor of Safety of Truss #2 in Final Design ............................................................ 106
Figure 50: von Mises Stress of Truss #2 in Final Design ........................................................... 106
Figure 51: Deformation of Truss #7 in Final Design .................................................................. 107
Figure 54: Displacement of Truss #3 in Final Design ................................................................ 109
Figure 57: Displacement of Bolt under Shear............................................................................. 111
Figure 58: Factor of Safety of Bolt under Shear ......................................................................... 111
Figure 59 : Sections for Trusses.................................................................................................. 115
Figure 60: Single Truss ............................................................................................................... 115
Figure 61: Pivot Point with Trusses ............................................................................................ 116
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Figure 62: Gear Set/ Motor Used ................................................................................................ 117
Figure 63: Kevin Cutting a Truss for the Visual Prototype ........................................................ 118
Figure 64: Jason and Tanisha Gluing Trusses Together for the Visual Prototype ..................... 119
Figure 65: Construction of Visual Prototype .............................................................................. 119
Figure 66: Kevin Cutting Base of Visual Prototype ................................................................... 120
Figure 67: Aerial View of Construction of Visual Prototype ..................................................... 120
Figure 68: Trusses and Links of Visual Prototype...................................................................... 121
Figure 69: Unfinishied Visual Protoype Deployed ..................................................................... 121
Figure 70: Kevin and Unfinished Visual Prototype .................................................................... 122
Figure 71: Unfinished Visual Prototype Mounted to Base ......................................................... 122
Figure 72: Circuit that will Power the Visual Prototype............................................................. 123
Figure 73: Pushbutton Switchbox Mounted to Base................................................................... 123
Figure 74: Final Functional Prototype ........................................................................................ 125
Figure 75: Air Boat Used for Testing ......................................................................................... 126
Figure 76 : Functional Prototype during Testing – Front ........................................................... 127
Figure 77: Distributed Force in Stringer 4 .................................................................................. 133
Figure 78: Stringer Design of the Dome ..................................................................................... 135
Figure 79: Stringer 4 ................................................................................................................... 135
Figure 80: Stringers 3 and 5 ........................................................................................................ 136
Figure 81: Stringers 2 and 6 ........................................................................................................ 136
Figure 82: Basic Wind Speed ..................................................................................................... 161
Figure 83: Transmission Assembly Drawing ............................................................................. 173
Figure 84: Spur Pinion 1 Drawing .............................................................................................. 174
Figure 85: Spur Gear 1 Drawing ................................................................................................. 175
Figure 86: Bevel Pinion 1 Drawing ............................................................................................ 176
Figure 87: Bevel Gear 1 Drawing ............................................................................................... 177
Figure 88: Spur Pinion 2 Drawing .............................................................................................. 178
Figure 89: Spur Gear 2 Drawing ................................................................................................. 179
Figure 90: Bevel Pinion 2 Drawing ............................................................................................ 180
Figure 91: Bevel Gear 2 Drawing ............................................................................................... 181
Figure 92: Shaft 1 Drawing......................................................................................................... 182
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List of Tables
Table 1: Saffir-Simpson Hurricane Scale ..................................................................................... 18
Table 2: Cost Analysis and Comparison for Hurricane Protection............................................... 28
Table 3: Comparison of Each Design ........................................................................................... 56
Table 4: Horsepower Requirement for Each Section ................................................................... 58
Table 5: Voltage Requirement for Each Section .......................................................................... 58
Table 6: Diameters and Area of Unified Screw Threads UNC and UNF ..................................... 62
Table 7: Power Screw Dimensions ............................................................................................... 62
Table 8: Dimensions of Each Section in Deployed and Retracted States..................................... 64
Table 9: Parameters for Transmission Design .............................................................................. 65
Table 10: Number of Teeth on Each Gear in Transmission ......................................................... 66
Table 11: Spur Set 1 Bending Stress Data .................................................................................... 69
Table 12: Spur Set 1 Allowable Bending Stress Data .................................................................. 69
Table 13: Brinell Hardness and Life Cycles for Spur Set 1 Bending ........................................... 69
Table 14: Bending Stress, Allowable Bending Stress and Bending Safety Factor for Spur Set 1 70
Table 15: Spur Set 1 Wear Data ................................................................................................... 72
Table 16: Spur Set 1 Allowable Wear Data .................................................................................. 72
Table 17: Brinell Hardness and Life Cycles for Spur Set 1 Wear ................................................ 72
Table 18: Wear, Allowable Wear and Wear Safety Factor for Spur Set 1 ................................... 72
Table 19: Bevel Set 1 Bending Stress Data .................................................................................. 74
Table 20: Bevel Set 1 Allowable Bending Stress Data................................................................. 74
Table 21: Brinell Hardness and Life Cycles for Bevel Set 1 Bending ......................................... 74
Table 22: Bending Stress, Allowable Bending Stress and Bending Safety Factor for Bevel Set 1
....................................................................................................................................................... 75
Table 23: Bevel Set 1 Wear Data .................................................................................................. 77
Table 24: Bevel Set 1 Allowable Wear Data ................................................................................ 77
Table 25: Brinell Hardness and Life Cycles for Bevel Set 1 Wear .............................................. 77
Table 26: Wear, Allowable Wear and Wear Safety Factor for Bevel Set 1 ................................. 77
Table 27: Spur Set 2 Bending Stress Data .................................................................................... 78
Table 28: Spur Set 2 Allowable Bending Stress Data .................................................................. 78
Table 29: Brinell Hardness and Life Cycles for Spur Set 2 Bending ........................................... 78
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Table 30: Bending Stress, Allowable Bending Stress and Bending Safety Factor for Spur Set 2 79
Table 31: Spur Set 2 Wear Data ................................................................................................... 79
Table 32: Spur Set 2 Allowable Wear Data .................................................................................. 79
Table 33: Brinell Hardness and Life Cycles for Spur Set 2 Wear ................................................ 79
Table 34: Wear, Allowable Wear and Wear Safety Factor for Spur Set 2 ................................... 80
Table 35: Bevel Set 2 Bending Stress Data .................................................................................. 80
Table 36: Bevel Set 2 Allowable Bending Stress Data................................................................. 80
Table 37: Brinell Hardness and Life Cycles for Bevel Set 2 Bending ......................................... 80
....................................................................................................................................................... 81
Table 39: Bevel Set 2 Wear Data .................................................................................................. 81
Table 40: Bevel Set 2 Allowable Wear Data ................................................................................ 81
Table 41: Brinell Hardness and Life Cycles for Bevel Set 2 Wear .............................................. 81
Table 42: Wear, Allowable Wear and Wear Safety Factor for Bevel Set 2 ................................. 82
Table 43: Revised Power Screw Dimensions ............................................................................... 84
Table 44: Revised Output Rotational Speed, Deploying Time and Revolutions of Power Screw 84
Table 45: Revised Dimensions of Each Section in Deployed and Retracted States ..................... 84
Table 46: Gantt Chart.................................................................................................................... 86
Table 47: Total Project Hours Spent by Each Team Member ...................................................... 86
Table 48: qz Velocity Pressure ...................................................................................................... 89
Table 49: Top Mesh ...................................................................................................................... 91
Table 50: Weight of the Beams .................................................................................................... 91
Table 51: Calculated for Perpendicular Sections .......................................................................... 92
Table 52: Max S ............................................................................................................................ 93
Table 53: Factor of Safety at 155 mph.......................................................................................... 93
Table 54: Factor of Safety at 175 mph.......................................................................................... 94
Table 55: External Pressure Factor ............................................................................................. 101
Table 56: Internal Pressure ......................................................................................................... 101
Table 57: Design Pressure .......................................................................................................... 102
Table 58: Head on Wind ............................................................................................................. 103
Table 59: Minimum Possible Beam Geometry........................................................................... 104
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Table 60: Cost Estimate of Full Scale Design ............................................................................ 112
Table 61 : Materials Used for the Visual Prototype ................................................................... 114
Table 62: Prototype Labor Hours ............................................................................................... 118
Table 63: Material Cost for Prototype ........................................................................................ 124
Table 64: Functional Prototype Test Results .............................................................................. 127
Table 65: Assumed Full Scale Wind Reduction ......................................................................... 128
Table 66: Top Mesh .................................................................................................................... 137
Table 67: Middle Mesh & Bottom Mesh .................................................................................... 138
Table 68: Calculations for Perpendicular Beams........................................................................ 140
Table 69: Calculations for Parallel Beams.................................................................................. 141
Table 70: Max S .......................................................................................................................... 142
Table 71: Factor of Safety at 155 mph........................................................................................ 143
Table 72: Factor of Safety at 175 mph........................................................................................ 143
Table 73: List of Constants ......................................................................................................... 144
Table 74: Head on Wind – Design Pressure ............................................................................... 145
Table 75: Side Wind – Design Pressure ..................................................................................... 146
Table 76: Mesh Area ................................................................................................................... 147
Table 77: Factor of Safety/Allowable Streght ............................................................................ 147
Table 78: Head on Wind Calculations ........................................................................................ 149
Table 79: Side Wind Calculations .............................................................................................. 151
Table 80: Occupancy Category of Building and Other Structures for Flood, Wind, Snow,
Earthquake and Ice Loads ........................................................................................................... 160
Table 81: Directionality Factor ................................................................................................... 162
Table 82: Main Wind Force Resisting System - Method 2 ........................................................ 163
Table 83: Main Wing Force Res.Sys. /Comp and Clad - Method 2 ........................................... 164
Table 84: Important Factor, I ...................................................................................................... 165
Table 85: Velocity Pressure Exposure Coefficients ................................................................... 166
Table 86: Spur Pinion 1 .............................................................................................................. 167
Table 87: Spur Gear 1 ................................................................................................................. 168
Table 88: Bevel Set 1 .................................................................................................................. 169
Table 89: Spur Pinion 2 .............................................................................................................. 170
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Table 90: Spur Gear 2 ................................................................................................................. 171
Table 91: Bevel Set 2 .................................................................................................................. 172
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Abstract
The purpose of this project is to design a retractable dome that would cover a home in the
event of a hurricane. The dome is designed to protect a home from high speed winds as well as
flying debris. It is designed to provide complete hurricane protection as research shows current
methods for hurricane protection leave the majority of the home exposed. The dome offers an
alternative to the tedious and taxing methods currently employed in home hurricane protection as
its effortless operation provides a level of comfort and peace of mind not found in hurricane
shutters. The inspiration for the initial design came from technological advances currently
utilized in structures all around the world. These advances include, but are not limited to,
retractable roof structures such as those used in sports stadiums, and the different materials used
in structures that have large fabric roofs. The system includes a mechanism powered by several
small electric motors which will automatically open and close the dome. Several designs were
developed and analyzed using SolidWorks to determine their feasibility. These designs were
subjected to lift, drag forces and wind loads used to simulate hurricane force winds. In addition,
these designs matched the numerical calculations that were generated by wind load analysis.
Two prototypes, a visual one and a functional one, were used to demonstrate the behavior of this
design. The visual prototype provides a visual representation of the final design and shows the
retracting and deploying of the structure. The functional prototype, created by Dr.Wu’s graduate
students, was used to analyze the behavior of the mesh when subjected to high speed winds using
an airboat.
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1. Introduction
1.1 Problem Statement
Every year hurricanes cost the world billions of dollars in damages. While some factors
such as flooding contribute to the damage, the majority of the damage is caused by the storms’
intense wind. It is not uncommon for a hurricane’s wind speed to reach over 150 mph. Hurricane
shutters and impact glass, the two most popular forms of home hurricane protection, protect only
the windows. The rest of the home is left exposed to the tremendous force of the wind.
If it were somehow possible to reduce the speed of the wind before it reached the home,
most of the damage to the home could be avoided. When a hurricane strikes, the strong winds are
the result of a large pressure difference between the low-pressure center of the storm and the
high-pressure surrounding air. This high-pressure air is sucked into the center of the storm and
driven upward. The upward direction of the hurricane’s wind is what causes roofs to rip from
their homes. Once the roof is damaged, the rest of the house becomes vulnerable and significant
damage is inevitable. Figure 1 demonstrates the effect of pressure differences on a home.
Figure 1: Wind Pressure Effects on a Residential Home [18]
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In order to drastically reduce wind speed by the time it reaches the home, the dome will
be covered by a very strong mesh material. This mesh will allow some wind to pass through the
dome, but the wind speed will be reduced to a manageable level. According to Miami-Dade
County building code, homes should be able to safely handle winds of up to 100 mph. The
purpose of the dome is not to completely isolate the home from any wind, but to reduce the
speed of the wind by the time it reaches the home.
1.2 Motivation
Even more important than the substantial amount of damage caused by hurricanes is the
loss of human life that comes from not having proper hurricane protection. Hurricane Katrina,
which struck Louisiana on August 29, 2005, is a prime example of the devastation that can occur
to a population that is not adequately prepared to face a hurricane. Hurricane Katrina resulted in
1,836 confirmed deaths and 705 missing individuals. Human life is priceless, and therefore every
possible measure must be taken to protect it. Today’s modern society has made incredible
advances in technology, yet people are still at the mercy of these powerful storms.
Hurricanes are responsible for over 50% of rebuilding costs when considering all natural
disasters, yet more funding is spent on earthquake research. In fact, of the U.S. hurricane-related
budget, less than 2% is devoted to research and design to protect buildings from high speed
winds [15]. It seems as though hurricanes do not become a top priority until they have already
caused billions of dollars in damage. If hurricane research was given more attention, the long
term financial impact of hurricanes would decrease significantly. Several applications exist
today, such as the retractable roofs of modern stadiums, which show that designing a form of
superior hurricane protection is well within the reach of modern society.
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The geometry of a dome is extremely aerodynamic, much more so than the traditional
rectangular shape of homes. Some homes are built as monolithic domes, where the structure is
cast in one piece using concrete or a similar structural material. These domes are less visually
appealing than traditional homes and have other downsides such as oddly shaped rooms resulting
in wasted space in narrow corners. A retractable dome would offer all the benefits of the dome’s
geometry while allowing the structure of the home to follow conventional design.
In the beginning, the dome will be mainly marketed toward single family homes.
Obviously the nature of the design will make it difficult to design a retractable dome for
apartment buildings or townhouses, but even single family homes make up a large part of the
population. Eventually, as new communities are constructed, the homes could be built with the
retractable domes preinstalled. This will make installation easier since the dome can be built
before the house, and a compartment can be built within the foundation which will house the
retracted dome. The retractable domes will also increase the value of not only these new
communities, but any home that has the system installed.
The long term goal of the retractable dome is to reduce the destruction caused by
hurricanes. If even a portion of the homes affected by hurricanes had this system installed, the
people in those homes would be completely safe from harm. A major benefit of the dome is that
residents will not have to evacuate in the event of a hurricane. The dome will allow people to
wait out these tremendous storms in the comfort of their own home. Additionally, the actual
houses would experience little to no damage. Therefore, the cost of insurance claims and
rebuilding would be practically nothing for these houses. This would be a huge advantage for
states such as Florida, where so much money is spent each year on rebuilding after hurricanes.
This money could be put to better use within the community, and the entire state would benefit.
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1.3 Literature Survey
1.3.1 Introduction to Hurricanes
In learning the nature of hurricanes, it is essential to keep in mind that hurricanes are
large and slow moving storms. These storms generate intense winds in different directions when
circling the eye of the storm. To identify the strength of the storm, the Saffir-Simpson hurricane
scale was developed. Under this scale, hurricanes are classified into five different categories.
Category One hurricanes carry sustained winds of 74–95 mph and can cause damage to some
building structures such as unanchored mobile homes. Category Two hurricanes can achieve
sustained winds from 96–110 mph. These winds can cause damage to the roofing material, doors
and windows of the house. These strong winds can also cause damage to glass windows from
flying debris. Category Three hurricanes can carry winds up to 111–130 mph; these winds can
cause minor damage to the walls of the house and the combined damages from the previous
categories. Category Four hurricane winds can go up to 131–155 mph, causing intense damage to
the roof and the windows of the house, including damage from flying debris. Category Five
hurricanes are the most disastrous; they can produce winds in excess of 155 mph. These highspeed winds can cause complete structural failure of the house, including damage to the roof as
well as the windows from major flying debris. Table 1 gives a concise description of the
different categories with their related pressure and wind speeds, also including degree of damage
correlated with each category. Figure 2 shows a visual representation of the Saffir-Simpson
hurricane scale.
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Table 1: Saffir-Simpson Hurricane Scale
Category Central Pressure (inHg) Sustained Winds (mph) Level of Damage
1
28.94
74–95
Minimal
2
28.50–28.91
96–110
Moderate
3
27.91–28.47
111–130
Extensive
4
27.17–27.88
131–155
Extreme
5
<27.17
≥156
Catastrophic
Figure 2: Saffir-Simpson Hurricane Scale - Graphic [13]
1.3.2 Hurricane Wind Testing
As previously discussed, there has been a lack of research done until recently to protect
homes from the damaging effects of hurricanes. Fortunately, a testing facility has been
constructed at Florida International University (FIU) called the Wall of Wind which is designed
for destructive testing on large-scale structures. This magnitude of wind testing will significantly
increase the understanding of hurricane wind effects. While there are many universities and
government facilities that currently have some form of wind testing facility, none is able to test
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large scale buildings and subject these structures to extreme wind effects the way the Wall of
Wind does.
In 1999, the Idaho National Engineering and Environmental Laboratory, in conjunction
with the U.S. Department of Energy, proposed to build a large-scale wind test facility (LSWTF).
The purpose of this facility would be to study how low-rise buildings behave under simulated
extreme wind conditions. It was determined that the cost of constructing this LSWTF would
range from $70 million to several hundred million dollars. Upon request from the Idaho
Operations Office of the DOE, the National Research Council (NRC) formed a committee to
determine whether such an LSWTF would make economic sense. The committee came to
conclusion that cost for the proposed LSWTF was too high, and therefore it would not be
economically wise to construct this LSWTF [15].
In 2003, the wind engineering research team at the International Hurricane Research
Center (IHRC) at FIU commenced plans to build a large-scale wind testing facility at a much
lower cost. This facility would be designed to give a better understanding of the effects of
hurricane force winds on residential structures. With a wind test facility of this magnitude, fullscale structures could be tested under varying wind conditions in a controlled and repeatable
environment. The facility would allow for the testing of realistic wind loading conditions in a
laboratory setting, rather than passively waiting for nature to produce a desired amount of wind.
One of the greatest benefits of testing structures on a large scale is that many of the restrictions
present in wind tunnel testing are virtually nonexistent. For example, it is impossible to scale
down the effects of gravity. Roofing materials such as tiles and shingles cannot be scaled down
and still be representative of their full-sized properties. The Wall of Wind is currently the only
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way to accurately test full-scale structures [15]. The Wall of Wind at FIU can be seen in Figure
3.
Figure 3: Wall of Wind at Florida International University [1]
The Wall of Wind is designed to not only simulate hurricane force wind, but also
hurricane force rain. The high speed wind present in hurricanes coupled with the rain also
present in hurricanes results in a “raining sideways” effect. This means that the wind is so strong
that it literally blows the rain drops before they hit the ground, making it appear as though the
rain is falling at an angle or horizontally. The Wall of Wind is fitted with a water-injection
system that sprays water horizontally to simulate this effect [15].
During hurricanes, rainwater often gets into buildings and homes. This results in
considerable damage to the building interior and its contents. Many homes survive hurricanes
structurally, but they suffer enough water damage to necessitate significant interior restoration.
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In addition, residents must be evacuated until repairs are completed. This is both inconvenient
and very frustrating for someone who has just been through the traumatic event of a hurricane.
The Wall of Wind simulates this rain and wind acting on real component products with full-scale
Reynolds and Froude numbers. In particular, it is a very useful tool for studying the effects of
high speed rain which will allow new products to be developed to reduce water damage suffered
during hurricanes [1].
One example of an improvement that can be made using Wall of Wind testing is
developing soffit systems with improved resistance to wind and rain. This will avoid having high
intensity rain enter buildings through the venting porosity underneath the roof overhang. This has
been shown to be a major cause of damage and loss in past hurricanes [1].
The Wall of Wind is comprised of two fans which together generate wind speeds of up to
120 mph [15]. The ability to generate such high speed winds, in addition to the rain testing just
discussed, makes the Wall of Wind unparalleled for hurricane testing. The Wall of Wind shows
that hurricane research is finally taking a step in the right direction. The ultimate purpose of the
Wall of Wind is to test homes and small buildings to make them more wind and rain resistant;
this includes their structure, roofing and framework. While this is obviously beneficial to future
structures being built, it does not really help those houses and buildings which have already been
built. A better invention for these structures would be a way to protect the home while still
allowing it to retain its structural integrity. Retrofitting older homes and buildings once newer
technology becomes available would be both costly and inconvenient.
Designing a form of hurricane protection such as the dome proposed in this project would
be revolutionary. In addition to the advances in building technology made by Wall of Wind
testing, homes and buildings could be completely protected using the dome. Newer homes that
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will benefit from safer building structures can have the hurricane protection dome installed to be
practically hurricane-proof. Perhaps the most exciting thing about the Wall of Wind in the scope
of this project is that it makes it possible to test the dome once it comes closer to production. The
only practical testing that can currently be carried out on the hurricane protection dome is smallscale prototype testing such as the airboat testing carried out in this project. Once the dome
comes closer to production, a large-scale prototype could be built, and the Wall of Wind could be
used to test it.
1.3.3 Hurricane Protection Methods
Every house is affected by the wind in different ways, depending on the location, house
design, and neighboring structures. Wind damages include ripping off the roof sheathing and
damages to the gable end walls as the internal pressure adds to the wall suction. High wind can
cause moving debris to damage the roof as well as break windows upon impact. Therefore, it is
essential to protect the four critical areas of the house: the roof, windows, doors and the garage
doors. Roofs that are exposed to strong winds can lead to a shorter life span. A typical roof
contains metal hurricane straps, also called clips. These clips are connected to the exterior walls
to add strength to the structure and increase safety. Another form of connection for the roof to
the exterior walls is toe nails; these are not sufficient, though, and can fail when placed under
high winds [18].
There are different kinds of roof covering material such as wood, clay or concrete tiles,
metal or wood shingles, wood shakes and standing seam metal roofs. Shingles are not resistant to
hurricane force winds because an adhesive is used to apply them to the roof. To gain more safety
in the shingles against high winds, quick setting asphalt cement can be used to bond them
together. Clay tiles on the other hand are brittle in material; therefore, they can break off easily
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when put through intense weather conditions. Clay tiles can be dangerous during high wind
storms. When broken up they can turn into windborne debris. Shingles and tiles require very
high maintenance because replacements are essential when they are damaged or missing after a
storm [18]. Figure 4 shows a shingle roof which has been damaged by intense wind.
Figure 4: Shingle Damage Caused by Intense Wind [17]
Another way to improve and strengthen the roof of the house is to correct the uplift
resistance of the roof deck from pressure within the attic by applying wood adhesive supports on
both sides of the roof, creating a balanced support. Studies show, based on static pressure tests,
that using the wood adhesive technique increases the uplift resistance of high winds up to three
times compared to the conventional methods of strengthening roofs [18].
Depending on the design of the house, various factors are taken in to account because
every house is affected differently by high speed winds. For example, a house that consists of
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gables end walls is subjected to high forces from the high winds and can collapse causing
tremendous damage. Therefore, strengthening these walls is essential to making this type of
house safer in case of a hurricane. Gable walls are connected to the gable end trusses on the top
and have to be secured in place; nails are used on the top and bottom of the wall. The position of
the gable's walls in this manner can resist high winds from pushing and pulling the structure back
and forth. To secure such a structure, the gable walls require proper bracing which can be done
in several different methods [18].
Other critical areas of the house that require extra safety measures are the garage doors
and entry doors. Garage doors are prone to more damage from high winds because of their
increased width. Lightweight garage doors can experience damage as they can be forced out of
the roller tracks they are initially installed in. This takes place because of the deflection force that
the garage door is put through while under high winds, thus causing the structure to fail. Several
measures can be taken to strengthen garage doors such as installing bracing on each panel or
using wood or metal girts and hinges to support the ends and the vertical supports. The entry
doors on the other hand are different in each home. For example, some houses consist of single
or double doors, and they can either be solid wooden doors or hollow metal doors. To secure
entry doors from hurricane damage a hollow metal door is recommended as it can withstand
more damage from windborne debris. Also, in the case of double entry doors, it is suggested to
install head and foot bolts on one of the doors to keep it constrained [18].
One of those common critical areas of the house to be protected is the most fragile
component: the windows. Impact resistant shutters are the most common and cost-effective way
to protect large windows and glass doors from high winds and windborne debris. Pressure
changes within a closed house could be devastating if a window or door were to break; therefore
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their protection is essential because of their fragile nature. Different types of shutters are
currently available on the market. One type of hurricane shutter, storm panels, comes in two
different materials: steel and aluminum. These shutters can directly attach to the walls
surrounding the window. Pieces of these shutters are overlapped for increased strength and are
attached by bolts on the tracks provided on the walls. These shutters tend to be the most
inexpensive shutters on the market; they are removable, yet very strong against high winds. Their
downfall on the other hand comes from their high maintenance as they need a place for their
storage after removal. These shutters are time consuming to install and require professional
installation.
Accordion hurricane shutters consist of one or two piece shutters that are attached on the
outside of the house against the walls near the windows. Accordion shutters are made out of
aluminum. They simply unfold similar to an accordion, hence the name, and lock at the ends.
Some advantages of accordion shutters are that they do not require any storage and they only
require initial installation. The only disadvantage is that they run on a wheel track, therefore
maintenance is required to make sure the winds have not caused damage to the system. Figure 5
shows an example of accordion shutters.
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Figure 5: Accordion Shutters [16]
Colonial hurricane shutters are similar to accordion shutters and are permanently joined
beside the windows; therefore, they require no storage. They are easy to set up and can be
installed by just one person. They are also considered to be decorative, as they embellish and
protect the windows from high winds. The only disadvantage these shutters carry is they require
a storm bar for safe set up which can prolong the installation time. These shutters are limited in
size; they cannot be used for protecting doors. Bahama hurricane shutters are similar to colonial
hurricane shutters. They are attached above the window and can be lowered down in case of a
hurricane. Their storage itself provides a good shade for the window when they are not being
used, although bahama shutters have been found to be weaker than other shutters. Electric roll
down shutters are placed right above the window, are stored in a box when not in use and can be
rolled down by pushing a button. These are the most expensive type of shutters but the easiest to
set up and offer a well rounded protection. They also do not demand a large storage space as they
roll up and the layers are stored on top of one another. Figure 6 shows an example of colonial
hurricane shutters, while Figure 7 shows an example of electric roll down shutters.
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Figure 6: Colonial Hurricane Shutters [16]
Figure 7: Electric Roll Down Shutters [16]
Hurricane glass is another form of hurricane protection for windows and doors. Hurricane
glass can withstand impact from hurricane debris and therefore completely eliminates the need
for hurricane shutters. It is difficult to install new hurricane glass windows in older houses, and it
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can end up being quite expensive; this technology is more easily installed on new houses.
Hurricane glass is similar to the glass of car windshields. It consists of a plastic layer which is
sandwiched between glasses, which prevents future damage to the glass. Tests have been done
on impact glass to provide codes for the ASCE (American Society of Civil Engineers) and gain
results to improve the strength of impact glass. For impact glass to qualify as impact resistant, it
needs to pass an impact test as well as a cyclic structural loading test with high wind speeds [9].
Window film is another alternative for window protection from high wind. The most popular
window film on the market is known as safety and security window film. The film thickness can
range from 4 mils (minimum 2 ply) to over 21 mils.
Table 2 gives a description of the most common hurricane protection systems currently
available on the market, as well as the material from which they are made. Table 2 also gives a
comparison of prices, arranged from lowest to highest.
Table 2: Cost Analysis and Comparison for Hurricane Protection
Type
Storm Panels Accordian Shutters Colonial Shutters
Impact Glass
Electric Roll Down Shutters
Steel, Al
Al
Al
Wood, Glass Polyester Film
Al
Materials
$18-30 / sq. ft.
$30-35 / sq. ft.
$65-75 / sq. ft.
Price Range $6-7 / sq. ft. $16-20 / sq. ft.
$6,300.00
$8,400.00
$11,375.00
$24,500.00
Est. Total Cost* $2,275.00
*Estimate was calculated using 350 sq. ft. of windows
1.3.4 Rail Road Couplers
For the hurricane dome designed in this project, a locking mechanism is required to join
each half of the dome and secure the frame in place. Such a locking mechanism would need to
withstand high hurricane winds and hold the structure together under extreme conditions. This
piece of equipment also needs to resist impact forces from flying debris during high winds.
Different locking mechanisms were researched based on the specifications given for the design
considering the weight and size of the structure.
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Rail road coupling was one of the locking mechanisms worth researching because of its
application related to heavy structures. These couplers are used to connect different parts of the
train called the rolling stocks that can include railroad cars or coaches. These couplers provide
flexibility and maximize convenience as they allow numerous rolling stocks to attach to each
other. The article “Failure Analysis of Three Reconditioned Rail Car Couplers” examines three
different couplers subjected to a variety of testing such as chemical analysis and impact testing
[19]. Each coupler was heat treated to hardness levels that were specified by the Association of
American Railroads rules and regulations. The impact tests resulted in a hardness value which
was suitable within the fracture surfaces and was passed by the AAR specifications for the
grading of E. The Charpy impact test showed that the reason the couplers fail is that the material
they are made from is too brittle; therefore steel couplers did not pass the test. This failure could
have been caused by improper quenching from the solution heat treat temperature, which in turn
caused the strength of the material to weaken. The chemical testing showed concentrations of
manganese and carbon within the structure, however the couplers were still able to pass the AAR
specifications for chemical testing [19]. Given the loading conditions the hurricane dome would
experience, these locking mechanisms may be useful to study in order to design a similar locking
mechanism. The locking mechanism would need to withstand high force winds as well as impact
without fracture. Figure 8 shows the fractured surface of a coupler.
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Figure 8: Fractured Coupler [19]
1.3.5 Retractable Roof Structures
The retractable roofs of many modern stadiums offer a blueprint for a retractable
hurricane protection dome. Stadiums such as Rogers Centre (formerly known as SkyDome) in
Toronto, Ontario, Canada, Reliant Stadium in Houston, Texas and University of Phoenix
Stadium in Glendale, Arizona all employ retractable roofs. These roofs are much larger in scale
than anything that would be produced to cover a single family home, but the mechanisms used to
retract and deploy the roofs were studied for reference. The final design for this project borrowed
many ideas from some of these roofs such as electric motors and gear sets.
Rogers Centre is one of the most innovative architectural structures of our time. It opens
up a whole new realm of possibilities to gather inspiration for new ideas. It consists of a
parabolic retractable roof which spans to 680 ft wide; this allows a 90% exposure to spatial view.
The concept of the design was originated by Michael Allen, a structural engineer, with
the help of architect Rod Robbie. Rogers Centre includes materials such as polyurethane and
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inflatable rubber to cover the spaces between the panels. The panels consist of trusses that are
made out of steel covered by corrugated steel cladding. Having such a strong combination of
materials, this structure can withstand up to 40 mph winds and the cyclic wear of opening and
closing the roof over 200 times a year, for 100 years. The design also takes into consideration the
expansion and contraction of the whole structure with the climate change. Another useful and
important fact about Rogers Centre is that the design provides easy access to maintaining
components such as gears, motors and wheels [8].
Many concepts and designs were put forth for the construction of Rogers Centre, but the
retracting roof idea was chosen because of its feasibility and costs for implementing. The idea for
a dome shape was considered by Adjeleian Allen Rubeli, who designed a mathematical model
for the dome using geometry and computer-aided programs. Computer visualization helped the
process of designing the most important component of the dome, the roof trusses. Different
factors played an important role in the design process such as fatigue, fracture, sliding, structural
vibration and panel deflection [8].
Rogers Centre’s retracting roof moves by retracting three different panels which are
placed on top of one another. The panels are of different sizes and are elevated from each other.
Different mechanical concepts are combined for Rogers Centre’s design, such as electric and
hydraulic power, as well as a push-pull system. The design includes logic controllers with power
and control signals, as well as cable reels that are attached to electric winches placed on the
moving panels. Motors ranging from 5 to 10 hp are used to drive the design along a track. Using
a gear box, the motor speed is reduced in each bogie. The design includes large trusses supported
in three directions which are connected to pins and spherical bearings; these bearings allow the
trusses to rotate in all directions. The bearings also provide an evenly distributed load to the four
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bogie wheels used. Each bogie requires support in four directions, resulting in a total of eight
wheels, two wheels assigned for each direction. Bogies are used to support and transport the roof
trusses using different propulsion techniques similar to those found in trains and cranes. The
bogies also experience external forces such as gravity, snow, wind and the dynamic forces
generated by the panels [8].
Another influence for the opening and closing mechanism of the dome comes from
University of Phoenix Stadium. Built from 2003-06, the stadium is home to the Arizona
Cardinals National Football League (NFL) franchise. The 495,000 ft2, 700 ft span roof includes a
97,000 ft2 movable roof that retracts to create an opening over the playing field. One important
feature of the architectural concept was that the roof mass presented a fairly low-rise form that
did not visually dominate the building’s profile. These requirements translated to a 52.5 ft
allowable rise over an eave perimeter span of 820 ft. This ratio would make it impossible to
realize traditional dome action economically. In addition, the design team was faced with the
challenging task of designing an opening for the retractable roof that would be just large enough
to give the feel of outdoor play when the roof is open. This would reduce the roof mechanization
costs and allow the roof panels to retain a slender profile [10].
Lateral loads on the roof structure are the result of unbalanced drag wind loads as well as
the impact and braking requirements of the retractable roof panels; similar loads will be
experienced by the retractable dome in the hurricane protection system. The primary trusses used
as spanning roof elements are referred to as “Brunel Trusses,” due to their similarity in form to
the trusses used by I.K. Brunel in the construction of the Royal Albert Bridge in 1859. The
retractable portion of the roof consists of two 180 ft wide x 259 ft span panels that open about
the center of the field. Each panel rides along the inclined top surface of the Brunel Truss unlike
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previous US retractable roofs, which usually ride on flat rails. Polytetrafluoroethylene (PTFE)coated fiberglass tensioned fabric covers the panels, allowing a considerable amount of light into
the stadium [10].
Each panel of the retractable roof is made up of eight trusses riding on four carriers at
each line of the panel support. The retractable trusses are shaped similarly to the Brunel Trusses,
but instead use a vierendeel system to resist unbalanced loads. A vierendeel system refers to a
system of trusses where the members form rectangular rather than triangular openings. In the
retractable roof mechanism, each pair of retractable trusses sits on a two wheeled carrier,
allowing for a predictable load distribution without a mechanical suspension system. The two
wheels of the carrier are over 3 ft in diameter and they ride on a hardened crane rail weighing
175 lbs. Two of the four carriers are powered and two are idler carriers. The powered carriers are
mounted to a cable drum which rides with the panel as it moves along the rail. On each side of
the rail, a wire rope cable connects each cable drum to a fixed point at the center peak of the
Brunel Trusses. When the roof is to be opened, the cables unwind at a steady rate while the
weight of the structure drives the panel downhill. The process is simply reversed, with the cables
winding back onto the drum, to close the roof [10].
1.3.6 Mesh Materials and Fabrics
The purpose of this design is to reduce the effects of wind in an attempt to prevent
damage that can occur to a home during natural disasters, such as hurricanes. In the design, the
trusses serve as the foundation; however there is an 8 to 9 foot section of free space in between
each truss in the Final Design. In order to span that distance, either a fabric or mesh material can
be used to resist the wind forces that a hurricane can create. This mesh material serves two vital
functions in the structure: it decreases the wind force by up to 60% and reduces loads of the
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standing structure. For example, wind gusts that occur during a Category 5 hurricane can reach
over 155 mph. The mesh material would decrease these wind gusts to a level which standard
homes can withstand. The mesh material would cover the entire dome and would be attached to
the joints of each truss.
The prime requirement for this mesh material is the ability to withstand high-speed, highforce impacts that are caused by flying debris. The combination of loose debris and the high
speed winds that occur during a hurricane can have catastrophic consequences. The debris can be
swept off the ground by the high speed winds, and objects such as branches can penetrate the
house through unsecured windows or doors. This not only results in damage to the structure of
the home but it also reduces its integrity. Flying debris is also a major safety issue as many
injuries during a hurricane are caused by projectiles flung by the high force winds. Since the
mesh material will be stored underground with the trusses, the material must be able to resist not
only the force of a flung projectile, but the effects of normal operation such as bending, folding
and the normal wear and tear caused by the opening and closing of the structure. The effect of
climate is also an issue to consider when choosing a material to span the trusses. Mesh and fabric
respond differently under different climates. Within high humidity and warm climates fabrics, if
exposed to standing water, can be exposed and develop the growth of mold which can weaken
the fabric and compromise its integrity [12].
Several materials were researched in attempt to find a mesh material which satisfied the
primary design requirements: the strength to withstand high winds, the ability to sustain high
impact and the ability to fold and bend without breaking between cycles of retracting the trusses.
The Incord Company is a provider of safety netting for different applications. Their products
include netting for various fields such as construction, sports use, and even for the home and
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garden. Construction nets are used in high impact situations such as falling equipment or debris
that can occur during a construction accident causing injuries and fatalities. Incord’s products
include highly durable nylon and polypropylene netting. These construction nettings come in
different mesh sizes depending on the application it is used for. This type of netting is considered
strong and can contain different types of mesh such as rope, wire roping, webbing, or even a
combination of all three styles which provides for an even stronger mesh. Figure 9 shows an
image of different mesh sizes available by the Incord Company.
Figure 9: Mesh Sizes Provided By Incord [6]
For this specific project, personnel safety netting and vertical perimeter debris netting
was researched. As the personnel safety netting meets the ANSI A10.11 standards and is treated
to withstand intense wear and tear, it satisfies the required criteria and is a suitable choice for use
in the design. Personnel safety nets are tested to withstand high impact and high loads of 17,500
lbs. This type of netting is also a good option when considering the effects of climate in
conjunction with consumer usage. Some consumers may opt to keep the structure fully erected
for more than a few months at a time. Use of the structure in this matter would require a durable
mesh which could withstand several season and climate changes. The Incord Company provides
netting that is also resistant to UV rays, thereby increasing the material’s life cycle. They also
offer vertical debris netting which is not only durable but it also made of a fire-retardant material
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which can also be used for prevention of wild fires. These nettings comply with the OSHA
regulation and meet the CPAI-84 rules and come in different mesh sizes. These nets also have an
advantage as they are lightweight, thus adding less weight to the entire structure and are easy to
install [6].
Another material that was researched is a fiberglass mesh cloth from Copperstate Roofing
Supply. These are rolls of high strength fiberglass cloth with a small mesh. They are mainly used
for high strength joints, roofing seams, deck seams, tile backing and repairs. This fiberglass mesh
has alkali resistant properties giving it a good resistance to heat. This material can also withstand
intense weather because it has good chemical corrosion resistance. The material has high warp
and weft strength. It can handle high impacts because the stresses caused by high impacts are
equally spread into different directions of the mesh and its polymeric binder coating serves to
provide additional reinforcement. By the ASTMD standards this material has a tensile strength of
85 psi and it is lightweight [4].
Advances in material technology have grown immensely through the years and those
advancements have been implemented in large scale structures and designs. An example of this
can be seen at the Jeddah International Airport in Saudi Arabia, shown in Figure 10. This airport
is home to the world’s largest roof constructed mostly of tensioned fabric.
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Figure 10: Hajj terminal at Jeddah International Airport in Saudi Arabia [5]
Fabric roofs can carry a large amount of loads and even strengthen the structure as the
loads are distributed to a grid structure made of individual threads. Fabrics can hold greater
amounts of tension compared to rigid materials such as steel and under wind loads the curvature
of the fabric helps in the reduction of wind speed. Depending on the application, fabrics can be
loosely or tightly woven to have a grid of different layers of thickness or have a plain weave with
a grid of layers of equal thickness. The most common types of fibers used for tensioned fabric
structures are nylon, polyester, glass and aramids. Nylon has a high strength but due to its lower
modulus of elasticity, it elongates faster than other materials under high load. Polyester on the
other hand is strong but vulnerable to climate. However this can be countered by using various
coatings to prevent degradation. Glass fibers have a high modulus of elasticity and have a high
tensile strength but come with the tradeoffs that glass fibers are brittle in nature. Aramids on the
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other hand are an organic material which have a high modulus of elasticity and are highly
resistant to fractures.
When utilized for architectural structure and design, these materials are covered in
different coatings in order to improve their strength and eliminate their drawbacks.
Polyvinylchloride (PVC) provides a resistance to UV light and is used for nylon and polyester
fabrics. Polytetrafluoroethylene (PTFE), also known as Teflon, is known for its resistance to
moisture and harsh climate thus extending a fabric’s life. The coatings themselves have qualities
such as high strength and fire resistance providing further strength and advances to the fibers.
They are mostly used on fiberglass fibers because the combination of these two creates a stable
material.
Based on the research done on various tensioned fabrics, PTFE, also known as Tefloncoated woven fiberglass, was by far the best option to consider when choosing a suitable fabric
for use in this structure. A company located in New York, Birdair Inc., has been a provider of
PTFE for years and their products have been utilized in various structural projects, large and
small. They supply an extremely durable and weather resistant form of PTFE which boasts an
impressive life cycle of over 30 years. Their product can be utilized in areas plagued with harsh
temperature, withstanding temperatures ranging from as low as -100°F to temperatures as high as
450°F. When used in conjunction with a polytetrafluoroethylene coating, the material becomes
resistant to even ultraviolet radiation. The supplied material by Birdair Inc. is certified by the
American Society for Testing and Materials (ASTM) [2].
A few of the specifications for this material include a tensile strength of 500,000 psi and
a modulus of elasticity of 10.5×106 psi. The fabric has somewhat of an elastic behavior but can
still hold its integrity by not incurring high stress or creep. Its mechanical strength is provided
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by its woven fiberglass membrane, also known as beta glass, which carries maximum flexibility
yet preserves strength. Figure 11 shows Taoguan County Stadium, the largest indoor stadium in
Taiwan. It’s also known as “The Giant Egg” because of its dome structure which consists of a
roof that takes advantage of the PTFE material [2].
Figure 11: Taoguan County Stadium [2]
1.3.7 Introduction to Gears
Since electric motors are to be used in the mechanism used by the dome, it will be
necessary to design a transmission, or gearbox. The transmission will make use of different types
of gears, such as spur and bevel gears. The purpose of the transmission will be to use gear
reduction to reduce the rotational speed of the motors. An engine or motor is set to be an
example of transmission power generated from a source. The main task for such a machine is to
create an output result. The most efficient way of transmitting power is through rotary motion of
a shaft which can be supported by bearings. For a unit to function with specification on output
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torques and different operating speeds it needs to incorporate gears, bearings, pulleys and more.
A design for a system that needs to transmit power as an output, these elements such as gears,
shafts and bearings are key to the selection process.
A gear is a machine part which rotates in order to transmit torque. The gear consists of
teeth or cogs which mesh together in order to transmit the force between each gear. Two or more
gears working together form a transmission which in turn contributes to a gear ratio which is a
big mechanical advantage. Such devices can contribute to speed, magnitude and direction of the
power source.
There are several different types of gears which can be used to transmit power. These
gears will now be examined in further details. Spur gears are gears that have their teeth parallel
to the axis of rotation. They are used to transmit power from one shaft to another parallel shaft.
The smaller gear is referred to as the pinion, while the larger is simply referred to as the gear.
Figure 12 shows an example of a spur gear set.
Figure 12: Spur Gear Set [11]
Bevel gears are used to transmit power between perpendicular shafts. Bevel gears are
useful when the direction of a shaft's rotation needs to be changed. They are usually mounted on
shafts that are 90 degrees apart, but can be designed to work at other angles as well. Just as with
spur gears, the teeth can be straight, as seen in Figure 13, or they can be at an angle.
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Figure 13 : Bevel Gears [11]
1.4 Discussion
The article on Rogers Centre portrays the concept and the complexity of the design. It
also gives a basic checklist for the production of the hurricane protection dome. The article
illustrates the importance of keeping in mind different factors that play a major part in the
building and computational process, such as fatigue, fracture, sliding, structural vibration and
panel deflection. It also demonstrates the mechanism behind the retractable roof, where ideas can
be gathered for different future technologies. Finally, this article provides information about
different materials used for Rogers Centre that can be researched in depth for other future
applications.
University of Phoenix Stadium offers a clue which may answer one of the biggest
questions posed by this project: “How is such a heavy structure going to safely open and close
over a residential home?” By using several small electric motors, this massive structure will be
able to be lifted several feet above ground and deployed over a residential home. The power
required to lift the dome will be distributed over each motor, meaning that the largest motor used
will be less than 1 hp. The calculations for this power requirement can be found in Appendix A.
The use of small electric motors will greatly reduce the final price of the structure.
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2. Project Formulation
2.1 Overview
The goal of this project is to develop a retractable dome that could realistically protect a
home during a hurricane. The dome will be made of a number of trusses forming the frame, and
will be covered by a mesh material. The first step to accomplish this goal is to perform an
analytical analysis of a dome under drag and lift forces. These drag and lift forces will simulate
the force of the hurricane winds. Different ideas and designs will be tested using SolidWorks as
well as COSMOSWorks. Once the best design is chosen, this simulation will be analyzed to
determine the stresses present in the beams. This data will aid in selecting the proper materials to
use for the final design. After selection of the proper materials, the mechanism that will be used
to open and close the retractable dome will be designed. This mechanism will also be designed
using SolidWorks.
Once all simulations are complete, two small scale prototypes will be built, a visual one
and a functional one. The visual prototype will be used to demonstrate the motion of the dome as
it retracts and deploys, while the functional prototype will be subjected to rigorous testing
through the use of an airboat similar to those used in the Everglades. The airboat will be turned
around so that the propeller is facing the prototype. The wind produced by the airboat propeller
will simulate the hurricane force winds that the retractable dome will experience. The purpose of
the prototype testing is to ensure the proper functioning of the design in a real world setting.
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2.2 Project Objectives
The entire objective of this project is summarized below:
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•
Analytical analysis of dome experiencing drag and lift forces
•
Simulation and testing of dome using SolidWorks and CosmosWorks
•
Designing of mechanism used to deploy and retract the dome
•
Testing of functional prototype
•
Building of visual prototype
3. Design Alternatives
3.1 Overview of Conceptual Designs Developed
A dome structure offers the best characteristics when it comes to lifting and drag forces
caused from high velocity winds. This was the main reason for choosing this shape of structure
to protect homes from the destructive winds generated by hurricanes. It would obviously be very
inconvenient to have a fixed dome structure placed permanently over a home. Therefore, it was
decided to make the structure retractable, or rather collapsible, so that it can be stored
underground until it is needed.
Each of the conceptual designs shared the same basic characteristics: several arched
trusses forming a frame with a protective mesh covering the dome. Since these guidelines are
very broad, this made it possible to experiment with many different design configurations until
the most desirable one was chosen. Different materials were tested, such as steel and aluminum.
Perhaps the biggest challenge was finding a way to retract and deploy the entire structure. The
following sections describe several of the original design alternatives.
3.2 Design 1
First, some calculations were made from equations for the dome roofed structure seen in
Figure 14. These calculations can be found in Appendix A. This preliminary analysis made it
possible to determine the lifting and drag forces that would be exerted on the protective dome.
From these values it was possible to roughly determine the force each truss would see, making it
possible to determine the proper I-beam needed for each section.
44 | P a g e
Figure 14: Dome Roofed Structure
Once the dimensions of each truss were determined, a mockup SolidWorks model was
created using structural steel as the material. This model gave a visual representation of the
protective dome, as seen in Figure 15.
Figure 15: Ribbed Structure of Protective Dome
A simulation was then done for the middle truss. Given the fact that this truss will need to
withstand the majority of the forces and that it stands vertically made it the simplest to model. A
sinusoidal lifting force was applied to the top surface of the structure with the assumption that
the greatest lift force is directly between the two ends. Also, a horizontal force was applied to the
45 | P a g e
same surface simulating the direct force and drag effect caused by the wind during a hurricane.
The SolidWorks model of this truss with the appropriate applied forces can be seen in Figure 16.
The results of this preliminary test showed a maximum displacement of about 3.94 in.
Figure 16: Displacement of Middle Truss
There is one major drawback to this design, and that is that when the unit is stored
underground, the trusses will all stack on top of one another since they are all the same size. This
means that a very deep hole will need to be dug underground to be able to house the entire
structure. This could prove to be problematic in some places such as South Florida, where the
natural deposits of limestone make digging fairly difficult. In order to address this problem, a
second design was proposed.
3.3 Design 2
The second proposed design also consisted of seven trusses, but these trusses were of
different sizes. As a result, the trusses would lie side by side when retracted, instead of on top of
each other. Figure 17 shows an image of the second design in its retracted state.
46 | P a g e
Figure 17: Alternate Design of Ribbed Structure – Retracted
Note that this second design would not need to be as deep underground, but the area it
covered around the home would be much wider. This may prove troublesome for neighborhoods
where the lots are smaller and there is less land to work with.
Figure 18 shows this second design in the process of being deployed.
Figure 18: Alternate Design of Ribbed Structure – Being Deployed
47 | P a g e
Finally, Figure 19 shows the second design in its deployed state.
Figure 19: Alternate Design of Ribbed Structure – Deployed
Since the dome in its deployed state would not form a perfect semicircle, as was the case
in the first design, the stresses experienced by the dome would not be symmetrical. This would
need to be taken into consideration in order to ensure that all seven trusses can safely handle the
force of the wind. Also, the area on the ground where the trusses meet is curved. This means that
the retracting mechanism may need to be redesigned since the dome would not be deployed
evenly. The curved joint where the trusses meet may also prove to be a vulnerable spot in the
dome, so this new structure would need to be analyzed thoroughly to ensure safety of the design.
3.4 Design 3
After some research on I-beams, it was clear that constructing trusses out of curved
sections was not an option. Curved sections of I-beam would have to be custom ordered, and
thus would be quite expensive. As a result, it was decided to use a piecewise construction of
straight sections of I-beam to create an arched truss. This piecewise truss will be comprised of
five straight sections of I-beams, four connecting joints and two end linkages that will be used to
48 | P a g e
attach the truss to its individual pivot joint. Figure 20 shows an example of one of these
piecewise trusses.
Figure 20: Piecewise Truss Formed from I-Beams
The pros and cons of the first two designs, symmetrical and concentric arches, were
analyzed to come up with the third design. As was stated before, the symmetrical design would
offer a more predictable profile of the passing wind. The concentric design would greatly
decrease the depth needed to dig into the ground so that the dome may be stored out of sight. The
final decision was made to go with the symmetrical design.
To compensate for the buildup of trusses from having the entire dome retracting to one
side, the dome would have to retract and deploy to both sides of the home, meaning that instead
of having the dome come completely around the home and lock on the ground, it will be
deployed from the two opposite ends and lock to itself where the trusses eventually meet up.
Figure 21 shows a side profile of this piecewise symmetrical dome fully retracted. Figure 22
shows a side profile of the same dome in the process of being deployed.
49 | P a g e
Figure 21: Side Profile of Piecewise Dome – Retracted
Figure 22: Side Profile of Piecewise Dome - Being Deployed
Even though this design is not as low profile as the concentric truss design, it does have
the benefit of having the simplest wind flow over the dome, as in the symmetric truss design,
while reducing the depth needed to dig into the ground.
3.5 Design 4
After studying this third design, a new problem arose. If only seven trusses were used,
there would be a 20 ft span between trusses that would be supported only by the mesh material.
This span was deemed too large, since it left much of the mesh exposed. Also, the mesh was the
50 | P a g e
only support between the trusses, so there was concern with the structure failing if the mesh
should be pierced by flying debris. To address this concern, the number of trusses was increased
from seven to twelve. Ten trusses would rise from the ground and two trusses would fix the
dome to the ground on either side of the home. With this design, the vertical distance from truss
to truss and truss to ground is no more than nine feet. Also, since this design has an even number
of trusses the two leading trusses meet and lock at the middle of the dome. This makes the forces
acting on the couplers symmetrical on either side.
The next change was to the middle section, the two leading trusses. As a result of the
trusses being symmetric, the middle section was making the dome itself too tall. To correct this,
the two leading trusses were made slightly shorter than the other eight by lengthening the Ibeams that lie horizontally over the house. This created a much more desired profile for the
dome to minimize the projected surface area that the wind will be in contact with. Figure 23
shows this new design with the shorter middle trusses, while Figure 24 shows the same design
from a side profile view.
Figure 23: Simulation of Design 4 - Fully Deployed
51 | P a g e
Figure 24: Side Profile of Design 4 - Fully Deployed
3.6 Design 5
Once the force vectors were determined for each truss it was determined that the trusses
would be under multi-directional forces. This was confirmed by the numerical analysis. I-beams
are only designed to endure bending and shear, not torsion. Thus, a new geometry was needed.
The most efficient geometry for a beam experiencing multi-directional forces is a
cylinder. With a cylindrical geometry, each beam within the truss will react the same to a
resultant force regardless of the direction. The truss design was changed from the I-beam
configuration to a round hollow structural section made of high strength steel (HSS). This solved
the issue of large displacements due to torsion in the sections. An example of one of these new
trusses, or tubes, made from cylindrical beams can be seen in Figure 25.
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Figure 25: Piecewise Truss Formed from Circular Tubes
3.7 Final Design
In Design 4, the assumption that there would be multidirectional forces acting on the
trusses was corrected after looking over the ASCE 7-05 standard. Since all loads along the dome
surface are perpendicular, the forces acting on the truss are in the same plane as the truss itself.
As a result, the design was reverted back to the I-beam configuration, which is a much lighter
structure. Figure 26 shows an I-Beam truss used in the Final Design.
Figure 26: I-Beam Truss for Final Design
53 | P a g e
The next change was the number of beams within the truss. In Design 4 there were 5
beams; since a lower profile is a much preferred design, the number was increased to 7 to better
clear the home when being deployed or retracted. The number of trusses was also increased
from 12 to 14. This creates mesh sections with smaller areas thus distributing the overall loads
on the individual trusses.
The structure will be stored about ten feet underneath the ground. Since most single floor
family homes are roughly 20 feet in height, the dome will need a height of 30 feet above the
ground, resulting in a truss 40 feet tall. Through the wind load calculations found in ASCE 7-05,
the necessary I-beams were selected to handle the 150 mph wind from a hurricane. Figure 27
shows a side profile of this new design.
Figure 27: Side Profile of Final Design
Each truss will be have its own pivot point due to the fact that all trusses are identical and
cannot share pivot joints. This resulted in the design of the central hub where all trusses will be
connected to. This hub is approximately 5 feet tall and 8 feet wide. It needs to be extremely
strong since it needs to take all the loads and moments that the entire dome feels. To get the
rigidity required, the hub is constructed of two 3 inch plates and three 1 inch ribs. This of course
54 | P a g e
is not what the actual central hub would be constructed of. In the real world this part would be a
combination of reinforced concrete and the embedded steel needed to construct and hold the
bearings in place. The hub can be seen in Figure 28.
Figure 28: Central Hub
Many different mechanisms have been looked at in order to deploy the dome from a flat
state to the fully deployed. To bring the trusses up, two of the most efficient ways would be by a
pulley system or some other method that pulls or pushes from the very top of the truss. The
pulley system was very attractive because of its mechanical advantage but would greatly
complicate the structure because a truss would still need to get to a vertical position and be rigid
enough to pull up the remaining trusses safely. The next best is a scissor lift mechanism. This
would be the simplest since the mechanism can be assembled off site and brought in ready-to-use
units. In the Final Design, it will be powered by four DC motors per section. A simulation of the
Final Design can be seen in Figure 29.
55 | P a g e
Figure 29: Simulation of Final Design
3.8 Comparison of Different Design Alternatives
The six design alternatives each have their pros and cons. Therefore, it became necessary
to measure each concept against the other to determine which would be the best design for the
hurricane protection dome. Several factors were taken into consideration such as the physical
size of the dome, as well as cost and manufacturability. The ideal choice for the final product
would need to be of reasonable size, low cost and easy manufacturability, among other criteria.
Table 3 shows the most important design criteria considered for this project and how each design
measured up against the others.
Table 3: Comparison of Each Design
Title
Cost
Size
Weight
Complexity
Manufacturability
Total Points
% Assigned
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Concept 1 Concept 2 Concept 3 Concept 4 Concept 5 Final Design
1
1
2
2
2
1
2
3
2
2
2
3
2
3
2
3
3
3
2
1
3
2
2
2
1
1
2
2
2
3
8
9
11
11
11
12
32.00%
36.00%
44.00%
44.00%
44.00%
48.00%
Excellent
Very Good
Good
Fair
Poor
Max # of Points
5
4
3
2
1
25
Of the four concepts developed, the Final Design is obviously the most favorable. While it is
still not a perfect design, it offers the best combination of cost, size, weight, complexity and
manufacturability. While the design has not yet been perfected, the Final Design is the best of the
concepts that have currently been developed. Therefore, this is the concept that will be analyzed
in all simulations and used to build the prototype.
3.9 Power Requirements
In order to minimize the power required to lift the dome, each truss will need to weigh
around 5000 lbs. The height of the dome has been estimated to be 40 ft. The goal for time is to
have the entire system deployed in 20 minutes. The span between each truss has been measured
to be 8.98 ft. This distance was calculated by modeling the dome as a semicircle with radius 40
ft. The circumference of the circle was divided by 14 since there are fourteen sections of mesh.
Htravel =40 ft π
=8.98 ft
14
Since each truss will need to travel the same distance, the only change will be in the
weight of each particular section. This is significant because while the section closest to the
ground will be lifting the weight of the seven trusses above it, the next section will only have to
lift the trusses above it and so on. Therefore, the largest motors will be on the two trusses closest
to the ground. Also, four electric motors will be used in each section to drive the cross beam
mechanism that will lift the trusses into place. Dividing the needed horsepower by 4 will then
give us the individual motor horsepower. Table 4 shows the horsepower requirement for each
section. Since electric motors will be used, there obviously needs to be a backup system in case
power fails during a hurricane. The primary backup system will be a generator which will supply
power to the motors in the case of a power outage. The secondary backup system will be a deep
57 | P a g e
cycle 12 volt battery, so the motors used will need to be 12 volt electric motors. Table 5 shows
the voltage and amperage requirements for each motor as well as the total of all motors.
Table 4: Horsepower Requirement for Each Section
Section
1
2
3
4
5
6
7
H, ft
8.98
8.98
8.98
8.98
8.98
8.98
8.98
Hp
0.71
0.61
0.51
0.41
0.31
0.20
0.10
Hp/Motor Total Hp Needed
0.18
5.71
0.15
KW
0.13
4.20
0.10
0.08
0.05
0.03
Table 5: Voltage Requirement for Each Section
Voltage
Hp
0.25
0.25
0.25
0.25
0.25
0.25
0.25
Total
12
Amps
21
21
21
21
21
21
21
Hp/Section
1
1
1
1
1
1
1
14
Amps
84
84
84
84
84
84
84
1176
Time Hrs
0.33
Amp-Hrs
392.00
Watt-Hrs
4704
3.10 Deploying/Retracting Mechanism
The mechanism which opens and closes the dome is driven by 56 electric motors, none
larger than ¼ hp. Each central section between the trusses is home to four electric motors, one at
each corner. The motors drive a scissor mechanism. This scissor operates in much the same way
as a scissor lift. As the ends of the scissor come together, the scissor itself expands, pushing the
trusses away from one another. Each motor is mounted to the truss and connected to a
transmission. The transmission is responsible for bringing the rotational speed from 1725 rpm,
58 | P a g e
the rated speed of the motors, down to about 20 rpm. The transmission transmits power from
each electric motor to a power screw. Each leg of the scissor is connected to the power screw by
a block which moves along the screw. As the power screw turns, the block translates toward the
center of the scissor, thus causing the dome to deploy. The motors used are reversible 12 volt
electric motors. The fact that they are reversible means they spin in both the clockwise and
counterclockwise directions. This made it possible to design a simple transmission without the
need for a reverse gear. The scissor mechanism is shown in its retracted state in Figure 30 and in
its deployed state in Figure 31.
Figure 30: Scissor Mechanism – Retracted
59 | P a g e
Figure 31: Scissor Mechanism - Deployed
In order to determine the dimensions of the mechanism, the first step was to consider the
relevant known dimensions of the dome. First of all, the scissor will only be along the middle
section of the dome. The span of that middle section when the dome is fully deployed, SD, is 8.9
ft. The span of the middle section when the dome is fully retracted, SR, is desired to be around 1
ft. The length of the middle I-beam of each truss is 18 ft. In order to give some clearance for the
motor and transmission, 1ft of clearance was given on each end. That means that when the dome
is fully retracted, the width of the section in between the legs of the scissor, WR, will be 16 ft.
The nomenclature for each configuration of the scissor mechanism can be seen in Figure 32 and
Figure 33.
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Figure 32: Scissor Nomenclature – Retracted
Figure 33: Scissor Nomenclature - Deployed
The next step was to determine the dimensions of the power screw. It was assumed that
the screw would need to have a large pitch to be able to safely handle the load of each truss.
Table 6 is a reproduction of Table 88-2
2 from Shigley’s Mechanical Engineering Design, 8th
Edition [14].
61 | P a g e
Table 6: Diameters and Area of Unified Screw Threads UNC and UNF
Since a large pitch is required, the largest screw from this table was chosen. This gives
the screw a 1.5 inch major diameter with 6 threads per inch. The pitch is given by taking the
inverse of the threads per inch, meaning that the screw has a pitch of 0.1667 inches or 0.01389
feet. The dimensions of the power screw can be seen in Table 7.
Table 7: Power Screw Dimensions
62 | P a g e
The length of the power screw came from assuming a total time for deployment of 5 minutes per
section. A rotational speed of 20 was assumed for the power screw. This gave the total number
of revolutions as follows,
20 rpm ×5 min=100 rev
Since the axial distance of one revolution is equivalent to the pitch, the total distance
traveled by the block was obtained by multiplying the pitch by the number of revolutions,
.01389 ft ×100 rev=1.389 ft
Since this distance would be traveled by the power screw on each end, the width of the
section in between the legs of the scissor when the dome is fully deployed, WD, would be
16 ft-21.389 ft=13.222 ft
Using the Pythagorean Theorem, the length of one leg of the scissor could be
approximated if the middle section is modeled as a right triangle. If the deployed span SD is one
leg of the triangle and the deployed width WD is the other, one leg of the scissor becomes the
hypotenuse. The leg of the scissor will be referred to as LX, and will be obtained as follows,
LX =WD 2 +SD 2 =(13.222 ft)2 +(8.9 ft)2 =15.94 ft
Since the scissor legs do not change in length, this means that when the dome is retracted
the scissor leg would be shorter than the retracted width WR of 16 ft. If the Pythagorean Theorem
is again used for the retracted configuration, this means that the hypotenuse of the triangle would
be longer than one of the legs. This is clearly not possible, so number of revolutions was reduced
to 96. The total deployment time at 20 rpm now becomes,
96 rev 20 rpm=4.8 min
which is still close to the desired 5 minute deployment time.
The total distance traveled by the block now becomes
63 | P a g e
.01389 ft ×96 rev=1.333 ft
which is the length of the power screw seen in Table #. The deployed with WD becomes
16 ft-21.333 ft=13.333 ft
The length of each scissor leg now becomes
LX =WD 2 +SD 2 =(13.333 ft)2 +(8.9 ft)2 =16.031 ft
Since this value is greater than the retracted width WR of 16 ft, the retracted configuration
can now be modeled using the Pythagorean Theorem. Using the scissor leg LX as the hypotenuse
of the right triangle and the retracted width WR as one of the legs, the other leg of the right
triangle becomes the retracted span, SR. This length can be calculated as follows,
SR =LX 2 -WR 2 =16.0312 -162 =0.994 ft
This is very close to the desired retracted span of 1 ft. Table 8 summarizes the deployed
and retracted dimensions of the middle section, including the length of the scissor legs. These
dimensions are graphically represented in Figure 34 and Figure 35.
Table 8: Dimensions of Each Section in Deployed and Retracted States
Section Dimensions
SD (ft)
8.9
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WD (ft)
13.333
SR (ft)
0.994
WR (ft)
16.000
LX (ft)
16.031
Figure 34
34: Retracted Dimensions of Scissor Mechanism
Figure 35
35: Deployed Dimensions of the Scissor Mechanism
The next step in the process of designing the mechanism was to design the transmission.
As previously stated, the transmission should reduce the rotational speed from 1725 rpm down to
20 rpm. The parameters for design of th
the transmission are shown in Table 9.
Table 9: Parameters for Transmission Design
0.5
Power to be Transmitted (HP)
1725
NIN (rpm)
20
NO UT (rpm)
Opposite
I/O Direction
65 | P a g e
The total gear reduction of the transmission is calculated by dividing the input rotational
speed by the output rotational speed as follows,
Gear Reduction=
1725 rpm
=86.25:1
20 rpm
In order to accomplish this, a transmission was designed using two sets of spur gears and
two sets of bevel gears. The gear reductions are as follows,
Spur Set 1:
2.5:1
Bevel Set 1:
6:1
Spur Set 2:
2:1
Bevel Set 2:
3:1
Thus, the total gear reduction of the transmission is
2.5×6×2×3=90:1
These gear reductions are also referred to as the velocity ratio VR of each gear set. The
gears used were chosen from the Boston Gear Catalog [3]. The number of teeth on each gear can
be seen in Table 10, where NP refers to the number of teeth of the driving gear and NG refers to
the
Table 10: Number of Teeth on Each Gear in Transmission
NP
NG
Spur Gear Set 1 Bevel Gear Set 1 Spur Gear Set 2 Bevel Gear Set 2
18
16
20
15
45
96
40
45
The pages from the Boston Gear Catalog showing the exact specifications of the gears
used can be found in Appendix D. The rotational speed of each gear set is obtained by dividing
the input speed by the gear reduction. Based on the gear reduction for each gear set, the
rotational speeds would be reduced as follows,
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Spur Set 1:
Bevel Set 1:
Spur Set 2:
Bevel Set 2:
1725 rpm
2.5
690 rpm
6
115 rpm
2
57.5 rpm
3
=690 rpm
=115 rpm
=57.5 rpm
=19.17 rpm
This means that the output rotational speed will be 19.17 rpm which is very close to the
desired value of 20 rpm. The data from the Boston Gear Catalog was used in order to determine
the bending and contact wear of all four gear sets. First, Spur Set 1 was tested for bending
failure. The procedure outlined in Figure 14-17 of Shigley’s Mechanical Engineering Design, 8th
Edition was followed to ensure that none of the gears failed. Figure 36 shows this figure as it
appears in Shigley’s textbook. Certain assumptions were made about all the gears used. First, all
gears will be made of Grade 2 steel and be hardened to 350 Brinell. Second, all driving gears,
referred to from here on as pinions, are rated to 1×109 cycles. The driven gears, referred to from
here on simply as gears, are rated to the pinion life cycle divided by the velocity ratio. Finally,
the temperature is assumed to be ambient temperature which is always less than 250°F and the
gears are rated for a reliability of 0.99.
67 | P a g e
Figure 36: Procedure for Spur Gear Bending Analysis
Table 11 shows the data needed to calculate the bending stress of Spur Set 1.
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Table 11: Spur Set 1 Bending Stress Data
σb
Wt (lbf)
40.60
NP
(teeth)
NG
(teeth)
dP (in)
dG (in)
φ (°)
nP (rpm)
nG (rpm)
VR
V (fpm)
YP
YG
Ko
1.250
Kv
1.332
(Ks)P
0.948
18
A
45
0.9
2.25
20
1725
690
2.5
406.44
0.309
0.400
B
Qv
(Ks)G
0.955
Pd (in)
20
(Km)P
1.168
(Km)G
1.162
54.77
Cmc
1
0.91
5
(Cpf)P
(Cpf)G
Cpm
Cma
Ce
0.031
0.025
1.1
0.135
1
0.349
F (in)
0.5
KB
1
(J)P
0.315
A
B
C
0.127
0.0158
-9.30E-05
(J)G
0.390
These values were all obtained using the steps outlined in Figure 14-17 of Shigley’s
textbook. The allowable bending stress for Spur Set 1 was obtained using the procedure outlined
in the same figure of Shigley’s textbook. The data needed to calculate the allowable bending
stress of Spur Set 1 can be seen in Table 12.
Table 12: Spur Set 1 Allowable Bending Stress Data
σb,all
St (psi)
52100
(YN)P
0.862
(YN)G
0.888
KT
1
KR
1
The Brinell hardness value and life cycle of Spur Set 1 is seen in Table 13.
Table 13: Brinell Hardness and Life Cycles for Spur Set 1 Bending
HB
350
LP (cycles) 1.00E+09
LG (cycles) 4.00E+08
The bending stress, allowable bending stress and safety factor of Spur Set 1 are shown in
Table 14.
69 | P a g e
Table 14: Bending Stress, Allowable Bending Stress and Bending Safety Factor for Spur Set 1
(σb)P (psi) 9510.7
(σb)G (psi) 7694.5
(SF)P
(SF)G
(σb,all)P (psi) 44900.1
(σb,all)G (psi) 46248.9
4.72
6.01
The safety factor, or factor of safety, was obtained by dividing the allowable bending
stress by the bending stress as follows,
Factor of Safety=
σb,all
σb
A safety factor greater than 1 is generally regarded as a safe design. Judging from the
safety factors of 4.72 for the pinion and 6.01 for the gear, Spur Set 1 can be assumed to be safely
designed.
Figure 14-18 from Shigley’s book can be seen in Figure 37. This process allows for the
analysis of a spur gear set under contact stress, or wear. This method was used to determine the
safety factor under wear of Spur Set 1.
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Figure 37: Procedure for Spur Gear Wear Analysis
Table 15, Table 16, Table 17, and
Table 18 show the data obtained for a wear analysis of Spur Set 1.
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Table 15: Spur Set 1 Wear Data
σc
Wt (lbf) Cp √(psi)
40.60
2300
NP
18
(teeth)
NG
45
(teeth)
0.9
dP (in)
2.25
dG (in)
20
φ (°)
nP (rpm) 1725
690
nG (rpm)
2.5
VR
V (fpm) 406.44
0.309
YP
0.400
YG
Ko
1.25
Kv
1.332
A
B
Qv
(Ks)P
0.948
(Ks)G
0.955
Pd (in)
20
F (in)
0.5
(Km)P
1.168
54.77
Cmc
1
mN
1
0.91
5
(Cpf)P
(Cpf)G
Cpm
Cma
Ce
0.031
0.025
1.1
0.135
1
mG
2.5
0.349
(Km)G
1.162
Cf
1
A
B
C
I
0.115
0.127
0.016
-9.30E-05
Table 16: Spur Set 1 Allowable Wear Data
σc,all
Sc (psi)
156450
(ZN)P
0.900
(ZN)G
0.919
CH
1
KT
1
KR
1
Table 17: Brinell Hardness and Life Cycles for Spur Set 1 Wear
350
HB
Table 18: Wear, Allowable Wear and Wear Safety Factor for Spur Set 1
(σc)P (psi) 87581.7
(σc)G (psi) 87654.5
(SF)P
(SF)G
(σc,all)P (psi) 140729.1
(σc,all)G (psi) 143726.4
1.61
1.64
The safety factors of 1.61 for the pinion and 1.64 for the gear show that Spur Set 1 will
not fail under contact stress.
72 | P a g e
The next step was to analyze Bevel Set 1 under bending stress and contact stress. Figure
38 shows Figure 15-15 from Shigley’s textbook, which is used to study a bevel gear set under
bending stress. The procedure is similar to the bending stress procedure previously discussed for
spur gear sets.
Figure 38: Procedure for Bevel Gear Bending Analysis
73 | P a g e
Table 19, Table 20, Table 21, and Table 22 show the necessary data for a bending stress
analysis of Bevel Set 1.
Table 19: Bevel Set 1 Bending Stress Data
σb
Wt (lbf)
91.34
Ko
1.25
NP
16
(teeth)
NG
96
(teeth)
1
dP (in)
6
dG (in)
20
φ (°)
690
nP (rpm)
115
nG (rpm)
6
VR
180.64
V (fpm)
Kv
1.222
Ks
0.500
A
54.77
B
Qv
0.91
5
Pd (in)
16
F (in)
0.62
Km
1.001
Kx
1
0.349
Table 20: Bevel Set 1 Allowable Bending Stress Data
σb,all
Sat (psi)
22780
(KL)P
0.862
(KL)G
0.913
KT
1
KR
1
Table 21: Brinell Hardness and Life Cycles for Bevel Set 1 Bending
350
HB
74 | P a g e
(J)P
0.261
(J)G
0.202
(σb)P (psi)
(σb)G (psi)
6909.5
8927.6
(SF)P
(SF)G
(σb,all)P (psi) 19630.8
(σb,all)G (psi) 20800.4
2.84
2.33
Table 22 shows the pinion safety factor of 2.84 and the gear safety factor of 2.33 for
Bevel Set 1. This is proof that Bevel Set 1 will not fail under bending stress. The contact stress
analysis of Bevel Set 1 was carried out following Figure 15-14 from Shigley’s textbook, as
shown in Figure 39.
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Figure 39: Procedure for Bevel Gear Wear Analysis
Table 23, Table 24, Table 25, and
Table 26 show the contact stress data for Bevel Set 1.
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Table 23: Bevel Set 1 Wear Data
σc
91.34
2290
NP
16
(teeth)
NG
96
(teeth)
1
dP (in)
6
dG (in)
20
φ (°)
690
nP (rpm)
115
nG (rpm)
6
VR
V (fpm) 180.64
Ko
1.25
Kv
1.222
A
54.77
B
Qv
0.91
5
Pd (in)
16
F (in)
0.62
Km
1.001
Cs
0.515
0.349
Table 24: Bevel Set 1 Allowable Wear Data
σc,all
Sac (psi)
156820
(CL)P
1.000
(CL)G
1.114
CH
1
KT
1
CR
1
Table 25: Brinell Hardness and Life Cycles for Bevel Set 1 Wear
350
HB
Table 26: Wear, Allowable Wear and Wear Safety Factor for Bevel Set 1
(σc)P (psi) 102450.2
(σc)G (psi) 102450.2
(SF)P
(SF)G
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(σc,all)P (psi) 156839.4
(σc,all)G (psi) 174702.8
1.53
1.71
Cxc
1.5
I
0.087
Judging from the safety factors of 1.53 for the pinion and 1.71 for the gear, Bevel Set 1
will not fail under contact stress.
The next step was to analyze Spur Set 2 and Bevel Set 2. These gear sets were analyzed
by following exactly the same procedure as Spur Set 1 and Bevel Set 1, respectively. The data
obtained from each analysis is seen in the following tables.
Table 27: Spur Set 2 Bending Stress Data
σb
Wt (lbf)
274.02
NP
(teeth)
NG
(teeth)
dP (in)
dG (in)
φ (°)
nP (rpm)
nG (rpm)
VR
V (fpm)
YP
YG
Ko
1.25
Kv
1.129
(Ks)P
1.035
20
A
40
2
4
20
115
57.5
2
60.21
0.322
0.389
B
Qv
(Ks)G
1.040
Pd (in)
10
F (in)
1.25
(Km)P
1.191
(Km)G
1.178
54.77
Cmc
1
0.91
5
(Cpf)P
(Cpf)G
Cpm
Cma
Ce
0.041
0.028
1.1
0.147
1
0.349
KB
1
(J)P
0.328
A
B
C
0.127
0.0158
-9.30E-05
Table 28: Spur Set 2 Allowable Bending Stress Data
σb,all
St (psi)
52100
(YN)P
0.862
(YN)G
0.881
KT
1
KR
1
Table 29: Brinell Hardness and Life Cycles for Spur Set 2 Bending
HB
LP (cycles)
LG (cycles)
78 | P a g e
350
1.00E+09
5.00E+08
(J)G
0.383
Table 30: Bending Stress, Allowable Bending Stress and Bending Safety Factor for Spur Set 2
(σb)P (psi) 11624.4
(σb)G (psi) 9890.1
(σb,all)P (psi) 44900.1
(σb,all)G (psi) 45916.7
3.86
4.64
(SF)P
(SF)G
Table 31: Spur Set 2 Wear Data
σc
274.02
2300
NP
(teeth)
NG
(teeth)
dP (in)
dG (in)
φ (°)
nP (rpm)
nG (rpm)
VR
V (fpm)
YP
YG
Ko
1.25
Kv
1.129
20
A
40
2
4
20
115
57.5
2
60.21
0.322
0.389
B
Qv
(Ks)P
1.035
(Ks)G
1.040
Pd (in)
10
F (in)
1.25
(Km)P
1.191
54.77
Cmc
1
mN
1
0.91
5
(Cpf)P
(Cpf)G
Cpm
Cma
Ce
0.041
0.028
1.1
0.147
1
mG
2
0.349
(Km)G
1.178
Cf
1
A
B
C
0.127
0.0158
-9.30E-05
Table 32: Spur Set 2 Allowable Wear Data
σc,all
Sc (psi)
156450
(ZN)P
0.900
(ZN)G
0.914
CH
1
KT
1
KR
1
Table 33: Brinell Hardness and Life Cycles for Spur Set 2 Wear
350
HB
79 | P a g e
I
0.107
Table 34: Wear, Allowable Wear and Wear Safety Factor for Spur Set 2
(σc)P (psi) 97023.6
(σc)G (psi) 96706.2
(σc,all)P (psi) 140729.1
(σc,all)G (psi) 142990.7
1.45
1.48
(SF)P
(SF)G
Table 35: Bevel Set 2 Bending Stress Data
σb
Wt (lbf)
365.36
NP
(teeth)
NG
(teeth)
dP (in)
dG (in)
φ (°)
nP (rpm)
nG (rpm)
VR
V (fpm)
Ko
1.25
Kv
1.112
Ks
0.529
15
A
54.77
45
3
9
20
57.5
19.2
3
45.16
B
Qv
0.91
5
Pd (in)
5
F (in)
1.32
Km
1.006
Kx
1
0.349
Table 36: Bevel Set 2 Allowable Bending Stress Data
σb,all
Sat (psi)
22780
(KL)P
0.862
(KL)G
0.893
KT
1
KR
1
Table 37: Brinell Hardness and Life Cycles for Bevel Set 2 Bending
350
HB
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(J)P
0.232
(J)G
0.182
(σb)P (psi) 4415.5
(σb)G (psi) 5628.5
(SF)P
(SF)G
(σb,all)P (psi) 19630.8
(σb,all)G (psi) 20339.9
4.45
3.61
Table 39: Bevel Set 2 Wear Data
σc
365.36
2290
NP
(teeth)
NG
(teeth)
dP (in)
dG (in)
φ (°)
nP (rpm)
nG (rpm)
VR
V (fpm)
Ko
1.25
Kv
1.112
15
A
54.77
45
3
9
20
57.5
19.2
3
45.16
B
Qv
0.91
5
Pd (in)
5
F (in)
1.32
Km
1.006
Cs
0.603
0.349
Table 40: Bevel Set 2 Allowable Wear Data
σc,all
Sac (psi)
156820
(CL)P
1.000
(CL)G
1.069
CH
1
KT
1
CR
1
Table 41: Brinell Hardness and Life Cycles for Bevel Set 2 Wear
350
HB
81 | P a g e
Cxc
1.5
I
0.074
Table 42: Wear, Allowable Wear and Wear Safety Factor for Bevel Set 2
(σc)P (psi) 90899.8
(σc)G (psi) 90899.8
(SF)P
(SF)G
(σc,all)P (psi) 156839.4
(σc,all)G (psi) 167562.9
1.73
1.84
After examining these tables, it is clear that both Spur Set 2 and Bevel Set 2 will safely
handle the applied bending stress and contact stress.
A simulation of the final transmission design in represented in Figure 40 and Figure 41.
Figure 40: Simulation of Transmission - Isometric View
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Figure 41: Simulation of Transmission - Rear View
The exact dimensions of all gears and shafts used in the transmission can be found in
Appendix D.
3.10.1 Revision to Deploying/Retracting Mechanism
After considering the weight of the trusses that would need to be supported by the power
screw, it was determined that the diameter of the power screw was too small at only 1.5 inches.
The diameter would need to be much larger, which means that the pitch must also be much larger
so that the power screw’s thread will be wide enough to be able to safely handle the weight of
the trusses. Also, in order to keep the deployed and retracted dimensions of the dome the same as
those seen in the previous section, the rotational speed of the power screw would need to be
much slower. A diameter of 4 inches was assumed for the power screw with a pitch of 2 inches.
It was determined that the optimal rotational speed would be 1.6 rpm. After making these
changes it was possible for the deployed and retracted dimensions of the dome to remain the
same as those seen in the previous section. The calculations are exactly the same as those
previously carried out, but the only new parameters are a 4 inch power screw diameter, 0.5
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threads per inch, a pitch of 2 inches and a rotational speed of 1.6 rpm. The revised results are
shown in Table 43, Table 44 and Table 45.
Table 43: Revised Power Screw Dimensions
Power Screw
-1
Diameter (in) Threads/Inch (in )
4
0.5
Pitch (in)
2
Pitch (ft) Length (ft)
0.1667
1.333
Table 44: Revised Output Rotational Speed, Deploying Time and Revolutions of Power Screw
Speed (rpm)
1.6
Time (min)
5.00
Revolutions
8
Table 45: Revised Dimensions of Each Section in Deployed and Retracted States
Section Dimensions
SD (ft)
8.9
WD (ft)
13.333
SR (ft)
0.994
WR (ft)
16.000
LX (ft)
16.031
The transmission, while accurate and safe for an output rotational speed of 20 rpm, will
obviously not work for this new output speed of 1.6 rpm. Future work on the project would be to
design a transmission which will reduce the 1725 rpm input rotational speed down to a 1.6 rpm
rotational output speed. The transmission will be redesigned following the same procedures
discussed earlier.
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4. Project Management
4.1 Overview
In order to complete the project by the given deadline, it became necessary to divide the
tasks evenly among each team member. The first step was to complete a literature survey. This
included researching different categories of hurricanes, the damage caused by hurricanes, current
technology available to protect against hurricanes, and any structures that would give ideas for a
better form of hurricane protection, such as the modern stadiums previously discussed.
Once the literature survey was completed, calculations were performed to determine the
dimensions for the dome. The next step was to decide upon the most effective way to incorporate
a retractable dome over a residential home. It was decided that the best way to do this would be
to form the frame of the dome using a high strength metal, and to cover this frame with a mesh.
This design was tested using SolidWorks until a proper material and geometry for the trusses
was chosen. After deciding upon the entire structure, the weight of the structure was used to
design a mechanism which would need to be able to lift the dome. This resulted in the current
configuration using several small electric motors.
After deciding upon a final design for the entire dome, it became necessary to build a
prototype. Research was done to determine the best materials to use in order to keep costs down,
but at the same time to obtain accurate results. It was determined that the prototype could be
constructed using mostly common materials that could be found at the local hardware store. This
made it much easier to build the prototype, since it was not necessary to deal with vendors and
ordering parts. Ordering parts and waiting for them to arrive may have delayed construction of
the prototype. The prototype made it possible to demonstrate that the entire structure could
deploy and retract in a real world environment. After it was determined that the structure would
85 | P a g e
be feasible for application on a full scale home, the final step of the project was to complete the
report and prepare the PowerPoint slides for presentation to the Industrial Advisory Board. The
progress of the entire project was tracked using tthe Gantt chart in Table 46.
Table 46: Gantt Chart
Each team member’s progress was tracked individually and is presented in Table 47.
Table 47:: Total Proj
Project Hours Spent by Each Team Member
Description
Jason Barrocas Kevin Hernandez Tanisha Richard
Senior Project Organization - In Class
20
20
20
Literature Survey
15
15
30
Poster
4
4
10
Structure and Frame Ideas
40
70
35
Researching & Contacting Companies
10
15
22
Mechanism Ideas
40
15
10
Calculations
40
90
30
Report
70
45
65
Total Prototype Hours
29
29
26
Presentation
6
6
12
Sum of Total Hours
274
309
260
4.2 Organization of Work and Timeline (Timeline for Senior Design
Organization and Senior Design Time Frame)
4.2.1 Month of November 2009
This month’s tasks include
included finishing a rough draft within the first week of November,
Novemb
consisting of 25% of the report. Specified tasks for each member consist
consisted of Kevin Hernandez
finishing up the Solidworks drawings with the results from Cosmo
CosmosWorks.
Works. Another task was for
86 | P a g e
Tanisha Richard to finish calculations for the different concepts, including the velocity pressure,
density pressure, the beams used and the initial cost. Tasks for Jason Barrocas included gathering
information on the structural design concepts and working on the specific parts of the final
report.
4.2.2 Month of December 2009
This month’s tasks consisted of finishing up most of the final report, including all written
parts of the report and beginning research on materials for the prototype. All three members
researched companies that provide the materials needed for the prototype. Also, these companies
pricing information was compared in order to find a suitable price.
4.2.3 Month of January 2010
This month’s tasks were to go back to the report and add information about the materials
and any future calculations done for the project. Another task was to start gathering the materials
for construction of the prototype. Around this time the report was shown to Dr. Wu for any
suggestions and corrections.
4.2.4 Month of February/March 2010
The main objectives accomplished during these months were to finish building the
prototype and start experimenting with a high velocity fan to test the strength of the structure.
Experiment briefs and calculations were obtained and included in the report. Another important
task was to start on the PowerPoint presentation for the final presentation in April.
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4.2.5 Month of April 2010
The full report and PowerPoint presentation were finalized. The team as a whole
practiced the presentation several times before presenting to the Industrial Advisory Board on
April 14th, 2010.
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5. Engineering Design and Analysis
5.1 Analytical Analysis and Structural Design of Design 4
The calculations below are based on a dome roofed building with a 100 ft diameter base.
The side walls are elevated to the height of 20 ft and the dome itself a height of 30 ft above the
side walls, resulting in a total height of 50ft.
Computation of Velocity Pressures
qz =0.00256Kz Kzt Kd V2 I (psf)
where
Kz
= Value obtained from Table 6-3 of the standard, Case 1 for C&C
and Case 2 for MWFRS
Kzt = 1.0 for homogeneous topography
Kd
= 0.95 for round tanks and similar structures (see Table 6-4 of the standard)
V
= 105 mph
I
= 1.15 for Category III classification (Table 6-1)
qz = 0.0025Kz 1.00.951052 (1.15)
qz = 30.8 Kz
(psf)
Values for can be obtained from Table 48 as it shows the value for different
heights and different cases.
Table 48: qz Velocity Pressure
MWFRS
Height (ft)
0 - 15
Eave Height = 20
Top of the dome =
50
89 | P a g e
C&C
kz
qz (psf)
kz
qz (psf)
0.85
0.9
26.2
27.2
0.85
0.9
26.2
27.2
1.09
33.6
1.09
33.6
Computation of Density Pressures
p = qG - (G )
where
q
= 33.6 psf
G
= 0.85, the gust factor for rigid structures
Cp
= External pressure coefficient
qi
= q h for all surfaces because the building is enclosed
GCpi = ±0.18, the internal pressure coefficient for enclosed buildings
p = 33.6(0.85)Cp - 33.6(±0.18)
p = 28.6Cp ±6.1
To calculate the drag forces following equation is used:
F = qz GCf Af
where
qz
= q at the centroid, mid length of the wall 10 ft
q
= 26.2 psf
G
= 0.85, the gust effect factor for rigid structures
Af
= 100ft x 20 ft = 2,000 sf
Gf
= 0.5
F = 26.20.850.5(2,000)
F = 22,270 lb
Wind Speed (Mph)
Drag Force (lb)
Lift Force (lb)
-------------------------------------------------------------------------------------------------105
22,270
11,135
150
44,000
22,000
-------------------------------------------------------------------------------------------------Additional calculations can be found in Appendix A.
90 | P a g e
After, viewing a scaled experiment on a simple dome shape covered with a mesh
material, it was evident that the force from the weight of the wind will be the largest contributor
to the forces acting on the dome. With this information the forces were calculated for each
section of mesh and then translated as the forces acting on each individual HSS section.
To calculate the wind load on each section of mesh, the projected surface area of the
section was determined by the prescribed configuration of the twelve truss design from both the
side and front of the dome. From there the force was calculated for a sustained 155 mph wind.
After finding the forces on the mesh sections, the resultant force acting on the individual beams
can be derived.
Table 49: Top Mesh
Perpendicular
Top Mesh
Section
1
2
3
4
5
Width (ft)
21
21
21
21
30
Height (ft)
6.0
9.0
9.1
8.7
0.5
2
Area (ft )
126
189
192
183
16
Pressure (psf)
61.5
61.5
61.5
61.5
61.5
Sum
Max
Force (lbf)
7749.5
11598.4
11792.2
11249.7
965.0
43354.8
11792.2
Table 49 is a sample of the wind load calculations. Here the force is generated for the top
mesh section between each truss from the ground to the middle truss (1 to 5). From this the total
force on the top beams is known.
Table 50: Weight of the Beams
Top Beam
1
2
3
4
5
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Weight (lbm)
9674.0
11695.3
11520.9
6107.3
6378.6
The same process was used for the middle and bottom sections in both the perpendicular
and parallel directions. The next step is to determine the maximum moment created by these
forces to select the correct outer diameter and wall thickness for a specific factor of safety (FOS).
In calculating the maximum moment some assumptions were made. First, the force from
the mesh sections on the beam is evenly distributed and secondly, the beam was simply
supported.
Table 51: Calculated for Perpendicular Sections
Perpendicular
3
Top
1
2
3
4
F (lb)
9674
11695
11521
6107
L (in)
252
252
252
252
w (lb/in)
38.39
46.41
45.72
24.24
M (in-lb)
304730
368402
362909
192381
s (in )
72.55
87.71
86.41
45.81
5
6379
360
17.72
287036
68.34
Once those two assumptions were made, the equation for the maximum moment was as
follows
wL2
M=
8
where
w = distributed load
L = length of the beam.
Now the modulus S can be determined from the moment divided by the allowable stress,
which is the yield stress of the material divided by the FOS.
S=
92 | P a g e
M
σy
A FOS of ten was used to determine the allowable stress. Materials that are under
consideration are the ASTM A500 grade B steel and the 6061-T6 aluminum alloy. Both
materials share the same yield stress, 42 Ksi.
S values are gained for the two directions and the larger of the two are grouped together
and averaged per: top, middle and bottom sections. Table 52 shows the greatest averaged value
needed for a FOS of about 10. With this knowledge, a tube geometry is generated to satisfy the
needed second moment of area.
Table 52: Max S
3
Max S (in )
#
1
2
3
4
Top
72.55
87.71
86.41
45.81
5 68.34
Ave 72.16
Middle
37.47
50.07
56.41
63.26
Bottom
4.62
18.73
39.01
49.88
47.32
50.91
52.65
32.98
OD (in)
11
ID (in)
9
Thickness (in)
1
2
Area (in )
31.44
The resultant geometry of the tube is an outer diameter of 11 inches with the wall
thickness of 1 inch. With this geometry, the minimum FOS is 8.23 on any beam in the structure
at a sustained wind speed of 155 mph. The minimum FOS at a wind speed of 175 mph is 6.45.
Table 53: Factor of Safety at 155 mph
Factor of Safety @ 155 mph
#
Top Middle Bottom
9.95
19.26
156.34
1
8.23
14.41
38.52
2
8.35
12.79
18.50
3
11.41
14.47
4 15.75
15.25
13.71
5 10.56
Min
93 | P a g e
8.23
#
Top Middle Bottom
7.80
15.11
122.64
1
6.45
11.31
30.22
2
6.55
10.04
14.51
3
8.95
11.35
4 12.36
8.28
11.96
10.75
5
Min
6.45
5.2
Major Components of Design 4
The main components of the structure are its twelve arched trusses. These trusses will be
made of steel, since it offers the best combination of strength and affordability. Once the dome is
deployed over the home, the entire frame will be covered by a mesh material. The exact material
of the mesh has yet to be determined, but the best material studied has been
Polytetrafluoroethylene (PTFE), the same material used in the roof of University of Phoenix
Stadium as previously discussed. The material should be strong enough to withstand hurricane
force winds, but it should also be somewhat flexible so that it will not buckle under the pressure
of the storm. This fabric has an extremely high yield strength, it is lightweight, and it allows light
to pass through so the home inside would not be in complete darkness.
Perhaps the most important component of the structure will be the mechanism which will
cause the dome to retract and deploy. The mechanism will be similar to those found in
retractable stadium roofs. Steel is the first choice for the gears to be used, but as further testing is
carried out the material of the mechanism can be changed. There will also be some sort of a
backup system, in case the primary system fails. The plan is to make communication with the
primary system electronic, so that the user will just have to push a button for the dome to deploy.
Obviously there is a concern with power outages during a hurricane, so if power to the primary
94 | P a g e
system is lost, the secondary system should still be operational. For this reason, the plans for the
backup system are to have it powered by its own generator, or to possibly have some sort of
battery backup system. A grid made up of about 10 individual 12 V batteries similar to those
found in most cars should supply enough power to operate the small electric motors. The motors
will be connected to the primary system by connecting to the power of the house. Additionally, if
the power should fail, the motors should switch to battery power so that the entire system will
remain electronic even during a power outage.
5.3
Simulations of Design 5
To verify the basic hand calculations of the S value with a FOS, the finite element
analysis program CosmosWorks was used to simulate various loading conditions. The
verification test was done on a cylindrical pipe. This length of pipe had the same S value that a
particular beam needed to reach a safety factor of 10. The pipe was simply supported and loaded
with a uniform load along the entirety of its length. When simulated with CosmosWorks the
same factor of safety was generated. This verified that our hand calculations were correct.
95 | P a g e
Figure 42: Displacement of Simply Supported Pipe
Figure 43: Factor of Safety of Simply Supported Pipe
At first, the approach to calculating the loads caused by the wind was strictly from a
physics standpoint. Based on the density of the air and the speed you have the velocity pressure,
multiply that with the projected area normal to the wind and the drag coefficient of a sphere and
96 | P a g e
you now have the load on that particular mesh section. Then, assuming that the load on the beam
in between any two meshes was the sum of the vectors that each mesh was normal too, resulted
in beam members undergoing torsion and large deflections.
Figure 44: von Mises Stress of Tube Truss
97 | P a g e
Figure 45: Displacement of Tube Truss
To counter these multidirectional forces it was decided to go with a hollow round section.
With this geometry the direction of the force would not change the amount of deflection. The
down side was that the trusses were now reaching the 8000 pound mark and was still not rigid
enough.
After going over the ACSE 7-05 on how the loads are distributed over a dome, it was
clear that the surface of the dome experiences a combination of internal and external pressures.
Meaning that all loads are perpendicular to the surface, with this new in site we went back to the
I-beam configuration.
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Figure 46: Factor of Safety of Tube Truss
5.4
Analytical Analysis and Structural Design of Final Design
5.4.1 Wind Loads Calculation
To calculate the wind loads generated on the outer surface of the dome the American
Society of Civil Engineers (ASCE) standard 7-05 is used; titled “Minimum Design Loads for
Buildings and Other Structures”. Chapter six of the ASCE 7-05 covers in detail the analytical
procedure in order to determine the design pressures that a building will need to withstand.
The first step is to define the building classification; this is based on occupancy and a
hazard to human life. Since this structure will be directly over and near other residential homes
this represents a “Substantial hazard to human life in the event of failure” and therefore is
classified as a category III structure.
The next classification is the enclosure level which consists of: open, partially enclosed
and enclosed. Buildings that are “open” have more than 80% of the envelope exposed to the
outside on each wall. Partially open buildings are defined as any one wall’s openings exceed the
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total area of openings on all other walls by 10%. Since neither one describes the dome being
designed in this project, it is then considered to be an “enclosed” structure.
The final classification is on how exposure the structure is. This is based on the surface
roughness of the surrounding environment labeled: B, C and D. Surface roughness B is for urban
and suburban areas, wooded or closely spaced single-family homes or larger buildings.
Roughness C is for open land with scattered obstructions less than 30 feet in height; including
grasslands and all water surfaces in hurricane prone regions. Category D, unobstructed areas and
water surfaces outside hurricane zones as in: salt flats and smooth mud flats. Since this structure
is meant to be used to protect residential homes from hurricane winds and due to its size the most
likely location in south Florida would be the more wooded areas where the homes have more
land surrounding them. This would give the structure the exposure category B.
Now that the structure has been defined, we determine the basic wind speed, V. This is
done by the use of a map that has plotted wind speeds based on three second gusts in miles per
hour (mph) at 33 feet above the ground, south Florida is rated at 150 mph. This basic wind
speed will be used in determining the velocity pressures along the surface of the dome. The
velocity pressures are adjusted by K factors accounting for all surrounding environments that
affect the wind.
qz = 0.00256Kz Kzt Kd V2 I ( lb⁄ft2 )
The velocity pressure exposure coefficient Kz is based on the total height of the structure
above the ground and the exposure category. At a height of 30 feet and exposure category B the
coefficient Kz is 0.7. Topographic factor K zt is for any wind speed-up effects caused by hills,
ridges and escarpments. Since this dome structure is intended for Florida the fact or K zt = 1.0.
The directionality factor Kd acts as a shape factor and since the structure is a dome Kd = 0.95.
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Lastly the importance factor I of the standard is defined by the structure category in and the basic
wind speed. Being in an area where the basic wind speed is greater than 100 mph and a category
III structure, I = 1.15, this gives a velocity pressure of qz = 44.05 psf.
Now that the velocity pressure is calculated the sum of the external and internal pressures
along the dome can be determined by the following equation:
p = qz GCp -qh GCpi psf
The external pressure coefficient Cp , found in Table 55 is determined by ratios of dome
height to diameter (f/D) and height of the base off the ground to diameter (hD/D). With a dome
height of 30 feet and an average diameter of 75 feet at ground level gives a ratio of f/D = 0.4;
since the dome starts underground, hD = 0 giving a ratio of hD/D = 0. With these two ratios we
get the three values: A, B, C. Point A is where the wind first makes contact with the dome.
Point B is directly in the center and point C at the end where the wind meets with the ground
once again, interpolating all points in between. The product of this external pressure factor with
the gust factor G = 0.85, and the velocity pressure produces the external pressure distribution
along the surface of the dome.
Table 55: External Pressure Factor
External Pressure Factor
Cp
0.65
-1
0
A
B
C
The internal pressure factor is based on the exposure classification B, giving us GCpi =
±0.18 in Table 56 and an internal pressure of 6.46 pound per square inch (psf).
Table 56: Internal Pressure
Internal Pressure Factor
Internal Pressure
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GCpi (+/-)
q(GCpi) (+/-)
0.18
6.46
psf
The design pressures are the sum of the external and internal pressure at any given point
along the dome that creates the highest absolute value, critical load.
Table 57: Design Pressure
Location (ft)
A
B
C
0.00
6.42
12.83
19.25
25.67
32.08
38.50
44.92
51.33
57.75
64.17
70.58
77.00
Cp
0.65
0.38
0.10
-0.18
-0.45
-0.73
-1.00
-0.83
-0.67
-0.50
-0.33
-0.17
0.00
External Pressure (psf) Design Pressure (psf)
24.95
14.40
3.84
-6.72
-17.27
-27.83
-38.39
-31.99
-25.59
-19.19
-12.80
-6.40
0.00
31.41
20.85
10.30
-13.17
-23.73
-34.29
-44.84
-38.45
-32.05
-25.65
-19.25
-12.85
-6.46
With the design pressures known the process to calculate the minimum design loads on
the beams can begin. To start with, there must be a labeling system for the mesh sections. The
meshes are labeled 1 to 7, 1being the mesh section that is attached to the beam closest to the
ground and 7 being the top most mesh sections. Also, the “sections” are labeled as the span in
between the trusses following the same logic as the meshes, 1 being the closest to the ground and
7 at the top.
In order to apply the correct design pressures to each individual mesh their location along
the dome in the direction of the wind and whether that particular mesh is above or below the
ground, based on centroid of the mesh. Next, the load is calculated as a uniform distribution in
pound per foot on each mesh based on the area of the mesh and the length of the beam it is
connected to.
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Table 58: Head on Wind
Mesh Section Height (ft)
4
Windward
3
Location (ft) Design Pressure (psf) Load (lb/ft) Mmax (lb-in) S (in )
1
-5.53
-1.25
2
3.19
0.74
3
4
5
6
7
11.26
18.25
23.84
27.73
29.74
4.62
10.19
17.17
25.23
33.94
0.00
0.00
0.00
30.19
265.96
152450.83
10.16
23.82
14.65
-5.58
-23.01
-37.35
209.79
129.05
-49.13
-202.66
-328.99
120250.26
73972.72
-28164.37
-116167.57
-188581.82
8.02
4.93
-1.88
-7.74
-12.57
From the “Height” column in Table 58, you see that mesh number 4 in section 1 has a
negative height, this means that this mesh underneath the ground and is not subject to direct wind
pressure. Although it will experience internal pressures, this is negligible due to the fact that we
are designing from the most critical loading.
The loading on the meshes are then used in determining the loads that the beams, that
they are connected to, will experience as a result. The load on either side of any beam is
averaged and assuming a uniform distribution the maximum moment is obtained. I-beam
selection is based on the maximum moment that they can withstand; this is the value “S”, which
is the second moment of area divided by one half of the beams height. Using the yield stress of
the I-beams material, we define this S value as the maximum moment divided by the allowable
stress.
In finding the smallest S value possible for each beam the largest loads were gathered
from both the head on and side wind directions. This resulted with the I-beam selection of:
W12x26 for beam 4, W12x22 for beams 3 and 2, and W12x16 for beam 1.
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Table 59: Minimum Possible Beam Geometry
4
Windward
3
1
-5.53
-1.25
2
3.19
0.74
3
4
5
6
7
11.26
18.25
23.84
27.73
29.74
4.62
10.19
17.17
25.23
33.94
0.00
0.00
0.00
30.19
265.96
152450.83
10.16
23.82
14.65
-5.58
-23.01
-37.35
209.79
129.05
-49.13
-202.66
-328.99
120250.26
73972.72
-28164.37
-116167.57
-188581.82
8.02
4.93
-1.88
-7.74
-12.57
5.4.2 Simulations of Final Design
With the ASCE 7-05 standard, critical loads per beams were calculated and simulated.
Since the trusses are made up of seven sections and only supported at the end joints it loses its
rigidity. Trial and Error was now the approach in creating a more rigid structure. The final truss
configuration is made up of W12 I-beam ranging from 26 to 19 pounds per foot; if this was a
static structure with rigid supports the trusses would weight about 2200 pounds. Yet, with this
structure the truss has to be its own support. To correct this lack of support a 1 by 3 inch steel
plate is welded to the bottom of the entire truss. This, plus a few adjustments for hot spots solved
the deflection and stress levels, yet after all adjustments were made the trusses weighed
approximately 5200 pounds.
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Figure 47: Joint of Final Design
Figure 48: Deformation of Truss #2 in Final Design
Figure 48 shows truss number 2, second from the floor, under the loading conditions of a
head on wind. This is the most critical loading under a positive external pressure. The maximum
deflection was 1.25 inches, also under this loading the truss had a FOS = 2.7.
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Figure 49: Factor of Safety of Truss #2 in Final Design
Figure 50: von Mises Stress of Truss #2 in Final Design
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Figure 51: Deformation of Truss #7 in Final Design
For the head on wind condition, the 7th truss seen in Figure 51 was under the greatest
loads. It had a maximum deflection of 1.78 inches and FOS = 1.8.
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The side wind condition was a different case altogether. Unlike in the head on case where
the external pressures on a truss were all negative minus for the second and third trusses, the side
wind gave all trusses the same worst possible loading case. In this loading case the first three
beams along the truss experience positive pressures while the rest are under negative pressure.
All adjustments for rigidity were made under this type of loading.
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Figure 54: Displacement of Truss #3 in Final Design
This truss had a maximum deflection of 2.91 inches under the side wind loading. This
resulted in a FOS = 1.2 .
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Next was the bolt that would act as the pivot for each truss. Based on a shear stress of
21ksi and the total moment under worst case loading plus the truss weight the static safety factor
and fatigue safety factor are calculated with the diameter as the variable. The minimum diameter
need was 5 inches. CosmosWorks verified this with a FOS = 1.1 and a maximum deflection of
9.44×10-3 inches.
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Figure 57: Displacement of Bolt under Shear
Figure 58: Factor of Safety of Bolt under Shear
5.4.3 Cost Analysis of Final Design
To determine the economic feasibility of this final design, the material costs needed to be
studied. First, most of the dome is made of steel so the price of steel was obtained. From
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speaking with several manufacturers, the wholesale price of steel was estimated to be around
$0.45/lb. Next, the cost of the mesh was determined. From speaking with companies such as
Incord, it became clear than any sort of mesh large strong enough to withstand impact and in
such quantity to cover this large dome would not be able to be purchased for less than $10,000.
The cost of the electric motors was obtained from Northern Tool and Equipment which sells
similar electric motors for around $250. These prices alone, not considering the cost of the
transmission and battery grid, were enough to determine that the project was not economically
feasible. A breakdown of the cost estimate can be seen in Table 60.
Table 60: Cost Estimate of Full Scale Design
Item #
1
2
3
4
5
Description
Total Steel Cost (I-Beams,pivots, joints and others)
Mesh Material/Fabric
Bolts, nuts - Miscellaneous Cost
Concrete and Foundation
Electric Motors
Labor Estimated Cost
Total Cost Estimate
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Cost
Quantity Total Cost
$0.45/lb 75,000 lbs $33,750
--$10,000
--$2,000
--$2,000
$250
56
$14,000
Same as Materials
$61,750
$123,500
6 Prototype Construction
6.1
Description of Prototypes
In order to demonstrate the features of the finished design, two prototypes were
constructed; each with a different function. The designs of these prototypes are based on similar
concepts that were described within the actual project details. One of the prototypes represents
the visual aspect of the design, scaled down to 26.6% or 1:45 of the original design dimensions
of the structure. This prototype also demonstrates a visual of the closing and opening of the
structure. The secondary prototype is the functional prototype which was constructed to perform
tests.
6.2
Visual Prototype
For the visual prototype, wood was the main material used to construct the foundation of
the model. Two wood boards were purchased one to provide the base of the structure which is
placed to show the trusses to be underground and other to provide the base for the house. This
model consists of ten trusses each with a height of 11 inches. Each truss is made up of seven
sections similar to the original design. These trusses are connected to a piece that represents the
pivot point and has allowable space within each truss to move on its path The gear box kit was
purchased to represent the mechanism of deploying and retracting of the structure. The electric
motor used runs at 9000 revolutions per minute but for the prototype requirements was reduced
to 3 revolutions per minute with the help of a gear reduction unit. The gear reduction allows the
structure to deploy and retract within 8 to 10 seconds. The electric motor was attached to the
ends of the top two trusses that meet at the highest point when deployed. The links between each
truss were constructed to represent the concept of the mechanism from the original design,
although the actual design is different. A different design for the mechanism is substituted for the
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one of the original used on the prototype due to its small scale and can’t be used to show the
complexity of the original designed concept. As the top trusses are ran by the motor it drives the
other trusses as they are pulled upwards by means of the links. To represent the mesh material
for the prototype a netting fabric called tulle is used and is attached to the joints that attach the
seven sections of the truss together.
Table 61 shows the materials used for the prototype and the quantities used. Error!
Reference source not found.
Table 61 : Materials Used for the Visual Prototype
Materials Used
3/16" Thick x 1/2" Wide x 24" Long Basswood Strip
Elmer's, 16 oz Carpenters Glue
Tulle Fabric
Gear Box Kits
Rust-Oleum 12oz. Satin Granite Spray Paint
Rust-Oleum 12oz. Meadow Green Spray Paint
24" x 24" Wood Boards
Other Materials Used : Nails, tape, paint and screws
Quantity
15
1
2
3
1
1
2
6.2.1 Visual Prototype – Process for Construction
1. One of the 24” 24” wood boards was chosen to be the bottom of the structure and
was painted white.
2. The strips of basswood were cut down to different sizes for each section as they were
scaled down from the original design sections.
i. Section 1 - 4.68 inches (corresponding to the length of 18 ft) with an
angle of 20° on one end and straight edge on the other end
ii. Section 2 - 3.90 inches (corresponding to the length of 15 ft) with an
angle of 12° on one end and 20° on the other end
iii. Section 3 - 4.16 inches (corresponding to the length of 16 ft) with an
angle of 10° on one end and 12° on the other end
iv. Section 4 - 4.42 inches (corresponding to the length of 17 ft) with an
angle of 10° on each ends
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Figure 59 : Sections for Trusses
3. Different sections were joined by the means of carpenter’s glue and were stapled to
ensure a stronger bond.
Figure 60: Single Truss
4. Holes were drilled on each of the ends of the trusses for the connections to the pivot
point.
5. Four pieces were cut out of a wooden block to re
represent
present the pivot points.
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Figure 61: Pivot Point with Trusses
6. Five holes were then drilled on these blocks where the ends of the trusses are attached
with nails.
7. Four small piece of wood are cut and added parallel to the top tr
trusses
usses where the shafts
for the gears (motor) will be attached because it requires an offset distance.
8. The gear set and the motor are then attached to the top truss allowing space for the
shaft to rotate.
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Figure 62: Gear Set/ Motor Used
9. More strips of basswood were cut for the construction of the links.
10. Two links were then connected from each truss to another by pieces of tape allowing
for smoother movement.
11. Next step was to attach everything to the base of the structure, theref
therefore
ore the ends of
the pivot point and the motor were glued to the base
12. The other 24 x 24 wood board was cut to the shape the trusses traced above, as they
would look underground
13. It was then painted green and placed on top and attached to a wood block beneath
beneat it.
14. The last step in the construction of this prototype was to add the tulle fabric, it was
glued on to each truss by the connections of the section joints
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6.2.2 Hours Put In for Visual Prototype
Table 62 shows the dates for the construction of the prototype,, including the hours spend
on the specific days. The sum of hours that were required to complete the project is listed to be
83 hours.
Table 62: Prototype Labor Hours
Days Met
1
2
3
4
5
Date
Members Present Hours Put In Sum of Hours
3/20/2010
3
6
18
18
3/27/2010
3
6
14
3/28/2010
2
7
18
4/10/2010
3
6
15
4/11/2010
3
5
Total Hours - Including Each Member
83
Figure 63
63: Kevin Cutting a Truss for the Visual Prototype
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Figure 64:: Jason and Tanisha Gluing Trusses Together for the Visual Prototype
Figure 65: Construction of Visual Prototype
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Figure 66: Kevin Cutting Base of Visual Prototype
Figure 67: Aerial View of Construction of Visual Prototype
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Figure 68: Trusses and Links of Visual Prototype
Figure 69: Unfinishied Visual Protoype Deployed
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Figure 70: Kevin and Unfinished Visual Prototype
Figure 71: Unfinished Visual Prototype Mounted to Base
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Figure 72: Circuit that will Power the Visual Prototype
Figure 73: Pushbutton Switchbox Mounted to Base
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6.2.3 Visual Prototype Cost Analysis
Table 63 shows the items that were purchased in order to construct the visual prototype.
It gives a brief description of the products and also the name of the suppliers that the items were
purchased from. The total cost of each item is stated for those items that had more than one
quantity. The sum of all the items costs was calculated and is shown in the end as the Total
material cost for the prototype which came out to be $67.70
Table 63: Material Cost for Prototype
Item #
1
2
3
4
5
6
9
6.3
Description
Suppliers
3/16" Thick x 1/2" Wide x 24" Long Basswood Strip
Pearl
Elmer's, 16 oz Carpenters Glue
Pearl
Tulle Fabric
Pearl
Gear Box Kits
Pearl
Rust-Oleum 12oz. Satin Granite Spray Paint
Home Depot
Rust-Oleum 12oz. Meadow Green Spray Paint
Home Depot
24" x 24" Wood Boards
Home Depot
Total Material Cost for Prototype
Cost Quantity Total Cost
$1.20
15
$18.00
$3.81
1
$3.81
$0.75
2
$1.50
$8.99
3
$26.97
$3.44
1
$3.44
$3.44
1
$3.44
$5.27
2
$10.54
$67.70
Functional Prototype
The secondary functional prototype was built mainly to perform tests and analyzing the
behavior of the structure under high winds. The dome is made of twelve trusses and is scaled
down from the final design dimensions. The height of the entire dome is 40 inches high and the
diameter of the dome is 75 inches. The prototype’s frame is constructed out of steel and is
covered with a mesh material. Since the mesh/fabric material is undergoing research performed
under Dr. Wu’s PhD students, a different material was used. The choice of mesh material for this
prototype has similar properties to a mesh material or fabric that will be used for the final design.
Therefore, the testing and the results that are achieved from this prototype can be considered to
be a guide on understanding how the house reacts in hurricane conditions. The mesh material is
bolted to the sections of the trusses allowing a better hold for the fabric. The prototype is placed
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over a small wooden model of a home which is situated on a stand and held down tight by means
of chains for extra protection. An airboat is used for testing this prototype therefore the platform
is placed about the same level with the airboat propeller to make testing easier.
Figure 74: Final Functional Prototype
6.3.1 Testing on Functional Prototype
As previously stated, the main testing done on the prototype is performed using an
airboat. Airboats produce very powerful winds during operation, reaching speeds of over 80
mph. These winds are used to simulate a scaled down hurricane. The airboat was placed
stationary, remaining on its trailer, and the propeller was aimed at the platform where the model
house and prototype dome was located. At the beginning of the testing the airboat was turned on
and the wind speed produced by the air boat propeller was measured. In order to simulate
Category 5 hurricane winds the highest setting for the air boat was used producing 80 mph
winds, which is a reasonable amount for the scaled down prototype size.
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Figure 75: Air Boat Used for Testing
6.3.2 Results from Testing on Functional Prototype
The test conducted was to have the airboat facing the front of the dome. The airboat was
set to full power and the wind was measured to be 80 mph. A sensor was placed inside the dome
to measure the wind speed inside the dome. Using the difference between the inside and outside
wind speeds, the percentage of wind speed difference could be scaled up to approximate what the
wind speed would be on the inside of the dome during hurricane force winds. Figure 76 shows
the dome during testing. The results from this test are presented in Table 64.
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Figure 76 : Functional Prototype during Testing – Front
Table 64: Functional Prototype Test Results
Table 64 shows that the mesh was responsible for approximately a 68% reduction in wind
speed. This is very close to the 60% wind speed reduction which was estimated at the beginning
of the project.
Table 65 shows some wind speeds that can be attributed to full scale Category 5 hurricanes, as
well as what the wind speed would be inside the dome. This was done by assuming a 68% wind
reduction as in the experiment, so the inside wind speed is 32% of the outside wind speed.
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Table 65: Assumed Full Scale Wind Reduction
What this means is that, as previously stated, homes built to code in Miami-Dade County
should be able to safely handle wind speeds of up to 100 mph. If the full sized dome works the
same way as this functional prototype, the home inside would only be experiencing wind speeds
of 81.6 mph for an outside wind speed of more than 255 mph which is stronger than any
Category 5 hurricane.
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7 Conclusion
7.1
Conclusion and Discussion
The overall purpose of this project was to design a well rounded protection dome for a
home which provides superior protection against the destructive winds produced by major
hurricanes. At the same time, it was also required to remain both cost and time efficient. The
possibility of building a retractable hurricane protection dome is well within reach as there is
sufficient technology available to design a complete protection system. The retractable domes
used in many sports arenas inspired many of the ideas and designs used in this project. This
dome would eliminate the various steps that are taken in order to completely secure a home in
the event of a hurricane, such as securing the windows, doors, walls, roofing systems and the
garage. The choice of a mesh material would benefit the dome by reducing the wind loads on the
structure and providing structural support to the foundation. An additional advantage to the mesh
material is that it can be used under different conditions such as in the prevention of wild fires
due to the fire resistant properties of some fabrics.
One of the initial challenges faced in the creation of the system was designing a product
that would not only provide effective protection against hurricane force winds, but would be
reasonably priced. The destructive hurricanes of the past have shown time and time again that the
underprivileged are the ones who suffer from the havoc a hurricane brings. Cost was a primary
factor in the design and marketing of this product. If the system provides protection at an
exorbitant cost, then the goal of providing an affordable system for the average-income
consumer has failed. However, if the system can be constructed in a cost-efficient manner that
does not compromise the integrity, strength and efficient operation of the design, then it will
revolutionize home hurricane protection. The system will also provide the added benefit of not
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only protecting the home against the forces of hurricane winds but against other natural disasters
such as tornados and wildfires. This can be accomplished based on mesh and fabric research,
thus increasing the design’s overall usefulness and marketability.
Based on the experience from two semesters of research and gathering ideas from all
directions, it can be concluded that this project requires an intense amount of knowledge in a
civil engineering background. Several road blocks were encountered as it required learning a
new discipline within just a few short months. Apart from the educational aspect of this project,
the real world feasibility of these large complex structures depends on years of research,
designing and analyzing. These projects also require a team of engineers from various fields such
as mechanical, civil, structural and even electrical. The project was carried out to the fullest
extent given the complex nature of the problem, and it opened doors to more learning
experiences. Several designs can be proposed and only one may have a possibility of working.
Perhaps the most challenging part of this project was building a structure with trusses formed
from I-beams that need to not only stabilize the effect of the wind, but also maintain their own
support as well.
Given the current work done on this project, it can be determined that such a structure
would not be economically feasible. The cost of the steel trusses, the concrete required to form
the foundation, the electric motors, the transmissions, the mesh material, and every other
component involved in the structure puts this dome out of reach for most average-income
families. The idea itself is not impossible, but there remains a great deal of work to be done to
make such a large scale, hurricane resistant dome available for the average consumer. With
continued future work, however, there is no doubt that such a structure will someday come to
fruition.
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http://www.birdair.com/tensileArchitecture/PTFE.aspx, 2010.
3. Boston Gear, “Boston Gear Catalog,” Gears, Couplings and Shaft Accessories,
http://www.bostongear.com, 2006.
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2004.
http://weather.about.com/b/2008/10/08/tropical-storm-marco-and-hurricane-norbert.htm,
2008.
http://www.incord.com/pdf/constcatalog.pdf, 2010
6. Incord, Inc., “Debris and Personnel Safety Net Systems for Construction,”
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8. Leo O' Connor, “Toronto SkyDome: The House that Engineers Built,” Mechanical
Engineering, Vol. 114, No. 10, pp. 54-57, 1992.
9. Mark Baker, “The Impact of Impact-Resistant Windows,” Smarter Buildings, pp. 52-53,
2009.
10. Mark C. Waggoner, “The Retractable Roof and Movable Field at University of Phoenix
Stadium, Arizona,” Structural Engineering International, Vol. 18, No. 1, pp. 11-14, 2008.
131 | P a g e
11. Oliver Boyd, "Some Types of Gears," The Science of Gears, SCDC Publications
http://www.fi.edu/time/Journey/Time/Escapements/geartypes.html, 1993.
12. R.E. Shaeffer (Editor), Task Committee on Tensioned Fabric Structures (Corporate Author),
“Tensioned Fabric Structures: A Practical Introduction,” American Society of Civil
Engineers, 1996.
13. Rachelle Oblack, “Tropical Storm Marco and Hurricane Norbert,” About.com: Weather,
14. Richard Budynas, and Keith Nisbett, “Shigley’s Mechanical Engineering Design”, 8th
Edition, McGraw-Hill, 2006.
15. Stephen P. Leatherman, Arindam Gan Chowdhury, and Carolyn J. Robertson, “Wall of Wind
Full-Scale Destructive Testing of Coastal Houses and Hurricane Damage Mitigation,”
16. Storm Shutters.com, “Shutter Pricing and Ordering,” AGI Group, Inc.,
http://www.stormshutters.com/, 2010.
17. United States Adjusters, “Roof Damage,” United States Adjusters Public Adjusters,
http://houstonhurricaneclaim.com/Roof_Damage.html, 2008.
18. Various, “Is Your Home Protected From Hurricane Disaster: A Homeowner’s Guide to
Hurricane Retrofit,” Institute for Business & Home Safety, pp. 1-23, 2002.
19. Verl E. Kahle, “Failure Analysis of Three Reconditioned Rail Car Couplers,” ASM
International, Vol. 6, No. 4, pp. 23-28, 2006.
132 | P a g e
Appendices
Appendix A: Detailed Raw Design Calculations and Analysis
A.1
Design 1 Calculations
1. The Cross-section Dimension of Stringer #4 – The Center Stringer
Assuming 40% of the Total Lift Force
The design of the dome with seven stringers (#1 - 7), 30° apart, as illustrated in Figure 2
and the center stringer take 40% of the lift force. For a 150 Mph hurricane, lift force at the center
stringer is calculated as follows
22,000 lb × 0.4 = 8,800 lb
For estimating the dimension of the I-beam, the arch of the stringer can be said to be L=
75ft. This arch can be observed as a sinusoidal as shown in the Figure 77.
Figure 77: Distributed Force in Stringer 4
Using the total lift force to be 8,800 lb and the equation of the sinusoidal distribution
load, the actual distributed load on the beam
Flift = 0 w0 sin
L
Flift = -
133 | P a g e
πx
L
dx
w0 L
πx
cos
π
L
From 0 to LFlift =
2 w0 L
=8,800 ; solving for wo
π
( L being 75 ft in this case)
wo = 184.3
lb
ft
and
wx = 184.3 sin
πx
L
The maximum moment M takes place at the mid section of the beam therefore,
wo L2
M max =
π2
184.3 ×752
M max =
π2
M max = 105,042 ft-lb
For this design, 2024 Aluminum is assumed for calculation therefore the yield strength
for Aluminum is used, σy 11 ksi
σy =
M
S
= 11,000 psi
To find the elastic section modulus S,
S=
I
M_max
=
C
11,000
Figure 78 shows the stringer design of the dome and lift forces corresponding to the
stringers:
134 | P a g e
Figure 78: Stringer Design of the Dome
For Stringer#4 – Center experiences 40% of the total lift force
11,000 x 0.4 = 4,400 lb
Figure 79: Stringer 4
For Stringer#3 and #5 – experiences 25% of the total lift force
11,000 x 0.25 = 2,750 lb
Similar steps are taking to derive the elastic module for the #3 and #5 stringers
Wo = 57.6 lb/ft
Mmax = 32,825 lb-ft
S = 35.8 in3
135 | P a g e
Figure 80: Stringers 3 and 5
For Stringer#2 and #6 – experiences 5% of the total lift force
11,000 x 0.05 = 550 lb
Similar steps are taking to derive the elastic module for the #3 and #5 stringers
Wo= 11.52 lb-ft
Mmax= 6,565 lb-ft
S = 7.16 in3
Figure 81: Stringers 2 and 6
136 | P a g e
A.2
Design 4 Calculations
The tables below are detailed versions of the tables discussed above throughout the report
for the calculations performed on the top mesh, middle mesh and the bottom mesh with
perpendicular wind force. For the following calculations wind speed of 155 mph is being used.
Table 66: Top Mesh
Top Mesh
Section
1
2
3
4
5
Width (ft)
21
21
21
21
30
Height (ft)
6.0
9.0
9.1
8.7
0.5
2
Area (ft )
126
189
192
183
16
Pressure (psf)
61.5
61.5
61.5
61.5
61.5
Sum
Max
Force (lbf)
7749.5
11598.4
11792.2
11249.7
965.0
43354.8
11792.2
The following calculations are details on the formulation performed to achieve the
results in Table 12:
Weight and height for the meshes are given therefore the area can be calculated by the
following equation:
For example for top mesh - Section 1
Width × Height = Area
21 ft 6 ft 126 ft 2
Pressure used for each section is calculated by using the specified wind speed and the
following equation
0.00256 × (Specified Wind Speed (mph) )2 = Wind Pressure psf
0.00256 × 155 2 mph = 61.504 psf
137 | P a g e
Using the results obtained from the pressure and area calculation, the force applied to the
individual section of the mesh size can be calculated
Pressure × Area = Force
61.504 psf × 126 ft2 = 7749.504 lbf
Table 67: Middle Mesh & Bottom Mesh
Middle Mesh
Section
1
2
3
4
5
2
Angle (rad)
0.698
0.698
0.698
0.698
0.698
Projected Area (ft )
58.8
111.8
114.1
109.9
34.2
2
Angle(rad)
1.396
1.396
1.396
1.396
1.396
Projected Area (ft )
0
12.4
12.5
12.4
7.2
Area (ft )
76.8
146.0
148.9
143.4
44.7
2
Pressure (psf)
61.5
61.5
61.5
61.5
61.5
Sum
Max
Force (lbf)
3616.1
6876.4
7016.8
6757.7
2104.6
52743.1
7016.8
2
Pressure (psf)
61.5
61.5
61.5
61.5
61.5
Sum
Max
Total
Force (lbf)
0
762.9
765.8
763.6
443.2
5471.0
765.8
101568.9
Bottom Mesh
Section
1
2
3
4
5
Area (ft )
71.4
71.7
71.5
41.5
For the middle mesh and the bottom mesh the area was calculated differently because of
the limited specifications such as the height, therefore angles were taken into consideration.
Using the following equations the projected area was calculated
Area × Cos angle = projected area
76.75 × cos 0.698132 = 58.79 ft2
The calculations for the pressure and the force were calculated in the same manner with
the equations used for the top mesh.
138 | P a g e
The table below includes similar calculations done on each part of the sections for the top
mesh from section 1 through 5. From then the sum of forces can be added and results in
43354.78 lbf, which acts on the mesh.
Top Beam
1
2
3
4
5
Weight (lbm)
9674.0
11695.3
11520.9
6107.3
6378.6
Middle Beam
1
2
3
4
5
Bottom Beam
1
2
3
4
5
Weight (lbm)
381.4
764.3
764.7
603.4
443.2
Weight (lbm)
5246.2
6946.6
6887.2
4431.1
4560.7
For tables above the following calculations were carried out:
The forces on the beams are calculated by taking the average of the forces between the
sections of meshes 1 and 2.
For top beam:
Force on section 1 + Force on section 2
2
= Force on the section 1 Beam
7749.504+11598.42
= 9673.96 lb
2
Similar steps are followed as for the results achieved for the forces on each section of the
beam
139 | P a g e
Table 68: Calculations for Perpendicular Beams
Perpendicular
140 | P a g e
3
Top
1
2
3
4
F (lb)
9674
11695
11521
6107
L (in)
252
252
252
252
w (lb/in)
38.39
46.41
45.72
24.24
M (in-lb)
304730
368402
362909
192381
s (in )
72.55
87.71
86.41
45.81
5
6379
360
17.72
287036
68.34
Middle
1
2
3
4
5
F (lb)
5246.23
6946.61
6887.24
4431.15
4560.71
L (in)
240
240
240
240
168
w (lb/in)
21.86
28.94
28.70
18.46
27.15
M (in-lb)
157386.98
208398.17
206617.23
132934.40
95774.96
s (in )
37.47
49.62
49.19
31.65
22.80
Bottom
1
2
3
4
5
F (lb)
381.44
764.32
764.69
603.42
443.22
L (in)
240
240
240
240
240
w (lb/in)
1.59
3.18
3.19
2.51
1.85
M (in-lb)
11443.15
22929.55
22940.76
18102.70
13296.67
s (in )
2.72
5.46
5.46
4.31
3.17
3
3
Table 69: Calculations for Parallel Beams
Parallel
3
Middle
1
2
3
4
5
F (lb)
4753.77
7010.37
7897.31
8856.26
9464.54
L (in)
240
240
240
240
168
w (lb/in)
19.81
29.21
32.91
36.90
56.34
M (in-lb)
142613.01
210311.05
236919.41
265687.81
198755.35
s (in )
33.96
50.07
56.41
63.26
47.32
Bottom
1
2
3
4
5
F (lb)
2584.87
5245.03
6068.60
6983.06
7371.16
L (in)
60
120
216
240
240
w (lb/in)
43.08
43.71
28.10
29.10
30.71
M (in-lb)
19386.56
78675.41
163852.31
209491.90
221134.67
s (in )
4.62
18.73
39.01
49.88
52.65
3
The following calculations are based on Table 15.
The forces and the length are carried on from the previous table and the value for the
distributed load can be calculated by the following equation
π × Force (lb)
lb
=w
2 × Lenght (in)
in
π × 9673.96 lb
lb
= 38.39
2 × 252 in
in
The moment acting on the beam is calculated using the results achieved for the even
distribution load and the length specified
lb
w in ×L2 in
= M (in-lb)
π2
38.39 × 2522
= 304729.872 (in-lb)
π2
141 | P a g e
The modulus of elasticity can be calculated by using the allowable stress which is
calculated using the yield strength and the factor of safety by the following equation:
yield strength
= Allowable Stress
FOS
4.2 ×104 psi
= 4.02 ×103 psi
10
Using this allowable stress, the modulus of elasticity is calculated below
M (in‐lb)
= s (in3 )
allowable stress (psi)
304429.87 (in‐lb)
3
4.02 ×10 psi
=72.55 (in3 )
The same procedure was carried out for the top, middle and the bottom beams including
both perpendicular and parallel forces.
Table 70: Max S
3
Max S (in )
#
1
2
3
4
Top
72.55
87.71
86.41
45.81
5 68.34
Ave 72.16
Middle
37.47
50.07
56.41
63.26
Bottom
4.62
18.73
39.01
49.88
47.32
50.91
52.65
32.98
Table 16 illustrates the maximum modulus of elasticity for each sections corresponding
to the top, middle and the bottom beam. The average shown above is calculated by adding all
the values and dividing them by the number of sections.
72.55+87.71+86.41+45.81+68.34
= 72.16
5
Same procedure is followed for each beam section.
142 | P a g e
#
Top Middle Bottom
9.95
19.26
156.34
1
8.23
14.41
38.52
2
8.35
12.79
18.50
3
11.41
14.47
4 15.75
15.25
13.71
5 10.56
Min
8.23
Following calculations are for the Table 17; the factor of safety can be calculated by the
following equation:
Result for top beam for the section 1:
yield strenght × ave Max s
= FOS
Max Moment
4.2 × 104 × 91.99
= 9.95
388443.38
Similar calculations were followed for the middle and the bottom beams related to their
sections as shown in Table 18.
#
Top Middle Bottom
7.80
15.11
122.64
1
6.45
11.31
30.22
2
6.55
10.04
14.51
3
8.95
11.35
4 12.36
8.28
11.96
10.75
5
Min
6.45
143 | P a g e
A.3
Final Design Calculation
Table 73 represents the constants and values that are used to calculated the wind factors
in order to study the external and design pressure
Table 73: List of Constants
Category
Enclosure Classification
Exposure
Height
Basic Wind speed
Wind Directional
Importance
H
V
Kd
I
Velocity Pressure Exposure
Kz
Topographic Factor
Gust Effect Factor
Kzt
G
qH
qh
Velocity Pressure
External Pressure Factor
Cp
Internal Pressure Factor
Internal Pressure
GCpi (+/-)
q(GCpi) (+/-)
3
Enclosed
B
30
150
0.95
1.15
0.76
0.7
0.57
1
0.87
44.05
35.87
0.65
-1
0
0.18
6.46
ft
mph
@40ft
@30ft
@15ft
psf
psf
A
B
C
psf
The table above consists of one value that was calculated for qh, the following equation is
used:
qh = 0.00256 × Kz × Kzt × Kd × I × V
35.87 = 0.00256 × 0.57 × 0.95 × 1.15 × 150
Velocity pressure equation relates the velocity pressure exposure, the topographic factor,
the wind directional factor, the importance factor and the basic wind speed.
144 | P a g e
The table below represents the calculation done for the external pressure (psf) and the
design pressure (psf)
Table 74: Head on Wind – Design Pressure
Head On Wind
MWFRS
Location (ft)
Cp
0.00
6.42
12.83
19.25
25.67
32.08
38.50
44.92
51.33
57.75
64.17
70.58
77.00
A
B
C
0.65
0.38
0.10
-0.18
-0.45
-0.73
-1.00
-0.83
-0.67
-0.50
-0.33
-0.17
0.00
24.95
14.40
3.84
-6.72
-17.27
-27.83
-38.39
-31.99
-25.59
-19.19
-12.80
-6.40
0.00
31.41
20.85
10.30
-13.17
-23.73
-34.29
-44.84
-38.45
-32.05
-25.65
-19.25
-12.85
-6.46
The external pressure can be calculated by the following equation,
External pressure psf qH G Cp
For example:
24.95psf 44.05 0.87 0.65 speci8ic for section A
The following results were calculated in the similar manner for each section (A, B and C)
using their specific values for external pressure factor. This equation relates the velocity
pressure, gust effect factor and the external pressure factor.
The design pressure is calculated by using an if statement depending on the results
achieved for external pressure
1. If external pressure is > 0 then following equation is used
145 | P a g e
Design pressurepsf = External pressure psf + Internal pressure
For example:
31.41 (psf) = 24.95(psf) + 6.46 (psf)
2. If external pressure is < 0 then following equation is used
Design pressurepsf = External pressure psf - Internal pressure
For example:
-13.17 (psf) = - 6.72(psf) - 6.46 (psf)
Similar procedure were followed for the side wind analysis shown in the table below
Table 75: Side Wind – Design Pressure
Side Wind
MWFRS
Location (ft)
A
B
C
146 | P a g e
0.00
6.06
12.13
18.19
24.25
30.31
36.38
42.44
48.50
54.56
60.63
66.69
72.75
Cp
0.68
0.39
0.13
-0.13
-0.39
-0.65
-1.00
-0.90
-0.74
-0.58
-0.43
-0.27
0.00
26.10
14.98
5.00
-4.97
-14.94
-24.92
-38.39
-34.46
-28.42
-22.37
-16.33
-10.28
0.00
32.56
21.43
11.46
-11.43
-21.40
-31.37
-44.84
-40.92
-34.87
-28.83
-22.78
-16.74
-6.46
The Table below shows the values for mesh area calculations
Table 76: Mesh Area
Length (ft)
18.68
17.92
17.35
19.55
1
2
3
4
Mesh Areas (ft^2)
19.43
105.05
143.21
172.20
The table below is used to calculate the allowable strength using the factor of safety with
the relation of yield strength
Allowable Yield Strenght
FOS
1.50E+04 =
6.00E+04
4
Table 77: Factor of Safety/Allowable Streght
Yield strength
FOS
Allowable
6.00E+04 psi
4
1.50E+04 psi
The table below shows the calculations done on the effects of wind as it hit head on
(Windward). The main parts of the calculations from this table are the Loads, Mmax and the S
value.
The load values are calculated by the following equation
Design Pressure(psf) × Mesh Area for the section(ft 2 )
Load (lb/ft) =
Length of the section ft
For example for Mesh 4, section 2
265.96 (lb/ft) =
30.19 (psf) × 172.20(ft2 )
19.55 (ft)
The Mmax values are calculated by the following equation
147 | P a g e
Load (lb/ft) × Lenght 2 (ft 2 )
Mmax (lb-in) = B
C 12
8
265.96 (lb/ft) × 19.552 (ft 2 )
152450.83 (lb-in) = B
C 12
8
To calculate the S (in3) following equation was used
S (in3) =
152450.83(lb-in)
Allowable psi
10.16 (in3) =
148 | P a g e
Mmax(lb-in)
1.50E+04psi
Table 78: Head on Wind Calculations
Head On Wind
4
3
2
1
Windward
3
1
-5.53
-1.25
2
3.19
0.74
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
11.26
18.25
23.84
27.73
29.74
-5.88
2.16
9.58
16.03
21.18
24.76
26.61
-7.06
-1.34
3.95
8.55
12.22
14.77
16.09
-7.94
-3.94
-0.23
2.98
5.55
7.34
8.26
4.62
10.19
17.17
25.23
33.94
1.55
3.40
7.00
12.18
18.68
26.16
34.27
12.09
13.41
15.98
19.69
24.33
29.68
35.47
28.97
29.45
30.38
31.71
33.39
35.32
37.41
149 | P a g e
0.00
0.00
0.00
30.19
265.96
152450.83
10.16
23.82
14.65
-5.58
-23.01
-37.35
209.79
129.05
-49.13
-202.66
-328.99
0.00
213.02
164.10
93.80
-91.41
-202.57
-312.58
0.00
0.00
-7.19
-86.56
-126.19
-177.80
-233.66
0.00
0.00
0.00
-35.04
-37.91
-41.21
-44.79
120250.26
73972.72
-28164.37
-116167.57
-188581.82
0.00
96223.64
74126.88
42370.20
-41292.72
-91501.87
-141194.15
0.00
0.00
-3464.11
-41697.94
-60792.36
-85653.61
-112564.04
0.00
0.00
0.00
-18331.83
-19832.03
-21561.23
-23432.96
8.02
4.93
-1.88
-7.74
-12.57
0.00
6.41
4.94
2.82
-2.75
-6.10
-9.41
0.00
0.00
-0.23
-2.78
-4.05
-5.71
-7.50
0.00
0.00
0.00
-1.22
-1.32
-1.44
-1.56
25.81
19.89
11.37
-11.08
-24.55
-37.88
-1.23
-14.77
-21.53
-30.33
-39.86
-33.68
-36.43
-39.61
-43.05
The table below represents the calculation based on the wind hitting the structure head on
although calculated on a different location (Leeward)
Head On Wind
Leeward
3
78.25
150 | P a g e
0.00
0.00
0.00
76.26
-7.19
-63.36
-36319.21
-2.42
72.38
66.81
59.83
51.77
43.06
75.45
73.60
70.00
64.82
58.32
50.84
42.73
64.91
63.59
61.02
57.31
52.67
47.32
41.53
48.03
47.55
46.62
45.29
43.61
41.68
39.59
-11.06
-16.61
-23.58
-31.61
-40.30
-97.41
-146.34
-207.70
-278.44
-355.00
0.00
-81.27
-110.91
-153.52
-206.96
-268.56
-335.23
0.00
0.00
-131.26
-152.90
-180.03
-211.31
-245.16
0.00
0.00
0.00
-39.62
-41.35
-43.36
-45.53
-55834.71
-83881.71
-119057.54
-159603.03
-203490.46
0.00
-36708.14
-50100.11
-69346.58
-93485.03
-121308.26
-151424.79
0.00
0.00
-63232.85
-73655.61
-86727.58
-101795.01
-118104.36
0.00
0.00
0.00
-20726.72
-21635.93
-22683.93
-23818.31
-3.72
-5.59
-7.94
-10.64
-13.57
0.00
-2.45
-3.34
-4.62
-6.23
-8.09
-10.09
0.00
0.00
-4.22
-4.91
-5.78
-6.79
-7.87
0.00
0.00
0.00
-1.38
-1.44
-1.51
-1.59
-9.85
-13.44
-18.60
-25.08
-32.54
-40.62
-22.39
-26.08
-30.71
-36.05
-41.83
-38.08
-39.75
-41.67
-43.75
The tables below shows the calculations done on the effects of wind as the structure are
being hit sideways. (Windward)
Table 79: Side Wind Calculations
Side Wind
4
3
2
1
Windward
3
1
-5.53
36.38
2
3.19
36.38
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
11.26
18.25
23.84
27.73
29.74
-5.88
2.16
9.58
16.03
21.18
24.76
26.61
-7.06
-1.34
3.95
8.55
12.22
14.77
16.09
-7.94
-3.94
-0.23
2.98
5.55
7.34
8.26
36.38
36.38
36.38
36.38
36.38
19.50
19.50
19.50
19.50
19.50
19.50
19.50
6.78
6.78
6.78
6.78
6.78
6.78
6.78
1.45
1.45
1.45
1.45
1.45
1.45
1.45
151 | P a g e
0.00
0.00
0.00
-44.84
-395.02
-226426.83
-15.10
-44.84
-44.84
-44.84
-44.84
-44.84
-395.02
-395.02
-395.02
-395.02
-395.02
0.00
-112.11
-112.11
-112.11
-112.11
-112.11
-112.11
0.00
0.00
118.72
118.72
118.72
118.72
118.72
0.00
0.00
0.00
31.11
31.11
31.11
31.11
-226426.83
-226426.83
-226426.83
-226426.83
-226426.83
0.00
-50642.73
-50642.73
-50642.73
-50642.73
-50642.73
-50642.73
0.00
0.00
57192.20
57192.20
57192.20
57192.20
57192.20
0.00
0.00
0.00
16275.76
16275.76
16275.76
16275.76
-15.10
-15.10
-15.10
-15.10
-15.10
0.00
-3.38
-3.38
-3.38
-3.38
-3.38
-3.38
0.00
0.00
3.81
3.81
3.81
3.81
3.81
0.00
0.00
0.00
1.09
1.09
1.09
1.09
-13.59
-13.59
-13.59
-13.59
-13.59
-13.59
20.25
20.25
20.25
20.25
20.25
29.90
29.90
29.90
29.90
The table below represents the calculation based on the wind hitting the structure
sideways although calculated on a different location (Leeward)
Side Wind
Leeward
3
36.38
152 | P a g e
0.00
0.00
0.00
36.38
-44.84
-395.02
-226426.83
-15.10
36.38
36.38
36.38
36.38
36.38
53.25
53.25
53.25
53.25
53.25
53.25
53.25
65.97
65.97
65.97
65.97
65.97
65.97
65.97
71.30
71.30
71.30
71.30
71.30
71.30
71.30
-44.84
-44.84
-44.84
-44.84
-44.84
-395.02
-395.02
-395.02
-395.02
-395.02
0.00
-248.70
-248.70
-248.70
-248.70
-248.70
-248.70
0.00
0.00
-102.31
-102.31
-102.31
-102.31
-102.31
0.00
0.00
0.00
-9.28
-9.28
-9.28
-9.28
-226426.83
-226426.83
-226426.83
-226426.83
-226426.83
0.00
-112341.52
-112341.52
-112341.52
-112341.52
-112341.52
-112341.52
0.00
0.00
-49286.30
-49286.30
-49286.30
-49286.30
-49286.30
0.00
0.00
0.00
-4853.36
-4853.36
-4853.36
-4853.36
-15.10
-15.10
-15.10
-15.10
-15.10
0.00
-7.49
-7.49
-7.49
-7.49
-7.49
-7.49
0.00
0.00
-3.29
-3.29
-3.29
-3.29
-3.29
0.00
0.00
0.00
-0.32
-0.32
-0.32
-0.32
-30.14
-30.14
-30.14
-30.14
-30.14
-30.14
-17.45
-17.45
-17.45
-17.45
-17.45
-8.92
-8.92
-8.92
-8.92
The table below represents the max loads similar to the mesh sectional considered for all
the cases.
Beam
4
3
2
1
153 | P a g e
Section
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
Max Load
(lb)
4159.29
-12355.12
-12355.12
-12355.12
-12355.12
-12355.12
-12355.12
2957.31
-6905.36
-6905.36
-6905.36
-6905.36
-8382.11
-8993.28
0.00
-1881.84
-4073.87
-4773.09
-5610.53
-6544.32
-7029.69
0.00
0.00
-591.90
-1209.77
-1265.66
-1327.98
-1349.37
M (lb-in)
S (in^3)
Smax
112300.72
-333588.16
-333588.16
-333588.16
-333588.16
-333588.16
-333588.16
79847.50
-186444.63
-186444.63
-186444.63
-186444.63
-226317.09
-242818.63
0.00
-50809.75
-109994.54
-128873.36
-151484.32
-176696.64
-189801.75
0.00
0.00
-15981.34
-32663.72
-34172.82
-35855.55
-36433.09
7.49
22.24
22.24
22.24
22.24
22.24
22.24
5.32
12.43
12.43
12.43
12.43
15.09
16.19
0.00
3.39
7.33
8.59
10.10
11.78
12.65
0.00
0.00
1.07
2.18
2.28
2.39
2.43
22.24
16.19
12.65
2.43
Appendix B: Engineering Drawings
Piecewise Truss Drawing
154 | P a g e
21 ft Aluminum Tube Drawing
155 | P a g e
20 ft Aluminum Tube Drawing
156 | P a g e
Top Joint Drawing
157 | P a g e
Middle Joint Drawing
158 | P a g e
End Joint Drawing
159 | P a g e
Appendix C: Wind Loads
Table 80: Occupancy Category of Building and Other Structures for Flood, Wind, Snow, Earthquake and Ice
Loads
160 | P a g e
Figure 82: Basic Wind Speed
161 | P a g e
Table 81: Directionality Factor
162 | P a g e
Table 82: Main Wind Force Resisting System - Method 2
163 | P a g e
Table 83: Main Wing Force Res.Sys. /Comp and Clad - Method 2
164 | P a g e
Table 84: Important Factor, I
165 | P a g e
Table 85: Velocity Pressure Exposure Coefficients
166 | P a g e
Appendix D: Transmission Design
Table 86: Spur Pinion 1
167 | P a g e
Table 87: Spur Gear 1
168 | P a g e
Table 88: Bevel Set 1
169 | P a g e
Table 89: Spur Pinion 2
170 | P a g e
Table 90: Spur Gear 2
171 | P a g e
Table 91: Bevel Set 2
172 | P a g e
Figure 83: Transmission Assembly Drawing
173 | P a g e
Figure 84: Spur Pinion 1 Drawing
174 | P a g e
Figure 85: Spur Gear 1 Drawing
175 | P a g e
Figure 86: Bevel Pinion 1 Drawing
176 | P a g e
Figure 87: Bevel Gear 1 Drawing
177 | P a g e
Figure 88: Spur Pinion 2 Drawing
178 | P a g e
Figure 89: Spur Gear 2 Drawing
179 | P a g e
Figure 90: Bevel Pinion 2 Drawing
180 | P a g e
Figure 91: Bevel Gear 2 Drawing
181 | P a g e
Figure 92: Shaft 1 Drawing
182 | P a g e
183 | P a g e
184 | P a g e
185 | P a g e
186 | P a g e

Whole Hurricane Protection, Jason Barrocas, Kevin Hernandez

Transcription

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