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Design optimization of Frp composite panel building systems

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Title:
Design optimization of Frp composite panel building systems emergency shelter applications
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English
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Bradford, Nicholas M
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University of South Florida
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Subjects / Keywords:
rapid deployment buildings
hurricane construction
high wind design
fiber reinforced polymers
interlocking
Dissertations, Academic -- Civil Engineering -- Doctoral -- USF   ( lcsh )
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Summary:
ABSTRACT: Using advanced composites, an emergency shelter system has been designed. The system parameters are hurricane resistance to 138 mph wind velocity, simple erection, light weight, high durability and rapid construction. The project involves the solicitation of design proposals from several building system manufacturers and the development of an optimized emergency shelter system. The usage is well suited to pultruded members made from fiber reinforced polymers (FRP). Due to the anisotropic nature of FRP composites, a limited amount of research has been conducted to develop design optimization techniques for panels used in construction. This project allows for the development of optimization techniques for use in pultruded FRP panel members.The Project consisted of a detailed literature review conducted of emergency building industry to assess the validity of existing shelter systems, a state of the art review of connection design in FRP structures with an emphasis on non-standard types of connectors (ie...snap type), systemic structural optimization of emergency shelter for building geometry, roof configuration, foundation anchorage and building envelope, development of statistical methods for evaluation of viable existing emergency shelter systems. Subsequent to the initial phase of the investigation, an interlocking FRP composite panel system was developed. The system was analyzed for local buckling, first ply failure and global deflection criteria using modified equations originally developed for open section members. The results were verified using Finite Element Methods analysis software.The findings from the study indicate the need for a second phase in which the most promising available systems and the concept developed are fully tested to verify their capacity to withstand high wind forces including impact of wind borne debris.
Thesis:
Thesis (Ph.D.)--University of South Florida, 2004.
Bibliography:
Includes bibliographical references.
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Statement of Responsibility:
by Nicholas M. Bradford.
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Includes vita.
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Title from PDF of title page.
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Document formatted into pages; contains 172 pages.

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University of South Florida
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aleph - 001498253
oclc - 57709149
notis - AJU6858
usfldc doi - E14-SFE0000484
usfldc handle - e14.484
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Design Optimization of Frp Compos ite Panel Buildi ng Systems: Emergency Shelter Applications by Nicholas M. Bradford A dissertation submitted in partial fulfillment of the requirement s for the degree of Doctor of Philosophy Department of Civil and En vironmental Engineering College of Engineering University of South Florida Major Professor: Rajan Sen, Ph.D. William Carpenter, Ph.D. Gray Mullins, Ph.D. Daniel Hess, Ph.D. Jose Danon, Ph.D. Steve Cooke, M.Arch. Date of Approval: August 24, 2004 Keywords: interlocking, fi ber reinforced polymers, hi gh wind design, hurricane construction, rapid deployment buildings Copyright 2004 Nicholas M. Bradford

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ACKNOWLEDGMENTS The research reported was funded by a gr ant from the University of South Florida’s Center for Disaster Management and Humanitarian Assistance (CDMHA) through the Office of Naval Re search. Dr. Mike Conniff, founding codirector of CDMHA initia ted the project and served as project manager during the initial phase. Dr. Tom Mason, co-directo r CDMHA took over as project manager for the later phase. We are very grateful for their support and contribution to the project. We also thank Mr. Eric Matos, Deputy Director, CDMHA for his keen interest and close interaction with the research team. Finally, the principal investigators wish to acknowledge the contribution of the other members of the research team : Dr. Gray Mullins, Steve Cooke, School of Architecture and Community Design, Dr. Jose Danon, Florida Department of Transportation and adjunct professor, Dr. Andres Torres Acosta currently with Instituto Mexicano del Transporte, Quer etaro, Mexico and graduate students Mr. Timothy Kimball, School of Architecture and Community Design and Dr. Niranjan Pai, Department of Mechanical Engineeri ng, University of South Florida.

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i TABLE OF CONTENTS List of Tables v List of Figuresvi Abstractviii Chapter 1:General Introduction and Overview 1 1.1Introduction 1 1.1.1 Project History 3 1.1.2 Project Goal 4 1.1.3 Methodology4 1.2Shelter System Geometry 6 1.3Alternative Building Systems 9 1.4Shelter Industry Systems10 1.5Design Optimization11 1.6Fiber Reinforced Polymers12 1.7Dissertation Contents14 Chapter 2:Background Emergency Shelters16 2.1Introduction16 2.2Emergency Shelter Industry Systems16 2.2.1CoreFlex18 2.2.1.1Main Contacts18 2.2.2Dr. Ayman Mosallam, P.E.18 2.2.2.1Main Contacts18 2.2.3Leading Edge Earth Products, Inc. (Leep)19 2.2.3.1Main Contacts19 2.2.4DuraKit Shelters20 2.2.4.1Main Contacts20 2.2.5Monolithic Dome Institute21 2.2.5.1Main Contacts21 2.2.6Pacific Yurt, Inc.22 2.2.6.1Main Contacts22 2.2.7Ambiente Housing Systems, Inc.23 2.2.7.1Main Contacts23 2.2.8American Structural Composites, Inc.24 2.2.8.1Main Contacts24

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ii 2.2.9Modular Engineering Company25 2.2.9.1Main Contacts25 2.2.10Royal Building System26 2.2.10.1Main Contacts26 2.2.11Futuristic Worldwide Homes / Lemay Center27 2.2.11.1Main Contacts27 2.3Summary 28 Chapter 3:Existing System Review29 3.1Introduction29 3.2Military Parameters30 3.2.1Cost30 3.2.2Erection Time31 3.2.3Constructibility31 3.2.4Durability32 3.2.5System Complexity32 3.2.6Material / Construction Adaptability34 3.2.7Transportability35 3.2.8Building System Flexibility36 3.2.9Ease of Maintenance37 3.3Structural Parameters38 3.3.1Flexural Capacity39 3.3.2In-Plane Shear40 3.3.3Connection Capacity Roof to Wall40 3.3.4Connection Capacity Wall to Foundation40 3.3.5Connection Capacity Member to Member40 3.4Screening Criteria41 3.4.1Construction Time41 3.4.2Transportability41 3.4.3Personnel Resources41 3.4.4Durability41 3.5Decision Matrix42 3.6System Proposal Information44 3.6.1CoreFlex44 3.6.1.1Main Contacts44 3.6.2Leading Edge Earth Products, Inc. (Leep)46 3.6.2.1Main Contacts46 3.6.3DuraKit Shelters48 3.6.3.1Main Contacts48 3.6.4 Futuristic Worldwide Homes / Lemay Center50 3.6.4.1 Main Contacts50 3.7Existing System Structural Conclusions52 3.7.1DuraKit Shelters52 3.7.2Leading Edge Earth Products, Inc. 52

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iii 3.7.3CoreFlex53 3.7.4Futuristic Worldwide Homes53 Chapter 4:Wind Analysis & Building Geometry56 4.1Introduction56 4.2Wind Design Process58 4.3Emergency Shelter Geometric Design62 4.3.1Step One62 4.3.2Step Two63 4.3.3Step Three63 4.3.4Step Four64 Chapter 5:USF System Assembly66 5.1Introduction66 5.2Component Geometry66 5.3Construction Process70 5.3.1Step One70 5.3.2Step Two72 5.3.3Step Three73 5.3.4Step Four74 5.3.5Step Five 76 5.3.6Step Six77 5.4Conclusions78 Chapter 6:Fiber Reinforced Polymers80 6.1Introduction80 6.2Manufacturing of FRP Composites80 6.3Laminate Lay-up and Material Properties81 6.3.1Material Properties82 6.4FRP Connection Review84 6.4.1FRP Connection Performance86 6.5Coordinate Systems and Sign Conventions91 6.6Laminate Design 92 6.7Summary99 Chapter 7:Design Optimization Overview101 7.1Introduction101 7.2Design Optimization General Process101 7.2.1Objective Function102 7.2.2Constrained Optimization103 7.2.3Neighborhood Searches104 7.3Integer Linear Programming104 7.4Genetic Algorithms106

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iv Chapter 8:Development of P anel Performance Criteria107 8.1Introduction107 8.2Local Buckling Performance108 8.2.1General Buckling Equations Axial Compression110 8.2.2Elastic Restraint112 8.2.3General Buckling Equations Shearing114 8.3Global Deflection Performance116 8.4First Ply Failure (FPF) Performance118 8.5Summary119 Chapter 9:Composite Panel Design Analysis / Results120 9.1Introduction120 9.2Design Restrictions121 9.3Performance Equations Buckling123 9.3.1Restraint Factor and Load Distribution Factor124 9.4Performance Equations Laminate Failure125 9.5Performance Equations Deflection125 9.6Example Design Process126 9.6.1Design Step One129 9.6.1.1Axial Compression Bending129 9.6.1.2Axial Compression Wind130 9.6.1.3Transverse Compression Wind130 9.6.1.4Shearing Forces Wind131 9.6.2Design Step Two132 9.6.3Design Step Three133 9.6.4Design Step Four135 9.6.5Design Step Five136 9.7Results 137 9.8Ansys Verification Model139 9.9Comparison of Analysis Results141 9.9.1Strength Discussion141 9.9.2Deflection Discussion143 9.10Conclusions145 Chapter 10:Conclusions and Recommendations147 10.1Project Summary148 10.2Conclusions: Historical Precedent149 10.3Conclusions: Existing System Review149 10.3.1Best System: DuraKit150 10.3.2Best System: Leading Edge Earth Products (LEEP) 151 10.4Conclusions: USF System Design152 10.5Contributions154 10.6Recommendations for Future Work156 References158 About The Author End Page

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v LIST OF TABLES Table 3.1Military Parameters Cost30 Table 3.2Military Parameters Time31 Table 3.3Military Parameters Constructibility32 Table 3.4Military Parameters Durability32 Table 3.5Military Parameters Complexity33 Table 3.6Military Parameters Material Availability34 Table 3.7Military Parameters Transportability35 Table 3.8Military Parameters Flexibility36 Table 3.9Military Parameters Maintenance37 Table 3.10Decision Matrix43 Table 3.11Military Parameter Summary45 Table 3.12Structural Parameters45 Table 3.13Military Parameter Summary47 Table 3.14Structural Parameters47 Table 3.15Military Parameter Summary49 Table 3.16Structural Parameters49 Table 3.17Military Parameter Summary51 Table 3.18Structural Parameters51 Table 6.1Material Properties Constituents83 Table 6.2Engineering Constants Plies83 Table 6.3A, B, D Matrices in terms of laminae invariants99 Table 8.1Buckling Factors116 Table 9.1Composite Panel Geom etric Properties 8 Ply132 Table 9.2Initial Design Values133 Table 9.3Local Buckling 0/45 Ply Laminate134 Table 9.4First Ply Failure135 Table 9.5Global Deflection 0/45 Laminate136 Table 9.6Panel Analysis 8 Ply Laminate137 Table 9.7Ansys Results 8 Ply Laminate140

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vi LIST OF FIGURES Figure 1.1Hurricane Mitch1 Figure 1.2Refugee Camp2 Figure 1.3Wind Pressure Effect on Buildings4 Figure 1.4FRP Panel Emergency Shelter5 Figure 1.5Preliminary Wind Analysis7 Figure 1.6Emergency Shelter Footprint8 Figure 2.1LEEP System19 Figure 2.2DuraKit Shelters20 Figure 2.3Monolithic Dome Institute21 Figure 2.4Pacific Yurt22 Figure 2.5Ambiente Homes23 Figure 2.6American Structural Composites24 Figure 2.7Modular Engineering25 Figure 2.8Royal Building System26 Figure 2.9Futuristic Worldwide Homes LLC27 Figure 3.1Structural Modes of Failure39 Figure 3.2Leading Edge Earth Products, Inc46 Figure 3.3DuraKit Shelters48 Figure 3.4Futuristic Worldwide Homes50 Figure 4.1Critical Wind Pressures Gable Roof60 Figure 4.2Critical Wind Pressures Mono Slope Roof61 Figure 5.1Basic Panel Geometry and Characteristics (Units in Inches)67 Figure 5.2Alternate Panel Geomet ry Transverse Web Stiffener68 Figure 5.3Typical Wall Section Panel System71 Figure 5.4Second Step: Wall Assembly72 Figure 5.5Third Step: Wall Assembly / Openings73 Figure 5.6Fourth Step: Wall Completion74 Figure 5.7Hurricane Connector Component75 Figure 5.8Fifth Step: Roof Assembly76 Figure 5.9 Sixth Step: Building Completion77 Figure 5.10Complete Construction Process79

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vii Figure 6.1Pultrusion Process81 Figure 6.2Laminate Lay-up Convention82 Figure 6.3Effect of Joint Flexibility (Mosallam 1990) 85 Figure 6.4Failure of FRP Angle (Mosallam 1994)85 Figure 6.5FRP Thread Failure (Mosallam 1995)85 Figure 6.6Typical Steel Type Connector FRP86 Figure 6.7Clip Angle Connections87 Figure 6.8 Stiffener Connections88 Figure 6.9 Full Thru-Bolting89 Figure 6.10 Coordinate Systems91 Figure 6.11 Force and Moment Resultants92 Figure 6.12 Laminate Stacking Convention96 Figure 8.1Division of Panel Member108 Figure 8.2Discrete Plate Elements109 Figure 9.1Critical Wind Pressures Mono Slope Roof127 Figure 9.2Emergency Shelter Footprint128 Figure 9.3Member Section128 Figure 9.4Strength Factors 8 Ply Laminate138 Figure 9.5Deflection Com parison 8 Ply Laminate138 Figure 9.6Panel Geometry Ansys140 Figure 9.7Comparison Buckling vs. Max Stress141 Figure 9.8Deflection Comparison Restrained144 Figure 10.1Durakit Emergency Shelter150 Figure 10.2LEEP Shelter System151 Figure 10.3Interlocking Panel Members153

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viii DESIGN OPTIMIZATION OF FRP COMPOSITE PANEL BUILDING SYSTEMS: EMERGENCY SHELTER APPLICATIONS Nicholas M. Bradford, PE SE ABSTRACT Using advanced composites, an emergency shelter system has been designed. The system parameters are hurricane resistance to 138 mph wind velocity, simple erection, light weight, high durability and rapid construction. The project involves the solicitation of des ign proposals from several building system manufacturers and the development of an optimized emergency shelter system. The usage is well suited to pultruded members made from fiber reinforced polymers (FRP). Due to the anisotropi c nature of FRP composites, a limited amount of research has been conduct ed to develop design optimization techniques for panels used in construction. This project allows for the development of optimization techniques for use in pultruded FRP panel members. The Proj ect consisted of a detailed literature review conducted of emergency building indus try to assess the validity of existing shelter systems, a state of the art review of connection design in FRP structures with an emphasis on non-standard types of connectors (ie...snap type), systemic structural optimization of emergen cy shelter for building geometry, roof

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ix configuration, foundation anchorage and building envelop, development of statistical methods for evaluation of viable existing emergency shelter systems. Subsequent to the initial phase of the investigation, an interlocking FRP composite panel system was developed. The system was analyzed for local buckling, first ply failure and global def lection criteria using modified equations originally developed for open section members. The results were verified using Finite Element Methods analysis software. The findings from the study indicate the need for a second phase in which the most promising available systems and t he concept developed are fully tested to verify their capacity to withstand high wind forces including impact of wind borne debris.

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1 Figure 1.1 Hurricane Mitch 1. GENERAL INTRODUCTION AND OVERVIEW 1.1 Introduction In October of 1998, the nations of the Caribbean and Central America experienced an event that directly a ffected more than 3,000,000 people. This event was called Hurricane Mitch (Figure 1.1), and it resulted in more than 10,000 dead, with ten-fold t hat number injured and in need of medical treatment. As for the housing stock, Mitch was no less devastating, with damage or destruction of 335,823 homes th roughout the Caribbean region.

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2 Figure 1.2 Refugee Camp (OFDA, 1998) In some areas, up to 90% of the agriculture and 80% of the potable water resources were lost (OFDA Report, 1998). Hurricane Mitch provides a stark reminder as to the mission of the United Stat es in the post cold war era. In areas like Kuwait, Africa and Central America, we have become our brother’s keeper, working to relieve the pain caused by the hands of fate and man. In the aftermath of Hurricane Mitch, more than $300 million was spent by the United States Government in relief to the Caribbean nations. Of that relief, $150 million was allotted to the Department of Defense to facilitate the conveyance of this aid (OFDA, 1998). Primary to the facilitation of this relie f is the issue of shelter (Figure 1.2). Shelter can come in many forms, be it as the canvas tent carried in battle, the mud hut on an open plain, or the wood framed box with back yard and white picket fence. In times of emergency, What materials are needed to build it? How long does it take to build?

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3 How much does it cost? What environm ental conditions can it withstand? How many people can it house? This project attempts to address some of these questions. 1.1.1 Project History This report summarizes the findings of a one year study conducted by the University of South Florida to inve stigate emergency shelters suitable for hurricane-devastated regions in the Caribbean and Latin America. The study commenced on January 1, 2000 ending on Dece mber 31, 2000. Originally, the goal of the study was to develop a m odular, light-weight, wind-resistant Fiber Reinforced Polymer (FRP) structure t hat could be fabricated using existing facilities at the Lemay Center for Compos ites Technology (LCCT), St. Louis, MO. Although LCCT collaborated actively with t he University of South Florida during preparation of the proposal, they were unable to continue with the study beyond the first quarter. In view of this, fabr ication aspects of the study were dropped and the primary focus became a review of what was currently available in terms of both FRP and traditional materials. An important secondary focus was the development of an in-house emergency s helter concept using FRP. Both developments are described in this report.

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4 Figure 1.3 Wind Pressure Effect on Buildings 1.1.2Project Goal The 1.1.3Methodology Two methods were used to identify the best solution. First, a detailed search conducted of all viable building systems currently available in the construction market. A “Request for Proposal” sent to all interested parties and subsequent proposals reviewed for compliance with shelter parameters Concurrently, an emergency shelter system

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5 Figure 1.4 FRP Panel Emergency Shelter developed by the research team using interconnected building panels made of FRP (Fiber Reinforced Polymers) as shown in Figure 1.4. All building submissions were reviewed using shelte r parameters developed by the military and structural/architectural paramet ers developed by the research team. Design equations will be developed to calculate localized plate buckling, global member deflection and first-ply failure loads. Design equations will be dependent on two criteria; ply orientation and laminate stacking sequence, The fixed parameters in all equations will in clude panel geometry, laminate thickness, laminae thickness and material properties of individual plies. Objective functions

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6 will be developed using each of the three performance equations as sub functions. The objective functions will then be optimized to provide the optimum laminate lay-up. Once the panel sect ion has been optimized, it will be reviewed against the applied loads encountered in the emergency shelter building. 1.2Shelter System Geometry In order to develop an optimal emergency shelter system, a suitable building geometry was developed by the re search team. The purpose of the building geometry was two-fold: 1) To provide a referential basis for conducting a side-by-side evaluation of available building systems during the indu stry review phase of the project. 2) To allow for an in-depth structural analysis of the environmental conditions (ie...hurricane wind velocities, exposur es) so as to develop a detailed picture of the required bu ilding component performance. Initially, the base geometric paramet ers proposed by the United States Southern Command (USSOUTHCOM) called for a 24'-0"x 36'-0" (7.32 m x 10.97 m) rectangular box, having a wall height of 8'-0" (2.44 m). A preliminary wind analysis, for a wind velocity of 138 mph (222 km/hr) and design pressures developed using ASCE 7 98, “Minimum Design Loads for Buildings and Other Structures”, was conducted to ascertain the magnitude of forces exerted on the structure (Figure 1.5). As a result of th is analysis, it was found that severe stress concentrations occurred at all buildi ng corners with magnitudes as high as 30,000 lbs (13,608 kg) of uplift force at some locations.

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7 Figure 1.5 Preliminary Wind Analysis Based on these findings, it was decided that the standard shelter geometry should be reduced in size so as to minimize the forces experienced by component members and connections. Subsequent modifications led to the development of a 12'-0"x 24'-0" (3. 66 m x 7.32 m) standard box geometry with 8'-0" (2.44 m) wall heights. Further modi fications led to the adoption of a 4:12 roof pitch and the use of 36" (0.914 m) wide openings on each of the long walls to facilitate the installation of doors and windows (Figure 1.6).

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8 Figure 1.6 Emergency Shelter Footprint Window and door placement were developed so as to allow for building adaptability according to usage. Specifically, the size and locations of openings allowed for the construction of two or more building units back to back, thus resulting in the creation of several interconnected ‘rooms’. Further, the development of the 4:12 monoslope roof wa s developed so as to allow for proper roof drainage and overhangs on the struct ure. It should be noted that the proposed roof slope constitutes a maximum and that most likely the finalized roof slope shall be much less in the field of oper ation. This roof slope facilitates the use of 12'-0" (3.66 m) and 8'-0" (2.44 m) members throughout the majority the building.

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9 The modifications to the basic geomet ry of the emergency shelter resulted in a significant reduction in the forc es and moments experienced by members and connections throughout the structure. Specifically, the maximum forces at the worst case members and reactions were reduced by a factor of 3, bringing these forces withing workable magnitudes. 1.3Alternative Building Systems A detailed review was conducted of the building industry to develop a list of viable candidates for use as emergency shelter structures. To facilitate this review, a side-by side analysis of each system had to be conducted. This analysis was performed as a “Request for Proposal” (RFP) in which the prototype building shown in Figure 1.6 was submitted to each interested group. Each party was then required to submit a detailed proposal for review by the research team. Throughout the RFP, the need for conf identiality was stressed with regard to all proprietary information and conten t. The research team stated a willingness to sign agreements regarding all proprietary information. It was pointed out that the research team had no interest in entering the composite manufacturing industry. It was stated that the sole inte rest was in the fulfillment of the design objectives for Office of Naval Research and the Military.

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10 1.4Shelter Industry Systems Subsequent to the detailed industry wide review conducted by the research team, several types of emergency shelters systems were found to provide viable alternatives. Specifically, as a result of our investigation, it was concluded that the viable emergency shelters fell into three types of construction. 1)Standard Construction New Materials: These systems emphasize the improved performance gained through the use of new materials. Such materials offer the user improved mechanical properties (on a localized basis), light weight, non-corrosive and non-metallic performance. Further, these systems attempt to use the new ma terials as direct substitutes for standard components in building systems. An example of this type of construction would be substituting FRP studs in a wood framed stud wall system or the use of styrofoam molds in lieu of masonry blocks in a filled masonry wall system. An RFP was sent to two manufacturers that fall into this category. 2)New Construction New Materials: These systems develop new construction systems in an attempt to best utilize the performance characteristics of the new materials. Typical examples of this construction consist of the development of pane lized wall and roof systems which are fabricated using FRP systems. An RF P was sent to six manufacturers in this category. 3)Alternate Systems: These systems wit hin this category constitute a fully alternate system of construction, based on geometry, materials and

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11 construction. Typical examples of this construction include monolithic domes and Yurts. An RFP was sent to two manufacturers that fall into this category. 1.5Design Optimization Concurrent to the industry-wide s earch for viable solutions to the emergency shelter problem, the research team is developing an optimized structural system for use in this situat ion. During our development of a design strategy, the following basic principles arose as being primary to the successful fulfillment of our design goals. These prin ciples include Structural Performance, Erection Simplicity, Cost and Durability/Adaptability. 1)Structural Performance is not a simple question when it comes to emergency shelters. One must design the components to withstand extreme conditions without failure. In our situation, the primary environmental situation involves hurricane force winds and flooding. The complexity of the problem is aggravat ed by the weight restrictions placed upon the shelter to facilitate manual erection. 2)Erection Simplicity is assessed by the speed of erection and the skill requirements of the workers. Furt her complicating the issue are the questions of connection and foundati on requirements. The optimal solution involves an integration of several functions into a single component.

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12 3)Cost runs in an inversely proportional relationship to all other issues addressed during the design optimizati on process. This question can only be circumvented through innovation in ei ther the areas of the materials or construction techniques used during erection. 4)Durability/Adaptability address the po ssible long term usage of the final buildings as ‘safe houses’ where pr imary facilities can be maintained during future disasters. Based on the four primary issues lis ted above, it was decided that the optimum solution would address the problem as a material issue and a building component issue. In order to answer both questions, our focus was turned to the use of Fiber Reinforced Polymer material s, which offer design customization for specific applications. 1.6Fiber Reinforced Polymers Fiber Reinforced Polymer (FRP) materials provide an incredible opportunity for structural engineers. T hey are light weight, non-magnetic and corrosion resistant. They offer mechani cal properties similar to those found in standard engineered materials such as steel, aluminum and concrete. Most important is the versatility of FRP materi als. Specifically, by allowing engineers to vary both fiber and matrix parameter s, FRP materials provide theoretically “exact” solutions to real-life structural problems.

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13 For these reasons, FRP materials have experienced wide and varied utilization throughout several engineering fields. First developed for use by the Aerospace industry, FRP materials have become the standard material in components ranging from landing gear to je t engines to heat protection on space shuttles. Within the automobile industr y, these materials have replaced metal components in vehicle body frames and engines. Within the civil engineering industry, acceptance of FRP materials has not been quite as widespread. The reason for this lack of utilization may be found in the direct relationship placing performance against cost. In the construction industry, this relationship is often of pr imary interest to Engineer, Contractor and Owner. Further, the complex nature of FRP materials, which are anisotropic, nonhomogeneous and viscoelastic, prohibits their evolution as a viable alternative to the relatively simpler c onstruction materials such as concrete or steel. As a result, FRP materials have been relegated to performing specialized structural tasks where either t he non-mechanical properties of FRP (ie...nonmetallic, corrosion resistant) are of primary concern or in retro-fitting applications where the utilizati on of steel or concrete is prohibitive. Further, the aesthetic versatility of FRP materials has led to their utilization in auxiliary structural systems such as building facade panels, handrails and fixtures.

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14 1.7Dissertation Contents The remainder of this dissertation documents the full review and development process of the “Design & Optimization of FRP Composite Panel Building Systems” investigation. The sect ions of this dissertation are as follows: 1)BACKGROUND EMERGENCY SHELTERS provides the reader with a detailed overview of the viable build ing systems involved in the evaluation process. 2)EXISTING SYSTEM REVIEW provides the reader with a review of four of the available building systems who responded to the RFP. The review is with respect to the parameters developed by the military and the structural/architectural parameter s developed by the research team. 3)WIND ANALYSIS & BUILDING DES IGN provides the reader with an overview of the wind analysis conduct ed during the investigation as well as the preliminary systemmic optimizat ion that resulted in the prototype shelter geometry. 4)USF SYSTEM ASSEMBLY provides the reader with step-by-step instructions for assembling the USF panelized FRP building as well as detailed component geometries and performance descriptions. 5)FIBER REINFORCED POLYMERS prov ides the reader with a detailed overview of advanced composites wit h an emphasis in the design of FRP materials.

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15 6)DESIGN OPTIMIZATION OVERVI EW provides the reader with an overview of design optimization procedures for advanced composite materials. 7)DEVELOPMENT OF PANEL PERFORMANCE CRITERIA develops each of the objective functions to be used in the investigation. 8)COMPOSITE PANEL DESIGN ANALYSIS / RESULTS reviews the optimization results using an ANSYS generated Finite Element Model for verification. 9)CONCLUSIONS AND RECOMMENDATIONS provides the reader with a finalized analysis of the viable system developed during the investigation.

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16 2. BACKGROUND EMERGENCY SHELTERS 2.1Introduction A detailed review was conducted of the building industry to develop a list of viable candidates for use as emergency shelter structures. To facilitate this review, a side-by side analysis of each system had to be conducted. This analysis was performed as a “Request for Proposal” (RFP) in which the prototype building shown in Figure 1.6 was submitted to each interested group. Each party was then required to submit a detailed proposal for review by the research team. Throughout the RFP, the need for conf identiality was stressed with regard to all proprietary information and conten t. The research team stated a willingness to sign agreements regarding all proprietary information. It was pointed out that the research team had no interest in entering the composite manufacturing industry. It was stated that the sole inte rest was in the fulfillment of the design objectives for Office of Naval Research and the Military. 2.2Emergency Shelter Industry Systems Subsequent to the detailed industry wide review conducted by the research team, several types of emergency shelters systems were found to

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17 provide viable alternatives. Specifically, as a result of our investigation, it was concluded that the viable emergency shelters fell into three types of construction. 1)Standard Construction New Materials: These systems emphasize the improved performance gained through the use of new materials. Such materials offer the user improved mechanical properties (on a localized basis), light weight, non-corrosive and non-metallic performance. Further, these systems attempt to use the new ma terials as direct substitutes for standard components in building systems. An example of this type of construction would be substituting FRP studs in a wood framed stud wall system or the use of styrofoam molds in lieu of masonry blocks in a filled masonry wall system. An RFP was sent to three manufacturers that fall into this category. 2)New Construction New Materials: These systems develop new construction systems in an attempt to best utilize the performance characteristics of the new materials. Typical examples of this construction consist of the development of pane lized wall and roof systems which are fabricated using FRP systems. An RF P was sent to six manufacturers in this category. 3)Alternate Systems: These systems wit hin this category constitute a fully alternate system of construction, based on geometry, materials and construction. Typical examples of this construction include monolithic domes and Yurts. An RFP was sent to two manufacturers that fall into this category.

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18 To further illustrate the variety and nature of the systems investigated during this project, we have enclosed t he following overview of each emergency shelter system manufacturer, involved in the initial Request for Proposals. Please note that not all of the manufactu rers provided below submitted proposals at the current time. 2.2.1CoreFlex FRP shapes, manufactured through t he pultrusion process and used as individual structural members in a pane lized construction system. Specifically, the FRP panels are hollow, narrow box shapes with internal ribs. 2.2.1.1 Main Contacts: Richard J. Alli, Sr. Corflex International, Inc. P.O. Box 830 Wilsonville, OR 97070 Phone(503) 582 8593Fax (503) 582 9373 2.2.2Dr. Ayman Mosallam, P.E. Panelized construction system consis ting of FRP composite sandwich materials. Adjacent panels to be interconnected using both epoxy adhesives and mechanical connections facilitated with universal connectors. 2.2.2.1 Main Contacts: Dr. Ayman Mosallam, P.E. Department of Civil & Env. Eng. & Mechanical Eng. California State University, Fullerton Phone(714) 278 2297Fax (714) 278 3916

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19 Figure 2.1 LEEP System 2.2.3Leading Edge Earth Products, Inc. (Leep) The system consists of composite panels composed of steel face sheet bonded to a foam core using sandwich construction. The panelized construction is supplemented using a metal frame syst em in which the panel sections are inserted. The building anchorage is provided through a system of manually placed deep set earth anchors. System Photographs: (from www.Leepinc.com) 2.2.3.1 Main Contacts: Bill Oakes Leading Edge Earth Products, Inc. P.O. Box 38636 Greensboro, NC 27438 Phone(336) 288 5668Fax (336) 288 4407 Website: www.leepinc.com E-Mail: rama@nr.infi.net

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20 Figure 2.2 DuraKit Shelters 2.2.4DuraKit Shelters The system consists of corrugated fi berboard that is factory-coated and treated to make a durable shelter with a fireproof interior and a weatherproof exterior. The fiberboard (similar to ca rdboard construction) is assembled as composite panels. The panels are connec ted to adjacent members using an adhesive system. Roof and floor connections are facilitated through the use of mechanically connected track systems. System Photographs: (from www. DuraKit.com) 2.2.4.1 Main Contacts: Tim Wimsatt DuraKit Shelters 2785 Hwy #27, P.O. Box 200 Bond Head, Ontario, Canada L0G 1B0 Phone(905) 778 00053Fax (905) 778 0054 Website: www.DuraKit.com E-Mail: shelters@DuraKit.com

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21 Figure 2.3 Monolithic Dome Institute 2.2.5Monolithic Dome Institute Dome shaped construction that is conducted through the use of an air filled permanent plastic form. Once t he form has been inflated on-site, concrete is sprayed on the exterior and exterior to create a monolithic structural system. System Photographs: (from www. Monolithicdome.com) 2.2.5.1 Main Contacts: David B. Smith, Mono lithic Dome Institute 177 Dome Park Place Italy, Texas 76651 Phone(972) 483 7423Fax (972) 483 6662 Website: www.monolithicdome.com E-Mail: mail@monolithic.com

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22 Figure 2.4 Pacific Yurt 2.2.6Pacific Yurt, Inc. Cylindrical shaped building geometry with a conical roof system. This system consists of a treated canvas mate rial installed over a wood and plexiglass frame system. Anchorage consists of mec hanical connections from roof to wall and wall to floor. System Photographs: (from www.yurts.com) 2.2.6.1 Main Contacts: Alan Bair Pacific Yurt, Inc. 77456 Hwy 99, South Cottage Grove, Oregon 97424 Phone(800) 944 0240Fax (541) 942 0508 Website: www.yurts.com E-Mail: pacyurt@yurts.com

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23 Figure 2.5 Ambiente Homes 2.2.7Ambiente Housing Systems, Inc. The house consists of a system of panels for the walls and roof, which are structurally reinforced with a comprehensiv e network of flexible glass fiber-rods throughout the entire structure and anchor ed to the ground through a structural concrete slab foundation in such a way as to withstand hurricane force winds. System Photographs: (from www.ambientehomes.com) 2.2.7.1 Main Contacts: Wayne DeWald P.O. Box 70005, Suite 266 Fajardo, P.R. 00738 70005 Phone(787) 889 1362Fax (787) 889 2944 Website: www.ambientehomes.com E-Mail: ambientehomes.com

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24 Figure 2.6 American St ructural Composites 2.2.8American Structural Composites, Inc. The system consists of six f oot wide panels incorporating phenolic fiberglass laminated sheets that are bonded with epoxy adhesives to an internal frame made up of extruded I-beams, wall to wall connectors and a base insert. System Photographs: (from www.asc-housing.com) 2.2.8.1 Main Contacts: Max Weir American Structural Composites 905 Southern Way, Suite 201 Sparks, NV 89431 Phone(775) 355 4444Fax (775) 355 4455 Website: www.asc-housing.com E-Mail: info@asc-housing.com

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25 Figure 2.7 Modular Engineering 2.2.9Modular Engineering Company The system consists of composite panels composed of steel face sheet bonded to a foam core using sandwich construction. The panelized construction is supplemented using a metal frame syst em in which the panel sections are inserted. System Photographs: (from www.modularengineering.com) 2.2.9.1 Main Contacts: Bob McGee Modular Engineering Company P.O. Box 8241 Erie, PA 16505 Phone(814) 838 6551Fax (814) 833 2577 Website: www.modularengineering.com E-Mail: info@modularengineering.com

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26 Figure 2.7 Royal Building System 2.2.10 Royal Building System The system consists of stay-in-place formwork constructed of FiberReinforced-Plymers. The structure is provided using a post and beam reinforced concrete system. System Photographs: (from www.rbsdirect.com) 2.2.10.1 Main Contacts: Royal Landmark Structures L.L.C. 16701 Greenspoint Park Drive Suite 120 Houston, Texas 77060 Phone: (281) 872-0200 Fax: (281) 875-8935 Website: www.rbsdirect.com E-Mail: info@rbsdirect.com

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27 Figure 2.9 Futuristic Worldwide Homes LLC 2.2.11 Futuristic Worldwide Homes / Lemay Center FRP shapes, manufactured through t he pultrusion process and used as individual structural members in a standar d construction system. Specifically, the overall system mirrors typical wood framed house construction. This system substitutes the FRP members for the wood studs, top plate and bottom plate. The system also includes styrofoam boar d insulation that is inserted between each stud to enhance the insulating and st ructural performance of the system. System Photographs: (from www.lemay.umr.edu) 2.2.11.1 Main Contacts: Advanced Composite Structures, LLC 2171 Eagle Creek Road Barnhart, MO 63012 Phone(314) 475 4928Fax (314) 475 3317

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28 2.3Summary Eleven viable building systems were found during an extensive review of the shelter manufacturing industry. Standard Construction New Material were two viable systems that emphasized the im proved performance gained through the use of new materials. New Construction New Material systems constituted the bulk of the buildings which developed new construction systems in an attempt to best utilize the performance c haracteristics of the new materials. Alternate systems were two shelter systems that constituted a fully alternate system of construction, based on geometry, materials and construction.

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29 3. EXISTING SYSTEM REVIEW 3.1Introduction A total of eleven available emergen cy building systems were identified in Chapter 2. To evaluate their suitabilit y for use in hurricane devastated regions and to facilitate direct comparison of the disparate systems, a “Request for Proposal” (RFP) was sent to all manufactu rers. In the RFP, the plan, elevation and wind load information was provided along with a request to address specific non-structural and structural parameters that would be used in the evaluation. This chapter reviews the responses that were submitted to the research team. The evaluation presented in this chapter is based on military, structural and architectural parameters. The non-st ructural parameters were developed by the military while the structural and ar chitectural parameters were developed by the research team. Sections 3.2-3.7 cover the non-structural and structural reviews and subsequent conclusions reached with respect to each viable building system.

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30 3.2Military Parameters The nine military parameters (Table 3.1-3.9) focused on the on-site construction of the building shell, incl uding the installation of all windows and doors. These parameters did not address ancillary systems such as electrical or mechanical that are included in the archit ectural review. Nor did the parameters evaluate construction of the foundation syst ems (ACT, 2000). In all cases, a higher numerical value signified better perfo rmance, e.g. on a scale of 1-5, 5 was the best. 3.2.1Cost The cost of the structure includes the co st of all materials, training, special tools and vendor representatives. Cost also includes all work/materials necessary to erect a waterproof structural shell as specified in the building plans. Cost were to be provided both in terms of the specific project as well as on a per square foot basis. The weighting parameter for cost in the overall evaluation was Table 3.1 Military Parameters Cost ValueCost 5$0 $17.36 / ft2 ($0 $186.87 / m2) 4$17.37 $34.72 / ft2 ($186.87 $373.52 / m2) 3$34.73 $52.08 / ft2 ($373.52 $560.12 / m2) 2$52.09 $69.44 / ft2 ($560.12 $746.68 / m2) 1$69.45 and up / ft2 ($746.68 and up / m2)

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31 3.2.2Erection Time The amount of time required for erec tion of the structure is crucial. Erection time is estimated as the fastes t time a trained crew erects a structure that provides weather tight, hurricane-resi stant protection. The weighting factor for this parameter in 3. Table 3.2 Military Parameters Time ValueTime 5< 20 man hours 421 40 man hours 341 60 man hours 261 80 man hours 1> 81 man hours 3.2.3Constructibility This is measured in terms of the number of untrained personnel required to erect the structure. Further, no single component should be too heavy; maximum weight 80 lb (36.29kg) to be maneuvered on-site by two female personnel. The weighting factor for this parameter is 3.

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32 Table 3.3 Military Parameters Constructibility ValueTime 5< 20 man hours 421 40 man hours 341 60 man hours 261 80 man hours 1> 81 man hours 3.2.4Durability This measures the manufacturer’s conf idence in the components. Typically, it is based on the manufacturer’s warrant y (in years). For the purpose of the parametric evaluation, this issue is given a parameter weight of 1. Table 3.4 Military Parameters Durability ValueDurability 55 years or more 44 to 5 years 33 to 4 years 22 to 3 years 11 year to 2 years 3.2.5System Complexity This is based on the number of days requi red to train construction personnel, the number of trainers r equired, and the number of building components utilized in the construction. This paramet er was given a weight of 1.

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33 Table 3.5 Military Parameters Complexity ValueComplexity 4Excellent 3Good 2Fair 1Poor System complexity is best described as a combination of the Erection Time and Constructibility parameters. The rating system for system complexity is clarified as: 1)Excellent: System can be construc ted from component form with less than one hour of instruction. No spec ialized tools and construction skills are required for erection. 2)Good: System construction requires one to four hours of instruction to complete erection and fabr ication. Minimal specialized tools (ie...electric drills, pneumatic tools) and constructi on skills (ie...rough carpentry) are required for erection and fabrication. 3)Fair: System construction requires fi ve to eight hours of instruction to complete erection and fabrication. Specialized tools (ie...electric drills, pneumatic tools) and construction skills (ie...rough carpentry, flat masonry work) are required for erection and fabrication. 4)Poor: System construction requires mo re than eight hours of instruction to complete erection and fabrication. Specialized tools and equipment

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34 (ie...cranes, concrete pumps) and construction skills (ie...survey work, masonry, steel erection) are r equired for erection and fabrication. 3.2.6Material / Construction Adaptability This is based on the mate rials required to be supplied by the host nation (ie...concrete, wood, etc... ma y not be available in host country). This parameter was given a weight of 1. Table 3.6 Military Parameters Material Availability ValueMaterial Availability 4Excellent 3Good 2Fair 1Poor Material Availability describes the dependence of the shelter construction on materials and services provided by the host nation. This paramet er is of crucial importance since the proposed post-disast er usage would prohibit the production and conveyance of construction materials to the job site. The rating system for system complexity is clarified as : 1)Excellent: System can be constructed using no supplemental materials provided by the host nation. Syst em can be constructed using no supplemental construction services provided by the host nation. 2)Good: System can be constructed with or without minor supplemental materials (ie.. electrical wiring, concrete) provided by the host nation.

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35 System can be constructed using no suppl emental services provided by the host nation. 3)Fair: System construction requi res minor supplemental materials (ie..electrical wiring, concrete) prov ided by the host nation. System can be constructed with or without supplemental construction services, depending on extent of shelter finishes. 4)Poor: System construction requires significant supplemental materials (ie..steel framing, wood framing, c oncrete) provided by the host nation. System requires supplemental construc tion services, provided by the host nation. 3.2.7 Transportability This is based on the number of sta ndard MILVAN contai ners and/or C130 pallets required to transport the component s. Each container has the storage dimensions of 8'-0"x 8'-0"x 20'-0" (2.44m x 2.44m x 6.1 m). For the purpose of the parametric evaluation, this issue wa s given a parameter weight of 2. Table 3.7 Military Parameters Transportability ValueTransportability 54 Units or more / C130 42 3 Units / C130 31 Unit / C130 21 2 C130 / Unit 13 or more C130 / Unit

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36 3.2.8Building System Flexibility This measures how flexible the build ing system is to adapt to changes in building geometry, wall height, roof confi guration, etc... For the purpose of the parametric evaluation, this issue wa s given a parameter weight of 1. Table 3.8 Military Parameters Flexibility ValueFlexibility 4Excellent 3Good 2Fair 1Poor Building System Flexibility describes the ability of the system to adapt to changes in the roof geometry wall heights, opening locations and building footprint. The rating system for system complexity is clarified as: 1)Excellent: Roof system can be modi fied with no engineering and changes to the members sizes and connections, and Wall system can be modified with no engineering and changes to the members sizes and connections, and Building geometry can be modified with no engineering and changes to the members sizes and connections. 2)Good: Roof system can be modified with minimal engineering and changes to the members sizes and connections, or Wall system c an be modified with minimal engineering and changes to the me mbers sizes and connections, or

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37 Building geometry can be modified with minimal engineering and changes to the members sizes and connections. 3)Fair: Roof system can be modified with significant engineering and changes to the members sizes and connections, or Wall system can be modified with significant engineering and changes to the members sizes and connections, or Building geometry can be modifi ed with significant engineering and changes to the members sizes and connections. 4)Poor: Roof system cannot be modified, or wall system cannot be modified, or building geometry cannot be modified. 3.2.9Ease of Maintenance Measures the ease with whic h the erected structures can be maintained and repaired. Further, this parameter addresse s the special tools and training required to facilitate the maintenance and repair of t hese structures. For the purpose of the evaluation, this issue was gi ven a parameter weight of 1. Table 3.9 Military Parameters Maintenance ValueMaintenance 4Excellent 3Good 2Fair 1Poor

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38 Maintenance describes the amount of monitoring and upkeep required to facilitate the usable life of the build ing system. The rating system for system complexity is clarified as: 1)Excellent: System requires less than one hour per month of monitoring and upkeep during the usable lif etime of the building system. Requires no major maintenance job (ie...roof replacement) during the usable lifetime of the shelter. 2)Good: System requires between one and two hours per month of monitoring and upkeep during the usable lifetime of the buildi ng system. Requires one major maintenance job (ie...roof repl acement) during the usable lifetime of the shelter. 3)Fair: System requires between two and four hours per month of monitoring and upkeep during the usable lifetime of the buildin g system. Requires one major maintenance job (ie...roof repl acement) during the usable lifetime of the shelter. 4)Poor: System requires more than f our hours per month of monitoring and upkeep during the usable lifet ime of the building system Requires more than one major maintenance job (ie...roof r eplacement) during the usable lifetime of the shelter. 3.3Structural Parameters A significant part of the review conc erned structural performance (see Figure 3.1) of the building under wind loading. The specific conditions addressed was 138 mph (222 km/hr) hurricane wind loads, as determined by The American Society of

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39 Figure 3.1 Structural Modes of Failure Civil Engineers (ASCE7 98), “Minimu m Design Loads for Buildings and Other Structures”. Further, the bu ildings were considered essential structures subjected to the worst environmental and geographical conditions. Each of the structural parameters is viewed as a pass / fail screening criteria. To conduct this review, the following structural information was required: 3.3.1Flexural Capacity This information required structural calculations and/or experimental test data showing flexural performance up to component failure. Further, information on load deflection performance had to be submi tted. This information was used to verify wind induced suction force resist ing capacity of roof members and wall members. Construction details were also required showing standard member profiles, material strengt hs and section properties.

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40 3.3.2In-Plane Shear This information required structural calcul ations and/or experimental test data showing in-plane shear performance up to fa ilure of standard wall assembly section (ie...pounds per linear foot). This informati on was used to verify wind shear resisting capacity of system. 3.3.3Connection Capacity Roof to Wall This information required structural calcul ations and/or experimental test data showing the performance up to failure of standard roof to wall connections. Construction details were also required to show how the connecti on is built on-site. 3.3.4Connection Capacity Wall to Foundation This information required structural calc ulations and/or experimental test data showing the performance up to failure of standard wall to foundation connections. Construction details were also required to show how the connection is built on-site. 3.3.5Connection Capacity Member to Member This information required structural calc ulations and/or experimental test data showing the performance up to failure of a ll other connections. Construction details were also required to show how the connection is built on-site.

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41 3.4Screening Criteria As per the investigation conducted by t he Military, four no n-structural pass / fail criteria were set as performance minimums. The four criteria were: 3.4.1Construction Time This criteria is based on the crucial aspect of rapid construction. The construction time excludes foundation work and is based on the complete erection of the building envelop. The pass / fail criteria is 15 days. 3.4.2Transportability Due to the need to use these systems on a global basis, it is crucial that any system be able to be flown into the theater of operation. T he pass / fail criteria is Air transport. 3.4.3Personnel Resources The criteria is based on the availability of Military personnel to facilitate the erection of the buildings. The pass / fa il criteria is based on standard company size and is set at a maximum of 12 soldiers and 96 man hours. 3.4.4Durability Due to the emergency nature of usage, it is crucial that shelters last for a minimum time period. The criteria is based on a minimum 1 year warrantee.

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42 3.5Decision Matrix The building systems were evaluat ed using the eighteen parameters reviewed in the two previous sections. The evaluation methodology is based on the process utilized by USSOUTHCOM in a si milar project conducted to evaluate proposals for Sea Hut building to be constr ucted in Yugoslavia (ACT, 2000). These parameters were developed for the Theater Contingency Operation (TCO)and were for a 16'-0"x 32'-0" (4.88m x 9.75m) shelter building. While the current investigation utilizes a 12'-0"x 24'-0" (3.66m x 7.32m) building, it is reasonable to assume that the two projects are similar in usage and design exposure. Table 3.10 summarizes the decision matrix for this study. Note that the weighting factors used in this evaluation are identical to those used in the TCO evaluation, with the exception being the we ighting factor used for Constructibility (3.0 instead of 1.0). The additional weighting value was used based on the importance of erection speed and simplicity in the overall success of the system.

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43 Table 3.10 Decision Matrix Construction CategoryBuildingSystems DuraKitLEEPCoreFlexFuturistic Homes Screening Criteria Constructibility: < 15 DaysYesYesYesYes Transportability. AirYesYesYesYes Resources: < 12 SoldiersYesYesYesYes Durability: 1 YearYesYesYesYes Structural Criteria Flexural / Bending CapacityPassPassPassPass In-Plane Shear CapacityPassPassPassPass Roof Wall ConnectionsPassPassPassFail Wall Foundation ConnectionsPassPassPassFail Adjacent Panel ConnectionsPassPassPassPass Military Parameters Cost5324 Time (3x)3441 Constructibility (3x) 2331 Durability 5555 Complexity5331 Material Availability 5331 Transportability (2x) 5352 Flexibility 4521 Maintenance4543 Totals53515025 (Fail)

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44 3.6System Proposal Information Proposals were solicited from twelve alternate construction manufacturers. The solicited systems represented both alternate and standard construction materials. Of the twelve solicited co mpanies, proposal packages were received from four companies. The following informa tion represents the fu ll proposal process with respect to each of the alternate building systems. 3.6.1CoreFlex FRP shapes, manufactured through t he pultrusion process and used as individual structural members in a panelized construction system. Specifically, the FRP panels are hollow, narrow box shapes with internal ribs. Adjacent panels are connected to each other using interlo cking connector shapes. The system allows for the hollow portions of the panels to be used for conduit installation or foam insulation. 3.6.1.1 Main Contacts: Richard J. Alli, Sr.Pierre Jordan Corflex International, Inc.Jordex Engineering P.O. Box 830 Wilsonville, OR 97070 Phone(503) 582 8593Phone (562) 590 7334 A summary of the information received re lating to the military and structural parameters may be found in Table 3.11 and T able 3.12. Inspection of these tables indicate that much of the required information relating to structural performance was not provided.

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45 Table 3.11 Military Parameter SummaryParameterSpecificationComments A1. Cost$ 18,300 or $ 63.54 / sq.ft. Includes Roof, Wall, and Uplift Anchors. No door/window, foundation or ancillary systems. A2. Erection Time5 workers for 5 hrs. 25 man hours No Comments A3. ConstructibilityNo submission (see A2. parameter) No Comments A4. Durability35 year warrantee on panels No Comments A5. System Complexity One hour of training required No Comments A6. Mat/Constr. Tech. Adaptability No informationFloor panels can be provided in areas where concrete is unavailable. A7. Transportability5 units fit in 8'-0"x 8'-0"x 20'-0" Panels weigh under 80 lbs. A8. Building System Flexibility No informationPanels may be added and size expanded without changing the design. A9. Ease of Maintenance Maintenance free materials. Class 1 fire retardant, insensitive to mildew, termite & rodent proof.Table 3.12 Structural ParametersParameterCapacityMethod of Verification Comments B1. Panel Bending160 mph wind with 2.8" deflection. No Calculations Received Acceptable panel bending based on foam filled core system. This is not part of the base system and has additional costs involved. B2. Wall ShearNo informationNo Calculations Received No Comments B3. Roof to Wall Connections No informationNo Calculations Received Provided using (8) marine grade stainless steel cables from roof to foundation. B4. Wall to Footing Connections No informationNo Calculations Received Each cable rated for 5000 lbs tensile load. B5. Adjacent Panel Connections No informationNo Calculations Received No Comments

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46 Figure 3.2 Leading Edge Earth Products, Inc 3.6.2Leading Edge Earth Products, Inc. (Leep) The system consists of composite panels composed of steel face sheet bonded to a foam core using sandwich cons truction. The panelized construction is supplemented using a metal fr ame system in which the panel sections are inserted. The building anchorage is provided thr ough a system of manua lly placed deep set earth anchors. Table 3.13 and Table 3.14 summarize the information submitted for review. 3.6.2.1 Main Contacts: Bill Oakes Leading Edge Earth Products, Inc. P.O. Box 38636 Greensboro, NC 27438 Phone (336) 288 5668Fax (336) 288 4407 Website: www.leepinc.com E-Mail: rama@nr.infi.net

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47 Table 3.13 Military Parameter Summary ParameterSpecificationComments A1. Cost$ 13,091 or $ 45.45 / sq.ft. Includes Roof, Wall, Doors, Windows and Uplift Anchors. No foundation or ancillary systems. A2. Erection Time4 workers for 8 hrs. 32 man hours No Comments A3. ConstructibilityNo submission (see A2. parameter) Each additional 2 man team reduces erection time by 2 hours. A4. Durability5 year warrantee on panels No Comments A5. System Complexity Factory 2 man team conducts all training. No Comments A6. Mat/Constr. Tech. Adaptability All materials are provided. No Comments A7. Transportability1 unit fits in 8'-0"x 8'-0"x 20'-0" Panels weigh under 80 lbs. A8. Building System Flexibility No informationPanels may be added and size expanded without changing the design. A9. Ease of Maintenance Minimal maintenance (painting). No CommentsTable 3.14 Structural ParametersParameterCapacityMethod of Verification Comments B1. Panel Bending93 psf (191 mph) Testing (Univ. of Washington, 2000) Acceptable panel bending based on out-of-plane testing. B2. Wall Shear2,000 lbs per ft. of wall Testing (Univ. of Washington, 1999) No Comments B3. Roof to Wall Connections No information No Calculations Received Uses steel skeleton frame anchor bolted to the foundation. B4. Wall to Footing Connections No information No Calculations Received Uses steel skeleton frame anchor bolted to the foundation. B5. Adjacent Panel Connections No information No Calculations Received No Comments

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48 Figure 3.3 DuraKit Shelters 3.6.3DuraKit Shelters The system consists of corrugated fiber board that is factory-coated and treated to make a durable shelter with a fireproof interior and a weatherproof exterior. The fiberboard (similar to ca rdboard construction) is assembled as composite panels. The panels are connec ted to adjacent members using an adhesive system. Roof and floor connecti ons are facilitated through the use of mechanically connected track systems. T able 3.15 and Table 3.16 summarize the submitted information. 3.6.3.1 Main Contacts: Tim Wimsatt DuraKit Shelters 2785 Hwy #27, P.O. Box 200 Bond Head, Ontario Canada L0G 1B0 Phone(905) 778 0053Fax (905) 778 0054 Website: www.DuraKit.com E-Mail: shelters@DuraKit.com

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49 Table 3.15 Military Parameter Summary ParameterSpecificationComments A1. Cost$ 6,624 or $ 23.00 / sq.ft. Includes Roof, Wall, and Uplift Anchors. No door/window, foundation or ancillary systems. A2. Erection Time2 workers for 30 hrs. 60 man hours No Comments A3. Constructibility80 man hours for unskilled workers No Comments A4. Durability5 year warrantee on panels. No Comments A5. System Complexity 20 25 students / trainer for 3 days. No Comments A6. Mat/Constr. Adaptability No informationFloor beams can be provided in areas where concrete is unavailable. A7. Transportability5 units fit in 8'-0"x 8'-0"x 20'-0" Panels weigh 72 lbs maximum. A8. Building System Flexibility No informationSystem has been designed specifically for geometry shown. A9. Ease of Maintenance Coated with Stucco and Elastomeric finish. Roof members using asphaltic roofing material. Maintenance mirrors standard construction.Table 3.16 Structural ParametersParameterCapacity VerificationComments B1. Panel Bending52.6 psf (141 mph wind velocity, BOCA) Testing (Univ. of Western Ontario) 1999 Acceptable panel bending based on gravity and lateral wind loading. B2. Wall Shear36.4 N/mm Inplane shear (2494 lb/foot) Testing (Univ. of Western Ontario) 1999 No Comments B3. Roof to Wall Connections 86.7 psfTesting (Univ. of Western Ontario) 1999 Provided using screws between \ component panels. B4. Wall to Footing Connections 86.7 psfTesting (Univ. of Western Ontario) 1999 Failure caused by delamination of composite layers at connections. B5. Adjacent Panel Connections No informationNo Calculations Received No Comments

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50 Figure 3.4 Futuristic Worldwide Homes 3.6.4Futuristic Worldwide Homes / Lemay Center FRP shapes, manufactured through t he pultrusion process and used as individual structural members in a standar d construction system. Specifically, the overall system mirrors typical wood fr amed house construction. This system substitutes the FRP members for the wood studs, top plate and bottom plate. Table 3.17 and Table 3.18 summarize the submitted information. 3.6.4.1 Main Contacts: Advanced Composite Structures, LLC 2171 Eagle Creek Road Barnhart, MO 63012 Phone(314) 475 4928Fax (314) 475 3317 Table 3.17 Military Parameter Summary

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51 ParameterSpecificationComments A1. Cost$ 26,000 or $ 30.09 / sq.ft. Includes Roof, Wall, and Uplift Anchors. No door/window, foundation or ancillary systems. A2. Erection Time8 workers for 16 hrs. 128 man hours No Comments A3. ConstructibilityNo submission (see A2. parameter) No Comments A4. Durability35 year warrantee on panels No Comments A5. System Complexity One hour of training required No Comments A6. Mat/Constr. Tech. Adaptability No informationFloor panels can be provided in areas where concrete is unavailable. A7. Transportability1 unit fits in C130Panels weigh under 80 lbs. A8. Building System Flexibility No informationPanels may be added and size expanded without changing the design. A9. Ease of Maintenance Maintenance free materials. Class 1 fire retardant, insensitive to mildew, termite & rodent proof.Table 3.18 Structural ParametersParameterCapacityMethod of Verification Comments B1. Panel Bending70 mph wind with 2.8" deflection. TestingNo Comments B2. Wall ShearNo informationNo Calculations Received No Comments B3. Roof to Wall Connections No informationNo Calculations Received No Comments B4. Wall to Footing Connections No informationNo Calculations Received No Comments B5. Adjacent Panel Connections No informationNo Calculations Received No Comments

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52 3.7Existing Systems St ructural Conclusions Of the twelve system manufacturers contact ed to participate in this project, four complete proposals were submitted for revi ew. Four expressed interest in the project, but could not provide the necessa ry support calculations and information. Two manufacturers expressed a great deal of interest, but did not provide the requested information. All potential manufac turers were contacted several times prior to and after the submission deadline. The four submitted building systems are ranked and described as follows: 3.7.1 DuraKit Shelters Resin saturated cardboard composite shelter constructed on-site. Components fastened to adjacent members using epoxy resin adhesive. 1)Rating:53 2)Pros:Very inexpensive, Economical, Simple Construction. Excellent supporting data (full scale testing and component testing) 3)Cons:Permanent construction (no disassembly), Durability issues in high temperature and humidity environment. 3.7.2 Leading Edge Earth Products, Inc. Composite panel systems consisting of co rrugated steel skins with a foam in-fill core. 1)Rating:51 2)Pros:Very strong, Ability to hav e two story construction. Simple Construction. Good supporting data (component testing)

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53 3)Cons:Relies on supporting structural fr ame system, Durability issues in high temperature and humidity environm ent due to steel corrosion. 3.7.3 CoreFlex Pultruded FRP panel members with snap fit connection ends. Can be foam filled to provided added insulation and stiffness. 1)Rating:50 2)Pros:Simple Construction. Ability to disassemble easily. 3)Cons:Supporting structural system requi red, Extra structural connections required, Durability issues in high temperature and humidity environment. Supporting data is very poor and is the engineering calculations are incomplet (no component testing). 3.7.4 Futuristic Worldwide Homes Pultruded FRP members used in substitution for wood members in a wood framed stud wall system. 1)Rating:25 (Fail structural calculations) 2)Pros:Ability to disassemble. 3)Cons:Building requires cranes for er ection. Supporting structural system required, Extra structural connecti ons required, Durability issues in high temperature and humidity envir onment. Supporting data is very poor and is suspect (no component testing).

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54 Aside from the performance rating re sults, the building systems reviewed during this phase of the investigation illust rated several areas of concern with regard to systemic performance. Most notabl e of these was the dependency of the systems on some type of supporting structur al system. Specifically, we noted several of the systems utilized structural steel framework and connections designed to resist the high wind forces. While this is an acceptable design concept, it illustrates the complexity of the problem at hand. Further, the reliance of the systems on standard construction materi als and methods becomes a serious impediment when one addresses the areas wher e these shelters will be constructed. In most cases, the shelters will be erec ted in areas where standard construction tools and techniques are not applicable. Further, long-term corrosion and maintenance becomes an issue in the ca se of systems utilizing steel support structures. Specifically, some conclusions made as a result of the investigation are as follow, 1)The optimal system would be one which would require no additional materials and tools to be provided on-site during the construction process. 2)Construction workers would require minimal experience and skill to erect the emergency shelter building. 3)The optimal system would be adaptable so that different building geometries and configurations could be constr ucted depending upon parameters such as usage, erection time, etc...

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55 4)The optimal system would be able to be built, taken down and re-built without significant damage to the building components or connections. 5)The optimal system would consist of materials that were corrosion resistant and require very little maintenance.

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56 4. WIND ANALYSIS & BUILDING GEOMETRY 4.1Introduction The design wind pressures for this investigation were developed using the 1998 edition of The American Society of Civil Engineers Standard 7, “Minimum Design Loads for Buildings and Other Stru ctures”. The following parameters were utilized to develop all necessary design wind pressures: 1)Design Wind Velocity: The wind speed was specified by the military as 138 mph (222km/hr) that corresponds to a Category IV hurricane. 2)Building Size: The building footprint was selected to be 12'0" x 24'0" (3.66m x 7.32m) on the basis of prelim inary structural analysis to optimize the structure for member forces and stresses. 3)Building Wall Height: The building height was selected as 8 ft (2.44m). It was assumed that the shelter was single-story with standard construction wall heights. 4)Roof Slope: A standar d roof slope 4:12 (18.4o) was selected use in the shelter. Such a roof slope provides fo r transfer of wind uplift forces as well as roof drainage.

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57 5)Mean Roof Height : Based on the assumed roof slope, the mean roof height taken at the mid height of the roof is 10 ft (3.05m). 6)Building Importance: The structur e is viewed as a primary emergency shelter and is therefore Category IV, I = 1.15 (ASCE7-98, Table 6-1). 7)Exposure D: The structures may be erected in any geographic location. It is also assumed that ground scour ma y have occurred prior to the erection of the building. Thus, Kz = 1.03 (ASCE7-98, Table 6-5). 8)Directionality: The probability of high wind occurrence on exposed main force systems and components and cladding sets Kd = 0.85 (ASCE7-98, Table 6-6). 9)Partially Enclosed Building Envelop: It is assumed that the shelters may be used as temporary buildings, lacking door and window assemblies rated for wind borne debris and forces. Consequently, GCpi= 0.55 (ASCE7-98, Table 6-7). 10)Hills or Escarpments: It is assum ed that the shelters are erected in “camps” where grading and excavation of surrounding lands may be conducted. The absence of hills and escarpments presents the most conservative geographic situation setting parameter Kzt= 1.00 (ASCE798, Figure 6-2).

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58 4.2.Wind Design Process The first step in evaluating design wind pressures is to calculate the base wind pressure. This base wind pressure is dependent upon the wind velocity, building importance, building exposur e and the geography of the surroundings. The base wind pressure is calculated using the following equation (ASCE7-98, Equation 6-13): (4.1)q z psfkPa000256103100085138 2 1154909235 .(.)(.)(.)()(.).(.)where the variables are taken from ASCE7 -98, Table 6-5, Table 6-6 and Table 61. The design wind pressure is further refined based on the geometry of the building (roof slope, wall height, corner proximity) and the area of wind surface supported by the member to be designed. The building is first divided into end and interior zones. The determination of these zones are based on the following equations (ASCE7-98, Note 7 of Figure 64, Note 6 of Figure 6-5a, Note 7 of Figure 6-5b, Note 5 of Figure 6-7a); Main Wind Force Resisting Systems a is smaller of = 0.1 (12'-0") or 0.4 (8'-0") but >3.0' End Zone =2a=6.0' (1.83m) Interior Zone=24.0' (2)*6.0'=12.0'(3.66m) Interior Zone=12.0' (2)*6.0'=0.0'(short side) Component and Cladding Systems End Zone=a=3.0' (0.91m) Interior Zone=24.0' (2)*3.0'=18.0'(5.49m) Interior Zone=12.0' (2)*3.0'=6.0'(1.83m)

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59pqGCGChpfpiThe building is further subdivided into windward and leeward surfaces, for which individual design wind pressures are calculated. For the purposes of design, worst case design wind pressures are chosen by comparing each member subjected to either windward or leeward locations. The direction of the applied wind is also subdivided into wind applied perpendicular to the roof ridge line and wind applied parallel to the roof ri dge line. Specific gust factors are then developed, based on location and type, for each structural member being designed. The final design pressure for each member is calculated by applying both localized gust and interior pressure factors to the base design wind pressure. The appropriate equation, shown below, applies for both Main Wind Force Resisting Systems (MWFRS) and Components and Cladding Systems (CC) (ASCE7-98, Eq. 6-16): (4.2) The Main Wind Force Resisting System consists of all structural members that facilitate the transfer of wind i nduced forces to the foundation system and include any beams, columns or connecti on members within the structure. Components and Cladding forces are used to evaluate the capacity of individual members to handle directly applied wind loads. Wind codes develop different coefficients based on the building and roof geometry as well as the type of system (MWFRS or CC) being addressed. For the current research, a wind analysis wa s performed using the initial emergency

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60 Figure 4.1 Critical Wind Pressures Gable Roof shelter geometry proposed by The Lemay C enter. This geometry consisted of a gable roofed, rectangular building having a 24'0" x 36'0" (7.32m x 10.92m) footprint. As a result of the analysis, the critical design pressures, shown in Figure 4.1, were developed for use during t he evaluation of this structure and in the subsequent design optimization of the emergency shelter system (Figure 4.2). A detailed breakdown of all wind design pressures and calculations have been provided in Appendix A.

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61 Figure 4.2 Critical Wind Pressures Mono Slope Roof

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62 4.3Emergency Shelter Geometric Design A multitude of structures have been developed and fabricated by the emergency shelter industry. Their geometry range from cubicle shaped boxes to monolithic dome type structures (see Sect ion 1.5). In order to develop an optimal geometric shape for use in this proj ect, special attention was paid to the needs of the end user. These were classified as: 1)Structural Performance: Of primar y concern is the capability of the structure to withstand hurricane force winds. 2)Anchorage Performance: Due to the wide variety of usage proposed for the emergency shelter, adequate foundat ion anchorage is required for a multitude of ground soil conditions. 3)Construction Simplicity: The emergency shelter should be simple to construct, both in terms of the constituent construction components and the technical skills of the laborers. 4)Geometric Adaptability: The emergen cy shelter must fit into a pod-like system of urban design. Specifically the end user should be able to add or subtract shelter units to “build” configurations to suit specific usage needs. 4.3.1Step One An initial geometry based on previous shelters developed by the military was selected as a starting point for the emergency shelter. This geometry

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63 corresponded to a rectangular box shape, 24'0" x 36'0" x 8'0" (7.32m x 10.97m x 2.44m) in shape, with a single roof ridge line and gable ends in the shorter 24'0" (7.32m) dimension. A preliminary structural analysis of the building exposed to the design wind design pressures indicated that very large force concentrations occurred at the cor ners of the building and at the transition between the roof and wall members. Due to the magnitude of these forces, it was concluded that the building geometry needed to be revised. 4.3.2Step Two In order to restrict the force concent rations to acceptable limits, the base geometry of the building was reduced to a 12'0"x 24'0"x 8'0" (3.66m x 7.32m x 2.44m) box shape. A preliminary st ructural analysis of the reduced geometry showed that the force concentrations were reduced by a factor of three. Further, the reduced geometry provides for a usable area of 288 ft2 (26.76m2). This reduced footprint area allows for a greater va riety of uses. Specifically, this area is more acceptable for usage as sleeping area, office space, storage area or medical facility. 4.3.3Step Three The initial roof geometry called fo r a gable end roof system. This system was found to be unacceptable due to the inherent structural weakness that

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64 occurs at the gable end wall connections. This weakness results in the development of a hinge joint failure in the gable end wall during high wind events. A double hipped roof configuration was in vestigated as a first alternative roof system. While this roof confi guration provides for adequate structural bracing at all wall roof trans ition points, it was concluded that the complexity of this construction prohibits its selecti on for use in a rapidly deployed emergency shelter where simplicity of the building construction is crucial to success. The geometry of the roof system is cr ucial to structural performance since it directly affects the magnitude and applicat ion of wind load forces. Further, the roof system geometry affects erection speed and construction complexity. Roof optimization led to the selection of a low rise mono sloped roof configuration. This roof configuration has several posit ive aspects. Specifically, a mono sloped roof system provides structur al stability at all roof wall transition points. Further, a mono sloped roof is simple to cons tructed, requiring one basic structural component (plank member). Additional positive aspects of the mono sloped roof system include the ability to use the same members as used in the wall system, and the ability to align adjacent shelter uni ts so as to create a variety of roof configurations (gable roof, sawtooth roof, etc...). 4.3.4Step Four The initial design of the shelter ut ilized a variety of door and window sizes, placed in all elevations of the build ing. For the purpose of adaptability and simplicity, it was concluded that all door and window sizes should use the same

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65 opening size. Further, it was concluded that openings should not be installed in either of the short dimension elevat ion wall, due to the need for lateral shear resisting members in these elevations. Subsequent design resulted in the use of a 36" (0.914m) wide nominal opening for all windows and doors. Further, the placement of these openings in the long dimension elevation of the shelter facilitates the placement of adjacent s helters to create “rooms” which can be arranged into usable building complexes.

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66 5. USF SYSTEM ASSEMBLY 5.1Introduction A lightweight FRP section was designed to overcome many of the shortcomings identified in available system s. This chapter provides step-by-step directions illustrating the assembly of FRP panel members to rapidly construct the emergency shelter. Section 5.2 includes additional information related to the FRP panel developed. The assembly of the structure is described in Section 5.3. Concluding remarks are summarized in Section 5.4. 5.2 Component Geometry The panel shape was developed to enhance structural performance. Specifically, the panel is comprised of a continuous truss system that helps stiffen the section and facilitates st ress transfer between the upper and lower skins that also act to resist bending induc ed stresses in two directions. The single panel configuration is detailed in Fi gure 5.1. However, the panels were developed to be used in an opposing, interlocking fashion, as shown in Figure 5.3.

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67 Figure 5.1 Basic Panel Geometry and C haracteristics (Units in Inches)

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68 Figure 5.2 Alternate Panel Geom etry Transverse Web Stiffener Aside from the structural performanc e characteristics inherent in the continuous truss configuration of the panel several positive attributes develop as a result of the geometry. Specifically, t he truss shape of the panel ribs allow for their usage as interlocking connectors. When opposing panels are connected in this fashion, the overall panel structure acts to restrict moisture and air infiltration. Another attribute of the panel member design are the lip connectors that run along the perimeter of each panel. These connectors, while not designed to transfer structural stresses between mem bers, are adequate to seal the joint that occurs between adjacent panel members. Such a lip connection is required to restrict moisture and air penetration through the system. In addition to the basic panel geometry, an alternative geometry concept was developed for use in loading situations where the member is subjected to large concentrated out of plane loads. Such loading conditions are experienced in members used in bridge deck applications. The alternative geometry incorporates additional transverse ribs in to the basic geometry to improve the

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69 ability of the panel to transfer concentra ted point loads throughout the member. The alternate panel geometry is shown in Figure 5.2. Note that both the standard panel and alternate panel geometri es have been developed to perform in an interlocking fashion. Critical to their performance is the interlocking nature of the ribs. This attribute allows the user to transfer forces between adjacent panels while ensuring that building env elop integrity is maintained. The interlocking nature of the panel member is illustrated in Figure 5.3. The interlocking connections of the panel system greatly simplifies the erection process due to the lack of a need for additional connections and members. This feature contrasts with one of the main observed weaknesses in existing building systems. Specifically, it was noted that all of the available systems required separate connector mem bers, both for member to member connection and member to support frame attachment. It may be argued that for each supplemental connector / attachment, an increase occurs in both erection complexity and the time required to construct the building. In summary, the member geometry was developed to provide the most efficient means for stress transfer. Further, the geometry was developed for use both in an interlocking panel, as shown in Figure 5.3, and in a one direction fashion where no interlocking performance occurs in the construction. The geometry also works to restrict mois ture and air penetration through the system. Finally, the simplicity of the geometry directly addresses the non-structural performance parameters of erection time system complexity, system adaptability and durability.

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70 5.3Construction Process The following construction sequence is provided to illustrate the simplicity and speed with which the optimized panel system can be erected in the field. It should be noted that all of the panel me mbers are made of FRP and will be light enough to be handled by one to two personnel. Further, the construction sequence assumes that the foundation system is already in place at the time of erection. This assumption is based on the need for the emergency shelters to be used in a wide variety of environments. Such usage precludes the development of one specific type of foundation system. In view of this, foundation development was excluded from the scope of this investigation. 5.3.1Step One As stated previously, no specific design for the foundation system was developed in this investigation. Nonetheless, several observations may be made with regard to the optimized panel system Firstly, the panel system can be utilized to provide direct anchorage bet ween a concrete foundation system and the shelter system. This connection, shown in Figure 5.3, utilizes the interlocking ribs of the standard member. To accomplish this connection, the base row of panel members is submerged into the concrete f ooting prior to curing of the concrete. Once the concrete has cured, a mechanism for uniform connection between the

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71 Figure 5.3 Typical Wall Section Panel System shelter and foundation is developed. A basic assumption with regard to the emergency shelter is that an earth floor system will be used to facilitate rapid construction. In cases where such a floor is inadequate, such as in a hospital or clean room facility, panel members c an be installed as a floor system. Specifically, individual panel members can simply span between the exterior walls of the shelter.

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72 Figure 5.4 Second Step: Wall Assembly 5.3.2Step Two The construction of the wall system involves sliding opposing panels into each other in an interlocking fashion as s hown in Figure 5.4. Note that the while the panels are shown to be erected in a horiz ontal fashion in this example, it can also be assembled vertically. Further, note that stiffening columns have been shown at the termination of each panel length. These columns are used at changes in geometry and to frame out wall openings. The dimensions of the FRP panel were selected so that they could be used in conjunction with standard pultruded FRP sections.

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73 Figure 5.5 Third Step: Wall Assembly / Openings 5.3.3Step Three As the walls continue to be assembled, openings are located and framed out using the standard FRP pultruded member s shown in Figures 5.5. These members also provide the user with t he ability to relocate opening locations and sizes as needed to facilitate each specif ic usage situation. It should be noted that, while the walls are shown to be c onstructed in a linear fashion, with each section erected from the ground to the roof, the user also has the option to construct the wall panels on the ground, tilting each section up into place between the column members.

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74 Figure 5.6 Fourth Step: Wall Completion 5.3.4Step Four After the walls have been completed, the roof members are prepared for assembly and installation onto the main stru cture. Once again, it should be noted that the roof members can be installed in an opposing, interlocking fashion, or in a non-interlocking fashion. The type of construction depends upon the types and magnitude of the roof loads to be experienced by the syst em. Further, it should be noted that the connection between the wall and roof members is provided by interlocking anchors, developed to slide into the panel rib members. These connectors, shown in Figure 5.7, provide direct transfer of wind induced uplift and shear forces between the roof and wall members.

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75 Figure 5.7 Hurricane Connector Component The use of a separate connector allows the engineer to customize the anchorage system to accommodate specific loading conditions. Furthermore, as each connector member is adjustable, it allows the engineer to develop pretensioned connections within the structural framework of the building. The offset panel construction shown in Figure 5.1 and Fi gure 5.3 provides an extra groove into which the connector member can slide. The connector strap is then tightened, locking the connector into place. This type of connection facilitates multiple construction and disassembly processe s without damage to th e system members.

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76 Figure 5.8 Fifth Step: Roof Assembly 5.3.5Step Five Each of the roof members are slid in to place, creating a roof system which performs as a structural plate system tr ansferring forces to the perimeter walls shown in Figure 5.8. The interlocking, opposing nature of t he system prevents both moisture and air penetration. This importanc e of this factor is evident with the subsequent conclusion that no additional r oof preparation is necessary prior to usage.

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77 Figure 5.9 Sixth Step: Building Completion 5.3.6Step Six The building shell is completed and ready for the installation of window and door assemblies. Due to the wide variety of high wind rated products available, neither assembly has been developed at this time. It is assumed that the frame out column members are adequate to receive a standard window / door assembly and will provide sufficient anchorage for these members.

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78 5.4Conclusions The preceding sections attempted to illustrate the power of the optimized panel system developed in this study. The ve rsatility of section geometry facilitates alternative applications. Thus, while t he panel shape was developed for use in an emergency shelter system, it can also pr ovide a viable solution for reinforced concrete roof/ floor applications in lieu of corrugated metal deck systems. Furthermore, variation of the panel geo metry permits its use in bridge deck applications. In summary, a major strength of the optimized panel system developed is the simplicity and speed it offers the user. Bo th issues are critical for the success of emergency shelters, where untrained workers must build shelters in the worst of conditions. Reducing the construction pr ocess to the six basic steps shown in Figure 5.10 allows the respons e team the best possible solution, in terms of training, simplicity and erection speed.

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79 Figure 5.10 Complete Construction Process

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80 6. FIBER REINFORCED POLYMERS 6.1Introduction The combination of high strength, li ghtweight, corrosion resistance and the facility with which it can be fabricated into complex shapes has made FRP the material of choice for the aerospace industry. This section provides basic information on the manufacturing process of FRP pultruded sections and also on the material properties assumed in t he analysis. More detailed information may be found in texts, e.g. Mallick 1988. 6.2Manufacturing of FRP Composites Pultrusion is a economical method of fabricating FRP shapes having a constant cross-section. In the proce ss, the constituent materials are pulled through a heated steel die, which forms the resulting laminate material into the desired shape. The putrusion process shown in Figure 6.1 consists of, 1)spools of uncured fiber rovings and mats, 2)Pre-form blocks which combine and coor dinate the fiber orientations prior to saturation, 3)Resin bath which saturates the fibers prior to final shaping and 4)Heated steel die which provides the final shaping and curing of the shape.

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81 Figure 6.1 Pultrusion Process 6.3Laminate Lay-up and Material Properties A pultruded FRP composite laminate cons ists of four specific component layers: 1)Thin layer of randomly oriented chopped fibers, heavily saturated with resin located on the surface of the shape. This layer, sometimes referred to as the Nexis, provides a smoot h surface and protection for the inner layers. 2)Unidirectional rovings, which contain fiber bundles running longitudinally down the axis of the pultruded shape. These layers provide tensile strength along the axis of the member, as would be required in flexural or tension applications. 3)Stitched Fabric Mat (SF) layers consist of unidirectional fiber bundles, woven into mats of off-axis angular or ientation. These layers, typically at 30, 45, 60 or 90 degree orientation to t he longitudinal axis of the member,

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82 Figure 6.2 Laminate Lay-Up Convention provide shear and weak direction fl exural strength for the members. 4)Cross Stitch Mats (CSM) consist of continuous or short randomly oriented fibers. These layers can be of va rious weights and attempt to simulate isotropic material behavior within the pl ane of the layer. Figure 6.2 shows the placement of the surface veil, the cross-stitched fabric mat and the rovings in the pultrusion of a flanged section. 6.3.1Material Properties Pultruded FRP shapes consist of a series of interconnected thin-walled plate and shell elements. The constituent parts of the laminate are the fiber and matrix. E-glass fiber, which provides the strength and stiffness characteristics for the laminate, is used in the pultrusion process. Polyester or Vinylester resin, which provides a protective matrix for the fibers and a medium for stress transferral, is used in the pultrusion process. For the purposes of this

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83 investigation, the elastic modulus, the shear modulus, Poisson’s ratio and density assumed are listed in Table 6.1. These we re taken from prior investigations and represent a good sampling of current i ndustry standard materials (Qaio, 1997). Note the order of magnitude difference in relative strengths of the fiber and the resin. The ply stiffness values shown in Table 6.2 were developed by Qiao (Qiao, 1997) for the roving, SF and CSM laminae using micromechanics for composites with periodic microstructure (Luciano, 1994). These ply stiffness values will be used during the des ign procedure in Chapter 9. Table 6.1 Material Properties ConstituentsMaterialE 106 psi G 106 psi (lb/in3) E-glass Fiber10.54.180.2550.092 Vinylester resin0.420.20.300.041Table 6.2 Engineering Constants PliesPlyE1106psi E2106psi G12106psi v1tkXc/t103psi Yc/t103psi S 103psi 3/4 oz. CSM 1.7101.7100.6100.4020.01521.358.5124.2 17.7 oz. SF 4.2071.2020.4650.2940.02696.88.4344.2 54 roving (62 yield) 5.71.240.5400.280.035548.44.2172.1

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84 6.4FRP Connection Review A critical limitation to the wide-spr ead usage of fiber reinforced polymers in structural framework centers on the design of connections between adjacent members. Within connection components, force concentrations and paths develop a highly complex map of stress and stra in. In materials such as steel, the complexity of the stress and strain can be simplified due to the isotropic nature of the material. Such is not the case in connections fabricated using FRP composite materials, where component performance varies greatly depending upon the direction of stress being applied (s ee Figure 6.3 through Figure 6.5). A significant amount of research has been conducted during the past two decades in the area of FRP connection design (Mosallam 1997, Mottram, 1997). Specifically, extensive research has been conducted to investigate connections which mirror shear and moment resisting connections in steel. “Steel type” connections typically consist of beam and column members as shown in Figure 6.6. Major work in this area is characterized in the following sections of this chapter.

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85 Figure 6.3 Effect of Joint Flexibility (Mosallam 1990) Figure 6.4 Failure of FRP Angle (Mosallam 1994) Figure 6.5 FRP Thread Failure (Mosallam 1995)

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86 Figure 6.6 Typical Steel Type Connector FRP6.4.1FRP Connection Performance Several tests have been conducted whic h investigate the performance of bolted connections which directly mirror those found in steel construction. Typically the work would entail full-scale testing of a moment frame constructed from standard W-shape or tube shaped FRP members (Bank, 1991; Bruneau, 1994; Mosallam, 1992). This body of research investigated a wide variety of connections, ranging from the typical clip angles shown in Figure 6.4 to the use of web stiffeners and thru-bolts that extend through both flanges of the column member. Several variations of the test connections have been shown below in Figure 6.6 through Figure 6.9.

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87 Figure 6.7 Clip Angle Connections. C lip angle shear and moment connections constructed using thru-bolting. In some case s, adhesives were also installed to provide supplemental connection mechanism. Testing entails rotation induced in the beam element with rotation measured through failure of the connection. Moment rotation curves are used to develop analytical models. (Bank 1991; Mottram 1994; Bruneau 1994)

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88 Figure 6.8 Stiffener Connections. A dditional web stiffeners installed to improve connection performance. Sti ffeners reduce the level of stress concentrations around bolt locations. The addition of web stiffeners were shown to account for a 33.6% increase in moment rotation capacity. (Bank 1991; Mottram 1994; Smith 1999)

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89 Figure 6.9 Full Thru-Bolting. Based on previous testing, which illustrated that connection failures were often due to localized shearing at the location of thru-bolts, connections were developed where bolts extended through both flanges. This connection ensur es greater joint stiffness by transferring forces more evenly into the connected members. These connections were shown to provi de up to 200% strength increases and 270% stiffness increases with res pect to simple clip angle connections (Mosallam 1997; Smith 1999).

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90 The testing of steel type connections has centered around the ability to transfer moment through the connection. As a result of these investigations, a variety of analytical models were developed by the researchers. Several observations can be made, based on the body of work previously done in this area, 1)Bolted connections exhibit non-linear moment rotation performance as the frame is loaded to failure. This non-linearity is due to the semi-rigid nature of the connection (Mosallam, 1992). 2)Typical failures of the simple clip angle connections involve localized buckling and separation of the column flange and web (Bank, 1994). 3)In connections where the members are braced using stiffeners or full thrubolting, typical failures occur due to delamination and buckling of the clip angle member (Bank, 1994). 4)A significant impediment to the capac ity of FRP connections is an inherent weakness in pultruded W-shaped members at the web flange intersection. Specifically, an under-reinforced triangle shaped zone at this intersection significantly reduces the capacity of connections members (Mosallam, 1994). 5)Significant increases in connection performance, both in terms of stiffness and strength, can be gained through t he development of new types of connectors, such as the Universal Connector and the installation of stiffeners and thru-bolts (Mo sallam, 1997; Smith, 1999).

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91 Figure 6.10 Coordinate Systems As a result of these observations it was concluded that steel type connections of FRP frame members can be developed which provide joint characteristics similar to steel fram e systems. But, the improved connection combinations (shown in Figure 6.9) are highly complex with respect to similar connections found in steel frames and would act to deter the use of such frames in typical construction situation 6.5Coordinate Systems and Sign Conventions The FRP shapes to be investigated are panelized pultruded members that, for the purposes of analysis will be designed as a series of interconnected flat panels. Global (X, Y, Z) and local (x, y, z) coordinate systems are defined as shown in Figure 6.10. The moment and force conventions used in the development of material properties withi n individual laminae is also provided below in Figure 6.11.

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92 Figure 6.11 Force and Moment Resultants 6.6Laminate Design Anisotropic materials such as FRP create a challenge for engineer due to the complexity of the material in comparison to homogeneous materials such as steel. One aspect of this complexity is the increased number of material constants required for analysis. G eneralized Hooke’s Law for anisotropic materials requires 21 independent stiffness c oefficients. While this makes the design of anisotropic materials in 3-dimensions very complex, the characterization of composites as pl ate elements consisting of orthotropic laminae, or layers, can be utilized to greatly reduce the number of independent coefficients.

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93s s s s s s e e e g g g11 22 33 23 13 12 111212 122223 122333 44 66 66 11 22 33 23 13 12000 000 000 00000 00000 00000 CCC CCC CCC C C CThe following sections describe Cla ssical Laminate Theory, beginning with the principle equations for stress and strain within an orthotropic laminae. These equations are then developed into stress and strain equations for the entire laminate based on the location and stress conditions of individual laminae. An orthotropic material is classified as one in which the material properties are identical in all three directions. The num ber of material coefficients reduces to 9 in an orthotropic material with the axis of orthotropy 1-2, with q = 0. The stress strain relationship in such a laminae is given in Equation 6.1. (6.1) This relationship is further simplified through the assumption that each layer exists in a plane stress state where, (6.2)stt323310this condition reduces Equation 6.1 to, (6.3)s s g e e g11 22 12 1112 1222 66 11 22 120 0 00 QQ QQ Qwhere the reduced stiffness coefficients Qij are given by four independent engineering constants in the principle material directions as folllow,

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94 (6.4) Q E Q EE Q E QG11 1 2112 12 122 2112 211 2112 22 2 2112 66121 11 1 uu u uu u uu uuThe principle material axes1-2 within each laminae are typically rotated with respect to the overall laminate reference ax es x-y. To account for this rotation, transformed reduced stiffness coeffici ents are developed using the following equations, (6.5) QQCosQSinQQSinCos QQSinQCosQQSinCos QQQQCosSinQQSinCos QQQQQCosSinQSinCos1111 4 22 4 1266 22 2211 4 22 4 1266 22 12112266 22 1266 22 6611221266 22 66 4422 22 422 22 qqqq qqqq qqqq qqqq() ()()Subsequently, the stress-strain relationship for each laminae, given in terms of the laminate reference axes x-y, is as follows, (6.6) s s t e e gx y xy x y xyQQ QQ Q 1112 1222 660 0 00The transformed reduced stiffness E quations 6.5 can be simplified with respect to the angular orientation of the principle laminae axes 1-2 and the laminate reference axes x-y. The first step of this simplification is the development of invariant coefficients Uk as follows,

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95 (6.7) UQQQQ UQQ UQQQQ UQQQQ UQQQQ111221266 21122 311221266 411221266 5112212661 8 3324 1 2 1 8 24 1 8 64 1 8 24 Substitution of Equation 6.7 into Equation 6.5 results in the following set of equations which are simpler than those shown in Equation 6.5 with respect to laminae orientation. This simplification is helpful during the optimization process. (6.8) QUUSin2UCos4 QUUCos4 QUUSin2UCos4 QUUCos411123 1243 22123 6653 Jq J JJ JClassical Laminate Theory (CLT) allows the engineer to create a relationship between the stress and strain characteristics of individual laminae and the performance of the entire laminate. In order to accomplish this, CLT makes the assumption that the laminate cons ists of N orthotropic layers, perfectly bonded to each other, that the bond line between layers is infinitely thin and nonshear deformable and that Kirchhoff Plat e Theory is used, in which in-plane displacements vary linearly through the th ickness of the layer. Specifically,

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96 mm w uu w egg ww 0 0 0 0 00 z d dx z d dyzxzyz Figure 6.12 Laminate Stacking Convention (6.9) where m and n are the in-plane displacements; ez, gxz, gyz and w describe the out of plane deformation and z is the distanc e from the layer to the laminate midplane as shown below in Figure 6.12,

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97 Subsequent to these assumptions, the st rain distribution within the laminate becomes, (6.10)e e g e e g k k kx y xy x y xyx y xyz 0 0 0where k are the midplane curvatures and e0 and g0 are the strain components at midplane of the laminate. Substitu tion of Equation 6.10 into Equation 6.6 results in the following stress strain relationship, (6.11) s s t e e g k k kx y xy 1112 1222 66 0 0 0 x y xyQQ0 QQ0 00Q zx y xy Resultant force and moment equati ons are developed using the laminae stress values derived in Equation 6.11 and summed through the thickness of the laminate as shown in Equations 6.12 and 6.13, (6.12)N N N dz AAA AAA AAA BBB BBB BBBx y xy x y xy h/2 h/2 111216 212226 616266 0 0 0 111216 212226 616266 x y xyx y xy s s t e e g k k k (6.13)M M M zdz BBB BBB BBB DDD DDD DDDx y xy x y xy h/2 h/2 111216 212226 616266 0 0 0 111216 212226 616266 x y xyx y xy s s t e e g k k kwhere Aij, Bij and Dij, are the extensional, shear coupling and bending coefficients, respectively. These coefficients are defined as follow,

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98 (6.14) AQzzij ij k kk k N 1 1 (6.15) BQzzij ij k k Nkk1 222 11(6.16) DQzzij ij k k Nkk1 333 11In order to simplify the number of va riables and the complexity of the equations, shear coupling can be eliminat ed through the symmetric placement of layers with respect to the mid-plane of the laminate. This allows for the elimination of the Bij coefficients from the engineering calculations. Equations 6.14 through 6.16 can be modified into a form more conducive to design optimization. This form uses laminae in variant coefficients Vi which are defined below (Gurdal, 1999), (6.17) Vh hAB,D 0 30 12(,),, (6.18)VttztzzzzAB,Dkkkkkkkkk k N 1 2 11 2 122(,)cos,, J(6.19)VttztzzzzAB,Dkkkkkkkkk k N 1 2 11 2 122(,)cos,, J (6.20)VttztzzzzAB,Dkkkkkkkkk k N 2 2 11 2 122(,)sin,, J(6.21)VttztzzzzAB,Dkkkkkkkkk k N 3 2 11 2 142(,)cos,, J

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99 where tk = zk-zk-1 represents the layer thicknesses and zk is the z coordinate of the mid-plane of the kth layer with reference to the mid-plane of the laminate. Use of the Vi and Ui laminae invariants a llows for a simplified representation of the A, B and D matrices, as shown below (Gurdal, 1999), Table 6.3 A, B, D Matrices in terms of laminae invariantsV0(A,B,D)V1(A,B,D)V2(A,B,D)V3(A,B,D)V4(A,B,D)(A11,B11,D11)U1U20U30 (A11,B11,D11)U1-U20U30 (A11,B11,D11)U400-U30 (A11,B11,D11)U500-U30 (A11,B11,D11)00U202U3(A11,B11,D11)00U20-2U36.7Summary This chapter has provided an extens ive foundation with which the design optimization and analysis will be performed in C hapter 7. The initial sections of this Chapter were intended to provide in sight as to the scope of the problem at hand. Specifically, the following observations can be made based on the background work conducted in the area of hurricane winds design and emergency shelters, 1)Advanced composite materials offer a highly adaptable solution to the emergency shelter problem. 2)A significant weakness in the des ign of advanced composite structures occurs at member connections. This weakness is due to the use of “steel

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100 type” connectors which do not fully utilize the strengths of composite materials.

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101 7. DESIGN OPTIMIZATION OVERVIEW 7.1Introduction Previous chapters of this inve stigation have dealt the pragmatic application of the shelter problem, issues of construction cost, availability and adaptability. Further the investigation has provided and overview in Classical Laminate Theory. The purpose of this chapt er is to provide a general overview of structural design optimization techniques While not intended to be a detailed review, this chapter shall provide the reader with an understanding of the typical terms, process and characteristics of design optimization. 7.2Design Optimization General Procedure Design optimization in structural engineering can best be described as an educated trial and error procedure, wher e performance functions are first developed and then analyzed to ascertain maximum or minimum values. Composite materials are well suited for design optimization, based on the extensive range of configurations ava ilable to the engineer. Similarly, the complex nature of composite materials can result in cumbersome performance functions which may be costly in terms of computation time (Haftka, 1990).

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102 Several design optimization procedures have been developed to locate the maximum and minimum values of design functions. While the procedure followed by each optimization technique may differ, all design optimization techniques follow the same basic format of 1)Selecting a group of initial trial values, 2)Calculating a value for the objective performance function for each of the trial values, 3)Removing the least successful trial values from the solution pool, 4)Re-calculation values using permuta tions of the most successful trial values from the previous round of optimization. This four step process is typically under taken until a global solution is found. While there are myriad variety of desi gn optimization techniques, the following terms and assumptions are generally found in most accepted methods and are described here to inform the reader. 7.2.1 Objective Function An objective function can be any performance function to be optimized. For example, the compression buckling formula developed by Qiao in his work with FRP beam optimization could be chos en as a objective function. This equation, shown below, is dependent on the D11, D12 and D22 within the laminae, which are in turn dependent on the orient ation of the plies and their stacking sequence (Qiao, 1997).

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103 (7.1) l pbxN b DDDD2 22 2 11221266Note the coefficient lb located at the beginning of Equation 7.1. This is a buckling factor and acts as the value to be optimized. In general notation, Equation 7.1 can be described by the objective function, (7.2)lloptimumbp()min() 1Another aspect of the objective func tion is the application of the penalty factor p. The penalty factor acts to penalize the proposed solution when certain design constraints, such as maximum la minate thickness, are violated. This factor is typically applied as a percent age reduction in the calculated value of lb. 7.2.2 Constrained Optimization Sometimes it is necessary to limit the search based on constraints placed on performance criteria related to t he design variables within the objective function. For example, a design cons traint may be placed on the laminate that requires Gxy to be below a certain value. Since the value of Gxy directly affects Equation 7.1, it can be seen that restricti ng this variable will result in constraint of the solution pool. Typical notation for Constraint is as follows, (7.3)005106Gpsixy.

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104 7.2.3 Neighborhood Searches Neighborhood search techniques are often used in conjunction with integer programming. In these situat ions, the neighborhood is defined as all single unit variations of the initial trial solution (Pai, 2001). For example, if the initial trial solution is described by t he integer sequence {1201}, the neighborhood would entail the following variations {0201}, {2201}, {1001}, {1101}, {1221}, {1211}, {1200} and {1202}. Note that each variation is gained by shifting one variable a single position. 7.3 Linear Integer Programming Integer programming is significant to optimization in that it allows the engineer to simplify the representati on and manipulation of design variables within each trial solution. In the case of optimization for composite laminates, integer programming is typically used to represent the ply orientations. Specifically, 00, +450, -450 and 900 ply orientations can be assigned integer values of 1, 2, 3 and 4, respectively. Therefore a laminate having the stacking sequence {0,+45,-45,90,90, -45,+45,0} could be represented as {1,2,3,4}s. Note the subscript s has been applied to represent symmetry. To further simplify the representation, the engineer can represent the +450 and -450 as a stacked pair, thus reducing the number of variables by one. The subsequent reduced notation would be {1,2,3}s, where the 900 ply is represented by the integer 3.

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105 The use of integer programming allows the designer to avoid the problems involved when design variables are not consecutive in nature, as in a variable set consisting of 00, 450 and 900 composite layers. Assigning these layer orientations integer values allows the designer to develop the objective and constraint functions into linear functions of the design values. The standard form of a Integer Linear Programming problem (ILP) is, minimize fxcxT()such thatAxbx ,0where c is an n x 1 vector of constant coefficients, A is an m x n matrix of constraint coefficients, and b is an m x 1 vector of constants (Gurdal, 1999). In optimizing composite laminates, t he designer sometimes uses integers to describe certain laminate characterist ics (such as layer orientation) while allowing other characteristics (such as layer thickness) to be continuous. This is referred to as Mixed Integer Linear Programming (MILP) and has the standard form, minimize fxcxcyTT()12such thatAxAyb12 ,where x is an integer greater than or equal to one and y is any number greater than or equal to one (Gurdal, 1999).

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106 7.4Genetic Algorithms Genetic Algorithms (GA) is a well k nown optimization procedure which is based on the principles of evolution found in nature. Specifically, GA utilizes the observation that survival of the fittest tends to propagate desirable characteristics while eliminating unwanted characterist ics from a subject pool. GA perform design optimization using similar techniques (Gurdal, 1999). The basic GA procedure begins with an initial population of trial solutions evaluated using the objective performance function. The fitness of each trial solution measures how desirable the result s of this evaluation. The possibility that a trial solution will be used in subs equent optimization runs is proportional to the level of its fitness. Therefore, t he better a trial solution performs during the evaluation, the better its chances to rema in in the solution pool as a potential parent for the subsequent generat ion of trial solutions. Subsequent generations of solutions are developed through the pairing and combination of the trial solutions, based on their evaluated fitness. The process is based on the evolution of a gene pool that occurs in nature. In addition to this basic process of evol ution, mutations and permutations are introduced into the GA process to prevent premature loss of solution characteristics which might be si gnificant to the final solution.

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107 8. DEVELOPMENT OF PANEL PERFORMANCE CRITERIA 8.1Introduction The design and optimization informa tion presented within Chapter 7 will eventually be utilized in Chapter 9 to optimize the composite laminate panel member. Before this optimization can be conducted the performance functions must be developed in a form conducive to t he eventual optimization process. To that end, the following tasks will be performed within this chapter, 1)Design equations will be developed to calculate localized plate buckling, global member deflection and first-ply failure loads. 2)Localized plate buckling equations will be developed by dividing the panel member into discrete plate elements. 3)Global member deflection will be developed based on the combined stiffness and geometric properti es of the panel element. 4)First-Ply Failure will be developed using the Tsai-Hill Failure Criteria to determine the strength envel ope for the panel element, 5)Design equations will be dependent on two criteria; ply orientation and laminate stacking sequence, 6)The fixed parameters in all equati ons will include panel geometry, laminate thickness, laminae thickness and ma terial properties of plies.

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108 Figure 8.1 Division of Panel Member 8.2Local Buckling Performance Pultruded FRP beam and panel members consist of a series of interconnected plate members. During loading conditions in which members are exposed to axial compression and bending, pr emature failure of the member due to local buckling of these plates can occur. The local buckling capacity of the constituent plates can be modeled using a series of discrete plates subjected to in-plane compression and shearing forces. Through variation of the discrete plate boundary conditions, the local buckling can be characterized (Qiao, 1997). To clarify the previous paragraph, the panel unit shown in Figure 8.1 has been divided into a series of discrete plates for the purpose of subsequent analysis in this chapter. The individual plate elements, including in-plane loading and retraint conditions, have been illustrated in Figur e 8.2. Division of the panel into component plate elements results in two load conditions. In each flange elements, the in-plane loading consists of compression (Nx) applied along the

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109 Figure 8.2 Discrete Plate Elements longitudinal axis of the panel. In the web elements, shear stress (Nxy) is induced in each plate. In Figure 8.2, (a) and (b) are the di mensions of each plate element and z is the restraint coefficient characteri zing the fixity of the plate boundary. Z is based on the stiffness of the adjoining plate element and is developed in the following section. The following sections will present general solutions for thin plate buckling due to axial compression and shearing force. Subsequent to the development of the solutions, equations fo r the calculation of the restraint coefficient will be presented.

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110 8.2.1General Buckling Equations Axial Compression Local buckling in thin plates under axial compression is governed by Equation 8.1, developed by Whitney for a symmetric anisotropic plate (Whitney, 1987). Within this equation, Dij are the plate bending stiffness coefficients; Nx is the uniform axial stress resultant and w(x, y) describes the buckled shape of the plate. This equation has been simplified based on the assumption that the laminate consists of balanced off-axis la minae, resulting in the elimination of bending-twisting coupling (D16 = D26 = 0). (8.1) D w x D w x w y D w xy D w x N w xx 11 4 412 2 2 2 266 4 2 22 4 4 2 2240j j j j j j j jj j j j j The general solution to this equation can be written in the form (Bleich, 1952), (8.2) wxy nx a CkyCkyCkyCky (,)sincoshsinhcossin p11223242where k1 and k2 are (Webber, 1985), (8.3) k n a1 22p aabm(8.4) k n a2 22p aabm(8.5) m p ab2 22 2 1266 22 11 222 N D a n DD D D Dx;;

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111 where the constants Ci are determined based on the specific boundary conditions for each plate element along the edges described by (a). The general solution listed above can be further simplified by assuming that the deflection of the pl ate results in a symmetric function of y as the buckling load is approached. Specifically, it is assumed that the plate forms a symmetric sin wave shape along the y-axis. The second assumption is that equal restraint exists along both of the unloaded edges of t he plate. These assumptions result in the following form of Equation 8.2, (8.6) wxy nx a CkyCky (,)sincoshcos p1132Qiao used Equation 8.6 to develop the following equation for the critical axial buckling stress resultant, Nx, for long simply supported plates (Qiao, 1997). (8.7) minN b DDDDx2 22 211221266pEquation 8.7 was further developed to account for elastic edge restraint. This condition occurs in Flange I, II and III in Figure 8.1. The boundary conditions for this condition are that no local deflection (w+b/2,-b/2 = 0) occurs along the boundary and that the rotation along t he boundary for the plate in question ( f ) is identical to the rotation in the adjoining plate which provides the elastic restraint ( f=fr). To represent the effect of th is elastic restraint, Bleich derived

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112 restraint coefficients p and q. The solution to the buckling equation for axial compression with elastic restraint is (Qiao, 1997), (8.8) minN b qDDpDDx p2 21122126622Note that the above equation constitutes the local buckling equation to be used for Flanges I, II and III of the panel member. Buckling load equations were also developed for biaxial loading conditions for a composite laminate plate by Liu. The buckling equations were developed under the assumption that the composite laminate could buckle into m and n halfwaves in the x and y directions (Liu, 2004). Subsequent to this assumption, they proposed the following critical buckling equation for a laminate plate under axial loading (no shearing), (8.9) n mn XYD m a DD m a n b D n b m a N n b N(,) 2 11 4 1266 22 22 4 2222 8.2.2Elastic Restraint The presence of elastic restraint along the unloaded boundaries of the plate element (see Figure 8.2) significant ly increases the complexity of the buckling equations. Elastic restraint is addressed through the development of a restraint constant, z which is based directly on the material and geometric properties of all plates t hat occur at that boundary.

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113 The development of this constant is based on the assumption that rotation about the boundary will be transferred without losse s. The restraint constant was first developed by Bleich for isotropic materials using a uniformly loaded column (Bleich, 1952). These equations were m odified by Qiao to account for material anisotropy and the effect of compressive st resses in thin walled sections. These modifications result in the followi ng equation for the restraint constant, z for a box section in which elastic restrain t occurs along both boundaries of the plate (Bleich, 1952; Qiao, 1997). (8.10) zb b D D rw f f w 22 22where w and f refer to the web and flange plate elements and r is a modification factor introduced by Bleich and modified by Qiao, (8.11) r b b DDDD DDDDw f ffff wwww 1 1 2 211221266 11221266Both of the equations above are dependent on the Bending Coefficients, Dij, of the laminate and the width, b, ov er which the plate would experience bending. It should be noted that for this in vestigation, Equations 8.10 and 8.11 simplify to be solely dependent upon the web and flange width geometries since all members are made of the same laminate.

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114 8.2.3General Buckling Equations Shearing Local buckling of the webs in the panel member is controlled by the development of shearing forces as flex ural moment is induced on the panel. Web member buckling is illustrated in Figure 8.2. For the purpose of this investigation, the web is modeled as a simply supported plate subjected to shear forces only. The flanges are assumed to restrain the web and deflection is assumed to be zero. For these c onditions, the restraint coefficient, zs, was developed as (Qiao, 1997), (8.12) zs f fD b222where f denotes the flange that restrains the web plate element being analyzed. The general equation for an anisotropic thin plate under shear loading was developed using the first variation of the total potential energy equation (Barbero, 1993), (8.13) D w x w x D w x w y D w y w y D w xy w xt N w x w y N w x w y xy w y w y wxyxy b a s yy s 11 2 2 2 212 2 2 2 2 22 2 2 2 266 22 0 0 004j j d j j j j d j j j j d j j j jj d j jj j j d j j d j j j j jj z j j d j j z j j d j j jy w y xybyb a 00A solution for the displacement w( x,y) which satisfies the boundary conditions defined by Equation 8. 12 is defined as (Qiao, 1997), (8.14) wA ix a jy bij j n i m sinsinpp1 1

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115 The critical buckling shear stress, Nxy, can be calculated for the web member as a linear eigenvalue problem using Equations 8.13 and 8.14. In an attempt to simplify the shear buckling equations shown above, the laminate panels can be assumed to have infinite length in the x direction (Whitney, 1985). Based on this assumption, critical shear buckling is defined by, (8.15) s XYDDD bN for 42 011221266 2,(8.16) s XYDD bN for4 111122 3 14 2 /,where variables are as defined below, (8.17) DD DD1122 12662

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116 Table 8.1 Buckling Factors B10.011.71 0.211.80 0.512.20 1.013.17 2.010.80 3.09.95 5.09.25 10.08.70 20.08.40 40.08.25 Infinite8.13 Under simultaneous loading conditions, the critical axial and shearing buckling interaction can be approximat ed through the following interaction equation (Lekhnitskii 1968, Liu 2004), (8.18) 1112 c mn n mn s,,8.3Global Deflection Performance The global performance properties of the panel member; axial compression, member bending and shear, have been developed in the past as a summation of the constituent plate element s. Using beam theory with no torsion and assuming that the off-axis plie s are balanced symmetric (no bending

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117 twisting coupling), Qiao developed simplified equations for the axial (Ai), bending (Di) and shear (Fi) stiffness coefficients (Qiao,1997). Specifically, the stiffness coefficients of individual plate elements are, (8.19) AEt D Et FGtix i i i x i ixy i ii 312where (Ex)i and (Gxy)i are the engineering properties of the ith plate and ti is its thickness. The stiffness coefficients ar e then combined to provide the beam axial (Ai), bending (Di) and shear (Fi) stiffness Equation 8.20, (8.20) AAb DA b Db FFbzii i n ziiii i n i ziii i ni 1 2 22 1 2 112 sincos sin where bi is the plate width, and qi is the cross sectional orientation of the ith plate. Subsequently, these stiffness coeffici ents can be used in conjunction with general formulas for maximum bending and shear deflection under uniform loading conditions. The resulting equati on for the maximum deflection of a simply supported beam of length L and uniform load W is, (8.21) totalbendingshear zzzWL D WL KF5 3844

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118 where Kz is a shear correction factor to account for the actual shear stress across the member cross section. For the purpos e of design, this correction factor can be set as 1.0 (Davalos, 1996). Further work by Giroux and Shao on FRP reinforced sheet piles resulted in the development of equivalent flexur al rigidity properties of a panelized member (Giroux, 2003). The equivalent rigidity properties were developed utilizing Timoshenko’s beam theory and are as follows, (8.22) EI b Ezz Et t Ishape x j jj j n flange x i w i w i m y web web 33 1 3 1 1The equivalent flexural rigidity val ue generated from Equation 8.22 would then be utilized in Equation 8.21 in place of Dz for the calculation of deflection due to bending. It should be noted that none of t he global deflection calculation shown above account for closed sections where stress sharing occurs between adjacent connected panel members. 8.4First Ply Failure (FPF) Performance When a laminate material is loaded, different stresses develop in each of the layers, depending on the orientation of t he fibers and the location of the layer with respect to the laminate mid-plane. As a result of these stress differences, it

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119 is likely that some laminae plies will fail prior to others. This phenomena is called first-ply failure (FPF). In FRP compos ites, the brittle nature of the laminate materials prevents strength per formance past FPF (Gurdal, 1999). The strength of the laminate is dependent upon the FPF. Several failure envelops have been developed to ascertain the stress levels at which FPF will occur. For the purposes of this investi gation, the Tsai-Hill failure criterion shall be used and is defined as follows (Gurdal, 1999), (8.22) P PXYXScr 1 2 2 2 12 2 12 21where s1, s2 and t12 are the laminae principle stresses; X, Y and S are the corresponding ply strengths; P is the applied load and Pcr is the critical load. 8.5Summary This chapter has developed four prim ary performance related optimization functions. These are the performance f unctions of local buckling (axial and shearing), global deflection and laminate ply failure. Additionally, an overall cost function, represented as the thickness of individual plies, will be optimized for the development of the best solution set.

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120 9. COMPOSITE PANEL DESIGN ANALYSIS / RESULTS 9.1Introduction The preceding chapters have laid a groundwork through which the reader was first introduced to the problem of temporary shelters needed for disaster relief and response. The basic requirements necessitate erection speed, weight minimization and strength. These desi gn requirement led to the conceptual development of an interlocking panel syst em made of composite materials. The previous three chapters provide the reader an overview of the basics of Composite Laminate Design (Chapter 6), Design Optimization (Chapter 7) and the Development of Performance Func tions (Chapter 8). This chapter will accomplish several things. 1)First, the reader will be re-intr oduced to the primary equations utilized in the design process. These will include equations for local buckling, first ply laminate failure and global deflection. 2)Second, the reader will be taken, st ep by step, through the laminate design and analysis process. This process will begin with an explanation of the loads exerted on the section and finish with the computation of the performance values for local buckling, first ply failure and global deflection.

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121 3)The reader will be presented with a ll possible laminate solutions. Due to manufacturing restrictions, the number of possible laminates is restricted to nine (based on a eight ply balanced symmetric laminate). 4)The solution pool will be verified utilizing the Finite Element Software Ansys 5.7. The comparison will evaluate each of the performance criteria. The resu lts will be discussed with reference to accuracy and significance. The next section explains the restrict ions that are placed on the design process prior to initiation. These rest rictions are based on a pultrusion industry review and have to do with value engineer ing of the end product and elimination of interlaminar stress coupling in the laminate pool. 9.2Design Restrictions Prior to the analysis phase of the inve stigation, an exhaustive review was conducted of the composite manufacturing industry and of existing techniques for the design of composites. Subsequent to this investigation, it was found that several restrictions were necessary to facilitate the economical production of a composite member. Specifically, the fo llowing design parameters were restricted based on the need for overall economy, 1)Lay-up Restrictions; Based on a revi ew of composite engineering / design, the candidate pool of composite lami nates was restricted to symmetric laminates (laminates having sy mmetry about the mid-plane) made of

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122 paired orientation stacked layers (ie ...45/-45/30/-30). These restrictions eliminate bending extension coupling from occurring within the laminate. Bending extension coupling refers to the generation of bending stresses due to in-plane loads placed on the laminate. 2)Thickness Restrictions; Through discussion with several pultrusion composite manufacturers, we were informed as to the standard stock material used in their production. For the purposes of economy, the minimum layer thicknesses and maxi mum laminate thickness have been restricted to those typically utiliz ed in the manufacturing process. 3)Laminate Uniformity; For the purpos es of economy, all walls of the composite panel member are assumed to be the same thickness and laminate lay-up. 4)Layer Orientations; For the purpos es of economy, all walls of the composite panel member are assumed to be the same thickness and laminate lay-up. Subsequent to the restrictions noted above, the solution sample pool was limited to nine lay-up orientations for an eight ply laminate and twenty five lay-up orientations for a twelve ply laminate. Based on this small pool, it was decided that all possible solution sets would be analyzed and compared.

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123 9.3Performance Equations Buckling Local buckling in thin plates consti tutes a primary area of design concern with respect to the strength characteri stics of the laminate. The following buckling performance equations, first pres ented in Chapter 8, will be used in the design, Local Buckling (Axial Compression) (9.1) n mn XYD m a DD m a n b D n b m a N n b N(,) 2 11 4 1266 22 22 4 2222 Local Buckling (Shear Forces) (9.2) s XYDDD bN for 42 011221266 2,(9.3) s XYDD bN for4 111122 3 14 2 /,where the variables are as defi ned in Sections 8.2.1 and 8.2.3. Local Buckling (Combined Forces) (9.4) 1112 c mn n mn s,,The factors m and n represent the number of half-sine waves that represent the deformed shape of the plate at buckling load. For this analysis, the maximum value of m and n was set to a maximum of 4. This restriction was based on initial analysis conducted to a maximum value of 20. It was noted during the

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124 preliminary analysis that the minimum buckling factors were found at small values of m and n. 9.3.1Restraint Factor a nd Load Distribution Factor To represent the effect of interc onnected panel members, the restraint factor developed by Bleich (Qaio 1997) was modified for use in a closed cell beam where more than two panels share a joint. The subsequent restraint factor is presented below, (9.5) R b bbbi1 1 121 111 where bi is the width of each panel member at the joint in question. Equation 9.5 also assumes all panel members to consist of the same laminate lay-up and thickness. In addition to the strengthening charac teristics of the interconnected panel members, this geometry allows for load distribution / sharing to be conducted throughout the panel. To represent this load distribution, the following equation was developed utilizing similar distribution methods used in moment distribution of structural frames,

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125 (9.6) DF at b at b at b at blam lamlamlam i1 3 1 3 1 3 2 31 12 1 12 1 12 1 12 9.4Performance Equations Laminate Failure Laminate Failure constitutes another primary area of design concern with respect to the strength characteristics of the laminate. For this investigation, laminate failure is determined through the us e of the Tsai Hill failure criteria. The following laminate failure performance equation, first presented in Chapter 8, will be used in the design, (9.7) P PXYXScr 1 2 2 2 12 2 12 21where the variables are as defined in Section 8.4. 9.5Performance Equations Deflection Global deflection constitutes a pr imary area of design concern with respect to the serviceability characteristic of the laminate. For this investigation, the deflection criteria developed by Qiao and Giroux and presented in Chapter 8 will be utilized. Specifically, the flexur al rigidity equations developed by Giroux will be utilized to calculate global deflection due to bending and the torsional

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126 EI b Ezz Et t Ishape x j jj j n flange x i w i w i m y web web 33 1 3 1 1 totalbendingshear shape zzWL EI WL KF5 3844rigidity equation developed by Qiao will be used to calculated the global deflection due to torsion. This criteria is as shown below, (9.8)FGt FFbixy i i ziii i n sin2 1(9.9) (9.10) where the variables are as defined in Section 8.3. 9.6 Example Design Process In order to best illustrate the design results, a step by step process will be presented using an example laminate lay-up. The numerical computations were conducted using Excel spreadsheets. These spreadsheets will be presented below for each primary step. The lami nate to be presented will be a 0/0/45/-45/45/45/0/0 eight ply laminat e represented by 0/45 in the results tabulation. The geometry of the shelter building is as shown in Figure 9.2. This building represents the geometric optim ization performed in Chapter 4. Subsequent to the wind analysis also perfo rmed in Chapter 4, the resulting

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127 Figure 9.1 Critical Wind Pressures Mono Slope Roofdesign wind pressures are presented in Figure 9.1. Since these values vary widely throughout the structure, it was dec ided to design the panel for the worst case load condition. This case corresponds to 198.1 psf (9.49 kPa). Further, the composite shell panel members have des igned for 151.8" (3.856 m) overall span length.

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128 Figure 9.2 Emergency Shelter Footprint Figure 9.3 Member Section

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129 9.6.1 Design Step One The first step in the process is to convert the wind pressure exerted globally on the building into Nx, Ny and Nxy forces exerted locally on the individual plates that constitute the composite panel section shown in Figure 9.3. The following assumptions were used to convert the wind pressure into local forces. 9.6.1.1 Axial Compression Bending The axial compression force generated as a result of bending in the member. As the member flexes, compre ssive and tensile forces build up in a moment couple about the centroid of the section. The worst case compression force due to bending is assumed to occur in the roof panels due to the wind exposure and span. Theses forces would be maximized on Plates 1, 2, 3 and 6, which constitute the extreme section components. (9.10) Loadpsf Spanft M psfftin in inlbin 1981 12649 19811264912 812 396192. .(.)() () ./The development of the bending stress into total bending induces compression force and subsequent distribution among component plates (as per Equation 9.9) is shown in Table 9.1.

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130 9.6.1.2 Axial Compression Wind The axial compression force generated as a result of the downward roof pressure acting on the perimeter walls. This force will be evenly carried throughout the member cross section. In addition, the selfweight of the structure and wall system combine to pr oduce axial loading. This loading is maximized at the base of the wall system. (9.11) LoadpsfMainForcesistingSystem SelfWeightpsfroofandwall Spanft N psfpsfft in psfft in Nlbinxaxial xaxial 748 15 12 7481512 212 1512 12 599 .(Re) () (.)() () ()() ./() ()9.6.1.3 Transverse Compression Wind The compression force acting along the short axis of the panel member induced by the lateral shear forces generated globally by the wind. These forces would be maximized on Plates 1, 2, 3 and 6, which are arranged parallel to the orientation of the applied global force. (9.12) LoadpsfMainForcesistingSystem Heightft Lengthft N psfftft ftin lbinyaxial 618 12 24 6181224 21212 618 .(Re) (.)()() ()() ./()

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131 9.6.1.4 Shearing Forces Wind The shearing induced in the panel section induced by the wind induced shear forces on the building. The shear forces would be maximized in Plates 1, 2 and 3, which constitute a uniform shear plate. (9.13) LoadpsfMainForcesistingSystem Heightft Lengthft N psfftft ftin lbinxy 618 12 24 6181224 21212 618 .(Re) (.)()() ()() ./At this time it would be wise to m ention the conservative nature of this analysis. As is illustrated above in the de scription of the four forces, all of the constituent plates do not experience the maximum forces. Further, it could be assumed that plates do not simultaneously experience the maximum forces. It could therefore be concluded that t he design forces used here are overly conservative. In response, it should be pointed out the these are building code specified wind design pressures, which themselves are equivalent static loads developed from a dynamic force (wind). The utilization of worst case load conditions in all applications provides the investigator with a level of conservatism that is necessary for guaranteed performance and subsequently, life safety.

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132Load Calculations (Taken using worst case pressures throughout) Bending 198.1psf(Roof Members Corner Condition) Shearing61.8psf(Wall Members) Axial198.1psf(Downward Wind Pressure on Walls) Geometric Properties memberthicknesslengthareaYAYIAd^2 10.2842.8480.8090.2130.1720.0052.131 20.2841.2410.3520.2130.0750.0020.928 30.2842.8480.8090.2130.1720.0052.131 40.2844.4631.2671.9372.4552.1040.013 50.2844.4631.2671.9372.4552.1040.013 60.2845.6721.6113.6625.8990.0115.371 Y bar1.836 Ix Total14.818 Bending Moment3962.000in-lb / in Nx (Bending)490.897lb / inNy (Wall Shear)61.800lb / in Nx (Walls)59.900lb / inNxy (Wall Shear)61.800lb / in Nx Force (Total)550.797lb / in RestraintCalculations a144.000Nx (total)3820.879Nxy (total)428.707 t0.284I0.275Ny (total)428.707 memberlengthb basedI/b basedNxNyNxy 12.8480.1650.132505.31156.69656.696 21.2410.3780.058220.18624.70524.705 32.8480.1650.132505.31156.69656.696 44.4630.1050.207791.85488.84788.847 54.4630.1050.207791.85488.84788.847 65.6720.0830.2631006.363112.915112.915 Table 9.1 Composite Panel Geometric Properties 8 Ply9.6.2 Design Step Two The design variables for the invest igation include the geometric properties of the composite panel member. For the purposes of the analysis, the composite panel member was divided into the individual repetitive cells made of interconnected plates as shown in Figure 9.1. The geometric properties of this section are as shown below,

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133Initial Design Informantion Composite Panels 8 Ply D111.03E+04D222.70E+03 D129.24E+02D661.28E+03NxNy a151.8Nx3820.8791505.31156.696 b15.70 Ny428.7072220.18624.705 b21.24Nxy428.7073505.31156.696 b32.854791.85488.847 b44.465791.85488.847 b54.4661006.363112.915 b65.67 Table 9.2 Initial Design ValuesAdditionally, it should be noted that the laminae thickness was set to 0.0355 in (0.869 mm). This complies with restrictions placed by pultrusion manufacturers and presented in Table 6.2 for 54 roving E-glass mat. The length of the member has been taken to be 144 in (3.658 m) and represents the component application in the emergency s helter. The load values are taken using the design wind pressures listed in Fi gure 4.2. The load values result from wind induced member bending, compression and wind shear. The restraint factors and load distribut ion factors are based on the fixed variables of member geometry and laminate thickness. Table 9.2 illustrates the development of these factors. The result s of the [D] matrix were developed using Classical Laminate Theory and are presented below in Table 9.2 for the illustrative laminate. Additionally, Table 9.2 summarizes the initial design information to be used in the buckling / first ply failure investigations. 9.6.3 Design Step Three Local buckling factors under axial compression and shearing forces are developed as two separate values for each panel member as per Equations 9.3

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134Axial Buckling 0/45 laminatebuckling mnb1b2b3b4b5b6 1114.35311699.78196557.79315414.96987214.969877.268574 1257.792800.02231.5660.1260.1229.27 13130.206300.41521.17135.38135.3865.93 14231.5611200.95926.62240.74240.74117.26 2113.99698.9057.4114.7314.737.09 2257.412799.13231.1759.8859.8829.07 23129.816299.52520.78135.14135.1465.74 24231.1711200.06926.23240.50240.50117.06 3113.44697.4356.7914.3614.366.81 3256.792797.65230.5359.4859.4828.76 33129.186298.04520.14134.73134.7365.42 34230.5311198.58925.59240.09240.09116.74 4112.78695.3955.9613.8913.896.48 4255.962795.59229.6558.9358.9328.35 43128.316295.97519.24134.17134.1764.98 44229.6511196.51924.69239.52239.52116.30 Min Buckling12.78695.3955.9613.8913.896.48 Shear Buckling Lambda1.510848 Beta1.20E+01 Buckling98.074741.42392.29101.94101.9449.66 Buckling (Total)10.14537.6743.5410.9110.915.14 Restraint Factor0.150.670.150.560.560.44 Final Buckling Factor8.85322.2538.007.007.003.57 Table 9.3 Local Buckling 0/45 Ply Laminatethrough 9.5. The cumulative buckling factors are then developed using restraint factors as described in previous secti ons. Note the resulting buckling factor describes how the applied load relates to the critical load at which localized buckling would occur. The table of these values is provided below,

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135First Ply Failure 8 ply laminate MaxMaxTsai LayerStressStrainHillHoffmanTsai-Wu (+)(+)(+)(+)(+) 143.2943.6131.5931.3635.76 243.2943.6131.5931.3635.76 320.9132.5816.9917.5219.57 49.7710.549.369.389.57 59.7710.549.369.389.57 620.9132.5816.9917.5219.57 743.2943.6131.5931.3635.76 843.2943.6131.5931.3635.76 --------------------------------Min9.7710.549.369.389.57 Table 9.4 First Ply Failure9.6.4 Design Step Four The First Ply Failure Criteria for the Laminates were developed using the Tsai-Hill Failure Equations. For the purpos e of this investigation, the material flexural stiffness matrix, the axial compression and shearing loads listed in Table 9.2 were utilized. The Tsai Hill crit eria was found to provide the most conservative values for failure when com pared to several other failure criteria. The table below provides the failure factors using the Maximum Stress, Maximum Strain, Tsai Hill, Hoffman and Tsai Wu failure criteria.

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136Deflection Calculations 0/45 laminate Ex3.73E+06 Gxy1.06E+06 t0.284F3.02E+05 w9.543Iy (web)EI (web)EI (flange)F b15.670.00 7050296.000.00 b21.240.00 1542563.000.00 b35.670.00 7047810.000.00 b44.462.127893532.10 984966.39 b54.462.127893532.10 984966.39 b65.670.00 7050296.000.00 15787064.2122690965.001969932.79 FlexureShear Deflection1.390.05 Total Deflection1.44 Figure 9.5 Global Deflection 0/45 Laminate9.6.5 Design Step Five Global deflection for the composit e panel member was developed through summation of the geometric stiffness proper ties of the individual panels. This development results in an equivalent mem ber section. Deflection is then calculated using this equivalent section in standard equations for a simple span beam exposed to bending and shearing forces. The table of these values is shown below,

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137COMPOSITE PANEL NUMERICAL ANALYSIS IterationLayupsDeflectionBucklingLaminate 1001.133.1514.00 20451.723.579.36 30901.844.356.17 44501.727.569.36 545453.798.076.48 645903.809.263.16 79001.8410.556.17 890453.8011.033.16 990905.1711.352.25 Table 9.6 Panel Analysis 8 Ply Laminate9.7Results The following results tabulation, show n in Table 9.6, represents all nine possible laminate lay-ups available for use in the panelized system. All calculations were developed using the same process as illustrated in Section 9.6. Further, the values shown in Table 9.6 are represented graphically in Figures 9.4 and 9.5. Figure 9.4 provides a comparis on of each laminate lay-up iteration with respect to the strength characteristics of buckling and first ply failure. Figure 9.5 provides a comparison of each laminate lay-up iteration with respect to the serviceability characteristic of global deflection.

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138 0 2 4 6 8 10 12 14 16 0123456789 Layup IterationStrength Factor Buckling Factor First Ply Failure Figure 9.4 Strength Factors 8 Ply Laminate 0 1 2 3 4 5 6 7 0123456789 Layup IterationDeflection (In) Panel Deflection (Unrestrained) Ansys Verification Deflection Figure 9.5 Deflection Comparison 8 Ply Laminate

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139 9.8 Ansys Verification Model A finite element model was developed to verify the results of the model for use in a more complex structural elemen t. For the purposes of the verification, Ansys 5.7 was utilized to conduct the analysis. The verification model utilized Shell99 elements. This element ty pe was selected to best represent the composite laminate properties of the material. Specifically, due to the manufacturing constraints presented in chapt er 4, the shell thickness could not be greater than 0.284" (7.214 mm). This thickness would allow for a maximum of eight layers. In order to reduce inter-laminar shear ing stresses, the lay-up is further limited to a symmetric twelve layer lay-up using balanced orientation pairs. Further, through discussion with the manufac turing industry, we were informed that typical composite laminates consist of 0, 45 or 90 degree layer orientations. The geometry of the panel are as shown below in Figure 9.6. To best represent the manufactu red component, the analysis was performed on a 151.8" (3.856 m) long shell member. The analysis was performed on one repetitive unit of the panel system. The material constraints listed above accurately represent the manufacturing and performance limitations involved in the component system. T he reduction of the possible lay-up configurations results in a solution set consisting of twenty five lay-up orientations. A full analysis was performed on all possible solution lay-ups in Ansys 5.7. The results of this analysis are presented below in Table 9.7 and above in Figure

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140ANSYS VERIFICATION ANALYSIS IterationLayupsDeflectionStress (-)Stress (+) 1001.001674.002650.00 20451.252047.002133.00 30901.311749.002637.00 44501.254359.002902.00 545452.275211.003026.00 645902.195334.002507.00 79001.312426.003456.00 890452.192351.003605.00 990905.857270.007998.00 Table 9.7 Ansys Results 8 Ply Laminate Figure 9.6 Panel Geometry Ansys9.4 and Figure 9.5. Note the layer or ientations shown are one quarter of the entire composite laminate thickness (i e...0/45 is 0/0/45/ -45/-45/45/0/0).

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141 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0123456789Layup Iteration Buckling Factor Maximum Stress Figure 9.7 Comparison Buckling vs. Max Stress9.9 Comparison of Analysis Results The values attained through the Ansys 5.7 run were used to verify the optimal solutions reached during the com posite panel laminate design. Through this review and verification process, the optimal solution was selected based on each of the following criteria. 9.9.1 Strength Discussion The localized buckling characteristics of the individual laminates were compared with respect to each other and to the maximum stress values attained through the Ansys verification model. A ll stresses and factors were linearized according to the maximum values. The comparison graph is as shown below, Through review of the buckling factor / maximum stress comparison shown in Figure 9.7, the following laminates are of principle interest,

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142 1)90/90 Laminate; This laminate provi des the maximum buckling factor while exhibiting the minimum stress under the prescribed loading conditions. Deeper review explains the results, as this laminate contains only plies running perpendicular to the long axis of the composite panel. Such a laminate would provide the highest buckling factor since all plies run in the direction resisting thin plate buckling along the short axis. The low maximum stress values also are direct ly related to the ply orientation. Since no plies run in the direction of the principle bending stresses, the maximum stress would not be developed in the fibers, but in the matrix. The matrix offers less material stiffness and would be able to generate less stress. It would be expected that the deflection in this laminate would be high. 2)0/0 Laminate; This laminate provi des a low maximum stress value while also providing a low buckling factor. The stress value results from the high stiffness provided by a laminate having all plies oriented in the direction of the applied principle stresse s. The low buckling factor is due to the lack of plies oriented to resist localized buckling along the short axis. It would be expected that this laminate would provide good resistance against deflection. 3)90/0; 0/45 Laminates; These lami nates provide a good combination of high buckling factors and low maximum stress values. These laminates should provide good all around performance due to the use of all available laminate orientations.

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143 9.9.2 Deflection Discussion The deflection results were compared directly to the verification model performed in Ansys 5.7. Both the composite panel and verification model were analyzed based on a simply supported single span beam. The comparison is shown previously in Figure 9.5. It can be seen immediately that all of the computed values for global deflection are more conservative compar ed to the verification values provided by Ansys. This is to be expected based on the use of Equation 9.9 for deflection in single span beam under uniform loading. The overestimation of deflection is due to the inability of Equation 9.9 to account for the closed nature of the composite panel system. This equation was originally utilized for open section laminate beams (such as W-shaped) and does not accurately account for the interaction of the panels in a closed beam. Review of the deflection results illustrates that the composite panel analysis follows the same deflection trends as the verification analysis. The following laminates are once again of interested and are discussed below, 1)90/90 Laminate; As expected it can be seen that this laminate provides the worst deflection resistance of all the possible solutions. This is due to the lack of layer orientation in the direction of the flexural stresses. 2)0/0 Laminate; This laminate provides the best overall deflection results, which follows with the understanding that all layers are oriented to resist the flexural stresses and provide the greatest amount of member stiffness. 3)90/45; 90/0 Laminates; These lami nates provide good performance with

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144FRFbziiii i n12 1sin EI b EzzR Et t IRshape x j jj j n flange i x i w i w i m y web web i 3 1 13 1 3 1 1respect to resisting global deflection. In an attempt to improve on the accuracy of the deflection equations in estimating the behavior of a closed beam sect ion, the restraint factors presented in Equation 9.5 have been used to modify the deflection equations as follows, (9.11) (9.12) where Ri is the restraint factor defined in Equation 9.5. Subsequent to this adjustment, the global deflection results are as shown below in Figure 9.8. The use of the restrained equations provides a better overall curve fit with the Ansys verification model.

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145 0 1 2 3 4 5 6 7 0123456789 Layup IterationDeflection (In) Ansys Verification Deflection Panel Deflection (Restrained) Figure 9.8 Deflection Comparison Restrained9.10 Conclusions The design process conducted in this Chapter resulted in several optimal solution sets, depending upon the specific crit eria being investigated. While this provides for a variety of solution, it al so illustrates the difficulty faced in the optimization of structural components fo r multiple performance criteria. The current investigation is a good example of this difficulty, with several laminates performing well against some performanc e criteria and doing poorly in other areas. Typically, multi-variable optimization problems such as this are addressed through the selection of one performance f unction. This function then becomes

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146 the objective of the optimization, wh ile all other performance criteria are developed as constraints on the process. Regardless, the results presented herei n illustrate that the panel members are well suited to performance criteria nec essary to fulfill the loading conditions in a temporary shelter application. The maxi mum deflections ranged from L /39 to L /177. The buckling factors ranged from 3.15 to 11.35. The first ply failure factors ranged from 2.25 to 14.0. The over all safety of this panel system at such high residential loading conditions implie s that the system may perform well in other applications, such as rapidly depl oyed bridge decking. The use of this panel system in other applicati ons will be dependent upon the deflection requirements of the project.

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147 10. CONCLUSIONS AND RECOMMENDATIONS 10.1Project Summary When addressing the aftermath of a natural disaster, t he aid worker is faced with three immediate tasks, 1)Provide protection from the environment, 2)Provide food and resources fo r the facilitation of life and 3)Provide health services for the tr eatment and prevention of illness. The development of an emergency shelter is central to the facilitation of each of the tasks that occur in post-disaster si tuations. The goal of this project was to investigate hurricane-resistant shelters that could be easily transported, rapidly built on-site and required minimal tools and skill to construct. In the study, a comprehensive search of the existing housing market was conducted to locate viable emergency shel ter manufacturers (Chapter 2). Eleven candidates shelters were located and a Request for Proposal (RFP) prepared containing information on the geometry and wi nd loading of a simple structure that permitted a side-by-side compar ison of the available systems. This was sent to all the manufacturers. Upon receipt of the completed proposals, four competing systems were evaluated (Chapter 3). In addition, an emergency shelter building concept was developed in-house. This build ing utilized lightweight, high strength,

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148 corrosion resistant Fiber Reinforced Poly mer (FRP)material and was optimized for global construction performance (Chapter 8 and Chapter 9). Assembly of this system is illustrated in Chapter 5. 10.2Conclusions: Historical Precedent A review of the history of emergency shelters (Chapter 1) showed that these structures are typically classified as eit her temporary shelters, that are rapidly constructed with an intended life span of less than six months, or temporary housing, that provide a more substant ial type of construction and have a much longer life span. Further, foreign aid prov iders have noted that key to the success of emergency shelters is the level of cultural acceptance it facilitates in the area of deployment. As a result, structurally s uperior shelter types, such as the geodesic dome or the Quonset hut prov e to be failures due to a la ck of usage during disaster events. Thus, aesthetic familiarity is key to the successful implementation and usage of emergency shelters. This refers not only to building geometry, but also wall, roof and floor surfaces. Since the 1950's, FRP materials have seen a wide range of use, from the aerospace industry to everyday ladders and tools. FRP materials provide a good fit for use in an emergency shelter, since their light weight and corrosion resistance facilitates storage, transportation and erecti on of the shelters. Further, their ability to be molded and designed for specific struct ural applications pr ovides the engineer with structural shapes that can perform mu ltiple structural tasks concurrently.

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149 While a variety of different FRP structural members have been developed, our review noted a lack of development in the area of connections. Specifically, FRP framing systems have, fo r the most part, been limited to the use of connections that mirror those found in structural st eel applications. Bolted connections were developed for use in homogeneous, isotropi c materials like steel, but they are not as suited for anisotropic materials like FRP (see Figure 6.5). 10.3Conclusions: Existing System Review The existing emergency shelter industry was reviewed for viable candidates. Due to the stringent performance requirements, only eleven existing building systems met project requirements. Within this group the viable emergency shelters fell into three types of construction: 1)Standard Construction New Materials emphasize improved performance gained through the use of new materials (Three manufacturers). Such materials offer the user improved mechanical properties (on a localized basis), light weight, non-corrosive and non-metallic performance. 2)New Construction New Materials dev elop new construction systems in an attempt to best utilize the performance characteristics of the new materials (Six manufacturers). 3)Alternate Systems constitute a fully alternate system of construction, based on geometry, materials and construction (Two manufacturers). As mentioned earlier, only four buildi ng system manufacturers su bmitted systems for review

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150 Figure 10.1 DuraKit Emergency Shelter and evaluation. From this evaluation, the following conclusions were reached with respect to the existing building systems: 10.3.1Best System: Durakit The DuraKit building system consists of corrugated fiberboard that is factorycoated and treated to make a durable shel ter with a fireproof interior and a weatherproof exterior. Fiberboard (similar to cardboard construction) is assembled as composite panels. The panels are c onnected to adjacent members using an adhesive system. 1)Rating:53 2)Pros:Very inexpensive, Economical, Simple Construction. Excellent supporting data (full scale testing and component testing) 3)Cons:Permanent construction (no disa ssembly), Durability issues in high temperature and hum idity environment.

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151 Figure 10.2 LEEP Shelter System 10.3.2Best System: Leading Edge Earth Products (LEEP) The system consists of composite panels composed of steel face sheet bonded to a foam core using sandwich cons truction. The panelized construction is supplemented using a metal fr ame system in which the panel sections are inserted. 1)Score:51 2)Strengths:Highest Wind Resist ance, Transportability, Simple Erection, Testing 3)Weaknesses:Permanent Adhesive/Mechanical Connections, Corrosion Issues The other two building systems, CoreFlex International and Futuristic Homes were eliminated from the review during the evaluation process for the following reasons: 1)Inadequate supporting structural info rmation (no test data, no detailed calculations) Coreflex.

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152 2)Inadequate structural capacity of connections Futuristic Homes. 3)Reliance on supplemental steel systems for connections and member stiffening Futuristic Homes. 4)Reliance on supplemental steel systems for connections Coreflex. 5)No building system components current ly being manufactured Coreflex. As a result of the exis ting emergency shelter review, we concluded that while two systems appear to have met the base criteria of the project, all of the systems investigated exhibit similar weaknesses. Specifically, we concluded that all of the system are designed as one time usage buildings, since disassembly would constitute a significant amount of work and possible member damage. Further, we concluded that all of the systems emphasize localized me mber performance issues of bending and shear, while failing to fully develop the global issues of member connections and systemic performance under load. 10.4Conclusions:USF System Design The development of the USF system building started with a conceptual design to address non-structural issues su ch as building system simplicity and the ability to disassemble and rebuild the st ructure with minimal work or member damage. Two conclusions resulted from this first level of design. First, it was concluded that the building should utilize a system of panel components that incorporated structural connections into the standard member shape. Second, the section needed to be optimized.

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153 Figure 10.3 Interlocking Panel Members The new system reduced the number of member types required during construction and facilitates systemic str ength through interlocking of component members. Moreover, the use of FRP materials provided the greatest amount of design flexibility. The resulting interlocking panel member, developed using trapezoidal shaped open ribs fastened to a st iffening plate surface is shown in Figure 10.3.

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154 The final level of design optimizati on uses Classical Laminate Theory (Jones, 1975) and Approximate Compos ite Laminate Properties (Nagraj, 1994) to develop composite laminate system s with the optimal Ex, Ey and Gxy developed previously. Based on these global material properties several composite laminate lay-ups will be compared and optimized for volume, based on work conducted by Qiao, Haftka and Giroux. The resulting composite lami nate represents the fully optimized structural system for the loading condi tions proposed in the emergency shelter problem. Further, the propos ed approach illustrates a truly powerful tool which enables the designer to separately design one member geometry for a multitude of loading situations and usage conditions.. 10.5Contributions The main contributions of this study are summarized as follows. 1)A state of the art review was conduc ted of the emergency shelter industry. While similar reviews have been conduct ed within the area of emergency shelter construction, this review is the first to emphasize the performance of emergency shelters under extreme environmental conditions engendered by hurricanes. 2)A new type of structural panel system is developed. This uses new FRP material in a novel construction syst em that incorporates structural connections into the member secti on. This design development acts to improve the member’s stru ctural efficiency while at the same time reducing the level of system complexity.

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156 3)A design optimization process is dev eloped in which member geometry and material properties can be optimiz ed independent of each other. This process illustrates the wide variety of uses available to the design limited to a small number of member geometries. 10.6Recommendations for Future Work This investigation has shown t hat several building systems appear to adequately fulfill the desi gn parameters laid out by the investigation team. However, this assessment is based on information provided and therefore needs independent verification. This is especially true with the new requirement in the forthcoming Florida Building Code that makes it mandat ory to conduct missile impacts for structures where wind velocities are as large as assumed in this study; 138 mph (222km/hr). The purpose of future work is to take each shelter from “the drawing board” to the field, through onsite erection, testing and eval uation. This goals of the recommended work may be attained in the following manner: 1)Prototype shelter buildings shoul d be purchased from each successful building system candidate. Two such structures, Durakit and LEEP were identified from available systems. 2)Prototype of the USF optimized FR P shelter buildi ng system should be fabricated and erected for testing and evaluation. 3)Prototype shelter buildings to be erec ted in a controlled environment, with all phases of construction reviewed and evaluated.

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157 4)Prototype shelter buildings to be test ed for global stability under laterally and vertically induced load conditions. 5)Prototype shelter buildings to be te sted for wind-borne projectile impact (hurricane force winds). Further, the optimization procedure devel oped within this body of work should be expanded to more accurately determine localized stresses developed in and around the integrated connect ion component of the FRP panel members. Such detailed stress analysis would allow the engineer to perform localized optimization in other applications, such as those f ound in more standard steel type bolted FRP connections.

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158 REFERENCES Aboudi, J. (1991). “Mechanics of Composite Materials A Unified Micromechanical Approach,” Elsevier, New York, NY. “Alternative Construction Technology (ACT ); A Study of Alternative Building Systems for Use by United States M ilitary Forces” (2000). Report for United States Southern Command (USSOUTHCOM) by 416th Engineer Command (ENCOM). Darien, IL. June 5. 2000 ASCE7-98, (1998). “Minimum Design Loads for Buildings and Other Structures”, American Society of Civil Engineers, New York, NY. Bank, I. C. and Mosallam, A. S. (1991) “Performance of Pultruded FRP Beamto-Column Connections”, Structures Congress ’91 Compact Papers, the American Society of Civil Engineers, NY, pp. 389-392. Bank, L., Mosallam, A. S., and McCoy, C.T. (1994). “Design and Performance of Connections for Pultruded Frame Structures”, Journal of Reinforced Plastics and Composites Vol. 13, pp.199-211. Bank, L.C. Yin, J. Moore, L. Evans, D.J. and Allison, R.W. (1996). “Experimental and Numerical Evaluation of Beam-to-Column Connections for Pultruded Structures” Journal of Reinfo rced Plastics and Composites Vol. 15, October 1996 pp.1052-1067. Barbero, E.J., Lopez-Anido, R. and Davalo s, J.F. (1993) “On the Mechanics of Thin-Walled Laminated Composite Beams, ” Journal of Composite Materials, 27 (8): 806 829. Bruneau, Michel and Walker, David (1994) “Cyclic Testing of Pultruded FiberReinforced Plastic Beam-Column Rigid Connection” Journal of Structural Engineering, Vol. 120, No. 9 September. Central America Hurricane Mitch Fact Sheet #22, 12/24/98. (1998) “US Agency for International Development (USAI D) Bureau For Humanitarian Response (BHR) Office of US Foreign Disaster Assistance (OFDA)”. Http://www.usaid.gov/hum_res ponse/ofda/mitch22fs.html.

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159 Eschenauer, H., Koski, J. and Osyczka, A. (1990). “Multicriteria Design Optimization,” Springer-Verlag, Berlin. Giroux, C and Shao, Y. (2003) “Flexura l and Shear Rigidity of Composite Sheet Piles”, Journal of Composites for Construction, 7(4): 348 355. Gurdal, Z., Haftka, R., Hajela,R. (1999) Design and Optimization of Laminated Composite Materials John Wiley & Sons. New York, NY. Haftka, R., Gurdal, Z. (1990) Elements of Structural Optimization Kluwer Academic Publishers. Boston, MA. Hull, D. (1981). An Introduction to Composite Materials Cambridge University Press. Cambridge, MA. Hurricane Mitch Image, 10/27/98 5:00 AM EST. (1998) “UN Hurricane Mitch Information Center”. Http://www.un.hn/mitch/entrada.htm. Jones, R.M. (1975). Mechanics of Composite Materials, Hemisphere Publishing Corporation, New York, NY. Lekhnitskii, S.G. (1968) Anisotropic Plates London: Gordon and Breach Sci. Publ.; translated by Tsai, S.W. and Cheron, T. Liu, B., Haftka, P., Trompette, P. (2004) “Maximization of Buckling Loads of Composite Panels Using Flexural Lam ination Parameters”, Structural Mulitdiscipline Optimization, 26: 28 36. Luciano, R. and Barbero, E.J. (1994) Fo rmulas for the Stiffness of Composites with Periodic Microstructures”, Journal of Composite Materials, 27 (8): 806 829. Mallick, P. K. (1988). Fiber-Reinforced Composites: Materials Manufacturing, and Design Marcel Dekker, Inc., New York. Mosallam, A.S. (1990). “Short and Long -Term Behavior of a Pultruded FRP Frame”, PhD Dissertation, The Catholic University of America, Washington, DC. Mosallam, A. S., and Bank, L. (1992). “S hort-Term Behavior of Pultruded FiberReinforced Plastics Frame”, Journal of St ructural Engineering, Vol. 118, No. 7, July. Mosallam, A.S. (1994). “Connections and Reinforcement Design Details for PFRP Composite Structures”, Journal of Reinforced Plastics and Composites, Vol 13, July pp. 752-784.

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160 Mosallam, A.S. (1997). “Structural Eval uation of Polymer Composite Connections for Civil Engineering Structures”, Proceedings, SAMPE Conference, April, Anaheim, pp. 269-280. Mottram, J.T. and Bass,A.J. (1994). “Mo ment-Rotation Behavior of Pultruded Beam-to-Column Connections” Structur es Congress, Vol. 1, pp.423-427. Mottram, J.T. and Zheung, Y. (1997). “Sta te-of-the-Art Review on the Design of Beam-to-Column Connections for Pultruded Frames”, Composite Structures, 35. Elsevier Science, pp. 387 401. Nagraj, V. (1994). “Static and Fati gue Response of Pultruded FRP Beams Without and With Splice Connections,” MS Thesis, Department of Civil and Environmental Engineering, West Virg inia University, Morgantown, WV. Pai, N.G., Kaw, A.K., Weng, M.X. (2001) “Optimization of Laminate Stacking Sequence for Failure Load Maximization Using Tabu Search”, Composite Structures, Pultruded Member Image (2000). “C reative Pultrusion Website” http://www.pultrude.com. Qiao, P., Davalos, J.F. and Barber o, E.J. (1994). “FRPBEAM: A computer Program for Analysis and Design of FR P Beams,” CFC-94-191, Constructed Facilities Center, West Virginia University, Morgantown, WV. Qiao, Pizhong. (1997). “Analysis and Desi gn Optimization of Fiber-Reinforced Plastic (FRP) Structural Beams”. Doctoral Dissertation, West Virginia University, UMI #9722181. Smith, Steven John (1997). “An Investigat ion of Beam-to-Column Connections for Composite Structural Systems (Pultrus ion, Cuff Joint), Doctoral Dissertation, University of Illinois at Urbana-Champaign. UMI #9812777. Smith, S.J. and Hjelmstad, K. D. (1999). “Experimental Comparisons of Connections for GFRP Pultruded Frames” Journal of Composites for Construction February, pp. 20-26. Timoshenko, S.P. and Woinowsky-Krieger, S. (1959). Theory of Plates and Shells McGraw-Hill, New York. Tomblin, J.S. (1994). “Compressive St rength Models for Pultruded Glass Fiber Reinforced Composites,” PhD Dissertat ion, West Virginia University, WV.

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161 Troitsky, M.S. (1988). Orthotr opic Bridges Theory and Design, 2nd Edition, James F. Lincoln Arc Welding Foundation, Cleveland, Ohio. UN Honduras Situation Report No 7. “ UN Hurricane Mitch Information Center”. Http://www.un.hn/mitch/unhsitrep7.html. Vedam, V.R. (1997). “Characterization of Composite Material Bridge,” MS Thesis, Department of Civil and Envir onmental Engineering, West Virginia University, Morgantown, WV 26506, USA. Whitney, J.M. (1985). Structural Analysis of Laminated Anisotropic Plates Lancaster: Technomic.

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ABOUT THE AUTHOR Nick M. Bradford graduated from The P ennsylvania State University with Bachelor’s and Master’s of Science degrees in Architectural Engineering. Subsequent to graduation, Mr. Bradford worked as an intern for structural engineering firms in Virginia, New York and Florida. In 1998, Mr. Bradford became licensed as a Professional E ngineer in Florida and opened a small structural engineering firm based in Tampa, Florida. While in the Ph.D. program at the Univ ersity of South Florida, Mr. Bradford has developed an impressive resume of engineering work, specifically in the areas of high wind construction and for ensic engineering. Mr. Bradford served as an adjunct professor at University of South Florida during the spring of 2002 and has worked with the Civil and Envir onmental Engineering Department on investigations into high wind construction. He currently lives with a wife and two cats, spending as much time on the water as possible.


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ABSTRACT: Using advanced composites, an emergency shelter system has been designed. The system parameters are hurricane resistance to 138 mph wind velocity, simple erection, light weight, high durability and rapid construction. The project involves the solicitation of design proposals from several building system manufacturers and the development of an optimized emergency shelter system. The usage is well suited to pultruded members made from fiber reinforced polymers (FRP). Due to the anisotropic nature of FRP composites, a limited amount of research has been conducted to develop design optimization techniques for panels used in construction. This project allows for the development of optimization techniques for use in pultruded FRP panel members.The Project consisted of a detailed literature review conducted of emergency building industry to assess the validity of existing shelter systems, a state of the art review of connection design in FRP structures with an emphasis on non-standard types of connectors (ie...snap type), systemic structural optimization of emergency shelter for building geometry, roof configuration, foundation anchorage and building envelope, development of statistical methods for evaluation of viable existing emergency shelter systems. Subsequent to the initial phase of the investigation, an interlocking FRP composite panel system was developed. The system was analyzed for local buckling, first ply failure and global deflection criteria using modified equations originally developed for open section members. The results were verified using Finite Element Methods analysis software.The findings from the study indicate the need for a second phase in which the most promising available systems and the concept developed are fully tested to verify their capacity to withstand high wind forces including impact of wind borne debris.
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