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Lr . 2. 1? 1.. _v .1. in. , i). 20/0 This is to certify that the thesis entitled OPTIMIZATION OF POLYSTYPENE FOAM CORE SANDWICH PANELS FOR SELF-SUPPORTED ROOF APPLICATIONS presented by MYRON JOHN MAURER has been accepted towards fulfillment of the requirements for the MS. degree in Mechanical Engineering Major Professor’s Signature 4 /2 ? /2 0/0 ' 7 Date MSU is an Affirmative Action/Equal Opportunity Employer LIBRARY * Michigan State Ul liversity ~.-»—-- PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 5/08 K:IProlecc&Pres/CIRC/DateDue.Indd OPTIMIZATION OF POLYSTYRENE FOAM CORE SANDWICH PANELS FOR SELF-SUPPORTED ROOF APPLICATIONS BY Myron John Maurer A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Mechanical Engineering 2010 ABSTRACT OPTIMIZATION OF POLYSTYRENE FOAM CORE SANDWICH PANELS FOR SELF-SUPPORTED ROOF APPLICATIONS By Myron John Maurer Energy efficiency in residential building applications is an important aspect in reducing greenhouse gas emissions such as carbon dioxide. Thus, significant emphasis is now being placed on the building enclosure and the importance of having a continuous boundary of insulation between the interior conditioned space and the external environment. Structural insulated panels (SIP’s) comprised of an expanded polystyrene (EPS) bead foam core sandwiched between oriented strand board (088) facings have been used predominantly in exterior wall applications to date due to deficiencies in meeting load-bearing requirements for structural roof panel applications. An alternative approach combines OSB facings with structural lath frames and orthotropic extruded polystyrene (XPS) foam core to render composite sandwich panels that satisfy allowable spans for self-supported installation. Foam constitutive material properties and finite element (FE) models of composite roof panels were constructed to investigate the effects of facing, lath and foam core characteristics on panel deflection and constituent strength factor of safety considerations. Such FE models were then used in conjunction with HEEDS automated design software to optimize the geometric configuration of various roof sandwich panels. To my wife, daughters, father and deceased mother iii ACKNOWLEDGMENTS I would like to thank The Dow Chemical Company for allowing me the opportunity to pursue my Master of Science degree in mechanical engineering at Michigan State University. I would also like to thank my colleagues Dr. Michael Mazor and Gary Parsons for the support and consultation they provided throughout my research. Special thanks to Casey Fiting and Sylvie Boukami for their assistance with the material property testing of candidate foam products. I greatly appreciate the managerial support provided by Daniel Schmidt, John Hacskaylo, Henry Kohlbrand and Simon Yeung throughout my research. I would also like to acknowledge Bill Heeschen for his assistance with Poisson’s ratio testing and image analyses. Deepest thanks to my loving wife, Jodi, for your support and encouragement throughout my graduate research. I would also like to thank my daughters; Taryn, Lyssa and Courtney for the personal sacrifices they endured throughout my graduate research. Special thanks to Dr. Thomas Fence and Dr. Fahrang Pourboghrat for serving as members of my thesis defense committee. Finally, I would like to extend my sincere thanks to Dr. Ronald Averill for serving as my research advisor. His academic, entrepreneurial and practical building experience was extremely valuable and insightful throughout the duration of the project. iv TABLE OF CONTENTS LIST OF TABLES ............................................................................................. vii LIST OF FIGURES ......................................................................................... viii CHAPTER 1 ........................................................................................................ INTRODUCTION .............................................................................................. 1 Problem Statement ...................................................................................... 2 Literature Review ......................................................................................... 3 The Current Study ....................................................................................... 6 CHAPTER 2 FOAM MATERIAL CHARACTERIZATION ....................................................... 7 Scanning Electron Microscope Imaging ...................................................... 8 Density Testing .......................................................................................... 13 Compression Testing ................................................................................ 17 Tension Testing ......................................................................................... 26 Shear Testing ............................................................................................ 36 Poisson’s Ratio Testing ............................................................................. 43 CHAPTER 3 FINITE ELEMENT MODELING OF SIP PANELS .......................................... 49 Oriented Strand Board Material Characterization ..................................... 49 Polystyrene Foam Core Material Models .................................................. 50 Isotropic PS Foam Core Material Modeling ......................................... 50 Orthotropic XPS Foam Core Material Modeling .................................. 51 SIP Bend Test Simulations ........................................................................ 55 Experimental SIP Bend Tests ................................................................... 57 FE Material Model Correlation ................................................................... 62 CHAPTER 4 OPTIMIZATION OF STRUCTURAL LUMBER FRAME PANELS .................. 66 Design Analysis ......................................................................................... 68 Finite Element Modeling ............................................................................ 73 Finite Element Model Validation ................................................................ 78 Optimization Studies .................................................................................. 80 Isotropic XPS SIP Roof Panel Optimization ........................................ 81 Baseline SIP Optimization Study ......................................................... 86 Composite Roof Lumber Frame Panel Design Optimizations ............. 89 Results and Discussion ........................................................................ 94 CHAPTERS SUMMARY AND CONCLUSIONS ................................................................. 98 REFERENCES ............................................................................................. .101 vi LIST OF TABLES Table 2.1 ASTM D1621 -04a Compression Test Results .................................... 18 Table 2.2 HD 300F-X Compression Test Results on Z—Direction Foam Sections ................................................................................................................ 25 Table 2.3 ASTM 01623-03 Type III Specimen Tension Test Results ................ 28 Table 2.4 HD 300F-X Tension Test Results on Foam Section Specimens ........ 32 Table 2.5 EN 12090 Foam Core Shear Test Results ..............., ......................... 38 Table 2.6 HD 300F-X Shear Test Results on Foam Section Specimens ........... 41 Table 2.7 Polystyrene Foam Core Poisson’s Ratio Test Results ....................... 47 Table 3.1 PS Foam Core Orthotropic Material Model Parameters ..................... 55 Table 3.2 Composite Sandwich Panel Bend Test Results ................................. 61 Table 4.1 Roof sandwich panel material matrix ................................................. 71 Table 4.2 OSB facer and structural lumber frame material properties .............. 74 Table 4.3 XPS foam core orthotropic material constants ................................... 77 Table 4.4 Isotropic XPS SIP optimization results ............................................... 85 Table 4.5 HEEDS baseline SIP optimization results assuming orthotropic foam properties ..................................................................................................... 87 Table 4.6 Structural lumber frame panel optimization conditions ...................... 91 Table 4.7 XPS structural lumber frame roof panel optimization variables ........ 94 vii LIST OF FIGURES Images in this thesis are presented in color Figure 2.1 Foam Plank Geometry and Reference Coordinate System ................ 8 Figure 2.2 Representative SEM Image of STYROFOAM HD 300F-X Cell Morphology @ Z=icl2 in Machine Direction of Board ........................................... 9 Figure 2.3 Representative SEM Image of STYROFOAM HD 300F-X Cell Morphology @ 2:0 in Machine Direction of Board .............................................. 10 Figure 2.4 Representative SEM Image of EPS Bead Foam Cell Morphology @ Z=-l_-c/2 in Machine Direction of Board ............................................................. 11 Figure 2.5 Representative SEM Image of EPS Bead Foam Cell Morphology @ 2:0 in Machine Direction of Board .................................................................. 12 Figure 2.6 Apparent Overall Density Distribution of PS Foam Specimens in Plank Transverse Direction ................................................................................. 14 Figure 2.7 Specimen Location for Density Variation through Plank Thickness ............................................................................................................. 15 Figure 2.8 Section Density Variation through the Thickness of PS Foam Planks ................................................................................................................... 16 Figure 2.9 Foam Compression Test Equipment ................................................. 17 Figure 2.10 Compressive Response of HD 300F-X in Orthogonal Directions 19 Figure 2.11 Compressive Response of EPS Bead in Orthogonal Directions ..... 20 Figure 2.12 STYROFOAM HD 300F-X Compressive Failure Mode Photos ...... 21 (a) Axial, (b) Transverse and (0) Thickness direction at 10 mm deformation ..... 21 (d) Axial, (e) Transverse and (f) Thickness direction at 25 mm deformation ...... 21 (9) Axial, (h) Transverse and (i) Thickness direction at 40 mm deformation ...... 22 Figure 2.13 EPS Bead Foam Compressive Failure Mode Photographs ............ 23 (j) Axial, (k) Transverse and (I) Thickness direction at 10 mm deformation ...... 23 viii (m) Axial, (n) Transverse and (0) Thickness direction at 25 mm deformation ..... 23 (p) Axial, (q) Transverse and (r) Thickness direction at 40 mm deformation ..... 24 Figure 2.14 HD 300F-X Compressive Response for Z-Direction Section Specimens ............................................................................................................ 26 Figure 2.15 Foam Tension Test Equipment for ASTM D1623-03 Type III Specimens ..................................................................... . ....................................... 27 Figure 2.16 Tensile Response of HD 300F-X in Orthogonal Plank Directions .............................................................................................................. 29 Figure 2.17 Tensile Response of EPS Bead Foam in Orthogonal Plank Directions .............................................................................................................. 30 Figure 2.18 HD 300F-X Foam Section Test Specimen Geometry ..................... 31 Figure 2.19 Tension Test Equipment for Abrasive Wire Cut Foam Section Specimens ............................................................................................................ 33 Figure 2.20 HD 300F-X Tensile Results for Axial Direction Section Specimens ............................................................................................................ 34 Figure 2.21 HD 300F-X Tensile Results for Transverse Direction Section Specimens ............................................................................................................ 35 Figure 2.22 EN 12090 Single Test Specimen Assembly Test Set-Up ............... 37 Figure 2.23 Transient Engineering Shear Stress vs. Strain Response of PS Foam Cores .......................................................................................................... 39 Figure 2.24 ASTM 0273 Shear Test Equipment ................................................ 40 Figure 2.25 HD 300F-X Shear Test Results for Axial Direction Section Specimens ............................................................................................................ 42 Figure 2.26 HD 300F-X Shear Test Results for Transverse Direction Section Specimens ............................................................................................................ 43 Figure 2.27 STYROFOAM HD 300F-X Pre-Test Photograph Depicting Grid Network ................................................................................................................. 45 Figure 2.28 STYROFOAM HD 300F-X Grid Intersection Displacement Illustration ............................................................................................................. 46 Figure 3.1 ABAQUS Composite Foam Core Sandwich Panel Representation. 56 Figure 3.2 Composite Foam Core Sandwich Panel Meshed Part ...................... 57 Figure 3.3 Composite Sandwich Panel of Overall Dimensions 1 12X1 50X450mm ................................................................................................. 58 Figure 3.4 Composite Sandwich Panel Bend Test Apparatus of 400mm Support Span ........................................................................................................ 59 Figure 3.5 Composite Sandwich Panel Bend Test Response.................. .......... 60 Figure 3.6 Force-Deflection Comparison of EPS Foam Core Sandwich Panels ................................................................................................................... 63 Figure 3.7 Force-Deflection Comparison of XPS Foam Core Sandwich Panels ................................................................................................................... 64 Figure 4.1 Representative structural lumber roof panel ..................................... 67 Figure 4.2 Post-applied insulated structural lumber frame roof panels ............ 68 Figure 4.3 Sandwich panel illustration for 4/12 roof pitch .................................. 69 Figure 4.4 Roof panel beam geometry and load configuration ......................... 70 Figure 4.5 Composite roof lumber frame panel minus sheathing ...................... 73 Figure 4.6 Optimization process flow diagram ................................................... 83 Figure 4.7 Representative Meshing of Isotropic XPS SIP ................................. 84 Figure 4.8 EPS SIP deflection contour plot for 3,350 N/m2 ground snow load. 88 Figure 4.9 Representative meshed geometry of structural lumber frame roof panel .............................................................................................................. 90 Figure 4.10 EPS lumber frame panel optimization study results ....................... 92 Figure 4.11 XPS lumber frame panel optimization study results ....................... 93 Figure 4.12 Total dead load of XPS structural lumber frame panels designed to carry 3,350 N/m2 snow loads ........................................................................... 96 Figure 4.13 Representative factory built LVL lumber frame roof panel .............. 97 CHAPTER 1 INTRODUCTION Energy efficiency in residential building applications is an important aspect in reducing greenhouse gas emissions such as carbon dioxide. Thus, significant emphasis is now being placed on the building enclosure and the importance of having a continuous boundary of insulation between the interior conditioned space and the external environment. One particular approach gaining popularity throughout the building industry involves the use of structural insulated panels (SlP’s) comprised of an expanded polystyrene (EPS) bead foam core sandwiched between oriented strand board (OSB) facings. To date, however, most SlP’s are used with structural reinforcement to satisfy deflection and strength safety factor requirements for structural roof panel applications. An alternative approach to traditional SIP technology for residential roofing applications is presented which combines factory built construction practices, continuous insulation and ease of installation while satisfying code prescribed structural performance requirements. OSB facings were combined with structural lumber frames and high shear strength, orthotropic extruded polystyrene (XPS) foam core to render composite sandwich panels that satisfy allowable spans for self-supported installation. This approach has led to the identification of improved sandwich panel designs versus conventional roof SIP’s for high ground snow load regions in the United States. Problem Statement Increasing energy efficiency of residential dwellings is a present focus of code agencies and homeowners. One approach to improving energy efficiency consists of dwellings built with an unvented cathedral attic. An unvented cathedral attic places thermal insulation at the roof plane whereas a vented attic places insulation at the attic floor within the void space defined by the depth of the rafter. The rafters are also a source of thermal bridging to further reduce the overall insulating performance. Most often, heating, ventilation and air conditioning (HVAC) ducts in an attic exhibit significant heat losses to the environment of a vented attic. Another key factor in unvented cathedral attics involves increasing the support span of an insulated roof panel to minimize or eliminate the need for full or partially supported reinforcements such as purlins. A self-supported composite roof panel may be defined as an insulated roof panel that is unsupported between the ridge and eave of a home. Self-supported insulated roof panels would further allow the interior surface of the attic space to be aesthetically finished with gypsum or any other finishing material to increase the living space of a home. Moreover, the thermal insulation performance of the roof could be varied within the region defined by the insulating core thickness of the roof panel. Composite roof panels could then be factory built with improved quality and subsequently transported to the job site. Once delivered, the contractor could erect the panels in place using a crane for quick and simple installation. Thus, the composite sandwich roof panels must be thick enough to satisfy both structural and thermal insulation code requirements. Literature Review Composite sandwich panels are used increasingly for structural applications requiring high stiffness-to-weight ratio. Moreover, researchers have previously explored various means to optimize composite sandwich panel performance for multiple potential failure modes. Steeves [1-2] investigated indentation models for composite sandwich beams comprised of a polyvinyl chloride (PVC) foam core in three point bending and obtained minimum weight designs. Triantafillou [3-4] developed failure mode maps and minimum weight designs that correlated with experimental tests performed on composite beams comprised of aluminum faces and rigid polyurethane (PU) foam cores. Demsetz [5] developed minimum weight designs for simply supported, circular sandwich plates comprised of aluminum skins and PU foam cores subjected to a uniformly distributed load. Gibson [6] optimized the stiffness of sandwich beams comprised of aluminum faces and a PU foam core. The foam core plays a vital role in the structural and insulating performance of a composite roof panel. In order to ascertain design feasibility, the constitutive behavior of candidate foam core materials must be fully understood. Horvath [7] reported material properties for EPS bead foams used in geotechnical applications. Mihlayanlar [8] investigated the effect of production process conditions on the mechanical properties of EPS bead foams whereas Di Landro [9] conducted research on deformation mechanisms in EPS bead foams for protective helmet applications. Masso-Moreu [10] characterized the response of XPS foam in uni-axial compression for protective packaging applications. Mills [11] reported dynamic compression and limited shear and tensile data for XPS foams to improve Finite Element Analysis (FEA) of crushable foam models for impact applications. FEA simulations were performed by del coz Diaz et al. [12] on stressed skin roof panels comprised of an XPS foam core sandwiched between facings of either OSB or waterproof agglomerates. Their investigation consisted of a span of 1.22 m and orthotropic material properties for 40-80 mm thick XPS. Finally, Wellnitz [13] recently characterized the orthotropic behavior of 50 mm thick XPS foam sandwich panels. The results of this study demonstrated non-homogeneous deformation through the thickness of an XPS foam board as observed both visually in compression testing and quantitatively in tensile testing wherein the modulus at the center was approximately 40% lower than that near the outer surface of the board. Material models used for FEA were constructed based on orthotropic behavior with no non-homogeneous dependency of shear, compression or tensile properties in the thickness direction of the board. In the building industry, foam core sandwich panels are highly desirable for minimizing enclosure thermal losses; thus reducing the load on HVAC systems. Rudd et al. [14-16] measured cooling and heating energy savings of 5% and 50%, respectively, in a Las Vegas, Nevada home equipped with an unvented cathedral attic versus a traditional home comprised of a vented attic. Desjarlais et al. [17] modeled heat and mass transfer effects across the US. of both an unvented and vented attic for a 4/12 pitch roof with R67 m2-K/W (Rus- 38 h-ft2-°F/BTU) insulation. Energy savings associated with heating and cooling effects were 22% to 40%. In addition, builders now desire that larger, thicker insulating panels be built in factories at higher quality and subsequently shipped to the job site for quick and efficient installation [18]. Traditional roof SlP’s are comprised of OSB faces and an EPS bead foam core [19] for somewhat limited span installations. Massachusetts Institute of Technology (MIT) developed a model [20-23], based on beam theory, to optimize residential roof panels comprised of OSB facings and a PU foam core that meet failure criteria and deflection requirements. Thomas [9] analyzed the feasibility of 4.6 m long, self-supported foam core roof panels designed for structural and thermal insulation performance. Deflection performance requirements resulted in compromised designs of shorter (i.e. 3.6 m) panels comprised of either i) 250 mm thick XPS foam and 15 mm OSB facers or ii) 280 mm XPS foam and 1mm steel facers. In addition, the range of XPS foam core properties used by Thomas et al. was much narrower than published data [10] for other potential XPS foam core products. Finally, Deblander [26] patented a composite building panel design comprised of a high shear strength XPS foam core with structural wooden laths adhesively bonded to the foam. The Current Study The goal of this research is to design a highly insulated, self-supported, polystyrene foam core roof panel capable of satisfying code-prescribed deflection and constituent strength safety factor requirements. Chapter Two details the respective failure modes and various material property tests that were performed on candidate EPS and XPS foam. Chapter Three describes the isotropic and orthotropic material models that were constructed for use in performing finite element analysis simulations of traditional SIP’s. Experimental sandwich panel bend test results are described to define the most appropriate material model approach for each candidate foam core material. In Chapter Four design optimization of structural lumber frame roof panels is performed for extreme ground snow load conditions. Final selection criteria were based upon minimization of total mass while satisfying deflection, constituent strength safety factor and minimum thermal insulation requirements. In Chapter Five, the final results are presented along with final conclusions. CHAPTER 2 FOAM MATERIAL CHARACTERIZATION In this chapter, the constitutive responses of XPS and EPS bead foam are characterized to investigate their suitability as a structural insulating core in composite roof panel applications. Investigation of foam failure modes dictated the extent of testing required to accurately model the deformation behavior of each foam type. For an insulated roof panel with a uniformly applied load, the maximum deflection may be obtained from the sum of flexural and shear components of a simply supported beam. Local buckling is controlled by the elastic and shear modulus of the foam core, among other factors, whereas core failure depends mostly on the shear properties. Thus, in order to accurately predict the mid- span deflection of composite sandwich panels, detailed material characterization is required for candidate foam core products. Mechanical property tests were performed on samples prepared from 100 mm thick by 600 mm wide by 2550 mm long STYROFOAMTM HD 300F-X brand insulation XPS foam boards obtained from The Dow Chemical Company and 102 mm thick by 1219 mm wide by 2438 mm long EPS bead foam purchased from Universal Packaging. The surface finish of the STYROFOAM HD 300F-X planks was planed [25] whereas the EPS bead foam planks had been wire cut from a block molded slab prior to shipping. TM STYROFOAM is a registered trademark of The Dow Chemical Company Henceforth, the axial direction, or X-axis, lies parallel to the length, L, of the plank. The transverse direction, or Y-axis, lies parallel to the width, b, of the plank and the vertical direction, or Z-axis, lies parallel to the thickness, c, of the foam plank as illustrated in Figure 2.1. Figure 2.1 Foam Plank Geometry and Reference Coordinate System Scanning Electron Microscope Imaging Images depicting the cellular morphology of candidate PS foam core materials were taken using a Leo 435VP Scanning Electron Microscope (SEM). Samples were cut with a razor blade and taped to a stage using double-sided tape. The samples were subsequently coated for approximately twenty-five minutes using an Anatech LTD 6.6 sputter coater, gold and argon gas. Representative SEM images of the cellular morphology of each PS foam core at the center (i.e. 2:0) and outer (i.e. Z=:l;c/2) region of the plank in the machine direction are shown in Figures 2.2 through 2.5 respectively. x .. _ vi. .. 2 0 r4... \ at. 1.. ;L\.2..2..r! r _ ‘21 «1.2 2m ‘ ‘ 500 um Figure 2.2 Representative SEM Image of STYROFOAM HD 300F-X Cell Morphology @ Z=ic/2 in Machine Direction of Board A ' ' r “t . 1‘ .1 .. ~ ’ . I . . .‘pwvx p. . ,prax. l Warn..— - -' \ . 2 r, '}?'rr;j,’f‘¥~ "I “ . . '. .‘. I Figure 2.3 Representative SEM Image of STYROFOAM HD 300F-X Cell Morphology @ 2:0 in Machine Direction of Board A? . lg< .. < .q . .34? “3‘3, iii /?,'«;' Y, ’3 551%.. «r AF? I Kiwi \ ,b-{- 1,: "m’ ‘é‘ ‘_ $53.73;. r Ig‘ti’éfifff}; " ’ f Figure 2.4 Representative SEM Image of EPS Bead Foam Cell Morphology @ Z:ic/2 in Machine Direction of Board Figure 2.5 Representative SEM Image of EPS Bead Foam Cell Morphology @ 2:0 in Machine Direction of Board The SEM images depict a vertically elongated XPS cell morphology at the center of the plank (i.e. 2:0) in comparison to horizontally stretched cells at the outer (i.e. Z=:l:C/2) surface of the plank. EPS bead foam, on the other hand, exhibits an isotropic cell structure throughout the foam thickness with visible evidence of interstitial void volume between adjacent beads. Density Testing The apparent overall density of each product was measured in accordance with ASTM D 1622-08 [27]. Twenty-four cubical foam specimens were prepared from six transverse foam slices that were band saw cut to the thickness of the plank. Test specimens were labeled as Y1, Y2, Y3 and Y4 to designate their location in the transverse direction of the plank. Y1 and Y4 were located near the plank edge whereas Y2 and Y3 lay near the plank center. Specimen dimensions were then measured using an Ono Sokki GS-503 linear gauge sensor while specimens were weighed using a Mettler-Toledo XP1203S precision balance top loading scale. The apparent overall density, D, was then calculated in units of kg/m3 as shown in Equation 2.1: D J1 V (2.1) where W is the specimen weight in units of kg and V is the specimen volume in units of ma. The apparent overall density for each product as a function of specimen location is shown in Figure 2.6. 13 55 0 HD 3OOF-X A EPS Bead 50 * B— _____ B_ _____ a... ————— E a)" ‘ E A 31 l A A ‘ 5 I ’I — — — -" \ k ‘ 45 " ’ ‘ \ 3" / I \ 2, . 2\\ Q! o A A z 40 ~ A A 35 . . . . , 1 Y1 Y2 Y3 Y4 Specimen Location Figure 2.6 Apparent Overall Density Distribution of PS Foam Specimens in Plank Transverse Direction The mean apparent overall density of HD 300F-X and EPS bead foam was 50.0 :1: 0.3 and 44.1 :1; 2.8 kg/m3 respectively. Means comparison test results conclude that there is no statistically significant effect of transverse location on specimen density for each foam material. Thus, transverse foam density, p( Y), was assumed constant for material modeling of both foam products. Previous research has reported significant variation in the density of foam sections taken through the thickness of extruded and molded expanded 14 polystyrene foam [28-30]. Thus, a series of test specimens were prepared by cutting thin foam sections approximately 19 mm thick and labeling them 21 through 25 as illustrated in Figure 2.7. z Y > z 1 Z1 u Y1 Y2 Y3 Y4 0 ‘ 23 :21 I 25 4 b 4 <— C —> Figure 2.7 Specimen Location for Density Variation through Plank Thickness Top (Z=c/2) and bottom (Z=-c/2) specimens were out first to include the outer region of the plank in density measurements. The section density variation through the thickness of each foam plank is shown in Figure 2.8. 15 55 [:1 B\\ «B A 2 \\ D / (OE 50 \Cl‘-2_______.——”’ D g 8 £945— to C 0 D §40~ A a L___:____L___ _____ 3. A 1 A m 35* A nHD3OOF-X AEPSBead 30 V I I r 21 22 23 Z4 Z5 Specimen Location Figure 2.8 Section Density Variation through the Thickness of PS Foam Planks The density of XPS sections taken from the center region were approximately 10% lower than sections from the outer region of the foam plank. EPS bead foam, on the other hand, exhibited a relatively constant density with a variation of <3% through the thickness of the foam plank. 16 Compression Testing The compressive properties of the rigid PS foams were determined in accordance with ASTM D1621-04a [31]. Eight replicate foam cubes were prepared with their sample thickness aligned in each orthogonal direction of the plank respectively. Specimens were cut using a band saw and the dimensions were measured using digital calipers. Compression testing was performed with a Materials Test System (MTS) Alliance RT-50 test machine equipped with a 50 kN load cell as shown in Figure 2.9. Figure 2.9 Foam Compression Test Equipment All tests were performed with a crosshead velocity of 2.5 1 0.25 mm/min for each 25.4 mm of specimen thickness as specified in section 8.3 of the standard. The crosshead displacement was programmed to compress the foam specimens approximately 40 mm. In accordance with section 3.1.5 of the standard, compressive strength is defined as the stress at yield or the stress at 10% strain, whichever is greater. Compressive strength and modulus values shown in Table 2.1 were computed and recorded using a MTS TestWorks software program operating at a sampling rate of 10 Hz. Table 2.1 ASTM D1621-04a Compression Test Results Deformation Modulus Compressive Strength Direction (MPa) (MPa) Material Mean Std. Dev. Mean Std. Dev. HD 3OOF-X X-Direction 12.41 0.68 0.268 0.004 Y-Direction 19.91 2.56 0.373 0.020 Z-Direction 44.86 1. 17 0.694 0.021 EPS Bead X-Direction 14.69 5.19 0.346 0.038 Y-Direction 1 8.78 2.43 0.328 0. 020 Z-Direction 9.92 1.64 0.249 0.018 HD 300F-X exhibits a highly orthotropic response with the highest strength in the Z-direction. EPS bead foam exhibits highly orthotropic moduli and less orthotropic compressive strength with the lowest strength in the Z-direction. A representative plot of the engineering stress versus engineering strain response 18 of both products in each orthogonal direction of the plank is shown in Figures 2.10 and 2.11 respectively. 1.0 —Z—Direction —Y-Direction 1? 0.8 — —X-Direction % E Hf g 0.6* U) O'l : ': 0.4 — 8 / IE / U) [I E 0.2 - 3 0.0 7 I r . 0.0 0.1 0.2 0.3 0.4 0.5 Engineering Strain (mm/mm) Figure 2.10 Compressive Response of HD 300F-X in Orthogonal Directions 1.0 —Z-Directlon -Y-Direction A 0.8 - —X-Direction cu CL .5. 3’: 0.6 . 2 25 c» g 0.4 — a: a: .E 2’ m 0.2 7 0.0 I l T i 0.0 0.1 0.2 0.3 0.4 Engineering Strain (mm/mm) 0.5 Figure 2.11 Compressive Response of EPS Bead in Orthogonal Directions Prior to testing, a grid was drawn on a plane orthogonal to the loading direction to allow for transient deformation to be observed. Representative photographs depicting compressive deformation after 10, 25 and 40 mm of crosshead displacement are shown in Figures 2.12 and 2.13. 20 (a) (b) (C) (d) (e) (t) Figure 2.12. STYROFOAM HD 300F-X Compressive Failure Mode Photos (a) Axial, (b) Transverse and (c) Thickness direction at 10 mm deformation (d) Axial, (e) Transverse and (f) Thickness direction at 25 mm defamation 21 Figure 2.12 (cont’d). (9) (h) (i) (9) Axial, (h) Transverse and (i) Thickness direction at 40 mm deformation 22 (m) (n) (0) Figure 2.13 EPS Bead Foam Compressive Failure Mode Photographs (j) Axial, (k) Transverse and (I) Thickness direction at 10 mm deformation (m) Axial, (n) Transverse and (0) Thickness direction at 25 mm deformation 23 Figure 2.13 (cont’d). (P) (Cl) (1) (p) Axial, (q) Transverse and (r) Thickness direction at 40 mm deformation HD 300F-X test specimens exhibited highly localized deformation in the plank thickness direction that originated near the mid-plane (2:0) and propagated toward the outer surfaces (Z=:l:C/2) while the other directions exhibited visible homogeneous deformation. EPS bead foam test specimens, on the other hand, exhibited predominantly uniform deformation in each orthogonal direction of the plank. A final series of compression tests were performed on thin HD 300F-X sections cut from the thickness (Z-direction) of the plank and labeled 21 through 25 (Table 2.2). 24 Table 2.2 HD 300F-X Compression Test Results on Z-Direction Foam Sections Foam Modulus (MPa) Compressive Strength (MPa) Label Mean Std. Dev. Mean Std. Dev. 21 29.98 0.73 0.89 0.04 22 34.87 0.22 0.84 0.04 23 35.47 1.45 0.78 0.06 24 35.70 1.23 0.84 0.03 25 30.85 1.71 0.84 0.03 Representative compression curves for each foam section are shown in Figure 2.14. The Z-direction compressions demonstrate that the modulus of foam sections taken near the top and bottom are 15-20% lower than sections from the middle region of the plank. These quantitative results combined with the previous failure mode photographs confirm non-homogeneous compressive deformation through the thickness of HD 300F-X specimens. 25 —Zl__AVG __. .0 CD I .0 o: 1 Engineering Stress (MPa) 9 A 9 N l 0.0 I I I I 0.00 0.02 0.04 0.06 0.08 0.10 Engineering Strain (mm/mm) Figure 2.14 HD 300F-X Compressive Response for Z-Direction Section Specimens Tension Testing The tensile properties of the rigid PS foams were determined in accordance with ASTM D1623-03 [32]. Three type III cubical foam specimens were prepared with the sample thickness aligned in each orthogonal direction of the plank respectively. Samples were cut using a band saw and the dimensions were measured using digital calipers. Cubical foam samples were then 26 adhered to metal grip assemblies using 3M® SCOTCH-WELDTM Epoxy Adhesive 2216. Tensile testing was performed with an lnstron 1123 electromechanical test system as shown in Figure 2.15. Figure 2.15 Foam Tension Test Equipment for ASTM D1623-03 Type III Specimens All tests were performed with a crosshead velocity of 5.08 mm/min as specified in section 8.1 of ASTM D1623. Tensile strength and modulus values shown in Table 2.3 were computed and recorded using Bluehill2 software. mSCOTCH-WELD is a registered trademark of Minnesota Mining and Manufacturing Company Corporation 27 Table 2.3 ASTM D1623-03 Type III Specimen Tension Test Results Modulus (MPa) Tensile Strength (MPa) Material Direction Mean Std. Dev. Mean Std. Dev. HD 300F-X X-Direction 17.37 0.59 0.605 0.010 Y-Direction 30.32 0.67 0.769 0.040 Z-Direction 51.23 0.67 1.008 0.107 EPS Bead X-Direction 26.42 4.82 0.552 0.047 Y-Direction 28.63 0.21 0.559 0.006 Z-Direction 16.58 0.24 0.410 0.007 The break for each specimen occurred within the foam, or cohesively, and not at the adhesive interface. A representative plot of the engineering stress versus engineering strain response of both materials in each orthogonal direction of the plank is shown in Figures 2.16 and 2.17 respectively. 28 1.6 —Z-Direction 1.4 2 —Y-Direction —X-Direction Engineering Stress (MPa) 0.00 0.02 Engineering Strain (mm/mm) 1 0.04 ‘1 0.06 I 0.08 I 0.10 0.12 Figure 2.16 Tensile Response of HD 300F-X in Orthogonal Plank Directions 29 1.6 1.4~ 1.2“ 1.04 0.8 ~ 0.6 - 0.4 2 Engineering Stress (MPa) 0.2 a 0.0 -- Z-Direction — Y-Direction — X-Direction I 0.00 0.02 Figure 2.17 Tensile Response of EPS Bead Foam in Orthogonal Plank Engineering Strain (mm/mm) I I 0.04 0.06 Directions I 0.08 I 0.10 0.12 A second series of 17.5 mm thick HD 300F-X tension test specimens (21- 25) were fabricated from foam slabs (Figure 2.18) abrasive wire cut through the thickness of the plank. Three replicate samples each were prepared with the specimen length aligned in the axial and transverse directions respectively. 30 R76 (typ) 50.8 65.5 (typ) 246.1 Figure 2.18 HD 300F-X Foam Section Test Specimen Geometry Tension tests were performed in accordance with ASTM 0638-08 [33] using a MTS equipped with an 8.9 kN load cell and a 0.50 mm/mm contact extensometer for transient strain measurements (Figure 2.19). The crosshead velocity was programmed at a rate of 5.08 mm/min for all tests. Transient data were collected with a sampling rate of 13 Hz. A compilation of the test results is shown in Table 2.4. 31 Table 2.4 HD 300F-X Tension Test Results on Foam Section Specimens Test Foam Modulus (MPa) Tensile Strength (MPa) Direction Label Mean Std. Dev. Mean Std. Dev. Axial X1 33.90 0.59 0.773 0.041 Axial X2 26.22 1 .01 0.806 0.027 Axial X3 16.89 0.66 0.603 0.022 Axial X4 21.18 2.30 0.582 0.006 Axial X5 30.54 1 .50 0.752 0.002 Transverse Y1 48.69 6.72 0.981 0.016 Transverse Y2 41 .88 6.50 0.925 0.039 Transverse Y3 40.63 3.15 0.879 0.070 Transverse Y4 44.47 3.28 0.893 0.078 Transverse Y5 50.79 2.55 0.985 0.038 32 Figure 2.19 Tension Test Equipment for Abrasive Wire Cut Foam Section Specimens A sub-routine was created in the data acquisition software to compute a representative average stress-strain curve for each section in all orthogonal directions of the plank as shown in Figures 2.20 and 2.21. 33 —z1_Avo —22_AVG 1-4 ‘ —Z3_AVG — ELLA <3 —25_AVG 1.2 — ’11? a. E m 1.0 . to .9-3 a) _ m 0.8 .E 78' .E 0.6 ‘ m C m // 0.4 - ” 0.2 ~ 0.0 . . . . 0.00 0.04 0.08 0.12 0.16 0.20 Engineering Strain (mm/mm) Figure 2.20 HD 300F-X Tensile Results for Axial Direction Section Specimens 34 1.6 —Z1_AVG 1_4 — —Z2_AVG E —Z3_AVG 2. — 5 w _ 3 1.0 13 at 0.8 — .E g 0.6 — .E m 0.4 — C |.I.| 0.2 ~ 0.0 . . . . 0.00 0.04 0.08 0.12 0.16 0.20 Engineering Strain (mm/mm) Figure 2.21 HD 300F-X Tensile Results for Transverse Direction Section Specimens The tabulated results and representative average tensile stress-strain curves reveal a distinct non-linear response through the thickness (Z-direction) of a HD 300F-X plank. Moreover, it is also worth noting that the ASTM D1623 test results are indicative of properties at the mid-plane (2:0) of the plank whereas the section results denote a much higher tensile modulus and strength at the outer surfaces (Z=i0.5'C) where such normal stresses exist. 35 Shear Testing The shear properties of both rigid PS foams were determined in accordance with EN 12090: 1997 [34]. Three foam specimens measuring 25 by 50 by 250 mm in thickness, width and length, respectively, were prepared with their sample length aligned in both the axial and transverse directions of the plank, respectively. Each test specimen contained the outer skin (2:10.50) of the foam plank surface. Samples were cut using a band saw and the specimen dimensions were measured using a digital linear gage. Foam samples were then adhered to single test specimen assembly supports of length 330 mm and width 50 mm using a two—component polyurethane adhesive comprised of SikaForce®-7710 L100 polyol and SikaForce®-7010isocyanate. Shear testing was performed with an lnstron 5567 electromechanical test system and grip assemblies as shown in Figure 2.22. All testing was performed in a tension mode of operation with a programmed crosshead velocity of 3 mm/min. Transient shear stress, I, in units of MPa, was then calculated in accordance with Equation 2.2 (2.2) where P denotes the instantaneous force on the specimen in units of kN and the specimen length, L, and width, b, are reported in units of meters. 36 Engineering shear strain, y, was measured using an lnstron 2620-601 dynamic strain gauge extensometer mechanically affixed to the metal glue plates. Transient data were recorded at a sampling rate of 20 Hz. Shear moduli were computed from a linear regression performed within a linear elastic range encompassing 35-40% of the maximum load as determined from the transient force-deflection curves. A compilation of the test results is shown in Table 2.5. Figure 2.22 EN 12090 Single Test Specimen Assembly Test Set-Up 37 Table 2.5 EN 12090 Foam Core Shear Test Results Modulus (MPa) Stress @ 5% Strain (MPa) Material Direction Mean Std. Dev. Mean Std. Dev. HD 300F-X Axial 11.63 0.47 0.509 0.017 Transverse 15.73 1.91 0.541 0.031 Edgewise 7.77 0.30 0.329 0.008 EPS Bead Axial 8.58 0.90 0.283 0.009 Transverse 8.68 0.89 0.269 0.009 Edgewise 8.22 0.52 0.263 0.016 The stress at 5% strain of HD 300F-X foam specimens was almost twice that of EPS bead foam samples whereas the shear modulus was 35% and 80% higher in the axial and transverse directions respectively. For composite roof panel applications, the axial shear properties, ze and 1x2, are of most practical importance as the span often corresponds to the longest dimension of the foam panel. Representative shear stress-strain curves for each PS foam core product in both directions of the plank are shown in Figure 2.23. 38 1.0 .2 :fioéoaixralf g —HD300 (Trans) a 0,8 — —EPS (Axial) (n — EPS (Trans) fl) g m 0.6 - I- a o .C a) m 0.4 ~ IE 5 0 8 '51 0.2- : I.I.I 0-0 I I I I 0.00 0.20 0.40 0.60 0.80 1.00 Engineering Shear Strain (mm/mm) Figure 2.23 Transient Engineering Shear Stress vs. Strain Response of PS Foam Cores In order to ascertain non-homogeneity of shear properties through the thickness of a foam plank, a series of 12.5 mm thick, 50.8 mm wide and 151.6 mm long test specimens were fabricated in accordance with section 8.2 of ASTM 0273 [35]. Specimens were fabricated from foam sections taken through the thickness of the foam plank with their length aligned in both the axial (X1-X5) and transverse (Y1-Y5) directions, respectively. Shear section tests were performed with a MTS equipped with a 17.8 kN load cell and an Omega LD610-50 linear variable differential transformer 39 (LVDT) mechanically affixed to the metal shear plates, respectively (Figure 2.24). All tests were performed in a tension mode of operation with a crosshead velocity of 2.54 mm/min. Transient force and displacement data were recorded at a sampling rate of 25 Hz using DATAAQ 17.39 software programmed in Visual Basic. Figure 2.24 ASTM C273 Shear Test Equipment Three replicate tests were performed for each condition (Table 2.6) as shown in Figures 2.25 and 2.26. 40 Table 2.6 HD 300F-X Shear Test Results on Foam Section Specimens Test Foam Modulus (M Pa) Shear Strength (MPa) Direction Label Mean Std. Dev. Mean Std. Dev. Axial X1 14.83 0.82 0.563 0.013 Axial X2 12.31 0.87 0.466 0.028 Axial X3 1 1 .45 0.75 0.434 0. 020 Axial X4 12.15 0.16 0.461 0.010 Axial X5 13.99 0. 82 0.561 0. 044 Transverse Y1 19.20 0.21 0.594 0.004 Transverse Y2 18.93 1.44 0.549 0. 009 Transverse Y3 18.03 1.86 0.541 0.044 Transverse Y4 1 7.78 0.43 0.539 0. 008 Transverse Y5 1 8.33 0.74 0.582 0. 004 The axial shear modulus and shear strength of sections taken near the mid- plane (2:0) of the foam plank were approximately 23% lower than foam sections taken near the outer region (2:10.50) of the plank thickness. The difference in the transverse shear modulus and shear strength in outer and mid- plane foam sections was approximately 6% and 9%. 41 Engineering Shear Stress (MPa) 1.0 -—Z1 —22 —Z3 —Z4 —Z5 0.8 ~ 0.6 - 0.4 — 0.2 - 0.0 I l l 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Engineering Shear Strain (mm/mm) I I I Figure 2.25 HD 300F-X Shear Test Results for Axial Direction Section Specimens 42 _L O .0 00 I .0 .o A O) I 1 Engineering Shear Stress (MPa) 0 i0 0.0 . 1 l I I .‘ I 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 Engineering Shear Strain (mm/mm) Figure 2.26 HD 300F-X Shear Test Results for Transverse Direction Section Specimens Poisson’s Ratio Testing Poisson’s ratio of closed cell foams was reported by Gibson and Ashby [36], however, no such data was reported for either extruded or expanded polystyrene foams. Chun et. al. [37] developed a relationship between Poisson’s ratio and density for 20-30 kg/m3 EPS-geofoams which resulted in 0:019 for 30 kg/m3 EPS bead foam. Maltinti [38] reported a linear empirical relationship (Equation 2.3) between density and Poisson’s ratio for EPS density in the range of 16-32 kg/m3 as shown 43 u=0.0056-p+0.0024 (2.3) where density, p, is reported in units of kg/m3. Thus, for 32 kg/m3 EPS bead foam, Poisson’s ratio is estimated from Equation 2.3 as 0.18. Throughout the remainder of this paper, a Poisson’s ratio of 0.18 will be assumed for EPS bead foam. Published values of Poisson’s ratio for orthotropic extruded polystyrene foams are presently lacking. Thus, Poisson’s ratio for orthotropic XPS foam was experimentally determined using an optical technique [39]. Cubical (100 mm) foam specimens were cut using a band saw and a series of evenly spaced (6.35 mm) lines within a 50 mm square grid were drawn on a plane orthogonal to the direction of applied load as shown in Figure 2.27. The grid was isolated to a 50 mm square region to neglect frictional effects near the platens. Foam . . . . ® specrmen drmensrons were measured usrng a 152.4 mm full-scale Ampro precision digital caliper. An 8.0 Megapixel Nikon Coolpix 8400 digital camera was mounted on an Optex T265 tripod and pre-test, high quality (3264x2448) foam images were taken of the un-deformed grid using a sensitivity setting of 50. Next, compressive load was applied in the Z-direction (plank thickness) of the specimen using a MTS in manual mode to subject the foam specimen to a compressive stress approximately 80% of yield conditions. Once the desired load had been applied, a photograph of the deformed specimen was taken and the load was removed. Intersection Points Figure 2.27 STYROFOAM HD 300F-X Pre-Test Photograph Depicting Grid Network The position of each intersection point within the grid region was recorded using image analysis software techniques. Transverse strain was recorded in both the axial (X-dir.) and transverse (Y-dir.) directions using the grid displacement data from the pre-test and post-test photographs respectively. A representative image depicting the grid intersection displacement is shown in Figure 2.28. 45 Z-Dir. <—-—————— Transverse Direction ——-——> Figure 2.28 STYROFOAM HD 300F-X Grid Intersection Displacement Illustration Poisson's ratio, 0, is calculated in accordance with Equation 2.4: _ Slateral 8 V: axial (2.4) 46 where £|atera| is the strain transverse to the direction of applied load and Eaxial is the strain in the direction of applied load. The axial and lateral strains were computed from the outer dimensions of the grid region to compute the results compiled in Table 2.7. Table 2.7 Polystyrene Foam Core Poisson’s Ratio Test Results Notation Poisson’s Ratio UXY 0.37 UYX 0.57 mg 0.26 UZY 0.38 uzx 0.52 uxz 0.16 An orthotropic material must obey the reciprocity relations [40] defined in Equations 2.5 — 2.7 below: 47 x y (2.5) ”212 =_g_ Ex Ez (2.6) _y = U... E y E: (2.7) The experimentally measured properties for XPS foam violate these conditions by only 10-14%. 48 CHAPTER3 FINITE ELEMENT MODELING OF SIP PANELS A linear static finite element model of a sandwich panel was developed based on the foam material properties measured above. This chapter describes the model and a comparison of its predictions against the experimental measurements. Oriented Strand Board Material Characterization For use in the finite element model, the material properties of 6 mm general purpose OSB facers were characterized in flexure using 50 by 172 mm specimens in the width and length directions. The specimen width, b, and thickness, d, were measured and recorded using digital calipers. Replicate tests were performed with the specimen length aligned in the axial, or machine, direction of a 2438 mm long OSB sheet. The aluminum sandwich panel bend test fixture was utilized with a 120 mm support span, L, and a crosshead velocity of 1.27 mm/min. The mid-span deflection, D, was measured and recorded on the bottom (i.e. tension) side of the specimen using an Omega LD610-50 LVDT. Transient force, P, and mid-span displacement data were recorded at a sampling rate of 13 Hz. The instantaneous bending stress, 6b, and maximum outer fiber strain, 8, were computed in accordance with Equations 3.1-3.2: 49 3PL 0" :— ” 219.12 (3.1) 6dD e: L2 (3.2) An elastic modulus of 1198 :I: 189 MPa was computed within the linear elastic regime whereas a Poisson’s Ratio of 0.10 was assumed from published literature [36]. Although OSB is well known to exhibit orthotropic behavior, only machine direction properties of the OSB sheet were needed to model the beam behavior. Hence, the OSB sheet was modeled as isotropic, based on machine- direction properties, for all finite element simulations of sandwich panel bend tests. Polystyrene Foam Core Material Models Isotropic Polystyrene Foam Core Material Modeling The isotropic material properties for both PS foam cores were based upon experimentally measured ASTM D1623 tensile moduli in the axial direction of the foam board. A Poisson’s ratio of 0.33 was assumed for both PS foam core products as reported in published literature [30]. 50 For homogeneous isotropic materials, a relationship exists between Young’s modulus E, shear modulus G, and Poisson’s ratio 1), as shown in Equation 3.3: E=2G~(1 +0) (3.3) Orthotropic XPS Foam Core Material Modeling A linear elastic orthotropic material can be modeled by defining the nine engineering constants that constitute the elastic stiffness matrix, D. For such orthotropic materials, the engineering constants are defined by Equations 3.4 - 3.14 [41]. (711 £11 022 822 0' 8 < 33 I=[D]< 33 > 0'12 712 0'13 713 .023, .723. (3.4) D1111 = E1(1-023032)T (3.5) 51 D2222 = E2(1-013031)T D3333 = E3(1-v12v21)T D1122 = E1 (021+031023)T = E2(012+032013)T D1133 = E1(031+021032)T = E3(013+012023)T D2233 = E2(032+u12031)T = E3(023+021013)T D1212= G12 D1313=G13 52 (3.6) (3.7) (3.3) (3.9) (3.10) (3.11) (3.12) D2323 = G23 (3.13) where _ 1 T- 1— 01202, _ 023032 - 031013 _ 2”21032013 (3.14) Furthermore, the restrictions on the elastic constants clue to material stability are detailed in Equations 3.15 — 3.19 [42]. D1111. D2222. D3333. D1212, D1313. D2323 > 0 (3.15) 1/2 ID1122| < (D1111D2222) (3.16) 1/2 ID1133| < (D1111D3333) (3.17) 53 1/2 ID2233| < (D2222D3333) (3.18) 2 2 D1111D2222D3333 + 2D1122D1133D22332- D2222D1133 - D1111D2233 - D3333D1122 > 0 (3.19) Orthotropic material models based upon the assumption of homogeneous deformation in each orthogonal direction of the foam plank were constructed using Young’s modulus results obtained from ASTM D1623 tensile testing and shear modulus values obtained from DIN EN 12090 shear testing. Orthotropic EPS bead foam stiffness constants were calculated using a Poisson’s ratio of 0.33 in each direction of the board. XPS foam was also modeled as non-homogeneous in the thickness direction. Five 20 mm regions were modeled through the foam thickness using orthotropic material constants calculated from ASTM D638 tensile test and ASTM C273 shear test results respectively. The PS foam core stiffness constants for orthotropic elastic material models are summarized in Table 3.1. 54 Table 3.1 PS Foam Core Orthotropic Material Model Parameters (All values are reported in units of E+07 Pa.) Homogeneous X PS Non-Homogeneous Constant EPS X PS Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 D1111 4.754 2.911 5.681 4.394 2.830 3.549 5.118 D1122 0.630 2.278 4.445 3.438 2.215 2.777 4.005 D2222 3.109 5.169 8.300 7.140 6.926 7.581 8.658 D1133 0.630 2.379 4.643 3.591 2.313 2.901 4.183 D2233 0.682 3.227 5.1 82 4.458 4.324 4.733 5.406 D3333 1.800 7.517 7.517 7.517 7.517 7.517 7.517 D1212 0.822 0.777 0.777 0.777 0.777 0.777 0.777 D1313 0.858 1.163 1.483 1.231 1.145 1.215 1.399 D2323 0.868 1 .573 1 .920 1 .893 1.803 1.778 1.833 SIP Bend Test Simulations A composite foam core sandwich panel was modeled using Abaqus Standard [43]. The panel was represented as a three-dimensional deformable solid part measuring 112 mm in the thickness or 2-direction, 150 mm in the width or Y-direction and 450 mm in the length or X-direction. Representation of the non-homogeneous foam properties was accomplished by partitioning the 100 mm thick PS foam core into five 20 mm sections as shown in Figure 3.1, and assigning the corresponding material properties to each region. 55 Figure 3.1 Abaqus Composite Foam Core Sandwich Panel Representation The supported edges were modeled as a pinned and a roller condition, and a uniform pressure of 1.186E+06 Pa was applied in a 10X150 mm area to simulate an applied load of 1779 N (400 Ibf). The results of a convergence study determined that a mesh size of 0.015 m was required for all FEA simulations as shown in Figure 3.2. 56 Figure 3.2 Composite Foam Core Sandwich Panel Meshed Part Experimental SIP Bend Tests A series of experimental bend tests were performed on composite sandwich panels comprised of 6 mm thick OSB facings and 100 mm thick PS foam cores. OSB was adhered to the PS foam core using MOR-AD® M-652, a one- component moisture cure polyurethane adhesive. All composite sandwich panels were fabricated with the machine direction of the OSB aligned in the length direction of the panel. Composite sandwich panels measuring 150 by 450 mm in width and length were prepared with the length of the foam core aligned in the axial direction of the plank. A representative photograph of a composite sandwich panel is shown in Figure 3.3. 57 Figure 3.3 Composite Sandwich Panel of Overall Dimensions 1 12X150X450mm Simply supported three-point bend tests were performed using an aluminum test fixture comprised of 32 mm diameter loading and support edges and a support span, L, of 400 mm as depicted in Figure 3.4. All testing was performed with a MTS equipped with an 8.89 kN load cell, a 127 mm displacement card and a programmable crosshead velocity of 1.27 mm/min. Mid-span deflection was measured on the bottom, or tension side, of the sandwich panel using an Omega LDB10-50 LVDT. Transient force and displacement data were recorded at a sampling rate of 10 Hz. 58 Figure 3.4 Composite Sandwich Panel Bend Test Apparatus of 400mm Support Span During the tests, all failures occurred within the foam specimen, or cohesively, and not at the adhesive interface. An overlay of the transient beam bending behavior of each series of composite sandwich panels is shown in Figure 3.5. 59 6,000 ?— XPS — EPS Bead 5,000 ~ 4,000 2 3,000 . Force (N) 2,000 ~ 1 ,000 ~ O I 7 I I I 0 1 2 3 4 5 6 Displacement (mm) Figure 3.5 Composite Sandwich Panel Bend Test Response The sandwich panel stiffness, in units of N/mm, was linearty regressed within a force range of 444 Figure 4.4 Roof panel beam geometry and load configuration The sandwich panel materials of construction investigated throughout this study consisted of the sheathing, structural frame and PS foam core products compiled in Table 4.1. 70 Table 4.1 Roof sandwich panel material matrix Constituent Material of construction Sheathing Oriented strandboard (OSB) Gypsum board (i.e. drywall) Structural frame Standard pine lumber (i.e. 2x4) Laminated veneer lumber (LVL) Foam core Expanded polystyrene (EPS) bead Extruded polystyrene (XPS) Local amendments to the 2006 lntemational Residential Code may prescribe a minimum exterior sheathing thickness based upon maximum ground snow loads. For example, the county of Larimer, CO [49] specifies a minimum sheathing thickness of 11.1 mm (0.4375 in.) for ground snow loads below 1915 N/m2 (40 psf) whereas a minimum sheathing thickness of 15.1 mm (0.594 in.) is required for a ground snow load of 3350 N/m2 (70 psf). The composite roof panels considered here are comprised of structural lumber frames adhesively affixed to the sheathing and foam core insulation surfaces respectively. OSB was selected as the candidate exterior sheathing material whereas both OSB and gypsum were considered as candidate interior sheathing materials. The interior OSB thickness was varied from 6 mm to 19.05 mm due to the lack of any specified code requirement for interior sheathings. The feasible thickness range of gypsum was varied between 11.11 mm (7/16”) 71 and 15.88 mm (5/8”) for industry standard board sizes. Standard dimensional lumber and 13-ply southern pine laminated veneer lumber (LVL) represent potential structural frame materials. Longitudinal lumber frames were spaced 610 mm apart whereas full-width transverse frames were positioned at both ends of the foam board and two short-span transverse frames were positioned at the panel mid-span respectively. Finally, candidate core insulation products consisted of 44 kg/m3 block molded EPS bead foam and 50 kg/m3 STYROFOAM H0300 F-X [25] XPS foam. Each foam type was assumed to be 1.2 m wide to accommodate industrially feasible panel sizes. Thermal effects were not modeled throughout the course of this study. The PS foam core thickness was varied by material type to ensure a minimum R-7.1 m2-KNV (Rug-40 h~ft2'°F/BTU) insulating performance of the SIP [24]. Thus, the EPS bead foam core thickness was varied from 254-305 mm to account for a nominal R-0.7 m2'K/W (Rug-4 h-ft2°°F/BTU) per 25.4 mm (1 in.) of thickness while the XPS foam core thickness was varied from 203-254 mm to account for a nominal R-0.9 m2-KNV (Rug-5 h-f12'°F/BTU) per 25.4 mm (1 in.) of thickness [50]. 72 FINITE ELEMENT MODELING A linear static finite element model of a composite roof panel was created in Abaqus Standard [51]. All panels measured 1219 mm in the width and 4816 mm in the length direction. Full width transverse lumber frames were positioned at the panel ends whereas two short span transverse lumber frames were positioned at the mid-span of the foam panel. OSB and gypsum sheathing were modeled using shell elements whereas structural lumber members and the foam core were modeled using 30 solid elements. The insulating foam core was partitioned in the thickness direction into five, equally spaced sections to allow for the varying material properties in this direction. A representative illustration of a composite roof panel assembly minus sheathing is shown in Figure 4.5. Figure 4.5 Composite roof lumber frame panel minus sheathing 73 OSB, gypsum and candidate lumber frame materials were modeled as isotropic, linear elastic materials. Required properties were density p, Young’s modulus E, and Poisson’s ratio 1). The ultimate stress, ou/t, was used in subsequent factor of safety considerations for potential sandwich panel designs. Because the predominant stresses are in the longitudinal direction, OSB [52], gypsum [53], standard pine lumber [54] and southern pine LVL [55- 56] were modeled as isotropic using their longitudinal direction material properties as compiled in Table 4.2. Table 4.2 OSB facer and structural lumber frame material properties Material p(kglm3) E(GPa) 11 cutt(MPa) OSB 630 6.6 0.10 8.6 Gypsum 700 2.5 0.30 3.8 Std. lumber 673 11.3 0.16 14.4 LVL 630 16.6 0.49 19.0 EPS bead foam was modeled as isotropic with a nominal mass density of 44 kg/m3, an elastic modulus of 30 MPa and a critical shear stress, Tc, of 0.28 MPa. Poisson’s ratio was taken to be 0.33 [24]. 74 XPS foam was modeled as orthotropic with varying material properties through the thickness of the core. A nominal density of 50 kg/m3 and To of 0.5 MPa were used for all five partitioned regions of the core. A linear elastic orthotropic material can be modeled by defining the nine engineering constants that constitute the elastic stiffness matrix, D. For such orthotropic materials, the engineering constants are defined by Equations 4.1-4.10 [57]. D1111 = 51(1'023032W (4.1) D2222 = E2(1 $13031” (4.2) D3333 = 5311-012U21IT (4.3) D1122 = Ei(U2t+031023)T = E2(U1z+032013)Y (4.4) D1133 = E1(Us1+U21032)T = E3(1>13+U12U23)T (4.5) 75 D2233 = E20)32+U12D31)T = E3(D2s+021013)T (4.6) D1212 = (312 (4.7) l31313 = (313 (4.8) D2323 = G23 (4.9) where _ 1 T _ 1— vizvzl _ ”23032 '7 v3lvl3 _ 2”217132153 (4.10) The XPS foam stiffness constants for the five partitioned regions through the thickness of the core are summarized in Table 4.3. 76 Table 4.3 XPS foam core orthotropic material constants Constant Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 0m, 56.81 43.94 28.30 35.49 51.18 91,22 44.45 34.38 22.15 27.77 40.05 02222 83.00 71.40 69.26 75.81 86.58 91,33 46.43 35.91 23.13 29.01 41.83 02233 51 .82 44.58 43.24 47.33 54.06 D3333 75.17 75.17 75.17 75.17 75.17 [3,212 7.77 7.77 7.77 7.77 7.77 0,3,3 14.83 12.31 11.45 12.15 13.99 02323 19.20 18.93 18.03 17.78 18.33 The OSB facings were modeled as 4-node, reduced integration shell elements of type S4R. Both lumber frames and the foam core sections were modeled as reduced integration, hourglass control 3D solid elements of type C3D8R. The supported edges were modeled as a pinned and a roller condition. The panel was loaded with a static, linear perturbation step comprised of both a gravitational dead load and a uniform ground snow load applied to the surface of the exterior OSB sheathing. 77 FINITE ELEMENT MODEL VALIDATION The design of a composite insulating roof panel must satisfy deflection requirements associated with external loads, including seismic, wind and ground snow loads. The total deflection, A, of a composite sandwich panel [58] may be expressed as the sum of deflections arising from bending, Ab, and shear, As, effects as shown in Equation 4.11. A=Ab+AS (4.11) For a simply supported beam of Span, L, width, b and core thickness, 0, subjected to a uniformly applied pressure q, the total deflection is further defined by Equation 4.12 [44]: _ 5PL3 + PL 384(EI) 8(AG) (4.12) where P=qu and (El) is the equivalent flexural rigidity as shown in Equation 4.13 for thin facings: 78 Ebc3 - Ebtd2 2 3 (El): Ebtd + Ebt + 6 12 2 (4.13) and (AG) is the equivalent shear rigidity as shown in Equation 4.14. 12de (AG) = __._ e bdGc C (4.14) d denotes the distance between centroids of the faces, as shown in Equation 4.15: d=c+t (4.15) where tis the thickness of the facing. Thus, the mid-span deflection of a simply supported beam subjected to a uniformly applied load can be expressed as 10qL4 quc A = 2 + 2 384Etd 86d (4.16) 79 For an isotropic linear elastic material such as EPS bead foam, the shear modulus is related to both the elastic modulus and Poisson’s ratio vfrom the expression in Equation 4.17. G: 2(1+v) (4.17) Moreover, the primary feature of a structural lumber frame is to increase the centroid distance between sheathing facings to increase the flexural rigidity of the composite sandwich panel. In comparing EPS bead foam deflection results for a 3,350 N/m2 snow load versus predictions based upon Equation 4.16, a difference of approximately 10% was observed. OPTIMIZATION STUDIES HEEDS® design optimization software [59] was used to automate the design optimization studies of composite sandwich panels for varying ground snow loads. HEEDS allows concurrent exploration of many design parameters in order to satisfy specific design objectives such as cost, mass, structural performance, etc. Using Abaqus Standard as the finite element solver within the HEEDS design study, an efficient full system composite roof optimization was achieved. ® HEEDS is a registered trademark of Red Cedar Technology. Inc. 80 Isotropic XPS SIP Roof Panel Optimization Two optimization studies were performed on a SIP comprised of OSB sheathings and isotropic XPS foam core properties taken from published literature [24]. Optimizations were performed for an applied snow load of both 958 N/m2 (20 psf) and 3,350 N/m2 (70 psf). The nominal foam density was 48 kg/m3, Young’s modulus was 26 MPa, Poisson’s ratio was 0.33 and the critical shear stress was 0.28MPa respectively. 81 The optimization statement was as follows: Objective: Minimize Total Mass Subject to: Maximum displacement 5 19.88 mm Dead Load 5 48.8 kg/m2 Foam strength factor of safety 2 3 OSB strength factor of safety 2 3 By varying: 958 Mm2 qround snow load: 11.11 mm 3 Exterior OSB thickness 515.08 mm 203 mm s Foam core thickness 5 254 mm 6 mm 5 Interior OSB thickness 519.05 mm 3.350 N/mz’ground snow load: 15.08 mm 5 Exterior OSB thickness 5 19.05 mm 203 mm 5 XPS core thickness 5 254 mm 6 mm 5 Interior OSB thickness 5 19.05 mm The automated design study progressed according to the process flow in Figure 4.6. 82 I Modify variable values in Abaqus input file Execute Abaqus HEEDS Extract Responses from Abaqus output file Converged? No Yes Optimized solution Figure 4.6 Optimization process flow diagram The entire SIP was meshed with a global seed size of 50mm whereas the foam core edge was locally meshed with a global seed size of 25 mm. For a representative SIP comprised of 12.7 mm interior OSB, a 205 mm XPS foam core and 12.7 mm exterior OSB sheathing, the number of elements for each sheathing layer was 2,304 each whereas the total number of foam elements was 23,040 respectively. A tie constraint was applied to the X-Y plane of the OSB sheathing and foam core instances to account for any subtle differences in 83 mesh sizing due to geometrical changes. The meshed geometry of a representative isotropic XPS SIP is shown in Figure 4.7. Figure 4.7 Representative Meshing of Isotropic XPS SIP During each design optimization study, HEEDS controls the panel geometry by first modifying and then executing the replay file (.rpy) that is created automatically during the building of the baseline finite element model in Abaqus CAE. Complete details of how HEEDS interfaces with Abaqus during an optimization study can be found in [60]. An optimal configuration was achieved for an applied snow load of 958 N/m2 whereas no acceptable (feasible) design was achieved for an applied snow load 84 of 3,350 N/m2. The constituent variables for both optimization studies are summarized in Table 4.4. Table 4.4 Isotropic XPS SIP optimization results Constituent Unit 958 Nlm2 3,350 Nlm2 OSB_EXT mm 11 .11 15.08 Foam_T mm 203.2 254.0 OSB_INT mm 6.00 19.08 Total__Mass_kg kg 1 1 6.96 1 97.81 Max_deflection_mm mm 8.40 10.03 DeadLoad_kg_sqm k9,”? 19.92 33.69 FS_OSB_EXT 5.83 3.28 FS_Foam 3.92 FS_OSB_INT 3.42 For an applied snow load of 3,350 N/m2, no feasible SIP design was obtained due to strength factor of safety limitations with the isotropic XPS foam core and interior OSB sheathing. Thus, it would be highly desirable to achieve a feasible XPS SIP panel design for an applied snow load of 3,350 N/m2. 85 Baseline SIP Optimization Study A series of four baseline HEEDS optimizations were performed on OSB sheathed SIP’s comprised of isotropic EPS bead and orthotropic XPS foam cores. The optimization objective involved minimizing total mass with the same constraints described in the previous section. For an applied snow load of 958 N/m2, the exterior OSB thickness was varied within a range of 11.11-15.08 mm versus 15.08-19.05 mm for an applied snow load of 3,350 N/m2. The thickness of the EPS and XPS foam core was varied within the ranges of 254-305 mm and 203-254 mm respectively. The optimal design variables and corresponding project responses for each baseline SIP design iteration is compiled in Table 4.5. 86 Table 4.5 HEEDS baseline SIP optimization results assuming orthotropic foam properties 953 N/m2 3,350 N/m2 Constituent Unit EPS XPS EPS XPS OSB_EXT mm 11 .11 11 .11 15.08 16.86 Foam_T mm 254.0 203.0 304.0 209.7 OSB_INT mm 6.00 6.00 19.05 17.06 Total_Mass_kg kg 1 28.9 1 22.9 204.8 187.0 Max_deflection_mm mm 5.61 7.96 7.39 11 .97 DeadLoad_kg_sqm kg/m2 21.95 20.93 34.33 31.36 FS_OSB_EXT 7.26 5.83 3.93 3.00 FS_Foam 3.67 6.96 3.18 FS_OSB_INT 4.27 3.41 301 3.00 A representative contour plot of the deflection of an EPS foam core SIP subjected to a 3,350 N/m2 ( 87 70 psf) ground snow load is shown in Figure 4.8. Figure 4.8 EPS SIP deflection contour plot for 3,350 N/m2 ground snow load The tabulated results clearly demonstrate that baseline XPS and EPS bead foam SlP’s subjected to a 958 N/m2 (20 psf) ground snow load are capable of satisfying the maximum deflection and minimum factor of safety requirements. For a ground snow load of 3,350 N/m2 (70 psf), however, EPS bead foam failed to satisfy the minimum factor of safety imposed on foam core stress whereas a 210 mm XPS foam core achieved a satisfactory design with 17 mm OSB sheathings. 88 Composite Roof Lumber Frame Panel Design Optimizations A series of eight HEEDS optimization studies were performed on structural lumber frame panels comprised of EPS bead and XPS foam cores and subjected to an applied snow load of 3,350 N/m2. The optimization statement was as follows: Objective: Minimize Total Mass Subject to: Maximum displacement 5 19.88 mm Dead Load 5 43.3 kg/m2 Foam strength factor of safety 2 3 Lumber frame strength factor of safety 2 3 OSB strength factor of safety 2 3 Gypsum strength factor of safety 2 3 By varying: 15.08 mm 5 Exterior OSB thickness 5 19.05 mm 25.4 mm 5. Exterior frame thickness 5 50.8 mm 25.4 mm 5 Exterior frame width 3 152.4 mm 203 mm 5 XPS core thickness 5 254 mm 254 mm s EPS core thickness 5 305 mm 25.4 mm 5 Interior frame thickness 5 50.8 mm 25.4 mm 5 Interior frame width 5 152.4 mm 6 mm 5 Int. sheathing thickness 5 19.05 mm 89 The entire roof panel was meshed with a global seed size of 50 mm whereas the foam core and frame edges (Y-direction) were locally meshed with a global seed size of 25 mm. For a representative structural lumber frame panel comprised of symmetrical 12.7 mm sheathings, a 205 mm PS foam core and structural lumber frames measuring 80 mm wide and 30 mm thick, the number of sheathing elements was 2,304 each, the total number of foam elements was 23,040 and the number of structural lumber frame elements was 1,042 each respectively. A tie constraint was applied to the X-Y plane of the sheathing and structural lumber frame instances as well as to the structural lumber frame and foam core instances to account for any subtle differences in mesh sizing due to geometrical changes. The meshed geometry of a representative structural lumber frame roof panel is shown in Figure 4.9. Figure 4.9 Representative meshed geometry of structural lumber frame roof panel 90 For each candidate foam core material, four design optimizations were performed with varying lumber frame and interior sheathing materials as detailed in Table 4.6. All Optimization studies were performed with OSB as the exterior sheathing. Table 4.6 Structural lumber frame panel optimization conditions Design Condition Constituent Material #1 #2 #3 #4 Structural lumber frame Std. lumber , - .’ i ‘ 142.2.rifimflfla2223wm” LVL 3.; .1 1 - 1,- Interior Sheathing EPS bead foam composite lumber frame panels failed to satisfy both the dead load and minimum strength factor of safety requirements as shown in Figure 4.10. For each design optimization study, the minimum strength factory of safety was governed by the foam core. 91 6011-11-11...--11--..1111—1—11—1 ,1, 1 .1—1 . . 1 . . 1 1 1 4.7 Unacceptable Dead Load Regime . . V7 " . ‘7 . ‘3M’7._9’.* ........ 1...... 50—. Ar -..--"""'" 2... ‘ ~~ 4.3 «A 5 E 40 —- ‘1" 3.9 E 3 2 x 2, a! " 8 g 30—— -— 35 E '5 3 a _E 8 s 20 2- 7” 3.1 E Unacceptable Safety Factor Regime . 1O‘F- .¢°-.-uo.-uu.--u”5 """ i'r"*3'r-n.. V 8' db 2.7 0 + 1 2.3 Int. Sheathing OSB OSB Gypsum Gypsum Frame Material Lumber LVL Lumber LVL Figure 4.10 EPS lumber frame panel optimization study results In all cases, XPS foam core composite lumber frame panels satisfied both the dead load and minimum strength factor of safety requirements as shown in Figure 4.11. For optimization studies performed with OSB as the candidate interior sheathing material, the minimum strength factor of safety was dictated by the foam core. For design optimizations performed with gypsum as the candidate interior sheathing material, the minimum strength factor of safety was governed by gypsum. 92 ’ Unacceptable"oead'LoadReglme 7 i ‘ ‘0 .- .a Dead Load (kg/m 2) “=1 Minimum Safety Factor 20 -I1- - ..... . ~~ Unaccemaotesarerytaotoraegne “j . o . ~ '- . ; . - 1 2.9 Int. Sheathing OSB OSB Gypsum Gypsum Frame Material Lumber LVL Lumber LVL Figure 4.11 XPS lumber frame panel optimization study results The optimal levels for each constituent as a function of design condition are compiled in Table 4.7. Table 4.7 XPS structural lumber frame roof panel optimization variables Design Condition Constituent Unit #1 #2 #3 #4 m FrameEXT_W mm 73.7 76.2 105.4 83.8 FrameEXT_T mm 30.2 25.4 29.5 26.7 Foam_T mm 226.5 227.0 211.7 218.8 FramelNT_W mm 77.5 66.0 118.1 77.5 FramelNT_T mm 27.7 26.2 46.2 27.9 Gypsum_lNT mm 13.8 11.7 OSB_INT mm 8.9 11.2 RESULTS AND DISCUSSION The baseline SIP optimization studies indicated that EPS bead foam core panels were not able to meet the structural requirements associated with an applied snow load of 3,350 N/m2. However, feasible design for SIP panels utilizing XPS foam core were found for this loading condition, provided that the experimentally measured orthotropic and non-homogeneous material properties are taken into account. Considering ventilation and installation issues associated with SIP’s such as joining of panels, routing electrical wires, plumbing, etc. along with ventilation concerns, an alternative design concept 94 was explored. Composite roof panels comprised of a stiff lumber frame adhered to opposing surfaces of an insulating foam core provide an opportunity to satisfy the performance objectives of a self-supported roof panel while enabling electrical wires and plumbing lines to be routed in void cavities. Moreover, a structural lumber frame panel further provides a ventilation cavity for air exchange. The most promising structural lumber frame panel design found here involved the use of structural LVL frames and gypsum as the interior sheathing material. Other designs comprising an OSB interior sheathing were also identified; however, the additional cost, weight and installation of post- installed gypsum make this concept less appealing. The total dead load associated with several design options is shown in Figure 4.12. 95 I Gypsum a Panel Dead Load (kg/m2) Int. Sheathing Frame Material Lumber Figure 4.12 Total dead load of XPS structural lumber frame panels designed to 2 carry 3,350 N/m snow loads The LVL lumber frame panel comprised of gypsum interior sheathing further allows for factory built panels to be constructed and shipped to the job site. A representative panel would be comprised of exterior OSB and structural LVL lumber frames adhered to an XPS foam core as shown in Figure 4.13. Upon being crane hoisted in place, the interior gypsum could be installed on the interior surface to provide a fire resistant barrier while satisfying code- prescribed deflection and strength safety factor requirements. 96 Figure 4.13 Representative factory built LVL lumber frame roof panel The staggered arrangement of exterior OSB sheathing would allow adjacent roof panels to be interconnected while the opposing surface would remain open to route electrical wires and plumbing lines. Traditional gypsum trades could then be contracted to finish the interior surface of the roof panel for aesthetics purposes. 97 CHAPTER 5 SUMMARY AND CONCLUSIONS In order to predict the mid-span deflection of structural SlP’s, a series of material characterization tests were performed on 100 mm thick XPS and EPS bead foam. Initial mechanical test results demonstrated substantially orthotropic properties for XPS and slight orthotropic behavior for EPS bead foam. Visual observation of foam compressive failure modes revealed highly localized or non-homogeneous deformation through the thickness direction of XPS foam in contrast to homogeneous deformation observed in EPS bead foam. Thus, additional XPS material characterization testing was performed on multiple foam sections taken through the thickness of the foam plank to allow for orthotropic, non-homogeneous constitutive material models to be created. Experimental sandwich panel bend testing and FEA simulations demonstrated that the most effective material modeling approach for EPS bead foam is isotropic whereas XPS should be modeled as orthotropic and non- homogeneous to accurately predict the mid-span deflection of composite sandwich panels subjected to three-point loading. Increasing energy efficiency of residential dwellings is a present focus of code agencies and homeowners. One approach to improving energy efficiency consists of dwellings built with an unvented cathedral attic. An unvented cathedral attic places thermal insulation at the roof plane whereas a vented attic places insulation on the attic floor. Most often, HVAC ducts in an attic exhibit significant heat losses to the environment of a vented attic. Another key factor 98 in unvented cathedral attics involves increasing the support span of an insulated roof panel to minimize or eliminate the need for structural reinforcements such as purlins. Thus, the composite sandwich roof panels must be thick enough to satisfy both structural and thermal insulation code requirements. In order to balance the requirements associated with mid-span deflection and resulting stresses imparted to self-supported insulated roof panels subjected to uniformly applied snow loads, a series of design optimization studies were performed using a coupled finite element and design optimization methodology. Initial design optimizations were performed on SIP’s comprised of 44 kg/m3 EPS bead foam and 50 kg/m3 XPS foam cores with variable OSB facing thickness. Results demonstrated that optimal SIP designs could be achieved for both foam types with an applied snow load of 958 N/m2 (20 psf) whereas, for the PS foam core materials investigated, only the SIP comprised of the XPS foam tested throughout this study could satisfy the design objectives for an applied snow load of 3,350 Wm2 (70 psf). Further optimizations were then conducted on insulated roof panels comprised of stiff lumber frames adhered to opposing surfaces of the foam core. Several feasible XPS foam core panel configurations were achieved with the most promising configuration comprised of LVL lumber frames, exten'or OSB and interior gypsum sheathing. 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