Finite Element Simulation and Assessment of Single-Degree-of-Freedom Prediction Methodology for Insulated Concrete Sandwich Panels Subjected to Blast Loads by Charles Michael Newberry A thesis submitted to the Graduate Faculty of Auburn University in partial fulfillment of the requirements for the Degree of Master of Civil Engineering Auburn, Alabama May 9, 2011 Keywords: insulated sandwich panel, single-degree-of-freedom, finite element modeling Copyright 2011 by Charles Michael Newberry Approved by James S. Davidson, Chair, Associate Professor of Civil Engineering Justin D. Marshall, Assistant Professor of Civil Engineering Robert W. Barnes, James J. Mallett Associate Professor of Civil Engineering Abstract This report discusses simulation methodologies used to analyze large deflection static and dynamic behavior of foam-insulated concrete sandwich wall panels. Both conventionally reinforced cast-on-site panels and precast/prestressed panels were considered. The experimental program used for model development and validation involved component-level testing as well as both static and dynamic testing of full-scale wall panels. The static experiments involved single spans and double spans subjected to near-uniform distributed loading. The dynamic tests involved spans up to 30 ft tall that were subjected to impulse loads generated by an external explosion. Primary modeling challenges included: (1) accurately simulating prestressing initial conditions in an explicit dynamic code framework, (2) simulating the concrete, reinforcement, and foam insulation in the high strain rate environment, and (3) simulating shear transfer between wythes, including frictional slippage and connector rupture. Correlation challenges, conclusions and recommendations regarding efficient and accurate modeling techniques are highlighted. The modeling methodologies developed were used to conduct additional behavioral studies and help to assess single-degree-of-freedom prediction methodology developed for foam-insulated precast/prestressed sandwich panels for blast loads. ii Acknowledgments This work was sponsored in part by the Air Force Research Laboratory and a research fellowship grant from the Precast/Prestressed Concrete Institute (PCI). The static tests from which the model validation data was generated were conducted at the University of Missouri Remote Testing Facility under the direction of Professor Hani Salim. Professor Clay Naito of Lehigh University was the lead technical advisor of the AFRL/PCI test program. The dynamic tests were conducted by the Engineering Mechanics and Explosives Effects Research Group, Force Protection Branch, Airbase Technologies Division, of the Air Force Research Laboratory (AFRL) at Tyndall Air Force Base Florida. The AFRL test program was coordinated by John Hoemann of Applied Research Associates, Inc. The test program also involved other employees of ARA and Black & Veatch, Federal Services Division. Dr. Jun Suk Kang, Postdoctoral Research Assistant, Auburn University, provided valuable technical assistance with the development of the many finite element models involved in the project. iii Table of Contents Abstract............................................................................................................................... ii Acknowledgments.............................................................................................................. iii List of Tables ................................................................................................................... viii List of Figures.................................................................................................................... ix Chapter 1 Introduction .......................................................................................................1 1.1 Overview ..........................................................................................................1 1.2 Objectives ........................................................................................................2 1.3 Scope & Methodology .....................................................................................2 1.4 Report Organization .........................................................................................3 Chapter 2 Technical Background ........................................................................................4 2.1 Overview ..........................................................................................................4 2.2 Blast Loading ...................................................................................................5 2.3 Precast/Prestressed Sandwich Wall Panels ......................................................7 2.4 Design of Precast/Prestressed Concrete Structures for Blast ...........................9 Chapter 3 Model Development and Validation ................................................................11 3.1 Overview ........................................................................................................11 3.2 Reinforced Concrete Beam Validation ...........................................................12 3.2.1 Concrete Model and Parameters ......................................................13 3.2.2 Mechanical Behavior and Concrete Plasticity ..................................14 iv 3.2.3 Yield Function ..................................................................................18 3.2.4 Material Parameters of Concrete Damage Plasticity Model.............20 3.2.5 Reinforcements (Rebar and Welded Wire Reinforcement ...............21 3.2.6 Geometry, Elements, Loading, and Boundary Conditions ...............23 3.2.7 Nonlinear Incremental Analysis .......................................................24 3.2.8 Static RC Flexure Test and FE Results Comparison ........................24 3.3 Static Tests of Sandwich Panels .....................................................................26 3.3.1 Shear Connectors ..............................................................................26 3.3.2 Static Shear Tie Tests........................................................................28 3.3.3 Shear Tie Modeling Methodology....................................................28 3.3.4 Implementation of the MPC Approach into Sandwich Panel Models .............................................................................................30 3.3.5 Simulation of Prestressing Effects in Sandwich Panel Models ........32 3.3.6 Insulation Foam Modeling................................................................33 3.3.7 Static Sandwich Panel Tests and Modeling Comparisons................37 3.4 Dynamic Modeling and Experimental Comparisons ......................................39 3.4.1 Full-scale Dynamic Tests..................................................................40 3.4.2 Dynamic Finite Elements Models.....................................................43 3.4.3 Simulation of Prestressing Effects in LS-DYNA .............................43 3.4.4 Simulation of Dynamic Increase Factors..........................................44 3.4.5 Dynamic Sandwich Panel Experiment and FE Model Comparisons ..................................................................................45 3.4.6 Single Span Results and Comparisons..............................................45 3.4.7 Multi-span Results and Comparisons ...............................................48 v Chapter 4 Study of Blast Response Behavior of Sandwich Panels ..................................56 4.1 Introduction......................................................................................................56 4.2 Energy Dissipation...........................................................................................56 4.2.1 Kinetic Energy .................................................................................57 4.3 Strain Distribution ...........................................................................................58 4.4 Reaction Force vs. FE Models.........................................................................61 Chapter 5 Single-Degree-of-Freedom Model Development..............................................65 5.1 Introduction .....................................................................................................65 5.2 General SDOF Methodology ...........................................................................66 5.2.1 Central Difference Numerical Method .............................................69 5.3 Development of Sandwich Panel SDOF Prediction Models ...........................71 5.3.1 Static Resistance of Sandwich Panels and SDOF Models................71 5.3.2 Correlation With Current Prediction Methods..................................73 5.3.3 Resistance Calculation......................................................................73 5.3.4 Material Dynamic Properties Calculation.........................................74 5.4 SDOF Prediction Model Comparisons ............................................................79 5.4.1 SDOF Prediction Model Matrix........................................................79 5.4.2 SDOF Prediction Model Comparisons ? Dynamic Series I..............80 5.4.3 SDOF Prediction Model Comparisons ? Dynamic Series II ............83 5.4.4 Resistance and Energy Comparisons................................................85 5.4.5 SDOF Prediction Model Comparisons ? FE Modeling ....................94 Chapter 6 Conclusions and Recommendations..................................................................98 6.1 Conclusions......................................................................................................98 vi 6.2 Recommendations............................................................................................99 References ......................................................................................................................100 vii List of Tables Table 3.1. Description of reinforced concrete beam samples...........................................14 Table 3.2. Material parameters of concrete damage plasticity model ..............................21 Table 3.3. Material strengths of reinforcements ...............................................................22 Table 3.4. Static sandwich panel validation matrix ..........................................................38 Table 3.5. Dynamic test specimen details.........................................................................41 Table 3.6. Primary detonation normalized pressures and impulses..................................42 Table 3.7. Pre-detonation comparison of single span experimental and FE model natural period .....................................................................................................................49 Table 3.8. Pre-detonation comparison of multi-span experimental and FE model natural period .....................................................................................................................54 Table 5.1. Dynamic yield strength for reinforcement (conventional and prestressed)......75 Table 5.2. SDOF prediction model comparison matrix.....................................................81 Table 5.3. Percent difference, Dynamic Series I SDOF prediction vs. measured support rotation ...................................................................................................................83 Table 5.4 Percent difference, Dynamic Series II - Experiment 1 SDOF prediction vs. measured support rotation......................................................................................84 Table 5.5 Percent difference, Dynamic Series II - Experiment 2 SDOF prediction vs. measured support rotation......................................................................................85 Table 5.6 Percent difference, SDOF prediction vs. FE model response............................95 Table 5.7 Percent difference, SDOF prediction vs. FE model response............................96 Table 5.8 Percent difference, SDOF prediction vs. FE model response............................97 viii List of Figures Figure 2.1. Pressure vs. time description for an arbitrary explosion ..................................6 Figure 3.1. Organizational chart of model development ..................................................12 Figure 3.2. University of Missouri loading-tree apparatus setup and reinforced concrete beam validation sample .....................................................................................................13 Figure 3.3. Layout of reinforced concrete beam specimens .............................................14 Figure 3.4. Response of concrete to uniaxial loading in (a) tension (b) compression.....18 Figure 3.5. Yield surfaces in the deviatoric plane, corresponding to different values of K c ...........................................................................................................20 Figure 3.6. Stress-strain relationship of rebar used in analyses........................................22 Figure 3.7. Stress-strain relationship of WWR used in analyses......................................22 Figure 3.8. Reinforced concrete ceam FE model illustration: (a) loading and boundary conditions and (b) concrete, rebar and WWR elements ........................................23 Figure 3.9. Reinforced concrete beam and FE model comparisons .................................25 Figure 3.10. Conventionally reinforced 3-2-3 static sandwich panel specimen...............27 Figure 3.11. Static shear tie test configuration .................................................................29 Figure 3.12. Shear tie MPC validation model configuration ...........................................29 Figure 3.13. Validation of MPC approach........................................................................30 Figure 3.14. Generalized shear tie resistances used in MPC approach ............................31 Figure 3.15. FE model of sandwich panel utilizing MPC for shear tie behavior .............32 Figure 3.16. Stress-strain relationship of rebar used in the analyses.................................33 ix Figure 3.17. Comparison of stress-strain response of various extruded polystyrene products..................................................................................................................34 Figure 3.18. Comparison of similar panel resistances with different foam insulation .....34 Figure 3.19. Test setup for static testing of insulation foam materials..............................35 Figure 3.20. Stress-strain curve of expanded polystyrene insulation foam samples .........36 Figure 3.21. Stress-strain curve of polyisocyanruate insulation foam samples.................36 Figure 3.22. Stress-strain curve of extruded expanded polystyrene insulation foam samples...................................................................................................................37 Figure 3.23. Static test results vs. finite element model comparisons ..............................39 Figure 3.24. Test set up for full-scale dynamic tests with single span reaction structure (left) and multi-span reaction structure (right).......................................................42 Figure 3.25. (a) Average primary detonation reflected pressure curves both experiments and reactions structures. (b) Average impulse curves associated with the average reflected pressure curves........................................................................................42 Figure 3.26. LS-DYNA default curve for concrete DIF....................................................45 Figure 3.27. Experiment 1 ? Primary detonation measured midspan displacement vs. finite element midspan displacement comparison for (a) SS1, (b) SS2, (c) SS3, and (d) SS4.............................................................................................................47 Figure 3.28. Experiment 2 ? Primary detonation measured midspan displacement vs. finite element midspan displacement comparison for (a) SS1, (b) SS2, (c) SS3, and (d) SS4.............................................................................................................47 Figure 3.29. Pre-detonation pressure and impulse for single span reaction structure ? Experiment 1..........................................................................................................48 Figure 3.30. Experiment 1 ? Pre-detonation measured midspan displacement vs. finite element midspan displacement comparison for (a) SS1, (b) SS2, (c) SS3, and (d) SS4.............................................................................................................48 Figure 3.31. Experiment 1 ? Primary detonation measured first floor midspan displacement vs. finite element midspan displacement comparison for (a) MS1, (b) MS2, (c) MS3, and (d) MS4.............................................................................50 x Figure 3.32. Experiment 1 ? Primary detonation measured second floor midspan displacement vs. finite element midspan displacement comparison for (a) MS1, (b) MS2, (c) MS3, and (d) MS4.............................................................................51 Figure 3.33. Experiment 2 ? Primary detonation measured first floor midspan displacement vs. finite element midspan displacement comparison for (a) MS1, (b) MS2, (c) MS3, and (d) MS4.............................................................................51 Figure 3.34. Experiment 2 ? Primary detonation measured second floor midspan displacement vs. finite element midspan displacement comparison for (a) MS2, (b) MS3, and (c) MS4 ............................................................................................52 Figure 3.35. Local failures examples along second floor support .....................................52 Figure 3.36. Pre-detonation pressure and impulse for multi-span reaction structure ? Experiment 1......................................................................................................53 Figure 3.37. Experiment 1 ? Pre-detonation measured first floor midspan displacement vs. finite element midspan displacement comparison for (a) MS1, (b) MS2, (c) MS3, and (d) MS4..................................................................................................53 Figure 3.38. Experiment 1 ? Pre-detonation measured second floor midspan displacement vs. finite element midspan displacement comparison for (a) MS1, (b) MS2, (c) MS3, and (d) MS4..................................................................................................54 Figure 3.39. Second floor support frame allowing interaction between the behaviors of all multi-span panels attached.....................................................................................55 Figure 4.1. Kinetic energy of sandwich panel system components-Experiment 1; a) SS1, b) SS2, c) SS3, d) SS4 ...........................................................................................58 Figure 4.2. SS1 ? Experiment 1: Strain of reinforcement of interior concrete wythe across panel height over time............................................................................................59 Figure 4.3. SS3 ? Experiment 1: Strain of reinforcement of interior concrete wythe across panel height over time............................................................................................60 Figure 4.4. SS4 ? Experiment 1: Strain of reinforcement of interior concrete wythe across panel height over time............................................................................................60 Figure 4.5. Average pressure for Experiment 1 used for finite element models simulating single span test specimens .....................................................................................61 Figure 4.6. Load cells recording reaction force for single span specimens.......................62 xi Figure 4.7. Comparison of measured reaction force and recorded FE model reaction force for Experiment 1 ?SS1...........................................................................................63 Figure 4.8. Comparison of measured reaction force and recorded FE model reaction force for Experiment 1 ?SS2...........................................................................................63 Figure 4.9. Comparison of measured reaction force and recorded FE model reaction force for Experiment 1 ?SS3...........................................................................................64 Figure 4.10. Comparison of measured reaction force and recorded FE model reaction forces for Experiment 1 ?SS4................................................................................64 Figure 5.1 (a) Displacement representation of sandwich panel subjected to blast load (b) Equivalent single-degree-of-freedom system...................................................68 Figure 5.2 Screenshot of SDOF model in Microsoft Excel spreadsheet format................71 Figure 5.3 Comparison of experimental resistance to bilinear resistance curve................73 Figure 5.4 Coefficients of cracked moment of inertia (UFC 3-340-02)............................77 Figure 5.5 Screenshots of SDOF prediction analysis spreadsheet resistance input...........78 Figure 5.6 Dynamic Series I, Detonation 2 measured displacement comparison to SDOF prediction using weighted resistance .....................................................................82 Figure 5.7 Dynamic Series I, Detonation 3 measured displacement comparison to SDOF prediction using weighted resistance .....................................................................83 Figure 5.8 Evaluation of weighted resistance prediction method vs. measured data. Dynamic Series II - Experiment 1 ? (a) SS1 (b) SS2 (c) SS3 (d) SS4 ..................84 Figure 5.9 Evaluation of weighted resistance prediction method vs. measured data, Dynamic Series II - Experiment 2 ? (a) SS1 (b) SS2 (c) SS3 (d) SS4 ..................85 Figure 5.10 Experiment 1 loading: Predicted response comparisons of weighted resistance SDOF and experimental resistance SDOF ? (a) SS1 (b) SS2 (c) SS3 (d) SS4.......................................................................................................86 Figure 5.11 Experiment 2 loading: Predicted response comparisons of weighted resistance SDOF and experimental resistance SDOF ? (a) SS1 (b) SS2 (c) SS3 (d) SS4.......................................................................................................87 Figure 5.12 Experiment 1 loading: resistance and energy comparisons for SS1...............89 Figure 5.13 Experiment 1 loading: resistance and energy comparisons for SS2...............89 xii Figure 5.14 Experiment 1 loading: resistance and energy comparisons for SS3...............90 Figure 5.15 Experiment 1 loading: resistance and energy comparisons for SS4...............90 Figure 5.16 Experiment 2 loading: resistance and energy comparisons for SS1...............91 Figure 5.17 Experiment 2 loading: resistance and energy comparisons for SS2...............91 Figure 5.18 Experiment 2 loading: resistance and energy comparisons for SS3...............92 Figure 5.19 Experiment 2 loading: resistance and energy comparisons for SS4...............92 Figure 5.20 Demonstration of bilinear resistance impact on conservative response prediction ..............................................................................................................93 Figure 5.21 FE model response vs. SDOF prediction using weighted resistance for (a) FE-1 (b) FE-2 (c) FE-3 (d) FE-4 ......................................................................95 Figure 5.22 FE model response vs. SDOF prediction using weighted resistance for (a) FE-5 (b) FE-6 (c) FE-7 (d) FE-8 .....................................................................96 Figure 5.23 FE model response vs. SDOF prediction using weighted resistance for (a) FE-9 (b) FE-10 (c) FE-11 (d) FE-12 ................................................................97 xiii CHAPTER 1 INTRODUCTION 1.1 Overview Threats to structures and the people residing within are increasing. Since the attacks on the World Trade Center and the Pentagon on September 11, 2001, the realization of such threats has promoted research in the field of structures subjected to impulse loads. The study of structures subjected to impulse loads has existed for decades; however, a shift in the type of risks structures face has occurred due to the more localized manner of current threats. Also, most of the criteria for designing structural components subjected to impulse loads were created before many modern concrete components were introduced. The behavior and design of structural components subjected to impulse loads differs from the behavior under static loads. Most loads such as wind and gravity loads are assumed to be static since the time in which they are applied is relatively large enough not to induce significant accelerations of structural components. Dynamic loads such as blasts last only a fraction of a second but may be quite large in magnitude and can induce significant accelerations and large displacements. The design of structural components for impulse loads is also different from design for typical loads in that the failure of the structural component is acceptable 1 depending upon how the component failed. Components are not intended to necessarily be functional after an incident; the primary goal in blast design is the safety of the people residing within the structure. Often in attacks, fragmentation of structural components leads to injuries or fatalities of occupants of the structure. A common type of modern exterior wall construction, the sandwich panel, contains two concrete wythes separated by a layer of foam insulation. The concrete wythes can be either conventionally reinforced or prestressed. Reinforcement allows the concrete to reach its full flexural strength and resist lateral, construction, and handling loads. Since these wall structures also serve the purpose of insulating the building, it is common for ties that connect concrete wythes to each other to be made of non-metallic materials (PCI, 2004). 1.2 Objectives The objective of this project was to develop ways of predicting dynamic response of precast insulated concrete sandwich panels using high-fidelity finite element (FE) modeling. With these models, a detailed study of sandwich panel behavior under blast loads was completed. Also single-degree-of-freedom (SDOF) prediction methodology was examined. Finite element models were used for comparisons to SDOF prediction models. 1.3 Scope and Methodology Due to the high costs associated with full-scale dynamic tests, the use of finite element models is crucial to understanding failure modes, energy dissipation, and damage 2 of sandwich panels subjected to impulse loads. Loading-tree tests conducted at the University of Missouri were used to validate the FE modeling approach and input parameters. Static tests used for validation consisted of (1) simple reinforced concrete beams, (2) conventionally reinforced sandwich panels, and (3) prestressed sandwich panels. Also, shear tests involving a variety of connectors were conducted to assess the shear transfer through ties and its impact on composite action. High-fidelity, dynamic FE models were developed, and full-scale dynamic tests conducted by the Air Force Research Laboratory (AFRL) were used to validate the dynamic analysis approach. Once the dynamic FE models were validated, behavioral studies were conducted that examined concentrated reinforcement strain at hinge locations, energy attenuation, and dynamic reactions. Single-degree-of-freedom (SDOF) models developed with Microsoft Excel to provide predictions for sandwich panels subjected to blast loads. FE models were used to expand the data points used for comparison against SDOF predictions. 1.4 Report Organization This report consists of six chapters. Chapter 1 lists the objectives, scope, methodology, and report organization. Chapter 2 provides a literature review and background of relevant history and analytical information. Chapter 3 discusses the model developments and validation. Chapter 4 consists of behavioral observations. Chapter 5 describes the assessment of single-degree-of-freedom prediction models and comparison to full-scale dynamic tests. Chapter 6 summarizes the report and provides conclusions and recommendations for possible future work. 3 CHAPTER 2 TECHNICAL BACKGROUND 2.1 Overview Heightened risks globally have motivated interest in the effects of structural components subjected to impulse loads. Throughout the Cold War, vast amounts of research were conducted on the effects of blasts on structures, leading to a majority of the current understanding of structures subjected to impulse loads. Design of structures subjected to blast loads is greatly influenced by the research motivated by the threat of large, nuclear airbursts. With the end of the Cold War came awareness of new, more localized threats. Attacks in which explosives in vehicles placed next to structures increased in frequency, the most known such attack being that of the Murrah Federal Building in Oklahoma City in 1995 (NRC, 1995). Overseas, attacks such as that which targeted the Khobar Towers in Riyadh, Saudi Arabia, killed 19 marines and injured hundreds others (Jamieson, 2008). With increased consciousness of more localized threats came increased funding for blast resistance of a diverse spectrum of structural components. A common type of component, the sandwich panel, is comprised of two precast concrete wythes separated by a layer of foam insulation. Cladding is the most common use of the sandwich panel; they also serve the purpose of insulating the building. For this reason, it is common for ties that connect concrete wythes to be made of non-metallic materials to keep the 4 thermal resistance of the panel at a maximum. Reinforcement can be conventional or prestressed. Reinforcement allows the concrete to reach its full flexural strength and resist lateral loads and transportation loads of the panels. The sandwich panel was introduced into the market after most research on concrete structural components was completed and design criteria were in place. It is anticipated that the present research fills this vacuum of understanding. 2.2 Blast Loading An explosion is a violent load scenario that occurs due to the release of large amounts of energy in a very short amount of time. This energy could come in the form of a chemical reaction as in explosive ordnances or from the rupture of high pressure gas cylinders (Tedesco, 1999). Trinitrotoluene (TNT) equivalence is used to compare the effects of different explosive charge materials. The equation used for calculating the TNT equivalence based on weight is as follows: D EXP E D TNT H W H =? EXP W (2-1) where W E is the TNT equivalent weight, W EXP is the weight of the explosive, H D EXP is the heat of detonation of the explosive, and is the heat of detonation of TNT. When an explosion occurs, an increase in the ambient air pressure, called overpressure, presents itself as a shock front that propagates spherically from the source. When the shock front comes in contact with a surface normal to itself, an instantaneous reflected pressure is experienced by the surface that is twice the overpressure plus the dynamic pressure. The dynamic pressure is the component of reflected pressure that takes in account the density of air and the velocity of the air particles (Biggs, 1964). This peak 5 positive pressure can be quite large and decays nonlinearly to a pressure below the ambient air pressure. The time period of positive pressure that the surface experiences is called the positive phase. The negative phase occurs when the pressure experience by the surface is negative (i.e. suction). The negative phase, although much smaller in magnitude than the positive phase, affects the surface for a relatively extended amount of time compared to the positive phase (USACE PDC, 2006). Figure 2.1 illustrates the basic shape, relative magnitudes, and durations for the positive and negative phases of a pressure wave created by an explosion. Fig. 2.1. Pressure vs. time description for an arbitrary explosion Structures at risk are designed to resist the reflected pressure of a blast load. Peak positive pressure and impulse (area under the pressure vs. time curve) are the most important considerations in design of structures for impulse loads. A conservative assumption used in design is to only consider the positive phase, since neglect of the negative phase ?will cause similar or somewhat more structural response?, while taking 6 into account the ?ratio of the blast load duration to the natural period of the structural component? (USACE PDC, 2006). Due to the violent nature of blast loading, a select few variables can be determined in tests considering blast. Under the conditions of dust, debris, and vibration that come with blast testing, it is possible to record deflection histories of certain locations of test specimens, reflected pressure histories, and high-speed video. All of these methods were used in full-scale dynamic tests referenced in this report. 2.3 Precast/Prestressed Sandwich Wall Panels The typical configuration of concrete sandwich wall panels is two wythes (i.e. layers) of reinforced concrete, either conventionally reinforced or prestressed, separated by a layer of insulating foam with some arrangement of connectors that secure the concrete wythes through the foam. Sandwich panels are commonly used for both exterior and interior walls and also can be designed solely for cladding or as load-bearing members (PCI, 1997). Sandwich panels have become popular due to their energy efficiency. The amount of mass provided by the concrete layers along with the layer of foam provide the designer with a wide variety of thermally-efficient options for walls. In the past, connectors used as shear ties have primarily consisted of steel tie or solid concrete sections. However, these create thermal bridges that can lower the thermal efficiency of the panel and cause cool locations on the interior concrete wythe, leading to condensation. The desire for more thermally efficient structures has in turn produced a variety of thermally efficient shear connectors. The exterior layer of concrete can receive architectural finishes that bring an 7 aesthetic appeal to sandwich panels. Only panels used solely for cladding purposes were studied in this effort. All full-scale dynamic tests specimens used energy-efficient shear connectors made of either carbon fiber or fiberglass materials. Sandwich panels are primarily designed to withstand handling, transportation, and construction loads. These conditions most often provide the largest stresses within the service life of the sandwich panel. The thermal efficiency desired can control the thickness of the concrete and insulation wythes; for instance, if the structure is used for cold storage, a required R-value (thermal efficiency index) will be needed (PCI, 1997). Once concrete and foam thickness have been chosen, the panel is checked against handling/erection loads. If the panel design withstands handling/construction stresses, the panel is then checked against an allowable deflection due to lateral loads (i.e. wind or seismic). Depending upon the amount of shear transfer desired, the sandwich panel can be designed as either a non-composite or composite panel. When designing non-composite panels, the concrete wythes are considered to act independently of each other. Composite panels are designed such that the concrete wythes act dependently or fully composite; this is accomplished by providing full shear transfer between the wythes, most commonly with the use of solid concrete sections or shear connectors produced with the intention of allowing the two concrete wythes to resist load together. ?Because present knowledge of the behavior of sandwich panels is primarily based on observed phenomena and limited testing, some difference of opinion exists among designers concerning such matters as degree of composite action and the resulting panel performance, the effectiveness of shear transfer connectors and the effect of insulation 8 type and surface roughness on the degree of composite action? (PCI, 2007). Pessiki and Mlynarczyk (2003) investigated the flexural behavior of sandwich panels and the contribution to composite action of various shear transfer mechanisms. Shear mechanisms included regions of solid concrete, steel M-ties that passed through the insulation, and bond between concrete and insulation wythes. Four sandwich panel specimens were created with one panel having all three shear transfer mechanisms and the other three panels each having only one of the shear transfer mechanisms. Research showed that solid concrete sections provided the most strength and stiffness with steel M- tie connectors only moderately affecting the composite behavior of the panels. The affect of bond between concrete and foam wythes was virtually negligible. Through their research, Pessiki and Mlynarczyk found that panels with the most robust shear transfer mechanisms that behaved either fully composite or nearly fully composite did not behave consistently in regards to flexural cracking. Flexural tensile strengths of nearly fifty percent below the theoretical tensile strength of concrete in flexure arose, conceivably from a lack of localized composite action, causing larger amounts of stress at midspan. 2.4 Design of Precast/Prestressed Concrete Structures for Blast The key blast design consideration of a structure is the safety of occupants of the structure. Much like the case of the attack on the Khobar Towers, Saudi Arabia in 1996, most injuries and fatalities occur due to building debris accelerated by the blast. Precast/prestressed components, along with their connections to the structure, should be designed to withstand the blast to prevent falling or flying debris, even if the structural component itself is damaged beyond repair or lost entirely (Alaoui and Oswald, 2007). 9 A common design technique of precast/prestressed concrete structures subjected to blasts is based on a single-degree-of-freedom (SDOF) methodology. ?Structural components subject to blast loads can be modeled as an equivalent SDOF mass-spring system with a nonlinear spring? (USACE PDC, 2006). A manual by the Departments of the U.S. Army, Navy, and Air Force (1990) titled ?Structures to Resist the Effects of Accidental Explosions? was written to support application of this method to different types of structures. The report is most commonly referenced by its U.S. Army report number, TM 5-1300 and has been published under the Unified Facilities Criteria system as UFC 3-340-02 (Department of Defense, 2008). 10 CHAPTER 3 MODEL DEVELOPMENT AND VALIDATION 3.1 Overview The primary challenges associated with FE modeling of foam-insulated concrete sandwich panels include: accurately describing and incorporating the fracture and damage behavior of reinforced concrete, integrating foam constitutive models, accurately describing the transfer of shear between concrete wythes, incorporating strain rate effects on material behavior, and simulating initial conditions associated with the prestressed reinforcement strands. Validation of input parameters was accomplished in four parts: (1) simple reinforced concrete beams subjected to uniform loading, (2) static testing of shear connectors, (3) static testing of sandwich panels (prestressed and conventionally reinforced) subjected to uniform loading, and (4) full-scale dynamic tests of sandwich panels (prestressed and conventionally reinforced). An organizational chart of FE model validation can be seen in Figure 3.1. Component and material level test results were used to define appropriate constitutive model input. Direct shear tests were used to evaluate the shear resistance input required to simulate the various ties used in the full-scale sandwich panels specimens. 11 Model Development I. Static Modeling II. Dynamic Modeling (1) (2) Shear Connector Tests (3) Static Sandwich Panel Tests (4) Full-scale Dynamic Tests Reinforced Concrete Beam Tests Pre-detonation Pressure Primary Pressure Single Span Panels (M-Series) Multi-span Panels (F-Series) Single Span Panels (M-Series) Multi-span Panels (F-Series) Fig. 3.1. Organizational chart of model development 3.2. Reinforced Concrete Beam Validation Two conventionally reinforced concrete beam designs were tested under a near- uniform distributed load using the University of Missouri loading-tree apparatus shown in Figure 3.2. All samples were 18 inches wide, simply supported, with a 120 inch clear span. Two samples of each design were constructed and total load and midspan vertical displacement were recorded for each sample. The test matrix and reinforcement description are provided in Table 3.1 and Figure 3.3. Concrete cylinders were cast and compressive strengths obtained via ASTM C39/C39M were used in the development of the concrete damage model. Reinforcements (steel and welded wire) were tested for tensile capacity using standards provided by ASTM E8. It should be noted that the 12 purpose of these reinforced beam tests was not finite element validation. These test results were selected since they provided flexural resistance data obtained using the same loading-tree apparatus later used in static tests of sandwich panel specimens. Fig. 3.2. University of Missouri loading-tree apparatus setup and reinforced concrete beam validation sample 3.2.1 Concrete Model and Parameters A numerical strategy for solving any boundary value problem with location of fracture should consider complex constitutive modeling. It is necessary to identify a large number of parameters if a structural, heterogeneous material such as concrete is taken into account. Concrete is comprised of a wide range of materials, whose properties are quantitatively and qualitatively different. The ABAQUS Concrete Damage Plasticity (CDP) constitutive model used in this study is based on the assumption of scalar 13 (isotropic) damage and is designed for applications where the concrete is subjected to arbitrary loading conditions, including cyclic loading (ABAQUS, 2008). The model takes into consideration the degradation of the elastic stiffness induced by plastic straining both in tension and compression. The model is a continuum plasticity-based damage model that assumes that the primary failure mechanisms are tensile cracking and compressive crushing of the concrete material. height 18 inches de p th Figure 3.3. Layout of reinforced concrete beam specimens Table 3.1. Description of reinforced concrete beam samples Name Height (inch) Reinforcement/depth RC Beam Design 1 11.5 Welded-Wire W4 x W4 /10? # 8/ 9.5? RC Beam Design 2 6 Welded-Wire W4 x W4 / 3.25? # 4/ 3? 3.2.2 Mechanical Behavior and Concrete Plasticity The evolution of the yield (or failure) surface is controlled by two hardening variables, tensile and compressive equivalent plastic strains ( pl t ?% and pl c ?% ), linked to failure mechanisms under tension and compression loading, respectively. The model assumes that the uniaxial tensile and compressive response of concrete 14 is characterized by damaged plasticity, as shown in Figure 3.4. Under uniaxial tension the stress-strain response follows a linear elastic relationship until the value of the failure stress, 0t ? , is reached. The failure stress corresponds to the onset of micro-cracking in the concrete material. Beyond the failure stress, the formation of micro-cracks is represented macroscopically with a softening stress-strain response, which induces strain localization in the concrete structure. Under uniaxial compression, the response is linear until the value of initial yield, 0c ? , is reached. In the plastic regime, the response is typically characterized by stress hardening followed by strain softening beyond the ultimate stress, cu ? . This representation, although somewhat simplified, captures the main features of the response of concrete. It is assumed that the uniaxial stress-strain curves can be converted into stress versus plastic-strain curves. This conversion is performed automatically by ABAQUS from the user-provided stress versus ?inelastic? strain data. As shown in Figure 3.4, when the concrete specimen is unloaded from any point on the strain softening branch of the stress-strain curves, the unloading response is weakened: the elastic stiffness of the material appears to be damaged (or degraded). The degradation of the elastic stiffness is characterized by two damage variables, and , which are assumed to be functions of the plastic strains, temperature, and field variables: t d c d ( ) ,, ;0 1, pl ttt i t dd f d??= ??% (3-1) ( ) ,, ;0 1 pl ccc i c dd f d??= ??% (3-2) The damage variables can take values from zero, representing the undamaged material, to one, which represents total loss of strength. If is the initial (i.e. undamaged) elastic 0 E 15 stiffness of the material, the stress-strain relations under uniaxial tension and compression loading are, respectively: 0 (1 ) ( ), pl tttt dE??=? ?? (3-3) 0 (1 ) ( ) pl ccc dE c ? ??=? ? (3-4) The ?effective? tensile and compressive cohesion stresses are defined as follows: 0 ( (1 ) plt t t E d ), t ? ??==? ? ? (3-5) 0 ( (1 ) plc c c E d ) c ? ? ??==? ? (3-6) The effective cohesion stresses determine the size of the yield (or failure) surface. Concrete plasticity can be simulated by defining flow potential, yield surface, and viscosity parameters as follows: The effective stress is defined as 0 D:( ) el pl ? ??=? (3-7) where is the initial (undamaged) elasticity matrix 0 D el The plastic flow potential function and the yield surface make use of two stress invariants of the effective stress tensor, namely the hydrostatic pressure stress, 1 trace( ), 3 p ?=? (3-8) and the von Mises equivalent effective stress, 3 (S:S), 2 q = (3-9) where S is the effective stress deviator, defined as S= + Ip? (3-10) 16 The concrete damaged plasticity model assumes non-associated potential plastic flow. The flow potential used for this model is the Drucker-Prager hyperbolic function (Drucker et al., 1952): G 22 0 (tan) tan t Gqp???=+?? (3-11) where ( , ) i f? ? is the dilation angle measured in the p?q plane at high confining pressure: 0 0, 0 (, ) pl pl tt tit f ?? ?? ? = = = & %% (3-12) is the uniaxial tensile stress at failure, taken from the user-specified tension stiffening data; ( , ) i f? ? is a parameter, referred to as the eccentricity, that defines the rate at which the function approaches the asymptote (the flow potential tends to a straight line as the eccentricity tends to zero). This flow potential, which is continuous and smooth, ensures that the flow direction is always uniquely defined. The function approaches the linear Drucker-Prager flow potential asymptotically at high confining pressure stress and intersects the hydrostatic pressure axis at 90?. The default flow potential eccentricity is 0.1? = , which implies that the material has almost the same dilation angle over a wide range of confining pressure stress values. Increasing the value of ? provides more curvature to the flow potential, implying that the dilation angle increases more rapidly as the confining pressure decreases. Values of ? that are significantly less than the default value may lead to convergence problems if the material is subjected to low confining pressures because of the very tight curvature of the flow potential locally where it intersects the p-axis. 17 Fig. 3.4. Response of concrete to uniaxial loading in (a) tension and (b) compression (ABAQUS, 2008) 3.2.3 Yield Function The model made use of the yield function of Lubliner et al. (1989), with the modifications proposed by Lee and Fenves (1998) to account for different evolution of strength under tension and compression. The evolution of the yield surface is controlled 18 by the hardening variables, pl t ?% and pl c ?% . In terms of effective stresses, the yield function takes the form ()()() max max 1 ?? 30 1 pl pl t Fqp???? ?? ?? ? =?+ ??? ? % c =% (3-13) with ( ) () 00 00 /1 ;0 0.5, 2/ 1 bc bc ?? ? ?? ? =? ? ?? (3-14) ( ) () (1 ) (1 ), pl cc pl tt ?? ? ? ?? =?? % % ?+ (3-15) 3(1 ) 21 c c K K ? ? = ? (3-16) Where max ? ? is the maximum principal effective stress; 0 / bc0 ? ? is the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress (the default value is 1.16); is the ratio of the second stress invariant on the tensile meridian, q(TM), to that on the compressive meridian, q(CM), at initial yield for any given value of the pressure invariant p such that the maximum principal stress is negative, c K max ? 0? < (see Figure 3.4); it must satisfy the condition 0.5 (the default value is 2/3); 1.0 c K20 ft). This would include both static and full- scale dynamic experiments. Also, a more in-depth study of material properties could be used to increase the effectiveness of finite element models. The effectiveness of SDOF predictions using bilinear weighted resistance could also be increased with continued study of sandwich panels and increased effectiveness of finite element models. 99 REFERENCES ABAQUS Standard User?s Manual Version 6.7. (2008). Hibbit, Karlsson & Sorensen, Inc., Pawtucket, R.I. Alaoui, S.and Oswald, C. (2007). ?Blast-resistant Design Considerations for Precast, Prestressed Concrete Structures,? PCI Journal, vol. 52, pp. 53-65 Biggs, J. M. (1964). ?Introduction to Structural Dynamics,? McGraw-Hill, New York. Chopra, A.K., (2001). ?Dynamics of Structures,? 3 rd Edition, Prentice Hall, Upper Saddle River, New Jersey Department of Defense (2008). ?Structures to Resist the Effects of Accidental Explosions,? UFC 3-340-02, Whole Building Design Guide, http://dod.wbdg.org/ (accessed Feb. 2010). Drucker, D. C. and Prager, W, (1952). Solid mechanics and plastic analysis for limit design. Quarterly of Applied Mathematics, vol. 10, no. 2, pp. 157?165. Franz, U., Schuster, P., Stahlschmidt, S. (2004). Influence of pre-stressed parts in dummy modeling-simple considerations. LS-DYNA Anwenderforum, Bamberg. Jankowiak, T., and Lodygowski, T (2005). ?Identification of Parameters of Concrete Damage Plasticity Constitutive Model,? Foundations of Civil and Environmental Engineering, No.6 100 Jamieson, P. (1998). Khobar Towers : Tragedy and Response, Air Force History and Museums Program. Washington, D.C. Jenkins, R.S. (2008). Compressive Properties of Extruded Expanded Polystyrene Foam Building Materials. M.S.C.E. report, University of Alabama at Birmingham. Lee, J., and G. L. Fenves (1998). ?Plastic-Damage Model for Cyclic Loading of Concrete Structures,? Journal of Engineering Mechanics, vol. 124, no.8, pp. 892? 900, 1998. Livermore Software Technology Corporation (LSTC) (2009). LS-DYNA Keyword User?s Manual. Lubliner, J., J. Oliver, S. Oller, and E. O?ate, (1989). ?A Plastic-Damage Model for Concrete,? International Journal of Solids and Structures, vol. 25, pp. 299?329. Malvar, L. Javier and John E. Crawford (1998). ?Dynamic Increase Factors for Concrete,? Twenty-Eighth DDESB Seminar, Orlando, FL August 1998. Naito, C., Hoemann, J., Bewick, B., and Hammons, M., (2009a). ?Evaluation of Shear Tie Connectors for Use in Insulated Concrete Sandwich Panels,? Air Force Research Laboratory Report, AFRL-RX-TY-TR-2009-4600, December 2009, 31 pages. Naito, C., Dinan, Robert J., Fisher, J., and Hoemann, J., (2009b). ?Precast/Prestressed Concrete Experiments - Series 1 (Volume 1)? Air Force Research Laboratory Report, AFRL-RX-TYTR-2008-4616, August 2009, 38 pages. Naito, C., Hoemann, J., Shull, J., Saucier, A., Salim, H., Bewick, B., and Hammons, M. (2010a). ?Static Performance of Non-Load Bearing Insulated Concrete Sandwich 101 Panels Subject To External Demands,? Air Force Research Laboratory Report, AFRL-RX-TY-TR-2009-XXXX, July 2010, 164 pages. Naito, C., Hoemann, J., Shull, J., Beacraft, M., Bewick, B., and Hammons, M. (2010b). ?Dynamic Performance of Non-Load Bearing Insulated Concrete Sandwich Panels Subject To External Demands,? Air Force Research Laboratory Report, AFRL-RX-TY-TR-2009-XXXX, September 2010, 123 pages. National Research Council (1995). ?Protecting Buildings from Bomb Damage: Transfer of Blast-effects Mitigation Technologies from Military to Civilian Applications Washington,? Washington D.C. : National Academy Press. Nawy, Edward G. (1996). ?Prestressed Concrete: A Fundamental Appraoch,? Upper Saddle River, New Jersey: Prentice-Hall Inc. PCI Committee on Precast Sandwich Wall Panels (1997). ?State-of-the-Art of Precast/Prestressed Sandwich Wall Panels,? Journal of the Precast/Prestressed Concrete Institute, 42 (2). PCI Industry Handbook Committee (2004). PCI Design Handbook Precast and Prestressed Concrete, 6th Edition. PCI MNL 120-04, Chicago, IL, USA. Pessiki, S. and Mlynarczyk, A. (2003). ?Experimental Evaluation of the Composite Behavior of Precast Concrete Sandwich Wall Panels,? PCI Journal, Precast/Prestressed Concrete Institute, Vol. 48, No. 2, March-April 2003, pp. 54-71. Stouffer, D. and Dame, L. (1996). ?Inelastic Deformation of Metals: Models, Mechanical Properties, and Metallurgy,? John Wiley and Sons, Inc. Tedesco, J. W., McDougal, W. G., and Ross, C. A. (1999). ?Structural Dynamics: 102 Theory and Applications,? Addison Wesley Longman, California. U.S. Army Corps of Engineers Protective Design Center (2006). ?User?s Guide for the Single-Degree-of-Freedom Blast Effects Design Spreadsheets (SBEDS).? PDCTR 06-02. 103