AN ENERGY FLOW APPROACH TO PROGRESS IVE COLLAPSE By JOHN ROBERT WILKES A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PH ILOSOPHY UNIVERSITY OF FLORIDA 2016
2016 John R. Wilkes
4 ACKNOWLEDGMENTS The author is indebted to his adviser, the Theodore R. Crom Professor of Civil Engineering, Ted Krauthammer the dir ector of the research presented herein, as well as all preceding CIPPS studies on which this work is based.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 8 LIST OF FI GURES ................................ ................................ ................................ ......................... 9 ABSTRACT ................................ ................................ ................................ ................................ ... 15 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 17 1.1 Problem Statem ent ................................ ................................ ................................ ............ 17 1.2 Research Significance ................................ ................................ ................................ ....... 18 1.3 Objectives ................................ ................................ ................................ ......................... 18 1.4 Scope ................................ ................................ ................................ ................................ 19 2 BACKGROUND ................................ ................................ ................................ .................... 20 2.1 A Review of PC: Seminal Events, Publications, and Regulatory Provisions ................... 22 2.2 The Alternate Path Method in Regulatory Design Provisions ................................ .......... 34 2.3 Structural Damage Incurred from Known Explosive Terrorist Threats ........................... 36 2.4 DSAS: Simulating Explosions ................................ ................................ .......................... 39 2.5 Ten Story Moment Resisting Steel Frame Building ................................ ........................ 39 2.5.1 Historical Reference and Relevant Antecedent Research ................................ ...... 39 2.5.2 Structural System ................................ ................................ ................................ .... 40 2.5.3 Reductionist Modelling of Connections by Yim and Krauthammer ...................... 41 2.6 Review of Energy and Traditional Approaches to Structural Behavior ........................... 43 2.6.1 Energy and Power Flow Analyses for Mechanical Engineering Applications ...... 43 2.6.2 Traditional Force Based Approaches to Progressive Collapse .............................. 43 2.7 Literature Review of Energy Approaches to Structural Phenomena ................................ 44 2.7.1 Energy Approaches Prior to CIPPS Research ................................ ........................ 44 2.7 .2 Energy Based Approach by Szyniszewski and Krauthammer ............................... 46 2.8 Summary ................................ ................................ ................................ .......................... 50 3 ENERGY FLOW APPROACH (EFA) TO PROGRESSIVE COLLAPSE (PC) .................. 58 3.1 Mid Rise Office Buildings ................................ ................................ ............................... 59 3.1.1 Development of Finite Element Model of Ten Story Moment Resisting Steel Frame ................................ ................................ ................................ ........................... 59 126.96.36.199 Boundary conditions ................................ ................................ .................... 60 188.8.131.52 Columns, girders, beams, and slabs ................................ ............................. 60 184.108.40.206 Connections ................................ ................................ ................................ .. 61 220.127.116.11 Non structural ................................ ................................ ............................... 64
6 18.104.22.168 Gravitational loads ................................ ................................ ....................... 65 22.214.171.124 Air blast loads: damage yields per DSAS ................................ .................... 66 3.1.2 Modified Version of the SAC Commissioned Mid Rise Building ........................ 69 3.2 Energy Principles ................................ ................................ ................................ .............. 70 3.2.1 Energy Flow Analyses using LS DYNA ................................ .............................. 70 3.2.2 Incorporating the Rate of Energ y Flow ................................ ................................ .. 71 3.3 Fluid Energy Flow Analogy of the EFA ................................ ................................ .......... 72 3.4 Energy Flow Approach (EFA) ................................ ................................ .......................... 76 3.4.1 Determination of Energy Flow (Magnitude and Rate) Failure Thresholds ............ 76 3.4.2 Rational for Selection of Mid Rise Building Structure ................................ .......... 78 3.4.3 Analysis of Building Response to Incremental Damage ................................ ........ 79 3.4.4 Incorporation of Connections as Structural Elements ................................ ............ 80 3.4.5 Energy Flow Based Response States for Evaluation of Alternate Path Method .... 80 4 RESULTS ................................ ................................ ................................ ............................... 92 4 .1 Non Collapse vs Collapse of SAC Commissioned Building Model ................................ 93 4.1.1 Global View: System Wide Energy Flow ................................ ............................. 96 4.1.2 Local Vi ew: Energy Flows of a Critical Column ................................ .................. 96 4.2 Two Collapse Scenarios with the Modified SAC Commissioned Building Model ......... 97 4.2.1 Global View: System Wide Energy Flow ................................ ............................. 97 4.2.2 Local View: Energy Flows of a Critical Column ................................ .................. 98 4.2.3 Regional View: Furcating Energy Flows ................................ .............................. 98 4.3 The SAC Commissioned vs The Modified SAC Commissioned Building Model ........ 100 4.4 Efficacy of Notional Single Col umn Removal ................................ ............................... 100 4.5 Extent of Redistribution ................................ ................................ ................................ .. 102 4.6 Recommendations ................................ ................................ ................................ ........... 102 5 CONCLUSIONS ................................ ................................ ................................ .................. 117 APPENDIX A DEMONSTRATIONS OF THE EFA WITH SMALL STRUCTURAL FRAMES ............ 118 A.1 Introduction ................................ ................................ ................................ .................... 118 A.2 Single Bay Single Story Steel Frame with Simplified Fixed Connections ................... 118 A.2.1 Processing Results from Collapse Arresting Simulation ................................ .... 119 A.2.2 Processing Results from Collapse Triggering Simulation ................................ .. 120 A.3 Twin Bay Two Story Portion of Mid Rise with Advanced Co nnections ..................... 122 A.3.1 Processing Results from Collapse Arresting Simulation ................................ .... 123 A.3.2 Processing Results from Collapse Triggering Simulation ................................ ... 124 B MID RISE BUILDING DETAILS ................................ ................................ ....................... 137 B.1 Introduction ................................ ................................ ................................ .................... 137 B.2 FEMA Specifications for the Mid Rise Building in Boston ................................ .......... 137 LIST OF REFERENCES ................................ ................................ ................................ ............. 143
7 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 152
8 LIST OF TABLES Table page 2 1 Efficacy of US based codes in mitigating the three most influential PC events (Source: reproduced from Nair, 2006 Figure 4). ................................ ............................ 52 4 1 Collapse result comparison between mid rise building models. ................................ ..... 104
9 LIST OF FIGURES Figure page 2 1 Ronan Point apartment tower in London in 1968 after collapse ................................ ....... 53 2 2 Alfred P. Murrah building in Oklahoma City after the blast induced collapse in 1995 .... 53 2 3 Damage to the Kansallis House in Bishopsgate area after 1993 bombing in London ....... 54 2 4 Detonation parameters and yield weights per tran sport vehicle ................................ ........ 54 2 5 ................................ ................................ ...................... 55 2 6 Pressure time history (for 0.504 m/kg 1/3 ) output from DSAS. ................................ .......... 55 2 7 Plan layout of beams with WUF ................ 56 2 8 Elevation of steel columns cross section s with splice locations. ................................ ....... 56 2 9 Qualitative Frequency Amplitude Distribution for Different Hazards .............................. 57 3 1 Energy based load impulse failure threshold. ................................ ................................ .... 81 3 2 Flowchart of Analytical Process. ................................ ................................ ....................... 82 3 3 LS DYNA Model of SAC commissioned Mid Rise in Bost on. ................................ ....... 83 3 4 Boundary conditions: fully fixed columns bases ................................ ............................... 83 3 5 Simplified model of single bay frame using resultant elemen ts ................................ ........ 84 3 6 Connections modeled with springs referencing nonlinear strength curves ....................... 84 3 7 Isometric view of LS D YNA model ................................ ................................ .................. 85 3 8 Sequence of failed members as determined with DSAS analyses. ................................ .... 86 3 9 Elevation of mid rise off ice building ................................ ................................ ................. 86 3 10 Elevation of ten story moment resisting steel frames modeled ................................ ......... 87 3 11 Typical energy based P I diagrams for multi failure modes ................................ ............. 87 3 12 Illustration of energy tank analogy ................................ ................................ .................... 88 3 13 Illustration of flui d energy conceptual analogy ................................ ................................ 89 3 14 Flexural failure corresponding to magnitude of energy flow threshold only .................... 89
10 3 15 Alternative illustration of fluid energy conceptual analogy for a single structural element in terms of structural behavioral modes. ................................ .............................. 90 3 16 Finite element model comprised ent ................................ .. 90 3 17 Loading rate buckling failure of eighteen foot columns supporting second story of the SAC commissioned mid rise building model. ................................ ............................. 91 3 18 Behavioral Response Comparison between nonlinear transient dynamic finite element simulations (NTFES) and Alternate Path method ................................ ................ 91 4 1 Non collapse vs collapse ................................ ................................ ................................ .. 105 4 2 Comparative strains throughout building ................................ ................................ ......... 106 4 3 Second fl oor interior column closest to location of charge ................................ ............. 106 4 4 Energy time history for referenced column corresponding to a blast yielding the destruction of two columns and four beams ................................ ................................ .... 107 4 5 Energy flow vs energy flow rate for multiple non collapse and collapse simulations. ... 107 4 6 Isometric vie w of mid rise building with soft story modified ................................ ......... 108 4 7 Comparative of different blast induced damages with modified building model ........... 109 4 8 Total system energy flow vs energy flow rate with the modified SAC commissioned mid rise building. ................................ ................................ ................................ ............. 110 4 9 Second floor interior column closest to locati on of charge ................................ ............. 110 4 10 Comparative energy time histories for second floor interior column closest to location of charge ................................ ................................ ................................ ............. 111 4 11 Energy histories for referenced column from all simulations with modified version of SAC commissioned mid rise building model ................................ ................................ .. 111 4 12 East west connections at base of second floor interior column closest to location of charge. ................................ ................................ ................................ .............................. 112 4 13 Comparative energy time histories for east west connections at base of second floor interior column closest to location of charge ................................ ................................ ... 112 4 14 North south connections at base of second floor interior column closest to location of charge. ................................ ................................ ................................ .............................. 113 4 15 Comparative energy time histories for north south connections at base of second floor interior column closest to location of charge ................................ .......................... 113
11 4 16 East west girders at base of second floor interior column closest to location of charge. ................................ ................................ ................................ .............................. 114 4 17 Comparative energy time histories for east west girders at base of second floor interior column closest t o location of charge ................................ ................................ ... 114 4 18 North south girders at base of second floor interior column closest to location of charge. ................................ ................................ ................................ .............................. 115 4 19 Comparative energy time histories for north south girders at base of second floor interior column closest to location of charge ................................ ................................ ... 115 4 20 Energy time histories for all columns on the second floor of the modified SAC commissioned mid rise building model ................................ ................................ ........... 116 4 21 Effective (Von Mises) beam stresses from a two columns and four beams removal ...... 116 A 1 Test Frame without damage ................................ ................................ ............................. 127 A 2 Test frame with damage applied failure of a single column ................................ ......... 128 A 3 Energy time histories of slab ................................ ................................ ........................... 128 A 4 Energy time histories of failed beams ................................ ................................ ............. 129 A 5 Internal energy time histories of slab and failed beams ................................ .................. 129 A 6 Kinetic energy time histories of slab and failed beams ................................ ................... 130 A 7 Example failure indicating criteria time histories ................................ ............................ 130 A 8 Stress and strains contours at the end of collapse ................................ ............................ 131 A 9 Portion of mid rise building analyzed for demonstrating efficacy ................................ .. 131 A 10 Reduced frame with moderate damage (one colu mn) collapse prevented ................... 132 A 11 Reduced frame with severe damage (three columns) collapse progresses ................... 133 A 1 2 Energy time histories of slab ................................ ................................ ........................... 133 A 13 Energy time histories of failed beams ................................ ................................ ............. 134 A 14 Internal energy time histories of slab and failed beams ................................ .................. 134 A 15 Kinetic energy time histories of slab and failed beams ................................ ................... 135 A 16 E xample failure indicating criteria time histories ................................ ............................ 135
1 2 A 17 Stress and strain contours at the end of collapse ................................ .............................. 136 B 1 Beam, sections, column sections, and doubler plates for three story building in Boston ................................ ................................ ................................ .............................. 141 B 2 Cover plate details for ten story Boston building post Northridge design ...................... 14 2 B 3 Floor plan and elevation for ten story Boston building ................................ ................... 142 B 4 Layout of moment resisting connections in ten s tory building ................................ ....... 142
13 LIST OF ABBREVIATION S ACI American Concrete Institute AISC American Institute of Steel Construction ANSI American National Standards Institute ASCE American Society of Engineers BMSP Blast Mitigation for Structures Program BO Boston BOCA Building Officials and Code Administrators International, Inc. BPAT Building Performance CIPPS Center for Infrastructure Protection and Physical Security D Dead Load DHS Department of Homeland Security DOD Dep artment of Defense DSAS Dynamic Structural Analysis Suite DTRA Defense Threat Reduction Agency E Energy Flow Rate of Energy Flow EFA Energy Flow Approach FEMA Federal Emergency Management Association GSA General Services Administration ICC Intern ational Code Council JV Joint Venture L Live Load LS Linear Static LVBIED Large Vehicle Borne Improvised Explosive Device
14 MM ALE Multi Material Arbitrary Lagrangian Eulerian NBCC National Building Code of Canada NBS National Bureau of Standards ND Nonlinear Dynamic NS Nonlinear Static OSHA Occupational Safety and Health Administration PBS Public Building Service PC Progressive Collapse PCA Portland Cement Association PCI Prestressed Concrete Association SAC Structural Engineers Association of California (SEAOC), Applied Technology Council (APC), and California Universities for Research in Earthquake Engineering (CUREe) SEI Structural Engineering Institute TNT Trinitrotoluene UBC Unified Building Code UFC United Facilities Criteria WTC Wor ld Trade Center WUF B Welded Unreinforced Flange with a Bolted web
15 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A N ENERGY FLOW APPROACH TO PROGRESSIVE COLLAPSE By John Robert Wilkes August 2016 Chair: Theodor Krauthammer Major: Civil Engineering To advance understanding and mitigation of progressive collapse (PC) a novel approach is offered an amalgamated derivati on of energy, and three antecedent studies performed by researchers at Center for Infrastructure Protection and Physical Security. The first of the antecedent studies revealed an energy c ollapse relatio nshi p by demonstrating failure did not progress when the sum of energies from failed member(s) and the stored potential energy was fully absorbed/converted into the internal, or strain, energy in adjacent structural members (Szyniszewski and Krauthammer 2 0 12 ). Potential, or gravitational, energy is released through displacement, or collapse. Conversely, collapse progresses if strain energy is unable to absorb fully the released potential and excess kinetic energy. The second study quantified the contrib ution of connections to PC (Yim and Krauthammer, 2009). The third examined energy flow yielding an energy based load impulse threshold for structural elements (Tsa i and Krauthammer, 2015) further substantiating the conclusions from the first study an ener gy approach is superior to current force based methods for determining damage A methodology is presented for an energy flow based PC assessment of multi story moment resisting frame buildings an extension of the energy approach by Szyniszewski and
16 Krautha mmer (2012), an expansion of modeling methods of steel connection s by Yim and Krauthammer (2010), and inclusion of energy flow rate characterization by Tsai and Krauthammer ( 2015). Th is research explains the contribution s of energy flow and the rate energy flow to the susceptibility of collapse for mid rise steel framed buildings. E nergy time histories of structural members we re analyzed to determine energy flow throughout the structural system. All structural elements including all connections were repre sented numerically t o determine the Assessing PC susceptibility with the incorporation of the rate of energy flow for a structure that accounts for the effects of connection stren gth constitute s a novel approach. Advanced analytical methods, namely nonlinear transient dynamic finite element simulations were used to reveal the energy flow energy flow rate failure relationship. In addition, the efficacy of the Alternate Path me thod and the extent of redistribution required to accommodate blast induced damage was examined
17 C HAPTER 1 INTRODUCTION 1 1 Problem Statement Progr essive collapse is a phenomenon whereby localized failure(s) propagates to collapse of an entire multi story structure, or a significant portion thereof. PC is a life safety issue, and although it can be initiated from a variety of loads, explosive effect s are of significant concern and thus considered exclusively herein. The following statements by two demolition experts is important to provide sufficient energy absorption and load transfer mechanisms into [ our ] building structures so [ that ] they never gain adequate momentum to result in catastrophic failure. Ultimately, we envision [ that ] energy equilibrium calculation methods will play an important role in the design of structures to resist progressive collapse and we suggest [ that ] future research be focused in the area of energy equilibrium design methods Engineers practicing in the field of protective design need an accurate, efficient, and reliable method to assess PC susceptibility. Design manual provisions addressing PC incorporate an approach known as the Alternate Path method, which includes multiple notional single column removals under prescribed factored load combinations. Unfortunately, this method is ineff icient, requiring an inordinate number of analyses due to a multitude of notional column removals. The Alternate Path method assures minimal redundancy of the vertical loading carrying system only, and given a lack of correlation with damage resulting fro m realistic air blasts, the efficacy of this approach for designing a PC resistant structure is questionable. Hence, there are no design guidelines offering an efficient and reliable means to perform PC assessments.
18 1 2 Research Significance It is widely known that fundamental energy principles govern the behavior of physical systems. Preliminary attempts were made to explore possible energy based methods for PC assessment, and a recent st udy showed that a threshold energy level could be associated with failures of specific structural elements. Nevertheless, characterizing the correlation between energy flow (magnitude and rate) and PC arguably constitutes a seminal contribution to the und erstanding of structural behavior under PC conditions. The Energy Flow Approach (EFA) presented here provides fundamental insight into the PC phenomenon, which the authors hope will lead to the development of an accurate, expedient, reliable, and effectiv e method for By using the EFA presented here, engineers can identify the most economical means for improving structural robustness, prioritize protective measures with utmost prudence and quantify the maximum sustainable threat, or conversely, the minimum threat capable of initiating PC. The EFA presented is an accurate and rational energy flow based analytical procedure for PC of significant value to the structural engineering community, and may directly cont ribute to the current efforts in developing a performance based disproportionate collapse design approach by the Structural Engineering Institute (SEI) of American Society of Civil Engineers (ASCE). 1 3 Objectives demonstrates an EFA can represent the behavior of a typical mid rise steel building in response to localized member failure(s), with repeatable ac curacy. By analyzing energy time histories from nonlinear transient dynamic finite element simulations, the results from this study correlate energy flow with member failure, and with subsequent effort, can evolve into an efficient
19 pragmatic approach for practicing engineers capable of accurately predicting the progression of collapsing members, i.e. PC. 1 4 Scope The research presented here includes studying mechanical energy flow through structural steel frames to demonstrate the viability of an EFA for characterizing PC, by identifying how and where PC is initiated, and the manner and paths in which failure propagates throughout the structure. A ten story moment resisting steel frame (Ap pendix B ), considered representative of typical mid rise office buildings, was analyzed using the nonlinear transient dynamic finite element simulations software code LS DYNA (Hallquist, 2014). Initiall y, the structure was analyzed under gravity loads per requirements of the United Facilities Criteria (UFC) 4 023 03 guideline (2013). The structure (under the same gravity loads) was then analyzed a second time after removing a single column on the first floor. Unlike the procedure defined in UFC 4 230 03 that requires performing several assessments with single column removals, this research entailed incrementally removing additional structural members (each additional member removal requiring a unique no nlinear transient dynamic finite element simulations ) to examine if and when PC is initiated. The sequence of member removal was determined with a separate computer program capable of determining blast induced structural damage (DSAS, 2012). Energy time histories from the PC inducing simulations were processed to confirm and quantify the energy flow member failure correlation. Patterns emerging during these analyses demonstrated the energy failure correlation. Displacement stress and strain time h istories were reviewed to confirm failure, as defined by UF guidelines. For select simulations, i.e. damage conditions, force time histories were recorded and reviewed (for a predetermined set of members) to determine the accuracy and reliability of the E FA presented in comparison traditional force based methods.
20 CHAPTER 2 BACKGROUND Progressive collapse (PC) is the propagation of localized failure(s) through a structural system, ultimately resulting in failure of the entire building or of a significant portion thereof. Disproportionate collapse refers to a collapse event in which the scale of the final collapsed state is disproportionately larger than the loading event. PC is often confused with DC. For example, the final collapsed state of World Trade Center Tower s 1 (North) and 2 (South) were disproportionate to the Boeing 767 and Boeing 757 impacts, respectively. In contrast, the final destructed state of the Alfred P. Murrah Federal Building can be considered commensu rate, or proportional, to the detonation, understanding the charge weight and associated level of explosive energy of the detonation approximately 4,000 lbs. of trinitrotoluene (TNT) (FEMA/ASCE, 1996). Several extensive discussions of collapse terminology including the difference between progressive and disproportionate collapse, are available (Arup, 2011; Cormie et al., 2009; Starossek and Haberland, 2010). PC is the exclusive focus of this research. PC mitigation efforts are categorized as either event control, addressing the loading event, or design methods (direct and indirect), which address the structural system. Items political measures, control of hazar dous substance access, etc. Focusing on the (the probability of) occurrence of abnormal loading, e vent control measures may be preferred, but are more often infeasible; e.g. increasing standoff distance in urban settings. Although instrumental and often the most effective, event control measures fall outside of the scope of this work, mentioned only to give the reader an understanding that a broad spectrum of non procedures are available.
21 Of the two design method options, indire implicitly. Three examples of such measures are given in the pending discussion of reactionary code development following catastrophic failures ductility and continuity (1968: gas explosion in the Ronan Point apa rtments), perimeter column loss and reinforcement for reverse bending (1995: bombing of the Alfred P. Murrah Federal building) and fireproofing (2011: explosive airliner impact ing W orld T rade C enter T owers 1 and 2) Direct design mitigates PC through exp licit measures. Specifically, direct design methods address the provision of minimum levels of strength, ductility and continuity, as well as tie force methods (for both vertical and horizontal ties). Examples of such methods include the Alternate Path method and specific load resistance method. The EFA presented is categorized as a direct design method. Additional nomenclature includes threat specific, or threat dependent, design, which falls in the direct design category. Threat dependency means spec ified threats are considered. Non specific threat, or threat independent, designs consider in a loose conceptual sense but do not identify, or quantify, a threat. A nominal level of protection or damage is chosen, hopefully on a rational basis, but not n ecessarily as prescriptive design specifics are not required. For example, the Alternate Path method is the notional removal of a single column, which is threat independent and unfortunately not rationally based on known blast loading events. Kirk Marcha nd and others have provided the pithiest descriptions defining threat dependent with, Further categorizing nomenclature i ncludes either prescriptive or performance based design. Prescriptive, specification, code, or provisional design uses known safety enhancing features. For example, afore mentioned seismic design requirements. Such methods are based
22 on experience and li mited to the more traditional and regular building types. Performance based design satisfies specific response criteria for defined threats. In contrast to prescriptive methods, this (performance based) approach lends itself to atypical, non traditional and irregular, buildings. Being so versatile to the considered threat, this approach can be threat dependent or independent, and designed indirectly or directly (Haberland and Starossek, 2009). To conclude this review of PC related nomenclature, design g uidelines published over the last decade allows engineers to use one of four analytical methods. Increasing in complexity, these analyses are static linear, static nonlinear, dynamic linear, and dynamic nonlinear. Typical of design codes, simpler methods are inherently more conservative due to (load) increasing and (strength) reduction factors. Detailed discussions of these four analytical methods are available (Marjanishvili, 2004; Marjanishvili and Agnew, 2006). 2 1 A Review of PC: Seminal Events, Publications, and Regulatory Provisions PC originated with the skyscraper, a consequence of advances in structural steel and ris increased from approximately 100 ft. 150 ft. prior to the turn of the century, to approximately 300 ft. 800 ft during the first two decades of the twentieth century. Advances in (steel and concrete) material production, fabrication machinery, erection methods, elevator safety, electrical lighting, and indoor plumbing yielded technologies resulting in the creatio n infrastructure capable of accommodating significantly higher population densities, thereby satisfying the increasing work force demands. In broader terms, the industrial revolution allowed for vertical expansion of the built environment, and vice versa. The result was the first generation infrastructure of modern day megalopolises the most densely populated cities in world history.
23 Most common in developing countries, building collapses have and continue to occur in relative proportion to high rise cons truction, e.g. Pemberton Mill (1860), Grover shoe factory fire protec Fortunately, design codes were developed for nationwide implementation at the turn of the century. American Concrete Institute (ACI) and American Institute of Steel Construct ion (AISC) began prescribing design regulations in 1910 and 1923, respectively. With the Chrysler and Empire State Buildings being the two notable exceptions, the great depression curtailed high rise construction for several years, indirectly retarding ad vances in understanding the PC phenomenon. To elucidate despite the ACI and AISC design codes continually improved since their respective inceptions at a rate (typically) no less than twice a decade engineers did not distinguish between collapse and PC un til WWII, i.e. the PC phenomenon was not even identified until the mid 20 th century. Prior WWII, and even until the advent of modern computing decades later, the understanding of such complex phenomena was constrained to hand calculations derived from theo retical formulations analytical methods incapable of quantifying physical phenomenon as complex as the PC of a multifaceted 3 D structure. Hence, these classical tools were extremely limited relative to the computational tools of today, e.g. simulating ex plosions with state of the art finite element (FE) and computational fluid dynamic codes. With minimal advances in dead and live loads such as self weight and human occupants, respective ly. Complementary to traditional loads, abnormal loads were not incorporated into design standards until several decades after WWII. A
24 thorough treatment of abnormal loads for occupied building structures is available (Wright et al., 1973). Focus on PC ( which yielded publications) began during WWII. Initial advances were made by engineers in the United Kingdom (UK), namely John Baker and others, due to the abundance of bombarded buildings (primarily) within metropolitan London. Engineers learned a grea t deal about the response of structures to explosive loadings after analyzing the damage incurred in correlation with the structural type and configuration. The two most significant contributions included the superior performance of masonry infill walls a nd the high vulnerability of connections in multi story steel framed buildings. A seminal text, with efforts showed PC is not solely a function of the (typica lly uncontrollable) extreme loading event, but the structural system as well. Consequently, the two PC mitigating categories were formed providing engineers concerned wit h protecting buildings with a substantial amount of data, which was used to help form the foundation of the field of protective design two decades later. However, PC was still rare ( for several reasons, primarily structure type, size, geometric proportion alities as well as construction materials and methods ) and so collapse related research was not a priority within the structural engineering community (Smith et al., 2010). This lack of investigative activity was even more prevalent in the US, where PC research lost support with the decreasing probability of WWII extending to US soil. did not have guidelines until after a gas leak explosion in 1968 within the corner un it on the 18 th story of the 22 story Ronan Point apartment tower in London caused a PC (Allen and Schriever,
25 1973; Pearson and Delatte, 2005). Unfortunately, a number of PC catastrophes causing multiple fatalities did occur prior to 1968, but did not garn er international attention. For example, the PC of a building under construction at Aberdeen University killed five workers and injured three others two years prior to the R onan P oint collapse (Hendry, 1967; Unknown, 1966). Published documents of this PC as well as other pre 1968 events are essentially non existent. This may be a result of R onan P oint being the first occupied high rise to have experienced PC due to an explosive loading event. In contrast to the lack of attention from the structural engin eering community at Aberdeen University, the Ronan Point collapse provided the impetus for development of PC guidelines around the world (Figure 2 1 ). This seminal event yielded codes or standards in the UK Australia/New Zealand, Canada, Western Europe, Hong Kong, Northern Ireland, Scotland, and the US (Ellingwood and Dusenberry, 2005). Furthermore, over 300 papers were published during the first decade after the collapse (Longinow and Ellingwood, 1998) an d more have continued to be published throughout the past forty seven years. The first sets of PC codes were established in 1970 with The Fifth Amendment in the UK. In the US, the ANSI Standard A58.1 1972 included a minimal reference to PC and a more com prehensive treatment was not published for another decade (A58.1 1982). US based codes were developed due to the tragedy at Ronan Point apartments at local, state, regional, national, and international levels from var ious industry regulating bodies. Exam ples included, but were not limited to, Building Officials and Code Administrators International, Inc. (BOCA), American Society of Civil Engineers (ASCE), Portland Cement Association (PCA), Prestressed Concre te Institute (PCI), N ew Y ork C ity building codes Connecticut Building Codes, American Concrete Institute (ACI), International Code Council (ICC), and so on (Pearson and Delatte 2005). Furthermore, Ronan Point related
26 code updates continued for over thirty years in both the US and Canada (ASCE, 2002 ). For example, in Canada, codes were developed to account for PC shortly after Ronan Point (NBCC 1970) and subsequently improved upon (NBCC 1975) through research (Taylor 1975). Although US codes did consider extreme loading events prior to Ronan Point they were limited to fire and earthquakes. The structural engineering community responded so strongly to the Ronan Point collapse Nielsen) was used extensively throughout the UK and abroad (System s, 1968) housing tens of thousands of residents at the time of the Ronan Point accident In fact, Ronan Point was one of nine identical buildings in London alone Following WWII, several governments, including the US, constructed large scale housing developments to shelter the booming post war population. For countries that experienced destruction (of significant portions) of housing infrastructure, expediently constructed housing was urgently needed. The Larsen Nielsen system was advantageous because all struc tural components, except for the foundation and columns, were precast concrete built off site, yielding a very rapid erection schedule. The engineering community made significant strides mitigating PC in response to the tragedy at Ronan Point However, co nstruction of mid and high rise buildings outpaced increased understanding of, and thus corresponding preventative measures for, PC in the following decades. Indicative of the dangers with high rise construction, all documented PC events with multiple fa talities in the U.S. over the next twenty seven years occurred during construction. Five of the most well known and documented accidents are listed as follows: 1. On January 25, 1971, in Boston, Massachusetts, a poorly constructed sixteen story building comp letely collapsed due to punching shear failure killing four laborers and injuring another twenty workers (King and Delatte 2004).
27 2. Premature removal of shoring killed fourteen and injured another thirty four during construction of the Skyline Plaza in Fair fax County, Virginia ( Burnett and Leyendecker, 1973). 3. Similarly but exacerbated due to design errors, the entire five story Harbour Cay Condominiums pancaked in Cocoa Beach, Florida on March 07, 1981 due to punching shear of the under designed and poorly constructed slabs, killing eleven and injuring another twenty three workers (Lew et al., 1981). 4. December 19, 1985, the twenty two story Wedbush building collaps ed due to the falling of a girder from a crane onto an already overloaded floor, killing three workers. 5. support from a lifting jack during placement of three slabs on upper levels twenty eight (Martin and De latte, 2000) Although not exclusive to PC, Occupational Safety and Health Administration (OSHA) investigated ninety six collapses during construction that in volved fatalities and injuries between 1990 & 2008 (Arup, 2011) Tens of fatal PC tragedies occurr ing in the US during construction did not garner major media attention for nearly three decades. This ended with the bombing of the Alfred P. Murrah Federal Building in Oklahoma City on April 19, 1995 (Figure 2 2 ). One hundred sixty eight people were killed, including nineteen children under the age of six and more than six hundred eighty were injured (Mlakar et al., 1998). Although several US occupied structures were attacked prior to 1995, these trag edies occur red on foreign soils. Thus, this bombing of the Alfred P. Murrah Federal Building was the first seminal event on US soil that caused improvements in the existing, or developments of new, PC codes, guidelines, and specifications (FEMA/ASCE, 1996 ). This tragic event is considered by many in the community of protection engineering as a turning point toward a new era of terrorism. Despite being designed and built in accord with all codes and provision at the time of construction in 1977 (Corley et al., 1998), approximately half of the entire Alfred P. Murrah Federal Building collapsed in a rapid and catastrophic manner. This horrific event revealed that the existing codes and provisions did not sufficiently address PC. Following the bombing,
28 Feder Building Performance Assessment Team (BPAT) investigated the tragedy and subsequently published The Oklahoma City bombing: Improving building performance through multi hazard mitigation ( FEMA, 1996). Hinman and Ha mmond, among others, provided several recommendations based upon the findings from this report. In addition to detailing the bombing, including, but not limited to, the progression of the collapse, this FEMA report focused on using seismic detailing to aid in mitigating PC an explicit responsibility assigned to the BPAT. Although many of the findings from this report were specific to the event the structure, site, charge weight, and charge location, the recommendations from this report were consequently ap plied to circumstances outside of appropriate applicability. To elaborate, the Alfred P. Murrah Federal Building had a unique design in that it had a very large transfer beam located on the second story a non redundant and vulnerable frame. In addition, the side of the building with this transfer beam had virtually no standoff from the street, allowing the terrorist to park the Large Vehicle Borne Improvised repeata ble, the quantity of the explosive material would be very difficult for potential terrorists to acquire following this event without garnering significant attention from national security agencies. Due to these structural aspects specific to the Alfred P. Murrah Federal Building, the significant charge weight approximately 2,000 of TNT equivalent, and detonation location, an offset distance roughly equivalent to the width of a sidewalk, the recommendations of the BPAT should have been provided with more ex tensive qualifications. and
29 reduce the likelihood of progressive collapse followi Again, although correct, many of the findings from this study were case specific. Unfortunately, some of the protective design community misused these seismic based design recommendations, and continue to do so, since the p ublication of the FEMA report. Unfortunately, the misapplication of seismic design methods to mitigate the effects from blast loading events occurred again the Northridge earthquake. Many in the seismic design community leveraged earthquake induced struct ural failures to p romote seismic design and retrofit methods regardless of their respective efficacies. Again, broad language stimulated many engineers, as well as researchers in academia, to over state the applicability and efficacy of seismic design fo r PC mitigation yielding misguided efforts through oversimplification of the PC phenomenon. Overstating the mitigating measures of seismic design resulted in practicing engineers inadequately addressing PC and arguably retarding understanding of PC. This problem was exacerbated with publications (Corley et al., 1998) and presentations (Corley, 2002) recommending the open ended use of seismic design for PC mitigation. These publications did not stipulate the appropriate limitations of seismic design provi sions for mitigating PC. Consequently, many engineers and industry entities proceeded with recommending seismic design for blast mitigation, often resulting in erroneous designs, i.e. yielding no mitigation against PC. For example, Portland Cement Associ ation (PCA) provided a guide with specificity regarding the applicability of the seismic design codes for beams to blast loading events. In fact, some designs have not only been ineffective against blast loadings, but have unduly increased the likelihood of a catastrophic PC, e.g. inappropriate use of the bridging design approach.
30 In contrast a few contributions from the seismic field have been applied astutely for use in blast mitigation, e.g. FEMA, 2010. However, there are significant differences betwe en the two seismic and blast loading events many of which are mutually exclusive and require approaches specific to the time domain of the applied loading. In addition, other researchers have shown taking a seismic reinforcing approach to prevent PC, by means of a single case study of the Alfred P. Murrah Federal Building only, can be misleading and dangerous (Baldridge and engineering practices would be sufficient to miti gate risk from abnormal loads and PC. Such Other prudent engineers/researchers specifically, mechanical fusing of a building structure (Osteraas, 2006). Fortunately, A few provisional codes have confirmed the fundamental differences here are also significant differences between seismic and blast design, so seismic upgrades should only be used as a basis 2011b). Additional differences were observ no concern about the occurrence of PC under seismic loading in a one column loss scenario for differences betwe 2013). In summary, the application o f seismic design provisions to address PC were overstated
31 and overused following the bombing of the Alfred P. Murrah Federal building and the Northridge earthquake. With continued effort from informed engineers with blast ex perience, the misapplication of seismic methods for blast mitigation can be eliminated. In contrast to the ( relatively ) more recent ly develop ed PC mitigating guidelines, seismic codes have been under continued development since 1927, e.g. the Unified Build ing Code (UBC). Interestingly and quite unfortunately, our society has been more reactive than proactive and thus codes addressing seismic activity and PC share a fundamental commonality both have been developed largely in response to catastrophic event s ; i.e. code development has been predominantly reactive. One limitation of this approach is that reaction based code development typically yields an indirect design approach. Some of the more significant examples include provisions of sufficient ductili ty and continuity (Ronan Point), designing for loss of a perimeter column and provisions of sufficient reinforcement for reverse bending in beams and slabs (Alfred P. Murrah Building), and sufficient fireproofing protection of steel members ( W orld T rade C e nter towers). Current regulatory guidelines include indirect and direct design methods. Indirect design methods include measures such as providing minimum levels of strength, ductility and continuity, and tie force methods (for vertical and horizontal t ies) D irect design methods include measures such as the Alternate Path method and specific load resistance me thod per the e 2013) and the Minimum Antiterrorism Standar ds for Buildings UFC 4 010 01 (DOD 2000; 2007; 201 3a). Although a significant amount of guidelines were provided to engineers after the bombing of the Alfred P. Murrah Federal Building and significantly more after the 9/11 attacks,
32 the efficacy of code provisions remain questionable. After the bombing in Oklahoma City the Defense Threat Reduction Agency (DTRA) published the document under the Blast Mitigation for Structures Program (BMSP). The charge of this document and the 1999 publication was the first and last edition. The followin g year, the US General Services Administration (GSA) published guidelines containing direct methods, although branded as a threat independent methodology, for assessing the potential for PC (GSA, 2000). This publication, the Public Building Service (PBS) Facilities Standards required one member redundancy, with no correlation to susceptibility, vulnerability, or threat level. The Department of Defense (DOD) also provided guidance to practicing engineers the following year prior to the September 11 attacks (DOD, 2001). After collapse of both World Trade Center skyscrapers in N ew Y ork C ity on September 11, 2001 (9/11), three different government agencies responded by publishing updated design guidelines. The US GSA updated the PBS Facilities Standards with another round of provisions containing threat independent design methods with significant reference to previous manuals which included general performance based provisions only, (GSA, 2003). These guidelines were an evolution of the 2000 PBS Facilities S tandards, but with an exemption for certain buildings from PC considerations, also with no correlation to susceptibility, vulnerability, or threat level. Again in 2003, the DOD published Collapse UFC 4 023 xpanding the 2001 document for the US civilian design com munity (Stevens et al., 2012). Even though the (2009) and
33 Progressive Co (2013b) are considered the provide indirect design methods only. 023, de rived from UK provisions, indirect methods prescribe minimum inter member connectivity, thereby eliminating requirements of abnormal loading. Similarly, Federal Emergency Reference Manual to Mitigate Potential Terrorist Attack s against Buildings which was part of the Risk Management Series (FEMA, 2003a). Unfortunately even less prescriptive and of less value to practicing engineers, ACI 318 has no explicit mention of redundancy or alternate load path and hence no t hreat specificity (2004). Similarly, ASCE 7 suggests an unspecified degree of redundancy and alternate load redundancy in all buildings, independent of the nat ure of level of threat to the building. The report also calls for the development of methods for the rational analysis and design of buildings (Nair, 2004). Ho wever, there are no requirements, only conceptual suggestions, thereby lacking the specificity required for practicable design. Furthermore, research has found codes would have been ineffectual even if the provisional methods were employed prior to the ab normal loading event (Table 2 1 ). An additional example of such shortcomings is load sensitivity forces just above the maximum design loads should not produce significantly different failure responses. Although is recommended that the good practice requirement is introduced that the design of a building should be insensitive to the design assumptions by examining the performance of the building
34 under higher than riteria does not exist (Arup 2011). Similar to the suggestive wording in design codes, with no explicit prescriptive provisions, this load sensitivity issue remains unimproved. Design codes are deficient in defining performance based criteria for loads beyond the traditional loads, and thus need further development for PC. Understanding so many shortcomings are abundant throughout PC design provisions and the ever increasing popularity of mid and high rise buildings, the need for improved understanding and mitigation of PC is an urgent need, and will continue to be increasingly imperative. 2 2 The Alternate Path M ethod in Regulatory Design Provisions The Alternate Path method is a direct design measure ensuring only minim al redundancy in the vertical load bearing system of a multi story structure. Procedurally the Alternate Path method entails removing a column at various prescribed locations. For US based guidelines, the Alternate Pat h method has origins in ASCE 7 88, which includes illustrations of structural systems. These illustrated Alternate Path method 95 editions. Alth ough ASCE 7 10 discusses the Alternate Path method Alternate Path method is more of a suggestion, not a requirement, in AS CE 7 10, and, due to the nature of this specification, considers loading related information only. As intended, ASCE 7 10 is referenced in all three of the bulleted codes listed below for prescribing (the required) combinations of traditional loads. The Alternate Path method is included in the provisions of several design specifications. For the sake of clarity, the specifics of the Alternate Path method discussed herein are per the following UFC specification: Design of Buildings to Resist Progressive Collapse UFC 4 023 03
35 o Includes 14 July 2009 and 1 June 2013 (Change 2) updates/revisions o Located in Â§ 3 2 p. 33 Two additional US regulatory provisions UFC 4 023 03, include the following: Alternate Pa th Analysis & Design Guidelines for Progressive Collapse R esistance o Includes 24 October 2013 o Located in Â§ 3.2, pp. 7 16 Blast Protection of Buildings ASCE/SEI 59 11 There are also a large number of additional domestic (local, regional, and national) and international design codes that include the Alternate Path method many of which reference ASCE, UFC, GSA, or others. Comprehensive presentations of such provisions are available, e.g. Dusenberry, 2003. In contrast, the UFC and GSA design guidelines are r equired for qualifying buildings. Qualification, or exclusion, of these guidelines is determined per the occupancy categories. More obvious are the specification designations, UFC 4 023 03 including change 2 evolved from the initial, and equally titled, 2003 edition. T he 2013 GSA document listed above evolved from essentially a subsequent and expanded version of t he 2000 GSA PBS Facilities Criteria. For purposes of performing a comprehensive review, the ten story office building is classified occupancy category III. This designation is most appropriate given this structure would be designed to accommodate over 500 occupants, as nearly 12,150 m 2 of office space is provided; UFC 4 023 03 Â§ 2 1 ref. UFC 3 310 01 Â§ 1 6.1 In addition, the Alternate Path method requires single column removals at three external and four internal locations on predetermined floors. The e xterior columns are: 1) near the middle of the long edge, 2) middle of the short edge, and 3) at a corner (UFC Â§ 3 126.96.36.199). Although removal is prescribed for
36 multiple stories (UFC Â§ 3 188.8.131.52), only columns at ground level are considered. As per the le ading US guidelines (ASCE 59 11, GSA, and UFC), three different analytical methods, with associated acceptance criteria for each, are allowed when performing the Alternate Path method These three methods include linear static (LS) Â§ 3 2.11, Nonlinear Sta tic (NS) Â§ 3 2.12, and Nonlinear Dynamic (ND) Â§ 3 2.13 all of UFC 4 023 03 Each analysis method includes unique modeling stipulat ions such as loading combinations, procedural methods and increase factors Force and displacement criteria are also assoc iated with each of these analytical methods as well as a fourth : nonlinear dynamic per 4 023 03 (UFC 2013) Moving forward, ASCE 7 16 will have a significant expansion of performance based design criteria for extreme loadings, e.g. an entire chapter will devoted to mitigation from Tsunami loading events. As the reader may have surmised, this is again a reactive measure in response to the tragic events at the Fukashima Daiichi Nuclear facility on March 11, 2011. For the reasons discussed above and in the f ollowing section below, the Alternate Path method is not an effective approach for mitigating PC. Fortunately, several PC experts have published their findings in an effort to minimize use of the Alternate Path method ; e.g. the alternate path method and specific local resistance should not and Juneja, 2003; Ellingwood and Dusenberry, 2005 ; Ellingwood, 2007; Ellingwood et al., 2007). 2 3 Structural Damage Incurred from Known Explosive Terrorist Threats The Alternate Path method correlates to a single column failure. However, blast induced damage from known explosions have resulted in destruction of the impacted building well in excess of a single column the Alfred P. Murrah Building was highly susceptible to PC, as evidenced by the rapid PC (recall
37 F igure 2 2 ) following the loss of three columns supported by the non redundant transfer beam (FEMA/ASCE, 1996). In contrast, the Kansallis House (Figure 2 3 ) exhibited robustness enduring the destruction of 1367 ft 2 (127 m 2 ) of the first floor, and 785.8 ft 2 (73 m 2 ) of both the second and third floors, in addition to three columns (Crowder, 2005). PC events have often had charge weights in the thousands of po unds, deliverable only by very large transport vehicles. Although the four explosive events discussed thus far ( Ronan Point Alfred P. Murrah Federal Building W orld T rade C enter T owers 1 and 2, and Kansallis House) may not be considered representative of the majority of blast threats, the overwhelming majority of explosive threats have resulted in damage well beyond destruction of a single column. The disparity between a single notional column removal and the damage incurred from actual blast loading even ts is contrasted further when considering the level of threat, i.e. explosive energy, required to initiate collapse. Typically, the charge weight commensurate with initiating PC of a multi story steel frame building is at least several hundred, if not tho usands of pounds. Thus, a heavy transport vehicle (capable of such a payload) is required, e.g. the 1983 Beirut barracks bombings. Hence, a vehicle transported explosion such as a car bomb is a likely threat, assuming a number of other factors. The diag rams below illustrate an extreme (explosive) loading event and charge weights as a function of vehicle size. Figure 2 4 A illustrates an airblast delivered by large van, or small truck, with the primary event par ameters illustrated. Figure 2 4 B defines damage levels as a function of standoff distance and weapon yield. For example, a 500 kg (1,102 lb.) charge of TNT which can be delivered by van detonated 4.0 m from t he building exterio r yields a scaled distance of 0.6348 m/kg 1/3 which is in the industry standard distance to target cube root weight of charge (dist./wt. 1/3 ) format. Additional information regarding blast events are available (FEMA 2003a; FEMA 2003b).
38 A lthough a myriad of viable threats exist, especially in more densely populated urban environments (with multiple forms of mass transportation adjacent, if not internal, to occupied buildings), the threats discussed are indicative of a vehicle transported t hreat, or car bombing. Specifics of the threats considered may be highly critical when designing and/or analyzing a structure, given any number of potential building characteristics and threat conditions. However, such specificities are of no import in t his study as threats capable of initiating PC are assumed. The methods used to simulate the air blasts considered are discussed (Â§ 2 4 ). Regardless of the severity of blast loading, accurately predictin g threat specific damage levels requires use of sophisticated numerical tools. The state of the art numerical modelling approaches typically employed are either Computational Fluid Dynamics, Finite Element Analysis, or a combination of both, e.g. Multi Ma terial Arbitrary Lagrangian Eulerian (MM ALE) simulations. Unfortunately, all of these methods are technically rigorous, time intensive, and computationally expensive, thus rendering this approach impractical for most practicing design engineers. In lieu of utilizing such technically rigorous software, several simplified programs have been developed to serve the protective design community. For example, several programs calculate the pressure and impulse to be applied to a structure in a significantly mo re efficient manner than explicitly modeling an explosion, e.g. ConWep (Hyde, 1988). However, such programs calculate the applied loading, i.e. pressure, time histories only. In compliment to such software, there are also simplified programs available to calculate damage once the impulsive loading curve has been characterized. Thus, a software package capable of using the detonation parameters to not only calculate the applied loads, but also determine the resulting structural damage was used: Dynamic St ructural Analysis Suite (DSAS) ( As tarlioglu and Krauthammer 2012)
39 2 4 DSAS: Simulating Explosions The following introduction to the Dynamic Structural Analysis Suite (DSAS) software progr am (version 184.108.40.206229) is included to aid in explaining the role of DSAS within this research study. DSAS is a multifunctional structural analysis program for modeling the response of a given structural component to static and dynamic loads ( Astarlioglu and Krauthammer, 2012 ). This program was developed to analyze severe dynamic loads by simplifying a structural single degree of freedom function, thereby expediting the analysis R einforced concrete, steel, and masonry materia ls are available. 2 5 ) generates the pressure impulse loading applied to a given structural member within the blast area. Using the pressure time history generated by th e Air Blast Loading module (Figure 2 6 ), DSAS performs a time history analysis for the structural member under consideration. In addition, moment curvature, resistance functions, and failure determination are als o generated. DSAS has been validated for assessing structural performance, most notably for identifying threat levels capable of causing structural damage. 2 5 Ten S tory M oment R esisting S teel F rame B uilding 2 5 1 Historical Reference and Relevant Antecedent Research The structure of interest is a ten story steel frame a hypothetical building designed to code as part of a large multi entity collaboration of engineers, researchers, and investigators a result of seismic mitigation efforts in response to the Northridge earthquake on January 17, 1994. The Structural Engineers Association of California ( S EAOC), Applied Technology Council ( A TC), and California Universities for Research in Earthquake Engineering ( C UREe) (SAC) joint venture (JV) commissioned the design of three buildings in seismically active US cities (FEMA, 2000). The stru cture in this study is the mid rise building located in Boston,
40 MA a designated Seismic Zone 2A. The primary interest was the pre Northridge (WUF B) moment connections, due to the failures during the Northridge earthquake (Gupta and Krawinkler, 2000). Alt hough initially for purposes related to seismic events, these buildings were later studied for addressing blast loading events, in part due to the plethora of published data developed from the seismic research. Several blast studies (Lim and Krauthammer, 2006; Krauthammer, 2007a; 2007b) focused on various building characteristics, including the WUF B connections. Multiple deficiencies were identified, thus requiring retrofits for preventing PC (Krauthammer et al., 2004b). Most relevant to the present stu dy, the ten story building designed for Boston was used in an earlier CIPPS study, where simplified models of the WUF B connections were developed for determining the effects of the connections on PC (Yim and Krauthammer, 2009). 2 5 2 Structural System The 10 story, or 9 story with a basement, building has 29,000 ksi steel throughout, with 50 ksi yield columns, and 36 ksi yield beams and girders. All slabs are comprised of 3,500 ksi concrete with a 4 ksi yield, are 100 mm thick with 1.5% 36 ksi yield mild steel reinforcing in both directions. The framing plan is shown illustrating all column orientations, connection type (moment or shear), and the associat ed perimeter beams tabulated per floor (Figure 2 7 ). An additional illustration provides all column cross sections with splice locations and elevations. For simplicity, the dissimilar column layout supp orting the penthouse (not depicted) is not included in the numerical models. Thus, columns C 3, C 4, D 3, D 4, E 3, and E 4 are modified to match the same cross sections and splice elevations of the remaining interior columns (Figure 2 8 ). Further details are available (Appendix B ).
41 2 5 3 Reductionist Modelling of Connections by Yim and Krauthammer As mentioned above (Â§ 2 5 1 ), an antecedent CIPPS study examined the effects of connections on PC (Yim, 2007). This prior study, of primary i mport to the work presented here, incorporated the moment and shear connections of the mid rise steel frame discussed above concluding connection strength is a significant contributor PC, thus requiring numerical representation assessments of susceptibilit y. I n this prior study, connections were modeled using a reductionist approach. Simulating PC of a structural frame that accounts for the behavior of all connections with highly discretized continuum elements is too computationally expensive. Thus, a si gnificantly more (computationally) efficient approach was taken, but with minimal loss in accuracy. Most succinctly, rotational springs were used to represent the connections, resultant beam elements represented the columns and girders, and shell elements represented the slabs. Initially, models with highly discretized resolutions of continuum (brick) elements represented all structural components in and around the connections. With rotation s defined as the relative motion s between the beam and column, qu asi static simulations were performed for both moment and shear connections. The moment and rotation time histories from these simulations were extracted to develop nonlinear moment rotation (M ) curves. The numerical results were validated with experimental data obtained from the AISC Northridge Test program (Engelhardt and Sabol, 1994). specific Join and Cardan features. The Join feature constra ined, or prevented, translation between the girder and column. Rotation was defined with a Cardan angle parameterization of finite rotations, also known as a 1 2 3 parameterization or yaw pitch roll parameterization. These Cardan angle parameterizations
42 were defined using the nonlinear moment phi (M ) curves from the computationally expensive continuum models. Additional quasi static simulations were performed, verifying the simplified connection method, i.e. Join + Cardan. Using equivalent boundary conditions, loads were applied to the resultant be am elements representing the girders, in both the vertical and horizontal planes. The resulting nonlinear M curves from these simplified connection models were then compared to the resultant curves from the continuum models. The simplified models descr ibed the connection behavior with acceptable accuracy and with significant reductions in computation model s This preceding study, antecedent in nature to the proposed verified using the nonlinear M curves from the quasi in PC rate quasi static analyses but in the blast rate dynamic analyses considering high velocity nonlinear and failure behaviors. The simplified frame models considering connector element properties were capable of maintaining good accuracy in the quasi static and blast rate loading simulations while effectively reducing simulation time. It was concluded that frame analyses could be carried out readily and acc urately using simplified beam and connector elements instead of modeling detailed and complicated combinations of the beam, column, and connection rotation curves developed by Yim ar e used in the LS DYNA models in the work presented here. These curves and all related support information are available (Yim, 2007).
43 2 6 Review of Energy and Traditional Approaches to Stru ctural Behavior 2 6 1 Energy and Power Flow Analyses for Mechanical Engineering Applications Mechanical engineers have been studying energy flow, ref erred to as energy or power flow in the mechanical engineering field, in structural components for several decades. In fact, finite element analyses became the preferred power flow approach to vibration problems nearly thirty years ago (Hambric, 1988). While this research is related to the proposed work, with respect to energy conservation and solid mechanics, such work has focused on vibrational and acoustical behavior under steady state conditions. In addition to the inherent disparity between steady state and failure, there a number of additional fundamental differences. Figure 2 9 illustrates differences between the frequency and amplitude domains of vibration and acoustics, seismic, blast, and wi nd. An additional region illustrating PC response was added to illustrate the relative period and amplitude of PC to the specified hazards, i.e. extreme event loadings. It is also understood structural materials are rate dependent, not to mention the dif ferences in linear and nonlinear behavior. Due to these disparities between the fundamentals of failure, and vibrational and acoustic phenomena, these prior energy and power flow studies are related to PC applications only from the broadest perspective f ramed with respect to energy principles. 2 6 2 Traditional Force Based Approaches to Progressive Collapse Multitudes of studies have analyzed PC from a pe rspective of either local (single member) or global (total structural system) failure. To illustrate the localized approach, Nassr et al. developed a single degree of freedom model to represent a steel beam column experiencing blast loading (2013). Other s have taken global approaches to PC, developing FE models of moment loading and as well as its resistance to PC. Although such studies have made strides in improving m odeling capabilities of blast induced PC loading events, such work is not relevant to
44 the energy flow approach presented here. Thus, an extensive list of traditional force based PC work is not discussed. 2 7 Literature Review of Energy Approaches to Structural Phenomena In contrast to such a plethora of research by mechanical engineers focused on vibrational and acoustical behavior and structural engineers using traditional force based meth ods, only four known studies have taken an energy based approach t o structural collapse phenomena 2 7 1 Energy Approaches P rior to CIPPS Research Th e first known study of relative significance incorporated energy capacity for single columns as an additional design parameter (Smythe and Gjelsvik, 2006). Hence, that study dealt with collapse of a single structural element only, not PC. However, Smythe research is conceptually very similar to the preceding CIPPS energy based approach (Szyniszewski and Krauthammer, 2012), as both studies addressed structural failure with respect to an energy threshold. Although similar in concept, Smythe example, elastic perfectly plastic material was assumed, the scope was limited to pin pin supports, one material, one cross section, and pseudo sta tic analyses only. Although methodologically distinct a second study similarly advanced the effort of (Dusenberry and Hamburger, 2006). The approach methods used in this prior wor k included push down analysis and flexural/catenary energy absorption. The approaches in both of these non CIPPS studies assumed a sequential formation of hinges to determine if PC occurs, and are founded upon the energy based principle that if the change in potential energy exceeds the energy absorbed by the structure, then PC occurs. Of significant contribution, this work better defined the global energy fundamentals for an energy based approach
45 the s tructure exceeds the change in potential energy, the structure has come to rest and has energy does not fully absorb the total energy flowing into the member of int erest, failure extends to adjacent members. Although this study has conceptual similarity on a global level, the analytical methods chosen by Dusenberry and Hamburger are not contributory to the study presented herein given the narrow and simplified metho ds of push down analysis and flexural/catenary energy absorption. The third study incorporating energy capacity (for individual structural elements) as an additional design parameter was the first to demonstrate an energy based approach for addressing syst em wide failure in structural frames as a viable method (Surahman, 2007). Although for the purposes of protecting against earthquake induced damage, Surahman showed an energy based approach could be used to develop a design method based on the distributio n of energy throughout the structural frame, using energy time histories to determine the energy distribution, and confirming energy distribution is a function of member strength. More Stronger or more flexible components suffer les s damage member energy absorption capacity is determined by the member ductility, strain hardening, strength degrada to all subsequent energy based approach work to coll apse mitigation. Although highly analogous to the preceding CIPPS study by Szyniszewski, a number of fundamental differences exist. The two most significant are the impulsive domain versus the dynamic domain and the application of damage in relation to t he event loading. In addition, the building was subjected to earthquake loads prior to incurring structural damage. In the antecedent research (Szyniszewski, 2009), as well as the work presented herein, analysis begins after damage is applied by means of
46 domain as the loading event, as opposed to analyzing behavior after load application. This is a highly significant disparity, especially for large mass structures, as inertia can govern the response of structures experiencing dynamic loading. Additional discussion of these differences is included (Â§ 2 1 ). One of the antecedent studies at CIPPS entailed the develo pment of an energy based approach for PC (Szyniszewski and Krauthammer, 2012). Using a typical moment resisting steel frame for a low rise building, this prior work showed an energy based approach could assess PC susceptibility successfully supported by a nalysis of the energy flow throughout the structure. Howe ver, this work did not consider the rate of energy flow transmitted throughout the structure, the connections, or a building of sufficient height to warrant concern for PC suscept ibility to PC is a function of its capacity to redistribute energy, the efficacy of an analytical approach based on energy flow (magnitude and rate) was investigated. Since the work presented herein extends this preceding CIPPS study, with the items liste d above, a cursory review of the antecedent research is offered. 2 7 2 Energy B ased Approach by Szyniszewski an d Krauthammer Given the antecedent nature o f work (2012) to the research presented herein, this prior study is discussed in further detail to compare and contrast these two research studies. F inite element models of th is mid rise building were developed and nonlinear transient dynamic finite element simulations were performed with varying levels of structural damage imposed by removing structural elements. Simulated damage ranged from the removal of a single column, per the Alternate Path method to the removal of th e minimum number of structural elements initiating PC. A unique n onlinear transient dynamic finite element
47 simulation w as performed with the removal of each additional structural member. Energy time histories were recorded and analyzed, resulting in usin g column energy to indicate collapse. Being the origins of th is preceding energy based approach th is approach begins with the principle of con servation of mechanical energy Equation 2 1 expressed in te rms of the E nergy B alance E quation : ( 2 1 ) Considering the system under consideration (building frame, applied loading, boundary conditions, and various prescribed damage levels) is isolated, the global mechanical e nergy remains constant. Energetic effects from frictional and other non conservative forces are negligible. Consequently, conservation of mechanical energy is an acceptably comprehensive accounting of the system. Thus, energy is transferred between vari ous forms, neither created nor destroyed, per the conservation principle. Using nonlinear transient dynamic finite element simulations this antecedent study began with characterizing the response of structural member s in both force and energy domains for numerous loading conditions. The energy forms considered included internal with Equation 2 2 kinetic with Equation 2 3 and potential, or gravitational with Equat ion 2 5 The potential energy associated with the gravitation field, or gravitational energy, is an energy source in this energy based approach that is released with the failure (by means of removal) of a load supporting structural member. Internal energy, the sum of elastic and inelastic strain energies, is: ( 2 2 )
48 where E int is internal energy, is elastic strain energy, is stress, is elastic strain increment, is permanent deformation work, and is plastic strain increment. Kinetic energy is: ( 2 3 ) where E kin and is kinetic energy, is mass density, and is particle velocity Work done on the system is the summation of the change in both kinetic and internal energies. Internal energy is the sum of elastic strain energy and pl astic strain energy or work done through permanent deformation. Referencing above formulations the consequent definition of work is: ( 2 4 ) Extending the energy wo Szyniszewski, 2009), potential energy associated with the gravitational field, or gravitational energy, is ( 2 5 ) where U grv is the gravitational energy, m is mass of all parts of the structure supported by the removed member(s), g is gravity, and y is vertical distance. Energy transfer with member removal is known to be proportional to the recoverable elastic strains in the remo ved member(s) as well as the mass supported by the removed element, which is a transfer from potential to kinetic energy. Thus, the elastic strain energy portion of Equation 2 2 can also be used to define the strain energy portion of the (internal) potential energy released upon the removal of (a) structural member(s). To translate the energy principle on which the antecedent and current work is based, in terms of the selected finite element code, recall the si mplified form of energy equilibrium with Eq uation 2 1 This C onservation of E nergy E quation is redefined with energy forms relevant to
49 finite element software in Eq uation 2 6 To elucidate, using the energy forms recorded by the nonlinear transient dynamic finite element code LS DYNA, the conservation of mechanical energy expressed in total energy equilibrium terms is defined as: ( 2 6 ) where E total = total energy, E kin = current kinetic energy, E int = current internal energy, E si = current sliding interface energy (including friction), E r w = current rigid wall energ y, E damp = current damping energy, E hg = current hourglass energy, E 0 kin = initial kinetic energy, E 0 int = initial internal energy, and W ext = external work. All energy forms listed were reviewed. Sliding interface, rigid wall, and hourglass energies wer e checked for quality control. Damping energy was employed to filter non relevant high frequency content, and reviewed to confirm the damping energy is negligible with respect to total system energy levels. The energy e quation above illustrates equilibri um principles are embedded in nonlinear transient dynamic finite element codes. Thus, the energy flow, magnitude and rate, failure relationship is understood to exist, even though this relationship has not been demonstrated for either failure or PC. The infused mechanical energy is equivalent to the potential energy released by all parts of the structure supported by the column removal (through gravitational forces). In other words, the strain energy in the column prior to removal is transferred to the remaining structure. This mechanical energy flow s through out the structure along multiple pathways concurrently Energy flows through a structure until it is fully transferred into structural displacements and material deformations whether failure is ar rested, or continues until collapse occurs. Hence, PC is known which is a function of constitutive material definitions, cross sectional properties, and struct ural parameters. Energy time histories of each mechanical form considered (total, potential, and
50 kinetic) were analyzed to determine correlation between energy capacity and collapse. In result, column failure energy was a more effective indicator of coll apse than traditional methods. concern for PC, connections, or the rate of energy flow. As discussed (Â§ 2 5 3 ), prior research has shown connections affect PC (Yim and Krauthammer, 2009). Although energy flow rate can affect failure, its role in PC has been unknown until the research presented here was conducted However, the above plot shows failure begins to be affected by loading rates above 3000 kip/s. A more recent CIPPS study showed structural failure, as well as the mode of failure, is a function of both energy flow as well as the rate of energy flow (Tsai and Krauthammer, 2015). In accord with both findi ngs, PC is affected by columns experiencing sufficiently high energy flow rates, i.e. above 3000 kip/s. This antecedent study analyzed two similar low rise frames only structures that neither exemplify PC susceptibility nor are of primary import to PC mit igation. Thus, the research presented herein applies the energy energy rate relationship rise frame susceptible to PC. 2 8 Summary Over two decades after formative advances following WWII, PC garnered international focus, primarily in response to the Ronan Point a partments collapse. Nearly fifty years after the Ronan Point tragedy a seminal event for the field of PC c omprehensive understanding of PC phenomenon remains outside the technical scope of the overwhelming majority of structural engineers practicing today. Given the state of practice lacks sufficient understanding of PC, an effective approach to PC mitigation is paramount one that needs to be both rational and efficient for practicing engineers. Unfortunately, no simplified method exists. Although nonlinear transient dynamic finite element analysis software codes are available, this technique is
51 too technica lly rigorous, time intensive, and computationally expensive to be provided by most structural engineering consultants. In addition, nonlinear transient dynamic finite element simulations yields a solution constrained to the threat and structure considered Not surprisingly, it is understood most engineers practicing in the field of protective design rely on the Alternate Path method solely, contrary to the unreliable nature of this notional approach that has no basis in physics. Unfortunately, the Altern ate Path method will continue to be used beyond preliminary design efforts until there is an efficient rational alternative. The Alternate Path method appears to be unrealistic, proven overly conservative in certain situations (McKay et al., 2012) and poss ibly insufficient for others. Beyond minimal redundancy, which obviously should be well exceeded for life safety issues for any occupied building, what the Alternate Path method achieves in mitigating PC is unknown and unproven. In addition, multiple ter rorist attacks in urban environments have yielded significant levels of damage, demonstrating no correlation between a single column failure and damages incurred from actual blast loading events. The Alternate Path method has not been shown to mitigate PC it establishes that minimal redundancy is present in the vertical load carrying system only with no correlation to the robustness needed to sustain a realistic threat In addition, the Alternate Path method is highly repetitive an imposition on practicin g engineers, resulting in higher costs, and extended job schedules without any corresponding improvement, accuracy, or precision. Again, a rational physics based approach to PC assessments is of utmost importance. To address this need, the energy based ap proach for PC present in this work has been developed. The antecedent study confirmed a meaningful correlation between energy and failure, and the developed energy based approach yielded more accurate failure predictions than traditional force based appro aches ( Szyniszewski and Krauthammer 2012 ). Although
52 successful in using pre calculated energy thresholds to determine failure, neither the structural connections nor the rates of energy flows were considered. In addition, low rise buildings are immateri al to PC a phenomenon proportional in relevance to the height of a building. Furthermore, there were two cases in which the energy failure threshold was exceeded with no corresponding member failure offering an opportunity for improvement with the demand over capacity (D/C) ratios presented. Hence, connections, the evaluation of energy flow rate on failure, and a mid rise structural relevant to PC is considered in the EFA presented here. In addition to developing a novel EFA for PC, the current study pre sents the limits of the effects, or energy redistribution, extending from a single column removal, larger blast damaged zones, and Alternate Path method procedures for assessing PC. Table 2 1 Efficacy of US based codes in mitigating the t hree m ost i nfluential PC e vents (Source: reproduced from Nair, 2006 Figure 4) Redund ancy Local Resistance Inter connection Threat depen dent analysis R onan P oint Murrah Bldg. W orld T rade C enter 1 & 2 W orld T rade Center 7 ASCE 7( 05) ? N N N ACI 318( 02) Y ? N N GSA PBS, 2000 ? N N -GSA PBS, 2003 N Y N N GSA PC, 2003 N N N N NIST 2005 N N N N
53 A B C Figure 2 1 R onan P oint a partment t ower in London in 1968 after collapse. A ) Photo courtesy of Cynthia Pearson Source: Pearson and Delatte, 2005. B ) Photo courtesy of David E. Allen. Source: Allen and Schriever, 1973. C ) Photo courtesy of David E. Allen. Source: Allen and Schriever, 1973. Figure 2 2 Alfred P. Murrah b uilding in Oklahoma City a fter the blas t induced collapse in 1995. Photo s courtesy of Chicago Sun Times Sources: https://s media cache ak0.pinimg.com/236x/ed/2a/c5/ed2ac5c56e49b61fd37b2d08 726c3451.jpg and https://s media cache ak0.pinimg.com/236x/a7/36/ae/a736ae79aeb7799562446468ae758713.jpg
54 A B Figure 2 3 D amage to the Kansallis House in Bishopsgate area after 1993 bombing in London A ) Photo courtesy of Daily Mail Pictures, 2011 Source: https:// po4ep.s3.amazonaws.com/785/l/19064000.jpg http://mailpictures.newsprints.co.uk/view/19064000/elib_assc mmglpict000005171717_jpg B ) Photo courtesy of Dick Polman. Source: Polman, 2013 A B Figure 2 4 Detonation p arameters and y ield w eights per t ransport v ehicle. A ) Offset explosive threat delivered by van with pressures to buildin g exterior visualized Image source: FEMA 427. B ) Weapon yield as function of standoff, or offset, distance and mode of vehicle transport Image source: FEMA 426
55 Figure 2 5 a ir b last l oading m odule Figure 2 6 Pressure t ime h istory (for 0.504 m/kg 1/3 ) output from DSAS
56 Figure 2 7 Plan l ayout of b eams with WUF B c onnect b eams tabula ted per f loor Figure 2 8 Elevation of s teel c olumns cross sections with s plice l ocations
57 Figure 2 9 Qualitative Frequency Amplitude Distribution for Different Hazards After source with inclusion of PC region : Ettouney, 2003.
58 C HAPTER 3 ENERGY FLOW APPROACH (EFA) TO PROGRESSIVE COLLAPSE (PC) This s tudy is based upon the thesis that member failure, and consequently (Progressive Collapse) PC, correlates with energy flow both magnitude ( E ) and rate ( ) more closely than any other measure of state, e.g. force as is currently done in traditional approach es. Thus measuring these two parameters provide s the most accurate and precise indicators of failure. This hypothesis was initially examined for a single structural element (Tsai and Krauthammer, 2015), for a single story single bay frame in the proposa l to this study, subsequently for a two story two bay by two bay frame for collapse (Appendix A ), and then ultimately for two ten story mid rise building s The energy flow approach (EFA) presented here is an amalgamated successor of three dissertations performed at CIPPS. The first study demonstrated the significant effects of connections in moment resisting steel frames on PC ( Yim, 2007 ; Yim and Krauthammer, 2009 ; Yim and Krauthammer 2010 ; Yim and Krauth ammer, 2012). Therefore in both this prior and current studies, the strength of all frame connections was considered using nonlinear strength curves developed from quasi static simulations with discretely modeled high resolution continuum models. The se cond study developed an energy based approach to PC, yielding a more accurate and more reliable failure assessment approach than traditional force based approaches ( Szyniszewski, 2009 ; Szyniszewski and Krauthammer, 2012). F ailure was defined using an ener gy threshold value, whereas th is work define s failure as a function of the magnitude and the rate of energy flow, herein referred to simply as energy flow. The third study demonstrated the use of an energy energy rate failure threshold (Figure 3 1 ) for an individual structural element (Tsai and Krauthammer, 2015). Combining this antecedent CIPPS research numerically representing structural connections, the use of energy parameter for determining
59 collaps e susceptibility, and using the combined energy flow and rate of energy flow as failure indicating parameter the work presented here considers the PC of a mid rise steel building and the demonstrates the efficacy of using energy flow for assessing PC susce ptibility. In short the EFA discussed here provides an unprecedented level of accuracy and reliability for assessing PC susceptibility within the most comprehensive physics based framework. A flowchart of the process employed (Figure 3 2 ) Procedures for development of this novel EFA are presented. 3 1 Mid Rise Office Building s The structural steel building of interest was part of a n ational seismic research project in response to the 1994 Northridge earthquake (FEMA, 2000). Additional details regarding the historical relevance and incorporation into prior studies was discussed (Â§ 2 5 ). This mid rise moment resisting frame is ten stories. Hypothetically located in Boston, this design served as a cautionary example for consulting engineers in reference to seismic loading; i.e. although designed to code, the frame was known to be hig hly susceptible to collapse. Additional structure related information, extracted directly from the FEMA document, is included for reference (Appendix B ). 3 1 1 Development of F inite E lement Model of Ten Story Moment Resisting Steel Frame A significant portion of the numerical methods employed in developing finite element models of the ten story buil ding (Figure 3 3 ) were presented (Â§ 2 5 ). For example, the LS DYNA features selected for representing the steel connections in this study were analog ous, if not equivalent, to the Abaqus features employed in the antecedent research on connections (Yim and Krauthammer, 2009). A comprehensive discussion of the modeling techniques used in both the antecedent and present study is available (Yim, 2007). G iven the high level of similitude in the finite element models of both studies, the methods for the proposed finite element model are presented in cursory fashion. All finite element techniques have either been verified with high
60 resolution models compris ed of continuum elements fully and/or validated with structural experiments With respect to all steel connections throughout the building, the finite element models used here are computationally efficient numerical representations of the mid rise building In short, resultant beam elements represented beams, girders, and columns, with shell elements for the reinforced slabs. Connections were represented with springs nonlinear curves developed from prior efforts verified with continuum models (Â§ 2 5 3 ). 3 1 1 1 Boundary conditions Fixed supports are applied at th e base of all columns (Figure 3 4 ). Given this simplification of rigidity for the foundation, the slab on grade is not considered. For visual clarity, the fixed supports are shown with a two bay x two bay x two story frame. For additional information regarding the fixed based assumption, see Appendix B in Report 355C (FEMA, 2000). 3 1 1 2 Columns, girders, beams, and slabs a high story steel frame is beyond available computing res ources, and thus time prohibitive, especially if nonlinearities are considered. To circumvent such expense, a computationally efficient numerical representation of the building was developed (Figure 3 5 ). Fortunately, there are well established modeling methods capable As modeled, there are sixteen different (16) column cross sections and ten (10) beam profiles, or cross sectio ns one (1) in fill beam, one (1) interior beam, one (1) interior girder, and eight (8) exterior girders in the ten story structure. All structural element types were defined with unique profiles, represented with Hughes Liu beam elements with cross sectio n integration
61 (Hallquist, 2014). The material model was elasto plastic with a nonlinear constitutive definition using effective true stress and effective true strain, including strain rate dependency, and failure. The Cowper Symonds strain rate material model was employed with material dependent C and Q factors of 40.5 sec 1 and 5, respectively (Jones, 1997). Failure was strain based, occurring in the highly plasticized region at 0.2 in./in. executed with LS (LS DYNA, 2014 ). Slabs were modeled with fully integrated, selectively reduced 4 node shell elements. The material definition was an elasto visco plastic material with a prescribed stress strain curve and strain rate dependency. In addition, damage was considered befo re rupture/failure occurs, which was defined by tensile strength based strain. The LS DYNA material model selected (MAT_PLASTICITY_WITH_DAMAGE) most closely parallels the Abaqus specified CONCRETE DAMAGE PLASTICITY (CDP) material definition used by Koh (2 011). Further discussion regarding the material properties used, e.g. the selected uniaxial compressive stress strain curve, the post failure tension stiffening stress strain curve, and a number of plasticity parameters, are available (Koh et al., 2011). Cross sectional properties were calculated by the finite element code subsequent prov iding dimensional input. 3 1 1 3 Connections Reductionist modeling approaches are necessary due to the computational expense of discretely representing all of the structural components contributing to the connections in steel frame with continuum elements, e.g. bolts, welds, shear tabs, c oped flanges, etc. A series of antecedent CIPPS studies entailed the development of simplified models capable of mimicking continuum element only models with satisfactory precision and accuracy across all relevant time loading domains from impulsive to qu asi static. Highly nonlinear finite element analyses with
62 high resolution continuum models of steel connections were developed to verify the simplified connection models. These simplified models, comprised of nonlinear spring elements, were subjected to a n array loading scenarios to examine the efficacy of representing such complicated structural componentry. Degree of freedom specific connecting elements proved to be significantly more economical, computationally, without any meaningful loss in fidelity. An illustration depicting the incorporation of six degree of freedom bema elements at the connections is included (Figure 3 6 ). As shown in multiple prior studies (Yim & Krauthammer, 2007, 2009, 2010, 2012), resultant elements with rotational springs can represent complicated connections with accuracy, i.e. (nearly) numerically equivalent to the full continuum models. In lieu of the Abaqus specific a similar method capable of accounting for all of the energy within the system was employed using LS DYNA. Six (6) degree of freedom discrete beam elements, often referred to as springs, represented the connections (Figure 3 7 ). In addition, it is important to note this connection model was used for all connections in the mid rise steel building, as in fill beams are present throughout the entire structure (Figure 3 7 C ), which connects the in fill beams to girders, not columns. In a more recent study from this series of connection related research, Yim and Krauthammer quantified the significant contributions of the connections in a structural steel f rame to PC (Yim and Krauthammer 2012). Thus, the research presented here accounts for all connections throughout the framing system an additional step beyond any known research toward a more accurate assessment of collapse susceptibility. All curves used in this research were derived, either directly or with equivalent methodology, from prior CIPPS research (Yim and Krauthammer, 2009). This reductionist approach was taken by using results from separate,
63 more numerically sophisticated continuum models. I n antecedent studies, computationally expensive models comprised solely of high resolution continuum elements were developed and loaded in quasi static simulations. The resulting nonlinear strength, or M curves were installed at all (moment and shear) connections in the ten story steel building. As presented in detail above (Â§ 2 5 3 ), the nonlinear curves developed in the antecedent work were used (Y im, 2007). A more extensive discussion of the methods used to represent the connections is available (Yim, 2007). Performing highly nonlinear quasi static analyses using high resolution continuum models of small portions of the structure affords represent ation of complicated structural componentry with simplified spring elements. Although employing nonlinear curves to represent connections with degree of freedom specific springs, a vastly more economical computational effort is yielded without any meanin gful loss in fidelity. As shown in multiple prior studies (Yim & Krauthammer, 2007, 2009, 2010, 2012), resultant elements with rotational springs can represent complicated connections with accuracy, i.e. (nearly) numerically equivalent to the full continu um models. The primary structural members (columns, girders, and beams) are represented with resultant beam elements, the secondary structural members (slabs) are modeled with shell elements, and the connections are modeled with degree of freedom specifi c beam, or spring, elements. In addition to using the aforementioned springs for capturing the effects of connection strength, employing the material model discussed above allows the connection to not only transfer energy but also absorb and dissipate ene rgy as well. In addition, a material definition incorporating nonlinear strain hardening and strain rate properties was used. The selected element type and material definition have proven effective in prior studies e.g. Wilkes, 2002.
64 Multiple approaches to represent the behavior of the connections were performed. Although multitudes of alternatives were considered, they were found to be (theoretically) flawed. More specifically, none of the constraint techniques could be used as it was revealed (during analyses of all types considered, e.g. *CONSTRAINED_JOINT_SPHERICAL,) energy is dissipated during employment of the constraint itself. If this energy was of significantly small (relative) value, it could have possibly been overlooked. However, the outpu t used to report the energy time history of the connections was the s pring and d amper e nergy, which includes this energy associated with the joint constraints. This energy type was selected due to the use of translational and rotational springs installed at the connections. In short, the energy dissipation from the constraint could not be parsed from the energy dissipated from the joint through motion, without an additional sensitivity study. Thus, the energy associated with application of a constraint re lationship could not be quantified independent of the connection energy, and hence not allowing for a quantification of the contribution of the constraint to the overall energetic behavior of the connection. 3 1 1 4 Non structural The effects of non structural members (on the propagation of stress waves through a structure) in response to blast loads are not considered. A dditional information regarding the mid rise building and finite element modeling methods is available per Yim (2007) and Yim and Krauthammer (2009), respectively. Given the importance of connections, proven by prior studies, this additional improvement i n finite element modeling methods increased the likelihood the EFA would yield improved assessments of PC susceptibility, as well as the mechanics of PC once initiated. Although non structural building components were neglected for this study, the extent of the numerical representation of all structural components for a mid rise building is
65 novel, and the consequent correlation between member failure, the magnitude, and rate of energy flow, and the collapse susceptibility is unprecedented. 3 1 1 5 Gravitational loads Gravity loads, superimposed dead and live, were determined using ASCE 7 specified live load reduction facto rs for columns. Given the exorbitant nature of applying conservative loadings for all stories of a mid rise building intended for typical office utilization, reductions for the application of live loads were appropriate and necessary. Furthermore, it is important to note the se building designs for the SAC commission were developed to highlight the inadequacy of the building codes at the time. Thus, these frames would likely collapse under the governing load combinations for extreme/abnormal events withou t the code permitted reduction factors. However, it should also be noted that the live load reductions for beams supporting large floor areas were not utilized incorporated into the applied loading calculations. For reference, results from a multitude of in depth studies to determine the effective live loads in buildings for typical office environments are available, e.g. Mitchell and Woodgate (1971), McGuire and Cormell (1974), Culver (1976), and Ellingwood and Culver (1977). To elaborate on the methods employed for this study, gravitational loads were applied using two different combinations of dead (D) and live (L) load The F inite element building models follow ed the Alternate Path method provision in UFC 4 023 03. This method entails notionally remo ving a single column (Â§ 3 220.127.116.11) from a building that is subjected to 1.2 D+0.5 L per the Equation 3 19 load combination (UFC, 2014). F inite element m odels of building els capable of initiating PC. This entailed subjecting the structure to a load combination of 1.0 D + 1.0 L.
66 Per ASCE 7 (2002; 2005), both load combinations used particular dead loading constituents, e.g. ceilings and partitions, with the prescribed press ures, and 50 psf for live loading (Robertson and Naka, 1980). The global application of gravity activates the self weight dead loads of the structural members modeled, calculated from the prescribed material density and volume (via the defined cross secti ons and element lengths for columns and beams). Although the Alternate Path method specified single column level of damage may be insufficient to initiate PC, it is understood conservatism is included with the Alternate Path method by using factored load combinations and strength reduction factors. For all simulations, gravity loads were superimposed and applied as pressure to the slab shell elements in a pseudo static manner. Lateral loads, which are 0.2% times the unfactored sum of the (D and L) gravit y loads to be applied per floor one side at a time in combination with the gravity loads, as prescribed by the UFC 4 023 03 specification, Equation 3 20, may not be included, if possible. This potential exclusion of lateral loading is appropriate given th e intent behind the loading requirement is satisfied indirectly with asymmetry being an inherent result from with the application of damage to the structure in an asymmetric manner. 3 1 1 6 Air blast loads: damage yields per DSAS Simulations with increasing damage levels were performed, in an incremental fashion. Fundamental to the tertiary objective of determining the ef ficacy of the Alternate Path method the structural response to notional removal of a single column must be determined. Thus, the minimum level of damage considered was a failed single column only, commensurate with the Alternate Path method Essential t o the primary objective of assessing PC, the minimum damage level capable of initiating PC must be determined. Consequently, applied damage began with single column removal under both factored and unfactored load combinations; continue with
67 incremental in creases, and end ing with the minimum number of structural elements necessary to trigger PC. The specific sequence of failed structural members was determined by DSAS. The specific sequence of structural element failed, or removals, is critical for modelin g realistic damage levels, capturing the response of a structure to realistic threats, and determining the minimum damage necessary to initiate PC. DSAS was used to determine the incremental levels of damage (Figure 3 8 ) to be considered for the nonlinear transient dynamic finite element simulations from single column destruction to multiple member failure capable of initiating PC. Specifically, the time of failure of all members in the blast vicinity w as calculated determined by simulating explosions adjacent the column of interest using DSAS (Â§ 2 4 ). DSAS determines the time of failure with respect to the detonation mark for all structural elements necessary to initiate PC. Using the consequent array of time of failure data, the damage was applied to the LS DYNA building model in the form of incremental element removal, with one element removed per simulation. As damage levels increase, any type of structural element may fail, include connections, girders, beams, and/or slabs. In effect, this iterative process entails performing analyses in a specific sequence, in accord with the results calculated by DSAS. A description of the process employed to estimate damage using DSAS was presented ( Â§ 2 4 ). Additional information regarding DSAS is also available (Astarlioglu and Krauthammer, 2012). Using the two model types as defined with i n the gravitational loading discussion (Â§ 3 1 1 5 ), the first simulation was performed with the Alternate Path method design model. This initial simulation includes factored loads, whereas all subsequent simulations (wi th the analysis model) had non factored loads. All Alternate Path method procedures are followed per the UFC specification for the stated ten story building of interest, i.e. the nine story building with a single story basement. Additional details regard ing the Alternate Path method were provided (Â§
68 2 2 ). The first simulation with the PC analysis model included removal of the same column in the Alternate Path method design model, but with the unfactored g ravitational load combination, as discussed (Â§ 3 1 1 5 ). To maintain consistency between the Alternate Path method design model and the PC analysis model, comparative analyses was performed under analogous conditions. I n other words, the detonation was adjacent the notionally removed column from the design model when performing the DSAS analysis. For example, an exterior column near the middle of the long side of the building was removed in the design model per the Alte rnate Path method ( Figure 3 9 A ), and so this same column was subjected to an offset (hemi spherical) air blast loading in DSAS for the analysis model ( Figure 3 9 B ). All at ground level, air blasts were detonated at a corner column, the edge column near middle of the long side (as illustrated), and an interior column: comprising three unique air blast threat locations, or column removal, scenarios. For the corner and interior columns, the explosion was diagonally offset, at grade, perpendicular to column centerline, also resulting in a hemispherical shock wave. These location s are chosen to maximize damage to the affected column while minimizing damage to adjoining structural members. Additional details regarding the processes employed for applying blast induced damage are available (Wilkes and Smith, 2015). Although a significant number of various blast events were considered, it is important that man y threat scenarios were not simulated. For example, blast events above the bottom floor level were not considered. Although nefarious attacks ( like those becoming increasing common in unstable regions ) are typically LVBIEDs the tragedy at the Ronan Poin t apartments occurred on the eighteenth floor due to a gas leak. A lthough such threats are anomalous, these types of potential loading scenarios would need to be considered prior to incorporation of energies
69 approaches into design provisions. D etonation locations near the corner of the building and interior to the building were also exempt from this study. Such additional threats should be incorporated in future numerical research. Consideration of some of these additional threat scenarios is available (Wilkes and Krauthammer, 2016). I n addition, partially damaged structural element s i.e. not experiencing complete failure w ere not represented numerically. Although inherently conservative for the damage assessments for columns, partially damaged depic tion of various horizontally oriented structural elements is not necessary conservative. Such considerations are suggested for future numerical research. 3 1 2 Modified Version of the SAC Commissioned Mid Rise Building The ten story, or nine story with basement, building was designed to expose the shortcomings of the design provisions current at the time of the Northridge earthquake. Thus, a code complian t soft story was incorporated into design. This soft, or weak, story was achieved for all remaining stories above ground level. In addition, the W shape cross section for the interior column locations was for the second floor was chosen to be the same as for the shorter first, third, and fourth floors. Furthermore, the top of the basement level was considered to be laterally braced. Thus, the SAC commiss ioned design s were intentionally made to be susceptible to failure of the second floor for earthquake loading events. Although useful for illustrating the efficacy of the EFA methodology, modifications were made to this design in order to develop a second numerical model of a mid rise building frame. This modified building model is a better representative of typical mid rise office buildings, and with moment connections included for the N S column girder connections allows for additional insights into t he energy flow behavior during a PC event. All SAC commissioned
70 buildings were designed to expose the shortcomings of the design provisions current at the time of the Northridge earthquake. Thus, these building designs were not necessarily intended to be representative of typical mid rise buildings, more so to highlig ht the inadequacy of the design codes for protecting aga inst seismic loading events. Due to this atypical soft story nature of the SAC commissioned building, a second version of this same bui lding was analyzed. In short, this modified version is equivalent in all respects with the exception of the second story being reduced from eightee n feet to thirteen feet in height (Figure 3 10 ) and the inclusion of moment resisting behavior for the girder column connections in the interior of the building, as was done in the preceding moment connection modeling research (Yim, 2007). 3 2 Energy Principles 3 2 1 Energy Flow Analyses using LS DYNA Energy principles used in the antecedent study, namely conservation of mechanical energ studies consider mechanical energy forms only. By removing extraneous terms and including the energy released with member failure, LS Equation 2 6 can be redefined as: ( 3 1 ) where I str is the internal strain energy, U grv is the potential gravitational energy, and ( I str + U grv ) is the total energy released from the removed, or failed, structural member(s). The additional energy summation term is included to represent the energy from removing a structural element, known to be proportional to the releas ed strain and gravitational energies. Removing failed structural members from a structure causes the transfer of potential energy to kinetic energy and recovery of elastic strains. In other words, every nonlinear transient dynamic finite
71 element simulati ons imbalance in the internal energy distribution, continuing until a new state of equilibrium, including collapse, is achieved. 3 2 2 Incorporating the Rate of Energy Flow There are multiple reasons in which the rate of energy flow should be considered when determining failure, and consequently studying PC In the interest of bre vity, only material behavior is discussed. Material behavior is substantively rate dependent, as briefly mentioned in relation to the mechanical engineering research on vibrational and acoustical behaviors. Dusenberry points out in Â§ 15.2.2 Connection Du ctility (pg. 386) and references in Chapter Seventeen (pg. 450) of Handbook for Blast Resistant Design of Buildings (2010), prior studies have clearly shown the differences in material behavior between dynamic and impulsive loading events can be highly dis similar (Malvar, 1998; Malvar and Ross, 1998; Crawford et al., 2001a; Crawford, 2001b). Other researchers have delved more deeply into material science to Alth ough such research is beyond the scope of this proposal, it is widely known loading rates cause changes in the observed behavior of structural materials. Material evolves from behaving elastically to plastically to fracture based, as the applied loads cha nge from the static to plastic to impulsive domains. Therefore, material behavior is flow rate dependent. Thus, the proposed work incorporates the rate of energy flow as an additional parameter for determining failure constituting a novel component of th e proposed research. In addition, it is important to note that the effects of rate on failure were investigated more extensively in the antecedent CIPPS study by Tsai and Krauthammer (2015). This prior study developed failure thresholds for not only an in dividual behavioral mode, but also for multi mode behavior (Figure 3 11 ). More details regarding this effort are detailed below.
72 3 3 Fl uid Energy Flow Analogy of the EFA Strictly speaking, energy is not visually observable. So, to communicate the proposed EFA in a visual manner a conceptually analogous system comprised of physica lly representable parameters is offered. Two fluid ener gy analogy illustrations are provided. The first was developed in the antecedent study by Tsai and Krauthammer, and best explains the energy flow behavior into, within, and out of a single structural element (Figure 3 12 ). The second was developed uniquely for this study and although it illustrates energy flow through a single structural element (Figure 3 13 ) it adds a dimension of magnitude to convey the relative energy form contributions Each energy form present within a structural element is represented with a tank. The fluid volume inside a given tank corresponds to the magnitude of energy flow ( E ) for a given form of energy, e.g. E K is the kinet ic energy. Thus, volumetric flow rate per tank represents energy flow rate ( ) for each energy form considered; e.g., PS is the internal plastic strain energy rate In accord with the cumulative nature of energy flow, the rate of energy flow within a giv en structural element ( ) is the summation of all (three) energy forms considered elastic strain ( ES ), plastic strain ( PS ), and kinetic energy flows ( K S ), per Equation 3 7 Consequent ly, energy flow ( E ) is the summation of elastic strain energy ( E ES ), plastic strain energy ( E P S ), and kinetic energy ( E K ). The rate of energy flow into a structural element ( I N ) is the sum of energy absorption rates of all forms per Equation 3 5 Mo re accurately the rate of input energy is initially absorbed internally as elastic strain ( ES IN ). If loading continues beyond the onset of yielding, input energy is absorbed internally as plastic strain ( PS IN ) This transition from elastic to plastic strain corresponds to the transition in material behavior from the linear elastic region to the non
73 recoverable nonlinear inelastic region as the element begins deforming plastically In addition, the rate of input energy is also transferred into the rate change of kinetic energy ( K IN ) through movement of the structural element. In compliment to the influx of energy, t he rate of energy flowing out of a structural element ( OUT ) is the summation of energy flow rates transferring to adjoining components through elastic strain ( ES OUT ), plastic strain ( PS OUT ), and kinetic energy ( K OUT ) per Equation 3 6 Using these definitions, the rate of energy flow absorbed into the element, the rate of energy transferred to con necting element(s), the rate of energy flowing through the element, and the energy flow in the element is defined by the following, respectively: ( 3 2 ) ( 3 3 ) ( 3 4 ) ( 3 5 ) ( 3 6 ) ( 3 7 ) The sum total ta nk capacity depicts the magnitude of energy flow threshold, E FAILURE the point at which failure occurs given the magnitude, or level, of energy flowing through the is threshold is the sum total of internal (elastic and plastic strain) and kinetic energy flows, but indicates failure occurs by means of excessive plastic deformation of the element material. Similarly, the change in the sum total volume per unit time of all three energy types is also limited with a rate of flow threshold, FAILURE which unfortunately is not depicted in the fluid analogy diagram. However, a non mechanical visual of the rate of energy flow parameters is
74 shown with positive ( ) and negative ( ) arrows for the plastic strain energy tank. An analogous non mec hanical visual for the elastic strain and kinetic energy tanks is not included for clarity. Analogous to E FAILURE FAILURE is the point in time at which failure occurs given the rate of energy flowing through the member. The magnitude and rate of energy flow thresholds, are not only temporal and dynamic, they are interactive and interdependent. In the context of the fluid energy analogy, the proposed approach entails recording the E time history for all structural components. This data was then be post processed to calculate the IN , and OUT The resulting time histories were analyzed to determine if and when, a structural element fails. Extending the fluid energy analogy from energy forms to behavioral modes, failure can be depicted for a given model of failure (Figure 3 14 ). This is significantly different, as this tank represents a behavioral mode (of failure) and the prior illustr ation represented energy modes, recall Figure 3 13 An extended version of this fluid energy analogy in terms of mode of behavior (Figure 3 14 ), a diagram analogous in breadth to the fluid energy an alogy in terms of energy forms, recal l F igure 3 13 Although illustrating the energetic behavior of a single element inside a larger structural system with the flu id flow diagram is instructive, recall Figure 3 13 this diagram does include multiple unintended inaccuracies and over simplifications. First, energy flow and energy flow rate are not only interactive, which is not visually represented, but the interdependency between these parame ters is dynamic. Prior research (Tsai and Krauthammer, 2015) revealed the strength of a structural member is a function of energy flow magnitude and rate, illustrating the Second, these two energy parameters also interact with the energies in connecting elements. Although there is visual reference to adjoining members with one input and four
75 output pipes, there is no physical representation of the adjoining members, much less interactio n with the energy in the illustrated member. Although not represented, it is known the cross section, material properties, and structural parameters of adjoining members have the utmost effect on energy flow in and out of any connected structural element. A third significant over simplification is flow directionality. Energy flow is not bi directional, much less unidirectional. The energy in any given structural element flows in 3 D, thus a 4 D problem when considering time. Analyzing, and hence describ ing, such phenomena becomes significantly more complicated due to the additional complexities from accounting for the energies in adjoining structural members a nd the energetic interactions between members. Subsequent the first energy pulse which travel s from the failed member to and through, all adjoining members, energy flow is highly complicated. Ensuing pulses flow in all directions, with varying wavelengths, frequencies, and magnitudes, yielding additive, subtractive, and other complicated energy f lows. As shown, energy is transferred in many directions, many times. For example, even the simplest 3 D frame, examined in the following section, exhibited complicated energy flows in response to the removal of a corner column. For a structural system that is neither significantly overdesigned nor highly susceptible to PC i.e. essentially non redundant, the structure must transfer energy in order to regain stability. Thus, arresting PC requires accommodating highly complicated energy flows not only wi thin a structural component but also between structural components and throughou t the entire structural system. The following is provided in addition to the energy form based fluid energy analogy. Due to the incomplete nature of the energy form based anal ogy, recall Figure 3 13 a structural mode of behavior based analogy is below (Figure 3 15 ). For example, Behavioral Mode A could refer to a crushing failure response, Behavioral Mode B could refer to a localized shear response,
76 and Behavioral Mode C could refer to a global flexural response. Thus, the following illustration is provided to stress the importance that the fluid energy diagram illustrate s the behavior of a structural element is limited to a single behavioral mode, and is thus inadequate to describing the energy flow behavior in a comprehensive manner. 3 4 E nergy F low A ppro ach (EFA) Although conceptually equivalent for all moment resisting frames, the simple (single bay single story) frame was selected to present the proposed EFA in the most concise manner. Consequently, some efforts that would be present for a larger struc ture were excluded due to analyzing a 3 D single bay frame. Pre analysis calculation of energy flow thresholds for the failed beams and slab were also not included. In addition, quantifying the scaled distance yielding damage commensurate with removal of single column was not performed. These items were intentionally excluded given the ancillary goal of analyzing the efficacy of the Alternate Path method is of negligible value for a simple 3 D frame. Although not included in the proof of concept analysi s presented above, force and stress time histories were analyzed for the mid rise building. The absent results and analyses from review of the simple frame simulations, to be applied when analyzing the three story office building (Â§ 2 5 ), are discussed in the following sections to provide a more comprehensive description of the proposed work. 3 4 1 Determination of Energy Flow (Magnitude and Rate) Failure Thresholds The EFA presented with the single bay frame included several simplifications. For example, vertical propagation of failure is impossible in a one story structure. In reality, continui ng failure through the vertical load bearing system is most catastrophic, and th u s it is the principal focus for progressive collapse mitigation. To aid in identifying failure in the vertical load bearing system, and provide a measure of quality assurance two series of nonlinear transient dynamic finite element simulations with single columns represented with both resultant
77 beam elements and continuum elements was performed prior to analyzing the mid rise frame. In contrast to the single column model ill 3 16 ), the single columns models had significantly higher mesh resolutions. All columns underwent loading simulations to a collapsed state well beyond initial (global buckling) failure, where failure is defined as the inability to carry permanent static loading. Only column failure was simulated, as all moment connections are measurably stronger than adjoining structural elements. Failure is a function of ener gy flow the combination of flow magnitude and flow rate. Given this co variable functionality, a s eries of nonlinear transient dynamic finite element simulations was performed to determine failure as a function of both energy flow parameters Although it is understood that progressive collapse occurs in the pseudo static domain, the range is undefined, thus a series of simulations were performed to describe failure throughout a measurably wider spectrum. In the interest of prudency, the load duration in these column collapsing nonlinear transient dynamic finite element simulations ranged from the dynamic domain ( 0.1 seconds) well into the pseudo static domain ( 10 seconds). Both energy flows corresponding to failure were recorded throughout this wider time spectrum. Analysis of the histories for all (near) collapsed columns against these predete rmined energy flow thresholds. To elaborate on develop ing the failure threshold for the columns that exp erience buckling, a study was performed on a single second story supporting column. To incorporate the time dependent aspect of the individual structural components, energy based failure thresholds were developed. Using a matrix of loading conditions var ying both the quasi static and (dynamic/impulsive) rates of loading for multiple degrees of freedom, failure curves were developed as a function of load and loading rate, and consequently, en ergy flow and energy flow
78 rate An example of one series effecti vely an array of collapse simulations within a larger matrix is shown with a curve fit of the force as a function of the loading rate (Figure 3 17 ). The energy flow and energy flow rate corresponding to each one of these data points was extracted to develop the failure threshold for that individual structural member. These matrices of loading conditions provide us with a better understanding of the structural elements behavior across all potential domain s. Hence, the application of an energy flow approach extends beyond impulsive loading events such as blast, throughout the dynamic region, e.g. earthquake events, and into the quasi static regime. 3 4 2 Rational for Selection of Mid Rise Building Structure Prior work has shown that localized failure does not typically extend beyond five stories from the initially failed region (Kirby, 1997; British Steel plc, 1999; Lennon, 2004). Accordingly, a structure more than five stories is necessary when considering, and thus for analyzing progressive collapse In addition, the concern for progressive collapse is proportional to the height of the structure. Low r ise structures are not typically relevant to progressive collapse phenomenon as there are insufficient degrees of separation in the vertical load carrying system between the localized failure region and the full structure. In other words, the structure do es not have sufficient vertical scale to provide opportunity for the ultimately failed region to be disproportionately larger than the initially failed region. To expand on the selection of analyzing a mid rise office building, the following is also consid ered. The ten story, or nine story with a single story basement, building may also prove more useful than the three potentially higher sensitivity to energy flow rate. Significantly taller, th e ten story building has significantly higher internal energy levels in columns near the base of the building. If buildings collapse over a similar span of time, i.e. regardless of the total height of the structure, the
79 collapse of the vertical load carry ing system in taller buildings are more sensitive to energy flow rate. In other words, if energy dissipates through column failure within a similar span of time, progressive collapse would be proportional to the height of the structure. Szyniszewski revealed a narrow range of loading rates (1000 2000 kip/s) were observed, regardless of the loading conditions or damage applied, in both the single column and three story building simu lations (2009). However, this narrow range of loading rates, and hence assumed energy flow rates, may apply low rise buildings only. The antecedent study ( Szyniszewski and Krauthammer 2012 ) analyzed two similar low rise structural frames only. So, multip le progressive collapse events of the ten story frame were simulated to determine if column loading rates exceed 3000 kip/s for a mid rise building. In other words, energy flow rates for mid rise structures were investigated by looking at realistic loadin g rates pending a wide variety of structural damage scenarios. 3 4 3 Analysis of Building Response to Incremental Damage As shown with the simplified fram e, results from the progressive collapse simulation were analyzed to reveal the energy failure correlation. Energy flow was extracted, processed, and differentiated to yield energy flow rates. More specifically, energy time histories of all failed memb ers was analyzed for progressive collapse inducing simulations, focusing on the levels of both energy flow parameters at the time of collapse for each affected structural element. Analysis of these simulations focused on identifying energy damage correl ations by examining how collapse progresses through the structure specifically, timing, location, and consequent sequence. Energy flow, both magnitude ( E ) and rate ( ), were calculated from energy input and the associated rate ( E IN and IN ), and energy ou tput and the associated rate ( E OUT and OUT ) to identify if, and when the structural element under consideration fails. Both energy time
80 histories were compared against the pre calculated thresholds discussed (Â§ 3 4 1 ) to determine if collapse corresponds to failure in the finite element model In other words, failure progression through the structure was compared against the energy time histories of individual structural members to seek correlation be tween the time at which failure occurs and energy flow. flow substantiated the efficacy of the EFA presented. 3 4 4 Incorporation of Connections as Structural Elements The simplified test frame did not consider connections. The test frame model, with lected the connections. For the proposed work, the strength of the connections was considered as well as the associated energetic behaviors, i.e. transmitting, absorbing, and, dissipating energy. Further details regarding the proposed modeling methods we re presented (Â§ 2 5 3 and Â§ 3 1 1 3 ). The story building with full rigid moment connections could withstand the 5 column removal case while only three column removal collapsed the building with the moment connections whose stiffness and brittleness are 3 4 5 Energy Flow B ased Response States for Evaluation of Alternate Path M ethod To improve understanding of structural behavior as defined by energy flow, analyses of energy time historie s and resulting energy rate time histories corresponding to three response states may serve as rational reference points allowing for a more in depth review of the Alternate Path method The selected response states are a) damage incurred is energetically equivalent to a single column removal, b) damage results in failure of the column with realistic damage sustained by adjoining structural members, and c) the energy flow thresholds at the onset of
81 progressive collapse initiation The damage criteria for the first two response states were determined in part, with DSAS, and the third with a combination of DSAS and LS DYNA. The energy flow corresponding to a single column failure was determined by means of examining permanent deformation and/or the remainin g strength of the weakened structures. Additional efforts identified the scaled ranges corresponding to the other aforementioned categories. In part due to the energy flows associated with the behavioral responses being successive, with no two points bei ng coincident, these three energy flows based on analyses with realistic damage levels yielded four (4) response categories (Figure 3 18 ) Graphical representation helps illustrate the correlation betwee n the Alternate Path method and nonlinear transient dynamic finite element simulations The illustration is also included to aid in convey ing that designing a structural frame to withstand removal of a single column is providing the absolute minimum level of redundancy in the vertical load carrying system Figure 3 1 Energy based load impulse failure threshold
82 Figure 3 2 Flowchart of Analytical Process
83 Figure 3 3 LS DYNA Model of SAC commissioned Mid Rise in Boston Figure 3 4 Bounda ry conditions: fully fixed columns bases (Note: Two bay by two bay by two story frame for illustration only)
84 A B Figure 3 5 Simplified model of single bay frame using resultant elemen ts A ) Resultant beam elements represent columns and girders (cross section not shown for clarity). B ) Column and girder resultant beam elements shown with shell elements representing slab Figure 3 6 Connections m odeled with s prings r eferencing n onlinear s trength c urves (Illustration limited to one (1) degree of freedom specific spring at four connections for clarity)
85 A B C Figure 3 7 Isometric v iew of LS DYNA m odel. A ) Single bay with beams and connections rendered B ) 6 degree of freedom beams represent all g irder to c olumn connections C ) 6 degree of freedom beam elements represent all i n f ill b eam to g irder connections
86 Figure 3 8 Sequence of failed members as determined with DSAS analyses. A B Figure 3 9 Elevation of mid rise office b uilding A ) Location of n otional ly removed c olumn B ) Location o f deto nation in DSAS
87 A B Figure 3 10 Elevation of ten story m oment r esisting steel frames modeled A ) SAC commissioned mid rise in Boston with eighteen foot second story. B ) Modified version of same building design with second story reduced to thirteen f ee t. Figure 3 11 Typical energ y based P I diagrams for multi failure modes. [Reprinted with permission from Krauthammer, Theodor. 2015. Energy Based Load Impulse Diagrams for Structural Elements. PhD dissertation (Page 124, Figure 3 12). University of Florida, Gainesville, Florida .]
88 Figure 3 12 Illustration of energy tank analogy. [Reprinted with permission from Krauthammer, Theodor. 2015. Energy Based Load Impulse Diagrams for Structural Elements. PhD dissertat ion (Page 123, Figure 3 10). University of Florida, Gainesville, Florida.]
89 Figure 3 13 Illustration of f luid e nergy c onceptual a nalogy A B Figure 3 14 Flexural f ailure c orresponding to m agnitude of e nergy f low t hreshold o nly ( threshold, interaction between energy modes, and adjoining members ignored for clarity) A) Bending only behavioral response mode. B) Fluid tank corresponding to bending behavioral response mode.
90 Figure 3 15 Alternative i llustration of f luid e nergy c onceptual a nalogy for a s ingle s tructural e lement in terms of structural behavioral modes Figure 3 16 Finite element mod
91 Figure 3 17 Loading rate buckling failure of eighteen foot columns supporting second story of the SAC commissioned mid rise building model Figure 3 18 Behavioral Response Comparison between nonlinear transient dynamic finite element simulations (NTFES) and Alternate Path method
92 CHAPTER 4 RESU LTS The Energy Flow Approach (EFA) presented here addresses multiple research objectives with a rational and highly accurate methodology. The primary was to develop an analytical framework capable of demonstrating a successful assessment of progressive co llapse susceptibility with an accuracy and precision on par with the most rigorous state of the art nonlinear transient dynamic finite element analys e s A n energy flow based presentation of energy time histories corresponding to structural instability (Â§ 4 1 ) demonstrates the EFA detailed here satisfied this primary objective. T he evidentiary support for concluding this EFA is effective is done using the results from a non collapse building response compared against a collapse inducing simulation In addition, the efficacy of the Alternate Path method for typical mid rise moment resisting steel framed buildings was evaluated With the Alternate Path method being a threat independent notional approach, this m ethod was evaluated for mitigating progressive collapse As expected, the damage induced from realistic explosive threats was not commensurate with failure of a single column. It is important to note the results from the two initial damage states discuss ed in the following section illustrate the efficacy of this EFA (Â§ 4 1 ) are commensurate with viable blast loads corresponding to LVBIED s or similar both of which are orders of magnitude, in terms of scaled d istance, from a single column removal, i.e. the Alternate Path method The tertiary goal entailed determining the extent of redistribution for blast loading threats that do no induce collapse, i.e. non collapse loading events E ffective stresses and strai ns were analyzed to identify where the effects of a variety of initial damage conditions stopped.
93 R esults for these three goals the primary, secondary and tertiary are presented accordingly, i.e. in order of importance: efficacy of the EFA (Â§ 4 1 ) efficacy of the Alternate Path method (Â§ 4 4 ) and the determination of the extent of redistribution is tertiary (Â§ 4 5 ) To aid in identifying the limits, or the applicability, of the novel EFA offered, the structures considered in this research were derived from the SAC [a joint venture (JV) of the Structural Engineers Association of California (SEAOC), Applied Technology Cou ncil (ATC), and California Universities for Research in Earthquake Engineering (CUREe)] commissioned mid rise building in Boston This ten story frame includes a single story basement, moment resisting WUF B connections, and single plate (shear tab) conne ctions (FEMA, 2000). Although all numerical results are structure specific the proposed EFA methodology can be to any ( moment resisting ) struc tural frame In fact, assuming a reliable resistance function for all potential failure modes can be calculated any structural system could be analyzed for failure with the proposed EFA for any loading events from impulsive to quasi static 4 1 Non Collapse vs Collapse of SAC Commissioned Buil ding Model The thesis of th is research is that energy flow ( E and ) determines failure. The energy failure correlation is inherent in physical systems, and exists in nonlinear transient dynamic finite element software because the development of these n umerical codes is based on energy equilibrium principles. Hence, progressive collapse ability to accommodate energy flowing through its components, which is a function of constitutive material definitions, cross sectional properties, and structural parameters. Given these understandings, energy time history, quantifiable with nonlinear transient dynamic finite element simulations was extracted, post processed, and compared to the behavior of the finite element m odel to determine the efficacy of using energy flow to predict progressive collapse susceptibility
94 Initially, the energy failure relationship was described using the results of analyses with a FEM of a simple 3 D frame (Figure A ) Execution of the proposed methodology on a simplified structure provided data that helped serve as a guide for best potential approaches when subsequently analyzing the larger mid rise building frame. Following success with t he preliminary simple frame, the effects of loading rates were examined further Specifically, the effects of loading/energy flow rates of a variety of columns within the mid rise structure of interest were analyzed in multiple sub studies (recall Figure 3 17 ) Following these results, the EFA was applied to a two bay by two bay two story portion of the SAC commissioned mid rise steel frame in Boston (Figure A 9 ). This larger frame was more complex not only due to more members, but also because significantly complicated techniques were employed to represent the column to girder connections. The connection modelling methods employed were not only theor etically consistent with the EFA a allowing for a comprehensive account for all energy forms, but all degrees of freedom were accounted for with nonlinear curves. The moment rotation degrees of freedom were derived from the curves developed from discrete models of the connections, and the translation curves from calculations incorporating the weakest connecting elements for the degree of freedom under consideration (Yim and Krauthammer 201 2 ) Following the se preliminary studies, the EFA was subsequently a pplied to the SAC commissioned mid rise steel frame building in Boston (recall Figures 2 7 and 2 8 ) To summarize this process, energy flow based fai lure thresholds were developed from analyses of individual structural elements (recall Figures 3 16 and 3 17 ) per the methodology developed by Tsai an d Krauthammer (2015). Utilizing these energy flow thresholds the sequence of members (nearly) exceeding these capacities were compared against the structural response observed from
95 the midrise finite element model s under consideration for a variety of bl ast induced damage conditions (Table 4 1 ). A flowchart of this method was provided (Figure 3 2 ). Consequently the efficacy of the proposed EFA to pro vide a rational means for progressive collapse was realized. To provide some additional information regarding the challenges encountered during the development and verification of the EFA, the following is offered. Out of concern that the preferred failur e indicating parameters, i.e. yielding the highest correlations, may differ between the simple frame model and the mid rise steel framed building multiple mini sensitivities studies were performed. For example, energy flow rate ( ) and displacement may y ield the highest correlation for simulations with the test frame, but plastic strain and both energy flow parameters ( E and ) may yield the highest correlation for simulations with the mid rise building. Regardless of the chosen parameters, the result s r eveal a reliable approach for damage specific assessments of progressive collapse After patterns suggesting correlation between energy flow and failure were identified, research efforts were focused on presenting a formalized EFA. Upon completion, result s showed the proposed EFA is more accurate and precise than traditional force based approaches. In addition, the EFA presented yielded superior assessments of progressive collapse than the antecedent energy based approach by Szyniszewski (2009). The ener gy failure relationship being proven by the antecedent study (Szyniszewski and Krauthammer, 2012), combined with understanding the rate of energy flow affects structural behavior, the proposed work promises an accuracy and precision beyond any known appr oach to progressive collapse This is expected given the additional considerations of modeling the structural connections, incorporating energy flow rates into failure prediction, and all done for a progressive collapse relevant mid rise steel framed buil ding
96 4 1 1 Global View: System Wide Energy Flow From a global perspective, information regarding the stability of the structure can be obtained fro m even the most superficial review of system wide energy time histories. If energy time histories reach equilibrium within a scale of the energy levels measured at the onset of the simulation, i.e. initial, albeit post blast damage, conditions, it is unde rstood that failure of any additional structural members has been arrested (Figure 4 1 A). More succinctly, progressive collapse does not occur. In contrast, when system wide energy increase markedly bey ond the initial system energy level, a catastrophic collapse event has occurred. To elaborate, the structure has become unstable, and this monumental release of energy is obvious well before the deformations and displacement become large enough to indicat e collapse is imminent (Figure 4 1 B). In addition to the stress contours plots in the frame referenced above, plastic strain contours are also provided for all of the structural elements to help illustra te the differences in the progression of failure, or lack thereof, throughout the model of the mid rise building frame. Plastic strains for all beam element types columns, column to girder connections, girders, girder to infill beam connections, and in fi ll beams are shown in Figure s 4 2 A and 4 2 B. Plastic strains for all shell element types, i.e. slabs, are shown in Figure s 4 2 C and 4 2 D 4 1 2 Local View: Energy Flows of a Critical Column To il lustrate variances in the energy flow at the local level, an individual column critical to the response of the structure was selected (Figure 4 3 ). Given the detonation location, various blast induced damage asses sment s considered, and origination of the failure progression observed, this second story first interior column is the most critical column for indicating a progressive collapse. In short, this column is the first to fail if a progressive collapse event i s going to occur. For this column location, the energy flow energy flow rate history for a damage condition on the lower spectrum of damages assessed in this study is provided (Figure
97 4 4 ). In additi on, for this same column location, energy flow energy flow rates are provided for a larger number of simulations conducted (Figure 4 5 4 5 ). As indica ted, superimposing the energy flow versus energy flow rate time histories of this column on top of the energy based load impulse failure threshold yields and accurate and precise, i.e. repeatable, collapse prediction. In the interest of brevity, not all c onditions simulated are discussed in detail here. However, a more comprehensive report with results from additional simulations is available (Wilkes and Krauthammer, 2016). 4 2 Two Collaps e Scenarios with the Modified SAC Commissioned Building Model Despite the final states of total building collapse for both of the simulations discussed in the following sections, the energetic behavior of the building model due to different initial blast i nduced damage states is strikingly different. The lower damage state considered consists of the removal of five columns and ten beams (Figure 4 6 A) The higher damage state considers the removal of fiv e columns and eighteen beams (Figure 4 6 B) Although both simulations result in a progressive collapse event, the behavior of the damaged structural frames is markedly different, which is illustrated wi th differences in the energy time histories at the global, regional, and local levels. The following investigation constitutes a novel analysis of the behavior of buildings 4 2 1 Global View: System Wide Energy Flow The analogous information presented for the finite element model of the SAC commissioned mid rise design in Boston above (Â§ 4 1 ), is presen ted for the modified finite element model with stiffened N S column connections and soft story eliminated (recall 3 10 ) Although not apparent from observing the deformed state of the building models as far along as thirteen seconds after the application of the blast induced damage (Figures 4 7 A and Figure 4 7 B), both buildings are in a state of comp lete structural collapse. As observed from the overall
98 system energies for the non modified building model, the stability of the structure can be obtained more astutely and rather quickly from observing the energy time histories ( Figure 4 7 C). To contrast the response of these two damage scenarios, the energy flow is plotted against the energy flow rate (Figure 4 8 ). In short, the energy flow rate of the damage severe blast induced damage assessment with eighteen columns is severe at the onset of the numerical analysis. Although this significantly higher damage incurred yields a more vulnerable structure, thus f ailure propagates more rapidly. 4 2 2 Local View: Energy Flows of a Critical Column Results from the same critical second floor column for the non modif ied building model are provided here for the modified building model (Figure 4 9 ). Since both of these simulations yield a prediction of total structural collapse, the differences in the energy time histo ries for this critical column is not instability vs stability, but with the differences in the rates of energy flow and thus the point at which collapse occurs (Figure 4 10 ). In addition, the energy tim e histories for this column with the initial damage state including the removal of eighteen columns also indicates the point in time in which the element fails beyond local buckling and is partially removed by means of element deletion a condition reache d due to a plastic yielding to a strain of 0.20 mm/mm. The energy flow vs energy flow rate s for this column for an array of initial blast induced damage assessments (recall Table 4 1 ) are provided (Figur e 4 11 ). Again not all conditions simulated are discussed in detail here in the interest of brevity, but a more comprehensive report with results from additional simulations is available (Wilkes and Kr authammer, 2016). 4 2 3 Regional View: Furcating Energy Flows Due to the soft second story of the SAC commissioned mid rise building, a modified (numeric al model) version of this design was developed more representative of typical mid rise
99 office buildings. The modification s to the SAC commissioned building design w ere reduction of the second story from eighteen feet to thirteen feet and stiffer N S colum n to girder connections. With this modified version of the mid rise building, differences in the energy flow behavior were observed. Although both simulations result in catastrophic progressive collapse scenarios, the behavior of the structure s between th e initial blast induced damage state and the final collapsed state are drastically different. The energy flow based comparison could be described as an antithesis of the butterfly effect whereby infinitesimally small differences in the initial input condi tions yield drastically results. In contrast, a markedly different set of initial conditions yield ed the same result a fully collapsed structure. However, as demonstrated, the likelihood of collapse is a path dependent process, and the two simulations in comparison here exhibit different behavior The two scenarios under review consist of an initial damage assessment of five columns and ten beams (Figure 4 6 A ) and an initial damage assessment of five co lumns and eighteen beams (Figure 4 6 B ). Specifically with the removal of an additional eight beams along the exterior face of the building ( adjacent the blast location ) the structure with the initiall y assessed higher level of damage experiences an approach towards collapse in a more accelerated fashion. Conversely, t he structure with ten removed beams approaches a structure wide collapse in a slower fashion. This is primarily due to the a significan tly lower energy flow rate at the beginning of the simulations due to the presence of the exterior column to column girders on the third, fourth and fifth floors. Interestingly, neither building models succumb to collapse until more than ten seconds after the initial blast induced damages are applied. A series of isometric views with corresponding energy time histories, emanating from the base of the first interior column on the second floor, adjacent the detonation location, through the connections and i nto
100 the girders is provided (Figures 4 12 through 4 19 ). In short, this sequence of energy time history plots illustrates the delay of energy flow fo r the ten beam damage scenario in comparison to the eighteen beam scenario. The energy time histories for all second floor columns of both damage scenarios for the modified version of the SAC commissioned building model are provided (Figure 4 20 ) to illustrate the energy behavior comparisons discussed above are representative of the entire second floor, and not a localized behavioral phenomenon. Please note the discontinuity in the energy time histories for many of the columns in Figure 4 20 B correspond to column failure by means of element deletion, as defined by a strain of 0.20 mm/mm. In addition, i t is important to note the energy levels shown in the energy time histories due not necessarily correspond to damage levels or proximity to collapse. 4 3 The SAC Commissioned vs The Modified SAC Commissioned Building Model The modified SAC commissioned building model included two changes to the original SAC commissioned building model. The first change entailed reducing the height of the second story from eighteen feet to thirteen feet and the second change entailed strengthening the North South column to girder connections were from shear to moment resisting. Although a number of significant behavioral changes resulted from these two modifications, the consequential effect with respect to initiating a PC event was not markedly differen t. In effect, the increased robustness of the SAC modified building model translated to the removal of one additional exterior column for an exterior detonation offset along the side of the building. A tabulated list of the collapse results for exterior side air blasts at ground level simulated for both mid rise building frame models is provided (Table 4 1 ). 4 4 Efficacy of Notional Sing le Column Removal The first ancillary po rtion of th is work focused on determining the efficacy of the Alternate Path method for mitigating progressive collapse for mid rise steel buildings, and
101 potentially setting limits for appropriate used of the Alterna te Path method ; e.g. quantifying an energy load limit for application the Alternate Path method Alternate Path method is unconservative once the imposed threat level causes damage in excess of failure of a single column. In a ddition, this energy level is expected to be less than the energy required to initiate progressive collapse As indicated from prior research studies and course teachings at CIPPS, DSAS was utilized to develop numerical representation of damaged structura l members following prescribed air blasts. The results were then be transcribed into the LS DYNA model in the form of member removal. In short notionally removing a column was compared with DSAS calculated damage To expand on this effort, localized dam age was applied to a complete building frame model, improving understanding of the relationship between localized damage and progressive collapse A gain, this portion of the proposed research compares results from using the UFC prescribed Alternate Path m ethod with a more realistic case specific threat, both using a FEM of a ten story moment resisting steel building. Namely, disparities between notional removal of a single column and damage resulting from realistic threats may demonstrate when the Alterna te Path method becomes unconservative, and thus insufficient to prevent progressive collapse If the Alternate Path method is determined to be of value, limitation of the Alternate Path method may be provided, e.g. a scaled range for a given structural sy stem. Results from this ancillary portion of the research aided in describing the efficacy of the threat independent Alternate Path method design provision for mid rise moment resisting steel frames. In short, realizing minimum redundancy does not equate to attaining the robustness needed to susta in a realistic explosive threat.
102 4 5 Extent of Redistribution An extensive series of experimental studies were performed to research the effects o f severe fire loading scenarios in multi story steel structures frames (British Steel plc, 1999) Although the loading events under consideration were a variety of fire scenarios, i.e. different from blast induced scenarios, researchers learned about the extent of the effects throughout the entire frame resulting from a loading condition causing localized failures. The results from this work helped to answer how many stories are required to support a frame structure above a decimated story. In other word s, the question of concern deals with determining how far (vertically) the effect of a removed column travels up a typical structural steel frame. In short, four to five stories above the failed members experienced increased loading. Thus, a loading scena rio in which localized damage is applied, on the order of multiple structural members including no less than one column, requires approximately four stories of framing above the damaged area in order to supporting the hanging portion of the structure, or study correspond well with the prior research conducted in the UK. In effect, no less than four stories were required to support the damage story for the steel st ructure considered in this study. 4 6 Recommendations Given the successful correlation shown between energy flow, energy flow rate, and failure, and thus consequently, the relationship betw een energy flow and the susceptibility to catastrophic collapse, the following includes a number of potential research endeavors intended to extend the aim of the present study. Such efforts could advance progressive collapse assessment methodologies for the protective structures industry. To start, development of failure thresholds for all viable failure modes as well as mixed mode failures is suggested. An extension of the success of the preceding work by Tsai and
103 Krauthammer (2015) would greatly furthe r the potential for the inclusion of energy based methodologies into structural engineering practice. Such a library, coupled with the efficient damage assessment capability of DSAS would provide a highly efficient approach capable of predicting more accu rate susceptibility estimates for structural engineers practicing in the protective design community. Within the framework of the UFC an EFA could be included within a fourth analytical category in and addition to th e three current options: LS, NS, and ND. In order to improve the likelihood of extending the findings of this research into the practice of structural engineers working on protective structures, a number of additional advancements are also suggested. By considering blasts on additional floors, results may give additional information regarding the sensitivity of blast location to collapse susceptibility, which would arguably be a structure specific investigation. In addition, evaluating the sensitivity of at the edge of the destruction zone. The methodology presented here offers opportunities in regar ds to quantifying collapse susceptibilities under loading conditions beyond that estimated by design provisions; i.e. determining a sensitivity to overloading. Such investigations could provide invaluable information for older structures needing to underg o retrofitting methods for modern applications and loading scenarios.
104 Table 4 1 Co llapse r esult comparison between mid rise building models SAC BO Building Bla s t Induced Damage Origin al Modified One Column Non Collapse Non Collapse One Column & One Girder " " One Column & Two Girders " " Two Columns & Two Girders " " Two Columns & Three Girders " " Two Columns & Four Girders " " Two Columns & Five Girders " " Two Columns & Six Gird ers " " Two Columns & Seven Girders " " Two Columns & Eight Girders " " Two Columns & Nine Girders " " Two Columns & Ten Girders " " Three Columns & Ten Girders Collapse " Four Columns & Ten Girders " Collapse Five Columns & Ten Girders " " Five Columns & Eleven Girders N/A " Five Columns & Twelve Girders N/A " Five Columns & Thirteen Girders N/A " Five Columns & Fourteen Girders N/A " Five Columns & Fifteen Girders N/A " Fi ve Columns & Sixteen Girders N/A " Five Columns & Seventeen Girders N/A " Five Columns & Eighteen Girders N/A "
105 A B C D E Figure 4 1 Non collapse vs collapse. A ) Beam element stresses with two columns and ten beams removed B ) Beam element stresses with three columns and ten beams removed. C) Energy with 2 columns and 10 beams removed. D ) Energy with 3 columns and 10 beams removed. E ) Total system e nergy histories
106 A B C D Figure 4 2 Comparative strains throughout building A ) Beam element strains with two columns and ten beams removed. B ) Beam element stra ins with three columns and ten beams removed. C ) Shell element strains with two columns and ten beams removed. D ) Shell element strains with three columns and ten beams removed Figure 4 3 Second floor interior column closest to location of charge
107 Figure 4 4 Energy time history for referenced column (recall Figure 4 3 ) correspond ing to a blast yielding the destruction of two columns and four beams Figure 4 5 Energy flow vs energy flow rate for multiple non collapse and collapse simulations.
108 A B Figure 4 6 Isometric view of mid rise building with soft story modified. A) Five columns and ten beams removed. B) Five columns and eighteen beams removed.
109 A B C Figure 4 7 Comparative of different blast induced damages with modified building model. A ) Five columns and ten beams removed. b) Five columns and eighteen beams removed. c) Comparative total system e nergy time histori es.
110 Figure 4 8 Total system e nergy flow vs energy flow rate with the modified SAC commissioned mid rise building Figure 4 9 Second floor interior column closest to location of charge
111 Figure 4 10 Comparative energy time histories for second floor interior column closest to location of charge (Recall Figure 4 9 ). Figure 4 11 Energy histories for referenced column (Figure 4 9 ) from all simulations with modified version of SAC commissioned mid rise building model
112 Figure 4 12 East west connections at base of second floor interior column closest to location of cha rge. Figure 4 13 Comparative energy time histories for east west connections at base of second floor interior column closest to location of charge (Recall Figure 4 12 ).
113 Figure 4 14 North south connections at base of second floor interior column closest to location of charge. Figure 4 15 Comparative energy time histories for north south connections at base of second floor interior column closest to location of charge (Recall Figure 4 14 ).
114 Figure 4 16 East west girders at base of second floor interior column closest to location of charge. Figure 4 17 Comparative energy ti me histories for east west girders at base of second floor interior column closest to location of charge (Recall Figure 4 16 ).
115 Figure 4 18 North south girders at base of second floor interior column closest to location of charge. Figure 4 19 Comparative energy time histories for north south girders at base of second floo r interior column closest to location of charge (Recall Figure 4 18 ).
116 A B Figure 4 20 Energy time histories for all columns on the s econd floor of the modified SAC commissioned mid rise building model. A) Blast induced damage of five columns and ten beams. B) Blast induced damage of five columns and eighteen girders. Figure 4 21 Effective (Von Mises) beam s tress es from a t wo c olumns and f our b eams removal
117 CHAPTER 5 CONCLUSIONS This work details an energy flow approach (EFA) for progressive collapse assessment superior to current force based methods. Redefining failure for individual structural members in terms of an energy threshold allows for a more accurate assessment of collapse susceptibility of the entire structural system. The methodology presented is a rational, highly effecti ve approach for assessing progressive collapse susceptibility with an accuracy and precision on par with state of the art numerical modeling techniques. This research has explicitly addressed the effects of the rates of loading and energy flow for the sele cted mid rise steel frame. Analyses of the energy time histories of a multitude of blast induced damage simulations of the mid rise steel frame considered in this work revealed a highly accurate and precise correlation between energy flow, energy flow rat e, and structural failure. M ore specifically, the efficacy of using energy flow (magnitude and rate) as failure indicators was proven by analyzing the structure of interest under a multitude of extreme loading events including both collapse arres ting and progressive collapse inducing scenarios. Beyond evidencing the efficacy of the EFA presented for assessing progressive collapse this research demonstrates the lack of efficacy of the Alternate Path method for moment resisting mid rise steel buildings. In addition to the known lack of correlation between the damage induced from realistic explosive threats and a notional single column removal, this work has demonstrated the threat independent notional Alternate Path method offers little to no mitigation aga inst a catastrophic collapse following a blast loading event. The EFA presented here allows for a number of seminal advancements in the field of protective structures.
118 APPENDIX A DEMONSTRATION S OF THE EFA WITH SMALL STRUCTURAL FRAMES A 1 Introduction Although conceptually equivalent for all moment resisting frames, the simple single bay single story frame was analyzed as a proof of concept for efficiency Consequently, some efforts that would be present for a larger structure were excluded due to analyzing a 3 D single bay frame. Pre analysis calculation of energy flow thresholds for the failed beams and slab were al so not included. In addition, quantifying the scaled distance yielding damage commensurate with removal of single column was not performed. These items were intentionally excluded given the ancillary goal of analyzing the efficacy of the Alternate Path m ethod is of negligible value for a simple 3 D frame. Although not included in the proof of concept analysis presented above, force and stress time histories were analyzed for the mid rise building. The absent results and analyses from review of the simpl e frame simulations applied for the analysis of t he mid rise office building are provided in the following sections to provide a more comprehensive description of the sequence of processes employed for this study. A 2 Single Bay Single Story Steel Frame with Simplified Fixed Connections For clarity and concision, the proposed EFA is presented with a single interior bay in the first floor of the ten story building. Results from two simulations with this simple non redundant frame are presented. The first simulation includes vertical and horizontal loads without damage. The second is equivalent in every way with the exception of the application of damage a single failed column. Isometric views and energy time histories of the undamaged (Figure A 1 ) and damaged (Figure A 2 ) frames are shown. Resultant data is reviewed, constituti ng a preliminary attempt at identifying the energy flow failure relationship.
119 A 2 1 Processing R esults from C ollapse A rresting S imul ation Time histories of energy flow and several failure indicators from nonlinear transient dynamic finite element simulations was processed and analyzed to identify patterns suggesting energy flow failure correlation. Differentaion is used to calculate energy flow rates. The viability of assessing progressive collapse susceptibility was realized by comparing energy time histories with multiple failure criteria time histories; e.g. displacement stress and strain time histories. Force time histories were reviewed to compare energy correlation from the EFA against those from the traditional force based approach. More specifically, total, kinetic, and internal energies of all structural elements was recorded, extracted, differentiated, and analyzed; w hich includes all columns connections, girders, beams and slabs. The extracted energy flow and calculated energy flow rate time histories were superimposed against energy thresholds. Comparing this combined data with the structural response observed in LS Prepost, the output data indicating the timing and sequence of failed members was analyzed for correlation with the superimposed time history threshold failure data. The efficacy of this approach was revealed after performing these post processing meth ods extraction, differentiation, plotting, and potential correlation methods for multiple loading conditions. For the simulation with the damaged frame, half of the slab and both beams adjoining the removed column failed, collapsing fully until contacting the ground surface. Results show the majority of internal energy produced during the collapse came from the failed beams primarily through plastic strains. The slab contributes internal energy, as do the two beams opposite the removed column. However, t he energetic contribution of these three elements is small relative to the collapsed beams, 10% per Figure A 4 B The remaining three columns express negligible
120 internal strain energy. In reviewing the kinetic energy, we observe the expected energy transfers, with the beams playing the primary and the slab playing the secondary role. Namely, the two beams above the removed column expend the most amount of energies until hitting the ground at approximat ely 2400 msec (2.4 sec). As expected, the slab transfers significant kinetic energy levels due to a 4.0 m drop height and approximately half of the slab mass being in motion. A 2 2 Processing R esults from C ollapse T riggering S imulation Reviewing the collapse inducing simulation with the damaged frame, energy time histories of individual structural members and are differentiated to yield the rates of energy flow. Comparative plotting between both energy parameter time histories and multiple failure indicating time histories are performed. Due to resultant values being dissimilar in scale by three orders of magnitude, kinetic energy time hist ories are plotted on separate, independent ordinate axes. The resultant time histories show collapse occurs over a time span of approximately 4.0 seconds, beginning at 3500 msec (3.5 sec) and ending at 7500 msec (7.5 sec). The failed beams release the mos t energy, in the form of internal strain primarily plastic strain, as expected. The internal and kinetic energies from the beams and slab illustrate the deformations and displacements occurring in these members, respectively. Notably, the energy flow rat e time histories demarcate the beginning and end of the collapse event in a more pronounced fashion. The potential and kinetic energy flows of all three failed structural elements are plotted using different scales, yielding a behavioral comparison. Nearl y equivalent internal energy flow is observed. However, observable differences exist between energy flow rates at higher subsequent models had frequency based d amping, with subsequent quality controls to verify damping energy plays an insignificant role throughout the modelled event.
121 The observed similarities in internal energies between the slab and beams are maintained for kinetic energy, reflected in both e ner gy flow time histories (Figure A 5 ). This is expected given internal and kinetic energies are the sum total energy. To confirm, the plastic strain energy equals the summed slab and beams internal energ internal energy. In effect, the equivalency of the plastic strain with the total internal energy flows confirms the absence of non physical spurious energy forms; e.g. hourglass energy. After reviewing all failure indicator parameters, vertical displacement of the connection and strain at the slab center were selected. Displacement of the unsupported slab corner at the onset of the simulation is due to self weight and superimposed dead and live loads. Thes e two parameters indicate collapse begins at 3500 msec (3.5 sec) and ends at 7500 msec (7.5 sec). Given the primarily vertical nature of the applied loading conditions, and single story test frame, column behavior does not warrant an independent discussio n. In the interest of brevity, vertical displacement and plastic strain are the only failure indicating parameters presented. However, effective stress and effective strain contours are shown for the final collapse state. The explosive loading events und er consideration occur over a time span of a few milliseconds. The structure responds over a duration of several seconds, corresponding to the pseudo static time domain. Given approximately three orders of magnitude separation between the time domain of applying damage in an instantaneous manner is reasonable In other words, any disparities between the damage sustained during a blast loading and immediate removal of structural members is inconsequential because the structure responds in the quasi static time domain. Studies examining the effect of applying damage instantaneously as opposed to over a time span of a several milliseconds have shown no observable differences result (Krautham mer et al. 2004a) in
122 addition to other studies that have focused solely on this approach and concluded the same (Yim and Krauthammer, 2009; and Szyniszewski and Krauthammer, 2012). All energy time histories reported by LS DYNA were reviewed to ensure equi librium was maintained throughout the simulation. All nonlinear transient dynamic finite element simulations are conducted with LS DYNA 971 version (Hallquist, 2014). A 3 Tw i n Bay Two Story Portion of Mid Rise with Advanced Connections The following is as an expanded proof of concept analysis beyond the single bay single story frame in the proposal, to a twin bay two story portion of the building under consideration. In addit ion, a complex representation of all structural connections is also incorporated. The selected portion of the mid rise building for this reduced model demonstration entails a corner portion of the first two levels, which includes one interior bay, two ext erior bays, and one corner bay for both bottom levels (Figure A 9 ). In addition, the lateral restraint applied to the first elevated floor level represents the interaction of the building exterior with soil, at grade, which is symbolized by a vertical roller (Figure A 9 A ), is not considered in numerical representation of this reduced frame model. To demonstrate the efficacy of the proposed EFA, energy time histories for a multitude of structural elements was processed, analyzed, and compared between two loading/damage condition states the first arrests failure, the second progresses to collapse. For clarity and concision, the proposed EFA is presented with two twin bays in the first two floors of the ten story building. Results from two simulations with this reduced frame are presented. The first simulation includes vertical loads with a single column removal. The second is equivalent in every way wi th the exception of the application of damage three removed columns, two exterior and one corner in lieu of a single corner column removal. Isometric views and energy time histories of both damaged simulated frames, moderate (one
123 column removed) and sever e (three columns removed), are shown. Resultant data is reviewed to an extent that constitutes a thorough presentation of the energy flow failure relationship. A 3 1 Processing R esults from C ollapse A rresting S imulation A twin bay two story portion of the mid rise building was analyzed following the removal of a corner column. In order to induce failure in several structural members dead and live loads were amplified. However, these superimposed loads were maintained at a level such that a progression of collapse did not occur; i.e. a catastrophic collapse of the frame. Isometric views and energy time histories of this moderately damaged frame are provided (Figure A 10 ). Time histories of energy flow and several failure indicators from nonlinear transient dynamic finite element simulations are processed and analyzed, identifying patterns sugg esting energy flow failure correlation. Differentaion is used to calculate energy flow rates. The viability of assessing progressive collapse susceptibility was realized by comparing energy time histories with multiple failure criteria time histories; e.g. displacement stress and strain time histories. Force time histories were also be reviewed to compare energy correlation from the EFA against those from the traditional force based approach. More specifically, total, kinetic, and internal energie s of all structural elements was recorded, extracted, differentiated, and analyzed; which includes all columns connections, girders, beams and slabs. The extracted energy flow and calculated energy flow rate time histories was superimposed with the energ y flow thresholds. Comparing this combined data with the structural response observed in LS Prepost, the output data indicating the timing and sequence of failed members was analyzed for correlation with the superimposed time history threshold failure dat a. The efficacy of this approach was revealed after performing these post processing methods extraction, differentiation, plotting, and potential correlation methods for multiple loading conditions.
124 For the simulation with the damaged frame, half of the s lab and both beams adjoining the removed column failed, collapsing fully until contacting the ground surface. Results show the majority of internal energy produced during the collapse came from the failed beams primarily through plastic strains. The slab contributes internal energy, as do the two beams opposite the removed column. However, the energetic contribution of these three elements is small relative to the collapsed beams, 10% per Figure A 4 B The remaining three columns express negligible internal strain energy. In reviewing the kinetic energy, we observe the expected energy transfers, with the beams playing the primary and the slab playing the secondary role. Namely, the two beams above th e removed column expend the most amount of energies until hitting the ground at approximately 2400 msec (2.4 sec). As expected, the slab transfers significant kinetic energy levels due to a 4.0 m drop height and approximately half of the slab mass being i n motion. A 3 2 Processing R esults from C ollapse T riggering S imulation This second simulation is analogous to the non collapse simulation presented above, but with an additional two exterior columns removed, resulting in a collapse. Isometric views and energy time histories of this severely damaged frame are shown (Figure A 11 ). Revi ewing the collapse inducing simulation with the damaged frame, energy time histories of individual structural members are differentiated to yield the rates of energy flow. Comparative plotting between both energy parameter time histories and multiple fail ure indicating time histories are performed. Due to resultant values being dissimilar in scale by three orders of magnitude, kinetic energy time histories are plotted on separate, independent ordinate axes. The resultant time histories show collapse occur s over a time span of approximately 4.0 seconds, beginning at 3500 msec (3.5 sec) and ending at 7500 msec (7.5 sec). The failed beams
125 release the most energy, in the form of internal strain primarily plastic strain, as expected. The internal and kinetic energies from the beams and slab illustrate the deformations and displacements occurring in these members, respectively. Notably, the energy flow rate time histories demarcate the beginning and end of the collapse event in a more pronounced fashion. The p otential and kinetic energy flows of all three failed structural elements are plotted using different scales, yielding a behavioral comparison. Nearly equivalent internal energy flow is observed. However, observable differences exist between energy flow rates at higher subsequent models had have frequency based damping, with subsequent quality controls to verify damping energy plays an insignificant role through out the modelled event. The observed similarities in internal energies between the slab and beams are maintained for kinetic energy, reflected in both e nergy flow time histories This is expected given internal and kinetic energies are the sum total energ y. To confirm, the plastic strain energy equals the energy. In effect, the equivalency of the plastic strain with the total internal energy flows confirms the abs ence of non physical spurious energy forms; e.g. hourglass energy. After reviewing all failure indicator parameters, vertical displacement of the connection and strain at the slab center were selected. Displacement of the unsupported slab corner at the onset of the simulation is due to self weight and superimposed dead and live loads. These two parameters indicate collapse begins at 3500 msec (3.5 sec) and ends at 7500 msec (7.5 sec). Given the primarily vertical nature of the applied loading condition s, and single story test frame, column behavior does not warrant an independent discussion. In the interest of brevity, vertical
126 displacement and plastic strain are the only failure indicating parameters presented. However, effective stress and effective strain contours are shown for the final collapse state. The explosive loading events under consideration occur over a time span of a few milliseconds. The structure responds over a duration of several seconds, corresponding to the pseudo static time doma in Given approximately three orders of magnitude separation between applying damage in an instantaneous manner is reasonable In other words, any disparities between t he damage sustained during a blast loading and immediate removal of structural members is inconsequential because the structure responds in the quasi static time domain. Studies examining the effect of applying damage instantaneously as opposed to over a time span of a several milliseconds have shown no observable differences result (Krauthammer et al. 2004a) in addition to other studies that have focused solely on this approach and concluded the same (Yim and Krauthammer, 2009; and Szyniszewski and Krauth ammer, 2012). All energy time histories reported by LS DYNA were reviewed to ensure equilibrium was maintained throughout the simulation. All nonlinear transient dynamic finite element simulations are conducted with LS DYNA 971 version (Hallquist, 2014).
127 A B C D Figure A 1 Test Frame without damage A ) Initial state prior to loading B ) Internal energy time history for a non collapse C ) Final displaced st ate ( 10,000 msec) D ) Kinetic energy time history for a non collapse (Note: displacement scale factor of 25 applied to subfigure c to illustrate deformations)
128 A B C D Figure A 2 Test frame with damage applied failure of a single column A ) Initial state prior to loading B ) Internal energy time history during collapse C ) Final collapsed state ( 7500 msec) D ) Kinetic energy time history during collapse A B Figure A 3 Energy time histories of slab A ) Energy flow as reported B ) Energy flow rate from differentiating energy flow
129 A B Figure A 4 Energy time histories of failed beams A ) Energy flow as reported B ) Energy flow rate from differentiation A B Figure A 5 Internal energy time histories of slab and failed beams A ) Energy flow as reported B ) Energy flow rate from differentiation
130 A B Figure A 6 Kinetic energy time h istories of slab and failed beams A ) Energy flow as reported B ) Energy flow rate from differentiation A B Figure A 7 Example failure indicating criteria time histories A ) Vertical displacement of the connection at the top of removed column B ) Plastic strain at the center of slab adjoining the removed column
131 Figure A 8 Stress and str ains c ontours at the end of collapse A ) Effective (Von Mises) stress B ) Effective plastic strain A B C Figure A 9 Portion of m id r ise b uilding a nalyzed for d emonstr ating e fficacy A ) Elevation v iew of b uilding B ) Plan v iew of b uilding C ) Isometric v iew of p ortion m odeled
132 A B C D Figure A 10 Reduced f rame with m oderate d amage ( o ne c olumn) c ollapse p revented A ) Initial state prior to loading B ) Internal energy time history for a non collapse C ) Final displaced state D ) Kinetic energy time history for a non collapse
133 A B C D Figure A 11 Reduced frame with s evere d amage ( t hree c olumns) c ollapse p rogresses A ) Initial state prior to loading B ) Internal energy time history during collapse C ) Final collapsed state ( 7500 msec) D ) Kinetic energy time history during collapse A B Figure A 12 Energy time histories of slab A ) Energy flow as reported B ) Energy flow rate from differe ntiating energy flow
134 A B Figure A 13 Energy time histories of failed beams A ) Energy f low as reported. B ) Energy Flow r ate from differentiation A ) B ) Figure A 14 Internal energy time histories of slab and failed beams A ) Energy flow as reported B ) Energy flow rate from differentiation
135 A B Figure A 15 Kinetic energy time his tories of slab and failed beams. A ) Energy flow as reported B ) Energy flow rate from differentiation A B Figure A 16 Example failure indicating criteria time histories A ) Vertical displacement of the connection at the top of removed column B ) Plastic strain at the center of slab adjoining the removed column
136 A B Figure A 17 Stress and strain c ontours at the end of collapse A ) Effective (Von Mises) stress B ) Effective plastic strain
137 APPENDIX B MID RISE BUILDI NG DETAILS B 1 Introduction For potential reference, the following is provided to supplement the introduction of the ten story, or nine story with a single story basement SAC commissioned building in Boston introduced in Â§ 2 4 The structural system under consideration is a ten story moment resisting frame established for seismic design research in response to the 1994 Northridge earthquake (FEMA, 2000). The structure is a typical moment resisting steel frame, with both shear and moment resisting connections. Specifically, this building contains WUF B type moment connections and single plate (shear tab) connections. This frame is considered representative of typical mid rise steel moment resisting office buildings. The ten story mid rise or nine story structural frame with single story basement is presented below. B 2 FEMA Specifications for the Mid Rise Building in Boston MA, 2000). The following description of the ten story building in Boston is included along with the referenced figures and tables: B. 1 Description of Buildings and Basic Loading Conditions As part of the SAC steel project, three consulting firms were com missioned to perform code designs for 3 9 and 20 story model buildings, following the local code requirements for the following three cities: Los Angeles (UBC 1994), Seattle (UBC 1994), and Boston (BOCA 1993). All prevailing code requirements for g ravity, wind, and seismic design needed to be considered. The buildings were to be designed as standard office buildings situated on stiff soil (soil type S2 The floor plans and elevations for the buildings were p reset, as shown in Figure B 1. The shaded area indicates the penthouse location. Gravity frame columns are located only below the penthouse in the 20 story buildings, resulting in two bays of 40 feet bounding a 20 foot bay in the gravity frames. The column bases in the 3 story buildings are considered as fixed. The 9 story buildings have a single level basement, and the 20 story buildings have a 2 level basement. The buildings were required to conform to a
138 t. The loading information provided was the following: Steel framing: as designed Floors and Roof: 3 inch metal decking with 2.5 inches of normal weight concrete fill and fireproofing Roofing: 7 psf average Ceilings/Flooring: 3 psf average, including fir eproofing Mech./Electrical: 7 psf average for all floors, additionally 40 psf over penthouse area for equipment Partitions: as per code requirements (10 psf for seismic load, 20 psf for gravity design) Exterior Wall: 25 psf of wall surface average, includ ing any penthouses. Assume 2 feet from perimeter column lines to edge of building envelope. Include 42 inch parapet at main roof level, none at penthouse roof. Live Load: typical code values for office occupancy (50 psf everywhere) Wind Load: as per code requirements, assuming congested area (exposure B as per Seismic Load: as per code requirements. Based on this basic information, the consulting firms were asked to carry out three types of structural designs: 1. Pre Northridge Desig ns : These designs were based on design practices prevalent before the Northridge earthquake, i.e., without consideration of the FEMA 267 (1995) document. These designs had the standard beam to column welded connection details. 2. Post Northridge Designs : These designs were to additionally conform to the provisions of FEMA 267 (1995). The designers decided on the use of cover plated beam flanges in order to move the location of the plastic hinge in the beam away from the face of the column. 3. Special Desi gns : Two types of special designs were carried out for the 9 story post Northridge structures in all three geographic locations. The first special design involved the use of reduced beam sections, while the other design involved the use of a higher streng th steel (A913) for the columns. Thus, the basic definitions for the buildings were kept constant between the different regions, but no other constraints concerning the design of the buildings (e.g., number of moment resisting connections, choice of membe r sections, etc.) were imposed. The buildings so designed can be considered as being representative of typical steel moment frame structures in the three geographic locations, designed according to either pre or post Northridge design practice.
139 All three design offices selected perimeter moment resisting frames as the structural system. In all cases the design of the moment frames in the two orthogonal directions was either identical or very similar, thus, only half of the structure is considered in the analysis. The ordinary difference between the NS and East West (EW) direction comes from the difference in gravity load effects on account of the orientation of the gravity beams and sub beams. Both the beams and sub beams are oriented in the NS direction. However, as the gravity loading on the girders of the perimeter WSMFs is small and has almost negligible effect on the seismic response, the decision to analyze the structure only in the NS direction is justified. The loading used for the analysis of the frames is based on the details given before, which result in the following floor load distribution (steel weight is assumed as 13 psf for all designs): Floor dead load for weight calculations: 96 psf Floor dead load for mass calculations: 86 psf Roof dead load excluding penthouse: 83 psf Penthouse dead load: 116 psf Reduced live load per floor and for roof: 20 psf Cladding and parapet loads are based on the surface area of the structures. Based on these loading definitions, the seismic mass for the struct ures is as follows (the values are for the entire structure): 9 story Structures: Roof: 73.10 kips sec 2 /ft Floor 9 to Floor 3: 67.86 kips sec 2 /ft Floor 2: 69.04 kips sec 2 /ft The design details (member sections, doubler plates, design basis, etc.) for the different structures are summarized in the following sections. B.4 Boston (BO) Structures The placement of the MR connections in the 9 story structure is identical to the placement in the LA 9 story structure (see Figure B 2). The strong axis of the gravity and 20 story structures are wind controlled designs. The member sections for the pre and post Northridge designs are given in Table B 7. A572 Gr. 50 steel has been used for both beams and columns in the Boston designs. The dimensions for the cover plates used in the Boston post Northridge designs are given in Table B of the plates. The top cover plates ha maintain this width for 2 inches from the column face, and then taper uniformly to a
140 There are striking differenc es between the pre and post Northridge designs for Boston. Boston lies in seismic Zone 2A, thus the pre Northridge designs are not required to comply with specific panel zone strength requirements or the strong column criterion, which are binding in seism ic Zones 3 and 4. The post Northridge designs, however, have to comply with both a minimum panel zone shear strength requirement as well as the strong column concept, in accordance with FEMA 267 (1995), thereby resulting in the use of significantly heavier column sections and extensive use of doubler plates.
141 Table B 7 A B Figure B 1 Beam, sections, column sections, and doubler plates for three story b ui lding in Boston A ) Pre Northridge design B ) Post Northridge design
142 Table B 8 Figur e B 2 Cover plate details for ten story Boston building post Northridge design Figure B 3 Floor plan and elevation for ten story B oston building Figure B 4 Layout of moment resisting connections in ten story building
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152 BIOGRAPHICAL SKETCH John Robert Wilkes has received a diploma from Palatka High School (1995), a Bachelor of Science in e ngineering from Tulane University (1999), and a Master of Engineering from University of Florida (2002). The author studied b iomedical e ngineering, m echanical e ngineering, and k inesiology during his undergraduate tenure and s tructural e ngineering graduate tenure His undergraduate resea rch included a study of the effects of prophylactic knee braces on gait and the design of a lift system for an individual with 20% r.o.m. of a non dominant arm. He graduate research during his m the development of a low profile bar rier for the Florida Department of Transportation using numerical simul ations of vehicle barrier impact events resulting in U.S. Patent 6767158. After consulting as a Professional Engineer for nearly a decade in over twenty states and in several countries abroad, John returned to the University of Florida in 2011 to earn a d octorate with a research focus on the numerical modeling of events for purposes of protecting against extreme loading scenarios. Under the direction of Professor Ted Krauthammer, he ha s earned a certificate in Critical Infrastructure Protection and will graduate in August 2016, where he will continue his career at Sandia National Laboratories.