EXPERIMENTAL AND ANALYTICAL ASSESSMENT
ON THE PROGRESSIVE COLLAPSE POTENTIAL
OF EXISTING BUILDINGS
THESIS
Presented in Partial Fulfillment of the Requirements for the Degree of Master of Science in the Graduate School of The Ohio State University
By
Brian Inhyok Song, B.S., E.I.
Graduate Program in Civil Engineering
The Ohio State University 2010
Master’s Examination Committee: Professor Halil Sezen, Advisor Professor Hojjat Adeli
Copyright by
Brian Inhyok Song
ABSTRACT
Progressive collapse has been of an increasing concern in the structural engineering community, especially since the collapse of the World Trade Center towers in 2001. As a result of increasing catastrophic events in recent years, the prevention of progressive collapse is becoming a requirement in building design and analysis. A large number of studies have been performed to improve the design of the building against progressive collapse and to evaluate the progressive collapse potential of existing and new buildings by using computer programs and analytical tools. However, experimental evidence is still necessary to validate the computational analysis tools to better simulate the progressive collapse of structures.
In this research, both experimental and analytical assessments of the progressive collapse potential of existing buildings were conducted. Two actual steel frame buildings, the Ohio Union building in Columbus, Ohio and the Bankers Life and Casualty Company (BLCC) building in Northbrook, Illinois were tested by physically removing four first-story columns prior to buildings’ scheduled demolition. During the field tests the changes in column axial forces were measured, and the recorded strains were compared with the analysis results from computer models. A commercially available computer
program, SAP2000 was used to model and analyze the test buildings, following the General Services Administration guidelines (GSA, 2003). Two-dimensional (2-D) as well as three-dimensional (3-D) models of each building were developed to analyze and compare the progressive collapse response. Also, two different analysis procedures were evaluated for their effectiveness in modeling progressive collapse scenarios; linear static and nonlinear dynamic procedures.
The measured strain data compared relatively well with the analysis results of SAP2000. In particular, 3-D model was more accurate than 2-D model, because 3-D models can account for 3-D effects as well as avoid overly conservative solutions. 3-D model had lower DCR values and vertical displacements than 2-D model, which was probably due to inclusion of transverse beams in 3-D model. 3-D model is believed to be more realistic than 2-D model for the progressive collapse analysis. Linear static analysis showed higher vertical displacements than nonlinear dynamic analysis for both 2-D and 3-D models. The amplification factor of 2 required for the dead load in linear static analysis may lead to very conservative analysis results.
This research is an initial step in developing analysis tools and design guidelines that could be easily and effectively used to evaluate the progressive collapse potential of new and existing buildings. It is expected that the field experiments and SAP2000 analyses performed in this research could provide structural engineers with both practical and fundamental information on the progressive collapse response of buildings.
DEDICATION
ACKNOWLEDGMENTS
I am heartily thankful to my Professor, Dr. Halil Sezen. His encouragement, supervision and support enabled me to develop an understanding of the subject. Without his dedication, this would have been an impossible task. I would like to thank the additional members of the Master’s committee, Dr. Hojjat Adeli and Dr. Shive Chaturvedi for their intuitive discussions regarding this work. I greatly acknowledge the sponsors of this research: AISC (American Institute of Steel Construction) and NSF (National Science Foundation) for the experimental research support, and URS Corporation for the travel supports of my conference presentations and tuition support.
Special thanks to the SMOOT Construction and Loewendick Demolish Contractors for Ohio Union Building Demolition, and the Environmental Cleansing Corporation in Markham, IL for BLCC Building Demolition. Their devotion has initiated this research. I give my deepest gratitude to Kyong-Yun Yeau, Tanmoy Chowdhury, and Firat Alemdar for helping the installation of strain gauges for the Ohio Union Building. I would never forget the night we spent in the Ohio Union Building without electricity. I want to give special thanks to Kevin Giriunas. He did not hesitate to share his experimental data and knowledge.
I would like to thank my sister, Michelle Song, brother-in-law, Hyungwoo Kim, and my lovely nephews, Minsu Kim, and Minjun Kim. I especially owe my deepest gratitude to my wife, Jungju Lee, for her love and understanding. Thank you for your prayers, and encouragement. I love you deeply every moment.
I would also like to dedicate this work to my parents, Dalwon Song and Kumpok Chung, for their absolute love and support. Their prayers and beliefs always gave me a direction to succeed. I love you.
VITA
March 6, 1977 ………... Born − Daegu, South Korea 2000 ………. B.S., Architectural Engineering,
Youngnam University, South Korea 2004 ………... B.S., Civil Engineering,
The Ohio State University, Columbus, OH 2007-2008 ………... Structural Engineer,
MS Consultant, Columbus, OH 2008-present ……… Structural Engineer,
PUBLICATIONS
Published Proceedings
1. Sezen, Halil, Song, Brian I. and Giriunas, Kevin I. 2010. “Progressive Collapse Response of Buildings and Multihazard Mitigation.” 9th US National and 10th Canadian
Conference on Earthquake Engineering, July 25-29, Toronto, Canada.
2. Song, Brian I., Giriunas, Kevin I. and Sezen, Halil. 2010. “Experimental and Analytical Assessment on Progressive Collapse Potential of Actual Steel Frame Buildings.” ASCE 2010 Structures Congress, American Society of Civil Engineers (ASCE). May 12-15, Orlando, Florida, USA.
3. Song, Brian I. and Sezen, Halil. 2009. “Evaluation of an Existing Steel Frame Building against Progressive Collapse.” ASCE 2009 Structures Congress, American Society of Civil Engineers (ASCE). April 30-May 2, Austin, Texas, USA.
4. Sezen, Halil and Song, Brian I. 2008. “Progressive Collapse of the Ohio Union Steel Frame Building.” 5th European Conference on Steel and Composite Structures, 2008 EuroSteel. September 3-5, Graz, Austria.
FIELDS OF STUDY
Major Field: Civil Engineering Specialization: Structural Engineering
TABLE OF CONTENTS Page Abstract ………. ii Dedication ……….………. iv Acknowledgments ……….……… v Vita ……….……… vii Table of Contents ……….. ix
List of Figures ……….…….. xiv
List of Tables ……….…… xx
Chapters 1. Introduction ……….…….. 1
1.1 General Background ….………..…. 1
1.2 Research Objectives ………..…... 2
1.3 Outline of the Thesis ……….………...…… 4
2. Background Information on Progressive Collapse …….………….………... 6
2.1 Introduction ……...……… 6
2.3.1 Ronan Point Apartment Tower Collapse ...………...……....…... 8
2.3.2 The Oklahoma City Bombing ...……...……….…... 9
2.3.3 World Trade Center Collapse ...………...……….…... 10
2.4 Design Approaches for Progressive Collapse ……….……….…… 12
2.4.1 Indirect Design Approach ……….…... 12
2.4.2 Direct Design Approach ………..……… 13
2.4.2.1 Specific Local Resistance Method ………... 13
2.4.2.2 Alternative Path Method …………...………... 14
2.5 Analysis Procedures for Progressive Collapse ……….………... 14
2.5.1 Linear Static Procedure ……….…... 15
2.5.2 Nonlinear Static Procedure ……….. 15
2.5.3 Linear Dynamic Procedure …..………...…. 16
2.5.4 Nonlinear Dynamic Procedure ……… 17
2.5.4.1 Dynamic Effect ……….………... 17
2.5.4.2 Nonlinear Effect …………...………... 18
2.6 Design Guidelines to Resist Progressive Collapse ………...……... 19
2.6.1 DoD Guidelines …..……….………...…. 21
2.6.2 GSA Guidelines ………...……… 22
3. Building Description …...………...……….... 24
3.1 Introduction ……...……… 24
3.2 The Ohio Union Building ………..………….………. 24
3.2.1 Description of the Ohio Union Building ……….………... 24
3.3 The Bankers Life and Casualty Company (BLCC) Building ...……..…. 26
3.3.1 Description of the BLCC Building ………. 26
3.3.2 Properties of Structural Members …………...……….... 26
Tables and Figures ………….………. 28
4. Analytical Modeling Procedures ………...…..…….………… 33
4.1 Introduction……….. 33
4.2 Modeling Assumptions ……..……….. 34
4.3 Configuration and Modeling of the Buildings ………. 35
4.3.1 Ohio Union Building Model ………..……….…. 35
4.3.2 Bankers Life and Casualty Company Building Model ………… 36
4.4 Material Properties ………..…...…. 37
4.5 Loading Conditions for Analysis ………...…..…...…. 37
4.5.1 Dead Load of the Ohio Union Building …………....……….…. 38
4.5.2 Dead Load of the BLCC Building ………...… 39
4.6 Slab Design ….………….……… 39
4.7 Acceptance Criteria for Progressive Collapse ….……… 40
4.7.1 Linear Static Analysis …..………...…. 40
4.7.2 Nonlinear Dynamic Analysis …………...……… 41
4.8 SAP2000 Analysis Procedures ….………...……… 42
4.8.1 Step-by-step Procedure for Linear Static Analysis …..……...…. 43
4.8.2 Step-by-step Procedure for Nonlinear Dynamic Analysis …… 43
5. Experimental Research ……….…… 57
5.1 Introduction …….……… 57
5.2 Column Removal Procedure …...………...……….. 58
5.3 Instrumentation …...………. 59
5.4 Strain Measurements ...………...………. 60
5.5 Summary of Measured Strain Data from the BLCC Building Test ……. 61
Tables and Figures ….………. 63
6. Computational Analysis of the Ohio Union Building ……....…….………… 74
6.1 Introduction……….. 74
6.2 2-D Progressive Collapse Analysis ………. 75
6.2.1 Linear Static Analysis ………..………..…….…. 75
6.2.2 Nonlinear Dynamic Analysis ………...… 77
6.3 Comparison of Results from 2-D and 3-D Analyses ……….…..…...…. 79
6.3.1 Calculated DCR Values …………....……….……….. 79
6.3.2 Comparison of Calculated and Measured Strains …………....… 80
6.3.3 Vertical Displacements …..………...………... 82
6.3.4 Plastic Hinge Rotations …………...……… 83
Tables and Figures ………….………. 85
7. Computational Analysis of the Bankers Life and Casualty Company Building ……....…….………. 101
7.1 Introduction……….. 101
7.2 Changes in Moments and Deformations ………. 102
7.3.1 2-D Model ………..………..………..….…. 103
7.3.2 3-D Model ………...………. 104
7.4 Comparison of Calculated and Measured Strains ...………. 105
7.5 Vertical Displacements ……….... 106
Tables and Figures ….………. 107
8. Conclusions and Future Work ………. 115
8.1 Summary ……….. 115
8.2 Conclusions ………...…….. 116
8.3 Recommendations for Future Research ……….. 119
Bibliography ………..…...………… 122
Appendix A. Ohio Union Building Structural Drawings ………..…... 126
Appendix B. BLCC Building Structural Drawings ………...…... 135
Appendix C. Pictures of the Test Procedures ………..……..……...… 142
LIST OF FIGURES
Figure Page
2.1 A partial collapse of Ronan Point apartment tower in 1968 ……….. 9
2.2 Exterior view of Alfred P. Murrah Federal building collapse ……….... 10
2.3 View of the north and east faces of the World Trade Center towers ………... 11
2.4 Progressive collapse of World Trade Center towers ……..…... 12
2.5 Timeline of major catastrophic events followed by major building codes changes for progressive collapse mitigation ….……….. 20
3.1 The Ohio Union building before demolition testing in 2007. The circle shows the tested portion of the building .………... 29
3.2 The east side of the Ohio Union building before demolition testing in 2007 … 29
3.3 The elevation of the four-story test building in the longitudinal direction ….… 30 3.4 Structural plan for the first floor level of the test part of the Ohio Union building and removed columns highlighted ………... 30
3.5 The north side of the Bankers Life and Casualty Company building prior to the demolition in 2008 .………....………... 31
3.6 The longitudinal end building frame of the north side of the Bankers Life and Casualty Company building ………... 31
3.7 The first floor plan for the test part of the BLCC building. The circles show
first floor removed columns ………... 32
4.1 The sensitivity analysis as different damping ratios using the 3-D model of the Ohio Union building after first column removal ……….... 48
4.2 Two-dimensional SAP2000 model of the Ohio Union building with frame member numbers …...………. 49
4.3 Three-dimensional SAP2000 model of the Ohio Union building (Circled columns are removed in the order shown) ………. 49
4.4 Two-dimensional SAP2000 model of the Bankers Life and Casualty Company building with frame member numbers (Circled columns are removed in the order shown) ………... 50
4.5 Three-dimensional SAP2000 model of the Bankers Life and Casualty Company building (Circled columns are removed in the order shown) ……… 50
4.6 Typical joint connection of the Ohio Union building ……… 51
4.7 The plan view of the one-way slab with a tributary area .……….. 51
4.8 Measurement of plastic hinge rotation following the removal of middle column …………....……… 52
4.9 Linear static analysis case definition in SAP2000 ………... 52
4.10 Hinge definitions for steel frame building in SAP2000 ………. 53
4.11 Definition of damping ratios in SAP2000 ……….…. 54
4.12 Nonlinear dynamic analysis case definition in SAP2000 at the first column removal .……….. 55
4.13 Nonlinear dynamic analysis case definition in SAP2000 at the last column
removal …………....………... 56
5.1 Exterior analysis cases considered in the progressive collapse analysis of framed structures (GSA, 2003) ……….………..……… 63
5.2 Maximum allowable collapse areas for a structure that uses columns for the primary vertical support system (GSA, 2003) ………..…….. 63
5.3 The tested part of the Ohio Union building and four exposed columns before demolition testing in 2007. The exposed columns in a circle were sequentially removed ……….. 64
5.4 Field testing: torched columns with a chain attached ………. 65
5.5 Field testing: column removal process ………...……… 66
5.6 Ohio Union building after all columns are removed ………..……… 67
5.7 Plan view of strain gauge placement in Ohio Union building with columns and beam labeled (15 strain gauges are shown in the circles) ……… 67
5.8 Strain gauges attached on steel columns and a beam connected to one of the removed columns ……… 68
5.9 Portable data acquisition system to monitor the strain ………... 69
5.10 All strain gauge measurements when (a) Column 7 and (b) Column 2 were torched ……… 70
5.11 Strain gauge measurements during column removals ……… 71
5.12 The north side of the Bankers Life and Casualty Company building before demolition test in 2008 (Giriunas, 2009). The red-circled columns were removed during the test ………... 72
5.13 The placement of strain gauges in the BLCC building with columns and beam
labeled ………..………...…… 72
5.14 Measurements from strain gauge 7 during the entire field test of the BLCC
building ………... 73
6.1 Bending moment diagram after removal of first column (Column 27) ……..… 89 6.2 Bending moment diagram after removal of second column (Column 22) ….… 89 6.3 Bending moment diagram after removal of third column (Column 2) ……..… 90 6.4 Bending moment diagram after removal of fourth column (Column 7) ……… 90 6.5 Moment diagram and corresponding DCR values after loss of four columns in
the Ohio Union building ………...…..……… 91 6.6 Change in DCR values of each frame member for all cases ………..………… 91 6.7 Column removal procedure for dynamic analysis ………..… 92 6.8 Time history function used to model sudden column loss ………. 92 6.9 Displacement of the joint above the first removed column (Joint 1) after the
first column removal ………... 93 6.10 Displacement of the joints above the first and second removed columns (Joint
1 and 2, respectively) after the second column removal ……….... 93 6.11 Displacement of the joints above the first, second, and third removed columns
(Joint 1, 2, and 3, respectively) after the third column removal ……….……… 94 6.12 Displacement of the joints above each removed column after all columns
removal ………... 94
6.14 Deformed shape of 3-D model with corresponding DCR values after the loss
of four columns ….………... 95 6.15 Comparison of DCR values determined from 2-D and 3-D linear static
analysis after four columns removal ………..…. 96 6.16 Comparison of measured and calculated strain values for Strain Gauge 4 ….... 97 6.17 Comparison of measured and calculated strain values for Strain Gauge 9 ….... 97 6.18 Comparison of measured and calculated strain values for Strain Gauge 11 ….. 98 6.19 Comparison of measured and calculated strain values for Strain Gauge 15 ….. 98 6.20 Changes in maximum joint displacement calculated from the 3-D linear static
analysis during the entire column removal process ……… 99 6.21 Time history of joint displacements calculated from 2-D nonlinear dynamic
analysis ………... 99 6.22 Time history of joint displacements calculated from 3-D nonlinear dynamic
analysis ………... 100 6.23 Plastic hinge locations in the 3-D model after all four columns were removed . 100 7.1 Bending moment diagram after removal of first column (Column 14) …….… 110 7.2 Bending moment diagram after removal of second column (Column 17) ….… 110 7.3 Bending moment diagram after removal of third column (Column 5) ……….. 110 7.4 Bending moment diagram after removal of fourth column (Column 2) ……… 110 7.5 Deformed shape of the BLCC building model after each column removal …... 111 7.6 Changes in DCR values of each frame member for all cases ……… 111 7.7 Comparison of DCR values determined from 2-D and 3-D models after four
7.8 2-D model with corresponding DCR values after loss of four columns ……… 112 7.9 3-D model with corresponding DCR values after loss of four columns ……… 113 7.10 Comparison of measured and calculated strain values ………... 113 7.11 Maximum joint displacements for 2-D model after each column removal …… 114 7.12 Maximum joint displacements for 3-D model after each column removal …… 114
LIST OF TABLES
Table Page
3.1 Column and beam sections of the Ohio Union building ……….. 28 3.2 Column and beam sections of the Bankers Life and Casualty Company
building .………...……….. 28 4.1 GSA specified DCR acceptance criteria for the steel building …...………. 46 4.2 Calculated DCR limits for structural members of the Ohio Union building 47 4.3 Calculated DCR limits for structural members of the Bankers Life and
Casualty Company building .……….……….. 47 6.1 DCR values calculated from 2-D models for selected frame members ….. 85 6.2 DCR values calculated from 3-D model for selected frame members ….... 86 6.3 Comparison of change in Strain (Δε) obtained from the field test after last
column torching with that calculated from 2-D and 3-D analyses after all columns removal ………...…………..……. 87 6.4 Comparison of vertical displacement (in.) after all columns removal ……. 88 6.5 Plastic hinge rotations (θ, degree) at the location where each column was
removed after all columns removal ………..…... 88 7.1 DCR values calculated from 2-D model for steel frame members ……... 107
7.2 DCR values calculated from 3-D model for steel frame members ……….. 108 7.3 Comparison of maximum vertical displacement (in.) after all columns
CHAPTER 1
INTRODUCTION
1.1 General Background
According to the American Society of Civil Engineers (ASCE) Standard 7-05, “Minimum Design Loads for Buildings and Other Structures”, progressive collapse is defined as “the spread of an initial local failure from element to element, eventually resulting in the collapse of an entire structure or a disproportionately large part of it” (ASCE 7-05, 2005). Progressive collapse has been of an increasing concern in the structural engineering community since the collapse of the Ronan Point apartment towers, in Newham, England in 1968 (Griffiths et al., 1968). A small accidental gas explosion in a kitchen on the 18nd floor resulted in a chain reaction of collapses all the way to the ground. Another famous example of progressive collapse was the Alfred P. Murrah building in Oklahoma City in 1995. A bomb blast that destroyed or severely damaged three perimeter columns led to the collapse of a large part of the building (FEMA-277, 1996). Since the collapse of the World Trade Center towers in 2001, interest in progressive collapse has been at its highest level ever (NIST, 2005). Terrorist attacks
against the Alfred P. Murrah Building and the World Trade Center showed that well-designed and robust modern buildings can be susceptible to progressive collapse.
As a result of increasing catastrophic events in recent years, the prevention of progressive collapse is becoming a requirement in building design and analysis. Many approaches have been proposed to minimize the risk of progressive collapse in new and existing buildings. Among a number of building codes, standards, and design guidelines for progressive collapse, General Services Administration (GSA, 2003) and Department of Defense (DoD, 2005) address progressive collapse mitigation explicitly. They provide quantifiable and enforceable procedures to resist progressive collapse.
Over the last decade, a large number of studies have been performed to improve the design of buildings against progressive collapse by modifying the design codes, as well as to evaluate the progressive collapse potential of new or existing buildings by computer modelling and analytical tools (Bao et al., 2008; Kaewkulchai and Williamson, 2006; Karns et al., 2006; Khandelwal et al., 2008; Luccioni et al., 2004; Sasani et al., 2007; Sasani and Sagiroglu, 2008; Sivaselvan and Reinhorn, 2006). Although various progressive collapse models were developed and extensive analysis studies were performed for progressive collapse, there is very little actual field data available for the reliable evaluation of the progressive collapse resistance of structures. Experimental evidence is necessary to verify the existing analytical and computational models.
1.2 Research Objectives
modeling and analysis. To achieve this goal, a commercially available computer program, SAP2000 was used to model and analyze the buildings following the General Services Administration guidelines (GSA, 2003). Two-dimensional (2-D) as well as three-dimensional (3-D) models of each building were developed in this study. Two different analysis procedures were evaluated for their effectiveness in modeling progressive collapse scenarios; linear static and nonlinear dynamic procedures. Difference and implications of each model and analysis were discussed.
The Ohio Union building, located on the Ohio State University campus, was tested by physically removing four first-story columns from one of the long perimeter frames prior to building’s scheduled demolition in 2007. Giriunas (2009) also tested the progressive collapse potential of the Bankers Life and Casualty Company building (Northbrook, IL), which was scheduled for demolition in 2008. The change in column axial forces of each building was measured using strain gauges and discussed in this paper. The strain values recorded in each field test were compared with the analysis results from computer models developed for each building. It was expected that our field experiments and analytical studies can provide both practical and fundamental information on the collapse response of an existing building with a regular structural configuration.
The specific tasks of this research can be summarized as follow:
1. Test actual buildings by physically removing first-story perimeter columns prior to building’s scheduled demolition and simulate the sudden column loss that may lead progressive collapse.
2. Investigate progressive collapse performance of two existing buildings using the commercially available computer program, SAP2000.
3. Develop the 2-D and 3-D models of steel frame buildings to analyze and compare the progressive collapse responses.
4. Evaluate the effectiveness of two different analysis procedures; linear static and nonlinear dynamic procedures.
5. Compare the strain values recorded in the field with the analysis results from a computer model of each building.
1.3 Outline of the Thesis
The thesis is composed of seven chapters including an introduction (Chapter 1), literature review (Chapter 2), description of the buildings (Chapter 3), analytical modeling procedures (Chapter 4), experimental research (Chapters 5), computer analysis of the Ohio Union building and the Bankers Life and Casualty Company building (Chapters 6 and 7, respectively), and conclusions and recommendations (Chapter 8).
Chapter 2 provides background information and a review of literature regarding the progressive collapse of buildings. The definition and famous examples of progressive collapse are presented. Current guidelines such as the GSA and DoD guidelines for the prevention of progressive collapse are reviewed. Various design methods for progressive collapse analysis are also described in Chapter 2.
Chapter 3 presents the description of two tested buildings (i.e., Ohio Union building and the Bankers Life and Casualty Company building). The geometric
Chapter 4 provides 2-D and 3-D computer models of each building using the structural analysis program, SAP2000. The analysis assumptions and detailed procedures for the building models are described. The loading conditions and the acceptance criteria recommended in the GSA guidelines are also provided in this chapter.
Chapter 5 presents experimental procedures including strain gauge instrumentation and column removal procedures. The strains recorded from each field test are shown in this chapter.
In Chapter 6, progressive collapse performance of the Ohio Union building was investigated through 2-D and 3-D computational analyses. Two different analysis procedures are evaluated for their effectiveness in modeling progressive collapse scenarios; linear static and nonlinear dynamic procedures. The results from each analysis method are described.
Chapter 7 presents the progressive collapse analysis of the Bankers Life and Casualty Company building. The results from both 2-D and 3-D linear static analysis of the building are presented, and compared with the strain values recorded in the field.
Chapter 8 presents a summary of the research, conclusions and recommendation for the future research.
CHAPTER 2
BACKGROUND INFORMATION ON PROGRESSIVE COLLAPSE
2.1 Introduction
This chapter provides background and a review of literature regarding the progressive collapse of buildings. First, the definition and famous examples of progressive collapse are presented. Next, design approaches and analysis procedures for progressive collapse of buildings are described. Lastly, the current guidelines for the prevention of progressive collapse are reviewed. Especially, overviews of the General Services Administration (GSA, 2003) and the Department of Defense (DoD, 2005) guidelines are described.
2.2 Definition of Progressive Collapse
Progressive collapse is a chain reaction of failures initiated by the instantaneous loss of one or a few supporting elements. Progressive collapse can be caused by manmade hazards such as blast, explosion, vehicle collision, and severe fire or by natural
Once a structural element fails, the structure should enable an alternative load-carrying path and transfer the loads carried by that element to neighboring elements. The release of internal energy due to the loss of a structural member leads to an increase in the dynamic internal forces of adjoining members. After the load is redistributed through a structure, each structural component supports different loads including the additional internal forces. If any redistributed load exceeds the bearing capacities of surrounding undamaged members, it can cause another local failure. Such sequential failures can spread from element to element, eventually leading to the entire or a disproportionately large part of the structure. In general, progressive collapse happens in a matter of seconds.
The definition of progressive collapse may incorporate the concept of disproportionate collapse, meaning that the extent of final failure is not proportional to the initial triggering events. For example, the American Society of Civil Engineer (ASCE) Standard 7-05 defines progressive collapse as "the spread of an initial local failure from element to element resulting eventually in the collapse of an entire structure or a disproportionately large part of it" (ASCE 7-05, 2005). A similar definition of progressive collapse is provided in GSA 2003 guidelines, “a situation where local failure of a primary structural component leads to the collapse of adjoining members, and hence, the total damage is disproportionate to the original cause” (GSA, 2003).
2.3 Examples of progressive collapse
Some of the most publicized examples of progressive collapse are described below: Ronan Point Apartment Tower in 1968, Alfred P. Murrah Federal Building in
1995, and World Trade Center in 2001. These three events increased interest in the development of codes and standards and in design of buildings to prevent progressive collapse of buildings.
2.3.1 Ronan Point Apartment Tower Collapse
The Ronan Point apartment tower collapse on May 16, 1968 is the first well-known case of disproportionate progressive collapse (Griffiths et al., 1968). The building was a 22-story precast concrete bearing wall system, located in Newham, England. The collapse was initiated by a gas-stove leak in a corner kitchen on the 18th floor. The pressure of the small gas explosion blew out the exterior walls of the apartment, and displaced a load-bearing precast concrete panel near the corner of building. Failure of the corner bay propagated up and down to cover almost the entire height of the building, resulting in a disproportionate collapse of the whole building that killed four people and injured seventeen. Figure 2.1 shows the partially collapsed structure. The Ronan Point collapse prompted the interest and concern in the structural engineering community all around the world. In particular, this collapse led to significant changes in building codes in England and Canada to prevent progressive collapse.
Figure 2.1. A partial collapse of Ronan Point apartment tower in 1968 (Wikipedia, 2010).
2.3.2 The Oklahoma City Bombing
A second wave of interest was the bombing of the Alfred P. Murrah Federal building in downtown Oklahoma City, OK on April 19, 1995 (FEMA-277, 1996). The collapse of this building is a typical example of progressive collapse, due to a bomb explosion. A bomb blast destroyed three perimeter columns, resulting in subsequent collapse (Sozen et al., 1998). The transfer girder supported by the damaged columns failed, and the upper floors and roof panels collapsed in a progressive fashion (Nair, 2004). The major structural damage was concentrated on the north side of the building, facing the explosion, as shown in Figure 2.2. The explosion destroyed about half of the occupiable space in the nine-story Federal Building. As a result of the massive explosion
followed by collapse, 168 people were killed and over 800 people were injured (Irving, 1995). After this collapse, interest in progressive collapse research increased. Extensive studies have been conducted on progressive collapse and corresponding structural designs.
Figure 2.2. Exterior view of Alfred P. Murrah Federal building collapse (FEMA-427, 2003).
2.3.3 World Trade Center Collapse
Since the collapse of the World Trade Center (WTC) towers due to terrorist attacks on September 11, 2001, interest in progressive collapse has further highlighted (NIST, 2005). As shown in Figure 2.3, each of the two steel towers of WTC in New York City was hit by Boeing 767 jetliners, and totally collapsed within a short time due to the enormous weight of the towers above the impact areas. Since the structure collapse
disproportionate collapse. The collapse of the twin towers caused the death of more than 3000 people, as well as extensive damage to the rest of the complex and nearby buildings (Dusenberry et al., 2004).
Figure 2.3. View of the north and east faces of the World Trade Center towers, showing fire and impact damage to both towers (FEMA-403, 2002).
In both collapse cases of the WTC towers 1 and 2, the same sequence of events applied; the damaged portion of the buildings failed, which allowed the section above the airplane impacts to fall onto the remaining structure below, and caused a progression of failures extending download all the way down to the ground, as shown in Figure 2.4. This collapse showed that well-designed and robust modern buildings can also be susceptible to progressive collapse.
Figure 2.4. Progressive collapse of World Trade Center towers (New York Times, 2001)
2.4 Design Approaches for Progressive Collapse
ASCE 7-05 (ASCE 7-05, 2005) defines two general design methods to minimize progressive collapse potential, which are indirect design method and direct design method. Each of these approaches is described in the following section.
2.4.1 Indirect Design Approach
The indirect design approach attempts to prevent progressive collapse through the provision of minimum levels of strength, continuity, and ductility (ASCE 7-05, 2005). The examples of this approach are to improve joint connections by special detailing, to improve redundancy, and to provide more ductility to a structure. The indirect design approach is generally integrated into most building codes and standards since it can create a redundant structure that will perform under any conditions and improve overall
progressive collapse design because of no special consideration of the removal of members or specific loads. The goal of the structural integrity requirements included in American Concrete Institute (ACI) (ACI 318-08, 2008) and in other guidelines is to improve the overall structural performance of the structure, not specifically the progressive collapse resistance.
2.4.2 Direct Design Approach
The direct design approach explicitly considers resistance of a structure to progressive collapse during the design process (ASCE, 2005). There are two direct design methods: the specific local resistance method and the alternate load path method. The specific local resistance method seeks to provide strength to be able to resist progressive collapse. The alternate load path method seeks to provide alternative load paths to adsorb localized damage and resist progressive collapse.
2.4.2.1 Specific Local Resistance Method
The specific local resistance method requires that a critical structural element be able to resist an abnormal loading. Regardless of the magnitude of the loads, the structural element should remain intact because of its robustness. For this method, a sufficient strength and ductility of the element must be determined during design against progressive collapse. The critical element can be designed to have additional strength and toughness to resist the loading, simply by increasing the design load factors.
2.4.2.2 Alternative Path Method
In the alternate path (AP) method, the design allows local failure to occur, but seeks to prevent major collapse by providing alternate load paths. Failure in a structural member dramatically changes load path by transferring loads to the members adjacent to the failed member. If the adjacent members have sufficient capacity and ductility, the structural system develops alternate load paths. Using this method, a building is analyzed for the potential of progressive collapse by instantly removing one or several load-bearing elements from the building, and by evaluating the capability of the remaining structure to prevent subsequent damage. The advantage of this method is that it is independent of the initiating load, so that the solution may be valid for any type of the hazard causing member loss.
The alternate load path method is primarily recommended in the current building design codes and standards in the U.S., including General Services Administration (GSA, 2003) and the Department of Defense (DoD, 2005) guidelines. Thus, this research also focuses primarily on the AP method and used it for progressive collapse analysis.
2.5 Analysis Procedures for Progressive Collapse
When analyzing a structure, four different analytical procedures may be used to investigate the structures behavior; Linear Static (LS), Nonlinear Static (NLS), Linear Dynamic (LD), and Nonlinear Dynamic (NLD), in order of increasing complexity. Many previous researchers investigated the advantage and disadvantage of each analysis procedures for progressive collapse analysis (Marjanishvili, 2004; Marjanishvili and
better and more realistic results representing the actual nonlinear and dynamic response of the structure during the progressive collapse. However, both GSA and DoD guidelines prefer the simplest method, linear static, for the progressive collapse analysis since this method is cost-effective and easy to perform. Therefore, one of the objectives in this research is to compare the performance of the simplest and most complicated analysis procedures (i.e., Linear Static and Nonlinear Dynamic procedures, respectively) for evaluation of the progressive collapse potential of two existing buildings.
2.5.1 Linear Static Procedure
The primary method of analysis presented in the GSA guidelines is the linear static (LS) approach. In general, the LS procedure is the most simplified of the four procedures, and thus the analysis can be completed quickly and easy to evaluate the results. However, it is difficult to predict accurate behavior in a structure, due to the lack of the dynamic effect and material nonlinearity by sudden loss of one or more members (Kaewkulchai and Williamson, 2003). The analysis is run under the assumptions that the structure only undergoes small deformations and that the materials respond in a linear elastic fashion. The LS procedure, therefore, is limited to simple and low- to medium-rise structures (i.e., less than ten stories) with predictable behavior (GSA, 2003).
2.5.2 Nonlinear Static Procedure
In a nonlinear static (NLS) procedure, geometric and material nonlinear behaviors are considered during the analysis. The NLS procedure is widely performed for a lateral load called pushover analysis. For progressive collapse analysis, a stepwise increase of
vertical loads is applied until the maximum loads are reached or until the structure collapses, which is known as vertical pushover analysis. This procedure is a step above the linear static procedure because structural members are allowed to undergo nonlinear behavior during the NLS analysis. However, vertical push over analysis for the progressive collapse potential might lead to overly conservative results (Marjanishvili, 2004). Also, the NLS procedure still does not account for the dynamic effects, therefore it is ineffective to use for progressive collapse analysis. NLS analysis is not used in this research mainly because the structural members in the test buildings did not experience large deformations or nonlinear material response.
2.5.3 Linear Dynamic Procedure
Dynamic analysis accounts for dynamic amplification factors, inertia, and damping forces, which are calculated during analysis. Considering these dynamic parameters, dynamic analysis is much more complex and time-consuming than static analysis, whether it is linear or nonlinear. However, the linear dynamic (LD) procedure provides more accurate results, compared with static analysis. The LD procedure still needs to consider nonlinear behaviors for better results. For the structure with large plastic deformations, it should be careful to use this analysis because of incorrectly calculated dynamic parameters (Marjanishvili, 2004). Since more accurate nonlinear dynamic analysis was performed in this research, linear dynamic analysis was not used.
2.5.4 Nonlinear Dynamic Procedure
The nonlinear dynamic (NLD) procedure is the most detailed and thorough method of progressive collapse analysis. This method includes both dynamic nature and nonlinear behavior of the progressive collapse phenomenon. More accurate and realistic results can be obtained from the NLD method while it is very time-consuming to evaluate and validate analysis results (Marjanishvili, 2004). In this research, NLD analysis is performed by instantaneously removing a load-bearing member from the already loaded structure and analyzing time history of the structure response caused by the loss of that member. Both dynamic effects and geometric and material nonlinearity were considered in the NLD analysis conducted in this research.
2.5.4.1 Dynamic Effect
Progressive collapse is an inherently dynamic event. Dynamic effects may come from many sources during the collapse. After a structural member is failed, the structure transfers the load of that member and comes to rest in a new equilibrium position. During this dynamic load redistribution, internal dynamic forces affected by inertia and damping are produced and vibrations of building elements are involved. A sudden release in forces from any failed member can be another source of dynamic effects. Moreover, progressive collapse is generally initiated by dynamic event such as explosion, impact, and instantaneous failure of a structural member such as a connection. Therefore, dynamic effects for frame structures should be taken into consideration in progressive collapse analysis.
2.5.4.2 Nonlinear Effect
Geometrical and Material Nonlinearity
The performance of any structure under abnormal loadings depends not only on its geometrical properties, but also on the properties of the materials used to construct the structure. Member stiffness ratio is derived to account for geometrical nonlinearity and member shear deformation. The effect of shear deformation is generally insignificant for the conventional framed structure, but it can be considerably important for heavy transverse loading. Geometric nonlinearity is commonly described in terms of “P-Delta Effect” in the model. Member axial compressive forces act through the displacement of one end of a member relative to the other amplify the lateral bending response of a beam-column. Therefore, the P-Delta effect influences the transverse bending stiffness of an element.
Most failure or collapse causing in typical structures are mainly due to the advent of nonlinear material behavior, referred to as post-elastic or plastic behavior. Therefore, material properties such as yield strength, ultimate strength, and ductility are important parameters to design buildings with safety.
Catenary Action
Failure of a column creates a double span condition in the adjoining beams above the failed column. If the beams have large moment capacity and the connections have sufficient ductility and substantial inelastic rotational capacity, excessive deformation
between columns, developing significant tensile forces that the connection must be able to withstand. The double span across the failed column can be supported by catenary action. Alternately, the vertical loads start to be transferred upward through tension in columns above the failed column and the remaining structure transfers the loads to adjacent and unfailed spans.
Catenary action has a significant effect on progressive collapse mitigation. About 20 story buildings can be supported by catenary action after the removal of a column at the first floor. Very conservative results are obtained if the progressive collapse analysis ignores the effect of catenary action. Catenary action can be applied to the finite element models, as “P-Delta with large displacement” in SAP2000.
2.6 Design Guidelines to Resist Progressive Collapse
Progressive collapse is of an important concern because local damage may cause massive destruction and collapse of a structural system. The progressive collapse by terrorist attacks in recent years has further created an urgent need for all code-writing bodies and governmental agencies to provide design guidelines and criteria to prevent or minimize progressive collapse. Figure 2.5 shows the timeline of major catastrophic events followed by major building codes changes for progressive collapse mitigation. The number of building disasters and related code changes has significantly increased during the last decade.
Figure 2.5 Timeline of major catastrophic events followed by major building codes changes for progressive collapse mitigation (modified from Humay et al., 2006).
There are a number of building codes, standards, and design guidelines for the prevention of progressive collapse, such as the General Services Administration (GSA, 2003) and the Department of Defense (DoD, 2005), National Institute of Standards and Technology (NIST, 2005), American Society of Civil Engineering (ASCE 7-05, 2005), and American Concrete Institute (ACI 318-08, 2008). Only two US agencies (i.e., GSA and DoD), however, explicitly address progressive collapse mitigation. ASCE 7-05 (2005) provides a definition for progressive collapse, but does not provide specific guidelines or requirements for the progressive collapse analysis. ACI 318-08 (2008) includes provisions to improve the structural integrity of concrete structures, but does not specifically address progressive collapse. The design guidance issued by GSA and DoD represents the most comprehensive information in the U.S. currently available on the progressive collapse mitigation, providing quantifiable and enforceable requirements (Humay et al., 2006).
2.6.1 DoD Guidelines
The U.S. Department of Defense published a document, “Design of buildings to
resist progressive collapse”, in the frame work of the Unified Facilities Criteria (UFC)
(DoD, 2005). This document was prepared for the new DoD construction such as military buildings and major renovations. Especially, all DoD buildings with three or more stories are required to consider progressive collapse. The DoD guideline can be applied to reinforced concrete, steel structures masonry, wood and cold-formed steel structural components.
The DoD guideline describes how to analyze and design the building structures to resist progressive collapse. A combination of direct and indirect design approaches was used, which depends on the required level of protection for the facility: indirect design for very low and low levels of protection, and both indirect and direct design (Alternate Path) for medium and high levels of protection. An appropriate level of protection can be provided to lessen the risk of mass casualties for all DoD personnel at a reasonable cost.
2.6.2 GSA Guidelines
The U.S. General Services Administration (GSA) guideline, entitled “Progressive
collapse analysis and design guidelines for new federal office buildings and major modernization projects”, was specifically prepared to ensure that the potential for
progressive collapse is addressed in the design, planning, and construction of new federal office buildings and major modernization projects (GSA, 2003). The intent of the guidelines is to prevent widespread collapse after a local failure has occurred.
Based on the GSA guidelines, progressive collapse analysis is accomplished by the implementation of the alternate path method of design. The primary method of analysis in this design guideline is the linear elastic and static approach. Linear procedures are used for low- to medium- rise structures, with ten or less stories and typical structural configurations. The GSA guideline recommends that the use of non-linear procedures should be considered for the buildings with more than ten stories. This document describes detailed procedures for the analysis of progressive collapse, the loads for use in the analysis, and the acceptance criteria for progressive collapse. The issues
related to the prevention of progressive collapse are discussed for reinforced concrete and steel building structures.
The GSA guidelines are useful guidance for minimizing the potential for progressive collapse in the design of new and upgraded buildings, as well as for evaluating the potential for progressive collapse in existing buildings. In this study, GSA progressive collapse guidelines are used to assess the progressive collapse potential of two existing steel buildings. The detailed GSA recommendations and loading conditions for a computer model and column removal used in this study are described in Chapters 4 and 5, respectively.
CHAPTER 3
BUILDING DESCRIPTION
3.1 Introduction
Progressive collapse performance of two existing buildings was investigated through experimental testing and computational analysis. The test buildings were the Ohio Union building (Columbus, Ohio) and the Bankers Life and Casualty Company building (Northbrook, Illinois). This chapter presents the description of these two buildings. The properties of the structural members for each building are also provided.
3.2 The Ohio Union Building
3.2.1 Description of the Ohio Union Building
The first test building, the Ohio Union building was located at the Ohio State University campus, Columbus, Ohio. The Ohio Union building was designed in 1949 and constructed in 1951. The building was scheduled for demolition in June 2007 when
the field experiment was conducted. Demolition of the 1951 structure was completed in September 2007.
Figure 3.1 shows the entire Ohio Union building complex with four adjacent buildings. Only the east side of this large building was considered in this research. Figure 3.2 shows the elevation of the test building just prior to the demolition. The test building was four stories high with a full basement. The building consisted of dining facilities at a lobby level followed by four floors of offices for student organizations. As shown in Figure 3.3, the heights of the basement and first story were 14 ft-7 in. The heights of the second and third floors were 16 ft-7in. and 14 ft-8 in., respectively. The top floor was 12 ft-1 in. high.
Figure 3.4 shows the first floor plan of the test building. The plan of the structure was roughly 66 ft by 189 ft, with eight bays in the longitudinal direction and two bays, spanning 25 ft wide, in the transverse direction. The longitudinal direction has eight bays with a column spacing of 25 ft-4 in. (four bays in the middle) or 21 ft-4 in. (two bays at the left end and two bays at the right end) in width.
3.2.2 Properties of Structural Members
The test building was a steel moment-resistant frame structure. The actual weight and properties of frame members were obtained from the drawings of the Ohio Union Building. The original structural drawings and design notes for the building can be found in Appendix A. Table 3.1 and Figure 3.3 show the column and beam properties and the longitudinal test frame geometry, respectively. In Table 3.1, the first and last numbers are the depth (in inch units) and nominal weight (lb per linear ft) of the column or beam,
respectively. The letters WF and B designated wide-flange (WF) shaped I-section and light I-section, respectively, which were commonly used in the 1950s (AISC, 1969). Beam numbers of B8 and B9 were not shown in Figure 3.3 since they are transverse beams presented in 3-D model.
3.3 The Bankers Life and Casualty Company Building
3.3.1 Description of the Bankers Life and Casualty Company (BLCC) Building
The second building, the Bankers Life and Casualty Company building was tested by Giriunas (2009). The building was located in Northbrook, Illinois, and built in 1968. As shown in Figure 3.5, only the longitudinal perimeter frame located on the north side of the BLCC building was tested and used in this study. The test part of the BLCC building was a two-story steel frame structure. The heights of first and second floors were 20 ft-6 in. and 14 ft-8 in., respectively, as shown in Figure 3.6. The building had a reinforced concrete (RC) framed basement, which was 10 ft-6 in. in height. Figure 3.7 shows the first floor framing plan of the building and removed columns are highlighted. The building had nine bays spanning 27 ft in the longitudinal direction and eight bays spanning 23 ft-6 in. in the transverse direction.
3.3.2 Properties of Structural Members
Table 3.2 shows designation of columns and beams of the BLCC building, which corresponds with Figure 3.6. The columns and beams in the basement are reinforced
shaped steel I-sections. The first and last numbers are the depth (inch) and nominal weight (lb per linear ft) of the steel column or beam, respectively.
Table 3.1 Column and beam sections of the Ohio Union building
Column section Beam section Column
number Column type
Beam
number Beam type
C1 10 WF 72 B1 24 B 76 C2 12 WF 133 B2 21 B 68 C3 12 WF 120 B3 16 B 58 C4 10 WF 100 B4 21 WF 62 C5 10 WF 89 B5 18 WF 50 C6 10 WF 54 B6 14 B 17.2 C7 10 WF 112 B7 14 B 22 C8 10 WF 60 B8 24 WF 76 C9 10 WF 33 B9 18 WF 45
Table 3.2 Column and beam sections of the Bankers Life and Casualty Company building Column section Beam section
Column
number Column type
Beam
number Beam type
c1 RC b1 RC Flat Slab
c2 10 WF 49 b2 24 I 79.9
c3 10 WF 72 b3 21 WF 62
Figure 3.1 The Ohio Union building before the demolition testing in 2007. The circle shows the tested portion of the building.
Figure 3.3 The elevation of the four-story test building in the longitudinal direction.
Figure 3.5 The north side of the Bankers Life and Casualty Company building prior to the demolition in 2008 (Giriunas, 2009).
Figure 3.6 The longitudinal end building frame of the north side of the Bankers Life and Casualty Company building.
Figure 3.7 The first floor plan for the test part of the BLCC building. The circles show first floor removed columns.
CHAPTER 4
ANALYTICAL MODELING PROCEDURES
4.1 Introduction
Computational progressive collapse analysis of the two tested buildings was performed using the commercially available computer program, SAP2000 (2009), and following the General Services Administration (GSA) guidelines (GSA, 2003). The actual test buildings were the Ohio Union building and the Bankers Life and Casualty Company building. Chapter 4 presents two-dimensional (2-D) and three-dimensional (3-D) computer models of each building using SAP2000 program. The assumptions and detailed procedures for the building model are described. Also, the calculations for loading conditions and the criteria regulated in the GSA guidelines are provided in this chapter.
4.2 Modeling Assumptions
When a building was modeled in this study, several assumptions were made to simplify and to clearly demonstrate the steps of progressive collapse analysis. The assumptions of the models are described below:
(1) The perimeter frames of the buildings were modeled as special moment resistant frames with connections that are stronger than beams. Thus, the model allowed plastic hinges to form in the beams, not in the connections or columns.
(2) The connections at the foundations were modeled as pinned connections. (3) Secondary members (e.g., transverse joist beams and braces) were disregarded,
and did not contribute to the progressive collapse resistance.
(4) The model did not consider the effect of large deflections. This is a reasonable assumption in this study because very large deflections or collapse was not observed in test buildings.
(5) The live load was assumed to be zero because non-structural loads were removed from the buildings prior to building demolition.
(6) Default hinge properties defined in FEMA-356 (2000) were used for nonlinear dynamic analysis in SAP2000 program.
(7) For the nonlinear dynamic analysis, damping ratio was assumed to be 1%. Before progressive collapse analysis, a sensitivity analysis of damping ratios was performed using the 3-D model of the Ohio Union building after the first column removal. Figure 4.1 shows changes in joint displacements above the
are typical damping ratios for steel buildings (Stevenson, 1980). Final displacements were the same for all damping ratios. The vibration within first 0.3-0.5 seconds was affected by damping ratio. As the damping ratio was lower, the vibration amplitudes of the Ohio Union building increased, resulting in larger displacements. Since the damping ratio of 0.5% is considered for the piping steel structures, 1% damping ratio was used in this research to examine the worst scenario for the dynamic response of the building.
4.3 Configuration and Modeling of the Buildings
Progressive collapse performance of two tested buildings was investigated using the SAP2000 computer program (SAP2000, 2009). The SAP2000 program is a well-known structural analysis and design software, commonly used in conventional building design and other applications. Using SAP2000 program, the longitudinal perimeter frame of each building was modeled and analyzed as a 2-D frame. 3-D frame models were also developed and analyzed for each building.
4.3.1 Ohio Union Building Model
Commercial SAP2000 program was used to analyze the progressive collapse response. Figure 4.2 shows 2-D model of the Ohio Union building with frame member numbers. Frame member numbers up to 45 are columns, and beams are numbered from 46 to 85. As illustrated in Figure 4.2, for the analysis, circled four columns were
sequentially removed in the same order as experimental procedures: (1) column 27, (2) column 22, (3) column 2, and (4) column 7.
3-D computer model of the building was also developed. Figure 4.3 shows a 3-D SAP2000 model for the Ohio Union building. While 2-D models help to investigate the general response, 3-D models can adequately account for 3-D effects and avoid overly conservative results. Both the DoD and GSA guidelines recommended the use of 3-D models in the progressive collapse analysis (DoD, 2005; GSA, 2003).
4.3.2 Bankers Life and Casualty Company (BLCC) Building Model
Figure 4.4 shows 2-D model of the BLCC building for the longitudinal end building frame. As shown, frame member numbers up to 26 are columns, and beams are numbered from 27 to 49. Based on field test results, most of the load redistribution between structural members has taken place during the torching phase in the field (Section 5.5). To better simulate the actual test results, circled four columns in the first story of the BLCC building were sequentially removed in the SAP2000 analysis, in the same order as the field torching process: (1) column 14, (2) column 17, (3) column 5, and (4) column 2.
A 3-D model of the BLCC building was also developed using SAP 2000, as recommended by the GSA guidelines, which is shown in Figure 4.5. The north side of the BLCC building, mainly considered in this study, had nine bays in the longitudinal direction and eight bays in the transverse direction. To simplify 3-D models, insignificant six bays in the back side were neglected. As shown in Figure 4.5, the 3-D
4.4 Material Properties
For 2-D and 3-D models, the actual weight and properties of frame members were obtained from the original structural drawings and available design notes of each building (see Appendix A and B). The Ohio Union building was a regular steel frame structure, including steel columns, beams, and connections. The tested steel moment resisting frames had rigid joint connections connecting vertical columns to horizontal beams, as shown in Figure 4.6. The yield strength of all steel frame members of the Ohio Union building was assumed to be 50,000 psi, as specified in the original design. The modulus of elasticity of steel was set equal to 29,000 ksi.
The Bankers Life and Casualty Company building had reinforced concrete (RC) columns with a compressive strength of 4,000 psi in the basement (Giriunas, 2009). The steel columns were rigidly connected to these RC columns at the first floor level. The steel columns and beams in the BLCC building had a specified yield stress of 36,000 psi and 42,000 psi, respectively (Giriunas, 2009). The steel girders, beams, and columns were connected with simple connections. The modulus of elasticity of the steel members was also set equal to 29,000 ksi.
4.5 Loading Conditions for Analysis
For progressive collapse analysis, GSA (2003) recommends a general loading factor to be used for every structural member in the building being evaluated or analyzed. Different loading conditions were applied to different analysis procedures. For example, GSA mandates the following loading conditions in downward direction for gravity loading for the linear static analysis of a structure:
Load = 2 (DL + 0.25·LL) [4.1] where DL is the self-weight of the structure (i.e., Dead Load), which can be automatically generated by SAP2000 based on element volume and material density, and LL is live load of the structure. A dynamic amplification factor of 2 is used to account for deceleration effects and simulate dynamic response when using static analysis procedures.
For nonlinear dynamic analysis, the following loading conditions are recommended in the GSA guidelines:
Load = DL + 0.25·LL [4.2] In this research, the live load was assumed to be zero because the test buildings were not occupied, and most of the partitions, furniture and other non-structural loads were removed from the buildings prior to building demolition. At the time of testing, the test building frames carried only dead loads due to the weight of various structural members, including walls, concrete slabs, beams, and columns.
4.5.1 Dead Load of the Ohio Union Building
Self-weights of the columns and beams were generated by SAP2000 program. The load of the slab was distributed to the adjacent beams with its tributary area. The density of concrete slab was considered to be 150 lb/ft3. The thickness of the slab on each floor and on roof was considered to be 4.5 in. and 3.5 in., respectively. To calculate the dead load of the walls, the density of glass was considered to be 160 lb/ft3, the concrete masonry units were assumed to be 135 lb/ft3, and exterior bricks were considered to be 120 lb/ft3. The thickness of the wall was 1.5 ft. The detailed wall
4.5.2 Dead Load of the Bankers Life and Casualty Company (BLCC) Building
The dead weights for various structural members on the BLCC building were obtained from Giriunas (2009). The weight of joists was 19 lb/ft. The roof material including corrugated steel plates, membranes and roof joists was assumed to be 25 lb/ft2. The slab was reinforced concrete slab with #4 rebar at 12″ center. The density of the slab was considered to be 150 lb/ft3. The thickness of the slab or wall on each floor was all 12 in. The wall contained glass, brick, and the concrete masonry units. To calculate the dead load of the walls, the densities of glass, reinforced concrete masonry blocks, and exterior bricks were assumed to be 160 lb/ft3, 135 lb/ft3, and 120 lb/ft3, respectively.
4.6 Slab Design
Figure 4.7 illustrates the plan view of the slab with the tributary area. As shown in the figure, the building consists of columns, main beams and secondary members in a slab. The intermediate steel beams (secondary members) were typically spaced 2 ft on center. In this research, the slab was considered as one-way spanning slab. The one-way slab is simply supported on two opposite sides only because the bending is in one direction only (McCormac and Nelson, 2006). The one-way slab was assumed to be a 12 in. wide beam.
The self weight (dead load) of the slab was distributed to the intermediate beams supporting the edges of the slab with its tributary area, and then transferred to the main beams as a uniform load. The loads transferred to the main beams were acting as a point load to each column. The stiffness of the building due to the slab was not considered in
the model since the joint connections of the intermediate beams were acting as a member trusses (pin-pin connections).
4.7 Acceptance Criteria for Progressive Collapse
4.7.1 Linear Static Analysis
To evaluate the results of a linear static analysis, the magnitude and distribution of predicted demands are determined by Demand-Capacity-Ratio (DCR). DCR for a structural component is defined as the ratio of the maximum demand (D) (e.g., moment,
Mmax) of the beam or column to its expected capacity (D) (e.g, ultimate moment capacity,
Mp). p M M C D DCR max [4.3]
where, moment demand, Mmax of the beam or column is calculated from linear static
analysis, and moment capacity, Mp is calculated as the product of plastic section modulus and yield strength. In Mp calculations for columns, the effect of the axial load is neglected in this study because the column axial loads were relatively small and did not affect the moment capacity of the cross section significantly. If a DCR value is greater than 1.0, theoretically the member has exceeded its ultimate capacity at that location. However, this alone does not signify failure of the structure as long as other members are capable of carrying the forces redistributed after the initial plastic hinge formation or