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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 Professor Shive K. Chaturvedi
Copyright by Brian Inhyok Song 2010
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 firststory 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 ii
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.
iii
DEDICATION
I dedicate this work to my father, mother, and wife.
iv
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. initiated this research.
Their devotion has
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.
v
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.
vi
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, URS Corporation, Warrenville, IL
vii
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
viii
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.
2.
Introduction …………………………………………………………….……..
1
1.1 General Background ….……………………………………………..….
1
1.2 Research Objectives ………………………………………………..…...
2
1.3 Outline of the Thesis …………………………….………………...……
4
Background Information on Progressive Collapse …….………….………...
6
2.1 Introduction …….....……………………………………………………
6
2.2 Definition of Progressive Collapse ……………………….…………….
6
2.3 Examples of Progressive Collapse …………………………...………...
7
ix
3.
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
Building Description …...………...…………………………………………....
24
3.1 Introduction …….....……………………………………………………
24
3.2 The Ohio Union Building ……………..………….…………………….
24
3.2.1 Description of the Ohio Union Building ……….……………...
24
3.2.2 Properties of Structural Members ……………………………...
25
x
4.
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
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
Tables and Figures ………….……………………………………………….
xi
46
5.
6.
7.
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
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
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 Calculated DCR Values …………………………..…………………….
103
xii
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
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
Appendix D. Experimental Testing of the BLCC building by Giriunas (2009) .
149
8.
xiii
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 ….………………………………..
3.1
20
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 …………………….......................
3.5
The north side of the Bankers Life and Casualty Company building prior to the demolition in 2008 .……………………………………………....………...
3.6
30
31
The longitudinal end building frame of the north side of the Bankers Life and Casualty Company building …………………………………………………... xiv
31
3.7
The first floor plan for the test part of the BLCC building. The circles show first floor removed columns …………………………………………………...
4.1
The sensitivity analysis as different damping ratios using the 3-D model of the Ohio Union building after first column removal ……………………………....
4.2
49
Three-dimensional SAP2000 model of the Ohio Union building (Circled columns are removed in the order shown) …………………………………….
4.4
48
Two-dimensional SAP2000 model of the Ohio Union building with frame member numbers …...………………………………………………………….
4.3
32
49
Two-dimensional SAP2000 model of the Bankers Life and Casualty Company building with frame member numbers (Circled columns are removed in the order shown) ………………………..........................................
4.5
50
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 .………………………………………………………………………..
xv
55
4.13
Nonlinear dynamic analysis case definition in SAP2000 at the last column removal …………....…………………………………………………………...
5.1
Exterior analysis cases considered in the progressive collapse analysis of framed structures (GSA, 2003) ………………….……………..………………
5.2
63
Maximum allowable collapse areas for a structure that uses columns for the primary vertical support system (GSA, 2003) …………………………..……..
5.3
56
63
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) …………………
5.8
67
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 ……………………………………………………...... xvi
72
5.13
The placement of strain gauges in the BLCC building with columns and beam labeled ……………..……………………………………………………...……
5.14
72
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 …………………………………………………………...
6.10
Displacement of the joints above the first and second removed columns (Joint 1 and 2, respectively) after the second column removal ……………………....
6.11
94
Displacement of the joints above each removed column after all columns removal ………………………………………………………………………...
6.13
93
Displacement of the joints above the first, second, and third removed columns (Joint 1, 2, and 3, respectively) after the third column removal ……….………
6.12
93
94
Deformed shape of the 3-D Ohio Union building model after each column removal as part of linear static analysis .………………………………………. xvii
95
6.14
Deformed shape of 3-D model with corresponding DCR values after the loss of four columns ….…………………..................................................................
6.15
95
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 ……………………………
6.21
Time history of joint displacements calculated from 2-D nonlinear dynamic analysis …………………………………………………..................................
6.22
99
99
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 columns removal ……………………………………………………………… xviii
112
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
xix
LIST OF TABLES
Table
Page
3.1
Column and beam sections of the Ohio Union building …………………..
3.2
Column and beam sections of the Bankers Life and Casualty Company
28
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
7.1
removed after all columns removal …………………………………..…...
88
DCR values calculated from 2-D model for steel frame members ……......
107
xx
7.2
DCR values calculated from 3-D model for steel frame members ………..
7.3
Comparison of maximum vertical displacement (in.) after all columns removal …………………………………………………………………....
xxi
108
109
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 1
against the Alfred P. Murrah Building and the World Trade Center showed that welldesigned 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 The overall objective of this research was to assess the potential for progressive collapse of two existing buildings through experimental testing and computational 2
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.
3
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). properties of the structural members for each building were also provided. 4
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.
5
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 hazards including earthquakes. 6
Once a structural element fails, the structure should enable an alternative loadcarrying 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 7
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 wellknown 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.
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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 9
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 was caused by a very large impact and fire, it is a progressive collapse but not a 10
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. 11
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 structural response (ACI 318-08, 2008). However, this method is not recommended for 12
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.
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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 loadbearing 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 Agnew, 2006; McKay, 2008; Powell, 2005). A complex analysis is desired to obtain 14
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 mediumrise 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 15
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.
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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.
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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 beamcolumn. 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 occurs in the double span, resulting in the sagging floor. The beams act as cables 18
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.
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Figure 2.5 Timeline of major catastrophic events followed by major building codes changes for progressive collapse mitigation (modified from Humay et al., 2006).
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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.
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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 nonlinear 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
22
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.
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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
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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, 25
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 concrete (RC) while others in the first and second floor level are wide-flange (WF) 26
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.
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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
c4
8 WF 31
b4
18 WF 45
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Figure 3.1 The Ohio Union building before the demolition testing in 2007. The circle shows the tested portion of the building.
Figure 3.2 The east side of the Ohio Union building before the demolition testing in 2007. 29
Figure 3.3 The elevation of the four-story test building in the longitudinal direction.
Figure 3.4 Structural plan for the first floor level of the test part of the Ohio Union building and removed columns highlighted. 30
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.
31
Figure 3.7 The first floor plan for the test part of the BLCC building. The circles show first floor removed columns.
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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 (3D) 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.
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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 removed column as different damping ratios ranging from 0.5% to 5%, which 34
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 wellknown 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
35
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 model displays only front two bays that were most impacted by column removals. 36
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: 37
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 section and slab section are presented in Appendix A. 38
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
39
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).
DCR
D M max C Mp
[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 failure.
40
Table 4.1 provides the GSA specified DCR limits for each steel frame component. If structural members with DCR values exceed those given in Table 4.1, the members are to be considered failed members, resulting in severe damage or potential collapse of the structure (GSA, 2003). Tables 4.2 Table 4.3 show the calculated DCR values of the structural
members, based on Table 4.1 and member properties, for the Ohio Union and the BLCC building, respectively. For both Ohio Union and BLCC buildings, a DCR value of 2.0 and 3.0 was used as acceptance criteria for columns and beams, respectively.
4.7.2 Nonlinear Dynamic Analysis The performance evaluation criteria for nonlinear dynamic analysis procedures are based on plastic hinge rotation and displacement ductility, while for linear static analysis methods the evaluation criteria are based on demand capacity ratio (DCR). Figure 4.8 shows the measurement of plastic hinge rotation angle, after the formation of plastic hinges caused by column removal. Based on Figure 4.8, plastic hinge rotation angle
for beam members on each side of the removed column can be measured between horizontal line and tangent to maximum deflected shape, which is defined by Equation 4.4.
max L
tan 1
[4.4]
where, θ is maximum hinge rotation, δmax is maximum displacement of columns at the location where the column is removed, and L is beam length or column spacing in the longitudinal direction.
41
Displacement ductility ratio (μ) is defined as the ratio of maximum displacement to elastic limit.
max e
[4.5]
where, δmax is maximum displacement of columns or beams at a reference point, which can be calculated from SAP2000 program, and δe is the elastic deflection limit at that point, which is vertical displacement when the first plastic hinge forms. Based on the GSA guidelines (GSA 2003, Table 2.1), the acceptance criteria of rotation for steel columns and beams are 12o (degree) or 21% radians. Displacement ductility should not exceed a value of 20 for both steel columns and beams at failure after the development of catenary action.
4.8 SAP2000 Analysis Procedures In this research, SAP2000 computer program (SPA2000, 2009) was used to create a model of the test buildings and to examine the redistribution of loads after the firststory columns were removed. Two different methods of analysis (i.e., linear static and nonlinear dynamic methods) were implemented using SAP2000. The behavior of the steel frame buildings after column removal was predicted through each method, and the analysis results were discussed based on GSA guidelines (GSA, 2003). The detailed analysis procedures for linear static and nonlinear dynamic methods are described below.
42
4.8.1 Step-by-step Procedure for Linear Static Analysis Linear static method is the most simplified and easiest method of progressive collapse analysis. This method is only capable of analyzing very simple structures with predictable behavior because neither geometric nor material nonlinear behavior is considered. Dynamic amplification parameters to account for inertia and damping effects should be estimated by the user. The analysis was run using the linear static option in SAP2000. The DCR values and displacements were determined from the SAP2000 model. This analysis procedure involves the following steps: 1. Build a 2-D or 3-D model in the SAP2000 computer program. 2. Set “Load Case Type” to be “Static” and “Analysis Type” to be “Linear”, as shown in Figure 4.9. 3. Apply the amplified static load combination, as defined in the Equation 4.1. As can be seen in “Loads Applied” section in Figure 4.9, a scale factor of 2 was applied to dead load. 4. Perform linear static analysis in SAP2000. 5. Hand-calculate DCR values by using maximum bending moments generated from SAP2000 program. 6. Evaluate the results based on the DCR values.
4.8.2 Step-by-step Procedure for Nonlinear Dynamic Analysis Nonlinear dynamic procedure is the most thorough and accurate method of progressive collapse analysis, ideally providing the most realistic results. In this analysis, 43
a primary load-carrying structural member is removed dynamically, and structural material is allowed to undergo nonlinear behavior beyond its elastic limit to failure. The analysis was run using the nonlinear time-history option in SAP2000. This method requires the users to define several dynamic and nonlinear parameters including time step, damping ratio, and plastic hinges. The steps required in performing the analysis are given below: 1. Build a 2-D or 3-D model in the SAP2000 computer program. 2. Use the default hinge properties for steel buildings provided in the SAP2000 program, which corresponds to the hinge definitions in FEMA 356 (FEMA356, 2000). Figure 4.10 presents a graphical representation of the hinge definition for the steel frame building. In Figure 4.10, Point A is the origin, Point B corresponds to yielding, Point C is for maximum capacity (Mp), Point D indicates failure, and Point E is the residual strength and deformation capacity. 3. Define a damping ratio. Viscous damping was considered in this research. As discussed in Section 4.1, damping coefficient was assumed to be 1 % (Figure 4.11). 4. Define an appropriate time step in the time history function definition. As shown in Figure 4.12, the output time step size of 0.01 was selected in this research. The number of output time steps up to maximum displacement was set to be 1000.
44
5. Set “Load Case Type” to be “Time History”, “Analysis Type” to be “Nonlinear”, and “Time History Type” to be “Direct Integration”, as shown in Figure 4.12. 6. Apply dynamic load combinations, as defined by Equation 4.2. A scale factor of 1 was used for the dead load applied (Figure 4.12). Live load was assumed to be zero (Section 4.1). 7. Define the initial conditions. For the first column removal (Column 27 of the Ohio Union building), zero initial condition was used (i.e., undamaged structure with gravity loading), as shown in Figure 4.12. From the second column removal to the fourth column removal, the initial conditions were continued from a previous nonlinear analysis. For example of the Ohio Union building analysis, initial conditions for the fourth column (Column 7) removal analysis were the same as the state at the end of nonlinear analysis for the third column (Column 2) removal which was saved and designated as a “LOSS2NLD” in Figure 4.13. 8. Perform nonlinear time history analysis. 9. Verify and evaluate the analysis results such as the maximum ductility and plastic hinge rotation values, which were defined in Equations 4.4 and 4.5, respectively.
45
Table 4.1 GSA specified DCR acceptance criteria for the steel building (GSA, 2003)
bf = Width of the compression flange tf = Flange thickness Fye = Expected yield strength h = Distance from inside of compression flange to inside of tension flange tw = Web thickness PCL = Lower bound compression strength of the column P = Axial force in member taken as Quf 46
Table 4.2 Calculated DCR limits for structural members of the Ohio Union building. Column section
Beam section
Column type
DCR limits
Beam type
DCR limits
10 WF 72
2
24 B 76
3
12 WF 133
2
21 B 68
3
12 WF 120
2
16 B 58
3
10 WF 100
2
21 WF 62
3
10 WF 89
2
18 WF 50
3
10 WF 54
2
14 B 17.2
3
10 WF 112
2
14 B 22
3
10 WF 60
2
24 WF 76
3
10 WF 33
2
18 WF 45
3
Table 4.3 Calculated DCR limits for structural members of the Bankers Life and Casualty Company building. Column section
Beam section
Column type
DCR limits
Beam type
DCR limits
10 WF 49
2
24 I 79.9
3
10 WF 72
2
21 WF 62
3
8 WF 31
2
18 WF 45
3
47
Figure 4.1 The sensitivity analysis as different damping ratios using the 3-D model of the Ohio Union building after first column removal.
48
Figure 4.2 Two-dimensional SAP2000 model of the Ohio Union building with frame member numbers (Circled columns are removed in the order shown).
Figure 4.3 Three-dimensional SAP2000 model of the Ohio Union building (Circled columns are removed in the order shown). 49
Figure 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).
Figure 4.5 Three-dimensional SAP2000 model of the Bankers Life and Casualty Company building (Circled columns are removed in the order shown).
50
Figure 4.6 Typical joint connection of the Ohio Union building (from original drawings).
Figure 4.7 The plan view of the one-way slab with a tributary area.
51
Figure 4.8 Measurement of plastic hinge rotation following the removal of middle column.
Figure 4.9 Linear static analysis case definition in SAP2000.
52
Notes for the assumed default properties of moment hinge (M3): (1) Slope between points B and C is taken as 3 % strain hardening. (2) Yield rotation (θy) is based on Equations 5-1 and 5-2 in FEMA-356 (2000). (3) Points C, D and E are based on FEMA-356 (2000), Table 5-6, for
bf 2t f
52 . Fye
(4) The PMM curve is the same as the uniaxial M3 curve, except that it will always be symmetrical about the origin. (5) The PMM interaction surface is calculated using FEMA-356 (2000) Equation 5-4.
Figure 4.10 Hinge definitions for steel frame building in SAP2000.
53
Figure 4.11 Definition of damping ratios in SAP2000.
54
Figure 4.12 Nonlinear dynamic analysis case definition in SAP2000 at the first column removal.
55
Figure 4.13 Nonlinear dynamic analysis case definition in SAP2000 at the last column removal.
56
CHAPTER 5
EXPERIMENTAL RESEARCH
5.1 Introduction The Ohio Union building, located at the Ohio State University campus, was tested by physically removing four first-story columns prior to demolition of the building scheduled in June, 2007. This chapter describes the testing procedures and methodology for the column removal test in detail. The location of the strain gauges on structural members and the measurement of the strain data are also described. Field experiments of the Bankers Life and Casualty Company (BLCC) building were conducted by Giriunas (2009), when the building was scheduled for demolition in August, 2008. Experimental data obtained from the BLCC field test are summarized in this chapter. Detailed testing results for the BLCC building were reported by Giriunas (2009), which are presented in Appendix D.
57
5.2 Column Removal Procedure For progressive collapse analysis, GSA (2003) mandates several column loss scenarios. The GSA guidelines require removal of first-story columns. As shown in Figure 5.1, GSA (2003) recommends that a structure be analyzed by instantaneously removing a column from near the middle of the short side of the building, near the middle of the long side of building, and at the corner of the building. It was implied that immediate removal of an exterior column causes serious damage to the structural bays directly linked to the removed column or to an area of 1800 ft2 at the floor level directly above the removed column (Figure 5.2). Consistent with the GSA analysis recommendations, in our experiments, four first-story exterior columns were sequentially removed from the Ohio Union building in the following order: (1) two columns near the middle of the longitudinal perimeter frame (i.e., Column 27 was removed first, and Column 22 was removed second), (2) column in the building corner (i.e., Column 2 was removed third), and (3) column next to the corner column (i.e., Column 7 was removed forth), as shown in Figure 5.3. Each test column was first torched or cut through its cross section near the top and bottom, as shown in Figures 5.4a and 5.4c. The columns were torched in the same order as the removal process, but Column 7 was torched third, and Column 2 was torched fourth. The torched lines were approximately 3 ft below from the top and 2 ft above the bottom of each column. After torching 20% of the web remained. The demolition team then punched a hole in between the torched lines of each column, and passed the cable through the hole (Figure 5.4b). The column segment between the torched sections was then pulled out by a bulldozer, as shown in Figure 5.5c. The removed column segment is 58
shown in Figure 5.5a. The column was removed within a very short period of time, simulating instantaneous removal of a column as recommended in the GSA design guidelines. Figure 5.6 shows the Ohio Union building after field testing. Even though four columns are removed from the first story of the building, the building did not collapse. No visible permanent deformations were observed in the connections or beams above the removed columns.
5.3 Instrumentation The strain gauges can measure the strain caused by the compressive and tensile forces, and hence the change in the axial forces and deflections can be monitored during the removal of columns. In order to measure the strains in various columns and beams, strain gauges were attached on the columns and beams closely linked to the removed columns prior to column removal tests. In this study, universal general purpose strain gauge with a resistance of 120±0.3% Ohms and a strain range of ±3% was used. A total of 15 strain gauges were installed on the columns and beams of the Ohio Union building. Figure 5.7 shows the location of the strain gauges on the structural members on the East side of the Ohio Union building. Except for one strain gauge (Gauge 15) attached on the beam (Beam 67), others were attached on the columns. As described in Section 4.3.1, Columns 27, 22, 2, and 7 were removed during the field tests. Four strain gauges were placed on the removed columns, approximately 10 in. from the top. As shown in Figure 5.7, Gauge 5 and 6 were attached on Column 7, and Gauge 13 and 14 were attached on Column 22. 59
Columns and beams were exposed by removing the exterior brick wall. The surface of columns and beams was ground down to remove all paint and debris. Before each strain gauge was attached, a degreaser, conditioner and a neutralizer were applied to the cleared surface of column or beam. Finally, the attached strain gauges were covered with a strain gauge shield to protect them from debris (Figure 5.8). All strain gauges were connected to a portable data acquisition system and laptop computer, as shown in Figure 5.9.
5.4 Strain Measurements The strain values from all 15 strain gauges were monitored and recorded by the computer during each column removal. Strain value, ε is calculated from the change in length of a structural member as:
ε
ΔL L0
[5.1]
where, ΔL is the change in length of a structural member, and L0 is the original length of the structural member. A positive strain value means the structural member elongates and is in tension, while a negative strain value indicates that the structural member contracts and is in compression. Figure 5.10 shows the strain data obtained from all 15 strain gauges during the torching process. Unfortunately, uninterrupted strain gauge readings were not recorded for a long time during the entire torching process. We could obtain the recorded strain values, only when the third and forth columns (Column 7 and 2, respectively) were torched. Strain values had to be manually set up to zero at the beginning of each column 60
torching process. As shown in Figure 5.10, all strain values dropped to negative values after each column was torched, and then stabilized after a certain amount of time. These negative strain values indicate that the structural members contracted and compressed when the neighboring columns were torched. Strain gauges 1, 2, 3, and 4 had relatively larger strain difference or drop (Δε) than other strain gauges since they were attached on the columns right next to the Column 7 and 2 (Figure 5.7). Most of the strain values dropped more when Column 2 (the last column) was torched. For example, strain drop,
Δε values of strain gauge 1 were approximately -45×10-6 and -170×10-6 after Column 7 and Column 2 were torched, respectively. Interestingly, after Column 7 was torched (Figure 5.10a), all 15 strain gauges values increased and went back up to zero or positive values within 30 seconds. It seems that the load redistribution has taken place during the torching process. Figure 5.11 shows measurements from strain gauge 1, 3, 6 10, 11, and 15 during the column removal process. Similar to the torching phase, strain gauge values dropped after each column removal, increased up to zero after a certain amount of time, and then stabilized.
5.5 Summary of Measured Strain Data from the BLCC Building Test Experimental data obtained from the BLCC building are summarized in this section. The BLCC building was tested by Giriunas (2009). Similar to the testing of the Ohio Union building, four first-story columns were removed sequentially in the following order: (1) two columns near the middle of the longitudinal perimeter frame with ten columns (i.e., Column 14 was removed first, and Column 17 was removed second), (2) 61
column in the building corner (i.e., Column 2 was removed third), and (3) column next to the corner column (i.e., Column 5 was removed forth), which is shown in Figure 5.12. Same as the Ohio Union building test, each column was first weakened by a blow torching prior to its removal in the following order: (1) Column 14, (2) Column 17, (3) Column 5, and (4) Column 2. Giriunas (2009) reported that most of the measured strain values dropped and had a negative value when each column was torched and poked. A change in the measured strain data (Δε) was much larger during torching phase than during removal phase. Strain gauge 7, attached on Column 11 (Figure 5.13), was selected from the experimental study because it was believed to have recorded the most consistent and accurate data in the field. Figure 5.14 shows the history of measured strain data for strain gauge 7 during the entire experiment including poking, torching, and removal processes. As shown in Figure 5.14, the strain values dropped after each torching or poking process. In particular, the most significant drop, approximately 300×10-6, occurred after the last column (Column 2) was torched (see the purple color section in Figure 5.14). The strain value continued to decrease between the last column being torched and the first column removed. Once the column removal process began, the strain values rarely changed and stayed almost constant. Details of the measured test data can be found in Appendix D and Giriunas (2009).
62
Figure 5.1 Exterior analysis cases considered in the progressive collapse analysis of framed structures (GSA, 2003).
Figure 5.2 Maximum allowable collapse areas for a structure that uses columns for the primary vertical support system (GSA, 2003). 63
Figure 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
(a)
(b)
(c)
Figure 5.4 Field testing: torched columns with a chain attached. 65
(a)
(b)
(c)
Figure 5.5 Field testing: column removal process. 66
Figure 5.6 Ohio Union building after all columns are removed.
Figure 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
Figure 5.8 Strain gauges attached on steel columns and a beam connected to one of the removed columns.
68
Figure 5.9 Portable data acquisition system to monitor the strain.
69
Figure 5.10 All strain gauge measurements when (a) Column 7 and (b) Column 2 were torched.
70
Figure 5.11 Strain gauge measurements during column removals.
71
Figure 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.
28
2
5
8
11
14
17
20
Figure 5.13 The placement of strain gauges in the BLCC building with columns and beam labeled (Giriunas, 2009). 72
Column 14 torching
Column 5 torching
Columns poking
Column 17 torching
Column 5 torching
Columns removal
Column 2 torching
Figure 5.14 Measurements from strain gauge 7 during the entire field test of the BLCC building (after Giriunas, 2009). 73
CHAPTER 6
COMPUTATIONAL ANALYSIS OF THE OHIO UNION BUILDING
6.1 Introduction In this chapter, progressive collapse performance of the Ohio Union building was investigated using the SAP2000 computer program (SAP2000, 2009). Two-dimensional (2-D) as well as three-dimensional (3-D) models of the building were developed to analyze and compare the progressive collapse response. The results from computer models were compared with the strain values recorded during field testing. Two different analysis procedures were evaluated to examine dynamic effects in modeling progressive collapse scenarios; linear static and nonlinear dynamic procedures. Difference between linear and nonlinear case would be negligible because almost all members stayed elastic with limited geometric nonlinear (P-delta) effects. The detailed modeling procedures and assumptions were described in Chapter 4. For the loading conditions, only dead load was used for gravity load and live load was assumed to be zero. Linear static analysis was used an amplified (by a factor of 2) combination of the dead loads, as shown in Section 4.5. For nonlinear dynamic analysis, 74
damping ratio was assumed to be 1 %, and the time step size of 0.01 was selected in this study (Section 4.8.2).
6.2 2-D Progressive Collapse Analysis
6.2.1 Linear Static Analysis The linear static analysis is the simplest method commonly used to investigate progressive collapse potential of a building (ASCE 7-05, 2005).
The results were
evaluated by comparing the demand-to-capacity ratios (DCR), based on the GSA guideline. The calculation of the DCR was defined in Equation 4.3 as the ratio of maximum calculated demand to the maximum strength of a member. Based on the GSA specified DCR limits for each steel frame component (Table 4.1), a DCR value of 2.0 and
3.0 was used as acceptance criteria for columns and beams of the Ohio Union building, respectively (Table 4.2). Figured 6.1 to 6.4 show the elastic moment diagrams after the removal of each column from the Ohio Union building (Figure 5.3). When the first two columns were removed, the largest bending moments were localized and typically occurred in the members above or immediately next to the removed columns. The maximum moments significantly increased and spread within the frame when three and four columns were removed. Table 6.1 summarizes the calculated DCR values for selected critical frame members for each column removal scenario. Frame members numbered below 25 are columns and above 25 are beams (see Figure 4.2). As shown in Table 6.1, in general, the 75
DCR values increase with increasing number of removed columns. DCR values for most members were less than the criteria of 2.0. It is, therefore, concluded that the Ohio Student Union building does satisfy the GSA 2003 progressive collapse criteria for most frame members of this structure. Columns were impacted more than beams when the four columns were removed from the frame. After all four columns were removed, no beams and only five columns (i.e., columns 8, 9, 10, 20 and 25) exceeded the DCR criteria. Figure 6.5 shows the moment diagram and the corresponding DCR values at the top of each column and at the end of each beam after four columns were removed from the frame. The columns in the top story show higher DCR values, indicating after loading-bearing columns removal, additional loads were transferred upward through tension in the columns above and the remaining structures transferred the loads to adjacent, undamaged spans. Smaller cross section used in the top-story columns can be another explanation for the higher DCR values observed in the top story. As shown in Figure 6.5, the maximum DCR value, 2.83 was calculated for Column 10 in the top story. The maximum DCR value calculated in beams was 0.94, which was in Beam 63 in the third floor level. Figure 6.6 shows DCR values for each frame member for all column removal cases. Frame member numbers up to 45 are columns, and beams are numbered from 46 to 85. After the first column was removed, DCR values for all columns and beams were below 0.5. The DCR values after the loss of second column was similar to those of third column loss, all of which were less than 1.5.
The DCR values for columns were
remarkably increased after the fourth column was lost. There were five columns with 76
DCR values exceeding the acceptance criteria in this case. However, the change in DCR values for beam was not significant, compared with that of columns. The DCR values of beams were always less than 1.0. This is probably due to potential redistribution of loads to the adjacent beams in the analyzed frame. After four columns were removed, the building was more susceptible to progressive collapse, which was also reflected in the maximum displacements calculated by linear static analysis. As columns were sequentially removed, the maximum vertical displacements were calculated as 4.49, 4.54, 12.10, and 7.06 in. at the joints immediate above the first (Column 27), second (Column 22), third (Column 2), and forth (Column 7) removed columns, respectively.
6.2.2 Nonlinear Dynamic Analysis Progressive collapse is a dynamic event involving vibrations of building elements and resulting in internal dynamic forces affected by inertia and damping. Progressive collapse is also inherently a nonlinear event in which structural elements are stressed beyond their elastic limit to failure. Nonlinear dynamic procedure includes the dynamic nature and nonlinear behavior of the progressive collapse phenomenon, and therefore nonlinear dynamic analysis is more realistic and accurate than linear static analysis (Marjanishvili, 2004). In nonlinear dynamic analysis, a major load bearing structural element is removed dynamically and the structural material is allowed to undergo nonlinear behavior. Figure 6.7 illustrates the replacement of a removed column by equivalent loads in nonlinear dynamic analysis. First, the building is modeled with its dead load assigned. After the 77
internal (equivalent) forces in a given column are determined, the column is replaced with its equivalent forces to simulate the instantaneous removal of the column. As shown in Figure 6.8, the equivalent load is first assigned with a uniform time history function. This corresponds to the initial case where the column is still in place carrying the dead load. Then the column is removed suddenly using a step function. The sum of a uniform time history function and the column loss function represents the column loss. This is referred to as a time-history analysis where the response of the structure is calculated during and after the removal of column(s) as a function of time. The vertical displacements of the joints above each removed column were calculated during and after removal of each column in the first story. Figures 6.9 to 6.12 show the vertical displacement history of Joint 1, 2, 3, and 4 above the first (Column 27), second (Column 22), third (Column 2), and fourth (Column7) removed columns, respectively (see Figure 4.2). The columns were removed at time of 0 second. Once each column was removed, negative values showed downward displacements in all cases. Figure 6.9 shows the displacements of Joint 1. The figure displays two displacement values; maximum vertical displacement during vibration, and permanent vertical displacement at the end of vibration. As shown in Figure 6.9, Joint 1 had its maximum displacement of 0.35 in. right after first column was removed, and then, it settled down in about 0.5 seconds at a permanent displacement of 0.22 in. When the second column was removed (Figure 6.10), the joints settled in approximately 1.5 seconds, and Joint 1 deflected 1.15 in. and Joint 2 settled at 1.17 in. As more columns are removed, it took more time for the joints (and other members) to settle down. As shown in Figure 6.11, after the third column removal, the joints settled in 1.5 seconds, and Joint 1, Joint 2, and 78
Joint 3 settled at 1.74, 1.76 and 1.13 in., respectively. After four columns were removed, all four joints settled in about 5 seconds. As shown in Figure 6.12, the joints above the four removed columns settled at 2.38, 2.41, 7.06, and 3.93 in., respectively.
The
maximum vertical displacements calculated from 2-D nonlinear dynamic analysis were 2.80, 2.85, 8.06, and 4.46 in. at Joint 1, 2, 3, and 4, respectively.
6.3 Comparison of Results from 2-D and 3-D Analyses A 3-D model of the Ohio Union building was developed, and progressive collapse analysis was performed using this model. Detailed procedures for modeling and SAP200 analysis were presented in Chapter 4. Figure 6.13 shows the deformed shapes obtained from 3-D linear static analysis after the removal of each column. As shown, the building was significantly deformed as more columns were removed. Larger deformations were observed in the beams and columns in the higher stories and next to the removed columns, which trends were consistent with DCR values calculated from 3-D models (Figure 6.14). In particular, transverse beams connected to the removed columns significantly deformed, indicating that their contribution to overall resistance of the frame was significant. The deformations in the 3-D model were smaller mainly due to contribution of slab and transverse beams, which were discussed below.
6.3.1 Calculated DCR Values Figure 6.15 shows a comparison of DCR values for moments determined from 2D and 3-D models after four columns were removed. As mentioned in Section 6.2.1, columns were more impacted than beams in 2-D linear static analysis. Five columns 79
exceeded the DCR criteria of 2.0 (GSA, 2003), but none for the beams after four columns were removed (Figure 6.6). The DCR values of all beams were less than 1.0, and the maximum DCR value observed in beams was 0.94. However, DCR values calculated from 3-D linear static analysis showed an opposite trend compared to 2-D results. Beams were more influenced by a column loss. As shown in Table 6.2, the maximum DCR value of beams was 1.49 (Beam 65 in the top story and next to the removed Column 22, in Figure 4.2) while that of columns was 0.96 (Column 23 right above removed Column 22, in Figure 4.2). The reason that beams had higher DCR values than columns in the 3D model was probably due to the larger deformation and participation of beams in the transverse directions. As can be seen in Figure 6.13, beams, especially in the top story, were significantly deformed in the transverse direction after each column removal. It can be concluded that 2-D model may lead to limited and underestimated demands for beams. More interestingly, it was observed that DCR values calculated from 3-D model were smaller than those from 2-D model for columns and most beams. As shown in Figure 6.15, all members had DCR values of less than 1.5, and satisfied GSA acceptance criteria of 2.0 for columns and 3.0 for beams. This could be mainly due to contribution of transverse beams. The transverse beams can more distribute loads to the connected columns and beams in the transverse direction, leading to a decrease of force demands in structural members.
6.3.2 Comparison of Calculated and Measured Strains Table 6.3 shows changes in strain (Δε) obtained from the field test, compared with those calculated from 2-D and 3-D models. During the field test, strain values 80
changed as each column was torched and removed (see Section 5.4). Most of the strain values dropped more when the last column was torched than when it was removed. Therefore, Δε (Field Test) reported in Table 6.3 are the changes in strain values recorded from the strain gauges in the field after last column torching. Δε (Computational Model) are the changes in strain values after last column removal.
Δε is calculated by
considering the combined effect of axial load and a bending moment, both of which were determined from the SAP2000 analysis:
Δε
ΔΡ ΔΜ AE SE
[6.1]
where, ΔP is the change in axial force determined from SAP 2000, ΔM is the change in bending moment determined from SAP 2000, A is the cross sectional area of the column or beam, E is the elastic modulus for a given structural member, and S is the section modulus. Equation 6.1 is based on the assumption that the section stays elastic under the applied loads. This assumption is reasonable because almost all measured and calculated
fy
E
strain values were under or near the yield strain ε y
50 ksi 1.72 10 3 . 29,000 ksi
The strain gauge 15, attached on Beam 67, was selected from the experimental study to compare the results from 2-D and 3-D models because it was the only strain gauge left in the perimeter frame in the 2-D model after the four columns were removed (location of strain gauges are shown in Figure 5.7). Strain gauges 1, 4, 8, 9 and 11 were attached on the interior columns.
As shown in Table 6.3, for strain gauge 15, Δε
calculated from the 3-D model was closer to the experimental result than that from the 2D model.
After the column was removed, the loads carried by that column were 81
transferred to neighboring columns and beams. 3-D model can account for redistribution of the building’s weight to both exterior and interior columns and beams while only exterior members were considered in the 2-D model. All of Δε values calculated from the 3-D models were very comparable to the measured strains. Figures 6.16 to 6.19 compare strain values (Δε) measured in the field and calculated from linear static and nonlinear dynamic analyses in 3-D models. For the interior columns (i.e., Strain gauge 4, 9, and 11) and the beam (i.e, Strain gauge 15), the measured strains were closer to the Δε values calculated from the 3-D nonlinear dynamic analysis. The strain increments (Δε) calculated from the linear static analysis were much larger than the measured values.
6.3.3 Vertical Displacements Figure 6.20 shows changes in maximum joint displacement calculated from the 3D linear static analysis during the entire column removal process. After all four columns were removed, the maximum calculated displacements were 3.09, 3.13, 3.95, and 2.90 in. at the joints above the first (Column 27), second (Column 22), third (Column 2), and fourth (Column 7) removed columns, respectively (Table 6.4).
Each maximum
displacement was shown by a horizontal line in the Figure 6.20 since the linear static analysis procedure did not consider dynamic behavior and vibration of structural members. Figures 6.21 and 6.22 show changes of the maximum joint displacements calculated from 2-D and 3-D nonlinear dynamic analysis, respectively. Whenever a column was removed, the building was allowed to deform until it settled, showing
82
dynamic response effects. Both models show similar trends; Joint 3 above the third removed column had the largest maximum and permanent vertical displacement. Table 6.4 shows the comparison of maximum vertical displacements calculated from linear static analysis and nonlinear dynamic analysis. Linear static analysis resulted in higher maximum vertical displacements than nonlinear dynamic analysis in both 2-D and 3-D models. For example, the maximum vertical displacement calculated from 2-D linear static analysis was 12.1 in. at Joint 3 while that from the 2-D nonlinear dynamic analysis was 8.06 in. It seems that the impact factor of 2 (i.e., dead loads multiplied by 2) in linear static analysis led to very conservative results. This observation is consistent with the strain results. Ruth et al. (2006) found that an impact factor of 1.5 better represented the dynamic effect, especially for steel moment frames. Marjanishvili (2004) also reported that a more complicated analysis method such as nonlinear dynamic analysis may result in less severe structural response, due to more accurate estimates of load distribution and less stringent evaluation criteria. Another observation from Table 6.4 was that 3-D models showed lower maximum displacements than 2-D models whether linear static analysis or nonlinear dynamic analysis. Similar to the DCR result, the transverse beams connected to the interior columns and the beams increased the overall resistance of structure, leading to smaller deformation in the 3-D model.
6.3.4 Plastic Hinge Rotations The acceptance criteria for nonlinear dynamic analysis are determined by plastic hinge rotations or displacement ductility (GSA, 2003). Plastic hinge rotation was chosen 83
as performance evaluation criteria for the nonlinear dynamic analysis. The plastic hinge locations in the 3-D model are shown in Figure 6.23. The default hinge properties provided in the SAP2000 program were used (see Figure 4.10), which corresponds to the hinge definitions in FEMA 356 (FEMA-356, 2000). As addressed in Equation 4.4, plastic hinge rotations can be calculated as the ratio of horizontal line and tangent to the maximum joint displacement. Table 6.5 shows plastic hinge rotations at the location where columns were removed after four columns removal. Hinge rotations calculated from the 3-D model were smaller than those from the 2-D model, because of lower maximum displacement values in 3-D nonlinear dynamic analysis. In spite of that, the maximum plastic hinge rotation was only 1.80o at the hinge above third removed column (Column 2) in linear static analysis. For both 2-D and 3-D nonlinear dynamic procedure, the values of plastic hinge rotation were much smaller than 12o of GSA (2003) criteria.
Thus, the building was considered not
susceptible to progressive collapse according to GSA guidelines (GSA, 2003). As shown in Figure 6.6, however, several columns were subjected to demands larger than the GSA (2003) DCR limit of 2.0. Considering that no significant deformations were observed during field testing, GSA criteria for plastic deformations or hinge rotations may be more realistic than the GSA criteria for force demands or DCR values.
84
Table 6.1 DCR values calculated from 2-D models for selected frame members. Frame member No.
Before removal
1 column removed
2 column removed
3 column removed
4 column removed
8
0.02
0.00
0.03
0.23
2.25
9
0.01
0.00
0.03
0.34
2.14
10
0.02
0.02
0.01
0.46
2.83
13
0.03
0.05
0.03
0.09
0.45
14
0.03
0.05
0.06
0.09
0.89
15
0.03
0.03
0.14
0.14
1.10
18
0.01
0.02
0.65
0.74
1.21
19
0.01
0.03
0.87
0.97
1.56
20
0.01
0.07
1.14
1.33
2.38
23
0.00
0.29
1.08
1.18
1.54
24
0.00
0.37
0.95
1.05
1.44
25
0.00
0.48
1.29
1.49
2.24
29
0.00
0.01
0.88
0.78
0.41
30
0.00
0.01
1.31
1.13
0.45
39
0.01
0.05
0.11
0.18
0.44
40
0.02
0.06
0.13
0.27
0.86
52
0.12
0.12
0.13
0.22
0.51
53
0.10
0.11
0.12
0.30
0.91
54
0.08
0.08
0.10
0.28
0.82
55
0.05
0.05
0.04
0.18
0.77
62
0.12
0.09
0.84
0.86
0.91
63
0.11
0.08
0.83
0.86
0.94
64
0.09
0.05
0.74
0.76
0.83
65
0.07
0.06
0.62
0.66
0.80
69
0.08
0.36
0.12
0.09
0.00
70
0.07
0.29
0.01
0.02
0.15
73
0.10
0.26
0.60
0.58
0.48
74
0.08
0.27
0.53
0.51
0.42
75
0.07
0.18
0.47
0.44
0.32
79
0.09
0.21
0.37
0.41
0.55
80
0.07
0.13
0.23
0.27
0.42
85
Table 6.2 DCR values calculated from 3-D model for selected frame members. Frame member No.
Before removal
1 column removed
2 column removed
3 column removed
4 column removed
8
0.09
0.08
0.09
0.35
0.89
9
0.05
0.04
0.05
0.21
0.83
10
0.03
0.03
0.03
0.18
0.80
13
0.10
0.11
0.08
0.11
0.49
14
0.06
0.07
0.06
0.07
0.36
15
0.04
0.04
0.07
0.09
0.33
18
0.08
0.08
0.55
0.57
0.62
19
0.04
0.06
0.46
0.50
0.59
20
0.04
0.06
0.41
0.47
0.59
23
0.07
0.29
0.89
0.92
0.96
24
0.04
0.28
0.85
0.88
0.93
25
0.04
0.24
0.81
0.87
0.94
29
0.04
0.22
0.81
0.78
0.74
30
0.04
0.19
0.82
0.76
0.71
39
0.04
0.06
0.08
0.11
0.14
40
0.04
0.05
0.07
0.12
0.17
52
0.17
0.17
0.17
0.31
0.86
53
0.15
0.15
0.15
0.32
0.86
54
0.13
0.14
0.14
0.30
0.85
55
0.12
0.12
0.12
0.23
1.04
62
0.16
0.27
0.81
0.83
0.85
63
0.14
0.26
0.83
0.85
0.85
64
0.13
0.27
0.82
0.82
0.81
65
0.20
0.23
1.49
1.36
1.36
69
0.12
0.50
0.51
0.50
0.50
70
0.20
0.92
1.19
1.01
0.81
73
0.14
0.53
0.86
0.84
0.82
74
0.12
0.51
0.83
0.81
0.79
75
0.20
0.92
1.47
1.32
1.21
79
0.13
0.27
0.39
0.41
0.45
80
0.23
0.32
0.46
0.55
0.68
86
Table 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. 2-D Model Strain Gauge
3-D Model
Field Test
Linear Static Analysis
Nonlinear Dynamic Analysis
Linear Static Analysis
Nonlinear Dynamic Analysis
2 (Column)
-55×10-6
N/A
N/A
-165×10-6
-32×10-6
4 (Column)
-37×10-6
N/A
N/A
-121×10-6
-17×10-6
8 (Column)
-29×10-6
N/A
N/A
-34×10-6
-4×10-6
9 (Column)
-28×10-6
N/A
N/A
-104×10-6
-20×10-6
11 (Column)
-33×10-6
N/A
N/A
-49×10-6
-7×10-6
15 (Beam)
-37×10-6
-118×10-6
-64×10-6
-53×10-6
-46×10-6
87
Table 6.4 Comparison of vertical displacement (in.) after all columns removal. 2-D Model Joints above removed columns
Linear Static Analysis
3-D Model
Nonlinear Dynamic Analysis Maximum
Permanent
Linear Static Analysis
Nonlinear Dynamic Analysis Maximum Permanent
Joint 1
4.49
2.80
2.38
3.09
1.66
1.44
Joint 2
4.54
2.85
2.41
3.13
1.68
1.46
Joint 3
12.10
8.06
7.06
3.95
2.22
2.00
Joint 4
7.06
4.46
3.93
2.90
1.45
1.33
Table 6.5 Plastic hinge rotations (θ, degree) at the location where each column was removed after all columns removal.
Removed Columns
2-D Nonlinear Dynamic Analysis
3-D Nonlinear Dynamic Analysis
Joint 1
0.53o
0.31o
Joint 2
0.54o
0.32o
Joint 3
1.80o
0.50o
Joint 4
1.00o
0.32o
88
unit: kip-ft
Figure 6.1 Bending moment diagram after removal of first column (Column 27).
unit: kip-ft
Figure 6.2 Bending moment diagram after removal of second column (Column 22).
89
unit: kip-ft
Figure 6.3 Bending moment diagram after removal of third column (Column 2).
unit: kip-ft
Figure 6.4 Bending moment diagram after removal of fourth column (Column 7).
90
0.39 0.34
0.77 2.83
0.40 0.38
1.10 0.82
0.91 2.25
0.21
0.80 2.38
0.56 0.89
2.14 0.47
0.32
0.49
0.51
1.56
0.45
1.44
1.21
0.32
0.00
0.94
0.24 0.16
2.24 0.83
0.58 0.45
0.15
0.91
0.48 0.63
0.27 0.86
0.55 0.35
0.41
0.09
0.22
0.37 0.42
0.07 1.54
0.42
0.44 0.56
0.17 0.40
0.12 0.34
0.45 0.41
0.07
0.17 0.26
0.14 0.18
0.11
0.03
Figure 6.5 Moment diagram and corresponding DCR values after loss of four columns in the Ohio Union building.
Figure 6.6 Change in DCR values of each frame member for all cases. 91
Figure 6.7 Column removal procedure for dynamic analysis.
Figure 6.8 Time history function used to model sudden column loss. 92
Permanent Vertical Displacement
Maximum Vertical Displacement
Figure 6.9 Displacement of the joint above the first removed column (Joint 1) after the first column removal.
Figure 6.10 Displacement of the joints above the first and second removed columns (Joint 1 and 2, respectively) after the second column removal. 93
Figure 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.
Figure 6.12 Displacement of the joints above each removed column after all columns removal. 94
Figure 6.13 Deformed shape of the 3-D Ohio Union building model after each column removal as part of linear static analysis.
Figure 6.14 Deformed shape of 3-D model with corresponding DCR values after the loss of four columns. 95
Figure 6.15 Comparison of DCR values determined from 2-D and 3-D linear static analysis after four columns removal.
96
Figure 6.16 Comparison of measured and calculated strain values for Strain Gauge 4.
Figure 6.17 Comparison of measured and calculated strain values for Strain Gauge 9. 97
Figure 6.18 Comparison of measured and calculated strain values for Strain Gauge 11.
Figure 6.19 Comparison of measured and calculated strain values for Strain Gauge 15. 98
Figure 6.20 Changes in maximum joint displacement calculated from the 3-D linear static analysis during the entire column removal process.
Figure 6.21 Time history of joint displacements calculated from 2-D nonlinear dynamic analysis. 99
Figure 6.22 Time history of joint displacements calculated from 3-D nonlinear dynamic analysis.
Figure 6.23 Plastic hinge locations in the 3-D model after all four columns were removed. 100
CHAPTER 7
COMPUTATIONAL ANALYSIS OF THE BANKERS LIFE AND CASUALTY COMPANY BUILDING
7.1 Introduction In this chapter, an evaluation of the Bankers Life and Casualty Company (BLCC) building for progressive collapse was performed using 2-D and 3-D models. The models were primarily analyzed by a linear static analysis approach, using an amplified (by a factor of 2) combination of the dead loads, as discussed in Section 4.5. The demandcapacity-ratio (DCR) values, strain variations, maximum vertical displacements, and changes in moments were obtained from each model using SAP2000 program. The analysis results were evaluated based on GSA guidelines (GSA, 2003). The strain values calculated from the SAP2000 analysis were compared with the field data measured by strain gauges. The columns were removed in the SAP2000 analysis in the same order as the torching process in the field test (i.e., Column 14→Column 17→Column 5→Column 2, see Figure 4.4). Based on field test results, the strains changed dramatically when the columns were torched, whereas there was little change in strains once the column 101
removal phase began, resulting in constant strain values (Section 5.5). This indicated that most of the load redistribution between structural members has taken place during the torching process in the field. In order to directly compare with the field data, therefore, the column removal order in the SAP200 analysis was taken as the column torching order in the field test. Structural properties of the building members presented in Sections 4.4 and 4.5.2.
7.2 Changes in Moments and Deformations The linear static analysis was performed on the 2-D and 3-D models after each column was removed in the same order as a torching process: (1) column 14, (2) column 17, (3) column 5, and (4) column 2. The structural response was mainly evaluated by demand-to-capacity ratios (DCR), which is defined as the ratio of the maximum moment at the member ends to member’s ultimate capacity (Equation 4.3).
The maximum
bending moments were first determined from SAP2000, and DCR values were handcalculated by dividing the moments with the product of plastic section modulus and yield strength. Figures 7.1 through 7.4 display the calculated bending moment diagrams with corresponding maximum moment values after each column removal. When the first two columns near the middle of the longitudinal perimeter frame were removed, bending moments occurred locally, in the members above or adjacent to the removed columns. The bending moments spread within the entire building frame after third columns were removed, as shown in Figures 7.3 and 7.4. Some of the maximum moments at the beams adjoining to first two removed columns slightly decreased after the fourth column was
102
removed, probably due to the change in tensile forces caused by the removal of columns in the building corner. Figure 7.5 shows the deformed shapes obtained from 3-D linear static analysis after the removal of each column. The deformed shapes were fairly related to the calculated moment diagrams. As shown, localized deformations by the removal of first two columns spread to the entire structure after the third and fourth column removal. The largest deformation was observed in the exterior beams and columns above and next to the first two removed columns.
7.3 Calculated DCR Values
7.3.1 2-D Model The response of the structure due to the loss of load-carrying columns was analytically evaluated by DCR values. As shown in Figure 7.6, calculated DCR values were excessively high and exceeded the acceptance criteria regulated by GSA guidelines (i.e., 2.0 for columns and 3.0 for beams) (GSA, 2003). Table 7.1 shows the DCR values of all exterior steel frame members, calculated from the 2-D linear static analysis. Even after the second column removal, some of columns and beams, which were above or next to the first two removed columns, exceeded the DCR criteria. When all four columns were removed, the DCR values of almost all structural members were much higher than the DCR limits. The maximum DCR values observed in columns and beams were 6.50 and 8.03, respectively.
103
Unlike the Ohio Union building, beams were more impacted by the loss of columns. As shown in Figure 7.6, higher DCR values were observed in beams rather than in columns for all cases. This was probably due to the different tributary areas of slab adjacent to the beam. The centerline distance of the transverse bays was 25 ft for the Ohio Union building, while it was 47 ft for the BLCC building. The longer transverse bays led to the larger tributary area of the slab. Because of the larger tributary area of the BLCC building, more loads were applied to the beams of the BLCC building, resulting in higher DCR values in the beams, compared with the Ohio Union building.
7.3.2 3-D Model Table 7.2 shows DCR values calculated from the 3-D linear static analysis. Compared with 2-D model, changes in DCR values by each column removal were relatively small in the 3-D model. The maximum DCR values observed in columns and beams were only 2.53 and 3.40, respectively, which were a lot smaller than 2-D model results. Figure 7.7 compares DCR values calculated from 2-D and 3-D models after all four columns were removed. The lower DCR values were observed in both columns and beams on the 3-D model. Since 3-D model had more structural members to transfer the additional load caused by column loss, the forces on each member could be smaller than the 2-D model. Figures 7.8 and 7.9 show the 2-D and 3-D models of the BLCC building with corresponding DCR values, respectively, after four column removals. In both models, a large number of calculated DCR values, especially, in the columns and beams above the first and second removed columns, were greater than the DCR limits (i.e., DCRs of 2.0 104
for columns and 3.0 for beams). Since the BLCC building did not satisfy the GSA (2003) progressive collapse criteria for most frame members of this structure, theoretically, the building was susceptible to progressive collapse. However, during the field test the building did not experience any visible large permanent deformations or collapse even after all four columns were removed. The static analysis results indicate that the structure was considerably stiffer than that predicted by SAP2000 static analysis.
7.4 Comparison of Calculated and Measured Strains SAP2000 numerical, computational results were compared with experimental strain data. Strain gauge 7 attached on Column 11 (Figure 5.13) was selected for the experimental study because it was believed to have recorded the most consistent and accurate data in the field (Giriunas, 2009). Strains were calculated by considering the combination of axial loading and a bending moment generated from 2-D and 3-D SAP2000 analyses, which was described in Equation 6.1 in Section 6.3.2. Figure 7.10 shows comparison between calculated strains and strain data recorded in the field. 2-D SAP2000 model significantly overestimated the measured response of the structure. The percent error was calculated for each column removal case, indicating that the results obtained from 3-D model were in close agreement with experimental results than 2-D model. Average 30% difference between the 3-D model and the field data was observed while the average difference between the 2-D model and the field data was 84%. The more accurate estimates by 3-D model were also found in strain analysis results of the Ohio Union building (Section 6.3.2).
105
7.5 Vertical Displacements The loss of columns significantly affects immediately surrounding structural members, causing deformation of the structure, especially in the area where columns were removed. Vertical displacements right above the removed columns of the BLCC building were measured at joints in the second floor. Figures 7.11 and 7.12 show changes in the joint displacements calculated by the 2-D and 3-D linear static analyses, respectively, during the entire column removal process. Joints 1, 2, 3, and 4 designated the joints above the first (Column 14), second (Column 17), third (Column 5), and fourth (Column 2) removed columns, respectively (see Figure 4.4). The joint displacements at failure were shown as a constant horizontal line due to the lack of dynamic effects in linear static analysis. In both models, Joint 1 and 2 above the first two removed columns had higher displacement values, indicating more significantly deformed.
This is
consistent with the 3-D deformed shape of the BLCC building in Figure 7.5, as well as DCR results presented in Figure 7.8 and 7.9. Table 7.3 compares the maximum vertical displacements calculated from 2-D and 3-D models after four columns were removed. 3-D linear static analysis showed lower vertical displacements than 2-D analysis. In the 3-D model, the transverse beams were connected to the beams above the removed columns, adding more stiffness to the structure. Also, the transverse beams can distribute loads to the columns in the transverse direction. Therefore, smaller deformation of structure was observed from the 3-D model simulation.
106
Table 7.1 DCR values calculated from 2-D model for steel frame members. Frame member No.
Before removal
1 column removed
2 column removed
3 column removed
4 column removed
2
0.47
0.46
0.43
2.25
Removed
3
0.11
0.19
0.99
1.67
2.81
5
0.55
0.57
0.61
Removed
Removed
6
0.06
0.16
1.13
1.43
4.02
8
0.55
0.54
0.37
1.67
1.81
9
0.03
0.17
2.00
3.86
2.35
11
0.55
1.61
3.13
3.24
3.54
12
0.04
1.54
3.26
3.33
5.02
14
0.55
Removed
Removed
Removed
Removed
15
0.03
0.35
5.15
4.95
6.50
17
0.59
1.56
Removed
Removed
Removed
18
0.07
2.10
5.22
5.57
3.75
20
0.61
0.67
3.90
3.98
3.92
22
0.61
0.63
0.92
0.90
1.09
24
0.62
0.62
0.59
0.60
0.85
26
0.38
0.39
0.26
0.24
0.45
28
0.23
0.21
0.42
2.45
1.13
29
0.14
0.11
0.51
2.27
1.17
31
0.21
0.31
0.68
3.18
2.60
32
0.09
0.29
0.70
2.66
1.79
34
0.19
1.25
3.17
3.66
3.96
35
0.10
1.18
4.01
4.76
4.42
37
0.19
2.46
4.99
4.85
5.15
38
0.09
2.18
4.90
4.71
5.00
40
0.20
2.42
7.95
8.03
7.91
41
0.14
2.19
3.29
3.40
3.21
43
0.22
1.24
6.15
6.27
5.86
45
0.23
0.36
4.60
4.66
4.55
47
0.24
0.26
0.92
0.94
0.90
49
0.31
0.31
0.45
0.44
0.51
107
Table 7.2 DCR values calculated from 3-D model for steel frame members. Frame member No.
Before removal
1 column removed
2 column removed
3 column removed
4 column removed
2
0.47
0.47
0.48
1.27
Removed
3
0.24
0.27
0.21
1.07
1.67
5
0.56
0.56
0.57
Removed
Removed
6
0.27
0.22
0.58
0.84
1.56
8
0.52
0.47
0.38
1.07
1.19
9
0.23
0.25
0.71
1.60
1.55
11
0.51
1.06
1.65
1.62
1.65
12
0.23
0.89
1.32
1.31
1.56
14
0.51
Removed
Removed
Removed
Removed
15
0.23
0.30
2.23
2.16
2.43
17
0.52
1.03
Removed
Removed
Removed
18
0.25
1.03
2.42
2.53
2.26
20
0.53
0.51
1.81
1.83
1.77
22
0.53
0.54
0.50
0.49
0.54
24
0.58
0.58
0.59
0.58
0.64
26
0.30
0.30
0.28
0.29
0.24
28
0.67
0.66
0.73
1.65
1.87
29
0.10
0.10
0.22
1.17
0.90
31
0.53
0.55
0.61
1.72
1.86
32
0.10
0.11
0.15
1.39
1.36
34
0.48
1.05
1.83
1.79
1.86
35
0.09
0.62
1.53
1.40
1.29
37
0.48
1.58
3.11
2.91
2.92
38
0.11
1.04
1.95
1.85
1.90
40
0.49
1.57
3.38
3.40
3.40
41
0.10
1.00
1.27
1.31
1.23
43
0.50
1.06
3.01
3.04
2.98
45
0.50
0.54
2.19
2.19
2.23
47
0.55
0.55
0.70
0.70
0.69
49
0.71
0.71
0.70
0.69
0.72
108
Table 7.3 Comparison of maximum vertical displacement (in.) after all columns removal.
Joints above removed columns
2-D Model
3-D Model
Joint 1
18.79
8.16
Joint 2
22.12
9.08
Joint 3
10.53
5.34
Joint 4
20.16
4.84
109
unit: kip-ft
Figure 7.1 Bending moment diagram after removal of first column (Column 14).
unit: kip-ft
Figure 7.2 Bending moment diagram after removal of second column (Column 17).
unit: kip-ft
Figure 7.3 Bending moment diagram after removal of third column (Column 5).
unit: kip-ft
Figure 7.4 Bending moment diagram after removal of fourth column (Column 2). 110
Figure 7.5 Deformed shape of the BLCC building model after each column removal.
Figure 7.6 Changes in DCR values of each frame member for all cases. 111
Figure 7.7 Comparison of DCR values determined from 2-D and 3-D models after four columns removal.
Figure 7.8 2-D model with corresponding DCR values after loss of four columns. 112
Figure 7.9 3-D model with corresponding DCR values after loss of four columns.
Figure 7.10 Comparison of measured and calculated strain values. 113
Figure 7.11 Maximum joint displacements for 2-D model after each column removal.
Figure 7.12 Maximum joint displacements for 3-D model after each column removal. 114
CHAPTER 8
CONCLUSIONS AND FUTURE WORK
8.1 Summary The major objective of this research was to investigate the progressive collapse performance of two existing buildings through experimental tests and computational analysis. Each building was tested in the field by physically removing four first-story perimeter columns prior to building’s scheduled demolition. The field test simulates the sudden column removal that may cause progressive collapse. Strains were measured from the strain gauges installed on neighboring structural members to examine the change in the axial forces and deflections due to the loss of columns. For the computational analysis, a commercially available computer program, SAP2000 was used to analyze progressive collapse potential of buildings, following the General Services Administration (GSA) guidelines. 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. Two different analysis procedures were evaluated for their effectiveness in modeling progressive collapse scenarios; linear static and nonlinear 115
dynamic analysis. The demand capacity ratio (DCR) and plastic hinge rotation were determined from linear static and nonlinear dynamic analysis procedures, respectively. These values were used to check the performance acceptance criteria for each analysis. Despite many previous studies on computational models and analysis to improve the building design against progressive collapse, there is very little actual field data available to evaluate and verify progressive collapse resistance of structures. Therefore, the field experiments and SAP2000 analyses performed in this research could provide both practical and fundamental information on the progressive collapse response of existing buildings.
8.2 Conclusions Two steel frame buildings were modeled and analyzed by the SAP2000 computer program, using either linear static analysis or nonlinear dynamic analysis. Experimental data from the field tests of two buildings were used to compare and verify the computational models and analyses.
Main conclusions and observations from the
calculated and measured structural responses are given below:
Strains from Experiments and SAP2000 During the field tests, the strain values changed as each column was removed, as well as torched. In the test of BLCC building, the strains changed dramatically during each column torching phase, but there was little change once the removal phase began. For both building tests, the strain values most significantly dropped when the last column
116
was torched.
This indicated that most of the load redistribution between structural
members has taken place during the column torching phase in the field. Strain data obtained from each field test was compared with the strain values calculated from 2-D and 3-D models. The strain values from 3-D model were closer to experimental results. It was indicated that 3-D computer models were more accurate to simulate response of buildings to removal of columns, probably because 3-D models can account for 3-D effects as well as avoid overly conservative solutions. Based on our findings, the use of 3-D models was recommended for progressive collapse analysis.
DCR values and Progressive Collapse Potential The performance evaluation criterion for linear static analysis procedures is based on the demand capacity ratio (DCR). Based on DCR values from both 2-D and 3-D analysis, the Ohio Union building satisfied the GSA acceptance criteria, with exception of five DCR values slightly higher than the criteria of 2.0 at the columns of the 2-D model. However, most structural members of BLCC building exceeded the DCR limits once the second column was removed, indicating that the BLCC building was more vulnerable to progressive collapse. Neither of buildings did experience a collapse during the field test, even after four columns were removed. This is probably because the response of the structures was considerably stiffer than that predicted by a SAP2000 analysis. In general, 3-D model had lower DCR results than 2-D model.
Since the
additional loads caused by the loss of load-bearing columns were distributed to more
117
structural members in the 3-D model, the forces on each member of 3-D model could be smaller than the 2-D model.
Plastic Hinge Rotation for Nonlinear Dynamic Analysis Nonlinear dynamic analysis was conducted for the Ohio Union building. Plastic hinge rotation was used as the performance evaluation criteria for this analysis, and was determined from both 2-D and 3-D models. Plastic hinge rotations calculated from the 3D model was smaller than that from the 2-D model, mainly because of lower vertical displacements calculated by 3-D nonlinear dynamic analysis. Plastic hinge rotations from both models were much smaller than GSA acceptance criteria of 12o, indicating that the Ohio Union building was not susceptible to progressive collapse. Considering that no significant deformations were observed during field testing, GSA criteria for plastic deformations or hinge rotations may be more realistic than the GSA criteria for force demands or DCR values.
Vertical Displacements and Deformations in the Buildings The maximum vertical displacements of each building were calculated from 2-D and 3-D linear static analysis. Results from both buildings showed that 3-D model had lower vertical displacement values than 2-D model, probably due to transverse beams in 3-D model. The transverse beams enable the structure to have more stiffness, as well as additional loads to be transferred to the columns in the transverse direction. This research also compared maximum displacements between linear static analysis and nonlinear dynamic analysis of the Ohio Union building. 118
In nonlinear
dynamic analysis, the Ohio Union building was allowed to deform until it settled after each column was removed. As more columns were removed, it took more time for the building to settle down.
Linear static analysis showed higher maximum vertical
displacements than nonlinear dynamic analysis for both 2-D and 3-D model, probably due to the impact factor of 2 required for the dead load for linear static analysis.
8.3 Recommendations for Future Research Results of this research suggest that computational simulation of progressive collapse, even including nonlinear dynamic analysis, is relatively simple to perform through available finite-element computer programs such as SAP2000.
Also,
experimental evidence is useful to verify the computational models and analyses. Based on the observations and analysis results, the followings are recommended to extend this research. (1) One of most important results from this research was the experimental data compared relatively well with the analysis results of SAP2000. The strain data obtained from each field-testing showed that 3-D model was more accurate than 2-D model. However, more experimental data would be required to validate computational analysis for the progressive collapse, and better simulate the actual behavior of structural members. For example, the experimental deflection data is needed in this research to validate vertical displacement values calculated from SAP2000. For the measurement of vertical displacements in the field, linear potentiometers can be used by measuring the change in the distances between their two ends (i.e., joints to the ground), as described in previous research (Sasani and Sagiroglu, 2008). A laser scanning device and a high 119
resolution line-scan camera could be also used to measure global and local deformations in the building. Installation of additional strain gauges in the upper floors would be useful to monitor changes in strains of columns and beams as the building floor gets higher. In this research, higher DCR values and larger deformations in the top story were observed from SAP2000 analysis. Strain data measured at each floor level would be very valuable to determine the alternate load path caused by the loss of load-bearing columns. (2) This research only considered the removal of exterior frame columns to evaluate progressive collapse potential. Even though the minimum requirement in the GSA (2003) and DoD (2005) guidelines was removal of exterior members, interior columns were also required to be considered for the removal of columns, especially, in underground parking area and uncontrolled public ground floor areas. Since interior frames have approximately twice gravity loads than exterior frames, the loss of interior columns enables the buildings more vulnerable to progressive collapse. For example, Yagob (2007) observed that the moderately ductile building was susceptible to progressive collapse when an interior column at the first story was removed, while no progressive collapse was expected when an exterior or corner column was removed. Therefore, it would be important to assess the potential of progressive collapse when interior frame columns of the building were removed. Both field tests and SAP2000 analysis could be performed to investigate the structure response resulted from the loss of interior columns. (3) In this research, only steel-frame structures were tested and analyzed to 120
investigate vulnerability of the buildings to progressive collapse. It would be interesting to evaluate the progressive collapse potential of other buildings with different structural systems and configurations, such as concrete-frame structures and atypical structural configurations. The experimental and computational assessments on progressive collapse potential of various buildings would enable making more specific conclusions for a wide range of building structures. (4) There are four types of analysis methods that may be used in the assessment of the potential for progressive collapse: linear static analysis, linear dynamic analysis, nonlinear static analysis, and nonlinear dynamic analysis. In this research, linear static and nonlinear dynamic analyses were conducted using SAP2000 computer program. It would be interesting to examine nonlinear static and linear dynamic analyses, and compare the analysis results. The effect of nonlinearity or the dynamic effect on the progressive collapse analysis could be examined by comparing the results from the four different analyses. It is also expected that this comparison can prove the most accurate and suitable method to analyze the progressive collapse vulnerability of the buildings.
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BIBLIOGRAPHY
ACI 318-08. 2008. Building code requirements for structural concrete and commentary. American Concrete Institute (ACI). Farmington Hills, MI. AISC. 1969. Manual of steel construction. 6th Edition. American Institute of Steel Construction (AISC), Chicago, IL. ASCE 7-05. 2005. Minimum design loads for buildings and other structures. Report: ASCE/SEI 7-05. American Society of Civil Engineers (ASCE). Reston, VA. ASCE 41-06. 2006. Prestandard and commentary for the seismic rehabilitation of buildings. Report: ASCE/SEI 41-06. American Society of Civil Engineers (ASCE). Reston, VA. Bao, Y., Kunnath, S., El-Tawil, S., Lew, H. S. 2008. Macromodel-based simulation of progressive collapse: RC frame structures. Journal of Structural Engineering. 134(7), 1079-1091. Byfield, M. P. 2006. Behavior and design of commercial multistory buildings subjected to blast. ASCE Journal of Performance of Constructed Facilities. 20(4), 324-329. Corley, W. G. 2002. Application of seismic design in mitigating progressive collapse. Multihazard Mitigation Council national workshop on Prevention of progressive collapse. National Institute of Standards and Technology (NIST). July. Chicago, IL. DoD. 2005. Design of buildings to resist progressive collapse. Unified Facilities Criteria (UFC) 4-023-03, Department of Defense (DoD) Dusenberry, D., Cagley, J., Aquino, W. 2004. Case studies. Multihazard Mitigation Council national workshop on Best practices guidelines for the mitigation of progressive collapse of buildings. National Institute of Building Sciences (NIBS). Washington, D.C.
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FEMA-274. 1997. NEHRP commentary on the guidelines for the seismic rehabilitation of buildings. Report : FEMA 274. Federal Emergency Management Agency (FEMA). Washington, D.C. FEMA-277. 1997. The Oklahoma City bombing: Improving building performance through multi-hazard mitigation, Report: FEMA 277. Federal Emergency Management Agency (FEMA). Washington, D.C. FEMA-356. 2000. Prestandard and commentary for the seismic rehabilitation of buildings. Report: FEMA 356. Federal Emergency Management Agency (FEMA). Washington, D.C. FEMA-403. 2002. World Trade Center building performance study: Data collection, preliminary observations and recommendation. Report: FEMA 403. Federal Emergency Management Agency (FEMA). Washington, D.C. FEMA-427. 2003. Primer for design of commercial buildings to mitigate terrorist attacks. Report: FEMA 427. Federal Emergency Management Agency (FEMA). Washington, D.C. Giriunas, K. A. 2009. Progressive collapse analysis of an existing building. Honors Thesis. Department of Civil and Environmental Engineering and Geodetic Science. The Ohio State University, Columbus, OH. Griffiths, H., Pugsley, A., Saunders, O. 1968. Report of inquiry into the collapse of flats at Ronan Point, Canning Town. Ministry of Housing and Local Government. Her Majesty’s Stationary Office. London, United Kingdom. GSA. 2003. Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projects. General Services Administration (GSA). Washington, D.C. Humay, F. K., Baldridge, S. M., Ghosh, S. K. 2006. Prevention of progressive collapse in multistory concrete buildings. Structures and Codes Institute (SCI). Irving, C. 1995. In Their Name. Random House, Inc. New York. Kaewkulchai, G., Williamson, E. B. 2003. Dynamic behavior of planar frames during progressive collapse. In: Proceedings of 16th ASCE engineering mechanics conference, July 16-18, University of Washington, Seattle. Kaewkulchai, G., Williamson, E. B. 2006. Modeling the impact of failed members for progressive collapse analysis of frame structures. Journal of Performance of Constructed Facilities. 20(4), 375-383.
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Karns, J. E., Houghton, D. L., Hall, B. E., Kim, J., Lee, K. 2006. Blast testing of steel frame assemblies to assess the implications of connection behavior on progressive collapse. Proceedings of ASCE Structures Congress, St. Louis, MO. Khandelwal, K., El-Tawil, S., Kunnath, S., Lew, H. S. 2008. Macromodel-based simulation of progressive collapse: Steel frame structures. Journal of Structural Engineering. 134(7), 1070-1078. Luccioni, B. M., Ambrosini, R. D., Danesi, R. F. 2004. Analysis of building collapse under blast loads. Engineering Structures. 26, 63-71. Marjanishvili, S. M. 2004. Progressive analysis procedure for progressive collapse. Journal of Performance of Constructed Facilities. 18(2), 79-85. Marjanishvili, S., Agnew, E. 2006. Comparison of various procedures for progressive collapse analysis. ASCE Journal of Performance of Constructed Facilities. 20(4), 365-374. McCormac, J. C., Nelson, J. K. 2006. Design of Reinforced Concrete (ACI 318-05 code edition). 7th edition. John Wiley & Sons, Inc. McKay, A. E. 2008. Alternate path method in progressive collapse analysis: Variation of dynamic and non-linear load increase factors. MS Thesis. Department of Civil and Environmental Engineering, University of Texas at San Antonio, San Antonio, TX. Nair, R. S. 2004. Progressive collapse basics. Proceedings of North American Steel Construction Conference (NASCC). March 24-27. Long Beach, CA. New York Times, September 12, 2001 NIST. 2005. Federal building and fire investigation of the World Trade Center disaster. Final report of the National Construction Safety Team on the collapses of the World Trade Center tower. National Institute of Standards and Technology (NIST). NCSTAR 1. Gaithersburg, MD. Powell, G. 2005. Progressive collapse: Case study using nonlinear analysis. In: Proceedings of the 2005 structures congress and the 2005 forensic engineering symposium. Apr. 20-24, New York, NY. Ruth P., Marchand, K. A., Williamson, E. B. 2006. Static equivalency in progressive collapse alternative path analysis: Reducing conservatism while retaining structural integrity. Journal of Performance of Constructed Facilities. 20(4), 349-364. SAP2000. 2009. SAP 2000 Advanced structural analysis program, Version 12. Computers and Structures, Inc. (CSI). Berkeley, CA, U.S.A.
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Sasani, M., Bazan, M., Sagiroglu, S. 2007. Experimental and analytical progressive collapse evaluation of an actual RC structure. ACI Structural Journal. 104(6), 731739. Sasani, M., Sagiroglu, S. 2008. Progressive collapse resistance of Hotel San Diego, Journal of Structural Engineering, 134(3), 478-488. Sivaselvan, M. V., Reinhorn, A. M. 2006. Lagrangian approach to structural collapse simulation. Journal of Engineering Mechanics. 132(8), 795-805. Sozen, M., Thornton, C., Mlakar, P. Corley, W. G. 1998. The Oklahoma City bombing: Structure and mechanisms of the Murrah building. Journal of Performance of Constructed Facilities. 12(3), 120-136. Stevenson, J. D. 1980. Structural damping values as a function of dynamic response stress and deformation levels. Nuclear Engineering and Design. 60(2), 211-237. Wikipedia. 2010. Accessed on July 21, 2010 and downloaded a picture from http://en.wikipedia.org/wiki/File:Ronan_Point_-_Daily_Telegraph.jpg. Yagob, O. S. A. 2007. Vulnerability of buildings to blast loads and progressive collapse. MS Thesis. Department of Civil and Engineering. University of Ottawa, Ottawa, ON, Canada.
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APPENDIX A
Ohio Union Building Structural Drawings
126
127
Figure A.1 Ohio Union Building Anchor Bolt Plan (Foundation Plan)
128
Figure A.2 Ohio Union Building First Floor Framing Plan
129
Figure A.3 Ohio Union Building Second Floor Framing Plan
130
Figure A.4 Ohio Union Building Third Floor Framing Plan
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Figure A.5 Ohio Union Building Roof Framing Plan
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Figure A.7 Typical Transverse Beam Detail
Figure A.6 Typical Steel Moment Frame Connection
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Figure A.8 Typical Wall Section of Basement (Left) and First Floor (Right)
134
Figure A.9 Typical Wall Section of Second Floor (Left) and Third Floor (Right)
APPENDIX B
Bankers Life and Casualty Company Building Structural Drawings
135
136
Figure B.1 BLCC Building Foundation Plan
137
Figure B.2 BLCC Building First Floor Framing Plan
138
Figure B.3 BLCC Building Second Floor Framing Plan
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Figure B.4 BLCC Building Roof Framing Plan
140
Figure B.5 BLCC Building Typical Section
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Figure B.7 BLCC Building Typical Girder Splice Detail
Figure B.6 BLCC Building Typical Joint Connection
APPENDIX C
Pictures of the Test Procedures
142
Figure C.1 Installed Strain Gauges
Figure C.2 Portable Data Acquisition device for strain readings
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Figure C.3 Column Exposure
Figure C.4 Column Torching
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Figure C.5 Column after torching
Figure C.6 Column after removal
145
Figure C.7 Ohio Union building after third and fourth column removal
Figure C.8 Ohio Union building after 4 columns removal.
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Figure C.9 Ohio Union building during demolish
147
148
Figure C.10 Ohio Union Experiment Results
APPENDIX D
Experimental Testing of the Bankers Life and Casualty Company building by Giriunas (2009)
149
D.1 Introduction
Field experiments of the Bankers Life and Casualty Company building were conducted by Kevin A. Giriunas, when the building was scheduled for demolition in August, 2008. Appendix D includes strain gauge charts and load distribution values during column removal, which was reported by Giriunas (2009).
150
151
Figure D.1- Strain versus Time Chart Measurements during Torching, (Time: 0-3200 seconds).
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Figure D.2- Strain versus Time Chart Measurements during Torching, (Time: 3200 – 6398 seconds).
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Figure D.3- Strain versus Time Chart during Removal of Columns (Time: 5000-5800 seconds).
Column 14 Torched @233secs -1465 seconds
Column 17 Torched @2141secs 2870.5 seconds
Column 5 Torched @3000secs 3676.9 seconds
Column 2 Torched @3799secs 4385.6 seconds
Strain 3
-23 up to 18-increase of 41
22 to 21- -decrease of 1
22up to 26--increase of 4
29 up to 41--increase of 12
Strain 4
-11 up to 17-increase of 28
17to 13- -decrease of 4
17up to 17--no change
18 up to 30--increase of 12
Strain 5
-11 up to 5-increase of 16
gone
gone
gone
Strain 7
-5 up to 16 to -37-decrease of 32
-40 to -105-- decrease of 65
-101 up to -138-decrease of 37
-153 to -447--decrease of 294
Strain 8
-13 up to 7-increase of 20 112 fluctuates wildly to 774increase 662
28 to 26--decrease of 2
28 up to 30--increase of 2
31 to 30--decrease of 1
746 to 741--decrease of 5
737 up to 880--increase of 143
133 to 0--decrease of 133
9 up to 12--increase of 3
27 to 25--decrease of 2
25up to 29--increase of 4
29 up to 32--increase of 3
Column 17 Removed @ 5308 seconds
Column 2 Removed @ 5449 seconds
Column 5 Removed @ 5532 seconds
Strain 9
Strain 11 Strain 12
-65 up to -38-increase of 27 -6 up to 16-increase of 22
768 to 749 -- decrease of 19 128 fluctuates up finally ends at 120-decrease of 8
Column 14 Removed @ 5269 seconds 45 to 44--decrease of 1
45 to 44--decrease of 1
45 to 45--no change
45 to 45--no change
Strain 4
38-37--decrease of 1
38 to 38-- no change
38 to 37--decrease of 1
37 to 37--no change
Strain 5
gone
gone
gone
gone
Strain 7
-650 to -652-decrease of 2
-671 to -668--decrease of 3
-669 to -668--decrease of 1
-690 to -691--decrease of 1
Strain 8
9 to 9--no change 882 to 882--no change
8 to 8-- no change
8 to 6--decrease of 2
6 to 6--no change
882 to 882-- no change
882 to 882-- no change
880 to 880-no change
29 to 29--no change
27 to 28--no change
33 to 33-- no change
33 to 33-- no change
32 to 32--no change
34 to 34-- no change
33 to 33-- no change
33 to 33-- no change
Strain 3
Strain 9 Strain 11 Strain 12
Figure D.4- Strain Values (10-6) and Change in Strain at Specific Times during Column Torching and Removal.
154
Bε
Figure D.5- Change in Strain (∆ε) Measurement.
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Strain Gauge On flange of 24 I 79.9 Beam: 10
Strain Gauge On flange of 24 I 79.9 Beam: 10 Strain Gauge On flange of 24 I 79.9 Beam: 10
BM only from Column 14 Torched (kip-ft.)
BM only from Column 17 Torched (kip-ft.)
BM only from Column 5 Torched (kip-ft.)
BM only from Column 2 Torched (kip-ft.)
9.25
0.84
1.68
1.26
BM only after Column 14 removed (kip-ft.)
BM only after Column 17 removed (kip-ft.)
BM only after Column 2 removed (kip-ft.)
BM only after Column 5 removed (kip-ft.)
No Change
No Change
No Change
No Change
Total BM
13.45
KEY f = (M*c)/I= Bending Stress : (ksi) ε=(f/Ε)= Strain : (unit less) BM= (∆ε *Ε*I)/c = ∆ε *Ε*S = Change in Moment determined by change in Strain: (kipft.) T=Member is in Tension C=Member is in Compression Figure D.6- Change in Bending Moment, ∆M (kip-ft), from Column Removal and Total ∆M (kip-ft) from Strain Gauge 12.
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