NIST NCSTAR 1-6D

Federal Building and Fire Safety Investigation of

the World Trade Center Disaster

Global Structural Analysis of the

Response of the World Trade Center

Towers to Impact Damage and Fire

(Chapters 1-3)

Mehdi S. Zarghamee

Yasuo Kitane

Omer 0. Erbay

Therese P. McAllister

John L. Gross

National Institute of Standards and Technology • Technology Administration • U.S. Department of Commerce

NISTNCSTAR1-6D

Federal Building and Fire Safety Investigation of the

World Trade Center Disaster

Global Structural Analysis of the

Response of the World Trade Center

Towers to Impact Damage and Fire

Mehdi S. Zarghamee

Yasuo Kitane

Omer O. Erbay

Simpson Gumpertz & Heger Inc.

Therese P. McAllister

John L. Gross

Building and Fire Research Laboratory

National Institute of Standard and Technology

September 2005

U.S. Department of Commerce

Carlos M. Gutierrez, Secretary

Technology Administration

Miclielle O'Neill, Acting Secretary for Technology

National Institute of Standards and Technology

William Jeffrey, Director
Disclaimer No. 1

Certain commercial entities, equipment, products, or materials are identified in this document in order to describe a procedure or concept adequately or to trace the history of the procedures and practices used. Such identification is not intended to imply recommendation, endorsement, or implication that the entities, products, materials, or equipment are necessarily the best available for the purpose. Nor does such identification imply a finding of fault or negligence by the National Institute of Standards and Technology.

Disclaimer No. 2 The policy of NIST is to use the International System of Units (metric units) in all publications. In this document,

however, units are presented in metric units or the inch-pound system, whichever is prevalent in the discipline.

Disclaimer No. 3

Pursuant to section 7 of the National Construction Safety Team Act, the NIST Director has determined that certain evidence received by NIST in the course of this Investigation is "voluntarily provided safety-related information" that is "not directly related to the building failure being investigated" and that "disclosure of that information would inhibit the

voluntary provision of that type of information" (15 USC 7306c).

In addition, a substantial portion of the evidence collected by NIST in the course of the Investigation has been

provided to NIST under nondisclosure agreements.

Disclaimer No. 4

NIST takes no position as to whether the design or construction of a WTC building was compliant with any code

since, due to the destruction of the WTC buildings, NIST could not verify the actual (or as-built) construction, the

properties and condition of the materials used, or changes to the original construction made over the life of the

buildings. In addition, NIST could not verify the interpretations of codes used by applicable authorities in determining

compliance when implementing building codes. Where an Investigation report states whether a system was

designed or installed as required by a code provision, NIST has documentary or anecdotal evidence indicating

whether the requirement was met, or NIST has independently conducted tests or analyses indicating whether the requirement was met.

Use in Legal Proceedings

No part of any report resulting from a NIST investigation into a structural failure or from an investigation under the

National Construction Safety Team Act may be used in any suit or action for damages arising out of any matter mentioned in such report (15 USC 281a; as amended by P.L. 107-231).

National Institute of Standards and Technology National Construction Safety Team Act Report 1-6D

Natl. Inst. Stand. Technol. Natl. Constr. Sfty. Tm. Act Rpt. 1-6D, 476 pages (September 2005)

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Abstract

Simpson Gumpertz & Heger Inc (SGH) developed global models of the World Trade Center (WTC)

towers using finite elements to gain an understanding of the roles of the aircraft impact damage and the

subsequent fires in the WTC towers with respect to structural stability and sequential failures of

components and subsystems and to determine the probable sequence of structural responses that led to

initiation of global collapse. The study was conducted as part of the investigation on the WTC disaster by

the National Instimte of Standards and Technology (NIST).

The developed finite-element global models of the WTC towers simulated the strucmral performance of

the part of the buildings in and above the aircraft impact zone. These models captured the nonlinear

responses of the towers subjected to the aircraft impact damage and the subsequent fire effects. The

nonlineanties included in the global models were temperature-dependent material properties such as thermal expansion, plasticity and creep of metals, large deflection and the resulting instability, and failure modes of members and connections.

NIST provided temperature-dependent nonlinear material properties, estimates of aircraft impact damage

to structural members, and temperature time histories of structural elements, which were used as input in this study.

The finite element analyses (FEA) of the global models and of the component and subsystem models

showed that the key structural responses that led to the collapse of the towers were as follows: 1) floor sagging caused by the failure of thermally-weakened truss members, resuhing in pull-in forces between

the floor and the exterior wall, and in some cases, discoimection of the floor from the exterior wall;

2) downward displacement of the core due to aircraft impact damage and shortening of the remaining core columns from increased load, plasticity, creep of steel at high temperatures, and buckling resulting from

fire-induced high temperatures, and unloading of the core; 3) bowing and buckling of exterior walls

caused by the pull-in forces and loss of lateral support from the sagged floors, and floor/wall

disconnections at high temperatures; and 4) redistribution of gravity loads among the columns locally,

among the exterior walls, and between the exterior walls and the core, resulting from impact damage,

relative thermal expansion, shortening of core columns, tilting of the tower above the impact zone, and

bowing and buckling of exterior walls.

In WTC 1 , the aircraft impact caused damage to the north and south walls, floors, some core columns, and

insulation. The subsequent fires caused sagging of the floors on the south side of the office area, where

insulation was damaged, and inward bowing of the south wall. The damage to the core columns resulted

in local load redistribution to the remaining core columns. The subsequent fire-induced high

temperatures caused the core to displace downward from plasticity and high creep strains in high stress and high temperatures. The downward displacement of the core resuhed in load redistribution from the core to the exterior walls. With continuously increased bowing, the entire width of the south wall buckled

inward. The section of the building above the impact zone tilted to the south as instability progressed

horizontally to the adjacent east and west walls. Global collapse occurred as potential energy of the

falling upper strucmre exceeded the strain energy capacity in the deforming structural members.

NISTNCSTAR 1-6D, WTC Investigation iii
Abstract

In WTC 2, the aircraft impact caused damage to the south and north exterior walls, floors, and columns in the southeast comer of the core. The floor damage and the subsequent fires caused sagging of the floors and local floor/wall disconnections, and resulted in bowing and buckling of the east wall. The damage to the core columns and fire-induced high temperatures resulted in local load redistribution to the remaining

core columns in the southeast comer, which redistributed the core column loads to the east and south wall

columns, as the core leaned toward the south and east. With continuously increased bowing, the entire

width of the east wall buckled inward. The section of the building above the impact zone tilted to the east and south as instability progressed horizontally to the adjacent north and south walls. Global collapse

occurred when the potential energy of the falling upper structure exceeded the strain energy capacity in the deforming stmctural members.

The results of global analysis of both WTC 1 and WTC 2 showed that global collapse of both towers was

initiated by the instability of the exterior walls pursuant to their excessive inward bowing which

progressed horizontally to adjacent walls.

Keywords.- Collapse, creep, large deflection, nonlinear finite element analysis, plasticity, stability,

stmctural response to damage, stmctural response to fire, World Trade Center.

iv NISTNCSTAR 1-6D, WTC Investigation
Table of Contents

Abstract iii

List of Figures vii

List of Tables xxv

List of Acronyms and Abbreviations xxix

Preface xxxi

Acknowledgments xli

Executive Simmiary xliii

Chapter 1 Introduction 1

1.1 Objective 1

1.2 Background 1

1 .3 Method of Approach 3

1 .4 Report Organization 4

Chapter 2 Global Models 7

2. 1 Description of Global Models 7

2.2 Impact Damage 12

2.2.1 Introduction 12

2.2.2 Initial Damage Sets 12

2.2.3 Final Damage Sets 23

2.3 Temperature Effects 34

2.4 Thermal Behavior of Floors 35

2.5 Fire-Induced Damage 36

2.5.1 FloorAVall Disconnections 36

2.5.2 Pull-in Forces 37

2.5.3 FloorAVall Disconnections and Pull-in Forces Included in the Global Model 39

Chapters

Isolated Wall and Core Model Analyses 61

3.1 Introduction 61

3.2 Exterior Wall Buckling 61

NISTNCSTAR 1-6D. WTC Investigation v
Table of Contents

3.2.1 Finite Element Analysis of WTC 1 Exterior Wall 65

3.2.2 FEA of WTC 2 Exterior Wall 102

3.3 Core Column Shortening and Downward Displacement of Core 134

3.3.1 FEA of WTC 1 Core 135

3.3.2 FEA of WTC 2 Core 154

Chapter 4

Global Analysis 167

4. 1 Conversion from SAP2000 to ANSYS 167

4.1.1 ANSYS Models 168

4. 1 .2 Validation of Translated ANSYS Global Models 1 70

4.2 Global Analysis with Creep 173

4.2.1 Introduction 173

4.2.2 Modifications to the Global Model with Creep and Inelastic Buckling of Columns 173

4.2.3 Boundary Conditions and Loading Steps 179

4.2.4 Simulation of WTC 1 Collapse 179

4.2.5 Simulation of WTC 2 Collapse 245

Chapter 5 Collapse Sequence 309

5.1 Introduction 309

5.2 WTC 1 Collapse Sequence 312

5.3 WTC 2 Collapse Sequence 319

5.4 Discussion 329

Appendix A

FEA of Floors 331

Appendix B

Floor Truss Dynamic Response Due to Impact of Dropping Floor 373

Appendix C

Global Analysis Without Creep 377

vi NISTNCSTAR 1-6D, WTC Investigation
List of Figures

Figure P-1 . The eight projects in the federal building and fire safety investigation of the WTC

disaster xxxiii

Figure 2-1 . Column designations 1

1

Figure 2-2. Structural damage condition on the exterior walls of WTC 1 for all cases of impact

damage 13

Figure 2-3. Structural damage condition on the exterior walls of WTC 2 for all cases of impact

damage 14

Figure 2-A. Core columns and core beams in the WTC 1 global model without aircraft impact

damage 14

Figure 2-5. Core columns and core beams in the WTC 2 global model without aircraft impact

damage 15

Figure 2-6. Case Aj structural damage condition on the core columns of WTC 1 15

Figure 2-7. Case C, structural damage condition on the core columns of WTC 2 16

Figure 2-8. Revised Case C, structural damage condition on the core columns of WTC 2 16

Figure 2-9. Case A, insulation damage conditions for WTC 1 floor trusses and beams 17

Figure 2-10. Case A, structural damage conditions for WTC 1 18

Figure 2-11. Case C, insulation damage conditions for WTC 2 floor trusses and beams 19

Figure 2-12. Case C, Structural damage conditions for WTC 2 floors 20

Figure 2-13. Case Dj insulation damage conditions for WTC 2 floor trusses and beams 21

Figure 2-14. Case Dj Structural damage conditions for WTC 2 floors 22

Figure 2-15. Case A structural damage condition on the core columns of WTC 1 23

Figure 2-16. Case C structural damage condition on the core columns of WTC 2 24

Figure 2-17. Case B structural damage condition on the core columns of WTC 1 (including

heavily damaged columns) 24

Figure 2-18. Case D structural damage condition on the core columns of WTC 2 (including

heavily damaged columns) 25

Figure 2-19. Case A insulation damage condition for WTC 1 floor trusses and beams 26

Figure 2-20. Case A structural damage condition for WTC 1 floors 27

Figure 2-21 . Case C insulation damage condition for WTC 2 floor trusses and beams 28

Figure 2-22. Case C structural damage condition for WTC 2 floors 29

Figure 2-23. Case B insulation damage conditions for WTC 1 floor trusses and beams 30

Figure 2-24. Case B structural damage conditions for WTC 1 floors 31

Figure 2-25. Case D insulation damage conditions for WTC 2 floor trusses and beams 32

NISTNCSTAR 1-6D, WTC Investigation vii
List of Figures

Figure 2-26. Case D structural damage conditions for WTC 2 floors 33

Figure 2-27. Comparison of vertical displacement of a simplified truss model at Column 333

extracted from the full floor model of Floor 96 of WTC 1 for Case Bj temperature

condition at 40 min with and without creep 39

Figure 2-28. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 1 between 0 min and 10 min for Case B conditions 41

Figure 2-29. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 1 between 10 min and 20 min for Case B conditions 42

Figure 2-30. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 1 between 20 min and 30 min for Case B conditions 43

Figure 2-3 1 . Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 1 between 30 min and 40 min for Case B conditions 44

Figure 2-32. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 1 between 40 min and 50 min for Case B conditions 45

Figure 2-33. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 1 between 50 min and 60 min for Case B conditions 46

Figure 2-34. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 1 between 60 min and 70 min for Case B conditions 47

Figure 2-35. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 1 between 70 min and 80 min for Case B conditions 48

Figure 2-36. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 1 between 80 min and 90 min for Case B conditions 49

Figure 2-37. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 1 between 90 min and 100 min for Case B conditions.. 50

Figure 2-38. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 2 between 0 min and 10 min for Case D conditions 54

Figure 2-39. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 2 between 10 min and 20 min for Case D conditions 55

Figure 2-40. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 2 between 20 min and 30 min for Case D conditions. 56

Figure 2^1. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 2 between 30 min and 40 min for Case D conditions 57

Figure 2-42. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 2 between 40 min and 50 min for Case D conditions 58

Figure 2^3. Locations of floor/wall disconnections and pull-in forces for the global analysis of

WTC 2 between 50 min and 60 min for Case D conditions. 59

Figure 3-1. Isolated exterior wall segments from WTC 1 and WTC 2 (horizontal lines show

spandrels and vertical lines show column) 62

Figure 3-2. Boundary conditions applied on the isolated exterior wall segment on the south wall

of WTC 1 62

viii NISTNCSTAR 1-6D, WTC Investigation
List of Figures

Figure 3-3. Case A temperature condition of south wall columns of WTC 1 at 10 min 66

Figure 3-4. Case A temperature condition of south wall columns of WTC 1 at 20 min 66

Figure 3-5. Case A temperature condition of south wall columns of WTC 1 at 30 min 67

Figure 3-6. Case A temperature condition of south wall columns of WTC 1 at 40 min 67

Figure 3-7. Case A temperature condition of south wall columns of WTC 1 at 50 min 67

Figure 3-8. Case A temperature condition of south wall columns of WTC 1 at 60 min 68

Figure 3-9. Case A temperature condition of south wall columns of WTC 1 at 70 min 68

Figure 3-10. Case A temperature condition of south wall columns of WTC 1 at 80 min 68

Figure 3-11. Case A temperature condition of south wall columns of WTC 1 at 90 min. 69

Figure 3-12. Case A temperature condition of south wall columns of WTC 1 at 100 min 69

Figure 3-13. Case A temperature condition of south wall spandrels of WTC 1 at 10 min 69

Figure 3-14. Case A temperature condition of south wall spandrels of WTC 1 at 20 min 70

Figure 3-15. Case A temperature condition of south wall spandrels of WTC 1 at 30 min 70

Figure 3-16. Case A temperature condition of south wall spandrels of WTC 1 at 40 min 70

Figure 3-17. Case A temperature condition of south wall spandrels of WTC 1 at 50 min 71

Figure 3-18. Case A temperature condition of south wall spandrels of WTC 1 at 60 min 71

Figure 3-19. Case A temperature condition of south wall spandrels of WTC 1 at 70 min 71

Figure 3-20. Case A temperature condition of south wall spandrels of WTC 1 at 80 min 72

Figure 3-2 1 . Case A temperature condition of south wall spandrels of WTC 1 at 90 min 72

Figure 3-22. Case A temperature condition of south wall spandrels of WTC 1 at 100 min 72

Figure 3-23. Response of Isolated south wall model of WTC 1 after aircraft impact 73

Figure 3-24. Vertical displacements of isolated south wall model of WTC 1 for Case A

temperature condition (downward displacement is negative) 74

Figure 3-25. Out-of-plane displacements of isolated south wall model of WTC 1 for Case A

temperature condition (inward displacement is positive) 75

Figure 3-26. Axial load in columns of isolated south wall model of WTC 1 for Case A

temperature condition (compression is negative) 76

Figure 3-27. Plastic strain in columns of isolated south wall model of WTC 1 for Case A

temperature condition at 100 min (compressive strain is negative) 77

Figure 3-28. Axial load in columns of south wall of WTC 1 at 100 min: isolated wall model for Case A temperature condition compared to global model without creep for Case Ai

conditions (compression is positive) 77

Figure 3-29. Responses of isolated south wall model of WTC 1 after corrective loads from the

global model were applied (Case A temperature condition at 100 min) 78

Figure 3-30. Total additional vertical load versus additional vertical displacement during pushdown analysis of isolated south wall model of WTC 1 for Case A temperature

condition (compression is positive) 79

NISTNCSTAR 1-6D. WTC Investigation ix
List of Figures

Figure 3-3 1 . Additional vertical load per column at different additional vertical displacements

during push-down analysis of isolated south wall model of WTC 1 for Case A

temperature condition (compression is positive) 79

Figure 3-32. Response of isolated south wall model of WTC 1 to Case A temperature condition

and push down at the end of the push-down analysis 80

Figure 3-33. Location of the out-of-plane supports and floor/wall disconnections between exterior

wall and the floor (WTC 1 south wall for Case B conditions at 100 min) 82

Figure 3-34. Case B temperature condition of south wall columns of WTC 1 at 10 min 82

Figure 3-35. Case B temperature condition of south wall columns of WTC 1 at 20 min 83

Figure 3-36. Case B temperature condition of south wall columns of WTC 1 at 30 min 83

Figure 3-37. Case B temperature condition of south wall columns of WTC 1 at 40 min 83

Figure 3-38. Case B temperature condition of south wall columns of WTC 1 at 50 min 84

Figure 3-39. Case B temperature condition of south wall columns of WTC I at 60 min 84

Figure 3-40. Case B temperature condition of south wall columns of WTC 1 at 70 min 84

Figure 3-41. Case B temperature condition of south wall columns of WTC 1 at 80 min 85

Figure 3-42. Case B temperature condition of south wall columns of WTC 1 at 90 min 85

Figure 3-^3. Case B temperature condition of south wall columns of WTC 1 at 100 min 85

Figure 3-44. Case B temperature condition of south wall spandrels of WTC 1 at 10 min 86

Figure 3-45. Case B temperature condition of south wall spandrels of WTC 1 at 20 min 86

Figure 3-46. Case B temperature condition of south wall spandrels of WTC 1 at 30 min. 86

Figure 3-47. Case B temperature condition of south wall spandrels of WTC 1 at 40 min 87

Figure 3-48. Case B temperature condition of south wall spandrels of WTC 1 at 50 min 87

Figure 3^9. Case B temperature condition of south wall spandrels of WTC 1 at 60 min 87

Figure 3-50. Case B temperature condition of south wall spandrels of WTC 1 at 70 min 88

Figure 3-51. Case B temperature condition of south wall spandrels of WTC 1 at 80 min 88

Figure 3-52. Case B temperature condition of south wall spandrels of WTC 1 at 90 min 88

Figure 3-53. Case B temperature condition of south wall spandrels of WTC 1 at 100 min 89

Figure 3-54. Vertical displacement of isolated south wall model of WTC 1 for Case B temperature

condition (downward displacement is negative) 90

Figure 3-55. Out-of-plane displacement of isolated south wall model of WTC 1 for Case B

temperature condition (inward displacement is positive) 91

Figure 3-56. Axial load in colunms of isolated south wall model of WTC 1 for Case B temperature

condition (compression is negative) 92

Figure 3-57. Plastic strain in columns of isolated south wall model of WTC 1 for Case B

temperature condition at 100 min (compressive strain is negative) 93

Figure 3-58. Axial load in columns of south wall of WTC 1 at 100 min: isolated wall model for Case B temperature condition compared to global model without creep for Case Aj

conditions (compression is positive) 93

X NISTNCSTAR 1-6D, WTC Investigation
List of Figures

Figure 3-59. Response of isolated south wall model of WTC 1 after corrective loads from the

global model were apphed (Case B temperature condition at 100 min) 94

Figure 3-60. Total additional vertical load versus additional vertical displacement during pushdown analysis of isolated south wall model of WTC 1 for Case B temperature

condition (compression is positive) 95

Figure 3-61. Additional load per column at different additional vertical displacements during

push-down analysis of isolated south wall model of WTC 1 for Case B temperature

condition (compression is positive) , 95

Figure 3-62. Response of isolated south wall model of WTC 1 to Case B temperature condition

and push-down 96

Figure 3-63. Locations of floor/wall disconnections and pull-in forces used between 80 min and

100 min of Case B temperature for south wall of WTC 1 98

Figure 3-64. Response of isolated south wall model of WTC 1 at 80 min of Case B temperature

condition with floor/wall disconnections and 6 kip pull-in forces over five floors 99

Figure 3-65. Response of isolated south wall model of WTC 1 at 90 min of Case B temperature

condition with floor/wall disconnections and 6 kip pull-in forces over five floors 100

Figure 3-66. Response of isolated south wall model of WTC 1 at 100 min of Case B temperature

condition with floor/wall disconnections and 6 kip pull-in forces over five floors 101

Figure 3-67. Axial load in columns between Floors 98 and 99 of isolated south wall model of

WTC 1 at 80 min, 90 min, and 100 min of Case B temperature condition with

floor/wall disconnections and 6 kip pull-in forces over five floors (compression is positive) 102

Figure 3-68. Column temperatures on the east wall of WTC 2 for Case C temperature condition at 10 min, 20 min, and 30 min 104

Figure 3-69. Column temperatures on the east wall of WTC 2 for Case C temperature condition at 40 min, 50 min, and 60 min 105

Figure 3-70. Location of the out-of-plane supports and floor/wall disconnections between exterior

wall and the floor (WTC 2 east wall for Case C conditions at 60 min) 106

Figure 3-71. Vertical displacement of isolated east wall model of WTC 2 for Case C temperature

distribution (downward displacement is negative; displacements scaled ten times) 107

Figure 3-72. Vertical displacement of isolated east wall model of WTC 2 for Case C temperature

distribution at 60 min (downward displacement is negative; displacements scaled ten times) 108

Figure 3-73. Out-of-plane displacement of isolated east wall model of WTC 2 for Case C

temperature condition (inward displacement is positive; displacements scaled ten times) 109

Figure 3-74. Out-of-plane displacement of isolated east wall model of WTC 2 for Case C

temperature distribution at 60 min (inward displacement is positive; displacements

scaled ten times) 1 10

Figure 3-75. Axial load on columns of isolated east wall model of WTC 2 under Case C

temperature condition (compression is negative) 1 1

1

Figure 3-76. Axial load on columns of isolated east wall model of WTC 2 for Case C temperatures

distribution at 60 min (compression is negative) 112

NISTNCSTAR 1-6D. WTC Investigation xi
List of Figures

Figure 3-77. Comparison of axial load in coluinns at Floor 83 of isolated east wall model of

WTC 2 at 60 min for Case C temperature conditions and the global model without

creep for Case C, conditions (compression is positive) 113

Figure 3-78. Vertical and out-of-plane displacements of isolated east wall model of WTC 2 after coluinn forces were corrected to those of global modal without creep for Case C,

conditions (displacements scaled ten times) 113

Figure 3-79. Vertical and out-of-plane displacements of isolated east wall model of WTC 2 after Case C temperature condition and push down analysis (displacements scaled five

times) 114

Figure 3-80. Axial load on east wall columns of isolated east wall model of WTC 2 after Case C

temperature condition and push-down (compression is negative) 1 14

Figure 3-8 1 . Additional vertical load versus additional vertical displacement during push-down

analysis of isolated east wall model of WTC 2 for Case C temperature condition 115

Figure 3-82. Variation of additional vertical load applied to columns of isolated east wall model of

WTC 2 at different levels of additional vertical displacements imposed after Case C

temperature condition (compression is positive) 115

Figure 3-83. Column temperatures on the east wall of WTC 2 for Case D temperature condition at 10 min, 20 min, and 30 min 117

Figure 3-84. Column temperatures on the east wall of WTC 2 for Case D temperature condition at 40 min, 50 min, and 60 min. 118

Figure 3-85. Location of the out-of-plane supports and floor/wall disconnections between exterior

wall and the floor (WTC 2 east wall for Case D conditions at 60 min) 119

Figure 3-86. Vertical displacement of isolated east wall model of WTC 2 for Case D temperature

condition (downward displacement is negative; displacements scaled ten times) 120

Figure 3-87. Vertical displacement of isolated east wall model of WTC 2 for Case D temperature

condition at 60 min (downward displacement is negative; displacements scaled ten times) 121

Figure 3-88. Out-of-plane displacement of isolated east wall model of WTC 2 for Case D

temperature condition (inward displacement is positive; displacements scaled ten times) 122

Figure 3-89. Out-of-plane displacement of isolated east wall model of WTC 2 for Case D

temperature condition at 60 min (inward displacement is positive; displacements

scaled ten times) 123

Figure 3-90. Axial load on east wall columns of isolated east wall model of WTC 2 for Case D

temperature condition (compression is negative) 124

Figure 3-91. Axial load on east wall columns of isolated east wall model of WTC 2 for Case D

temperature condition at 60 min (compression is negative) 125

Figure 3-92. Comparison of axial load in columns at Floor 83 of isolated east wall model of

WTC 2 at 60 min for Case D temperature conditions and the global model without

creep for Case Cj structural damage condition and Case Dj temperature condition

(compression is positive). 126

xii NISTNCSTAR 1-6D, WTC Investigation
List of Figures

Figure 3-93. Vertical and out-of-plane displacements of columns of isolated east wall model of

WTC 2 after column forces were corrected to those of global model without creep for Case Ci structural damage condition and Case D, temperature condition

(displacements scaled ten times) 126

Figure 3-94. Vertical and out-of-plane displacements of isolated east wall model of WTC 2 after Case D temperature condition and push down (displacements scaled five times) 127

Figure 3-95. Axial load on east wall columns of isolated east wall model of WTC 2 after Case D

temperature condition and push down (compression is negative) 127

Figure 3-96. Additional vertical load applied to columns versus additional vertical during

displacement for push-down analysis of isolated east wall model of WTC 2 for after Case D temperature condition (compression is positive; see Fig. 3-95 for column

locations) 128

Figure 3-97. Variation of additional vertical load applied to columns of isolated east wall model of

WTC 2 at different levels of additional vertical displacements imposed after Case D

temperature condition (compression is positive) 128

Figure 3-98. Out-of-plane displacements of the east wall of WTC 2 estimated by NIST from

photographs (inward displacement is positive; displacements are in in.) 129

Figure 3-99. Out-of-plane displacement of isolated east wall model of WTC 2 with 0.5 kip and 5.0 kip pull-in force with uniform magnitude distribution at 20 min and 18 min (inward

displacement is positive) 130

Figure 3-100. Out-of-plane displacement of isolated east wall model of WTC 2 with 0.5 kip pull-in

force with uniform magnitude distribution at 32 min (inward displacement is positive) 130

Figure 3-101. Out-of-plane displacement of isolated east wall model of WTC 2 with nonuniform

pull-in force with magnitude of 1.0 kip on the south half and 4.0 kip on the north half

(inward displacement is positive) 132

Figure 3-102. Out-of-plane displacement of isolated east wall model of WTC 2 with nonuniform

pull-in force with magnitude of 1.5 kip on the south half and 5.0 kip on the north half

(inward displacement is positive) 133

Figure 3-103. Isolated core models 134

Figure 3-104. Vertical displacement of isolated core model of WTC 1 after aircraft impact

(downward displacement is negative) 136

Figure 3-105. Vertical displacement of isolated core model of WTC 1 for Case A temperature

condition at 10 min (downward displacement is negative) 136

Figure 3-106. Vertical displacement of isolated core model of WTC 1 for Case A temperature

condition at 20 min (downward displacement is negative) 137

Figure 3-107. Vertical displacement of isolated core model of WTC 1 for Case A temperature

condition at 30 min (downward displacement is negative) 137

Figure 3-108. Vertical displacement of isolated core model of WTC 1 for Case A temperature

condition at 40 min (downward displacement is negative) 138

Figure 3-109. Vertical displacement of isolated core model of WTC 1 for Case A temperature

condition at 50 min (downward displacement is negative) 138

NISTNCSTAR 1-6D, WTC Investigation xiii
List of Figures

Figure 3-110. Vertical displacement of isolated core model of WTC 1 for Case A temperature

condition at 70 min (downward displacement is negative) 139

Figure 3-1 1 1 . Vertical displacement of isolated core model of WTC 1 for Case A temperature

condition at 100 min (downward displacement is negative) 139

Figure 3-1 12. Horizontal displacement of isolated core model of WTC 1 for Case A temperature

condition at 100 min 140

Figure 3-1 13. Axial load in columns of isolated core model of WTC 1 after aircraft impact

(compression is negative) 141

Figure 3-1 14. Axial load in columns of isolated core model of WTC 1 for Case A temperature

condition at 100 min (compression is negative) 142

Figure 3-1 15. Plastic strain in columns of isolated core model of WTC 1 for Case A temperature

condition at 100 min (compressive strain is negative) 143

Figure 3-116. Vertical displacement after push down of isolated core model of WTC 1 for Case A

temperature condition (downward displacement is negative) 144

Figure 3-117. Total additional vertical load versus additional vertical displacement during pushdown analysis of isolated core model of WTC 1 for Case A temperature condition

(compression is positive) 144

Figure 3-1 1 8. Additional axial load (kip) in columns at Floor 98 when the total axial load reached

the maximum during push down analysis of isolated core model of WTC 1 for Case A temperature condition (compression is positive) 145

Figure 3-119. Vertical displacement of isolated core model of WTC 1 for Case B temperature

condition at 10 min (downward displacement is negative) 146

Figure 3-120. Vertical displacement of isolated core model of WTC 1 for Case B temperature

condition at 20 min (downward displacement is negative) 146

Figure 3-121. Vertical displacement of isolated core model of WTC 1 for Case B temperature

condition at 30 min (downward displacement is negative) 147

Figure 3-122. Vertical displacement of isolated core model of WTC 1 for Case B temperature

condition at 40 min (downward displacement is negative) 147

Figure 3-123. Vertical displacement of isolated core model of WTC 1 for Case B temperature

condition at 50 min (downward displacement is negative) 148

Figure 3-124. Vertical displacement of isolated core model of WTC 1 for Case B temperature

condition at 70 min (downward displacement is negative) 148

Figure 3-125. Vertical displacement of isolated core model of WTC 1 for Case B temperature

condition at 100 min (downward displacement is negative) 149

Figure 3-126. Horizontal displacement of isolated core model of WTC 1 for Case B temperature

condition at 100 min 150

Figure 3-127. Axial load in columns of isolated core model of WTC 1 for Case B temperature

condition at 100 min (compression is negative) 151

Figure 3-128. Plastic strain in columns of isolated core model of WTC 1 for Case B temperature

condition at 100 min (compressive strain is negative) 152

Figure 3-129. Vertical displacement after push down of isolated core model of WTC 1 for Case B

temperature condition (downward displacement is negative) 153

xiv NISTNCSTAR 1-6D, WTC Investigation
List of Figures

Figure 3-130. Total additional vertical load versus additional vertical displacement relationship

obtained from push down analysis of isolated core model of WTC 1 for Case B

temperature condition (compression is positive) 153

Figure 3-131. Additional axial load (kip) in columns at Floor 98 when the total axial load reached

the maximum during push down analysis of the WTC 1 core for Case B temperature

condition (compression is positive) 154

Figure 3-132. Vertical displacem.ent of isolated core model of WTC 2 for Case C temperature

condition (downward displacement is negative) 156

Figure 3-133. Vertical displacement of isolated core model of WTC 2 for Case C temperature

condition at 60 min (downward displacement is negative).. 157

Figure 3-134. Axial load in core columns of isolated core model of WTC 2 for Case C temperature

condition at 60 min (compression is negative) 158

Figure 3-135. Axial plastic strains in core columns of isolated core model of WTC 2 for Case C

temperature condition at 60 min (compressive strain is negative) 159

Figure 3-136. Vertical displacement after push down of isolated core model of WTC 2 for Case C

temperature condition (downward displacement is negative) 160

Figure 3-137. Additional average vertical load versus additional vertical displacement during pushdown analysis of isolated core model of WTC 2 for Case C temperature condition

(compression is positive; core column locations are shown in Fig. 3-136) 160

Figure 3-138. Vertical displacement of isolated core model of WTC 2 for Case D temperature

condition (downward displacement is negative) 162

Figure 3-139. Vertical displacement of isolated core model of WTC 2 for Case D temperature

condition at 60 min (downward displacement is negative) 163

Figure 3-140. Axial load in core columns of isolated core model of WTC 2 for Case D temperature

condition at 60 min (compression is negative) 164

Figure 3-141. Axial plastic strains in core columns of isolated core model of WTC 2 for Case D

temperature condition at 60 min (compressive strain is negative) 165

Figure 3-142. Vertical displacement after push down of isolated core model of WTC 2 for Case D

temperature condition (downward displacement is negative) 166

Figure 3-143. Additional average vertical load versus additional vertical displacement during pushdown analysis of isolated core model of WTC 2 for Case D temperature condition 166

Figure 4-1 . Coordinate system used in the analysis models 167

Figure 4-2. Office and core area floors and core beams 169

Figure 4-3. Location and IDs of outriggers and supporting columns 170

Figure 4-4. Displaced shape of WTC 1 at the end of gravity analysis 171

Figure 4-5. Displaced shape of WTC 2 at the end of gravity analysis 171

Figure 4-6. Comparison of vertical displacement between WTC 1 models with and without

construction sequence 177

Figure 4-7. Comparison of vertical displacement between WTC 2 models with and without

construction sequence 178

NISTNCSTAR 1-6D. WTC Investigation xv
List of Figures

Figure 4-8. Vertical displacement of exterior wall of WTC 1 before aircraft impact (downward

displacement is negative) 186

Figure 4-9. Vertical displacement of exterior wall of WTC 1 after aircraft impact for Case B

conditions (downward displacement is negative) 187

Figure 4-10. Vertical displacement of exterior wall of WTC 1 at 80 min for Case B conditions

(downward displacement is negative) 188

Figure 4-11. Vertical displacement of exterior wall of WTC 1 at 100 min for Case B conditions

(downward displacement is negative) 189

Figure 4-12. Vertical displacement of north wall of WTC 1 before aircraft impact 190

Figure 4-13. Vertical displacement of north wall of WTC 1 after aircraft impact for Case B

conditions (downward displacement is negative) 190

Figure 4-14. Vertical displacement of north wall of WTC 1 at 80 min for Case B conditions

(downward displacement is negative) 191

Figure 4-15. Vertical displacement of north wall of WTC 1 at 100 min for Case B conditions with

5 kip pull-in forces (downward displacement is negative) 191

Figure 4-16. Vertical displacement of east wall of WTC 1 before aircraft impact (downward

displacement is negative) 192

Figure 4-17. Vertical displacement of east wall of WTC 1 after aircraft impact for Case B

conditions (downward displacement is negative) 192

Figure 4-18. Vertical displacement of east wall of WTC 1 at 80 min for Case B conditions

(downward displacement is negative) 193

Figure 4-19. Vertical displacement of east wall of WTC 1 at 100 min for Case B conditions with

5 kip pull-in forces (downward displacement is negative) 193

Figure 4-20. Vertical displacement of south wall of WTC 1 before aircraft impact (downward

displacement is negative) 194

Figure 4-21. Vertical displacement of south wall of WTC 1 after aircraft impact for Case B

conditions (downward displacement is negative) 194

Figure 4-22. Vertical displacement of south wall of WTC 1 at 80 min for Case B conditions

(downward displacement is negative) 195

Figure 4-23. Vertical displacement of south wall of WTC 1 at 100 min for Case B conditions with

5 kip pull-in forces (downward displacement is negative) 195

Figure 4-24. Vertical displacement of core of WTC 1 before aircraft impact (downward

displacement is negative) 196

Figure 4-25. Vertical displacement of core of WTC 1 after aircraft impact for Case B conditions

(downward displacement is negative) 197

Figure 4-26. Vertical displacement of core of WTC 1 at 50 min for Case B conditions (downward

displacement is negative) 198

Figure 4-27. Vertical displacement of core of WTC 1 at 80 min for Case B conditions (downward

displacement is negative) 199

Figure 4-28. Vertical displacement of core of WTC 1 at 100 min for Case B conditions with 5 kip

pull-in forces (downward displacement is negative) 200

xvi NISTNCSTAR 1-6D, WTC Investigation
List of Figures

Figure 4-29. Vertical displacement of core columns of WTC 1 before aircraft impact (downward

displacement is negative) 201

Figure 4-30. Vertical displacement of core columns of WTC 1 after aircraft impact for Case B

conditions (downward displacement is negative) 202

Figure 4-3 1 . Vertical displacement of core columns of WTC 1 at 80 min for Case B conditions

(downward displacement is negative) 203

Figure 4-32. Vertical displacement of core columns of WTC 1 at 100 min for Case B conditions

with 5 kip pull-in forces (downward displacement is negative) 204

Figure 4-33. Vertical displacement at Floor 99 of WTC 1 before aircraft impact 205

Figure 4-34. Change in vertical displacement at Floor 99 of WTC 1 from the time before impact to the time after impact for Case B conditions 205

Figure 4-35. Change in vertical displacement at Floor 99 of WTC 1 from the time before impact to 50 min for Case B conditions 206

Figure 4-36. Change in vertical displacement at Floor 99 of WTC 1 from the time before impact to 80 min for Case B conditions 206

Figure 4-37. Change in vertical displacement at Floor 99 of WTC 1 from the time before impact to 100 min for Case B conditions with 5 kip pull-in forces 207

Figure 4—38. Out-of-plane displacement of south wall of WTC 1 before aircraft impact (inward

displacement is positive) 208

Figure 4-39. Out-of-plane displacement of south wall of WTC 1 after aircraft impact for Case B

conditions (inward displacement is positive) 208

Figure 4-40. Out-of-plane displacement of south wall of WTC 1 at 80 min (at the end of Analysis

Step 17) for Case B conditions (inward displacement is positive) 209

Figure 4-41 . Out-of-plane displacement of south wall of WTC 1 at 100 min for Case B conditions

with 5 kip pull-in forces (inward displacement is positive) 209

Figure 4-42. Time history of maximum out-of-plane displacement of south wall of WTC 1 for Case B conditions with 5 kip pull-in forces (from Analysis Step 18 to Step 21) 210

Figure 4-43. Out-of-plane displacement of south wall of WTC 1 at 100 min for Case B conditions

with 4 kip pull-in forces (inward displacement is positive) 210

Figure 4-44. Axial load in exterior columns of north wall of WTC 1 before aircraft impact

(compression is negative) 211

Figure 4-45. Axial load in exterior columns of north wall of WTC 1 after aircraft impact for Case B conditions (compression is negative) 211

Figure 4-46. Axial load in exterior columns of north wall of WTC 1 at 80 min for the Case B

conditions (compression is negative) 212

Figure 4-47. Axial load in exterior columns of north wall of WTC 1 at 100 min for Case B

conditions with 5 kip pull-in forces (compression is negative) 212

Figure 4-48. Axial load in exterior columns of east wall of WTC 1 before aircraft impact

(compression is negative) 213

Figure 4-49. Axial load in exterior columns of east wall of WTC 1 after aircraft impact for Case B

conditions (compression is negative) 213

NISTNCSTAR 1-6D, WTC Investigation xvii
List of Figures

Figure 4-50. Axial load in exterior columns of east wall of WTC 1 at 80 min for the Case B

conditions (compression is negative) 214

Figure 4-51. Axial load in exterior columns of east wall of WTC 1 at 100 min for the Case B

conditions with 5 kip pull-in forces (compression is negative) 214

Figure 4-52. Axial load in exterior columns of south wall of WTC 1 before aircraft impact

(compression is negative) 215

Figure 4-53. Axial load in exterior columns of south wall of WTC 1 after aircraft impact for Case B conditions (compression is negative) 215

Figure 4-54. Axial load in exterior columns of south wall of WTC 1 at 80 min for Case B

conditions (compression is negative) 216

Figure 4-55. Axial load in exterior columns of south wall of WTC 1 at 100 min for Case B

conditions with 5 kip pull-in forces (compression is negative) 216

Figure 4-56. Variation of axial load in exterior columns at Floor 98 of north wall of WTC 1 for Case B conditions with 5 kip pull-in forces (compression is positive) 217

Figure 4-57. Variation of axial load in exterior columns at Floor 98 of east wall of WTC 1 for Case B conditions with 5 kip pull-in forces (compression is positive) 217

Figure 4-58. Variation of axial load in exterior columns at Floor 98 of south wall of WTC 1 for Case B conditions with 5 kip pull-in forces (compression is positive) 218

Figure 4-59. Variation of axial load in exterior columns at Floor 98 of west wall of WTC 1 for Case B conditions with 5 kip pull-in forces (compression is positive) 218

Figure 4-60. Axial load in core columns of WTC 1 before aircraft impact (compression is negative) 219

Figure 4-61 . Axial load in core columns of WTC 1 after aircraft impact for Case B conditions

(compression is negative) 220

Figure 4-62. Axial load in core columns of WTC 1 at 80 min for Case B conditions (compression

is negative) 221

Figure 4-63. Axial load in core columns of WTC 1 at 100 min for Case B conditions with 5 kip

pull-in forces (compression is negative) 222

Figure 4-64. Axial load in columns at Floor 98 of WTC 1 before aircraft impact (compression is positive) 223

Figure 4-65. Axial load in columns at Floor 98 of WTC 1 after aircraft impact for Case B

conditions (compression is positive) 223

Figure 4-66. Axial load in columns at Floor 98 of WTC 1 at 80 min for Case B conditions

(compression is positive) 224

Figure 4-67. Axial load in columns at Floor 98 of WTC 1 at 100 min for Case B conditions with

5 kip pull-in forces (compression is positive) 224

Figure 4-68. Maximum demand-to-capacity ratio for axial load in core columns between Floor 93

and Floor 99 of WTC 1 before aircraft impact 232

Figure 4-69. Maximum demand-to-capacity ratio for axial load in core columns between Floor 93

and Floor 99 of WTC 1 after aircraft impact for Case B conditions 232

xvni NISTNCSTAR 1-6D, WTC Investigation
List of Figures

Figure 4-70. Maximum demand-to-capacity ratio for axial load in core columns between Floor 93

and Floor 99 of WTC 1 at 80 min for Case B conditions 233

Figure 4-71. Maximum demand-to-capacity ratio for axial load in core columns between Floor 93

and Floor 99 of WTC 1 at 100 min for Case B conditions with 5 kip pull-in forces 233

Figure 4-72. Maximum elastic-plus-plastic strain for columns between Floor 93 and Floor 99 of

WTC 1 before aircraft impact (compressive strain is positive; strain values are in percent) 234

Figure 4-73. Maximum elastic-plus-plastic strain for columns between Floor 93 and Floor 99 of

WTC 1 after aircraft impact for Case B conditions (compressive strain is positive;

strain values are in percent) 234

Figure 4-74. Maximum elastic-plus-plastic strain for columns between Floor 93 and Floor 99 of

WTC 1 at 10 min for Case B conditions (compressive strain is positive; strain values

are in percent) 235

Figure 4-75. Maximum elastic-plus-plastic strain for columns between Floor 93 and Floor 99 of

WTC 1 at 40 min for Case B conditions (compressive strain is positive; strain values

are in percent) 235

Figure 4-76. Maximum elastic-plus-plastic strain for columns between Floor 93 and Floor 99 of

WTC 1 at 80 min for Case B conditions (compressive strain is positive; strain values

are in percent) 236

Figure 4—77. Maximum elastic-plus-plastic strain for columns between Floor 93 and Floor 99 of

WTC 1 at 1 00 min for Case B conditions with 5 kip pull-in forces (compressive

strain is positive; strain values are in percent) 236

Figure 4-78. Maximum elastic-plus-plastic-plus-creep strain for columns between Floor 93 and

Floor 99 of WTC 1 at 10 min for Case B conditions (compressive strain is positive;

strain values are in percent) 237

Figure 4-79. Maximum elastic-plus-plastic-plus-creep strain for columns between Floor 93 and

Floor 99 of WTC 1 at 40 min for Case B conditions (compressive strain is positive;

strain values are in percent) 237

Figure 4-80. Maximum elastic-plus-plastic-plus-creep strain for columns between Floor 93 and

Floor 99 of WTC 1 at 80 min for Case B conditions (compressive strain is positive;

strain values are in percent) 238

Figure 4-8 1 . Maximum elastic-plus-plastic-plus-creep strain for columns between Floor 93 and

Floor 99 of WTC 1 at 100 min for Case B conditions with 5 kip pull-in forces

(compressive strain is positive; strain value are in percent) 238

Figure 4-82. Axial load (kip) in core columns at Floor 105 of WTC 1 at 100 min for Case B

conditions with 5 kip pull-in forces (compression is positive) 241

Figure 4-83. Tension demand-to-capacity ratio for core column splices at Floor 106 of WTC 1 at 100 min for Case B conditions with 5 kip pull-in forces 241

Figure 4-84. Primary load path within the hat truss of WTC 1 243

Figure 4-85. Location of the hat truss connections in the primary load path 243

Figure 4-86. Vertical displacement of exterior wall of WTC 2 for Case D conditions (downward

displacement is negative) 253

NISTNCSTAR 1-6D. WTC Investigation xix
List of Figures

Figure 4-87. Vertical displacement of exterior wall of WTC 2 for Case D conditions (downward

displacement is negative) 254

Figure 4-88. Vertical displacement at Floor 83 of WTC 2 for Case D conditions (downward

displacement is positive) 255

Figure 4-89. Vertical displacement at Floor 83 of WTC 2 for Case D conditions (downward

displacement is positive; note the tilt toward east and south) 256

Figure 4-90. Total displacements of WTC 2 above Floor 86 at 43 min of Case D conditions

(deformed shape magnified 20 times). Note the tilt toward east and south 257

Figure 4-91. Vertical displacement of core of WTC 2 for Case D conditions (downward

displacement is negative) 258

Figure 4-92. Vertical displacement of core of WTC 2 for Case D conditions (downward

displacement is negative) 259

Figure 4-93. Vertical displacement of 800 series core columns of WTC 2 for Case D conditions

(downward displacement is negative) 260

Figure 4-94. Vertical displacement of 800 series core coluinns of WTC 2 for Case D conditions

(downward displacement is negative) 261

Figure 4-95. Vertical displacement of 900 series core columns of WTC 2 for Case D conditions

(downward displacement is negative)... 262

Figure 4-96. Vertical displacement of 900 series core columns of WTC 2 for Case D conditions

(downward displacement is negative) 263

Figure 4-97. Vertical displacement of 1000 series core columns of WTC 2 for Case D conditions

(downward displacement is negative) 264

Figure 4-98. Vertical displacement of 1000 series core columns of WTC 2 for Case D conditions

(downward displacement is negative) 265

Figure 4-99. Out-of-plane displacement of the east wall of WTC 2 for Case D conditions (inward

displacement is positive) 266

Figure 4-100. Out-of-plane displacement of the east wall of WTC 2 for Case D conditions (inward

displacement is positive) 267

Figure 4-101. Variation of maximum inward bowing of the east wall of WTC 2 over time for Case D conditions 268

Figure 4-102. Lateral displacements above Floor 86 of WTC 2 in the x-direction (north-south) for

Case D conditions 269

Figure 4-103. Lateral displacements above Floor 86 of WTC 2 in the y-direction (east-west) for Case D conditions 270

Figure 4-104. Axial load in the east wall of WTC 2 for Case D conditions (compression is negative) 271

Figure 4-105. Axial load in the east wall of WTC 2 for Case D conditions (compression is negative) 272

Figure 4-106. Axial load in the south wall of WTC 2 for Case D conditions (compression is negative) 273

XX NISTNCSTAR 1-6D, WTC Investigation
List of Figures

Figure 4-107. load in the south wall of WTC 2 for Case D conditions (compression is negative) 274

Figure 4-108. Axial load in the north wall of WTC 2 for Case D conditions (compression is negative) 275

Figure 4-109. Axial load in the north wall of WTC 2 for Case D conditions (compression is negative) 276

Figure 4-1 10. Axial load in the east and the west wall columns at Floor 83 of WTC 2 for Case D

conditions (compression is positive) 277

Figure 4-1 1 1 . Axial load in the south and the north wall columns at Floor 83 of WTC 2 for Case D

conditions (compression is positive) 278

Figure 4-1 12. Axial load in 800 series core columns of WTC 2 for Case D conditions (compression

is negative) 279

Figure 4-1 13. Axial load in 800 series core columns of WTC 2 for Case D conditions (compression

is negative) 280

Figure 4-114. Axial load in 900 series core columns of WTC 2 for Case D conditions (compression

is negative) 281

Figure 4-115. Axial load in 900 series core columns of WTC 2 for Case D conditions (compression

is negative) 282

Figure 4-1 16. Axial load in 1000 series core columns of WTC 2 for Case D conditions

(compression is negative) 283

Figure 4-117. Axial load in 1000 series core columns of WTC 2 for Case D conditions

(compression is negative) 284

Figure 4-118. Core column loads (kip) at Floor 83 of WTC 2 for Case D conditions (compression is positive) 285

Figure 4-1 19. Core column loads (kip) at Floor 83 of WTC 2 for Case D conditions (compression is positive) 286

Figure 4-120. Axial load in Floor 83 columns of WTC 2 for Case D conditions (compression is positive) 287

Figure 4-121 . Maximum elastic-plus-plastic strains for columns between Floor 78 and Floor 83 of

WTC 2 for Case D conditions (compressive strain is positive; strain values are in percent) 288

Figure 4-122. Maximum elastic-plus-plastic strains for columns between Floor 78 and Floor 3 of

WTC 2 for Case D conditions (compressive strain is positive; strain values are in percent) 289

Figure 4-123. Maximum elastic-plus-plastic-plus-creep strains for columns between Floor 78 and

Floor 83 of WTC 2 for Case D conditions (compressive strain is positive; strain values are in percent) 290

Figure 4-124. Axial load in core columns (kip) at Floor 105 (at hat truss level) of WTC 2 for Case D conditions (compression is positive) 291

Figure 4-125. Axial load in core columns (kip) at Floor 105 (at hat truss level) of WTC 2 for Case D conditions (compression is positive) 292

NISTNCSTAR 1-6D, WTC Investigation xxi
List of Figures

Figure 4-126. Progressive failure of core column splices at Floor 105 of WTC 2 (compression is positive; values are in kip) 293

Figure 4-127. State of core column splices at Floor 105 of WTC 2 294

Figure 4-128. Axial force in hat truss members of WTC 2 for Case D conditions (tension is positive) 295

Figure 4-129. Axial force in hat truss members of WTC 2 for Case D conditions (tension is positive) 296

Figure 4-130. Axial stress in hat truss members of WTC 2 for Case D conditions (tension is positive) 297

Figure 4-131. Axial stress in hat truss members of WTC 2 for Case D conditions (tension is positive) 298

Figure 4-132. Primary load path within the hat truss of WTC 2 301

Figure 4-133. Location of hat truss connections that were in the primary load path 301

V

Figure 5-1 . Vertical displacement of the truss model under thennal loading 311

Figure 5-2. Catenary action in the floor system 311

Figure 5-3. Total column loads at Floor 98 of the south wall of WTC 2 global model for Case B

conditions (compression is positive) 315

Figure 5^. Vertical displacements of full floor models of WTC 1 for Case Bi temperature

condition at 100 min (downward displacement is negative) 316

Figure 5-5. Loss of vertical supports obtained in Floor 97 and Floor 98 full floor models of

WTC 1 for Case Bi temperature condition at 100 min (Ix displacement

magnification) 3 1

6

Figure 5-6. Inward bowing of exterior columns of the South wall of WTC 1 at 10:23 a.m. (97 min after impact). Displacements were estimated by NIST from the analysis of

this photograph 317

Figure 5-7. Inward bowing of south wall of WTC 1 global model with creep at 100 min for Case B conditions with 5 kip pull-in forces (5x displacement magnification) 318

Figure 5-8. Collapse initiation and tilting of WTC 1 (view from the northeast) 318

Figure 5-9. Vertical displacements of full floor models of WTC 2 for Case D, temperature

condition at 40 min (downward displacement is negative) 323

Figure 5-10. Floor sagging observed on the east wall of WTC 2 at different times 324

Figure 5-1 1 . Total column loads at Floor 83 of the east wall of WTC 2 global model for Case D

conditions (compression is positive) 325

Figure 5-12. Maximum elastic + plastic + creep strain magnitudes for columns between Floor 78

and Floor 83 of WTC 2 global model for Case D conditions at 20 min, 30 min, and

40 min (compressive strain is positive; strain values are in percent) 326

Figure 5-13. Inward bowing of the east wall of WTC 2 global model for Case D conditions at 43 min at the instant of collapse initiation (deformed shape scaled four times) 327

Figure 5-14. Inward bowing of exterior columns of the west wall of WTC 2 just before collapse 327

xxii NISTNCSTAR 1-6D, WTC Investigation
List of Figures

Figure 5-15. Total displacements of WTC 2 global model above Floor 86 for Case D conditions at 43 min at collapse initiation (note the tilt toward east and south; deformed shape

magnified 20 times) 328

Figure 5-16. Initiation of Collapse of WTC 2. Note the tilt toward east and south 328

Figure 5-17. Full floor model of Floor 96 of WTC 1 for Case B, temperature condition at 100 min. ... 330

NISTNCSTAR 1-6D, WTC Investigation xxiii
List of Figures

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XXIV NISTNCSTAR 1-6D, WTC Investigation
List of Tables

Table P-1 Federal building and fire safety investigation of the WTC disaster xxxii

Table P-2 Public meetings and briefings of the WTC Investigation xxxv

Table 2-1 . Element types used in the global models 8

Table 2-2. Temperatures of exterior seats at east wall of Floor 82 of WTC 2 51

Table 2-3. Demand-to-capacity ratios of exterior seats at east wall of Floor 82 of WTC 2

predicted by the full floor model 52

Table 3-1. Analysis steps conducted on WTC 1 isolated exterior wall model 64

Table 3-2. Analysis steps conducted on WTC 2 isolated exterior wall model 64

Table 4-1. Conversion from SAP2000 element types to ANSYS element types 168

Table 4—2. Comparison of maximum displacements and base reactions of WTC 1 from

translated ANSYS and SAP2000 models 172

Table 4—3. Comparison of maximum displacements and base reactions of WTC 2 obtained from

translated ANSYS and SAP2000 models 172

Table 4—4. Comparison of axial forces in randomly selected elements from WTC 1 model at the

end of gra\ ity analysis 172

Table 4—5. Comparison of axial forces in randomly selected elements from WTC 2 model at the end of gravity analysis 173

Table 4—6. Global model properties before and after modifications for computational efficiency 174

Table 4-7. Comparison of total column loads between WTC 1 models with and without

construction sequence 176

Table 4-8. Comparison of total column loads between WTC 2 models with and without

construction sequence 176

Table 4-9. Analysis steps of WTC 1 ANSYS global model 180

Table 4—10. Total column loads at Floor 98 of WTC 1 for Case B conditions 225

Table 4—11. Total column loads at Floor 105 of WTC 1 for Case B conditions 225

Table 4-12. Total column loads on the north wall of WTC 1 for Case B conditions 226

Table 4-13. Change in total column loads on the north wall of WTC 1 for Case B conditions from

the state before aircraft impact 226

Table 4—14. Total column loads on the east wall of WTC 1 for Case B conditions 227

Table 4-15. Change in total colimin loads on the east wall of WTC 1 for Case B conditions from

the state before aircraft impact 227

NISTNCSTAR 1-6D. WTC Investigation xxv
List of Tabs

Table 4-16. Total column loads on the south wall of WTC 1 for Case B conditions 228

Table 4-17. Change in total column loads on the south wall of WTC 1 for Case B conditions from

the state before aircraft impact 228

Table 4-18. Summation of total column loads on the west wall of WTC 1 for Case B conditions 229

Table 4-19. Change in total column loads on the west wall of WTC 1 for Case B conditions from

the state before aircraft impact 229

Table 4-20. Total column loads on the core of WTC 1 for Case B conditions 230

Table 4-21 . Change in total column loads on the core of WTC 1 for Case B conditions from the

state before aircraft impact 230

Table 4-22. Change in total column loads before and after aircraft impact. (Loads after impact) -

(Loads before impact) 231

Table 4-23. Change in total column loads after aircraft impact and at 80 min for Case B

conditions. (Loads at 80 min) - (Loads After Impact) 231

Table 4-24. Change in total column loads at 80 min and at 100 min for Case B conditions. (Loads

at 1 00 min) - (Loads at 80 min) 23

1

Table 4-25. Tension capacity of core column splices at Floor 106 239

Table 4-26. Axial load in core columns at Floor 105 of WTC 1 for Case B conditions 240

Table 4—27. Demand-to-capacity ratio for axial load in outriggers of WTC 1 for Case B

conditions (outrigger IDs are indicated in Fig. 4-3) 242

Table 4-28. Demand to capacity ratio for axial load in exterior columns supporting outriggers at Floor 107 of WTC 1 for Case B conditions 242

Table 4-29. Demand and capacity of the hat truss connections (kip) in the primary load path at 80

min (connection IDs are shown in Fig. 4-85) 244

Table 4-30. Analysis Steps of WTC 2 ANSYS global model with Case D conditions 245

Table 4-31. Total column loads (kip) at Floor 105 at different stages of splice failures at 40 min

(compression is positive) 294

Table 4-32. Demand-to-capacity ratios for outriggers of WTC 2 for Case D conditions (outrigger

IDs are shown in Fig. 4-3) 299

Table 4-33. Demand to capacity ratios for columns supporting outriggers at Floor 107 of WTC 2

for Case D conditions 300

Table 4-34. Demand and capacity of the hat truss connections (kip) in the primary load path at 40

min (cormection IDs are shown in Fig. 4-133) 302

Table 4-35. Total column loads at Floor 83 of WTC 2 for Case D conditions 302

Table 4-36. Total column loads at Floor 105 of WTC 2 for Case D conditions 303

Table 4-37. Change in total column loads before and after aircraft impact. (Loads After Impact) -

(Loads Before Impact) 303

Table 4-38. Change in total column loads between 40 min and 43 min. (Loads at 43 min) -

(Loads at 40 min) 303

Table 4-39. Total column loads over the height for the east wall of WTC 2 for Case D conditions. ... 304

XXVI NISTNCSTAR 1-6D, WTC Investigation
List of Tabs

Table 4-40. Total column loads over the height for the south wall of WTC 2 for Case D

conditions 305

Table 4-41. Total column loads over the height for the north wall of WTC 2 for Case D

conditions 306

Table 4-42. Total column loads over the height for the west wall of WTC 2 for Case D

conditions 307

Table 4-43. Total column loads over the height for the core of WTC 2 for Case D conditions 308

Table 5-1 . Summary of main events that led to the collapse of WTC 1 312

Table 5-2. Observations on WTC 1 provided by NIST 3 1

2

Table 5-3. Total column loads at Floor 98 and Floor 105 of WTC 1 global model for Case B

conditions 315

Table 5-4. Summary of main events that led to the collapse of WTC 2 319

Table 5-5. Observations on WTC 2 provided by NIST 319

Table 5-6. Total column loads at Floor 83 and Floor 105 of WTC 2 for Case D conditions 322

NISTNCSTAR 1-6D, WTC Investigation xxvii
List of Tabs

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xxvni NISTNCSTAR 1-6D, WTC Investigation
List of Acronyms and Abbreviations

Arrnnvm^

ARA Applied Research Associates, Inc. ASTM American Society for Testing and Materials

BPS Building Performance Study

CAEAI Computer Aided Engineering Associates, Inc. FEMA Federal Emergency Management Agency

FEA finite element analysis

LERA Leslie E. Robertson Associates

NIST National Institute of Standards and Technology

PANYNJ The Port Authority of New York and New Jersey

SEAoNY Structural Engineers Association of New York

SGH Simpson Gumpertz & Heger Inc. use United States Code

WTC World Trade Center

Abbreviations

°C degrees Celsius

op degrees Fahrenheit

ft feet

in. inch

L liter m meter

fim micrometer

min minute

s second

lb pound

kip a force equal to 1 ,000 pounds

pcf pound per cubic foot

NISTNCSTAR 1-6D, WTC Investigation XXIX
List of Acronyms and Abbreviations

psf . pound per square foot

psi pound per square inch

ksi 1 ,000 pounds per square inch

XXX NISTNCSTAR 1-6D, WTC Investigation
Preface

Genesis of This Investigation

Immediately following the terrorist attack on the World Trade Center (WTC) on September 11, 2001, the

Federal Emergency Management Agency (FEMA) and the American Society of Civil Engineers began

planning a building performance study of the disaster. The week of October 7, as soon as the rescue and

search efforts ceased, the Building Performance Study Team went to the site and began its assessment. This was to be a brief effort, as the study team consisted of experts who largely volunteered their time

away from their other professional commitments. The Building Performance Study Team issued its report in May 2002, fulfilling its goal "to determine probable failure mechanisms and to identify areas of

future investigation that could lead to practical measures for improving the damage resistance of buildings

against such unforeseen events."

On August 21, 2002, with funding from the U.S. Congress through FEMA, the National Institute of

Standards and Technology (NIST) announced its building and fire safety investigation of the WTC

disaster. On October 1, 2002, the National Construction Safety Team Act (Public Law 107-231), was

signed into law. The NIST WTC Investigation was conducted under the authority of the National

Construction Safety Team Act.

The goals of the investigation of the WTC disaster were:

• To investigate the building construction, the materials used, and the technical conditions that contributed to the outcome of the WTC disaster.

• To serve as the basis for: - Improvements in the way buildings are designed, constructed, maintained, and used; - Improved tools and guidance for industry and safety officials; - Recommended revisions to current codes, standards, and practices; and - Improved public safety.

The specific objectives were:

1. Determine why and how WTC I and WTC 2 collapsed following the initial impacts of the

aircraft and why and how WTC 7 collapsed;

2. Determine why the injuries and fatalities were so high or low depending on location,

including all technical aspects of fire protection, occupant behavior, evacuation, and

emergency response;

3. Determine what procedures and practices were used in the design, construction, operation,

and maintenance of WTC 1, 2, and 7; and

4. Identify, as specifically as possible, areas in current building and fire codes, standards, and

practices that warrant revision.

NISTNCSTAR 1-6D, WTC Investigation XXXI
Preface

NIST is a nonregulatory agency of the U.S. Department of Commerce's Technology Administration. The

purpose of NIST investigations is to improve the safety and structural integrity of buildings in the United

States, and the focus is on fact finding. NIST investigative teams are authorized to assess building

performance and emergency response and evacuation procedures in the wake of any building failure that has resulted in substantial loss of life or that posed significant potential of substantial loss of life. NIST

does not have the statutory authority to make findings of fault nor negligence by individuals or organizations. Further, no part of any report resulting from a NIST investigation into a building failure or from an investigation under the National Construction Safety Team Act may be used in any suit or action

for damages arising out of any matter mentioned in such report (15 USC 281a, as amended by Public

Law 107-231).

Organization of the Investigation

The National Construction Safety Team for this Investigation, appointed by the then NIST Director, Dr. Arden L. Bement, Jr., was led by Dr. S. Shyam Sunder. Dr. William L. Grosshandler served as Associate Lead Investigator, Mr. Stephen A. Cauffman served as Program Manager for Administration,

and Mr. Harold E. Nelson served on the team as a private sector expert. The Investigation included eight

interdependent projects whose leaders comprised the remainder of the team. A detailed description of

each of these eight projects is available at http://wtc.nist.gov. The purpose of each project is summarized

in Table P-1, and the key interdependencies among the projects are illustrated in Fig. P-1.

Table P-1. Federal building and fire safety investigation of the WTC disaster.

Technical Area and Project Leader Project Purpose

Analysis of Building and Fire Codes and

Practices; Project Leaders: Dr. H. S. Lew

and Mr. Richard W. Bukowski

Document and analyze the code provisions, procedures, and

practices used in the design, construction, operation, and

maintenance of the structural, passive fire protection, and

emergency access and evacuation systems of WTC 1, 2, and 7. Baseline Structural Performance and

Aircraft hnpact Damage Analysis; Project Leader: Dr. Fahim H. Sadek

Analyze the baseline performance of WTC 1 and WTC 2 under

design, service, and abnormal loads, and aircraft impact damage on

the structural, fire protection, and egress systems.

Mechanical and Metallurgical Analysis of

Structural Steel; Project Leader: Dr. Frank

W. Gayle

Determine and analyze the mechanical and metallurgical properties

and quality of steel, weldments, and connections from steel recovered from WTC 1, 2, and 7. Investigation of Active Fire Protection

Systems; Project Leader: Dr. David

D. Evans; Dr. William Grosshandler

Investigate the perfonnance of the active fire protection systems in WTC 1,2, and 7 and their role in fire control, emergency response, and fate of occupants and responders.

Reconstruction of Thermal and Tenability

Environment; Project Leader: Dr. Richard

G. Gann

Reconstruct the time-evolving temperature, thermal environment,

and smoke movement in WTC 1, 2, and 7 for use in evaluating the

structural performance of the buildings and behavior and fate of

occupants and responders.

Structural Fire Response and Collapse

Analysis; Project Leaders: Dr. John

L. Gross and Dr. Therese P. McAUister

Analyze the response of the WTC towers to fires with and without

aircraft damage, the response of WTC 7 in fires, the performance

of composite steel-trussed floor systems, and determine the most

probable structural collapse sequence for WTC 1, 2, and 7. Occupant Behavior, Egress, and Emergency

Communications; Project Leader: Mr. Jason

D. Averill

Analyze the behavior and fate of occupants and responders, both

those who survived and those who did not, and the performance of

the evacuation system.

Emergency Response Technologies and

Guidelines; Project Leader: Mr. J. Randall

Lawson

Document the activities of the emergency responders from the time

of the terrorist attacks on WTC 1 and WTC 2 until the collapse of

WTC 7, including practices followed and technologies used.

XXXll NISTNCSTAR 1-6D, WTC Investigation
Preface

WTC Building

Performance Study

Recommendations

Government,

industry,

Professional,

Academic Inputs ^

Public inputs / %

NIST WTC Investigation Projects

Nisr

Figure P-1. The eight projects in the federal building and fire safety

investigation of the WTC disaster.

National Construction Safety Team Advisory Committee

The NIST Director also established an advisory committee as mandated under the National Construction

Safety Team Act. The initial members of the committee were appointed following a public solicitation. These were:

• Paul Fitzgerald, Executive Vice President (retired) FM Global, National Construction Safety

Team Advisory Committee Chair

• John Barsom, President, Barsom Consulting, Ltd.

• John Bryan, Professor Emeritus, University of Maryland

• David Collins, President, The Preview Group, Inc.

• Glenn Corbett, Professor, John Jay College of Criminal Justice

• Philip DiNenno, President, Hughes Associates, Inc.

NISTNCSTAR 1-6D, WTC Investigation XXXUl
Preface

• Robert Hanson, Professor Emerinis, University of Michigan

• Charles Thornton, Co-Chairman and Managing Principal, The Thomton-Tomasetti Group,

Inc.

• Kathleen Tiemey, Director, Natural Hazards Research and Applications Information Center,

University of Colorado at Boulder

• Forman Williams, Director, Center for Energy Research, University of California at San

Diego

This National Construction Safety Team Advisory Committee provided technical advice during the

Investigation and commentary on drafts of the Investigation reports prior to their pubhc release. NIST

has benefited from the work of many people in the preparation of these reports, including the National

Construction Safety Team Advisory Committee. The content of the reports and recommendations,

however, are solely the responsibility- of NIST.

Public Outreach

During the course of this Investigation, NIST held public briefings and meetings (listed in Table P-2) to

solicit input from the public, present preliminary findings, and obtain comments on the direction and

progress of the Investigation from the public and the Advisory Committee.

NIST maintained a publicly accessible Web site during this Investigation at http://wtc.nist.gov. The site contained extensive information on the background and progress of the Investigation.

NIST's WTC Public-Private Response Plan

The collapse of the WTC buildings has led to broad reexamination of how tall buildings are designed,

constructed, maintained, and used, especially with regard to major events such as fires, natural disasters,

and terrorist attacks. Reflecting the enhanced interest in effecting necessary change, NIST, with support

from Congress and the Administration, has put in place a program, the goal of which is to develop and

implement the standards, technology, and practices needed for cost-effective improvements to the safety

and security of buildings and building occupants, including evacuafion, emergency response procedures,

and threat mifigation.

The strategy to meet this goal is a three-part NIST-led public-private response program that includes:

• A federal building and fire safety investigation to study the most probable factors that contributed to post-aircraft impact collapse of the WTC towers and the 47-story WTC 7 building, and the associated evacuation and emergency response experience.

• A research and development (R&D) program to (a) facilitate the implementation of

recommendations resulting from the WTC Investigation, and (b) provide the technical basis

for cost-effective improvements to national building and fire codes, standards, and practices

that enhance the safety of buildings, their occupants, and emergency responders.

xxxiv NISTNCSTAR 1-6D, WTC Investigation
Preface

Table P-2. Public meetings and briefings of the WTC Investigation.

Date Location Principal Agenda

June 24, 2002 New York City, NY Public meeting: Public cominents on the Draft Plan for the pending WTC Investigation.

August 21. 2002 Gaithersburg. MD Media briefing announcing the fonnal start of the Investigation.

December 9. 2002 Washington, DC Media briefing on release of the Public Update and NIST request

for photographs and videos. April 8, 2003 New York City, NY Joint public forum with Columbia University on first-person interviews. April 29-30, 2003 Gaithersburg, MD NCST Advisory Committee meeting on plan for and progress on WTC Investigation with a public comment session. May 7, 2003 New York City, NY Media briefing on release of May 2003 Progress Report.

August 26-27, 2003 Gaithersburg, MD NCST Advisory Committee meeting on status of the WTC

investigation with a public comment session. September 17.2003 New York City, NY Media and public briefing on initiation of first-person data

collection projects.

December 2-3, 2003 Gaithersburg, MD NCST Advisory Committee meeting on status and initial results and release of the Public Update with a public comment session. Februar\' 12. 2004 New York City, NY Public meeting on progress and preliminary findings with public

comments on issues to be considered in fonnulating final recommendations.

June 18. 2004 New York City, NY Media/public briefing on release of June 2004 Progress Report. June 22-23, 2004 Gaithersburg, MD NCST Advisory Committee meeting on the status of and

preliminary findings from the WTC Investigation with a public

comment session. August 24, 2004 Northbrook, IL Public viewing of standard fire resistance test of WTC floor system at Underwriters Laboratories, Inc. October 19-20, 2004 Gaithersburg, MD NCST Advisory Committee meeting on status and near complete

set of preliminary findings with a public comment session. November 22, 2004 Gaithersburg. MD NCST Advisory Committee discussion on draft annual report to Congress, a public comment session, and a closed session to discuss pre-draft recommendations for WTC Investigation.

April 5, 2005 New York City, NY Media and public briefing on release of the probable collapse sequence for the WTC towers and draft reports for the projects on

codes and practices, evacuation, and emergency response. June 23. 2005 New York City, NY Media and public briefing on release of all draft reports for the WTC towers and draft recommendations for public comment.

September 12-13.

2005

Gaithersburg, MD NCST Advisory Committee meeting on disposition of public

comments and update to draft reports for the WTC towers. September 13-15,

2005

Gaithersburg, MD WTC Technical Conference for stakeholders and technical community for dissemination of findings and recommendations

and opportunity for public to make technical comments.

• A dissemination and technical assistance program (DTAP) to (a) engage leaders of the

construction and building community in ensuring timely adoption and widespread use of

proposed changes to practices, standards, and codes resulting from the WTC Investigation

and the R&D program, and (b) provide practical guidance and tools to better prepare facility owners, contractors, architects, engineers, emergency responders, and regulatory authorities

to respond to future disasters. The desired outcomes are to make buildings, occupants, and first responders safer in future disaster events.

NISTNCSTAR 1-6D, WTC Investigation XXXV
Preface

National Construction Safety Team Reports on the WTC Investigation

A final report on the collapse of the WTC towers is being issued as NIST NCSTAR 1. A companion

report on the collapse of WTC 7 is being issued as NIST NCSTAR lA. The present report is one of a set that provides more detailed documentation of the Investigation findings and the means by which these

technical results were achieved. As such, it is part of the archival record of this Investigation. The titles of the full set of Investigation publications are:

NIST (National Institute of Standards and Technology). 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Final Report on the Collapse ofthe World Trade

Center Towers. NIST NCSTAR 1 . Gaithersburg, MD, September.

NIST (National Institute of Standards and Technology). 2006. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Final Report on the Collapse of World Trade Center 7. NIST NCSTAR 1 A. Gaithersburg, MD.

Lew, H. S., R. W. Bukowski, and N. J. Carino. 2005. Federal Building and Fire Safety Investigation of

the World Trade Center Disaster: Design, Construction, and Maintenance ofStructural and Life Safety

Systems. NIST NCSTAR 1-1. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Fanella, D. A., A. T. Derecho, and S. K. Ghosh. 2005. Federal Building and Fire Safety

Investigation of the World Trade Center Disaster: Design and Construction ofStructural Systems.

NIST NCSTAR 1-1 A. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Ghosh, S. K., and X. Liang. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Comparison ofBuilding Code Structural Requirements. NIST

NCSTAR 1-lB. National Institute of Standards and Technology. Gaithersburg, MD, September.

Fanella, D. A., A. T. Derecho, and S. K. Ghosh. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Maintenance and Modifications to Structural

Systems. NIST NCSTAR 1-lC. National Institute of Standards and Technology. Gaithersburg,

MD, September.

Grill, R. A., and D. A. Johnson. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Fire Protection and Life Safety Provisions Applied to the Design and

Construction of World Trade Center 1, 2, and 7 and Post-Construction Provisions Applied after Occupancy. NIST NCSTAR 1-lD. National Institute of Standards and Technology. Gaithersburg,

MD, September.

Razza, J. C, and R. A. Grill. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Comparison of Codes, Standards, and Practices in Use at the Time ofthe

Design and Construction of World Trade Center 1, 2, and 7. NIST NCSTAR 1-lE. National

Institute of Standards and Technology. Gaithersburg, MD, September.

Grill, R. A., D. A. Johnson, and D. A. Fanella. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Comparison ofthe 1968 and Current (2003) New

xxxvi NIST NCSTAR 1-6D, WTC Investigation
Preface

York Cin- Building Code Provisions. NISTNCSTAR 1-lF. National Institute of Standards and

Technology. Gaithersburg, MD, September.

Grill, R. A., and D. A. Johnson. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Amendments to the Fire Protection and Life Safety Provisions ofthe New

York City Building Code by Local Laws Adopted Wliile World Trade Center 1, 2, and 7 Were in Use. NIST NCSTAR 1-1 G. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Grill, R. A., and D. A. Johnson. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Post-Construction Modifications to Fire Protection and Life Safety Systems

of World Trade Center 1 and 2. NIST NCSTAR 1-lH. National Institute of Standards and

Technology. Gaithersburg, MD, September.

Grill, R. A., D. A. Johnson, and D. A. Fanella. 2005. Federal Building and Fire Safety Investigation

ofthe World Trade Center Disaster: Post-Construction Modifications to Fire Protection, Life

Safety, and Structural Systems of World Trade Center 7. NIST NCSTAR 1-1 1. National Institute of

Standards and Technology. Gaithersburg, MD. September.

Grill, R. A., and D. A. Johnson. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Design, Installation, and Operation ofFuel System for Emergency Power in World Trade Center 7. NIST NCSTAR 1-1 J. National Institute of Standards and Technology.

Gaithersburg, MD, September.

Sadek, F. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center Disaster:

Baseline Structural Performance and Aircraft Impact Damage Analysis ofthe World Trade Center

Towers. NIST NCSTAR 1-2. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Faschan, W. J., and R. B. Garlock. 2005. Federal Building and Fire Safety Investigation ofthe

World Trade Center Disaster: Reference Structural Models and Baseline Performance Analysis of

the World Trade Center Towers. NIST NCSTAR 1-2A. National Institute of Standards and

Technology. Gaithersburg, MD, September.

Kirkpatrick, S. W., R. T. Bocchieri, F. Sadek, R. A. MacNeill, S. Holmes, B. D. Peterson,

R. W. Cilke, C. Navarro. 2005. Federal Building and Fire Safety Investigation ofthe World Trade

Center Disaster: Analysis ofAircraft Impacts into the World Trade Center Towers, NIST

NCSTAR 1-2B. National Institute of Standards and Technology. Gaithersburg, MD, September.

Gayle, F. W., R. J. Fields, W. E. Luecke, S. W. Banovic, T. Foecke, C. N. McCowan, T. A. Siewert, and

J. D. McColskey. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: Mechanical and Metallurgical Analysis ofSti-uctural Steel. NIST NCSTAR 1-3. National

Institute of Standards and Technology. Gaithersburg, MD, September.

Luecke, W. E., T. A. Siewert, and F. W. Gayle. 2005. Federal Building and Fire Safety

Investigation of the World Trade Center Disaster: Contemporaneous Structural Steel

Specifications. NIST Special Publication 1-3 A. National Institute of Standards and Technology.

Gaithersburg, MD, September.

NISTNCSTAR 1-6D, WTC Investigation xxxvn
Preface

Banovic, S. W. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: Steel Inventory and Identification. NIST NCSTAR 1-3B. National Institute of Standards

and Technology. Gaithersburg, MD, September.

Banovic, S. W., and T. Foecke. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Damage and Failure Modes ofStructural Steel Components. NIST

NCSTAR 1-3C. National Institute of Standards and Technology. Gaithersburg, MD, September.

Luecke, W. E., J. D. McColskey, C. N. McCowan, S. W. Banovic, R. J. Fields, T. Foecke,

T. A. Siewert, and F. W. Gayle. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Mechanical Properties ofStructural Steels. NIST NCSTAR 1-3D.

National Institute of Standards and Technology. Gaithersburg, MD, September.

Banovic, S. W., C. N. McCowan, and W. E. Luecke. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Physical Properties ofStructural Steels. NIST

NCSTAR 1-3E. National Institute of Standards and Technology. Gaithersburg, MD, September.

Evans, D. D., R. D. Peacock, E. D. Kuligowski, W. S. Dols, and W. L. Grosshandler. 2005. Federal

Building and Fire Safety Investigation ofthe World Trade Center Disaster: Active Fire Protection

Systems. NIST NCSTAR 1-4. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Kuligowski, E. D., D. D. Evans, and R. D. Peacock. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Post-Construction Fires Prior to September II, 2001. NIST NCSTAR 1-4A. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Hopkins, M., J. Schoenrock, and E. Budnick. 2005. Federal Building and Fire Safety Investigation

ofthe World Trade Center Disaster: Fire Suppression Systems. NIST NCSTAR 1-4B. National

Institute of Standards and Technology. Gaithersburg, MD, September.

Keough, R. J., and R. A. Grill. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Fire Alarm Systems. NIST NCSTAR 1-4C. National Institute of Standards

and Technology. Gaithersburg, MD, September.

Ferreira, M. J., and S. M. Strege. 2005. Federal Building and Fire Safety Investigation ofthe

World Trade Center Disaster: Smoke Management Systems. NIST NCSTAR 1-4D. National

Institute of Standards and Technology. Gaithersburg, MD, September.

Gann, R. G., A. Hamins, K. B. McGrattan, G. W. Mulholland, H. E. Nelson, T. J. Ohlemiller,

W. M. Pitts, and K. R. Prasad. 2005. Federal Building and Fire Safety Investigation ofthe World Trade

Center Disaster: Reconstruction ofthe Fires in the World Trade Center Towers. NIST NCSTAR 1-5. National Institute of Standards and Technology. Gaithersburg, MD, September.

Pitts, W. M., K. M. Butler, and V. Junker. 2005. Federal Building and Fire Safety Investigation of

the World Trade Center Disaster: Visual Evidence, Damage Estimates, and Timeline Analysis.

NIST NCSTAR 1-5 A. National Institute of Standards and Technology. Gaithersburg, MD,

September.

xxxvni NIST NCSTAR 1-6D, WTC Investigation
Preface

Hamins, A., A. Maranghides, K. B. McGrattan, E. Johnsson, T. J. Ohlemiller, M. Donnelly,

J. Yang, G. Mulholland, K. R. Prasad, S. Kukuck, R. Anleitner and T. McAllister. 2005. Federal

Building and Fire Safety Investigation ofthe World Trade Center Disaster: Experiments and

Modeling ofStructural Steel Elements Exposed to Fire. NIST NCSTAR 1-5B. National Institute of

Standards and Technology. Gaithersburg, MD, September.

Ohlemiller, T. J., G. W. Mulholland, A. Maranghides, J. J. Filliben, and R. G. Gann. 2005. Federal

Building and Fire Safety Investigation ofthe World Trade Center Disaster: Fire Tests ofSingle

Office Workstations. NIST NCSTAR 1-5C. National Institute of Standards and Technology.

Gaithersburg, MD, September.

Gann, R. G., M. A. Riley, J. M. Repp, A. S. Whittaker, A. M. Reinhora, and P. A. Hough. 2005.

Federal Building and Fire Safety Investigation ofthe World Trade Center Disaster: Reaction of

Ceiling Tile Systems to Shocks. NIST NCSTAR 1-5D. National Institute of Standards and

Technology. Gaithersburg, MD, September.

Hamins, A., A. Maranghides, K. B. McGrattan, T. J. Ohlemiller, and R. Anleitner. 2005. Federal

Building and Fire Safety Investigation ofthe World Trade Center Disaster: Experiments and

Modeling ofMultiple Workstations Burning in a Compartment. NIST NCSTAR 1-5E. National

Institute of Standards and Technology. Gaithersburg, MD, September.

McGrattan, K. B., C. Bouldin, and G. Forney. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Computer Simulation ofthe Fires in the World

Trade Center Towers. NIST NCSTAR 1-5F. National Institute of Standards and Technology.

Gaithersburg, MD, September.

Prasad, K. R., and H. R. Baum. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Fire Structure Interface and Thermal Response ofthe World Trade Center

Towers. NIST NCSTAR 1-5G. National Institute of Standards and Technology. Gaithersburg,

MD, September.

Gross, J. L., and T. McAllister. 2005. Federal Building and Fire Safety Investigation ofthe World Trade

Center Disaster: Structural Fire Response and Probable Collapse Sequence ofthe World Trade Center

Towers. NIST NCSTAR 1-6. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Carino, N. J., M. A. Stames, J. L. Gross, J. C. Yang, S. Kukuck, K. R. Prasad, and R. W. Bukowski.

2005. Federal Building and Fire Safety Investigation ofthe World Trade Center Disaster: Passive

Fire Protection. NIST NCSTAR 1-6A. National Institute of Standards and Technology.

Gaithersburg, MD, September.

Gross, J., F. Hervey, M. Izydorek, J. Mammoser, and J. Treadway. 2005. Federal Building and

Fire Safety Investigation ofthe World Trade Center Disaster: Fire Resistance Tests ofFloor Truss

Systems. NIST NCSTAR 1-6B. National Institute of Standards and Technology. Gaithersburg,

MD, September.

Zarghamee, M. S., S. Bolourchi, D. W. Eggers, O. O. Erbay, F. W. Kan, Y. Kitane, A. A. Liepins,

M. Mudlock, W. I. Naguib, R. P. Ojdrovic, A. T. Sarawit, P. R Barrett, J. L. Gross, and

NIST NCSTAR 1-6D, WTC Investigation XXXIX
Preface

T. P. McAllister. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: Component, Connection, and Subsystem Structural Analysis. NIST NCSTAR 1-6C.

National Institute of Standards and Technology. Gaithersburg, MD, September.

Zarghamee, M. S., Y. Kitane, O. O. Erbay, T. P. McAllister, and J. L. Gross. 2005. Federal

Building and Fire Safety Investigation ofthe World Trade Center Disaster: Global Structural

Analysis ofthe Response ofthe World Trade Center Towers to Impact Damage and Fire. NIST

NCSTAR 1-6D. National Institute of Standards and Technology. Gaithersburg, MD, September.

McAllister, T., R. W. Bukowski, R. G. Gann, J. L. Gross, K. B. McGrattan, H. E. Nelson, L. Phan,

W. M. Pitts, K. R. Prasad, F. Sadek. 2006. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Structural Fire Response and Probable Collapse Sequence of World Trade

Center?. (Provisional). NIST NCSTAR 1-6E. National Institute of Standards and Technology.

Gaithersburg, MD.

Gilsanz, R., V. Arbitrio, C. Anders, D. Chlebus, K. Ezzeldin, W. Guo, P. Moloney, A. Montalva,

J. Oh, K. Rubenacker. 2006. Federal Building and Fire Safety Investigation ofthe World Trade

Center Disaster: Structural Analysis ofthe Response of World Trade Center 7 to Debris Damage

and Fire. (Provisional). NIST NCSTAR 1-6F. National Institute of Standards and Technology.

Gaithersburg, MD.

Kim, W. 2006. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: Analysis ofSeptember II, 2001, Seismogram Data. (Provisional). NIST NCSTAR 1-6G.

National Institute of Standards and Technology. Gaithersburg, MD.

Nelson, K. 2006. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: The Con Ed Substation in World Trade Center 7. (Provisional). NIST NCSTAR 1-6H.

National Institute of Standards and Technology. Gaithersburg, MD.

Averill, J. D., D. S. Mileti, R. D. Peacock, E. D. Kuligowski, N. Groner, G. Proulx, P. A. Reneke, and

H. E. Nelson. 2005. Federal Building and Fire Safety Investigation of the World Trade Center Disaster:

Occupant Behavior, Egress, and Emergency Communication. NIST NCSTAR 1-7. National Institute of

Standards and Technology. Gaithersburg, MD, September.

Fahy, R., and G. Proulx. 2005. Federal Building and Fire Safety Investigation of the World Trade

Center Disaster: Analysis ofPublished Accounts ofthe World Trade Center Evacuation. NIST

NCSTAR 1-7A. National Institute of Standards and Technology. Gaithersburg, MD, September.

Zmud, J. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: Technical Documentationfor Swvey Administration. NIST NCSTAR 1-7B. National

Institute of Standards and Technology. Gaithersburg, MD, September.

Lawson, J. R., and R. L. Vettori. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: The Emergency Response Operations. NIST NCSTAR 1-8. National Institute of

Standards and Technology. Gaithersburg, MD, September.

xl NIST NCSTAR 1-6D, WTC Investigation
Acknowledgments

The Authors would hke to thank Glenn R. Bell and Ronald O. Hamburger of Simpson Gumpertz & Heger

Inc. (SGH) for re\'iewing the report and assisting in its revision. The assistance of the SGH internal

Structural Performance Review Committee (Glenn R. Bell, Ronal O. Hamburger, and Pedro J. Sifre) and

the Computation'Modeling Review Committee (Said Bolourchi, Atis A. Liepins, and Peter R. Barrett of

Computer Aided Engineering Associates, Inc., an SGH subconsultant in this project) is acknowledged.

The authors would also like to thank the technical staff of Computer Aided Engineering Associates, Inc., for their effort at converting SAP2000 finite element models to ANSYS and for their assistance in finite element modeling in ANSYS.

NIST NCSTAR 1-6D, WTC Investigation xli
Acknowledgments

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xlii NISTNCSTAR 1-6D, WTC Investigation
Executive Summary

E.1 INTRODUCTION

Simpson Gumpertz & Heger Inc. (SGH) developed global models of the World Trade Center (WTC)

towers using finite elements and performed analyses of the global models to gain an understanding of the

roles of the aircraft impact damage and the subsequent fires in the WTC towers in the structural stability

and sequential failures of components and subsystems and to determine the probable sequence of

structural responses that let to the global collapse initiation. The study was conducted as part of the

investigation of the WTC disaster by the National Institute of Standards and Technology (NIST).

The work presented in this report was performed as a part of Project 6 of the NIST WTC investigation.

This report complements the work performed by SGH on the structural response to the fire environment

of connections such as truss seats and knuckles, components such as trusses and columns, and subsystems

including full floors and exterior walls of the WTC towers.

Global analyses of the WTC towers were also guided by observations. NIST examined photos and videos

for visual evidence, damage estimates, and timeline of the collapse process in NIST NCSTAR 1-5 A. A

trial and error procedure was used in this study, which was (1) to identify the major observations at different times during the collapse process, (2) to determine the deviation between the observations and

calculations, and to identify the likely assumptions that led to such deviations, and (3) to use the

obser\'ations to correct the state of the structure at that time and continue the calculation to collapse

initiation point. Actual obser\'ations based on NIST's examination of photos and videos are summarized

in Tables E-1 and E-2 for WTC 1 and WTC 2, respectively. Columns that are referenced by column

numbers can be located in Fig. E-1.

NIST NCSTAR 1-6D, WTC Investigation xliii
Executive Summary

Table E-1. Observations on WTC 1 provided by NIST.

Time

Time

from

Impact

(min) Observation

8:46:26 0 Aircraft impact on the north wall of WTC 1 between Floor 93 and Floor 99 and Columns 112 and 151.

9:25:28 39 Fire on west side of south wall.

9:40 54 No bowing of columns was observed between Columns 301 and 323 on the east side of south

wall.

10:18:43 92 Smoke suddenly expelled on Floor 92 north wall; Floor 94 east side of north wall; Floor 95

to Floor 98 on west side of north wall; Floor 95 and Floor 98 on north side of west wall; lower floor on south side.

10:22:59 97 Inward bowing from Floor 95 to about Floor 99 between Columns 308 and 326 (maybe to 340) on the south wall, maximum amplitude approximately 55 in. at Floor 97.

10:28:18 102 Smoke puff out of north edge and center of west wall; smoke and debris clouds out of the

north, east, and west walls on Floor 98. Fire out of windows on the north, east, west, and

south walls between Floor 92 and Floor 98. and on Floor 104.

10:28:20 102 WTC 1 began to collapse. First exterior sign of collapse was at Floor 98. Rotation of at least 8 degrees to the south occurred before the building section began to fall vertically under

gravity.

Table E-2. Observations on WTC 2 provided by NIST.

Time

Time

from

Impact

(min) Observation

9:03 0 Aircraft impact on the south wall of WTC 2 between Floors 77 and 85, Columns 404 to 443.

9:21 18 Columns of the east wall bowed inward over the entire width of Floors 78 to 83; maximum of

7-9 in. at Floor 80.

9:38 35 Floor 83 disconnections on the east wall appeared to extend.

9:54 51 Columns of the east wall bowed inward between Floor 78 and Floor 84, 12-20 in. at Floor 80. East side of Floor 83 draped between Columns 310 to 342.

9:59 56 WTC 2 began to collapse.

Column splices failed at every third panel and columns sprung back from inward bowing as collapse initiated on the east wall near the northeast comer Smoke and debris clouds were expelled from Floor 8 1 on the east, north, and west walls of the building.

WTC 2 appeared to tilt around the base of Floor 82 and initial downward motion was visible at the same location.

Tilt of approximately 3 to 4 degrees to the south and 7 to 8 degrees to the east occurred before

building section fell. Kink (change in slope) on the southeast comer near Floor 94 (halfway along building section above failure). Kink (change in slope) and offset about at the Floor 106.

xliv NISTNCSTAR 1-6D, WTC Investigation
Executive Summary

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Figure E-1. Column designations.

NISTNCSTAR 1-6D, WTC Investigation xlv
Executive Summary

E.2 GLOBAL MODEL ANALYSIS

E.2.1 Global Models

SGH developed global finite-element structural models of WTC towers in ANSYS to perform collapse

analysis of WTC 1 and WTC 2 subjected to the combined effects of gravity and thermal loads. The

geometry, the connectivity, and the member shapes of the global models for WTC 1 and WTC 2 were

obtained from an ANSYS model converted from the reference SAP2000 model developed by NIST

(NIST NCSTAR 1-2) and the study conducted by SGH on components and subsystems of the WTC

towers. The global models were then modified by truncating the models below the aircraft impact zone and including changes to the modeling of coluinns, trusses, and slabs to capture the failure modes

calculated in the structural analysis of components, connections, and subsystems of the WTC towers. Material properties of steel were modified to include: temperature-dependent material properties, such as thermal expansion, elastic properties, isotropic hardening plasticity, and creep. In addition, global models

allowed geometrically nonlinear analysis and large deflection effects needed for elastic and inelastic structural instability at high temperatures.

E.2.2 Impact Damage

Aircraft impact damage to the structural members and the fireproofing of steel members of the WTC

towers were determined in NIST NCSTAR 1-2 and NIST NCSTAR 1-6. In the global analysis the

severed exterior wall columns, spandrels, core columns, core beams, and parts of the floors were removed

at the appropriate stage of analysis.

The NIST investigation identified four aircraft impact damage sets (two damage sets for each tower)

consisting of an impact damage condition and a fireproofing damage condition. These damage sets were named Case A and Case B for WTC 1 and Case C and Case D for WTC 2. Case B and Case D damage

sets were used in the final global analyses. Case B and Case D impact damage sets for columns are shown in Figs. E-2 to E-5, where severed columns are shown as missing vertical lines. For comparison,

core columns and beams before aircraft impact are shown in Figs. E-6 and E-7 for WTC 1 and WTC 2,

respectively. (Note that the global models included only core beams that had moment connections;

hence. Figs E-3 and E-5 do not show all the core beams that existed in the WTC towers.)

159

Floor 99 —

Floor 97 —

Floor 95 —

Floor 93 —

Li

01 359 301

(a) North face (b) South face

Figure E-2. Structural damage condition on the exterior walls of WTC 1 for all cases of

impact damage.

xlvi NIST NCSTAR 1-6D, WTC Investigation
Executive Summary

West

Floor 97

Floor 95

Floor 93

Floor 91

Floor 97

Floor 95

Floor 93

Floor 91

508 501 608 601 708 701

(a) 500 series columns (b) 600 series columns (c) 700 series columns

807 801 908 901

(a) 800 series columns (b) 900 series columns

Figure E-3. Case B structural damage condition on the core columns of WTC 1 (including heavily damaged columns).

Figure E-4. Structural damage condition on the exterior walls of WTC 2 for all cases of

impact damage.

NISTNCSTAR 1-6D, WTC Investigation xlvii
Executive Summary

708 701

(a) 700 series columns

908 901

1 ,

1

j ~f~

!

(c) 900 series columns

807 80

(b) 800 series columns

1008 1001

(d) 1000 series columns

Floor 81

Floor 79

Floor 77

Floor 84

Floor 82

Floor 79

Floor 77

North

Figure E-5. Case D structural damage condition on the core columns of WTC 2

(including heavily damaged columns).

West

508 501 608

Floor 99

Floor 97

Floor 95

Floor 93

Floor 91

Floor 99

Floor 97

Floor 95

Floor 93

Floor 91

(a) 500 series columns

807 801

708 701

(b) 600 series columns

908 901

1—i—

1

r 1

1

1

(c) 700 series columns

1008 1001

(d) 800 series columns (e) 900 series columns (f) 1000 series columns

Figure E-6. Core columns and core beams in the WTC 1 global model without aircraft

impact damage.

xlviii NISTNCSTAR 1-6D. WTC Investigation
Executive Summary

North

508

Floor 85

Floor 83

Floor 81 Floor 79

(a) 500 series columns (b) 600 series columns (c) 700 series columns

807 801 908 901 1008 1001

}

(d) 800 series columns (e) 900 series columns (f) 1000 series columns

Figure E-7. Core columns and core beams in the WTC 2 global model without aircraft

impact damage.

E.2.4 Loads and Boundary Conditions in the Global Models

The global models were fully restrained at the base of the vertical springs. The loads on the structure consisted of gravity loads and temperature loads. The gravity loads included dead load and live load

(equal to 25 percent of the design live load). Temperature loads consisted of temperature time histories

provided by NIST based on their fire dynamics and heat transfer analyses performed for different

conditions of structural and fireproofmg damage. Temperature data were provided for every structural node at 1 0 min intervals. Temperatures between the 10 min intervals were determined by linear

interpolation.

E.2.5 Fire-Induced Damage

It was not practical to develop global models that could capture all the failure modes found in the study of

components, connections, and subsystems, and to perform global analyses within a reasonable time

period. Since detailed modeling of the floors was not included in the global models, important floor

behavioral modes could not be captured directly from the global analyses. Key floor behavioral modes

include sagging that imposed pull-in forces on the exterior wall and failure of support of the trusses at the

exterior wall resulting in local disconnection of the floor from the exterior wall. Moreover, the sagging

and the resulting bowing of the exterior walls calculated from the full floor model did not match the

observed inward bowing. To account for these effects, the pull-in forces on the exterior wall and

floor/wall disconnections were input into the global models as fire-induced damage at certain points in time, as illustrated in Figure E-8. Fire-induced damage calculated by the full floor models were then

calibrated to the damage observed by NIST through their examination of photographs and videos during

the heating period up to the final collapse. In addition, the magnitudes of pull-in forces were determined

01 608 601 708 701

Floor 85

Floor 83

Floor 81 Floor 79

NISTNCSTAR 1-6D, WTC Investigation xlix
Executive Summary

by trial and error to match the observed inward bowing of exterior walls using the isolated exterior wall

models from the global models.

100

99

E2 96 ooE 95

94

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360 350 340 330 320 Column ID

310 300

(a) South wall of WTC 1 between 80 min and 90 min

84

83

82

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g 80

79

78

77

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360 —I—350 340 330 320 Column ID

310 300

(b) East wall of WTC 2 between 40 min and 50 min

Figure E-8. Examples of locations of floor/wall disconnections and pull-in forces used in

the collapse analyses of the global model with creep.

NISTNCSTAR 1-6D, WTC Investigation
Executive Summary

E.3 COLLAPSE SEQUENCE

The final global models were developed based on the following assumptions:

• Floor subsystem was modeled by plate elements with elastic properties without ability to simulate sagging and its effect on the development of pull-in forces and floor/wall

disconnections. Pull-in forces resulting from floor sagging and floor/wall disconnections were

determined based on the results of fiill floor models and isolated wall models and modified by

visual obser\'ations. They were input in the global model analyses at different times as fire- induced damage.

• Spandrels were modeled by beam elements. Axial degree of freedom of the beam elements

representing spandrels was released to enhance numerical efficiency and avoid thermallyinduced buckling. The exterior wall subsystem analysis showed that large deformations and

buckling of spandrels would not affect the stability of exterior columns significantly.

• Columns were modeled to capture inelastic buckling, but not the kink-type buckling initiated by the local buckling of plates and resuhing in significant distortion of the cross section. The

analysis of columns showed that when buckling occurs on a column that spans several floors and is at high temperatures, inelastic buckling, rather than kink-type buckling, governs its load deformation characteristic.

• The sections below the impact zones were removed, and the vertical stiffness of the removed

sections was replaced with equivalent vertical springs. Preliminary analyses of the global

models showed that sections below the impact zone did not contribute much to the overall

behavior of the towers.

• Construction sequence was not considered to enhance computational efficiency. A

comparative study showed that the total column load on each face of the exterior wall

increased by 7 to 15 percent, and the total column load on the core decreased by about

10 percent, by neglecting the construction sequence.

• Structural members that were severed or heavily damaged by aircraft impact were removed

from the final global models before gravity loads were applied to enhance computational

efficiency.

• Break elements were not used in the final global models to represent component failures such

as failure of column splices. However, the results of the global model analyses were examined to determine whether any component failure occurred and to what extent its failure impacted the collapse sequence.

The key structural events common to both towers are discussed below.

• Sagging of floors caused by the elevated steel temperatures resulting from loss of

fireproofing. Elevated temperature caused buckling of the truss web diagonals, with the floor

deforming into a catenary. The catenary action in this study refers to the combined action

that results when the bending capacity of the truss is exceeded and additional load is carried

NISTNCSTAR 1-6D, WTC Investigation li
Executive Summary

by the floor system acting as a tensile structure. Sagging of the floor resulted in pull-in forces

at floor/exterior wall connections, and led to inward bowing of the exterior wall

• Bowing and buckling of the entire exterior wall of a tower under the combined effects of

temperature, the redistributed gravity load, pull-in force from sagging floors, and loss of

lateral support due to sagging or floor/wall disconnections. Floors deformed into catenaries

did not restrain the exterior wall columns from buckling.

• Downward displacement of the core due to severed core columns from the aircraft impact and

redistributed column loads to non-severed core columns, and shortening of the core columns

caused by buckling, plasticity, and creep of core columns at elevated temperatures.

• Redistribution of gravity loads among exterior and interior columns resulting from damage

due to aircraft impact, restrained thermal expansion, shortening of core columns, tilting of the

tower above the impact region, and bowing and buckling of exterior walls. Redistribution of

the loads from aircraft impact or fire-induced damaged columns, both in the core and exterior

walls, was primarily to the neighboring columns. Redistribution of gravity loads from the core to the exterior walls and from the exterior walls to the core was primarily through the hat

truss. Redistribution between adjacent exterior walls was primarily through the spandrels,

and to a lesser extent through the hat truss. Major load redistribution mechanisms were as follows:

- Aircraft impact reduced the load on the impacted wall and on the opposite wall thiough

the pivoting action of the hat truss, and increased the load on side walls. - Thermal expansion caused increased loads in thermally restrained members. - Shortening of core columns caused a redistribution of the load from the core to the

exterior walls. - Tilting of the tower redistributed the load among the exterior walls, resulting in increased

load on the compressed part of the exterior walls. - Buckhng of the exterior wall caused rapid unloading of the buckled wall and of the

opposite wall through the pivoting action of the stiff hat truss and increased the load on

the other two exterior walls. The collapse sequences of the two towers are discussed separately below.

E.3.1 WTC 1 Collapse Sequence

The aircraft impacted the north wall of WTC 1 at 8:46 a.m. The aircraft severed exterior columns and

floors on the north side of the tower and core columns and floor members between Floor 93 and Floor 98. The subsequent fires weakened structural subsystems, including the core columns, floors, and exterior

walls. The core displaced downward, the floors sagged, and the south exterior wall bowed inward. At

10:28 a.m., about 102 min after the aircraft impact, WTC 1 began to collapse. The collapse sequence of

WTC 1 consists of five main structural events: 1) aircraft impact, 2) unloading of core, 3) sagging of

floors and floor/wall disconnections, 4) inward bowing of south wall, and 5) buckling of south wall and

collapse initiation.

lil NISTNCSTAR 1-6D, WTC Investigation
Executive Summary

Aircraft Impact. The aircraft impacted WTC 1 at the north wall. The aircraft severed or heavily damaged

Columns 1 12 to 151 between Floors 94 and 98 on the north wall. After breaching the building's

perimeter, the aircraft continued to penetrate into the building. The north office area floor system

sustained severe structural damage between Columns 112 and 145 at Floors 94 to 98. Core Columns 503,

504, 505, 506, 604, 704, 706, 805, and 904 were severed or heavily damaged between Floor 92 and

Floor 97. The aircraft also severed a single exterior panel at the center of the south wall from Columns

329 to 331 berw^een Floor 93 and Floor 96. In summary, 38 of 59 columns of the north wall, three of 59

columns of the south wall, and nine of 47 core columns were severed or heavily damaged. In addition,

thermal insulation on floor framings and columns were damaged fi-om the impact area to the south

perimeter wall, primarily through the center of WTC 1 and over one-third to one-half of the core width.

Gravity loads in the columns that were severed were redistributed mostly to the neighboring columns.

Due to the severe impact damage to the north wall, the wall section above the impact zone moved

downward. The hat truss resisted the downward movement of the north wall and rotated about its east- west axis, which reduced the load on the south wall. As a result, the north and south walls each carried

about 7 percent less gravity loads at Floor 98 after impact, the east and west walls each carried about

7 percent more loads, and the core carried about 1 percent more gravity loads at Floor 98 after impact.

Column 705 buckled, and Columns 605 and 804 showed minor buckling.

Unloading of Core. Temperatures in the core area rose quickly, and thermal expansion of the core was

greater than the thermal expansion of the exterior walls in early stages of the fire. This increased the

gravity loads in the core columns until 10 min after impact. The additional gravity loads from adjacent

severed columns and high temperatures caused high plastic and creep strains to develop in the core columns in the early stages of the fire. More columns buckled inelastically due to high temperatures.

Creep strain continued to increase to the point of collapse. By 30 min, the plastic-plus-creep strains exceeded thermal expansion strains. Due to high plastic and creep strains and inelastic buckling of core columns, the core columns shortened, and the core displaced downward. At 100 min, the downward

displacement of the core at Floor 99 became 2.0 in. on the average.

The shortening of core columns was resisted by the hat truss, which unloaded the core with time and

redistributed the gravity loads from the core to the exterior walls. As a result, the north, east, south, and

west walls at Floor 98 carried about 12 percent, 27 percent, 10 percent, and 22 percent more gravity loads,

respectively, at 80 min than the state immediately after the impact, and the core carried about 20 percent

less loads. The net increase in the total column load on the south wall, where exterior wall failure

initiated, was only about 10 percent due to core downward displacement. At 80 min, the total core column loads reached their maximum. As the floor pulled in starting at 80 min on in the south side, the

south exterior wall began to shed load to adjacent walls and the core.

Sagging ofFloors and Floor/Wall Disconnections. The long-span trusses of Floor 95 through Floor 99

sagged due to high temperatures. While the fires were on the north side and the floors on the north side

sagged first, the fires later reached the south side and the floors on the south side sagged. Full floor models underestimated the extent of sagging because cracking and spalling of concrete and creep in steel under high temperatures were not modeled, and because the extent of insulation damage was

conservatively estimated. The sagging floors pulled in the south wall columns over Floors 95 to 99. In

addition, the exterior seats on the south wall in the hot zone of Floors 97 and 98 began to fail due to their reduced vertical shear capacity at around 80 min, and by 1 00 min about 20 percent of the exterior seats on

NISTNCSTAR 1-6D. WTC Investigation liii
Executive Summary

the south wall of Floors 97 and 98 failed. Partial collapse of floor may have occurred at Floors 97 and 98,

resulting from the exterior seat failures, as indicated by the observed smoke puff at 92 min (10:19 a.m.),

but this phenomenon was not modeled.

Bowing ofSouth Wall. The exterior columns on the south wall bowed inward as they were subjected to high temperatures, pull-in forces from the floors beginning at 80 min, and additional gravity loads

redistributed from the core. Figure E-9 shows the observed and the estimated inward bowing of the south

wall at 97 min after impact (10:23 a.m.). Since no bowing was observed on the south wall at 69 min

(9:55 a.m.), it is estimated that the south wall began to bow inward at around 80 min when the floors on

the south side began to substantially sag. The inward bowing of the south wall increased with time due to continuing floor sagging and increased temperatures on the south wall (Fig. E-10). At 97 min

(10:23 a.m.), the maximum bowing observed was about 55 in.

Buckling ofSouth Wall and Collapse Initiation. With continuously increased bowing, as more columns

buckled, the entire width of the south wall buckled inward. Instability started at the center of the south

wall and rapidly progressed horizontally toward the sides. As a result of the buckling of the south wall,

the south wall significantly unloaded, redistributing its load to the softened core through the hat-truss and

to the south side of the east and west walls through the spandrels. At 100 min, the north, east, and west

walls at Floor 98 carried about 7 percent, 35 percent, and 30 percent more gravity loads than the state immediately after impact, and the south wall and the core carried about 7 percent and 20 percent less loads, respectively. The section of the building above the impact zone tilted to the south (observed at about 8°) as column instability progressed rapidly from the south wall along the adjacent east and west

walls (see Fig. E-11), resuhing in increased gravity load on the core columns. The release of potential

energy due to downward movement of building mass above the buckled columns exceeded the strain energy that could be absorbed by the structure. Global collapse ensued.

liv NISTNCSTAR 1-6D, WTC Investigation
I

Executive Summary

Figure E-9. Inward bowing of the south wall of WTC 1 at 10:23 a.m. Displacement

estimated by NIST.

NISTNCSTAR 1-6D, WTC Investigation Iv
Executive Summary

Figure E-10. Inward bowing of south wall of WTC 1 global model with creep at 100 min

for Case B conditions with 5 kip pull-in forces (5x displacement magnification).

Tim Mam / Mike Balloy © 2001

Figure E-11. Collapse initiation and tilting of WTC 1 (view from the northeast).

Ivi NISTNCSTAR 1-6D, WTC Investigation
Executive Summary

E.3.2 WTC 2 Collapse Sequence

The aircraft traveling in a north-northeast direction impacted the south wall of WTC 2 at 9:03 a.m. The

aircraft mostly severed columns and floors that were on the east side of the building between Floor 78 and

Floor 84. The subsequent fires were also on the east side of the building. At 9:59 a.m., about 56 min

after the aircraft impact, the building started to collapse with the east wall buckling inward, followed by

tilting of the building above Floor 82 to the east and south. The collapse sequence of WTC 2 consists of

five main structural events: 1) aircraft impact, 2) sagging of floors and floor/wall disconnections, 3)

bowing of the east wall, 4) unloading and tilting of core, and 5) buckling of east wall and collapse

initiation.

Aircraft Impact. The aircraft impacted the south wall of WTC 2, severing a number of exterior columns

on the south wall from Floor 78 to Floor 84. The south office area floor system sustained severe

structural damage between Columns 410 and 436 from Floor 79 to Floor 83. Core columns 701, 702,

801,802, 803,901,903, 1001, 1002, 1003, and 1 004 were severed or heavily damaged between Floor 77

and Floor 84. The aircraft also severed Column 253 of the north wall. The aircraft damaged the floor

framing and core columns at the southeast comer of the core. In summary, 32 of 59 columns of the south

wall, two of 59 columns of the north wall, and 11 of 47 core columns were severed or heavily damaged.

Thermal insulation was damaged from the impact area through the east half of the core to the north and

east exterior walls. The floor truss seat connections over about one-quarter to one-half of the east side of

the core were severed on Floor 80 and Floor 81 and over about one-third of the east wall on Floor 83.

Gravity loads in the columns that were severed on the south wall and in the southeast comer of the core were redistributed to adjacent intact columns and also to the columns on the east wall. In this redistribution, the total axial load on the core columns reduced by 6 percent, and the total axial load on

the north wall columns reduced by 10 percent. The total axial load on the east wall columns increased by

24 percent, and the total axial load on the west and south wall columns increased by 2 percent to 3 percent. The large increases in loads in the east wall resulted from their proximity to the severed core columns at the southeast comer of the core. The total load on the south wall at Floor 83 did not change,

as some of the loads from the core area were redistributed to that wall through the hat tmss.

At Floor 105, splices in the columns at the southeast comer of the core failed (Columns 1001 and 1002

and most likely Columns 701, 801, 901, 902, and 1003). This increased the core tendency to lean toward

southeast and also increased the vertical downward displacement of the core at the impact zone. After the core column splices failed, 73 percent of the loads released from the failing core columns were

redistributed through the hat tmss to the exterior walls.

About 20 percent (= 227 kip / 1,263 kip) of the redistributed load at the hat tmss level of the south wall was transferred through columns and the rest of the load (about 1,000 kip) was transferred to the columns

of the east and west walls through the spandrels.

After load redistribution following impact, the core was prevented from tilting excessively toward the east by the north and the south exterior walls through the action of floors and the hat tmss.

Sagging ofFloors and Floor/Wall Disconnections. Aircraft impact and high temperatures due to subsequent fires caused Floors 79 through 83 to sag. The sag was greater at Floor 80 and Floor 81 where

the tmss seats on the east side of the core failed at aircraft impact. High temperamres weakened the tmss

NISTNCSTAR 1-6D, WTC Investigation Ivii
Executive Summary

seats on the east exterior wall and caused truss seats to fail at Floor 83 and Floor 82 (see Fig. E-12) which

in turn increased the sag in those floors. Floor sagging induced pull-in forces on the east wall columns,

beginning approximately 10 min after impact and increasing with time.

Bowing ofEast Wall. The east wall columns bowed inward as a result of increasing temperatures

(reduced strength and stiffness) and pull-in forces induced by sagging floors. The inward bowing in the

east wall increased with time due to the combined effects of pull-in from sagging floors, increased axial

loads, and a continuous increase in plastic and creep strains. As columns bowed, they shed load to adjacent unbowed columns, but the total column load on the east wall did not change significantly after impact until buckling of the east wall started near the collapse time.

Unloading and Leaning of Core. With increasing time and temperatures, the core columns developed

high plastic and creep strains, especially on the east side of the core. Plastic and creep strains exceeded

the thermal expansion strains beginning about 30 min after the aircraft impact. High plastic and creep

strains caused unloading on the east side core columns. This increased leaning of the core toward the east and transferred more loads to the east wall. Calculations showed that resistance to core leaning was

provided by the north and south exterior walls, partly through the floors and partly through the hat truss. Leaning of the core resulted in tilting of the upper part of the tower as the east wall buckled.

Buckling ofEast Wall and Collapse Initiation. With continuously increased bowing and axial loads, the

entire width of the east wall buckled inward (Fig. E-13). The instabihty started at the center of the wall

and rapidly progressed horizontally toward the sides. As a result of the buckling of the east wall, the east wall significantly unloaded, redistributing its load to the softened core through the hat truss and to the east side of the south and north walls through the spandrels (see Fig. E-14). The section of tower above the

buckled wall suddenly moved downward, and the building tilted toward the east (see Fig. E-15).

The section of the building above the impact zone tilted to the east and south (observ'cd at about 7° to 8°

to east and about 3° to 4° to south, Fig. E-16) as column instability progressed from the east wall to the

adjacent south and north walls. The release of potential energy due to downward movement of the

building mass above the buckled columns exceeded the strain energy that could be absorbed by the

structure. Global collapse ensued.

Iviii NISTNCSTAR 1-6D. WTC Investigation
Executive Summary

(a) After impact damage

(d) At 9:54 a.m.

(51 min after impact)

Figure E-12. Floor sagging observed on the east wall of WTC 2 at different times.

NISTNCSTAR 1-6D, WTC Investigation lix
Executive Summary

(a) View from east (b) View from soutlieast

Figure E-13. Inward bowing of the east wall of WTC 2 global model for Case D

conditions at 43 min at the instant of collapse initiation (deformed shape scaled four

times).

Figure E-14. Inward bowing of exterior columns of the west wall of WTC 2 just before

collapse.

Ix NISTNCSTAR 1-6D, WTC Investigation
Executive Summary

MAR 14 2005

12:38:28 •FL110

Undeformed

building edge

NODAL SOLUTION

STEP=7

SUB =1 TINE=.0Q7 USUM (AVG) RSYS=0 DMX =21.501 SMN =3.298 SMX =21.601

3.298

5.332 9.399 Severe Case Temperature Analysis

11.433 15.5 13.467

Figure E-15. Total displacements of WTC 2 global model above Floor 86 for Case D

conditions at 43 min at collapse initiation (note the tilt toward east and south; deformed

shape magnified 20 times).

Figure E-16. Initiation of collapse of WTC 2. Note the tilt toward east and south.

NISTNCSTAR 1-6D. WTC Investigation Ixi
Executive Summary

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Ixii NISTNCSTAR 1-6D, WTC Investigation
Chapter 1 Introduction

1.1 OBJECTIVE

The objective of this report is to present the resuhs of finite element analyses (FEA) performed by

Simpson Gumpertz and Heger Inc. (SGH) on global models of the World Trade Center (WTC) towers. The purpose of the analyses is to determine the roles of aircraft impact damage and of subsequent fires in the probable sequence of structural responses that led to global collapse of the WTC towers.

This report complements the work that SGH performed on the structural response of components in the

WTC towers, such as trusses and columns, connections such as truss seats and knuckles, and subsystems

including full floors and exterior walls to the fire environment. Results were reported in NIST

NCSTAR 1-6C'.

On the morning of September 11, 2001, two Boeing 767 aircraft were hijacked after they left Boston's

Logan International Airport for Los Angeles. At 8:46 a.m., American Airhne Flight 11, traveling from

the north at an estimated speed of 440 miles per hour, impacted near the center of the north face of

WTC 1 between Floor 94 and Floor 98, 1,100 ft above the plaza level. At 9:03 a.m.. United Airlines

Flight 175, traveling at an estimated speed of 540 miles per hour from the south, impacted the south face

of WTC 2 between Floor 78 and Floor 84, 901 ft above the plaza level (NIST NCSTAR 1).

Although both WTC towers suffered substantial damage over several floors, they withstood the aircraft impact damage without global collapse. Subsequent fires, ignited with aircraft fuel and fed by the

building and aircraft contents, led to the collapse of the two towers. The collapse of WTC 2 occurred at 9:59 a.m., 56 min after impact, and the collapse of WTC 1 occurred at 10:28 a.m., 102 min after impact

(NIST NCSTAR 1).

Since the collapse of these tall steel frame buildings were unprecedented, questions were raised about the

safety of tall steel buildings in fires. Before drawing conclusions regarding the safety of tall steel buildings in fire, it is necessary to understand how and why the WTC towers collapsed. Various aspects

of the WTC towers and their collapses have been investigated by many researchers and engineers (Bazant

and Zhou 2002, FEMA 2002, Kausel et al. 2002. Levy and Abboud 2002, Usmani et al. 2003). NIST

initiated a comprehensive investigation of the WTC disaster on August 21, 2002, and SGH was retained

under contract in October, 2003. The work presented in this report was performed by SGH as part of

Project 6 of the NIST WTC Investigation.

This reference is to one of the companion documents from this Investigation. A list of these documents appears in the Preface

1.2 BACKGROUND

to this report.

NIST NCSTAR 1-6D. WTC Investigation 1
Chapter 1

Aircraft impact damage to the structural components of the WTC buildings were investigated and

reported in NIST NCSTAR 1-2 and NIST NCSTAR 1-2B. These studies assessed structural damage and

thermal insulation damage caused by aircraft impact. Although the computed aircraft impact damage to the exterior wall system of each building can be validated from the many photographs and videos taken,

aircraft impact damage to the interior columns and floor systems and to the insulation cannot be validated

using this same technique.

NIST performed a fire dynamics study to estimate the thermal input to the building following the aircraft impact. The fire dynamics analysis depends on the distribution of the building and aircraft contents following the impact, the spread of aircraft fuel throughout the structure upon impact, the amount of ftiel that ignited and burned off immediately upon impact, and the availability of air in fire-involved areas, flowing through broken windows and through damaged interior partitions and structures to support

continued combustion. Of these factors, only the distribution of broken windows on the exterior of the

building can be verified, through examination of photographic and video evidence. Other factors were

estimated and validated against recorded smoke plumes and other data. These calculations were

perfomied by NIST and were reported in NIST NCSTAR 1-5 and NIST NCSTAR 1-5F.

Based on the results of the fire dynamics model, NIST calculated the steel and concrete temperatures at various times from the time of aircraft impact for the estimated extent of remaining insulation. Before

aircraft impact, WTC 1 had thicker insulation on floor trusses in the areas principally involved in the fires than did WTC 2. The columns, spandrels, and core beams had similar insulation in both of the towers. No insulation had been applied to the steel deck supporting the concrete slabs in either building, though

there was overspray from application of insulation to the trusses. Based on the path of the debris

determined from the aircraft impact analysis, NIST estimated the extent of the insulation that was

dislodged from the structural components of the WTC towers. These estimates considered insulation to be removed only in areas where direct impact from debris was predicted. Possible additional

dislodgement of insulation due to the shock and resulting vibration from the aircraft impact was

neglected. The extent of dislodged insulation predicted by the aircraft impact analysis is discussed in NIST NCSTAR 1-6A, and the calculation of steel and concrete temperatures is presented in NIST

NCSTAR 1-5G.

NIST determined mechanical and metallurgical properties of structural steel recovered from the WTC

towers. NIST also estimated the mechanical properties of WTC steel for elevated temperatures. Results were reported in NIST NCSTAR 1-3 and NIST NCSTAR 1-3D. Temperature-dependent mechanical

properties of WTC steel include modulus of elasticity, Poisson's ratio, coefficient of thennal expansion,

yield strength, tensile strength, and nonlinear stress-strain relationship. NIST also predicted temperaturedependent creep properties for the WTC steels.

Prior to the development of the global finite element models of the WTC towers, SGH used hand and

finite element analyses to study the structural behavior of subcomponents such as knuckles and

connections, components, and subsystems. Results from structural analyses of truss seats and knuckles were used in a detailed model of a slice of a floor that included a single truss and a section of slab, which was referred to as the truss model. It was found that when subjected to elevated temperatures, the trusses sagged after diagonal web members buckled. Based on the truss model analyses, a simplified truss model was constructed and used in a model of a typical full floor. Full floor model analyses showed that in a

fire environment floors sagged significantly at areas where insulation was dislodged, and exterior seats failed under extreme temperatures causing floors to disconnect from the exterior wall. The structural

2 NIST NCSTAR 1-6D, WTC Investigation
Introduction

perfonnance of columns and exterior walls was studied with the analysis of single column and exterior

wall subsystem models, which gave guidance in choosing element size and type for exterior columns in the global model that captured inelastic buckling behavior under elevated temperatures.

SGH developed global models that would simulate the key failure modes discovered in the analysis of

components and subsystems. In addition, certain damage that could not be accurately modeled without

significant loss of computational efficiency, such as certain fire-induced damage, were introduced to the

global models at appropriate times. Types of fire-induced damage that were important in the collapse

analysis of the global model included sagging of the floors that applied pull-in forces on the exterior

columns and disconnections of floors from the exterior walls. The fire-induced damage incorporated in the global model is discussed in detail in Section 2.5.

1 .3 METHOD OF APPROACH

SGH developed global finite element structural models of the WTC towers in ANSYS, based on reference

structural models developed in SAP2000 (NIST NCSTAR 1-2 A), and based on the studies that SGH

conducted on components and subsystems of the WTC towers (NIST NCSTAR 1-6C). Owing to the

existing limits of computational software and hardware, all potential structural behaviors and failure modes that could contribute to the collapse of the WTC towers were not explicitly included in the global

models. A single global model that included all structural behaviors and failure modes would not be

practical due to the extremely large time period required for analyses.

An alternative approach, a trial and error procedure, was used in this study to (1) perform global structural time histor)' analyses for an assumed set of fire-induced damage, (2) identify major observations of

subsequent fire-induced structural damage at different times up to the initiation of collapse, (3) determine

the deviation between the calculated and observed fire-induced damage, (4) develop a structural explanation of the deviation, and (5) use the observed fire-induced damage to correct the state of the

structure at that time and continue the calculation. This approach reduced the error margin (hence

increased the accuracy) of the results due to epistemic uncertainties in modeling and load estimation by

updating the response of the WTC towers according to observed facts at specific time points.

In developing the global models, the knowledge obtained from extensive investigation of components'

and subsystems' responses to various temperature-dependent nonlinear actions was utilized. The

pertinent structural actions and failure modes between and within components and subsystems that were

obtained from the isolated model investigations allowed us to include or represent in a more efficient way

all essential nonlinear responses in the global models without sacrificing accuracy and computation time.

The important features of the detailed component and subsystem models and their influence on the global

building response during the collapse process are discussed in NIST NCSTAR 1-6C. Similar discussions

for two additional substructure models isolated from the global models (isolated core and exterior wall

models) are provided in Chapter 3 of this report.

As discussed earlier, collapse analyses of the WTC towers were also guided by observations from the

photos and videos taken during the collapse process. Visual evidence, damage estimates, and the timeline

of the collapse process are reported in NIST NCSTAR 1-5 A. The key observations of collapse sequences

of the WTC towers are presented in Chapter 5.

NIST NCSTAR 1-6D, WTC Investigation 3
Chapter 1

The global and subsystem models were capable of capturing material nonlinearities due to plasticity and

creep in steel, geometric nonlinearities due to large deflection, and elastic and inelastic buckling of the

columns and other structural members at high temperatures.

The global models developed in this study were first validated against the SAP2000 models under gravity

loads. Then, aircraft impact damage was included in these models by removing corresponding elements

based on results from Project 2. Impact damage is discussed in detail in Section 2.2. The global models

with impact damage were then subjected to temperature time histories derived from reconstructed fires in the WTC towers in Project 5.

Based on the results from FEA of the isolated and global models and the results of component and

subsystem models, collapse sequences of WTC 1 and WTC 2 were identified as a conclusion of this study.

1.4 REPORT ORGANIZATION

This report presents results from the isolated models and the global models of the WTC towers. All the

results are based on FEA and hand calculations. The "observed values" when used refer to the estimates

obtained from photographs and videos.

This report consists of six chapters:

• Chapter 1 serves as an introduction of this report and includes objectives, background, and

methods of approach of this study.

• Chapter 2 introduces the global models of WTC 1 and WTC 2. It gives general descriptions

of the global models and of temperatures and aircraft impact and fire-induced damage used in the global model analyses.

• Chapter 3 gives the results from FEA of isolated wall and core models subjected to gravity

and thermal loadings. The results shown in this chapter do not form a major link in the chain

of collapse sequence arguments and may be skipped by those interested only in this chain of

arguments.

• Chapter 4 describes the details of the global models and presents the results of FEA of the

global models with creep subjected to gravity and thermal loadings.

• Chapter 5 presents the collapse sequences of WTC 1 and WTC 2 concluded from this study

and provides supporting evidence.

• Chapter 6 provides a list of references.

This report also includes three appendices:

• Appendix A summarizes the results from FEA of full floor models.

• Appendix B summarizes a study on dynamic response of a floor to impact from collapse of a

floor above.

4 NISTNCSTAR 1-6D, WTC Investigation
Introduction

• Appendix C summarizes the results of FEA of the global models without creep subjected to gravity and thermal loadings. The analyses presented in this appendix are preliminary global

analyses and were primarily used to get a better understanding of the interaction between

various structural components in the overall global response of the towers.

NISTNCSTAR 1-6D, WTC Investigation 5
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NISTNCSTAR 1-6D, WTC Investigation
Chapter 2

Global Models

2.1 DESCRIPTION OF GLOBAL MODELS

Simpson Gumpertz& Heger Inc. (SGH) developed two different finite element models to simulate the

global structural behavior of the World Trade Center towers, WTC 1 and WTC 2, incorporating the

aircraft impact damage and the fire environment that followed the impact. The finite element models of

the towers were developed using ANSYS commercial structural analysis software package. The finite element models were developed to determine the roles of aircraft impact damage and of subsequent fires in the probable sequence of structural responses that led to global collapse of the WTC towers.

SGH obtained the basic building geometry, member types and cross sections, and their connectivity from

models developed by Leslie E. Robertson Associates (LERA) as described in Chapter 4 of the National

Instiutute of Standards and Technology (NIST) NCSTAR 1-6C. LERA developed the original models

using SAP2000 structural analysis softu^are.

The observation of photographic and video evidence of the behavior of both structures, following the time

of aircraft impact and until collapse initiation, strongly suggested that nonlinear behavior and structural collapse initiation occurred within the upper portions of the structures, generally above the zone of

aircraft impact. Therefore, to reduce the model size and improve solution time, the model of WTC I was

truncated at Floor 89, five floors below the zone of impact, and a series of equivalent vertical linear

springs were introduced at the base of this truncated model to represent the stiffness of the interior columns and exterior walls beneath the level of truncation. Similarly, the model of WTC 2 was truncated

at Floor 73. This truncation is believed to have negligible effect on the predicted behavior of the

structure.

As a first step in the analyses, the truncated SAP2000 models were converted to ANSYS. Wliile the

geometry from the SAP2000 model was directly transferable to ANSYS, it was necessary to substitute the elements with those from ANSYS element library. Table 2-1 summarizes the element types used in the

ANSYS global models. The element names used in the table correspond to specific ANSYS (ANSYS,

Inc. 2004) element formulations. All element types listed in Table 2-1 have temperature-dependent

material properties.

In the original SAP2000 models, LERA represented the structural floors as rigid constraints with no out- of-plane stiffness. In order to capture the potential behavior of the floor slabs in transferring loads

between the core and the exterior walls, these rigid constraints were replaced with grids of plate elements

with the same membrane stiffness as the composite floor system (slab and trusses). Floors in the global

models were not intended to capture floor response and failure modes during fires. Important failure modes were identified in the truss and full floor analyses and incorporated into the global models as floor/wall disconnections and pull-in forces at appropriate time intervals. See Chapter 7 in NIST

NCSTAR I-6C and Chapter 2 in this report for a detailed discussion of how floor behavior was modeled

in the global analyses.

NIST NCSTAR 1-6D, WTC Investigation 7
Chapter 2

SGH next performed a series of modifications to the models, to simulate the structural damage resulting

from the aircraft impacts and the effects of fire. The damage to the exterior walls was modeled by

removing structural elements in a pattern that replicated the damage observed in available photographic

and video evidence. The damage to interior structural elements was modeled based on aircraft impact

simulations reported in NIST NCSTAR 1-2. The effects of fire damage to the structure were also

included in the global models, based on thermal predictions developed by NIST, and the results of

structural analyses performed by SGH of individual structural subsystems, including individual floor

trusses, entire floor assemblies, and portions of exterior walls. Since projection of these subsystem

analyses to global behavior entailed substantial uncertainty, visual photographic and video evidence of the

behavior of the exterior structure were also used to benchmark the projections from the subsystem

analyses.

The models were also modified to include a number of nonlinear behavioral modes including:

• Geometric nonlinearity associated with large deflections,

• Nonlinearity in stress-strain behavior as a function of applied loading and thermal effects, as described in Chapter 3 of NIST NCSTAR 1-6C,

• Creep behavior as the time-dependent effect of sustained stress and elevated temperatures on

strain as described in Chapter 3 of NIST NCSTAR 1-6C,

• Failure of a connection between elements, resulting in a complete loss of load transfer ability

and deformation compatibility.

The converted ANSYS models were validated against the SAP2000 models by comparing gravity load

response, natural frequencies, and mode shapes.

Table 2-1. Element types used in the global models.

Name Element Type Description Usage in the Model

BEAM188 3-D linear finite strain beam

BEAM 188 is a linear (2-node) or a quadratic beam

element in 3-D based on Timoshenko beam theory.

Each node has six degrees of freedom or seven degrees

of freedom (6+warping). Shear deformation effects are included. This element is supported for plasticity, creep,

large deflection. A cross-section can be a built-up section referencing more than one material. Creep strain

is calculated by implicit time integration method.

Exterior columns

Core columns

Core beams

Spandrels Hat truss members

BEAM24 3-D thin-walled

beam

BEAM24 is a 3-D beam element of arbitrary open or closed cross-section with axial, bending, and St. Venant

torsional capabilities. Each node has six degrees of

freedom. The element has plastic, creep, large

deflection, and shear deflection capabilities. Creep

strain is calculated by explicit time integration method.

Exterior columns

Core columns

SHELL63 4-node elastic shell SHELL63 has both bending and membrane capabilities.

The element has six degrees of freedom at each node:

three translations and three rotations. Large deflection

capability is also included.

Floors

8 NIST NCSTAR 1-6D, WTC Investigation
Global Models

Name Element Type Description Usage in tlie Model

SHELL181 4-node finite strain shell SHELL181 is a 4-node shell element with six degrees of

freedom at each node: three translations and three

rotations. Plasticity, creep, and large deflection

capabilities are supported. In nonlinear analyses,

change in shell thickness is accounted for. SHELL181

may be used for layered applications.

Floors

LINKS 3-D truss LINKS is a uniaxial tension-compression element with

three degrees of freedom at each node. It has plasticity, creep, and large deflection capabilities.

Vertical springs at the base

Damage modified the geometry and connectivity of and load distribution in the towers. Types of damage

included in the global models were aircraft impact damage to the exterior wall that were visible and

documented by photos and videos and interior damage resulting from the movement of aircraft impact

debris through the interior space of the towers which were obtained from the aircraft impact analyses.

Structural damage caused by the fires, such as disconnection of the floor from the exterior wall, was

determined from the structural analysis of the full floor subsystems. Some structural behaviors caused by

the fires were not adequately captured by the frill floor analysis, such as pull-in forces at the floor/wall

connections. The pull-in forces were estimated through additional analyses with exterior wall models that were conducted to estimate the pull-in force required to match the observed inward bowing of the exterior

walls.

The models were then analyzed for the effects of gravity and temperature loads. Gravity loads considered

included; the dead load of the structure itself; superimposed dead load consisting of the estimated weights

of ceilings, mechanical and electrical equipment, thermal insulation, and floor finishes; and live load,

taken as 25 percent of design live load specified in the original construction documents. The use of 25

percent of the design live load as service live loads is discussed in NIST NCSTAR 1-2. Wind loads were

negligible and were not considered (see NIST NCSTAR 1-6 for the recorded wind data).

Due to the height of the structures, substantial column shortening occurred under the application of dead

loads. If these loads were applied to the model while the stiffness of the hat trusses was present, the hat

trusses would restrain the downward deflection of the columns and in the process experience higher levels of stress. These stresses did not occur in the real buildings, because the columns experienced most of

their dead load-induced shortening before the hat trusses were erected. In order to account for this effect,

except for those simulations in which the effect of creep was also considered, the sequence of

construction was considered during gravity load application. The loading of the structure was staged so

that the stiffness of the hat trusses was not present when dead loads below Floor 106 level were applied.

Construction sequence effects were not considered in the global analyses that included creep effects to enhance computational efficiency. The effect of construction sequence is discussed in more detail in Section 4.2.2.

NIST NCSTAR 1-6D, WTC Investigation 9
Chapter 2

Thermal loading of a structure resulted in several effects:

• restrained axial thermal expansion of members causing local redistribution of loads, e.g., heated columns of WTC towers that attracted more load,

• differential thermal expansion across member depth, resulting in bowing if unrestrained or bending moment if restrained,

• reduction in the stiffness and strength of members, and

• high creep strain when accompanied by high stress. SGH applied thermal loading in the form of temperature time histories. NIST developed these

temperature time histories using gas dynamic and heat transfer models. Each temperature time history

corresponded to a unique set of assumptions regarding the extent of impact damage to the structure,

glazing, fire separation elements, and insulation. Each temperature time history was defined discretely at 10 min time intervals which were linearly interpolated for times in between.

The behavior of columns in the two structures was significant to the collapse behavior of the towers. Throughout this report reference is made to the behavior of various columns and lines of columns, using

the specific column numbering system found in the original PANYNJ structural drawings'. In WTC 1, columns in the exterior north wall were assigned a number ranging from 101 at the west end to 159 at the

east end. Columns in the exterior east wall were assigned a number ranging from 201 at the north end to 259 at the south end. Columns in the exterior south wall were assigned a number ranging from 301 at east end to 359 at the west end. Columns in the west wall were numbered sequentially from 401 at the

south end to 459 at the north end. Columns 100, 200, 300 and 400 were located, respectively, at the

northwest, northeast, southeast and southwest building comers. Within the rectangular core of the

structure, there were six rows of either seven or eight columns each. Columns of the northern-most row

were numbered 501 through 508 with column 501 located at the west end and 508 at the east end.

Successive rows of columns, reading from north to south were designated 601-608, 701-708, 801-807,

901-908, and 1001-1008. This numbering scheme is illustrated in Fig. 2-1 (a). The column numbering

system used for WTC 2 is similar. However, for WTC 2 Columns 101-159 were located along the west

wall. Columns 201-259 along the north wall, 301-359 along the east wall, and Coluinns 401-459 along

the south wall. Column 100 was located at the southwest comer, 200 at the northwest comer, 300 at the

northeast comer and 400 at the southeast comer. In the core of WTC 2, Columns 501-508 were located

along the extreme west side of the core and Columns 1000-1008 along the extreme east side of the core with the 600, 700, 800, and 900 series columns arranged progressively from west to east. Figure 2-1 (b)

illustrates the column numbering system used in WTC 2.

The technical data required to conduct the analyses of the WTC towers reported herein were obtained from drawings that were

provided by the Port Authority of New York and New Jersey (PANYNJ) and their contractors.

10 NISTNCSTAR 1-6D, WTC Investigation
Global Models

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sot

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(a) WTC 1

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t

2Sn 203 ZB ZOB 21? 2:S 21B 2?: 2a« 2Z7 230 233 236 2S 242 246 2«e 251 2M 2S7 ; 200 1.1.. 111! 1 1 1.. 1 .1 .1. 1.. .,1.

1

I 1 1 eOS TUB 807 DOB lUUt)

1 807 , 501 , 907 1 M7

506 606 006 1 D06

985 1005

904 1004

1 > 606 705 804

50* M 704

1 703 803

SOS> 603 803 1 DOS —i

S02 902 iom

'1

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I I 433 OOI «!7r

<Mr471 <ie

I <>&IF412 409in406 «X3 401

N

1

(b) WTC 2

Figure 2-1. Column designations.

NISTNCSTAR 1-6D, WTC Investigation 11
Chapter 2

2.2 IMPACT DAMAGE

2.2.1 Introduction

The extent of aircraft impact damage to the structural components of the WTC towers has been separately

investigated as part of NIST Project 2 and was reported in NIST NCSTAR 1-2 and NIST NCSTAR 1-2B.

SGH incorporated the results of these studies into the global models of the WTC towers to characterize

the aircraft impact damage to exterior columns and spandrels, core columns, beams, and floors. Specifically, those elements identified in the aircraft impact studies as severed or heavily damaged were removed from the global models.

NIST's investigation initially identified two sets of aircraft impact damage for each of the two towers,

consisting of a structural damage condition, which was damage to the structure, and a insulation damage

condition, which affected the temperatures in members. These damage sets represent a base case and a more severe case of damage estimates. They were named as Case A, and Case B, for WTC 1 and Case C; and Case D, for WTC 2. These initial damage sets were used in early analyses to study the structural response of full floor subsystem models and global models without creep. The results of the full floor

subsystem analyses were presented in Section 5.4 of NIST NCSTAR 1-6C and summarized in Appendix

A of this report. The results of the global model analyses without creep are discussed in Section 4.1 of

this report.

NIST refined the initial damage sets at later stages of the investigation and renamed them as Case A and

Case B for WTC 1 and Case C and Case D for WTC 2. These damage sets were used in isolated wall and

isolated core models and global models with creep. The results of the isolated wall and core models are discussed in Chapter 3, and the results of the global model analyses with creep are discussed in Section 4.2 of this report.

For each tower, the impact damage on the exterior columns and spandrels was primarily obtained from

photographs and video footage that were taken before and during the collapse of the buildings. For this reason, the impact damage on the exterior columns and spandrels were the same for all damage sets for

each tower. The differences between damage sets existed in the way that the impact damage was defined

for the core columns, core beams, and floors. The initial and final damage sets are summarized in Sections 2.2.2 and 2.2.3.

The difference between Case A, and Case B„ Case C, and Case D„ Case A and Case B, and Case C and

Case D damage sets are the structural damage condition in core columns and beams, floors, and the extent of insulation damage that ensued from the abrasion of flying debris on the structural components. The

differences in insulation damage condition resulted in different temperatures of the structural components.

For this reason, each impact damage set has an associated temperature set. Temperature sets have the same names as the impact damage sets.

2.2.2 Initial Damage Sets

Case Aj, Case Bj, Case C„ and Case D, damage sets were the initial aircraft impact damage sets defined by

NIST. In terms of structural damage condition in exterior columns. Case A, and Case B, and similarly

Case C, and Case Dj damage sets were identical. For this reason, only one set of structural damage

condition in exterior columns is presented for each tower. The structural damage condition for the floors

12 NIST NCSTAR 1-6D, WTC Investigation
Global Models

and core columns was not provided for Case B, of WTC 1, and the structural damage condition for the core columjis was not provided for Case D, of WTC 2. The damage sets presented in this section were

used in the full floor subsystem models and global models without creep.

The severed columns and spandrels on the exterior walls of WTC 1 and WTC 2 are shown in Figs. 2-2

and 2-3. For comparison, core columns and beams before aircraft impact are shown in Figs. 2-4 and 2-5

for WTC 1 and WTC 2, respectively. The severed columns in the core area for Case A, of WTC 1 and for Case Cj and revised Case Q are shown in Figs. 2-6, 2-7, and 2-8. The core column series that are not shown in these figures did not include severed columns. Since global models included only core beams

that had moment connections at the ends as described in Chapter 4, these figures do not show all the core beams that existed in the WTC towers. The difference between Case Cj and revised Case Cj is only in the

impact damage to the core columns (see Figs. 2-7 and 2-8). Revised Case Cj damage was received later and, consequently, was not included in some of the earlier analyses. The associated temperature sets are

identical.

Case A„ Case C„ and Case Dj floor impact damage conditions are shown in Figs. 2-9 throuth 2-14. The

figures show damage to structural elements, including slabs and supporting steel framing, as well as to the

insulation on the framing. The shell elements of the floors and beam elements of core beams were removed from the global models at appropriate locations to replicate the areas of structural damage

indicated in these figures. For regions where the floor slab was coarsely meshed in the global models, the

elements were removed in such a way as to capture force discontinuities resulting from the structural damage in that region. This sometimes resuhed in the removal of a somewhat larger floor area in the

global models than indicated in Figs. 2-10, 2-12, and 2-14.

159 101 359 301

Floor 99 — l lll l

'

l l ll l H l lll l l l l l l 'i 'lll l llll l l l llll l lllll^ | || | || |l |||||| | ||l|||||l|||||||l i n

Floor 97 —

Floor 95 —

Floor 93 —

(a) North face (b) South face

Figure 2-2. Structural damage condition on the exterior walls of WTC 1 for all cases of

impact damage.

NISTNCSTAR 1-6D, WTC Investigation 13
Chapter 2

Figure 2-3. Structural damage condition on the exterior walls of WTC 2 for all cases of

impact damage.

West

Floor 99

Floor 97

Floor 95

Floor 93

Floor 91

508 501 608 708 701

(a) 500 series columns (b) 600 series columns (c) 700 series columns

Floor 99

Floor 97

Floor 95

Floor 93

Floor 91

807 801 908 —1 -1

J—

I

„i,„

i ___|_

3

901 1008 1001

(d) 800 series columns (e) 900 series columns (f) 1000 series columns

Figure 2-4. Core columns and core beams in the WTC 1 global model without aircraft

impact damage.

14 NISTNCSTAR 1-6D, WTC Investigation
Global Models

North

Floor 85

Floor 83

Floor 81 Floor 79

Floor 85

Floor 83

Floor 81

Floor 79

508 501 608 601 708 701

(a) 500 series columns (b) 600 series columns (c) 700 series columns

807 801 908 901 1008 1001

(d) 800 series columns (e) 900 series columns (f) 1000 series columns

Figure 2-5. Core columns and core beams in the WTC 2 global model without aircraft

impact damage.

West ^ 508 501 608 601 708 701

Floor 97

Floor 95

Floor 93

(a) 500 series columns (b) 600 series columns (c) 700 series columns

Figure 2-6. Case Ai structural damage condition on the core columns of WTC 1.

NISTNCSTAR 1-6D, WTC Investigation 15
Chapter 2

908 901 1008 1001

North

Floor 84

Floor 82

Floor 79

Floor 77

(a) 900 series columns (b) 1000 series columns

Figure 2-7. Case Ci structural damage condition on the core columns of WTC 2.

908 901 1008 1001

North

Floor 84

Floor 82

Floor 79

Floor 77

(a) 900 series columns (b) 1000 series columns

Figure 2-8. Revised Case Cj structural damage condition on the core columns of WTC 2.

16 NISTNCSTAR 1-6D, WTC Investigation
Global Models

(c) Floor 96 (d) Floor 97

(e) Floor 98

Figure 2-9. Case Aj insulation damage conditions for WTC 1 floor trusses and beams.

NISTNCSTAR 1-6D, WTC Investigation 17
(a) Floor 94 (b) Floor 95

m

r^' A AAA A -»t •

lillHHtH-iNMilliii !!

(c) Floor 96

i

4. A * 4, A i

Z ^ 4, * A *, •of"

nil

(e) Floor 98

Li

I r

^niili nii nil liii

(d) Floor 97

N

I

n

Structural damage to concrete slab, core beams, and trusses

Figure 2-10. Case Aj structural damage conditions for WTC 1.

NISTNCSTAR 1-6D, WTC Investigation
Global Models

iHhrn tift nife m m it' -sis' i» m m » m » «)^. Si' utr

(c) Floor 81 (d) Floor 82

Figure 2-11. Case Ci insulation damage conditions for WTC 2 floor trusses and beams.

NISTNCSTAR 1-6D, WTC Investigation 19
Chapter 2

(a) Floor 79

LI.

mi

* -4:

- .1- T.

(c) Floor 81

nXi,iiiizi.:,:i.ixii.ii.i,

««»*«-

- i

« > - - ^TTTT

(e) Floor 83

vii..m.;,ix:.:.i:^i

(b) Floor 80

'1 ^ ^

-5

(d) Floor 82

I

n

Structural damage to concrete slab, core beams, and trusses

Figure 2-12. Case Cj Structural damage conditions for WTC 2 floors.

20 NISTNCSTAR 1-6D, WTC Investigation
Global Models

(c) Floor 81 (d) Floor 82

Figure 2-13. Case Dj insulation damage conditions for WTC 2 floor trusses and beams.

NISTNCSTAR 1-6D, WTC Investigation 21
Chapter 2

(c) Floor 81 (d) Floor 82

4. A

N

t

Structural damage to concrete slab, core beams, and trusses

(e) Floor 83

Figure 2-14. Case Di Structural damage conditions for WTC 2 floors.

22 NISTNCSTAR 1-6D, WTC Investigation
Global Models

2.2.3 Final Damage Sets

NIST provided a series of final damage sets for use in the global analyses. Two sets were provided for each of the two buildings, together with temperature time history data sets computed by NIST based on

the damage set. The final damage sets for WTC 1 were designated Case A and Case B, respectively,

representing different scenarios of aircraft impact damage to the structure and thermal insulation. The

final damage sets for WTC 2 were designated Case C and Case D. The exterior wall damage contained in the final damage sets are identical to those in the contained in the initial damage sets, described in the

previous section and illustrated in Figs. 2-2 and 2-3. However, the projected damage to floor and core elements differed from the initial damage sets. The final damage sets were used in SGH analyses of the

isolated wall models, the isolated core models, and the global analyses with creep.

The severed columns in the core area of WTC 1 for Case A and Case B and WTC 2 for Case C and

Case D are shown in Figs. 2-15 through 2-18. For Case B and Case D structural damage condition,

heavily damaged core columns were also considered as severed and removed from the analysis. Columns

removed from the global models are shown as missing vertical lines in these figures. For WTC 2, core column 902 was assigned a moderate damage state after aircraft impact at Floor 79 and Floor 80 by NIST.

The preliminary analyses showed that this column buckled after aircraft impact and caused numerical

problems in the temperature time history analyses. Therefore, in the Case D damage set, this column was

also treated as heavily damaged and removed from the model. The core column series that are not shown

in Figs. 2-15 through 2-18 did not include severed colunms for all the cases or heavily damaged columns

for Case B of WTC 1 and Case D of WTC 2.

West

508 501 608 601 708 701

Floor 97

Floor 94

Floor 92

(a) 500 series columns (b) 600 series columns (c) 700 series columns

Figure 2-15. Case A structural damage condition on the core columns of WTC 1.

NISTNCSTAR 1-6D, WTC Investigation 23
Chapter 2

908 901 1008 1001

North

(a) 900 series columns (b) 1 000 series columns

Floor 84

Floor 82

Floor 79

Floor 77

Figure 2-16. Case C structural damage condition on the core columns of WTC 2.

West —

Floor 97

Floor 95

Floor 93

Floor 91

508 501 608 601 708 701

(a) 500 series columns (b) 600 series columns (c) 700 series columns

Floor 97

Floor 95

Floor 93

Floor 91

807 801 908 901

(a) 800 series columns (b) 900 series columns

Figure 2-17 Case B structural damage condition on the core columns of WTC 1 (including heavily damaged columns).

24 NISTNCSTAR 1-6D, WTC Investigation
Global Models

708 701 807

! i

(a) 700 series columns

908 901

(c) 900 series columns

80

i

j

(b) 800 series columns

1008 1001

(d) 1000 series columns

Floor 81

Floor 79

Floor 77

Floor 84

Floor 82

Floor 79

Floor 77

North

Figure 2-18. Case D structural damage condition on the core columns of WTC 2

(including heavily damaged columns).

The floor insulation and structural damage conditions are shown in Figs. 2-19 and 2-20 for Case A, in Figs. 2-23 and 2-24 for Case B, in Figs. 2-21 and 2-22 for Case C, and in Figs. 2-25 and 2-26 for Case D.

The shell elements of the floors and beam elements of core beams were removed from the global models

at appropriate locations to replicate the areas of structural floor damage indicated in these figures. For the regions where the floor slab was coarsely meshed, the elements were removed in such a way as to capture

force discontinuities resulting from the structural damage in that region. This sometimes resulted

somewhat larger floor openings than indicated in Figs. 2-20, 2-22, 2-24, and 2-26. However, as discussed in Chapter 4, the dead and live loads of the floor system were applied as concentrated loads to the connecting columns; this minimized the effect of slightly larger floor openings.

NISTNCSTAR 1-6D, WTC Investigation 25
Chapter 2

i AAA &

'

! 1

»

r

, -»

(a) Floor 94

-•Ml

(c) Floor 96

-3v

[lit:::

f

-

(b) Floor 95

El

I !

(d) Floor 97

t

Insulation damage to core beams and

trusses

(e) Floor 98

Figure 2-19. Case A insulation damage condition for WTC 1 floor trusses and beams.

26 NISTNCSTAR1-6D, WTC Investigation
Global Models

(c) Floor 96 (d) Floor 97

(e) Floor 98

Figure 2-20. Case A structural damage condition for WTC 1 floors.

NISTNCSTAR 1-6D, WTC Investigation 27
Chapter 2

rri.

A A

1 TT

(a) Floor 79

.

(c) Floor 81

!li|i|l|ltiE

A W

J. 4> AA

j ^

(e) Floor S3

jii::

r4

I:

1.

1 t T V

(b) Floor 80

i

45.

(d) Floor 82

I

Insulation damage to core bean'is and

trusses

Figure 2-21. Case C insulation damage condition for WTC 2 floor trusses and beams.

28 NISTNCSTAR 1-6D, WTC Investigation
Global Models

(c) Floor 81 id) Floor 82

N

Structural damage to concrete slab, core beams, and trusses

Severed floor area

(e) Floor 83

Figure 2-22. Case C structural damage condition for WTC 2 floors.

NISTNCSTAR 1-6D, WTC Investigation 29
Chapter 2

(e) Floor 98

Figure 2-23. Case B insulation damage conditions for WTC 1 floor trusses and beams.

30 NIST NCSTAR 1-6D, WTC Investigation
Global Models

ff • » -

(a) Floor 94 (b) Floor 95

(c) Floor 96 (d) Floor 97

N

Structural damage to concrete slab, core beams, and trusses

(e) Floor 98

Figure 2-24. Case B structural damage conditions for WTC 1 floors.

NISTNCSTAR 1-6D, WTC Investigation 31
Chapter 2

V. i

4> '«tii * 4» -4

(a) Floor 78

(c) Floor 80

* &

44

(e) Floor 82

r

^ J

A

t

(b) Floor 79

4» i

(d) Floor 81

:r2 1 r J. - i

, I* i , * ^1

7Sm *

(f) Floor 83

AT

I

Insulation

damage to core beams

and trusses

Figure 2-25. Case D insulation damage conditions for WTC 2 floor trusses and beams.

32 NISTNCSTAR1-6D, WTC Investigation
Global Models

jHIIIHIHilE

(a) Floor 78

(c) Floor 80

(b) Floor 79

N

i t 'i . i

(d) Floor 81

Structural damage to concrete slab, core beams,

and trusses

Severed floor area

(fj Floor 83

Figure 2-26. Case D structural damage conditions for WTC 2 floors.

NISTNCSTAR 1-6D. WTC Investigation 33
Chapter 2

2.3 TEMPERATURE EFFECTS

The fires resulting from the combustion of the jet fuel, followed by the combustion of building contents and the debris from the aircraft produced high-temperature gases that in turn increased the temperature of

the exposed structural members. Fire is dynamic in nature. As fire consumes combustible materials in the area of ignition, the high temperature gases produced by the fire spread to other areas of the building,

heating the structure and igniting combustible contents in these other areas. Even as the fire spreads, it consumes the fuel in areas already involved, extinguishing itself and allowing the structure in those areas

to cool. As a result of this behavior, the temperature of the exposed structural members in the two towers

varied with time, from the instant of aircraft impact until the final collapse. NIST performed a series of

computational fluid dynamics analyses to predict the distribution with time of gas temperatures in various

locations in the structures and also to produce temperature time histories for the structural members in the

affected areas of the buildings. These analyses are reported in NIST NCSTAR 1-5.

In the analyses performed by NIST, a key factor in the calculation of the temperature distribution for the

structural members was the extent of insulation that was in place after the impact. NIST assumed that any

damage to the insulation was by direct abrasion from flying debris created as the aircraft impacted,

disintegrated, and transited across the building. A series of aircraft impact analyses were performed to predict the pattern of debris flow as well as the probable damage to structural members inside the

building. In these analyses, the trajectories of the debris flow and, therefore, of the extent and distribution

of insulation damage predicted was dependent on the estimted values for aircraft speed and direction of

travel, point of impact on the structure, and impact trajectory. The several damage sets (Case A„ Case Bj,

Case C„ etc.) resulted from variation in the values of these parameters and, therefore, the estimated

damage and temperature time histories. One temperature time history data set was derived for each set of

structural and insulation damage". As discussed in Section 2.2, Case C, and revised Case Ci have the same temperature time histories for structural components.

The high temperature gases produced by the fires primarily heated the floor trusses and the bottom face of

the slabs through convection and the top face of the slabs through radiation. The temperatures predicted

in the structural members depended on the extent of insulation assumed to be in place and on the material

properties and geometry of the structural members. In the actual buildings, the temperature in the

structural members varied through the length and cross section and changed with time. The temperature

at every node in the global models was calculated by interpolation of temperatures from the thermal

analysis, which had a much finer mesh than the global structural models. A linear temperature gradient was assumed across column cross sections and along the length of members. To reduce data handling,

the continuous temperature time histories were replaced with piecewise linear time-histories without

significant loss of accuracy. Consequently, snapshots of the spatial distribution of temperature were taken

at 10 min intervals, initiating at the time of impact and extending through the time of collapse (or

approximately the time of collapse) for each of the buildings (see NIST NCSTAR 1-5G for more

discussion of the 10 min intervals).

" Temperature cases were formerly called by different names. Case A; and Case Cj conditions were called "baseline case", and

Case B, and Case Dj conditions were called "maximum damage case". Case A and Case C conditions were called "best estimate case" or "realistic case", and Case B and Case D conditions were called "upper bound case" or "severe case". These

former temperature case names may appear on graphics produced in ANSYS.

34 NIST NCSTAR 1-6D, WTC Investigation
Global Models

Structural response of a building to fire-induced temperature is a complex phenomenon involving the

following phenomena:

• Axial thermal expansion of members as they heat and thermal contraction of members as they

cool; if these members are restrained, this expansion and contraction can induce a change in the stress distribution in the structure.

• Differential thermal expansion of members across their cross section if they are heated

unevenly, resulting in bowing of the members along their length; if members are under

significant compression, this bowing can lead to onset of buckling.

• Significant reduction in modulus of elasticity and strength of steel and concrete as temperature increases beyond 500 °C (NIST NCSTAR 1-6C).

• Creep in steel at high stresses and high temperatures.

Creep is a time-dependent phenomenon and, in the analyses that SGH performed, was found to have

resulted in shortening of core columns with high temperatures and high stresses.

In the global models, NlST-provided temperatures were applied to structural members between Floor 93

and Floor 99 in WTC 1 and between Floor 79 and Floor 83 in WTC 2. In each case, the temperatures were applied to exterior columns, spandrels, core columns and beams, and floor slabs.

In general, temperatures were assigned to the node locations in the global models. The distribution of

temperature was assumed to be uniform throughout the member cross section except in the case of the

exterior columns where temperature gradients within the cross section were considered in the direction

normal to the exterior walls.

All temperamres reported in this study are in units of °C.

2.4 THERMAL BEHAVIOR OF FLOORS

It was not practically possible to develop global models that could capture all structural behaviors or

failure modes found in the study of components and subsystems and to perform the global analysis within

a reasonable time period. To enhance computational efficiency, selected modeling details were omitted in the global models, and structural behaviors or failure modes that could not be captured by the global

models were introduced in the global analysis as fire-induced damage at appropriate points in time.

Key failure modes of the floor subsystem were identified in NIST NCSTAR 1-6C for components and

subsystems subjected to temperature time histories. These analyses indicated that as floor system

temperature increased, web diagonals in the floor trusses buckled, allowing the floors to sag. In extreme

cases, the analyses showed loss of vertical support for individual trusses, as either the truss seats supporting the trusses lost strength and failed under the influence of vertical gravity loads or sagging of

the trusses caused them to walk off the supporting seats.

This floor truss behavior was incorporated into the finite element models of entire individual floors that are referred to as full floor models. The models included representation of the floor slabs, trusses, beams,

and columns that extended full height to the floors immediately above and below the level under

NIST NCSTAR 1-6D, WTC Investigation 35
Chapter 2

consideration. When an entire full floor model was subjected to the temperature time histories, the

analyses showed that the floors sagged in areas where insulation was damaged and that individual floor trusses lost their vertical support at the exterior wall in some areas. However, it was found that these full floor models could not accurately capture the pull-in forces that the sagging floors were expected to apply

to the exterior walls. Discussions on these pull-in forces can be found in Section 2.5.2.

Since detailed modeling of the floors was not included in the global analysis models, important floor behavioral modes could not be captured in these global analyses. Key floor behavioral modes include

floor sagging that imposes pull-in forces on the exterior wall and loss of support of the trusses at the

exterior wall resulting in local disconnection of the floor from the exterior wall. To account for these

effects, pull-in forces on the exterior wall and disconnections of the floors from the wall were introduced

in the global analyses at appropriate times as fire-induced damage. In the process of developing the fire- induced damage, the behaviors predicted by the full floor model analyses as well as the damage observed

by NIST in their review of photographic and video evidence were both considered.

2.5 FIRE-INDUCED DAMAGE

Disconnections of the floors from the exterior walls caused by fire-induced connection failure between

the floor and the exterior wall and pull-in forces on the exterior wall exerted by sagging floors were

included in the global analyses as fire-induced damage. The locations of the floor/wall disconnections

and the locations and magnitudes of the pull-in forces were determined based on a combination of the

results from the full floor model analyses, the results from the isolated wall model analyses, and the actual

observafions in photographic and video evidence of WTC 1 and WTC 2.

2.5.1 FloorA/Vall Disconnections

In areas where the connection of the floor to the exterior wall failed and the floor was locally

disconnected from the exterior wall, the floor could no longer provide out-of-plane support for the wall at the locations of floor/wall disconnections, which resulted in a reduction of the buckling capacity of the

exterior columns. In order to simulate this behavior in the global analyses, the connection between floor

and wall elements was removed. When either one of the following condifions was encountered in the full floor analyses, the floor was disconnected from the exterior wall in the global model as it lost vertical

support:

• Gusset plate failure + seat failure due to vertical shear

• Gusset plate failure + bolt shear-off + truss walk off the truss seat Most disconnections obtained in the full floor models were due to the first of these conditions.

NIST performed extensive review of the available photographic and video evidence of the condition of

the two towers prior to their collapse. Some of the photographs NIST reviewed were taken immediately

after the aircraft impacts, while others were taken at various times leading up to the collapse. From this visual evidence, NIST constructed a time-variant map of the locations of observed floor/wall

disconnections. During the global analyses, floor/wall disconnections were introduced at those locations

and those times indicated in NIST's damage maps, if these discormections had not previously been

36 NISTNCSTAR 1-6D, WTC Investigation
Global Models

indicated by the full-floor analyses. Although FEA results and the observations were generally in good

agreement, the visual evidence suggested a somewhat greater extent of floor/wall disconnections.

2.5.2 Pull-in Forces

WTien the floor sagged while it was still connected to the exterior wall, the floor developed tensile forces

that tended to pull the exterior wall inward. There were four types of structural elements that connected

the floor system to the exterior wall system: 1 ) diagonal strap anchors that extended from the top chords

of trusses to the spandrel (they are referred to as strap anchors in this report), 2) headed studs on the

spandrels that extended into the floor slab edges, 3) gusset plates that were horizontal field-welded plates

that joined the top chords of the trusses to the spandrels, and 4) seat bolts that fastened bearing angles to the seats that were attached to the spandrels.

Pull-in force was applied to the exterior column in the global analyses, where either one of the following

conditions was encountered in the full floor analyses:

• Gusset plate failure + bolt shear-off + significant deflection (>25 in.) of the floor slab in that area (floor remains vertically connected)

• Tensile force between the exterior wall and the floor system

However, locations and magnitudes of pull-in forces were not accurately simulated by the full floor models for the following reasons:

• The full floor models did not and could not have an accurate set of boundary conditions on

the columns. Columns extended from one floor below to one floor above, and the top and

bottom of exterior columns were restrained in the direction normal to the exterior wall. These boundary conditions could not accurately portray the thermally-induced movements of

floors above and below the floor being analyzed and could not accurately capture the stiffness of columns in the exterior walls. Photographs of the towers taken before collapse indicated

that the exterior walls bowed inward over a height of several floors. Bowing of exterior

columns as observed could not be captured in the floor model because the boundary condition

of a full floor model could not be formulated to represent the observed bowing of the exterior

wall over several floors.

• In the actual buildings, the strap anchors and studs must have been capable of transmitting a significant amount of force between the floor system and exterior wall. However, the full floor analysis with the strap anchors and studs resulted in sequential failure of these

components and an extremely slow convergence in the analyses. Because these components

were found to fail at early stages of fire, these elements were then removed from all the full floor models to obtain solution within a reasonable period of time. Therefore, in these

analyses, the only structural elements in the full floor model that could transfer horizontal

interface forces between the floor system and the exterior walls were the gusset plates and

seat bolts. This caused premature failure of the gusset plates and seat bolts in the analyses,

which resulted in horizontal floor/wall disconnections. In addition, friction between bearing

angles and seats was not modeled in the full floor analyses. Therefore, the full-floor model

did not show significant tension at the floor/exterior wall interface. In the real structures,

NISTNCSTAR 1-6D, WTC Investigation 37
tension forces could develop between the floor system and walls following failure of the

gusset plates and seat bolts through the mechanism of friction between the truss seats and

bearing angles and through the strap anchors that had not failed.

- There is considerable uncertainty as to what the actual capacity of the strap anchor

system was to transfer pull-in forces from the floors to the walls. Assuming that the strap

anchors were installed as shown on the PANYNJ drawings, with only the minimum

length and size of welds specified actually installed, the tensile capacity of the strap

anchor system was controlled by the strength of weld at the strap anchors to the truss the

top chords. Typically, 5/16 in., 4 in long fillet welds were specified for this joint. For a

pair of floor trusses, joined to the wall by a pair of diagonal strap anchors, this translates

into a computed tensile capacity of 68 kip at room temperature and 6.6 kip at 800 °C. In

full floor model analyses that incorporated the strap anchors, these capacities were used.

However, if longer welds were provided, say in excess of 6 in., or somewhat larger fillets were actually placed, the ultimate tensile strength of the strap anchor (1-1/2 in. x 5/8 in.

flat plate) could have controlled the capacity of this system. In such a case, the strap

anchors for a pair of floor trusses could develop a 101 kip tension force at room

temperature and a 9.8 kip tension force at 800 °C. - Assuming a coefficient of friction of 0.33 and vertical reaction at an exterior seat of

13 kip, the friction force can be as much as 4.3 kip for a pair of trusses. The capacity of

the two 5/8 in. -diameter seat bolts present in each pair of trusses in shear is 44 kip at room temperature and 4.0 kip at 800 °C. Therefore, at elevated temperature, the

combined action of friction and bolts could develop on the order of an 8 kip tension force

at the exterior seat.

Creep at high temperature was found to significantly increase the sag of a floor system. A

thermal response analysis of a simplified truss model removed from the full floor model

showed a significant increase in vertical deflection when creep was considered, as shown in Fig. 2-27. However, full floor models were made with BEAM 188/ 189 element types and were not run with creep due to inherent convergence problems of BEAM18 8/ 189 when used

under thermal loadings with materials having temperature-dependent creep property.

In the full floor models, crushing or cracking of the concrete slab was neglected. Extreme

temperatures can crack and spall concrete, further reducing the floor stiffness, and increasing

both the floor sag and the floor/wall pull-in forces. NIST may have underestimated the amount of thermal insulation that was damaged by the

aircraft impacts. The estimates developed by NIST were limited to the insulation on sections

of framing that were exposed to direct abrasion by the debris field, predicted in the impact

analyses. Potential loss of insulation due to impact shock and vibration effects was not

included. More severe insulation damage would have resulted in higher temperatures of the

trusses than those used in the full floor analyses. This in turn would result in larger areas in which the floors would have sagged.

NISTNCSTAR 1-6D, WTC Investigation
Global Models

Figure 2-27. Comparison of vertical displacement of a simplified truss model at Column 333 extracted from the full floor model of Floor 96 of WTC 1 for Case Bj

temperature condition at 40 min with and without creep.

Given these uncertainties and inaccuracies in the evaluation of the Ukely magnitude and location of pullin forces on the exterior wall, in the global analyses, pull-in forces were applied in some locations where

the full floor analyses did not predict the development of such behavior. The magnitude and location of

pull-in forces were selected by trial and error to produce a computed bowing of the exterior walls that matched that observed in the photographic and video evidence, as discussed in Chapter 3.

In the actual buildings, floor attachment to the exterior wall occurred continuously along the length of the

wall. Headed studs were spaced uniformly along the length of the wall. Pairs of trusses, with truss seats and gusset plates were present at alternate column locations, and diagonal strap anchors connected to the

columns between those supporting trusses. Therefore, pull-in forces were applied to columns attached to trusses as well as those attached to strap anchors.

2.5.3 FloorAA/all Disconnections and Pull-in Forces Included in the Global Model

In the global models, nodal couplings tied the exterior columns to the floors. The nodal couplings were removed at locations of floor/wall disconnections. If disconnections were projected to occur or were

obser\'ed in visual evidence at a time intermediate to the 10 min intervals used in the analyses, for example, between 10 min and 20 min, they were imposed starting at the earlier time point, in this example, at 10 min. Once a portion of a floor was disconnected from the exterior wall, it remained

disconnected for the remainder of the analysis. Similarly, pull-in forces were also applied to the global

models at the beginning of the 10 min time intervals in which they were predicted to occur or were

observed, and they were maintained at a constant level for the 10 min time interval.

Outward expansion of the floors was not included in the global models. Floor analyses showed that the

floors initially pushed exterior column outward by a few inches. However, significant outward bowing was not observed and several inches of outward deflection of exterior columns would not affect the global

stability of the towers.

NISTNCSTAR 1-6D, WTC Investigation 39
Chapter 2

WTC1

Figures 2-28 to 2-37 show the locations of floor/wall disconnections and pull-in forces imposed on the

WTC 1 global model for Case B conditions. Each figure covers a 10 min time interval, the first initiating

at 0 min, when the initial impact occurred, and the last initiating at 90 min. Until 80 min, the locations of

floor/wall disconnections and pull-in forces were determined solely on the basis of full floor model

analyses. After 80 min, the observations from the photographic and video evidence were also considered

in determining these events to capture floor/wall disconnections and pull-in locations that were not

evident in the full floor analyses. Section 3.2.1 discusses the process used to incorporate the actual

observations.

As is discussed in Chapter 5, inward bowing of the exterior south wall of WTC 1 was actually observed at 10:23 a.m., about 97 min after the aircraft impact (NIST NCSTAR 1-6), while inward bowing of the

south wall was not observed in photos or videos at 9:55 a.m. (about 69 min after the aircraft impact). The

observed inward bowing extended from Floors 95 to 99 between Columns 308 to 326 (possibly to 340),

and the maximum bowing estimated by NIST from photographs was about 55 in. at Floor 97. Subsystem

analyses of the full floors and the exterior walls suggested that this observed bowing of the south wall was caused by sagging of the floors. As the floors sagged, they imposed tension force on the exterior

wall, and the exterior wall was pulled in. However, sagging of floors in such a wide range over five floors was not predicted by the full floor model analyses. Possible reasons for floor sagging in areas not

predicted by the full floor analyses include loss of insulation outside of the areas considered by NIST

when formulating the temperature time histories, the additional structural softening caused by concrete cracking and spalling, and debris weight from different sources including the aircraft, accumulation of

debris from the impact, and partial floor collapse, none of which were modeled in the full floor analyses.

To match the observations, the south wall was assumed to be pulled in by the floors between Floor 95 and

Floor 99 across the entire width of the wall except at locations of floor/wall disconnections, starting at 80

min. The magnitude of the pull-in force was determined, by trial and error, by matching the observed

bowing magnitude as discussed in Section 3.2.1. The pull-in forces were selected as 4 or 5 kip per

column. Results from the analysis with 5 kip pull-in forces are presented in Chapter 4.

40 NIST NCSTAR 1-6D, WTC Investigation
Global Models
Chapter 2

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50 NISTNCSTAR 1-6D, WTC Investigation
Global Models

WTC 2

Figures 2-38 to 2-43 show the locations of floor/wall disconnections and pull-in forces imposed on the

WTC 2 global model for Case D conditions. Each figure covers a 10 min time interval, the first initiating

at 0 min, when the initial impact occurred, and the last initiating at 50 min.

In determining the locations of floor/wall disconnections from the full floor models, the results of Case Ci

and Case D, temperature conditions were considered jointly for the uncertainties in truss seat temperatures. This uncertainty is illustrated in Tables 2-2 and 2-3. Table 2-2 compares the temperature

predicted for the exterior truss seats at selected columns of the east wall at Floor 82 at times of 30 min, 40

min. 50 min, and 60 min. Table 2-3 shows demand-to-capacity ratios for vertical support of these same

exterior seats. Temperatures of the exterior seats at the east wall of Floor 82 rapidly dropped after 40 min

in Case D,; whereas, in Case Cj they continued to increase with time. Due to this difference, the truss seats that were very close to failure (such as the seat at Column 303) at 40 min of Case D, did not fail at 50 min in the full floor analysis. If high temperatures had continued for a few more minutes for Case Di,

these seats would have failed. The actual temperature time history may not have descended rapidly

between 40 min and 50 min, as is deduced from the consideration of piecewise linear temperature time

history in this study.

The state of the floor/wall connections in the full floor analysis were reevaluated considering the effects of uncertainties in the seat capacities by comparing the demands to the seat capacities that were

10 percent lower than the calcuated seat capacities. As a result of this comparison, the seats adjacent to the already disconnected seats at Floors 82 and 83 were found to be progressively failing, and the extent of floor/wall disconnection was extended to nearly the entire width of the east wall. These worst-case

floor/wall disconnections were included in the floor/wall disconnections for Case D conditions in the

global analysis.

Table 2-2. Temperatures of exterior seats at east wall of Floor 82 of WTC 2.

Column ID

Case Cj Temperatures (°C) Case Di Temperatures (°C)

30 min 40 min 50 min 60 min 30 min 40 min 50 min 60 min

301 763 788 811 813 818 819 507 345

303 752 774 809 808 822 820 509 348

305 750 769 807 804 823 821 513 348

307 750 769 804 799 823 821 511 342

309 727 748 787 790 822 816 485 334

311 677 698 738 758 816 804 458 328

313 636 657 700 724 809 803 487 342

315 591 605 632 662 816 794 481 347

317 574 580 615 637 815 799 494 351

NISTNCSTAR 1-6D, WTC Investigation 51
Chapter 2

Table 2-3. Demand-to-capacity ratios of exterior seats at east wall of Floor 82 of WTC 2

predicted by the full floor model.

Column ID

Case Ci Temperatures (°C) Case Dj Temperatures (°C)

30 min 40 min 50 min 60 min 30 min 40 min 50 min 60 min

301 0.35 0.31 failed failed 0.63 0.54 0.02 0.08 303 0.66 0.81 failed failed 0.92 0.97 0.18 0.14 305 0.39 0.53 failed failed 0.63 0.70 0.20 0.19 307 0.41 0.51 failed failed 0.59 0.60 0.15 0.13 309 0.35 0.43 failed failed 0.60 0.60 0.13 0.13 311 0.38 0.46 failed failed 0.87 0.71 0.09 0.05 313 0.23 0.27 failed failed 0.64 0.48 0.10 0.09 315 0.20 0.24 failed failed 0.49 0.41 0.08 0.09 317 0.10 0.09 0.96 failed 0.45 0.50 0.14 0.13

In addition to the reevaluation of the seat capacities, the location of floor/wall disconnections estimated

from full floor analyses were compared and were updated based on the floor/wall disconnections

observed in the photographs and videos. Observed floor/wall disconnections were provided for the east wall at 9:03 a.m., 9:38 a.m., and 9:55 a.m. and for the north wall at 9:10 a.m., 9:14 a.m., and 9:58 a.m. All observed floor/wall disconnections were included in the global analysis for Case D conditions at appropriate points in time, whether predicted by the full floor analyses or not.

As previosusly described above for the case of WTC 1, the photographic and video evidence was also

reviewed by NIST to determine the extent of inward bowing of the east wall of WTC 2. These

displacement measurements were used to update the location and the magnitude of the pull-in forces

applied to the global model. The earliest observations of inward bowing for WTC 2 were made at 9:21 a.m., 18 min after impact (NIST NCSTAR 1-6), when the east wall was observed to be bowing

inward between Column 301 and Column 345 between Floor 78 and Floor 83. At this time, NIST

estimated the maximum inward deformation to be about 10 in. at Floors 80 and 81 between Column 322

and Coluinn 329. To replicate this inward bowing, pull-in forces were applied at Floors 79, 80, 81, and

82. The full floor analyses correctly predicted the floors that were pulled in, but underestimated the

location of the pull-in forces across the width of the east wall, relative to that required to replicate the

observed bowing. The locations of pull-in forces predicted by the full-floor analyses were concentrated

toward the south side of the east wall and typically ranged between Columns 329 and 359 at Floor 82 and

between Columns 357 and 359 at Floor 79. The locations of pull-in forces estimated from the

observation were used to augment those obtained from the full floor analyses. Based on this augmented

data, at 20 min after imact, pull-in forces were applied over the entire width of the east wall at Floors 79,

80, 81, and 82 in the global analysis.

The photographic and video evidence, obtained at 9:53 a.m., about 50 min after impact (NIST

NCSTAR 1-6), show the east wall bowing inward from Column 301 to Column 353 between Floor 77

and Floor 84. At this instant, NIST estimated the maximum inward deformation to be about 15 in. to 20 in. at Floor 81 between Column 320 and Column 330. To replicate this observed bowing geometry, a combination of pull-in forces and floor/wall disconnections were applied between Floor 77 and Floor 84. Except for Floor 78, which was not analyzed using a full floor model, the full floor analyses correctly

predicted the floor levels at which the exterior wall was observed to be pulled in, but underestimated the

locations of pull-in forces. The locations of the pull-in forces estimated from the full floor analyses were

52 NIST NCSTAR 1-6D, WTC Investigation
Global Models

concentrated toward the south side of the east wall and t>'pically ranged between Column 333 and

Column 359 at Floor 81 and between Column 355 and Column 359 at Floor 79. Based on the full floor analyses and the ree\'aluated seat capacities. Floor 83 was disconnected from the east wall between

Column 302 and Column 357, and Floor 82 was disconnected between Column 301 and Column 349.

For this reason, no pull-in forces were applied at these column locations. The locations of the pull-in

forces estimated from the obser\'ations at 50 min were used to augment those estimated from the full floor

analyses. As a result of this addition, at 50 min after impact, pull-in forces were applied over the entire

width of the east wall at Floors 78, 79, 80, and 81, and between Column 350 and Column 359 at Floor 82.

As is discussed in Section 3.2.2. the magnimde of the pull-in force was estimated through a trial and error process by applying different levels of pull-in forces to the isolated wall models and by comparing the

resulting inward bowing to that estimated from obser\'ations at 9:21 a.m. and 9:53 a.m. From these

comparative analyses, the magnitude of pull-in forces were determined to range from 1.0 to 2.0 kip on the

south side of the east wall and 4.0 to 5.0 kip on the north side of the east wall. It was necessary to apply

larger pull-in forces on the north side than on the south side of the east wall because column temperatures on the north side were higher than the column temperamres on the south side of the east wall. Higher

temperatures resulted in more outward bowing of columns, and thus larger pull-in forces were required to overcome this out^A ard bowing.

NIST NCSTAR 1-6D. WTC Investigation 53
Chapter 2

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Global Models

NISTNCSTAR 1-6D, WTC Investigation 59
Chapter 2

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60 NISTNCSTAR 1-6D, WTC Investigation
Chapter 3

Isolated Wall AND Core Model Analyses

3.1 introduction

The isolated models were parts of the global models that were isolated and subjected to the same gravity

and thermal loads as the global models. Obviously, the boundary conditions of the isolated models were

not realistic, and the results cannot capture the interaction between the isolated model and the rest of the

global model. Nevertheless, the isolated models provided insight into the structural behavior of the major

parts of the global models under gravity and temperature time histories. Specifically, the trial values of

the magnitude of pull-in forces resulted in calculated bowing of the exterior wall that did not agree well

with the observed damage. Muhiple analyses were required to match the results of calculations with the

actual observations. Such multiple analyses could not have been performed on the global models within

the time frame of this study and, therefore, were performed on the isolated models.

The isolated model analyses were performed pursuant to the global model analyses without creep and

prior to the global model analyses with creep. The results shown in this chapter do not form a major hnk

in the chain of collapse sequence arguments and may be skipped by those interested only in this chain of

arguments.

The south exterior wall of WTC 1 and the east exterior wall of WTC 2 bowed and buckled as observed in photographs and videos. Both walls were isolated from the global models of WTC 1 and WTC 2. The

isolated models were subjected to both Case A and Case B temperature conditions for WTC 1 and both

Case C and Case D temperature conditions for WTC 2. In the following sections, the details of the

isolated models, the results, and their comparison with the actual obser\'ations for different assumed input

parameters are discussed.

3.2 EXTERIOR WALL BUCKLING

The south exterior wall of WTC 1 and the east exterior wall of WTC 2 were isolated from the global

models and subjected to the combined effects of gravity loads and temperature time histories to determine

whether the exterior walls of WTC 1 and WTC 2 would buckle as observed in the photographs and

videos, and to determine conditions required to buckle them such as locations and magnitude of pull-in

force from the sagging floors, locations of the floor/wall disconnections, and the need for additional

vertical loads.

The isolated exterior walls from WTC 1 and WTC 2 are shown in Fig. 3-1. The exterior wall segment of

WTC 1 included all the exterior columns from Column 301 to Column 359 and floors from Floor 89 to Floor 106. The exterior wall segment of WTC 2 included all the exterior columns from Column 301 to Column 359 and floors from Floor 73 to Floor 90. The springs at the base of the global models represent

the vertical flexibility of the exterior walls below Floor 89 for WTC 1 and Floor 73 for WTC 2 for a uniform loading condition. For the south wall model of WTC 1, members that were severed by the

aircraft impact were removed. The east wall of WTC 2 sustained no aircraft impact damage.

NISTNCSTAR 1-6D, WTC Investigation 61
Chapter 3

(a) Segment from South wall of WTC 1 (b) Segment from East wall of WTC 2

Figure 3-1. isolated exterior wall segments from WTC 1 and WTC 2

(horizontal lines show spandrels and vertical lines show column).

ELEMENTS

TYPE NUM

'

Apply axial

force of the

above column

as a nodal force

to the top of

each column

the isolated

region

WTCl Isolated South Wall

in ^^^^^^^^^^^

ANSYS

DEC 28 2004 11:10:25

Restrain only

^ out-of-plane

translation at i columns at floor levels

Full restraint at the base of the vertical springs

Figure 3-2. Boundary conditions applied on the isolated exterior wall segment on the

south wall of WTC 1.

The applied boundary conditions for both isolated exterior wall models were identical and are shown for

WTC 1 in Fig. 3-2. The isolated exterior wall models were fully restrained at the base of the vertical

62 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

springs. In the out-of-plane direction (direction y) they were supported at floor levels. At predetermined

points in times, these supports were removed at locations where either calculations or observations

showed floor/wall disconnections. For the east wall of WTC 2, there were floor/wall disconnections or

pull-in forces calculated by the full floor models along the edges of the model (Column 301 and

Column 359). In the analyses of the isolated wall model for Case C and Case D temperature conditions,

the out-of-plane supports were removed at disconnections located on the edges of the model. However, in the analysis of the pull-in forces needed to match the observed bowing (see Section 3.2.2), the

disconnections on the edges of the model were not modeled, and all nodes along the vertical edges of the

model were restrained.

To represent the column loads after aircraft impact, a set of axial loads and moments were applied at the

top of the isolated wall segments. These axial loads and moments, taken from the preliminary global

model analyses with Case A (for WTC 1) and Case C and Case D (for WTC 2) structural damage

conditions, represented the axial load and moment in the columns at the floor right above the top of the

isolated wall segments after aircraft impact. For instance, for the WTC 2 exterior wall segment, the

isolated wall terminates at Floor 90. In order to represent the axial load coming from Floor 90 and above,

the axial loads from the columns between Floor 90 and Floor 91 of the global model were extracted at the

end of the aircraft impact analysis and were applied on the top of the isolated wall model of WTC 2. In

addition to the set of vertical loads applied at the top of the isolated walls, loads representing the dead and

25 percent of the design live loads of the floors were applied at each column node at floor levels.

The isolated exterior wall models were subjected to a set of loading conditions as summarized in Table 3-1 for WTC 1 and Table 3-2 for WTC 2. After the gravity analysis, the isolated exterior wall

models were subjected to temperature loads at 10 min increments. The analyses were conducted with

Case A and Case B temperature conditions for WTC 1 and Case C and Case D temperature conditions for

WTC 2. For each temperature analysis, the column and spandrel temperatures at time t were ramped to the column and spandrel temperatures at time = t + 10 min. Before applying the temperatures, the out-ofplane supports were removed at disconnected column to exterior wall connections at or prior to t +

10 min. Once the temperature analyses were completed (WTC 1 was analyzed to 100 min and WTC 2 to 60 min), both isolated exterior wall models were pushed down by imposing additional displacements to determine additional axial-load-carrying capacity remaining in the exterior wall system. For push-down

analysis, the vertical displacements at the top of the isolated exterior wall models at the end of

temperature analyses were extracted. These displacements were applied on top of the isolated exterior

wall models, and additional uniform displacement increments were imposed in a displacement-controlled

analysis. During push-down analysis, the temperature of the columns and spandrels were kept constant at the values specified at the end of the temperature analyses (WTC 1 column and spandrel temperatures were kept at 1 00 min temperatures and WTC 2 column and spandrel temperatures were kept at 60 min

temperatures). The results of isolated exterior wall model analyses are discussed in the following

sections.

NISTNCSTAR 1-6D, WTC Investigation 63
Chapter 3

Table 3-1. Analysis steps conducted on WTC 1 isolated exterior wall model.

Analysis Step Description

1 Gravity Apply gravity loads with aircraft impact

2 Temperature

at 1 0 min

Remove the out-of-plane supports at floor to exterior wall connections disconnected at or prior

to 10 min. Apply column and spandrel temperatures at 10 min.

3 Temperature

at 20 min

Remove the out-of-plane supports at floor to exterior wall connections disconnected at or prior

to 20 min. Apply column and spandrel temperatures at 20 min.

4 Temperature

at 30 min

Remove the out-of-plane supports at floor to exterior wall connections disconnected at or prior

to 30 min. Apply column and spandrel temperatures at 30 min.

5 Temperature

at 40 min

Remove the out-of-plane supports at floor to exterior wall connections disconnected at or prior

to 40 min. Apply column and spandrel temperatures at 40 min.

6 Temperature

at 50 min

Remove the out-of-plane supports at floor to exterior wall connections disconnected at or prior

to 50 min. Apply column and spandrel temperatures at 50 min.

7 Temperature

at 60 min

Remove the out-of-plane supports at floor to exterior wall connections disconnected at or prior

to 60 min. Apply column and spandrel temperatures at 60 min.

8 Temperature

at 70 min

Remove the out-of-plane supports at floor to exterior wall connections disconnected at or prior

to 70 min. Apply column and spandrel temperatures at 70 min.

9 Temperature

at 80 min

Remove the out-of-plane supports at floor to exterior wall connections disconnected at or prior

to 80 min. Apply column and spandrel temperatures at 80 min.

10 Temperature

at 90 min

Remove the out-of-plane supports at floor to exterior wall connections disconnected at or prior

to 90 min. Apply column and spandrel temperatures at 90 min.

11 Temperature

at 1 00 mm

Remove the out-of-plane supports at floor to exterior wall connections disconnected at or prior

to 100 min. Apply column and spandrel temperatures at 100 min.

12 Push Down Extract the vertical displacements at the top of the isolated wall model and impose these displacements and additional uniform displacement increments with column and spandrel

temperatures kept at 100 min.

Table 3-2. Analysis steps conducted on WTC 2 isolated exterior wall model.

Analysis Step Description

1 Gravity Apply gravity loads right after aircraft impact

2 Temperature

at 10 min

Remove the out-of-plane supports at floor to exterior wall connections that were discormected

at or prior to 10 min. Apply column and spandrel temperatures at 10 min.

3 Temperature

at 20 min

Remove the out-of-plane supports at floor to exterior wall connections that were disconnected

at 20 min. Apply column and spandrel temperatures at 20 min.

4 Temperature

at 30 min

Remove the out-of-plane supports at floor to exterior wall connections that were discoimected

at 30 min. Apply column and spandrel temperatures at 30 min.

5 Temperature

at 40 min

Remove the out-of-plane supports at floor to exterior wall connections that were disconnected

at 40 min. Apply column and spandrel temperatures at 40 min.

6 Temperature

at 50 min

Remove the out-of-plane supports at floor to exterior wall connections that were disconnected

at 50 min. Apply column and spandrel temperatures at 50 min.

7 Temperature

at 60 min

Remove the out-of-plane supports at floor to exterior wall connections that were disconnected

at 60 min. Apply column and spandrel temperatures at 60 min.

8 Push Down Extract the vertical displacements at the top of the isolated wall model and impose these displacements and additional uniform displacement increments with column and spandrel

temperatures kept at 60 min.

64 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

3.2.1 Finite Element Analysis of WTC 1 Exterior Wall

Case A Temperature Condition

As calculated in the full-floor model analyses for Case A, condition, described in Appendix A, the floors were assumed to remain connected to the south wall of WTC 1 throughout the temperature history for Case A condition.

Figures 3-3 to 3-12 show the temperature distributions of Case A condition in columns of the WTC 1 south wall from 10 min to 100 min. A linear temperature gradient in the direction normal to the exterior

wall was assumed to exist in the cross section of beam elements for exterior columns. As Figs. 3-3 to 3-12 show, temperatures on the south wall were not very high; the peak temperature was only 455°C for Case A temperature condition. The temperature distributions of Case A condition in spandrels are shown

in Figs. 3-13 to 3-22. Temperatures were assumed to be uniform over the entire cross section of beam

elements for spandrels.

Figure 3-23 shows vertical displacements, out-of-plane displacements, and axial loads in columns of the

WTC 1 south wall after the impact. In contour plots created by ANSYS, "MN" and "MX" indicate the

locations of the minimum and maximum values, respectively. Columns from Column 329 to Column 331

between Floor 93 and Floor 97 were severed by the aircraft impact, and the maximum displacement

occurred at Column 330 at Floor 106. Column 328 and Column 332 between Floor 93 and Floor 97 on

both sides of the aircraft impact damage area were heavily loaded, and the maximum axial load was 377

kip at Column 332.

Figures 3-24 to 3-26 show vertical displacements, out-of-plane displacements, and axial loads in the

columns of the WTC 1 south wall for Case A temperature condition, respectively. At 100 min, the

maximum vertical displacement was nearly the same as the vertical displacement of 2.6 in. after the

impact. The out-of-plane displacement was insignificant during thermal loading. The maximum out-ofplane displacement was 0.35 in. outward, occurring at Column 332 between Floor 96 and Floor 97. During thermal loading, the axial load in Column 332 between Floor 96 and Floor 97 increased from 377

kip to 756 kip.

Figure 3-27 shows plastic strains in columns at 100 min. The maximum plastic strain of 4 percent

occurred in Column 332 between Floor 96 and Floor 97.

As described m Appendix C for the preliminary global model without creep and in Chapter 4 for the final global model with creep, gravity loads on the south wall varied under thermal loads as the loads were

redistributed within the tower through the hat truss and the spandrels. Figure 3-28 compares the axial

loads in columns derived from the preliminary global model without creep and with Case Aj structural damage condition to those of the isolated model wall model with Case A structural damage and

temperature conditions. The preliminary global model without creep was the only available source for

this comparison at that time. The differences in the axial loads were applied to the columns at Floor 99 as corrective loads. Figure 3-29 shows the response of the south wall after applying these corrective loads. The WTC 1 south wall remained stable after the application of these corrective loads.

To determine the additional load-carrying capacity of the south wall at the end of the temperature analysis

at 100 min, the top of the isolated exterior wall model was pushed down by converting the model from a

NISTNCSTAR 1-6D. WTC Investigation 65
Chapter 3

force-control analysis to a displacement-control analysis and by imposing additional vertical displacement

increments on top of the isolated model. The analysis was terminated at an additional vertical

displacement of 13.2 in. This model reached a peak total vertical load at an additional vertical

displacement of 1 1.3 in. Figure 3-30 shows the relationship between the total additional vertical load and

the additional vertical displacement. Figure 3-3 1 shows additional vertical load per column at different

additional vertical displacements of 2 in., 4 in., 6 in., 8 in., and 10 in. Figure 3-32 shows the response of

the WTC 1 south wall at the additional displacement of 13.2 in. When an additional 2 in. of vertical

displacement was imposed, the variation among the additional vertical loads on columns was within

50 kip for the average additional vertical load of about 160 kip. However, at an additional displacement

of 10 in., the variation became large, indicating some columns were softer than others; the softer columns

had reached their load-carrying capacities and were in the post-buckling regime. The WTC 1 south wall

model carried an additional vertical load of 33,000 kip (560 kip per column on the average). Therefore,

the south wall possessed significant reserve capacity after the application of Case A temperature

condition.

TEMPERATURES

THIK-CI

COL359

I

I llil!

nnl

ml

in ill!

lililii

iliiii! inni

AN

COL301

•-99

-98

-97

-96

-95

-94

-93

Floors

Wall Mjd«l (FL95-FL991 - Best Estima te

(a) Outside

ELEKENTE TEMPERATURES

COL301

W7C: SoLtl Wall Mod'=: (FL93-rL99) - Best Estimate Temperature at 600 :

AN

COL359

I -99

-98

-97

-96

-95

-94

-93

Floors

(b) Inside

Figure 3-3. Case A temperature condition of south wall columns of WTC 1 at 10 min.

TMAX-16J>.59i COL359

I

WTCl Soutl. Wal

AN

DEC -^i 2004

COL301

I -99

-97

-96

-95

-94

-93

Floors

(a) Outside

ELEMENTS

TEMPERATURES

COL301

I

IP

I f

0 200 400

100 300 51 ViTCl South Wall M'jd.rl (FL91*-F1^3I - B*st Estimate '

AN

COL359

I -99

-97

-96

-95

-94

-93

Floors

(b) Inside

700 850

Figure 3-4. Case A temperature condition of south wall columns of WTC 1 at 20 min.

66 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

COL359

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AN

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•-99

-97

-96

-95

-94

-93

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".~''~'°TMi?>l]^M

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-97

-96

-95

-94

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l-rCl Sr.uLl.

(a) Outside (b) Inside

Figure 3-5. Case A temperature condition of south wall columns of WTC 1 at 30 min.

COL359

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DEC 2A 2004

11 :34:09

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-96

-95

-94

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WTCl Sooth Wall Made! (Pt93-FL99J - Best EsLimaLe Tenperoture at 2<inc s«c

(a) Outside (b) Inside

Figure 3-6. Case A temperature condition of south wall columns of WTC 1 at 40 min.

TEMrEMTDSSr

7MIK-0

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(a) Outside (b) Inside

Figure 3-7. Case A temperature condition of south wall columns of WTC 1 at 50 min.

NISTNCSTAR 1-6D. WTC Investigation 67
Chapter 3

AN

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Figure 3-8. Case A temperature condition of south wall columns of WTC 1 at 60 min.

TEMPERATURES

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ELEMENTS TEMrERRTURES

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Figure 3-9. Case A temperature condition of south wall columns of WTC 1 at 70 min.

COL359

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(b) Inside

Figure 3-10. Case A temperature condition of south wall columns of WTC 1 at 80 min.

68 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

COL359

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-97

-96

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-94

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Figure 3-1 1 . Case A temperature condition of south wall columns of WTC 1 at 90 min.

ELZKZKtr

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TEHrERATURES

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^-93

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South Woll Model (FL93-rL99) - Btst EsLimdLe '

(a) Outside (b) Inside

Figure 3-12. Case A temperature condition of south wall columns of WTC 1 at 100 min.

zizklkt:

TM:K-32.3e3 THAX-n6.87 COL359

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AN

TEC .lA .'004

11 : 32 : 10

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c 600 snc

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Figure 3-13. Case A temperature condition of south wall spandrels of WTC 1 at 10 min.

NISTNCSTAR 1-6D, WTC Investigation 69
Chapter 3

TEKPEBATURES

TKIU'AA

.

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AN

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Figure 3-14. Case A temperature condition of south wall spandrels of WTC 1 at 20 min.

TEMPERATURES AN

COL30I

Floors — "C

WTC: Sjutt, Kal] Mjd^i (FL93-FLy9) - Best Es

Figure 3-15. Case A temperature condition of south wall spandrels of WTC 1 at 30 min.

TEMPERATURES

TMIN-72.301

TMAX-211 .999 COL359

AN

COL301

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•96 M-95

-94

— 93 Floors

inc 300

ut^. Wail M'J^: (FL?'^-nyyi - Best. E5t:

700 850

Figure 3-16. Case A temperature condition of south wall spandrels of WTC 1 at 40 min.

70 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

Floors

Figure 3-17. Case A temperature condition of south wall spandrels of WTC 1 at 50 min.

COL359

1

AN

COL301

1

1 Floors

C 200

IOC 30C

-

400 600

50C

eoc JOC 85C

Figure 3-1 8. Case A temperature condition of south wall spandrels of WTC 1 at 60 min.

ELZKZHTZ TEHPERArCBES

TKIK-lOS.fcSe AN

DEC 24 200A

11 :3fc:fl4

COL359

1 COL301

1

Floors

W7C1 South Mycl-: ( FL&'t-FL'- 3 ) - B-^L Es

60C 800

5nC 700 650

inatfe TemperoLure ot 4200 sec

Figure 3-19. Case A temperature condition of south wall spandrels of WTC 1 at 70 min.

NISTNCSTAR 1-6D, WTC Investigation 71
Chapter 3

COL359

I

AN

COL301

I MM -98

-97

«-96

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Figure 3-20. Case A temperature condition of south wall spandrels of WTC 1 at 80 min.

TEMPERATURES

TKIK-15;.ie7

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AN

DEC 2A 200-1

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Figure 3-21. Case A temperature condition of south wall spandrels of WTC 1 at 90 min.

TKAX-1S4.557 COL359

I

AN

DEC 24 .iOOA

COL301

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HK-98

ms-97

w-96

M-95

SM-94

BK -93

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:TT'^T'i'iii"iii' °c

IOC 300

! Wall MDdei (rL93-FL99) - Bes

Figure 3-22. Case A temperature condition of south wall spandrels of WTC 1 at 100 min.

72 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(a) Vertical displacement (b) Out-of-plane displacement

(downward displacement is negative) (inward displacement is positive)

(c) Axial force in columns

(compression is negative)

Figure 3-23. Response of Isolated south wall model of WTC 1 after aircraft impact.

NISTNCSTAR 1-6D, WTC Investigation 73
Chapter 3

ANSYS

COL359

I

-FL99 —FL97

^FL95

^FL93

^FL91

(a) At 20 min (b) At 40 min

ANSYS

ZZC 21 ZOOA 15:59:17

^FL99 —FL97

^FL95 —FL93

-FL91

-2.7 -2.: ' -1.5 -.5 -.3 -2.4 -:.8 -:.2 -.6 c WTCI Isolated Sox;th Wall - B^st Estindte TeTiDsrature at 36CC ssc

(c) At 60 min (d) At80 min

(e) At 100 min

Figure 3-24. Vertical displacements of isolated south wall model of WTC 1 for Case A

temperature condition (downward displacement is negative).

74 NISTNCSTAR 1-6D. WTC Investigation
Isolated Wall and Core Model Analyses

(a)at20min (b)at40min

(c)at60min (d)at80min

(e) at 100 min (f) Close-up view at 100 min

(30X displacement magnification)

Figure 3-25. Out-of-plane displacements of isolated south wall model of WTC 1 for Case

A temperature condition (inward displacement is positive).

NISTNCSTAR 1-6D, WTC Investigation 75
Chapter 3

(e)atlOOnnin

Figure 3-26. Axial load in columns of isolated south wall model of WTC 1 for Case A

temperature condition (compression is negative).

76 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

COL359

iiiiiiliiii

ANSYS

iiillll ii

m

iililil

t —FL99

UfL97

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UfL91

(in./in.)

'.ated South '

Figure 3-27. Plastic strain in columns of isolated south wall model of WTC 1 for Case A

temperature condition at 100 min (compressive strain is negative).

600

500

400

'a. :5 300

200

2 100

0

1

1

1 — ^

1 ! 1

1

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1

1

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300 310 320 330 340 350 360

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• Global model w/o creep

Column ID

Figure 3-28. Axial load in columns of south wall of WTC 1 at 100 min: isolated wall

model for Case A temperature condition compared to global model without creep for

Case Aj conditions (compression is positive).

NISTNCSTAR 1-6D, WTC Investigation 77
Chapter 3

ANSYSI

-FL99

-FL97 —FL95

-FL93

-FL91 — 3 (in.)

(a) Vertical displacement (b) Out-of-plane displacement

(downward displacement is negative) (inward displacement is positive)

(c) Axial force in columns (d) Plastic strain in columns

(compression is negative) (compressive strain is negative)

Figure 3-29. Responses of isolated south wall model of WTC 1 after corrective loads

from the global model were applied (Case A temperature condition at 100 min).

78 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

0.0 2.0 4.0 6.0 8.0 10.0 12.0 Additional Vertical Displacement (in.)

14.0

Figure 3-30. Total additional vertical load versus additional vertical displacement during

push-down analysis of isolated south wall model of WTC 1 for Case A temperature

condition (compression is positive).

800

a

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uC 400

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re 300 c

o

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1 L 1 —Additional displ. of 1 .9 in —Additional displ. of 4.0 in — —Additional displ. of 6.0 in —Additional displ. of 8.0 in —Additional displ. of 10.1 in

300 310 320 330

Column ID

340 350 360

Figure 3-31. Additional vertical load per column at different additional vertical

displacements during push-down analysis of isolated south wall model of WTC 1 for

Case A temperature condition (compression is positive).

NISTNCSTAR 1-6D, WTC Investigation 79
Chapter 3

ANSYS

-FL99

^FL97

^FL95 —FL93 —FL91

(a) Vertical displacement

(downward displacement is negative)

(b) Out-of-plane displacement

(inward displacement is positive,

5X displacement magnification)

COL359

I

ANSYS

FL99 ; FL97

; FL95

'

(c) Axial force in columns

(compression is negative,

5X displacement magnification)

(d) Plastic strain in columns

(compressive strain is negative,

5X displacement magnification)

Figure 3-32. Response of isolated south wall model of WTC 1 to Case A temperature

condition and push down at the end of the push-down analysis.

Case B Temperature Condition

In the full floor model analyses, described in Appendix A, Floors 97 and 98 disconnected from the

exterior walls at several columns between 80 min and 90 min. Figure 3-33 shows locations of the out-ofplane supports of the exterior wall model of WTC 1 at 100 min.

Figures 3-34 to 3^3 show the temperature distributions of Case B condition in the south wall columns of

WTC 1 from 10 min to 100 min. Figures 3-34 to 3^3 show that temperatures on the south wall became

very high near the impact damage area, reaching 801°C. Figures 3-44 to 3-53 show the temperature

distributions of Case B condition in spandrels. The temperatures of the spandrels are also quite high,

reaching 778°C.

80 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

Figures 3-54 to 3-56 show the vertical displacements, the out-of-plane displacements, and the axial

loads, respectively, in the south wall coluinns of WTC 1 for Case B temperature condition. Throughout

the temperature time history the maximum vertical displacement changed negligibly, starting at 2.64 in. immediately after impact and ending at 2.60 in. at 100 min. The maximum inward out-of-plane

displacement was 0.66 in. at Column 336 at Floor 98 at 100 min, while the maximum outward out-ofplane displacement was 2.3 in. at Column 342 at Floor 97. At these locations, the floor was disconnected

from the exterior wall so that the unsupported length of the columns was two to three stories.

Figure 3-57 shows the plastic strains in the south wall columns at 100 min. The maximum plastic strain was only 0.5 percent at Column 325 at Floor 96.

Load redistribution to the south wall was accounted for by comparing the results of the isolated wall

model to the global model, using a similar procedure to that described above for Case A (Fig. 3-58). The

differences in axial loads in these two models were applied to the isolated wall model as corrective loads. Figure 3-59 shows the response of the south wall after applying these corrective loads. The WTC 1 south

wall remained stable after the application of these corrective loads.

To determine the additional load-carrying capacity of the south wall at the end of the temperature analysis

at 100 min, the top of the isolated exterior wall model was pushed down by converting the model from a

force-control to a displacement-control analysis and by imposing additional vertical displacement

increments on top of the isolated model. The analysis was terminated at an additional vertical

displacement of 10.3 in. This model reached a peak total vertical load at an additional vertical

displacement of 9.0 in. Figure 3-60 shows the relationship between the total additional vertical load

applied and the additional vertical displacement applied. Figure 3-61 shows additional vertical load per

column at different additional vertical displacements of 2 in., 4 in., 6 in., 8 in., and 10 in. Figure 3-62

shows the response of the WTC 1 south wall with the additional displacement of 10.3 in. When an

additional 2 in. vertical displacement was imposed, the additional vertical load ranged from 110 kip to 200 kip, and the center columns. Column 330 to Column 340, started to buckle. Note that the additional

load for the center columns dropped significantly after the onset of buckling. At an additional

displacement of 10 in., the variation in columns loads became extremely large, and the additional column

loads became negative at Column 332 to Column 337, indicating local instability of the exterior wall

around Column 335. At the end of analysis, the outward displacement at Floor 97 increased as Column

332 to Column 337 between Floor 95 and Floor 96 buckled inward. If local instabihty of the exterior

wall does not initiate a progressive instability (not captured by this model), the WTC 1 isolated south wall

model could carry an additional vertical load of 23,000 kip (average column load of 390 kip).

NISTNCSTAR 1-6D, WTC Investigation 81
Chapter 3

Figure 3-33. Location of the out-of-plane supports and floor/wall disconnections

between exterior wall and the floor (WTC 1 south wall for Case B conditions at 100 min).

(a) Outside (b) Inside

Figure 3-34. Case B temperature condition of south wall columns of WTC 1 at 10 min.

82 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

COL359

I

AN

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Figure 3-35. Case B temperature condition of south wall columns of WTC 1 at 20 min.

COL359

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Figure 3-36. Case B temperature condition of south wall columns of WTC 1 at 30 min.

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Figure 3-37. Case B temperature condition of south wall columns of WTC 1 at 40 min.

NISTNCSTAR 1-6D, WTC Investigation 83
Chapter 3

COL359

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Figure 3-38. Case B temperature condition of south wall columns of WTC 1 at 50 min.

TEMPERATl'hES TKIK-0

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TEMPERATURES

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Figure 3-39. Case B temperature condition of south wall columns of WTC 1 at 60 min.

AN

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WTCl South Mall Model (FL93-FL99) - 'Jpper tiound Temperature at -1200

(a) Outside (b) Inside

Figure 3-40. Case B temperature condition of south wall columns of WTC 1 at 70 min.

84 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

COL359

I mm

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IS: 0= : 5^

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Figure 3-41. Case B temperature condition of south wall columns of WTC 1 at 80 min.

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Figure 3-42. Case B temperature condition of south wall columns of WTC 1 at 90 min.

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•c

(b) Inside

Figure 3-43. Case B temperature condition of south wall columns of WTC 1 at 100 min.

NISTNCSTAR 1-6D, WTC Investigation 85
Chapter 3

TEMPEKATL'KES THIK-2b.774 THAX-26S.772 COL359

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Figure 3-44. Case B temperature condition of south wall spandrels of WTC 1 at 10 min.

AN

TEMPERATL'BES APR 2S 2005

ISiOSr-lt

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vrrCl Sciuth Will M^d-l (~.9^-FL^?l - 'h-v^t B Dur,d TeraL-rr^ture at: 12nr sec

Figure 3-45. Case B temperature condition of south wall spandrels of WTC 1 at 20 min.

AN

COL359 COL301

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-96

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-94

-93

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Figure 3-46. Case B temperature condition of south wall spandrels of WTC 1 at 30 min.

86 NISTNCSTAR1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

TEMPERATURE

c

THIN-3S.S6S TMAX-619.873

AN

COL301

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500 700

iisd Temperature at ^qui: set

Figure 3-47. Case B temperature condition of south wall spandrels of WTC 1 at 40 min.

COL359

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Figure 3-48. Case B temperature condition of south wall spandrels of WTC 1 at 50 min.

TEKPEKATUREr

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-r-nriTT[ing|- °C

Figure 3-49. Case B temperature condition of south wall spandrels of WTC 1 at 60 min.

NISTNCSTAR 1-6D, WTC Investigation 87
Chapter 3

TEKFERRTL'RES

COL359

AN

COL301

-99

-98

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Figure 3-50. Case B temperature condition of south wall spandrels of WTC 1 at 70 min.

rKAX-631.031 COL359

AN

COL301

-99

-98

-97

-96

-95

-94

-93

Floors

Figure 3-51 . Case B temperature condition of south wall spandrels of WTC 1 at 80 min.

Figure 3-52. Case B temperature condition of south wall spandrels of WTC 1 at 90 min.

88 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

AN

COL301

Floors

70 c pr>c Boutid T^mi>=raty;r% at €C

Figure 3-53. Case B temperature condition of south wall spandrels of WTC 1 at 100 min.

NISTNCSTAR 1-6D, WTC Investigation 89
Chapter 3

(a) At 20 min (b) At 40 min

(c) At 60 min (d) At 80 min

(e) At 100 min

Figure 3-54. Vertical displacement of isolated south wall model of WTC 1 for Case B

temperature condition (downward displacement is negative).

90 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(c) At 60 min (d) At80 min

(e) At 100 min (f) At 100 min

(SOX displacement magnification)

Figure 3-55. Out-of-plane displacement of isolated south wall model of WTC 1 for Case

B temperature condition (inward displacement is positive).

NISTNCSTAR 1-6D, WTC Investigation 91
Chapter 3

(e) At 100 min

Figure 3-56. Axial load in columns of isolated south wall model of WTC 1 for Case B

temperature condition (compression is negative).

92 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(SOX displacement magnification)

Figure 3-57. Plastic strain in columns of isolated south wall model of WTC 1 for Case B

temperature condition at 100 min (compressive strain is negative).

Figure 3-58. Axial load in columns of south wall of WTC 1 at 1 00 min: isolated wall

model for Case B temperature condition compared to global model without creep for

Case Ai conditions (compression is positive).

NISTNCSTAR 1-6D, WTC Investigation 93
Chapter 3

(a) Vertical displacement

(downward displacement is negative)

(b) Out-of-plane displacement

(inward displacement is positive)

ANSYS

COL359

ONCOL359

1!"!!!!!!

ANSYS

iliP^

.(in./in.)

-692869 -543883 -391897

-618376 -4G9390 -32011 WTCi South Wall - Upper Bound TemperaLure

(c) Axial force in columns

(compression is negative)

(d) Plastic strain in columns

(compressive strain is negative)

Figure 3-59. Response of isolated south wall model of WTC 1 after corrective loads from

the global model were applied (Case B temperature condition at 100 min).

94 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

25,000

12.0 Additional Vertical Displacement (in.)

Figure 3-60. Total additional vertical load versus additional vertical displacement during

push-down analysis of isolated south wall model of WTC 1 for Case B temperature

condition (compression is positive). —Additional displ. of 2.0 in —Additional displ. of 4.0 in —Additional displ. of 6.1 in —^Additional displ. of 8.0 in —Additional displ. of 10.1 in

-100 H .

>

>

1 300 310 320 330 340 350 360

Column ID

Figure 3-61. Additional load per column at different additional vertical displacements

during push-down analysis of isolated south wall model of WTC 1 for Case B

temperature condition (compression is positive).

NISTNCSTAR 1-6D, WTC Investigation 95
Chapter 3

(a) Vertical displacement

(downward displacement is negative)

ANSYS

COL359

^FL97 —FL95

-FL93 —FL91

(b) Out-of-plane displacement

(inward displacement is positive,

3X displacement magnification)

(c) Axial force in columns

(compression is negative,

3X displacement magnification)

ONCOL359

I

(d) Plastic strain in columns

(compressive strain is negative,

3X displacement magnification)

Figure 3-62. Response of isolated south wall model of WTC 1 to Case B temperature

condition and push-down.

Pull-in Forces to Cause Observed Bowing

As discussed in Chapter 5, inward bowing of the exterior wall on the south face of WTC 1 can be seen in photographs of the event at 10:23 am (about 97 min after the aircraft impact), while no bowing of the

south wall is evident at 9:55 am (about 68 min after the aircraft impact). The inward bowing at 97 min

extended from Floors 95 to 99 between Columns 308 to 326 (possibly to 340); NIST estimated the

maximum bowing to be 55 in. at Floor 97. ...

The isolated south wall model of WTC 1 did not bow inward under Case A temperature condition, and it bowed slightly over a very limited area under Case B temperature condition. The isolated wall model

results did not capture the actual bowing.

96 NISTNCSTAR 1-6D. WTC Investigation
Isolated Wall and Core Model Analyses

The most plausible explanation for the discrepancy between the observed and modeled bowing of the

exterior walls is that the pull-in forces were not captured in the full floor models, and floors sagged to a greater extent than these models predicted. Following are reasons the floor models likely underestimated

sagging and did not accurately calculate pull-in forces.

• The exterior wall boundary conditions used in the floor models were realistic only if a single

floor was heated. The floor trusses were supported on exterior columns that extended one

story above and one story below the floor modeled. The far ends of the columns were

restrained against translation in the direction normal to the exterior wall and rotation about

the axis parallel to the exterior wall. This boundary condition was much stiffer in translation

normal to the exterior wall than actually occurred for sequential floors heating

simultaneously.

• The floor models did not include creep behavior in the steel or cracking of the concrete

floors.

• The floor models did not include strap anchors or studs.

• More thermal insulation may have been dislodged from the trusses than estimated from the

impact analysis. The impact analysis did not account for the effect of impact or vibrations on

dislodging insulation.

• The floor models assumed a uniform live load. Debris accumulated in large piles was

observed in some floor areas. To model the effect of pull-in forces on inward bowing of the columns, trial values of pull-in forces were

applied to the exterior columns of the south wall over five floors from Floor 95 to Floor 99 where bowing

was observed.

The magnitudes of the pull-in forces were determined by trial and error, matching the observed inward

bowing of exterior walls for Case B temperature condition. The Case B temperature condition was used

because temperatures of the south office area floors and south wall columns were much higher than those

of the Case A temperature condition, and because the full floor models with the Case Bj temperature

condition showed much larger floor sagging in the south office area than did the floor models with the

Case A, temperature condition.

The floor models for Case B temperature condition showed that floors began to disconnect from the south

wall about 80 min after impact. In the temperature time histories of the Case B condition, temperatures of

the south wall and south office area had begun to rise again after 80 min, having been relatively constant

for some time. Consequently, pull-in forces were applied to the exterior wall model starting at 80 min

and, the temperature time history was analyzed with these pull-in forces to 100 min. Figure 3-63 shows

locations of floor/wall disconnections and pull-in forces for this analysis.

Figures 3-64, 3-65, and 3-66 show the results of the analysis performed with a 6 kip pull-in force per

column. After applying 6 kip pull-in forces at 80 min, the maximum inward bowing increased to 12.2 in. as shown in Fig. 3-64. At 90 min, the maximum inward bowing became 19.0 in., and at 100 min, it reached 31.3 in., as shown in Figs. 3-65 and 3-66. The thermal loading from 80 min to 100 min

increased the inward bowing significantly where there was inward bowing initially. Figure 3-67 shows

the axial loads in columns between Floors 98 and 99 at 80 min, 90 min, and 100 min. At 100 min.

NISTNCSTAR 1-6D, WTC Investigation 97
Chapter 3

Columns 320 to 346 were in the post-buckling regime and were unloading. The maximum bowing of

3 1 .3 in. was smaller than the observed maximum bowing of 55 in.. The wall remained stable at 100 min,

In the global model, the exterior wall boundary conditions were different from the isolated wall model:

generally the stiffness against inward bowing in the global models was softer. In addition, the exterior

walls were expected to carry additional gravity loads redistributed from the core due to downward

displacement of the core resuhing from creep and inelastic buckling. Consequently, it is likely that the

inward bowing of the global model would be significantly larger than 3 1 in. with the same 6 kip pull-in

forces. Therefore, 4 or 5 kip pull-in forces were selected for the WTC 1 global analysis.

100

99 - ooocoooooocoooooooooooooocoooc^^

CX3000<XKX)CK300CK3®CKDO®©©®®®®OOOOCKD^^

0)

s - <XXXXXXXXXX5®00000@©®@@CODCXXXXXXXXXX30<XOX)C^^

95

94

93

g 96 - <XXXXXXXXXXXXXXXXXXXXXXXXXX)»»»OOOOC)C)CXD^^

<XXXXXXXXXXXXXXXX30CXD0CO00CKD»»«CKDC^^

360

• Disconnection O Inward Pull • Impact Damage

350 340 330 Colum ID320 310 300

(a) Between 80 min and 90 min

100

99

98

97

96

95

94

93

0CKDCKD0CKDCKDC)CO300C00CKDC^

00000CKXXXXXXXXXXXXXXXX)0000»»«COC)00000(X>^^

C00C000C)000CXDCXDCOD(XOX)CKDC0«»»00^^ • Disconnection O Inward Pull • Impact Damage

360 350 340 330 Colum ID320 310 300

(b) Between 90 min and 100 min

Figure 3-63. Locations of floor/wall disconnections and pull-in forces used between

80 min and 100 min of Case B temperature for south wall of WTC 1.

98 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

ANSYS ANSYS

^FL95

^FL93

-FL91

COL359

-FL99 —FL97

-FL95

-FL93

^FL91

(a) Vertical displacement (downward displacement (b) Out-of-plane displacement (inward displacement

is negative, 10X displacement magnification) is positive, 10X displacement magnification)

*ird 7«no dt 4800 sec (MIST i

(c) Axial force in columns (compressive is negative, 10X displacement magnification)

COL359

I

ANSYS

iilliliiiniiljilf/^^

iLed South Wall - "Jpoer Bound ?emp at A90D sec {MIST w/ 6kip)

(d) Plastic strain in columns (compressive strain

is negative, 10X displacement magnification)

ANSYS

COL359

(KOAVCI

^

.^FL99

.>. ^FL97

-FL93

I'i ' .^FL91i

und Tenp at -1800 sec (NIST w/ fikip)

(e) Creep strain in columns (compressive strain is negative, 10X displacement magnification)

Figure 3-64. Response of isolated south wall model of WTC 1 at 80 min of Case B

temperature condition with floor/wall disconnections and 6 kip pull-in forces over five

floors.

NISTNCSTAR 1-6D. WTC Investigation 99
Chapter 3

ANSYS

COL359

— FL97

-FL95

-FL93

-FL91

COLS59 ANSYSI

—FL97 —FL95

^FL93

-FL91

(a) Vertical displacement (downward displacement (b) Out-of-plane displacement (inward displacement

is negative, 10X displacement magnification) is positive, 10X displacement magnification)

ONCOL359

ANSYSI

(in./in.)

(c) Axial force in columns (compressive is negative, 10X displacement magnification)

(d) Plastic strain in columns (compressive strain

is negative, 10X displacement magnification)

COL359

ANSYS

IL359 II gj

iiiiiiii

(e) Creep strain in columns (compressive strain is negative, 10X displacement magnification)

Figure 3-65. Response of isolated south wall model of WTC 1 at 90 min of Case B

temperature condition with floor/wall disconnections and 6 kip pull-in forces over five

floors.

100 NISTNCSTAR 1-6D. WTC Investigation
Isolated Wall and Core Model Analyses

ANSYS

COL359

I

» _ ^FL99

WTCl Isolated S3i:th Wall - Uc 000 sec (N:ST w/ fikio)

(a) Vertical displacement (downward displacement (b) Out-of-plane displacement (inward displacement

is negative, 10X displacement magnification) is positive, 10X displacement magnification)

ANSYS

COL359

I

^ i

^FL97

^FL95

^FL93

^FL91

(c) Axial force in columns (compressive is negative, 10X displacement magnification)

WTCl Isolated South Wall - Uooer Bound Temo at 6000 sec (NIS7 w/ 6kiD)

(d) Plastic strain in columns (compressive strain

is negative, 10X displacement magnification)

ANSYS

COL359 „«i!lllllH«l!!!lii '".^-o""

olaL-d Soi.t.h Wall - Uooer Bound Teno at 6000 sec (NIST w/ 6itLp)

(in./in.)

(e) Creep strain in columns (compressive strain is negative, 10X displacement magnification)

Figure 3-66. Response of isolated south wall model of WTC 1 at 100 min of Case B

temperature condition with floor/wall disconnections and 6 kip pull-in forces over five

floors.

NISTNCSTAR 1-6D, WTC Investigation 101
Chapter 3

350

0360 350 340 330 320 310 300

Column ID

Figure 3-67. Axial load in columns between Floors 98 and 99 of isolated south wall

model of WTC 1 at 80 min, 90 min, and 100 min of Case B temperature condition with

floor/wall disconnections and 6 kip pull-in forces over five floors (compression is positive).

3.2.2 FEA of WTC 2 Exterior Wall

Case C Temperature Condition

Figures 3-68 and 3-69 show Case C temperature distributions in the columns of the isolated east exterior

wall of WTC 2. The highest temperature, 850°C, occurred at 60 min in Column 303 between Floor 81

and Floor 82 for Case C temperature condition. Column temperatures were higher on the inside face of

the exterior wall. Figure 3-70 shows the locations of the out-of-plane supports for Case C conditions at 60 min.

The vertical and the out-of-plane displacements at the end of the gravity load step after aircraft impact

and at the end of each temperature step are shown in Figs. 3-71, 3-72, 3-73, and 3-74. The maximum

vertical displacement of 3.6 in. occurred at Column 301 at Floor 90 at 60 min. The maximum out-ofplane deflection of 4.0 in. occurred at Column 302 at Floor 82 at 60 min (out-of-plane displacement is positive outward). The south side of the isolated east exterior wall displaced vertically after aircraft impact more than other parts of the east wall, as the impact damage was concentrated mostly on the

southeast comer of the WTC 2. The maximum vertical displacement shifted to the north during the

heating period. As time approached 60 min after the aircraft impact, the columns on the north side

buckled, and the out-of-plane displacement increased.

The axial load distributions of the columns at the end of the gravity load step and each 10 min time

interval are shown in Figs. 3-75 and 3-76. The maximum axial load occurred at Column 332 between

Floor 83 and Floor 84 at 50 min. The axial load in this column increased from 330 kip after the aircraft

102 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

impact to 750 kip at 50 min. The axial load on the buckled columns on the north side of the isolated wall

remained approximately constant throughout the temperatijre time history.

To consider the effect of load redistribution within the tower, the same corrective technique described

earlier in this chapter for WTC 1 was used. The axial loads in columns between Floor 83 and Floor 84 in the isolated east wall model were compared with those obtained from the preliminary global model

analysis without creep and with Case C, temperature and impact damage conditions (Appendix C).

Column loads obtained from the preliminary global model and isolated exterior wall model at 60 min are shown in Fig. 3-77. The difference between the two column loads was applied to the columns of the

isolated wall model at Floor 84 as corrective loads. The resulting vertical and out-of-plane displacements

are shown in Fig. 3-78. The additional column loads increased the maximum vertical displacement by

only 0.1 in., and the maximum out-of-plane displacement by less than 0.1 in.

Also as described earlier for the WTC 1 isolated wall model, a push-down analysis of the WTC 2 isolated

exterior wall model was performed. At an additional 5.6 in. of vertical displacement the model failed to converge, and the analysis was terminated. The vertical and out-of-plane displacements at the end of

5.6 in. of push down are shown in Fig. 3-79. At the end of push down, the maximum total vertical

displacement increased to 9.4 in., and the maximum out-of-plane displacement increased to 17.2 in. Axial column loads are shown in Fig. 3-80. This figure also shows the location of the columns for which

the load-deflection relationships are shown in Fig. 3-81. As can be seen from Fig. 3-81, the buckled

columns on the north side of the isolated east exterior wall carried, on average, an additional 300 kip at 60

min temperatures, compared to 470 kip for the average of the entire east wall columns. The additional

axial loads on individual columns at different additional vertical displacements are shown in Fig. 3-82.

NIST NCSTAR 1-6D, WTC Investigation 103
Chapter 3

COL301 ANSYS,

iHU'iiK iilllillltr't II iunli

^ "C

0 148. li* 297.489 446.233 594. 9'7 74.372 223.116 3*71. 861 520.605 669.349

HIC2 Isolated Wall sodel 600s

(a) Outside at 10 min (b) Inside at 10 min

COL359 COL301 ANSYS \,,^„.,3 COL359 COL301

41= !:b i|:yi...i

iMiiiiiijiiiiiiiiijisiiiiiiiimiissiiiiiiit isnuiiiini

(c) Outside at 20 min

WTC2 Isolated Ball .Model 1200s .

(d) Inside at 20 min

COL359 COL301 ANSY-S,

llliiiffiiliilllil^

COL359 COL301

il{|i||{ijiniii|j|||h'!Ui{i|||jiiiii||iiiiiHmHiiiit|i

I Ill , .

I l l

I M i um / -C

0 185.717 371.434 557.151 742.868 92.858 278.575 464.292 650. COS 835.726

WTC2 Isolated Wall .Model 1800s

(e) Outside at 30 min (f) Inside at 30 min

Figure 3-68. Column temperatures on the east wall of WTC 2 for Case C temperature

condition at 10 min, 20 min, and 30 min.

104 NIST NCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

COL301 ANSYS,

(a) Outside at 40 min

(e) Outside at 60 min (f) Inside at 60 min

Figure 3-69. Column temperatures on the east wall of WTC 2 for Case C temperature

condition at 40 min, 50 min, and 60 min.

NISTNCSTAR 1-6D. WTC Investigation 105
Chapter 3

106 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

COL359

I —FL85

, ' —FL83

:' r/— FL81 " —FL79

^--J--fr'lL^':n ^FL77

.:: .^.1 /.iii-rl nZZ'=z iTCact

(a) After aircraft impact (b) At 1U mm

COL359

:r-,ia-ea »<»el 12CCs

ANSYS.

'':.^FL85

;.i::^FL83

FL81

FL79

'-^rtl1-nffii^^FL77

(c)At 20 min (d) At 30 min

(e) At 40 min (f) At 50 min

Figure 3-71. Vertical displacement of isolated east wall model of WTC 2 for Case C

temperature distribution (downward displacement is negative; displacements scaled ten

times).

NISTNCSTAR 1-6D. WTC Investigation 107
Chapter 3

ANSYS

JAN 12 2005 . 07:59:04

^FL85

^FL83

MN

[I —FL81

^FL79

. —FL77

MX

(in.) -.396007

-.792013 0

NODAL SOLUTION

STEP=14

SUB =1 TIME=90

UZ (AVG) RSYS=0

DMX =5.339

SMN =-3.564

-2.772 -1.96 -2.376 WTC2 Isolated Wall Model 3600s

Figure 3-72. Vertical displacement of isolated east wall model of WTC 2 for Case C

temperature distribution at 60 min (downward displacement is negative; displacements

scaled ten times).

108 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

ANSYS

COL359

1— FL85. —FL83 —FL81 —FL79

(a) After aircraft impact (b) At 10 min

(e) At 40 min (f) At 50 min

Figure 3-73. Out-of-plane displacement of isolated east wall model of WTC 2 for Case C

temperature condition (inward displacement is positive; displacements scaled ten times).

NISTNCSTAR 1-6D, WTC Investigation 109
Chapter 3

NODAL SOLUTION

STEP=14

SUB =1 TIME=90

UY (AVG) RSYS=0

DMX =5.339

SMN =-4.048

SMX =.210223

ANSYS

COL359

-.262958

.736139 .210223 WTC2 Isolated Wall Model 3600s

Figure 3-74. Out-of-plane displacement of isolated east wall model of WTC 2 for Case C

temperature distribution at 60 min (inward displacement is positive; displacements

scaled ten times).

110 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(c)At20min (d)At30min

Figure 3-75. Axial load on columns of isolated east wall model of WTC 2 under Case C

temperature condition (compression is negative).

NISTNCSTAR 1-6D. WTC investigation 111
Chapter 3
Isolated Wall and Core Model Analyses

700

Global Model

Isolated Exterior Wall Model

-100

360 350 340 330

Column ID

320 310 300

Figure 3-77. Comparison of axial load in columns at Floor 83 of isolated east wall model

of WTC 2 at 60 min for Case C temperature conditions and the global model without

creep for Case Ci conditions (compression is positive).

(a) Vertical displacement

(Downward displacement is negative)

(b) Out-of-plane displacement

(Inward displacement is positive)

Figure 3-78. Vertical and out-of-plane displacements of isolated east wall model of

WTC 2 after column forces were corrected to those of global modal without creep for

Case Ci conditions (displacements scaled ten times).

NISTNCSTAR 1-6D, WTC investigation 113
Chapter 3

(a) Vertical displacement (b) Out-of-plane displacement

(downward displacement is negative) (Inward displacement is positive)

Figure 3-79. Vertical and out-of-plane displacements of isolated east wall model of

WTC 2 after Case C temperature condition and push down analysis (displacements

scaled five times).

Figure 3-80. Axial load on east wall columns of isolated east wall model of WTC 2 after

Case C temperature condition and push-down (compression is negative).

114 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

500

9- 400 Q.

D

03O

300 ^

COg

CD >_ 200

COc

o

-o<

100

J

1

1 , J > »

^^^^

^1 1 1

1

///

' X„ 1 X xv

X,, i -*- Column 1 — 1 —Column 6 !

- Average of last 1 0 columns ] Average of all columns 1

i

\ \ \ 0 1 2 3 4 5 6

Additional Vertical Displacement (in)

Figure 3-81. Additional vertical load versus additional vertical displacement during

push-down analysis of isolated east wall model of WTC 2 for Case C temperature

condition (compression is positive; see Fig. 3-80 for column locations).

900

T3

COO

3 500

I 400

I 300

o

D

<

200

100

0

L ^m^jUf^y^ _ _ _

-^Additional displacement of 2.7 in

1 _ Additional displacement of 3.8 in _ -^Additional displacement of 5.6 in

360 350 340 330 320

Column ID

310 300

Figure 3-82. Variation of additional vertical load applied to columns of isolated east wal

model of WTC 2 at different levels of additional vertical displacements imposed after

Case C temperature condition (compression is positive).

NISTNCSTAR 1-6D, WTC Investigation 115
Chapter 3

Case D Temperature Condition

Figures 3-83 and 3-84 show Case D temperature distributions in the columns of the isolated east exterior

wall model of WTC 2. The highest temperature, 845°C, occurred at 20 min in Column 307 between

Floor 81 and Floor 82. Column temperatures were higher on the inside face of the exterior wall. Figure

3-85 shows the locations of the out-of-plane supports for Case D conditions at 60 min.

The vertical and the out-of-plane displacements at the end of the gravity load step after aircraft impact

and at the end of each temperature step are shown in Figs. 3-86, 3-87, 3-88, and 3-89. The maximum

vertical displacement of 3.2 in. occurred at Column 359 at Floor 90 immediately after aircraft impact.

The maximum out-of-plane displacement of 7.8 in. occurred at Column 359 at Floor 81 at 60 min. (The

out-of-plane displacement is positive inward.) The south side of the isolated exterior wall displaced

vertically after aircraft impact more than other parts of the east wall, as impact damage was concentrated

mostly on the southeast comer of the WTC 2. As time approached 60 min, the columns on the south side

buckled, and the out-of-plane displacements increased.

The axial load distributions on the columns at the end of the gravity load step and each time interval are shown in Figs. 3-90 and 3-91. The maximum axial load occurred at Column 301 between Floor 82 and

Floor 83 at 10 min. The axial load in this column increased from 200 kip after aircraft impact to 920 kip

at 10 min. The axial load of 920 kip was very close to the theoretical local buckling load of 985 kip for Column 301 at 3 14 °C and less than the yielding or Euler buckling load of the column. Since local buckling of plates in exterior columns could not be captured by the beam elements that were used in the

model of the exterior wall, the model overestimated the buckling capacity of exterior columns. The axial

loads on the buckled columns on the south side of the isolated wall remained approximately constant throughout the temperature time history.

To consider the effect of load redistribution within WTC 2, the same corrective technique as described

earlier in this chapter for WTC 1 was used. The axial loads at 60 min in columns between Floor 83 and

Floor 84 in the isolated exterior wall model were compared to the corresponding values from the global

model without creep and with Case C, structural damage condition and Case Di temperature condition, as shown in Fig. 3-92. The difference between the two curves in Fig. 3-92 was then apphed to the columns

at Floor 84 as corrective loads. The resulting vertical and out-of-plane displacements are shown in Fig. 3-93. As can be seen, the additional loads increased the maximum vertical displacement by 0.4 in. and the maximum out-of-plane displacement by about 0.8 in.

Also as described earlier for the WTC 1 isolated wall models, a push-down analysis of the WTC 2

isolated exterior wall model was performed. At an additional 5.3 in. of vertical displacement the model

failed to converge, and the analysis was terminated. The vertical and out-of-plane displacements at the

end of 5.3 in. of push down are shown in Fig. 3-94. At the end of push down, the maximum vertical

displacement reached 8.0 in. and the maximum out-of-plane displacement reached 26.1 in. Figure 3-95

shows the column loads. This figure also shows the location of the columns, for which the loaddeflection relationships are shown in Fig. 3-96. As can be seen from Fig. 3-96, the buckled columns on

the south side of the isolated east exterior wall carried, on the average, an additional load of 410 kip at 60

min, compared to 630 kip for the average of the entire east wall columns. The additional axial loads on

individual columns at different levels of additional vertical displacements are shown in Fig. 3-97.

116 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(a) Outside at 10 min

COL301 /^^i

WTC2 Isolated Kali Model 600s

(b) Inside at 10 min

(c) Outside at 20 min

COL359 COL301 ANSYS

llli|i|l!!illl|||||HII{i|H|lil!

i*TC2 Jsalated Wall y.ia&l 120

(d) Inside at 20 min

COL359

r?HP=:sA7ua£S ItCK-O >lAX-e39.<22

COL301 '^SYS

JAN 11 2005 16:11:55

II il Min ! nil i|

iiiiiii:ri;j! illllll|:i!IIU<-M!ll lll|l|ll||fgM||l| 1

J

0 186.538

93.269

VfTC? Isolated Wall vodel 1800s 1

(e) Outside at 30 min (f) Inside at 30 min

Figure 3-83. Column temperatures on the east wall of WTC 2 for Case D temperature

condition at 10 min, 20 min, and 30 min.

NISTNCSTAR 1-6D. WTC Investigation 117
Chapter 3

COL301 ANSYS

iillil WliiilUllliii

(a) Outside at 40 min (b) Inside at 40 min

COL359 1 COL301 ANSYS COL359 COL301

HMiii mh mw mm

ll!!iii!!'i!!^4!l!|U.|l!i!p^i!!;;||||H!i||!lij||liii!i

(c) Outside at 50 min

0 171.617 343.235 514.. B5.809 257.426 429.043

WTC2 Isolated Wall Model 30005

686.47

(d) Inside at 50 min

(e) Outside at 60 min

COL359 COL301

77.708 233.125

WTC2 Isolated Wall ^^odel 3600s

(f) Inside at 60 min

Figure 3-84. Column temperatures on the east wall of WTC 2 for Case D temperature

condition at 40 min, 50 min, and 60 min.

118 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

Figure 3-85. Location of the out-of-plane supports and floor/wall disconnections

between exterior wall and the floor (WTC 2 east wall for Case D conditions at 60 min).

NISTNCSTAR 1-6D, WTC Investigation 119
Chapter 3

(a) After aircraft impact (b)At10min

(c) At 20 min (d) At 30 min

(e) At 40 min (f) At 50 min

Figure 3-86. Vertical displacement of isolated east wall model of WTC 2 for Case D

temperature condition (downward displacement is negative; displacements scaled ten

times).

120 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

Figure 3-87. Vertical displacement of isolated east wall model of WTC 2 for Case D

temperature condition at 60 min (downward displacement is negative; displacements

scaled ten times).

NISTNCSTAR 1-6D, WTC Investigation 121
Chapter 3

(a) After aircraft impact (b) At 10 min

(c) At 20 min (d) At 30 min

(e) At 40 min (f) At 50 min

Figure 3-88. Out-of-plane displacement of isolated east wall model of WTC 2 for Case D

temperature condition (inward displacement is positive; displacements scaled ten times).

122 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

NODAL SOLUTION

STEP=14

SUB =1 TIME=90 UY (AVG) RSYS=0

DMX =8.206

SMN =-7.825

SMX =6.065

COL359

ANSYS

JAN 11 2005

16:39:10,.^

-7.825 -4.738

-6.281 WTC2 Isolated Wall Model 3600s

Figure 3-89 Out-of-plane displacement of isolated east wall model of WTC 2 for Case D

temperature condition at 60 min (inward displacement is positive; displacements scaled

ten times).

NISTNCSTAR 1-6D, WTC Investigation 123
Chapter 3

(e) At 40 min (f) At 50 min

Figure 3-90. Axial load on east wall columns of isolated east wall model of WTC 2 for

Case D temperature condition (compression is negative).

124 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

Figure 3-91. Axial load on east wall columns of isolated east wall model of WTC 2 for

Case D temperature condition at 60 min (compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 125
Chapter 3

Figure 3-92. Comparison of axial load in columns at Floor 83 of isolated east wall model

of WTC 2 at 60 min for Case D temperature conditions and the global model without

creep for Case Ci structural damage condition and Case Dj temperature condition

(compression is positive).

(a) Vertical displacement

(downward displacennent is negative)

COL359

WTC2 Isolated Wall .Yodel Update Axial Fo

(b) Out-of-plane displacement

(inward displacement is positive)

Figure 3-93. Vertical and out-of-plane displacements of columns of isolated east wall

model of WTC 2 after column forces were corrected to those of global model without

creep for Case Cj structural damage condition and Case Dj temperature condition

(displacements scaled ten times).

126 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(a) Vertical displacement (b) Out-of-plane displacement

(downward displacement is negative) (inward displacement is positive)

Figure 3-94. Vertical and out-of-plane displacements of isolated east wall model of

WTC 2 after Case D temperature condition and push down (displacements scaled five

times).

Figure 3-95. Axial load on east wall columns of isolated east wall model of WTC 2 after

Case D temperature condition and push down (compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 127
Chapter 3

Q.

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o

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600

500

400

300

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Additional Vertical Displacement (in)

Figure 3-96. Additional vertical load applied to columns versus additional vertical during

displacement for push-down analysis of isolated east wall model of WTC 2 for after Case

D temperature condition (compression is positive; see Fig. 3-95 for column locations).

D

<

300

200

100

0

Additional displacement of 3.7 in Additional displacement of 4.7 in •Additional displacement of 5.3 in

360 350 340 330

Column ID

320 310 300

Figure 3-97. Variation of additional vertical load applied to columns of isolated east wal

model of WTC 2 at different levels of additional vertical displacements imposed after

Case D temperature condition (compression is positive).

128 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

Pull-in Forces to Cause Observed Bowing

As discussed in Section 2.5, the pull-in forces and their locations and the calculated floor/wall

disconnections and pull-in locations were updated based on the observations from the photographs and

videos. This section describes the analyses performed on the isolated wall model to estimate the

magnitude of pull-in forces on the east wall of WTC 2, which would result in an inward bowing shape

similar to that estimated from the photographs and videos. The estimated pull-in forces were used in the

global analysis with Case D temperature condition.

The load steps that were used in the current analyses are similar to the load steps used in the earlier wall

runs. At the beginning of each temperature load step, disconnections and lateral pull-in forces were

applied to each floor connection to the east wall, as shown in Section 2.5. The magnitude and the

distribution of the pull-in forces were obtained by trial and error. The magnitude of the pull-in force was

kept constant till the end of the analysis, unless the column-floor connection fully disconnected before the

analysis ended; at which point the pull-in force was set to zero. For each trial, the wall model was

analyzed from the beginning (time = 0 min), accounting for large deflections and temperature-dependent

plasticity and creep. The out-of-plane displacements calculated at the end of 20 min and 50 min were compared to the displacements estimated at the same points in time from the photographs, as shown in Fig. 3-98.

83

82

61

80

79

78

77

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0

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View blocked by another building (a) Displacement measurements at 9:21 a.m. (18 min after impact)

83

82

81

80

79

78

77

II II II II II II

7 4 4 (1 II II

7 K

0 ii

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-5

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BIcLktrd h\ jnclhcr hidi; View blocked by another building (b) Displacement measurements at 9:53 a.m. (50 min after impact)

Figure 3-98. Out-of-plane displacements of the east wall of WTC 2 estimated by NIST

from photographs (inward displacement is positive; displacements are in in.).

NISTNCSTAR 1-6D, WTC Investigation 129
Chapter 3

For the first set of trials, the pull-in forces were assumed to be uniformly distributed over the entire width

of the model. Two different magnitudes for pull-in forces were tried: 0.5 kip and 5.0 kip. The analysis

for 0.5 kip ran to 32 min, at which point it failed to converge. As shown in Fig. 3-99(a), the wall

primarily bowed outward at 20 min (positive displacement direction is inward). These results disagreed

with what was observed in the photographs and videos, indicating that the assumed magnitude of pull-in

force of 0.5 kip was not sufficient to cause inward bowing. In a second trial, the 5.0 kip pull-in force was

used. This analysis ran to 18 min, at which point it failed to converge. Contrary to the first trial with

0.5 kip pull-in force, the wall bowed inward, as shown in Fig. 3-99(b). The maximum inward

displacement in this trial was 3 1 in. This value is about three times larger than the displacement

estimated from photographs, indicating that the 5.0 kip pull-in force is greater than the actual magnitude

of pull-in force. Based on these two runs, it was concluded that the magnitude of the pull-in forces for a uniform distribution is between 0.5 kip and 5.0 kip.

(a) Pull-in force = 0.5 kip (b) Pull-in force = 5.0 kip

t = 20min t=18min

Figure 3-99. Out-of-plane displacement of isolated east wall model of WTC 2 with 0.5 kip and 5.0

kip pull-in force with uniform magnitude distribution at 20 min and 18 min (inward displacement is positive).

Pull-in force = 0.5 kip

t = 32 min

Figure 3-100. Out-of-plane displacement of isolated east wall model of WTC 2 with 0.5 kip pull-in

force with uniform magnitude distribution at 32 min (inward displacement is positive).

130 NISTNCSTAR 1-6D. WTC Investigation
Isolated Wall and Core Model Analyses

From these two runs, it was also possible to learn about the distribution of the pull-in forces over the

width of the east wall. When a unifonn distribution of a 0.5 kip pull-in force was used at 20 min over the

entire width of the east wall, the resuking out-of-plane displacements were inward on the south side and

outward on the north side of the wall, as shown in Fig. 3-99. The primary reasons for the outward

bowing on the north side of the east wall are as follows: (1) the higher temperatures in the north side of

the wall resulted in restrained thermal expansion and larger column loads; (2) the higher temperatures of

the inside face of the columns, relative to the outside, caused higher plastic and creep strains and resuhed

in differential shortening of the inside relative to the outside; and (3) the plastic softening and creep of the

inside caused an outward shift in the neutral axis, and a resulting outward bow of the columns. This

phenomenon can be seen in the displacement results presented in Figs. 3-99 and 3-100, where inward

displacements on the south side of the east wall became smaller and smaller and eventually changed to outward displacements toward the north side of the east wall. Consequently, a simple non-uniform pullin force distribution was selected with higher loads on the north side to ensure inward bowing as observed

in photographs and videos.

Two cases were analyzed for the second set of trials. In the first case, the magnitude of the pull-in forces on the south half of the east wall was set to 1 .0 kip and the magnitude of the pull-in forces on the north

half was set to 4.0 kip. The wall analysis with these pull-in force magnitudes ran to 60 min.

Figure 3-101 shows the out-of-plane displacements at different stages of the analysis. As can be seen, the

maximum inward bowing was 7.5 in. at 20 min, located approximately at the middle of Floor 81 of the

east wall. This agreed well with the observed displacements, which showed maximum inward

displacement of about 10 in. around the middle of Floor 81. In the earher trial with a unifonn 0.5 kip

magnitude of pull-in force, the inward bowing started to decrease with increasing time after 20 min, and

at around 40 min it bowed outward The bowing at 50 min was mostly outward, disagreeing with the

observed displacements. In the second trial, the magnitude of the pull-in force on the south half was

increased from 1 .0 to 1.5 kip, and on the north half was increased from 4.0 to 5.0 kip. This analysis ran to 50 min. at which point the analysis failed to converge. Figure 3-102 shows the magnitude of inward

bowing at different stages of the analysis. The maximum inward bowing in this trial was 9.5 in. at 20

min, located approximately at the middle of Floor 81 of the east wall. This result agreed well with the

observed displacements. The inward bowing continued to increase with time and reached a maximum of

37 in. at 50 min. As seen in Fig. 3-102, the location of the maximum displacements agreed well with the observations. However, the magnitude of the calculated displacements was about twice the magnitude of

the observed displacements.

From these trial runs, it was concluded that the magnitude of pull-in forces ranged from 1.0 kip to 1.5 kip on the south half and from 4.0 kip to 5.0 kip on the north half of the east wall. Based on these ranges, and

also considering the possible increase in column loads of the east face after impact for Case D conditions,

a pull-in force of 1 .0 kip on the south half and 4.0 kip on the north half of the east wall was initially

selected for the global model analysis with creep. As will be discussed in Chapter 4, at 30 min, the

magnitude of the pull-in force was increased to 1.5 kip on the south half and decreased to 3.0 kip on the

north half of the east wall and kept constant after that time.

NISTNCSTAR 1-6D, WTC Investigation 131
Chapter 3

(a) At lU mm (b) At20 min

(e) At 50 min (f) At 60 min

Figure 3-101. Out-of-plane displacement of isolated east wall model of WTC 2 with

nonuniform pull-in force with magnitude of 1.0 kip on the south half and 4.0 kip on the

north half (inward displacement is positive).

132 NISTNCSTAR 1-6D. WTC Investigation
Isolated Wall and Core Model Analyses

COL359

I CAEAI

.213C3 .164335 1.842

.255652 ;.3:3 2.3

iast Wail -rd»r Severe Case Da.*age ard

(a) At 10 min (b) At20 min

(e) At 50 min

Figure 3-102. Out-of-plane displacement of isolated east wall model of WTC 2 with

nonuniform pull-in force with magnitude of 1.5 kip on the south half and 5.0 kip on the

north half (inward displacement is positive).

NISTNCSTAR 1-6D, WTC Investigation 133
Chapter 3

3.3 CORE COLUMN SHORTENING AND DOWNWARD DISPLACEMENT OF

CORE

To examine whether or not the core columns shortened and the core displaced downward when subjected

to fire-induced temperature loads, the core models were isolated from the global models of WTC 1 and

WTC 2. The isolated core models extended from Floor 89 to Floor 106 for WTC 1 and from Floor 73 to Floor 106 for WTC 2, and did not include any parts of their hat trusses. At the base of the models,

vertical springs connected Floor 89 and Floor 73 to fixed ground; the spring stiffness represented the

vertical stiffness of the columns below. The isolated core models included core columns, core beams, and

core slabs, as in the global models (see Chapter 4 for details).

The WTC 2 core model was restrained in two horizontal directions at every floor level to represent the

lateral restraint of the exterior walls. Without the lateral restraints, the WTC 2 core model would tilt significantly, due to the extensive impact damage to the southeast part of the core. The WTC 1 core model was not restrained in the horizontal directions at floor levels.

Gravity dead and live loads were directly obtained from the global models and applied to the core model

nodes. Internal forces and moments of the columns of Floor 1 06 of the global models after aircraft impact were imposed at the ends of the Floor 106 columns of the isolated core models. Only the Case A

structural damage condition was used for the WTC 1 core model, and only the Case C structural damage

condition was used for the WTC 2 core model. The isolated core models with Case B and Case D

structural damage conditions were also run, but the models did not converge, even with lateral restraints.

The models were then subjected to two temperature conditions for each tower: Case A and Case B (for

WTC 1) and Case C and Case D (for WTC 2). Temperature data were provided at 10 min intervals up to 100 min for WTC 1 and up to 60 min for WTC 2.

Since the models included only the core, the load transfer between the core and the exterior wall through

either the hat truss or floors was not captured.

(a) WTC 1 (b) WTC 2

Figure 3-103. Isolated core models.

134 NIST NCSTAR 1-6D, WTC Investigation

il
Isolated Wall and Core Model Analyses

3.3.1 FEA of WTC 1 Core

Case A Temperature Condition

Figures 3-104 to 3-1 1 1 show the vertical displacements of the WTC 1 isolated core model subjected to Case A temperatures from aircraft impact to 100 min. At 30 min, the vertical displacement of the

northwest comer at Column 501 became large above Floor 98, and grew larger with time. The core

started to tilt toward the northwest comer at 30 min, and the analysis was terminated due to nonconvergence. The analysis was restarted at 30 min by restraining comer Column 501 in the horizontal

directions at floor levels above Floor 98 to represent lateral restraint from the exterior walls and office

floors. At 100 min, the maximum vertical displacement of 21.7 in. occurred at Column 501. Figures

3-1 14 and 3-115 show axial loads and plastic strains in the core columns at 100 min. Columns at the

northwest comer experienced large plastic strains. The maximum plastic strain was about 14 percent.

The vertical displacement at Floor 106 at 100 min ranged from 3.3 in. to 21.7 in. The maximum vertical

displacement of the south side was limited to 1 1.2 in. at Column 1004. The average vertical displacement

of Floor 106 was 7.4 in. The average vertical displacement of the south side at Floor 106 was 6.0 in. Considering the average vertical displacement of 5 in. after the aircraft impact, the average additional

downward displacement of the core due to thermal loads was about 2 in.

To determine the additional axial load-carrying capacity of the core, the isolated core model at 100 min

was pushed down by imposing additional incremental vertical displacement. The analysis was converted

from a force-control analysis to a displacement-control analysis by imposing the vertical displacements

calculated at 100 min under force control and then imposing additional vertical displacement increments on the top of the columns at Floor 106. The analysis was terminated when the additional vertical displacement reached 9.5 in. Figure 3-116 shows the total vertical displacements of the model at the end

of the push-down analysis. Figure 3-117 shows the relationship between the total additional vertical force and the additional vertical displacement. The additional vertical force reached its maximum at 7.2

in. of additional vertical displacement. Figure 3-118 shows the additional axial loads in columns of Floor

98 when the total additional vertical force is at its maximum. The maximum total additional vertical force

of 37,142 kip was about 95 percent of the total column force at Floor 98 prior to push-down. Therefore,

the core still had significant reserve capacity at the end of Case A temperature condition.

I

NISTNCSTAR 1-6D, WTC Investigation 135
Chapter 3

(a) North and east sides (b) South and east sides

Figure 3-104. Vertical displacement of isolated core model of WTC 1 after aircraft impact

(downward displacement is negative).

(a) North and east sides (b) South and east sides

Figure 3-105. Vertical displacement of isolated core model of WTC 1 for Case A

temperature condition at 10 min (downward displacement is negative).

136 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(a) North and east sides (b) South and east sides

Figure 3-106. Vertical displacement of isolated core model of WTC 1 for Case A

temperature condition at 20 min (downward displacement is negative).

(a) North and east sides (b) South and east sides

Figure 3-107. Vertical displacement of isolated core model of WTC 1 for Case A

temperature condition at 30 min (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 137
Chapter 3

KODAL SOLUTION

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(a) North and east sides (b) South and east sides

Figure 3-109. Vertical displacement of isolated core model of WTC 1 for Case A

temperature condition at 50 min (downward displacement is negative).

138 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

ANSYS

JAN 12 200 5 10:10:47

N

(in.)

(a) North and east sides (b) South and east sides

Figure 3-110. Vertical displacement of isolated core model of WTC 1 for Case A

temperature condition at 70 min (downward displacement is negative).

(a) North and east sides (b) South and east sides

(c) Northwest corner (b) South side

(5X displacement magnification) (5X displacement magnification)

Figure 3-1 1 1 . Vertical displacement of isolated core model of WTC 1 for Case A

temperature condition at 100 min (downward displacement is negative).

NISTNCSTAR 1-60, WTC Investigation 139
Chapter 3

(a) X-displacement of north and east sides (b) X-displacement of south and east sides

(c) Y-displacement of north and east sides (d) Y-displacement of south and east sides

Figure 3-112. Horizontal displacement of isolated core model of WTC 1 for Case A

temperature condition at 100 min.

140 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

-FL104 —FL102 -FLIOO

-FL98

i-FL96

i-FL90

(a) 500 series columns (b) 600 series columns

-FL104I —FL102; -FLIOO

'

(c) 700 series columns (d) 800 series columns

-FL104 —FL102 -FLIOO

-FL98

-FL96

(e) 900 series columns (f) 1000 series columns

I Figure 3-113. Axial load in columns of isolated core model of WTC 1 after aircraft impact

(compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 141
Chapter 3

ELEMENT SOLUTIOI STEP-13

SU3 =187 TIKE-6000

skis: TOP

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^OLpuo6^SYS

JAK 12 2005 — FL104 —FL102 — FLIOO

i- FL92 i— FL90

i^sbm (lb)

(e) 900 series columns (f) 1000 series columns

Figure 3-114. Axial load in columns of isolated core model of WTC 1 for Case A

temperature condition at 100 min (compression is negative).

142 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(c) 700 series columns (d) 800 series columns

(e) 900 series columns (f) 1 000 series columns

Figure 3-115. Plastic strain in columns of isolated core model of WTC 1 for Case A

temperature condition at 100 min (compressive strain is negative).

NISTNCSTAR 1-6D, WTC Investigation 143
Chapter 3

(a) North and east sides (b) South and east sides

Figure 3-116. Vertical displacement after push down of isolated core model of WTC 1 for

Case A temperature condition (downward displacement is negative).

40,000

Additional Vertical Displacement (in)

Figure 3-117. Total additional vertical load versus additional vertical displacement

during push-down analysis of isolated core model of WTC 1 for Case A temperature

condition (compression is positive).

144 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

Figure 3-118. Additional axial load (kip) in columns at Floor 98 when the total axial load

reached the maximum during push down analysis of isolated core model of WTC 1 for

Case A temperature condition (compression is positive).

Case B Temperature Condition

Figures 3-119 to 3-125 show the vertical displacements of the WTC 1 isolated core model subjected to Case B temperature condition. At 30 min, the vertical displacement of the south side above Floor 96

between Column 1004 and Column 1005 became large. At 100 min, the maximum vertical displacement was 44.2 in. on the south side at Column 1005.

Figures 3-127 and 3-128 show axial loads and plastic strains in columns at 100 min. The following

columns buckled: Column 904 spanning Floor 97 and Floor 98, Column 1004 spanning Floor 97 and

Floor 98, Column 1005 spanning Floor 95 and Floor 96, and Column 1006 spanning Floor 95 and

Floor 96. These columns also experienced large locahzed plastic strains.

The northeast comer, where the largest displacement occurred for Case A temperature condition, did not

displace significantly for Case B temperature condition. The vertical displacement at Floor 106 ranged

from 4.8 to 44.2 in. The average vertical displacement of Floor 106 was 1 1.9 in. The average

displacement of the south face was 20 in. Considering the 5 in. displacement after the aircraft impact, the

average additional downward displacement of the core due to thermal loads was about 7 in.

To determine the additional axial load-carrying capacity of the core, a push-down analysis was performed

for Case B temperature condition in the same manner as described for the isolated core model for Case A

temperature condition. The analysis was terminated when an additional vertical displacement of 9.4 in. was applied to the top. Figure 3-129 shows vertical displacements of the model at the end of analysis.

Figure 3-130 shows the relationship between the total additional vertical force and the additional vertical displacement. The total additional vertical force reached its maximum at an additional displacement of

4.9 in. Figure 3-131 shows the additional axial loads in columns of Floor 98 when the total additional

vertical force was at its maximum. The maximum total additional vertical force of 24,002 kip was about

NISTNCSTAR 1-6D. WTC Investigation 145
Chapter 3

61 percent of the total column force at Floor 98 prior to push-down. Thus, the reserve capacity of the core at the end of Case B temperature condition was substantial, but less than that of Case A temperature

condition.

(a) North and east sides (b) South and east sides

Figure 3-119. Vertical displacement of isolated core model of WTC 1 for Case B

temperature condition at 10 min (downward displacement is negative).

(a) North and east sides (b) South and east sides

Figure 3-120. Vertical displacement of isolated core model of WTC 1 for Case B

temperature condition at 20 min (downward displacement is negative).

146 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(a) North and east sides (b) South and east sides

Figure 3-121. Vertical displacement of isolated core model of WTC 1 for Case B

temperature condition at 30 min (downward displacement is negative).

(a) North and east sides (b) South and east sides

Figure 3-122. Vertical displacement of isolated core model of WTC 1 for Case B

temperature condition at 40 min (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 147
Chapter 3

(a) North and east sides (b) South and east sides

Figure 3-123. Vertical displacement of isolated core model of WTC 1 for Case B

temperature condition at 50 min (downward displacement is negative).

(a) North and east sides (b) South and east sides

Figure 3-124. Vertical displacement of isolated core model of WTC 1 for Case B

temperature condition at 70 min (downward displacement is negative).

148 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(a) North and east sides (b) South and east sides

(c) South side

{IX displacement nnagnification)

Figure 3-125. Vertical displacement of isolated core model of WTC 1 for Case B

temperature condition at 100 min (downward displacement is negative).

NISTNCSTAR 1-6D. WTC Investigation 149
Chapter 3

(a) X-displacement of north and east sides (b) X-displacement of south and east sides

(c) Y-displacement of north and east sides (d) Y-displacement of south and east sides

Figure 3-126. Horizontal displacement of isolated core model of WTC 1 for Case B

temperature condition at 100 min.

150 NISTNCSTAR 1-6D, WTC Investigation
508 50

STEP- I

:

sea -::-i9 08:50:43 -FL104

-FL102

-FLIOO

-FL98

-FL96

'-FL94

-FL92

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Isolated Wall and Core Model Analyses

JTCl Core (6C0 Column Lire) - Upper Bound '

08:50:43 -FL104

-FL102

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-FL96

-FL94

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pwiiiii,-. - i (lb)

500 series columns (b) 600 series columns

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^°l-PU06^Sp

-FL104

-FL102

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-FL98 —FL96

-FL94

-FL92

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(e) 900 series columns (f) 1000 series columns

Figure 3-127. Axial load in columns of isolated core model of WTC 1 for Case B

temperature condition at 100 min (compression is negative).

NISTNCSTAR 1-6D, WTC Investigation 151
Chapter 3

Figure 3-128. Plastic strain in columns of Isolated core model of WTC 1 for Case B

temperature condition at 100 min (compressive strain is negative).

152 NISTNCSTAR 1-6D, WTC Investigation
Isola ted Wall and Core Model Analyses

(a) North and east sides (b) South and east sides

Figure 3-129. Vertical displacement after push down of isolated core model of WTC 1 for

Case B temperature condition (downward displacement is negative).

30.000 ^ 25,000 --

Additional Vertical Displacement (in)

Figure 3-130. Total additional vertical load versus additional vertical displacement

relationship obtained from push down analysis of isolated core model of WTC 1 for

Case B temperature condition (compression is positive).

NISTNCSTAR 1-6D, WTC Investigation
Chapter 3

Figure 3-131. Additional axial load (kip) in columns at Floor 98 when the total axial load

reached the maximum during push down analysis of the WTC 1 core for Case B

temperature condition (compression is positive).

3.3.2 FEAof WTC 2 Core

Case C Temperature Condition

The isolated core model of WTC 2 was unstable after the aircraft impact damage, tilting excessively

towards the southeast comer. To simulate the restraining effect of office floors and the exterior walls, the

isolated core model was restrained in the horizontal directions at all floors.

Figures 3-132 to 3-133 show the vertical displacements of the WTC 2 isolated core model when

subjected to Case C temperature condition from just after the aircraft impact to 60 min. The vertical

displacement was always the highest at the southeast comer of the core as the aircraft impact severed the

southeast comer core columns in Floors 79 to 82. After aircraft impact damage, the vertical displacement

of the southeast comer was 5.6 in. This displacement increased to 6.1 in. at 60 min. Figures 3-134 and

3-135 show axial load and plastic strain in columns at 60 min. Columns at the southeast comer

experienced plastic strains immediately following aircraft impact. The maximum plastic strain in the

900-series core columns was 1.2 percent, and 0.5 percent in the 1000 series core.

The vertical displacement of the core at Floor 106 at 60 min ranged from 2.3 in. to 5.3 in. The maximum

vertical displacement of the southeast comer was less than 5.3 in. at Column 1001. The average vertical

displacement of Floor 106 at 60 min was 3.7 in., close to the 3.9 in. average vertical displacement after the aircraft impact. None of core columns buckled during thermal loading.

Similar to the WTC 1 isolated core models, the WTC 2 isolated core model was pushed down following

the analysis for Case C temperature condition to determine the additional axial load-carrying capacity of

the core. The analysis was terminated at an additional vertical displacement of 17.0 in. even though the core was still continuing to carry more axial load. The vertical displacements at the end of 17.0 in. pushdown are shown in Fig. 3-136. Figure 3-137 shows the relationship between the additional

154 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

displacements and the average additional vertical load of comer columns, comer and middle columns on

the east face, and all core columns (there column locations are shown in Fig. 3-136). The columns on the southeast comer of the isolated core at 60 min temperature condition carried an additional load of about

900 kip without failure, compared to about 1,500 kip for the average of the entire core columns prior to push-down. The additional load was about 1 .6 times that of the average load in Floor 82 columns at 60 min temperature condition.

NIST NCSTAR 1-6D. WTC Investigation 155
Chapter 3

(b) At 10 min

FL90 -

FL85 -

FL80 -

FL75 -'

WTC2 Core - Realistic Case Tempsrafjre at 1300 sec

(c) At 20 min (d) At 30 min

ANSTS

FL75

(e) At 40 min (f) At 50 min

Figure 3-132. Vertical displacement of isolated core model of WTC 2 for Case C

temperature condition (downward displacement is negative).

156 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

NISTNCSTAR 1-6D. WTC Investigation 157
Chapter 3

(a) 500 series columns (b) 600 series columns

(c) 700 series columns (d) 800 series columns

(e) 900 series columns (f) 1000 series columns

Figure 3-134. Axial load in core columns of isolated core model of WTC 2 for Case C

temperature condition at 60 min (compression is negative).

158 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

(a) 500 series columns (b) 600 series columns

ANSYS

701

- ANSYS

801 --=^j-=

ZPf.X (tZA-.-SI 708

net i

EPP-JC (KC3AVG> 807

SKK —.37CE-C3 1

£ n[j !

.,1

•

(in./in.) (in./in.)

WTci Cere (5CC C=i-xn.T Line) - ?€3iisci c Case sroerature at 36CC sec

(c) 700 series columns (d) 800 series columns

(e) 900 series columns (f) 1 000 series columns

Figure 3-135. Axial plastic strains in core columns of isolated core model of WTC 2 for

Case C temperature condition at 60 min (compressive strain is negative).

NISTNCSTAR 1-6D. WTC Investigation 159
Chapter 3

NODAL SOLUTION.; STEP=9

SUB =12438 TIME=3600

uz (AVG) •; RSYS=0 ' DMX =31.876

SMN =-22.239 ',

ANSYS

JAN 12 2005 08:40:55

Corner + middle

Columns

701-702, 801-802,

901-903, 1001-1003i

Corner columns

901-903, 1001-1003

(in.) -22.239 -17.297 -12.355 -7.413 -2.471 -19.768 -14.826 -9.884 -4.942 0 WTC2 Core - Best Estimate Temperature at 3600 sec

Figure 3-136. Vertical displacement after push down of isolated core model of WTC 2 for

Case C temperature condition (downward displacement is negative).

1,600

0 5 10 15 20

Additional Vertical Displacement (in)

Figure 3-137. Additional average vertical load versus additional vertical displacement

during push-down analysis of isolated core model of WTC 2 for Case C temperature

condition (compression is positive; core column locations are shown in Fig. 3-136).

160 NISTNCSTAR 1-6D, WTC Investigation

i
Isolated Wall and Core Model Analyses

Case D Temperature Condition

As mentioned in the previous section for Case C temperature condition, the isolated core model of WTC 2 was unstable after the aircraft impact damage, so the model was restrained in the horizontal directions.

Figures 3-138 to 3-139 show the vertical displacements of the WTC 2 isolated core model subjected to Case D temperamre condition from just after the aircraft impact to 60 min. The vertical displacement was

always the highest at the southeast comer of the core as the aircraft impact severed the southeast comer

core columns in Floors 79 to 82. After aircraft impact damage, the vertical displacement of the southeast comer was 5.6 in. This displacement increased to 8.2 in. at 60 min. Figures 3-140 and 3-141 show axial

load and plastic strain in columns at 60 min. Columns at the southeast comer experienced plastic strains immediately following aircraft impact. The maximum plastic strain in the 900-series core columns was

2.5 percent, and 0.7 percent in the 1000 series core columns.

The vertical displacement of the core at Floor 106 at 60 min ranged from 3.3 in. to 6.0 in. The maximum

vertical displacement of the southeast comer was less than 6.0 in. at Column 1001. The average vertical

displacement of Floor 106 after thermal loading at 60 min was 4.1 in., similar to the 3.9 in. average

vertical displacement after the aircraft impact. None of core columns buckled during thennal loading.

To determine the additional axial load-carrying capacity of the core, the isolated core model was pushed

down following the analysis for Case D temperature condition as described before. The top of the isolated core was pushed down an additional 30.0 in. The analysis was stopped even though the core was

continued to carry additional load. The vertical displacement at the end of 30.0 in. push-down is shown

in Fig. 3-142. Figure 3-143 shows the relationship between the additional vertical displacement and the

average additional vertical load on core columns, the comer columns, and the comer and middle columns

shown in Fig. 3-143. As it can be seen from Fig. 3-143 at 60 min temperature condition, the columns on

the southeast comer of the isolated core continued to carry, on the average, an additional load of about

1,200 kip without failure, compared to about 1,700 kip for the average of the entire core columns prior to push down. The additional load on the core columns was about 1.8 times that of the average load in Floor 82 columns at 60 min temperature condition.

The results of the isolated core models of WTC 2 show that significant downward displacement of the core and core column buckling are not likely to occur for WTC 2 during the global analysis.

NIST NCSTAR 1-6D, WTC Investigation 161
Chapter 3

After aircraft impact (b) At lU mm

(e) At 40 min (f) At 50 min

Figure 3-138. Vertical displacement of isolated core model of WTC 2 for Case D

temperature condition (downward displacement is negative).

162 NISTNCSTAR 1-6D, WTC Investigation

I
Isolated Wall and Core Model Analyses

Figure 3-139. Vertical displacement of isolated core model of WTC 2 for Case D

temperature condition at 60 min (downward displacement is negative).

NISTNCSTAR 1-6D, WTC Investigation 163
Chapter 3

(a) 500 series columns

708 701

(c) 700 series columns

ANSYS

(lb)

(b) 600 series columns

(d) 800 series columns

1008 1001

WTC2 Core {1000 Coia-nn Line) Temperature at 3600 sec

(e) 900 series columns (f) 1000 series columns

Figure 3-140. Axial load in core columns of isolated core model of WTC 2 for Case D

temperature condition at 60 min (compression is negative).

164 NISTNCSTAR 1-6D, WTC Investigation
Isolated Wall and Core Model Analyses

ELEMEKT SOLUTION 601 ANSYS

JAi; 15- 300 5

TIM=:=3600 EPPLX (i;0AVGI

DKX ^ti.20b 608

1

1

1

i

!

!

!

A. (in./in.;

WTC2 Core (600 Column Li ne) - Severe Case Te:i oerature at 3S00 sec

(a) 500 series columns (b) 600 series columns

(e) 900 series columns (f) 1000 series columns

Figure 3-141. Axial plastic strains in core columns of isolated core model of WTC 2 for

Case D temperature condition at 60 min (compressive strain is negative).

NISTNCSTAR 1-6D, WTC Investigation 165
Chapter 3

NODAL SOLUTION.! STEP=9 ' SUB =8367

" TIME=3600

UZ (AVG) RSYS=0 : DMX =48.416 I SMN =-41.149 I SMX =10.699 :

-41.149

ANSYS

JAN 13 2005 13:19:05

Corner + middle

Columns

701-702,801-802, i 901-903, 1001-1003

Corner columns

901-903, 1001-1003

i (in.) -29.627 -6.584

35.388 -23.866 -12.344 -.822749 WTC2 Core - Upper Bound Temperature after Push Down

Figure 3-142. Vertical displacement after push down of isolated core model of WTO 2 for

Case D temperature condition (downward displacement is negative).

2,000

D

o 1,500

Id

o

CD >

>

<

"toc

*-*— g

•

T3

5

1,000

500

''

1 1 1

1 1 «--' _„---T^

„..s ^

Corner

Corner+Middle

All Columns

1 10 15 20 25

Additional Vertical Displacement (in)

30

Figure 3-143. Additional average vertical load versus additional vertical displacement

during push-down analysis of isolated core model of WTC 2 for Case D temperature

condition, (compression is positive; core column locations are indicated in Fig. 3-142.)

166 NISTNCSTAR 1-6D. WTC Investigation