Progressive-Failure Analysis of Steel Building Structures under Abnormal Loads

234 Pages·2007·1.92 MB·English

by  Yuxin Liu

Progressive-Failure Analysis of Steel
Building Structures under Abnormal Loads

by

Yuxin Liu

A thesis
presented to the University of Waterloo
in fulfillment of the
thesis requirement for the degree of
Doctor of Philosophy
in
Civil Engineering

Waterloo, Ontario, Canada, 2007

©Yuxin Liu, 2007
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any
required final revisions, as accepted by my examiners.

I understand that my thesis may be made electronically available to the public.

ii
Abstract
Engineered structures are designed to resist all expected loadings without failure. However, structural
failures do occasionally occur due to inadequate design and construction, especially for extreme and
abnormal loads. This thesis concerns the progressive collapse of structures due to abnormal loading
events, and develops a method of advanced analysis for predicting the progressive collapse behaviour
of building structures in the plastic limit state.
A new procedure for progressive-failure analysis is developed that computes structural responses
accounting for geometric/material nonlinearities and axial/flexural/shear deformations. The nonlinear
behaviour of materials is discussed in detail. Combined-stress failure states and stiffness degradation
models are proposed to simulate plastic deformation of structural members. Elliptic force-
deformation relationships are employed to model the nonlinear material behaviour of members, and
corresponding model parameters are determined from published experimental data.
Having the proposed nonlinear model, a generic member stiffness matrix is derived taking into
account elastic-plastic bending, shearing and axial deformations. A modified moment distribution
method is employed to obtain the stiffness coefficients. A computer-based incremental-load nonlinear
analysis procedure is developed that progressively updates member stiffness using reduction factors
that simulate degraded stiffness behaviour. Studies are conducted to demonstrate the effectiveness of
the proposed method in predicting the progressive failure of structures under abnormal loading.
A general model of a compound element is proposed to consider the influence of semirigid
connections on the progressive failure of steel frameworks. The stiffness degradation of semirigid
connections is modeled by a moment-rotation relationship with four parameters. The stiffness
degradation of a compound element resulting from the combined influence of member plasticity and
nonlinear connection behaviour is modeled by a moment-rotation relationship with three parameters.
The results from the proposed analysis method involving semirigid connection behaviour are
compared with the results of other methods.
The proposed progressive-failure analysis method is threat-independent, in the sense that it is
initially assumed that some type of short-duration abnormal loading has caused local damage
represented by the removal of one (or more) critical member(s). The degree of damage to connections
due to member-end disengagement is accounted for by a so-called health index factor. Three types of
localized damage modes are investigated to identify different damage scenarios for the structure.
Account can be taken of the connection damage that occurs when members disengage from the
iii
structure. Account is taken of any debris loading that occurs when disengaged structural components
fall onto lower parts of the structure. The associated dynamic effect is taken into account for the
quasi-static analysis by utilizing an impact amplification factor. Any progressive collapse occurring
thereafter involves a series of failure events associated with topological changes.
The progressive-failure analysis procedure is based on the alternate-load-path method suggested in
the design and analysis guidelines of the General Services of Administration (GSA, 2003) and the
Department of Defense (DoD, 2005). The residual load carrying capacity of the damaged framework
is analyzed by incrementally applying prevailing long-term loads and impact debris loads. The
deterioration of structural strength is progressively traced to the state at which either global stability is
reached or progressive collapse to ground level occurs for part or all of the structure. The analysis
procedure is extensively illustrated for several planar steel moment frames, including rigid and
semirigid frames designed with and without consideration of seismic loading. The results obtained
demonstrate that the proposed method is potentially an effective tool for the analysis of steel building
structures under normal and abnormal loads.
Finally, with a view to improve modeling, the failure of a member cross-section under combined
bending moment, shearing force and axial force is modeled by an Euler-Lagrange energy functional
defining the three-dimensional stress distribution at failure. A corresponding combined-stress failure
surface is developed for bi-symmetrical cross-sections, and a related model is proposed to simulate
stiffness degradation. The interactive influence of bending moment, shear force and axial force is
investigated for rectangular and W-shape cross-sections, and the results are compared with test results
to demonstrate the significance of strain hardening and the contribution of the flange to shear
strength. In future extensions of the research work, it is envisioned that the 3-dimensional M-V-P
failure criterion will replace the 2-dimensional M-V and M-P failure criteria employed herein for
progressive-failure analysis.

iv
Acknowledgements
I would like to acknowledge the enthusiastic and meticulous supervision of Professors Donald E.
Grierson and Lei Xu, and their insightful discussions, comments and suggestions during my Ph.D
studies. Without their wisdom, guidance and patience, this thesis would have been impossible to
complete.

I greatly appreciate Professors Marianna Polak, Gord Savage, G. Wayne Brodland, and Sriram
Narasimhan for their comments and constructive suggestions, and to Professors S. T. Ariaratnam,
Reinhold M. Schuster, Roger Green, Wei-Chau Xie, Mahesh Pandey and Stanislav Potapenko for
their help.

Special thanks to Professor Bruce R. Ellingwood, of Georgia Institute of Technology, Atlanta, USA,
for serving as the external examiner and for improving the quality of my thesis.

I thank my colleagues, Yanglin Gong, Joel Martinez, Xianxun Yuan, Mohammad Safi, Ying An and
Hongtao Liu for their valuable discussions and help. In particular, I would like to acknowledge the
help of Ignac Zajac, Gloria Rose, Joyce King, and Clayton Morgan towards revising the draft of this
thesis.

Since a researcher cannot live on ideas and analyses alone, I cordially express my gratitude for the
generous financial support I have received: the research assistantships provided by the Natural
Sciences and Engineering Research Council of Canada; the graduate scholarships provided through
the Ontario Graduate Scholarship Program; the University of Waterloo Faculty of Engineering
Graduate Scholarships; the University of Waterloo President’s Graduate Scholarship for 2005-2006;
and the Teaching Assistantships granted by the Department of Civil Engineering.

Finally, I dedicate this thesis to my wife Hua Wang and my daughter Suya Liu. I am forever indebted
to them for their understanding, endless patience, encouragement, support, and sacrifice when it was
most required.

v
Table of Contents
Abstract.................................................................................................................................................iii
Acknowledgements................................................................................................................................v
List of Figures........................................................................................................................................x
List of Tables......................................................................................................................................xiv
Nomenclature.......................................................................................................................................xv
Chapter 1 Introduction...........................................................................................................................1
1.1 Project Failure....................................................................................................................1
1.1.1 Foreseen Project Failure...........................................................................................1
1.1.2 Unforeseen Project Failure.......................................................................................3
1.2 Design Considerations for Unforeseen Failures.................................................................5
1.2.1 Structural Integrity Design.......................................................................................6
1.2.2 Specifying Localized Resistance..............................................................................7
1.2.3 Alternate Load Paths................................................................................................8
1.3 Structural Analysis for Abnormal Loading........................................................................8
1.3.1 Structural Analysis Methods....................................................................................9
1.3.2 Progressive Collapse Analysis...............................................................................11
1.4 Objectives and Scope........................................................................................................12
1.5 Assumptions and Idealizations.........................................................................................13
1.6 Thesis Organization..........................................................................................................13
Chapter 2 Geometrical and Material Nonlinearity...............................................................................19
2.1 Geometrical Nonlinearity Associated with Shear Deformation.......................................19
2.1.1 Governing Differential Equation............................................................................20
2.1.2 Derivation of Elastic Stiffness Coefficients...........................................................23
2.2 Effects of Shear Deformation on Structural Response.....................................................27
2.2.1 Effect of Shear Deformation on Elastic Buckling..................................................28
2.2.2 Effect of Shear Deformation on Fixed-End Reactions...........................................30
2.3 Stiffness Degradation.......................................................................................................31
2.3.1 Force-Deformation Model......................................................................................32
2.3.2 Determination of Stiffness Degradation Factors....................................................33
Appendix 2.A Derivation of Flexibility Coefficients.............................................................34
Appendix 2.B Post-Elastic Stiffness Degradation..................................................................36
vi
2.B.1 Bending Stiffness Degradation...............................................................................36
2.B.2 Shearing Stiffness Degradation..............................................................................38
2.B.3 Axial Stiffness Degradation...................................................................................40
Chapter 3 Nonlinear Analysis of Steel Frameworks............................................................................50
3.1 Nonlinear Member Stiffness Matrix................................................................................50
3.2 Derivation of Member Stiffness Coefficients..................................................................51
3.2.1 Stiffness Coefficients due to End Rotations...........................................................51
3.2.2 Stiffness Coefficients due to End Translations.......................................................53
3.2.3 Stiffness Coefficients due to Axial Displacement..................................................54
3.2.4 Summary of Stiffness Coefficients.........................................................................55
3.3 Combined Stress States....................................................................................................57
3.3.1 Bending Moment plus Axial Force.........................................................................57
3.3.2 Bending Moment plus Shear Force.........................................................................60
3.4 Nonlinear Analysis Procedure..........................................................................................62
3.5 Example Studies...............................................................................................................63
3.5.1 Two-Span Continuous Beam..................................................................................64
3.5.2 Low-Rise Steel Building Framework.....................................................................66
Appendix 3.A Accounting for Bending Stiffness Degradation............................................68
3.A.1 Modified Moment Distribution Method.................................................................68
3.A.2 Member Stiffness Coefficients...............................................................................71
Chapter 4 Frameworks with Semi-rigid Connections..........................................................................84
4.1 Introduction......................................................................................................................84
4.2 Rotational Compound Element........................................................................................85
4.2.1 Series Element Model.............................................................................................85
4.2.2 Determining Connection Stiffness R .....................................................................86
c
4.2.3 Stiffness Degradation Factors.................................................................................88
4.3 Characteristics of Compound Rotational Element...........................................................89
4.4 Nonlinear Analysis of Frameworks with Semi-rigid Connections..................................93
4.5 Example Studies...............................................................................................................95
4.5.1 Example 1: Semi-rigid Portal Frame......................................................................95
4.5.2 Example 2: One-Bay Two-Storey Frame................................................................97
4.5.3 Example 3: Two-Bay Two-Storey Frame...............................................................99
4.6 Final commentary..........................................................................................................101
vii
Chapter 5 Progressive-Failure Analysis.............................................................................................117
5.1 Local Failure Modes and Debris Loading......................................................................117
5.1.1 Failure Modes of Components.............................................................................117
5.1.2 Impact Debris Loading.........................................................................................120
5.2 Damage Degree due to Local Collapse..........................................................................120
5.2.1 Connection damage..............................................................................................122
5.3 Progressive-Failure Analysis Procedure.........................................................................123
5.3.1 Load Combinations due to Abnormal Loading Events........................................123
5.3.2 Incremental-Load Analysis..................................................................................126
5.4 Example Case Studies....................................................................................................130
5.4.1 Example 1: Low-Rise Steel Frame.......................................................................131
5.4.2 Example 2: Internal Explosion in Medium-Rise (Los Angeles) Frame...............136
5.4.3 Example 3: Car/Truck Collision with Medium-Rise (Los Angeles) Frame.........137
5.4.4 Example 4: Airplane Crash into Medium-Rise (Los Angeles) Frame.................137
5.4.5 Example 5: Internal Explosion in Medium-Rise (Boston) Frame........................138
5.5 Commentary and Discussion..........................................................................................139
Chapter 6 Combined M-V- P Failure Criterion (Future Research)....................................................166
6.1 Introduction....................................................................................................................166
6.2 Energy Functional...........................................................................................................167
6.3 Stress-Strain Relationship at Failure State.....................................................................170
6.3.1 Euler-Lagrange Function......................................................................................170
6.3.2 Concave Function.................................................................................................171
6.4 Failure Criterion Accounting for M-V-P Interaction......................................................173
6.4.1 Internal Forces......................................................................................................173
6.4.2 Force-Deformation Relationships........................................................................176
6.4.3 M-V-P Yield-Failure Surface for Rectangular Sections.......................................178
6.4.4 M-V-P Yield-Failure Surface for Wide-Flange Sections.....................................180
6.5 Comparisons with Experimental Results........................................................................181
6.6 Combined Failure Model................................................................................................184
6.6.1 Initial Yield...........................................................................................................184
6.6.2 Full Yield..............................................................................................................185
6.7 Example Application of M-V-P Failure Surface............................................................186
Appendix 6.A Anti-Derivatives for Evaluating Resultant Stresses......................................188
Appendix 6.B Residual Shear Stress....................................................................................190
viii
Chapter 7 Conclusions........................................................................................................................200
7.1 Summary........................................................................................................................200
7.2 Conclusions....................................................................................................................201
7.3 Future Work...................................................................................................................202
References..........................................................................................................................................205
ix
List of Figures
Figure 1.1 Save-on-Foods Grocery Store failure, Canada (Closkey, 1988).........................................15
Figure 1.2 Progressive collapse of Husky Stadium, USA (© John Stamets, 1987)..............................15
Figure 1.3 Progressive collapse of Ronan Point Flats, UK (Griffiths et al., 1968)...............................16
Figure 1.4 Local damage of World Trade Centre building, New York (Bureau of ATF, 1993)..........16
Figure 1.5 Progressive collapse of Murrah Office Building, Oklahoma (Hinman, 1997)....................17
Figure 1.6 Progressive collapse of World Trade Centre tower, New York (FEMA , 2002).................17
Figure 1.7 Damaged building due to Hurricane Katrina, New Orleans (CNN, 2005)..........................18
Figure 1.8 Walls as transfer girders compensating for column loss, Pentagon, USA (SEI, 2003).......18
Figure 2-1 Force-deformation due to end rotation................................................................................42
Figure 2-2 Deformations of a differential segment...............................................................................42
Figure 2-3 Flexibility coefficients and member-end numbering..........................................................43
Figure 2-4 Force-deformation due to end translation...........................................................................43
Figure 2-5 Column with different end constraints................................................................................44
Figure 2-6 Relative difference of critical load due to shear deformation.............................................44
Figure 2-7 Fixed-end reactions and deflections due to transverse loading...........................................45
Figure 2-8 Force-deformation relationship in the post-elastic range....................................................45
Figure 2-9 Bending member model......................................................................................................46
Figure 2-10 Shearing member model....................................................................................................46
Figure 2-11 Axial member model.........................................................................................................46
Figure 2-12 Flexibility coefficients due to unit end moment................................................................47
Figure 2-13 Experimental-based moment-rotation curve (Kusuda & Thurlimann, 1958)....................47
Figure 2-14 Experimental-based shear force-transverse deflection curve............................................48
Figure 2-15 Experimental-based axial force-deformation curve (Huber & Beedle, 1954)...................48
Figure 3.1 Hybrid beam-column member.............................................................................................74
Figure 3.2 Stiffness coefficients due to rotation...................................................................................74
Figure 3.3 Stiffness coefficients due to translation...............................................................................75
Figure 3.4 Axial force and deformation................................................................................................75
Figure 3.5 M+P first-yield and full-yield capacities.............................................................................76
Figure 3.6 M+P stiffness degradation...................................................................................................76
Figure 3.7 M+V first-yield and full-yield capacities.............................................................................77
Figure 3.8 M+V stiffness degradation...................................................................................................77
x