PROGRESSIVE COLLAPSE ANALYSES OF STEEL FRAMED MOMENT RESISTING STRUCTURES

ABSTRACT

 

Progressive collapse has been an important issue in building failures since the collapse of the Ronan Point apartment building in 1968. Progressive collapse is a failure sequence that relates local damage to large scale collapse in a structure. If any load exceeds the load-carrying capacity of any member, it will cause additional local failures. Such sequential failures can propagate through the structure. Therefore, a local member failure analysis is the basic element for the progressive collapse analysis.

Three different failure criteria have been considered in this study. They are material failure, buckling failure, and connection failure. Material and buckling failures were analyzed by using a second-order inelastic method. Connection failures were analyzed by using a moment-curvature relationship calculated by a power model using three parameters.

The finite element code ABAQUS/Explicit has been used for the analyses. Single column failure results from the ABAQUS/Explicit simulations and from the NFA developed for this study based on the second-order inelastic method were compared for a verification purpose.

Various numbers of spans and stories with rigid, semi-rigid, and reinforced semirigid frames were studied for 2D frame analyses. As the number of spans increased, the collapse mode tended to change from total collapse to partial collapse. As the number of stories increased, the collapse mode tended to change from partial collapse to total collapse. However, the analyses of the semi-rigid frames showed different trends. All semi-rigid frames collapsed partially by joint failures. The 2D frame analyses showed that a vertical failure was caused by connection failures, a horizontal failure was caused by column buckling.

The 3D frame analyses showed a different tendency. Four different span frames with rigid and semi-rigid connection with a single column size, were used for six initial failure cases. The assumed rigid and semi-rigid connection did not make a big difference in the 3D cases. Therefore, semi-rigid connection would not be a critical factor if the initial damage is localized. Inner columns were more critical than outer columns.

However, the single column initial failure caused total collapse for the most of the frame with a more realistic design. The 3D frame with realistic designs showed three facts. First, a more realistic design, using two different column sizes, is more vulnerable to progressive collapse than a single size column design. Second, a semi-rigid connection could trigger total collapse of a structure, while a rigid frame just caused internal damage. Third, the lengths of columns did not affect collapse modes. However, it could be a factor when the frame is overdesigned to resist progressive collapse.

 

 

TABLE OF CONTENTS

 

List of Figures …………………………………………………………………………………………………… vii

List of Tables …………………………………………………………………………………………………….. x

Acknowledgements …………………………………………………………………………………………….. xi

 

1. Introduction ………………………………………………………………………………………………….. 1
   • Problem Statement ………………………………………………………………………………….. 1
   • Objective ……………………………………………………………………………………………….. 2
   • Scope …………………………………………………………………………………………………….. 3
2. Background ………………………………………………………………………………………………….. 6
   • Introduction ……………………………………………………………………………………………. 6 2.2. Prevention of Progressive Collapse …………………………………………………………… 8
   • Analyses of Progressive Collapse ……………………………………………………………. 12
   • Concluding Remarks ……………………………………………………………………………… 18
3. Analysis Theory of Steel Frame Structure ……………………………………………………….. 20
   • Introduction …………………………………………………………………………………………… 20
     • The Effective Length Factor K Method …………………………………………… 20
     • Advanced Analysis of Steel Frame Structure …………………………………… 23
     • Semi-Rigid Connections ……………………………………………………………….. 30
   • Formulation of 2D Finite Element Method for Plastic Zone Analysis …………… 32
     • General ……………………………………………………………………………………….. 32
     • Strain-Displacement Relationships …………………………………………………. 35
     • Stress-Strain Relationships ……………………………………………………………. 38
     • Stress Resultants ………………………………………………………………………….. 40
     • The Principle of Virtual Displacements ………………………………………….. 41
     • Discretization of the Virtual Work Equation …………………………………… 43
     • Solving the Nonlinear Equilibrium Equations …………………………………. 50
     • Transformation, Condensation, and Recovery of Nodal Variables …….. 52
     • Cross-Sectional Analysis ……………………………………………………………… 55
   • Semi-Rigid Connections ………………………………………………………………………… 60
     • General ………………………………………………………………………………………. 60
     • Modeling of Semi-Rigid Connections ……………………………………………. 61

 

4. Analysis ……………………………………………………………………………………………………… 69
   • Numerical Implementation ……………………………………………………………………… 69
     • Code Selection …………………………………………………………………………….. 69
     • Mesh Sensitivity …………………………………………………………………………… 73
   • Single Column Analysis………………………………………………………………………….. 78
     • General ……………………………………………………………………………………….. 78
     • Specifications of the Models ………………………………………………………….. 81
     • Results ………………………………………………………………………………………… 84
     • Concluding Remarks …………………………………………………………………….. 98
   • 2D Frame Analysis ………………………………………………………………………………… 99
     • General ……………………………………………………………………………………….. 99
     • Specifications of the Models ………………………………………………………….. 99
     • Results ………………………………………………………………………………………. 105
       • Rigid Frame ………………………………………………………………………… 105
       • Semi-Rigid Frame ……………………………………………………………….. 117
       • Reinforced Semi-Rigid Frames ……………………………………………… 123
       • Member Buckling ……………………………………………………………….. 127 4.3.3.5. First Order Inelastic and Second Order Elastic

with Stress Failure Criterion Analyses of Rigid Frames …………… 131

• Concluding Remarks ………………………………………………………………….. 133

• 3D Frame Analysis ………………………………………………………………………………. 136
  • General ……………………………………………………………………………………… 136
  • Specifications of the Models ………………………………………………………… 136
  • Initial Column Failure Cases ……………………………………………………….. 138
  • Results ………………………………………………………………………………………. 139
    • 2x2x2 Span Frame ………………………………………………………………. 139
    • 3x3x3 Span Frame ………………………………………………………………. 142
    • 4x4x4 Span Frame ………………………………………………………………. 146 4.4.4.4. 5x5x5 Span Frame ………………………………………………………………. 150

4.4.4.5.  5x5x5 Span Frame with a More Realistic Design ……………………. 154

• Concluding Remarks ………………………………………………………………….. 169

5. Conclusions ………………………………………………………………………………………………. 171
   • Conclusions ………………………………………………………………………………………… 171
   • Recommendations ……………………………………………………………………………….. 174

REFERENCES ……………………………………………………………………………………………… 176

 

APPENDIX A. Flow Charts of the NFA …………………………………………………………….. 183

APPENDIX A-1. The Main Routine of the NFA …………………………………………………. 187

APPENDIX A-2. A Subroutine for the Stiffness Matrix of the NFA ……………………… 192

APPENDIX A-3. Other Subroutines of the NFA …………………………………………………. 198

1. Introduction

1.1. Problem Statement

Progressive collapse has been one of the issues in building failures since the collapse of the Ronan Point apartment building in 1968 (Griffiths, et al. 1968). It was a 22-story precast concrete panel construction building in England. A gas explosion in the kitchen of an apartment on the 18^th floor of the building blew out an exterior wall panel. That caused a chain reaction of structural collapse from the roof down to the ground, as debris from above fell on successive floors below (Figure 1-1). The particular type of joint detail used in the Ronan Point apartment building relied heavily on joint friction between elements. This resulted in a structure that has been termed a “house of cards”, indicating that buildings with similar joint characteristics were particularly susceptible to progressive collapse (Breen 1980).

 

Figure 1-1. Damage at the Ronan Point Apartment Building

Progressive collapse is a failure sequence that relates local damage to large scale collapse in a structure. The local failure can be defined as a loss of the loadcarrying capacity of one or more structural components that are part of the whole structural system. Preferably, once any structural component fails, the structure should enable an alternative load-carrying path. After the load is redistributed through a structure, each structural component will support different loads. If any load exceeds the load-carrying capacity of any member, it will cause another local failure. Such sequential failures can propagate through the structure. If a structure loses too many members, it may lead to partial or total collapse. This type of collapse behavior may occur in framed structures, such as buildings (Griffiths, et al. 1968, Burnett, et al. 1973, Ger, et al. 1993, Sucuoglu, et al. 1994, Ellis and Currie 1998, Bazant and Zhou 2002), trusses (Murtha-Smith 1988, Blandford 1997), and bridges (Ghali and Tadros 1997, Abeysinghe 2002).

Progressive collapse is an important issue because local damage may cause massive destruction of a structural system. Small accidents, such as a local gas explosion or vehicle collision, can cause total collapse of a structure. It is an obvious undesired risk since small accidents cannot be prevented completely. Therefore, investigating the nature of progressive collapse is very important.

 

1.2. Objective

The main objective of this study is to enable the development of a rational numerical analysis of progressive collapse by studying simple frame systems with simple material models focusing on the role of material models and buckling. Several factors may contribute to progressive collapse. It usually occurs when a structure is subjected to an abnormal loading event. (i.e., such loading conditions are not normally considered in the design of structures (Breen and Siess 1979)). Abnormal loads could generate local failure, which may lead to progressive collapse. Geometry of structure, material properties of members could be other factors to influence progressive collapse. However, it is unrealistic to include all the factors in a single study. Therefore, only a few key factors in progressive collapse will be included to simplify the analysis.

Three key issues need to be considered. Those are structural stability, semirigid joint connection behavior, and dynamic frame analysis. Each issue requires a separate analysis step. However, they will be combined in this study because they could occur simultaneously and influence each other in progressive collapse. Therefore, this study will be focused on developing a simplified numerical analysis method and setting up the numerical procedure that combines these issues.

 

1.3. Scope

This research will be limited to understanding the characteristics of progressive collapse in simple, moment resisting steel frame buildings. The initial structural responses to abnormal loadings (e.g., an explosion) will not be considered. Damage for the conditions cited above will be assumed to be the removal of one or more columns at critical locations.

Structural details such as walls and partitions can affect the response of the structure. Including these secondary elements in the analysis would increase the complexity of the responses. Therefore, the effect of secondary elements will not be considered because the responses of the major load carrying members should be clarified first. The analysis including the effects of the secondary elements could be a future study.

A buckling analysis procedure will be set up at the first stage of the study. Buckling failure in steel structure includes flexural buckling, torsional buckling, lateral-torsional buckling, and local buckling. Only flexural member buckling will be considered in this study. A single structural member will be analyzed to verify a buckling analysis procedure to be included in the overall analysis of a structure.

Simple material properties such as elastic, elasto-plastic will be used for the collapse analysis.

Influence of connection rigidities will be studied next. Since real connection behavior is neither rigid nor pinned, semi-rigid behavior will be considered. Steel connection simulations could be used to obtain the moment-curvature relationship that will be included in the structural models.

Once each analysis step has been completed, it will be combined into the dynamic analysis of steel frame structures. Several configurations of structures will be used from a simple structure such as a 2X2X2 bay and story configuration to larger structures such as up to 5X5X5 bay and story configurations. Critical damage cases will be assumed. Columns at the corner, the center, and other locations will be removed to simulate the initial failures. Each configuration will use the simplified analysis procedures obtained in the previous steps.

Results from these analyses will be used to analyze the general behavior of progressive collapse. Behavior differences between failure criteria, geometries, and connections rigidities will be compared and discussed. Conclusions and

recommendations will be provided as the last stage of the study.

PROGRESSIVE COLLAPSE ANALYSES OF STEEL FRAMED MOMENT RESISTING STRUCTURES

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