Dissertation2007-DavilaArbona

Istituto Universitario di Studi Superiori

Universit degli Studi di Pavia

EUROPEAN SCHOOL FOR ADVANCED STUDIES IN REDUCTION OF SEISMIC RISK

ROSE SCHOOL

PANEL ZONE BEHAVIOUR IN STEEL MOMENT

RESISTING FRAMES

A Dissertation Submitted in Partial Fulfilment of the Requirements for the Master Degree in

EARTHQUAKE ENGINEERING AND

ENGINEERING SEISMOLOGY

by

FRANCISCO JOSE DAVILA-ARBONA

Supervisors: Dr MIGUEL CASTRO, Dr AHMED ELGHAZOULI

May, 2007

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The dissertation entitled Panel Zone Behaviour in Steel Moment Resisting Frames, by Francisco Jose Davila-Arbona, has been approved in partial fulfilment of the requirements for the Master Degree in Earthquake Engineering and Engineering Seismology.

Dr. Miguel Castro _______

Dr. Ahmed Elghazouli_____

Abstract

i

ABSTRACT The response of a moment-resisting frame depends on the characteristics of its main components, namely the columns, the beams and the connections. For the connection type considered in this study the response is mainly governed by the panel zone. This component is defined as the column web portion delimited by the beam continuity plates and the column flanges. The panel is described to be an element mainly subjected to shear stresses and therefore its failure mode is governed by shear yielding. Tests demonstrated that the shear failure mode was stable and ductile under cyclic loading. This dissertation aims to provide a better understanding of the panel zone role in the seismic behaviour of steel moment-resisting frames. The influence of this component on the global and local seismic demands is examined through numerical studies carried out using idealized systems. The ultimate goal of the work is to suggest a design criterion for the panel zone that leads to a more optimized performance of the various components of a structure. The numerical studies undertaken clearly illustrated the importance of this component and the need for its consideration in both the analysis and design stages.

Keywords: panel pone; distortions, shear yielding; plastic rotations, curvatures.

Acknowledgements

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ACKNOWLEDGEMENTS To God To my supervisors: Dr. Miguel Castro and Dr. Ahmed Elghazouli To my parents and family To my lovely wife To my friends To the European Commission, Rose School staff and Imperial College staff.

Index

iii

TABLE OF CONTENTS

Page

ABSTRACT ............................................................................................................................................i ACKNOWLEDGEMENTS....................................................................................................................ii TABLE OF CONTENTS ......................................................................................................................iii LIST OF FIGURES ................................................................................................................................v LIST OF TABLES...............................................................................................................................viii 1. INTRODUCTION.............................................................................................................................9

1.1 General.......................................................................................................................................9 1.2 Objective ..................................................................................................................................10 1.3 Dissertation Outline .................................................................................................................10

2. LITERATURE REVIEW................................................................................................................12 2.1 Introduction..............................................................................................................................12 2.2 Experimental studies to understand the Panel Zone role .........................................................12 2.3 Strength and Energy Dissipating Capacity of the Panel Zone .................................................13 2.4 Stiffness and deformability of the Panel Zone.........................................................................14 2.5 Numerical Studies ....................................................................................................................15 2.6 Recent Developments ..............................................................................................................16 2.7 Recommendations to Design Guidelines and Code Provisions ...............................................16 2.8 Concluding Remarks................................................................................................................17

3. PANEL ZONE BEHAVIOUR AND DESIGN...............................................................................18 3.1 Introduction..............................................................................................................................18 3.2 Panel Zone under Shear ...........................................................................................................19 3.3 Representing Analytically Panel Zone Strength and Stiffness ................................................19

3.3.1 Elastic Range .................................................................................................................20 3.3.2 Post-elastic range ...........................................................................................................21

Index

iv

3.4 Modelling the Panel Zone ........................................................................................................23 3.5 Design Guidelines and Code Provisions..................................................................................23

3.5.1 FEMA 350 Seismic Guidelines......................................................................................24 3.5.2 AISC Seismic Provisions ...............................................................................................25 3.5.3 Eurocode ........................................................................................................................27

4. NUMERICAL INVESTIGATION..................................................................................................28 4.1 Introduction..............................................................................................................................28 4.2 Cruciform Sub-Assemblage.....................................................................................................29

4.2.1 Description.....................................................................................................................29 4.2.2 Analytical Demands in the Panel Zone..........................................................................30 4.2.3 Design Criterion for the Panel Zone ..............................................................................31

4.3 Numerical Modelling ...............................................................................................................33 4.3.1 OpenSees Finite Element Program for Non-linear Analysis .........................................33 4.3.2 OpenSees Model representation.....................................................................................33

4.4 Analysis Procedures and Response Parameters .......................................................................35 4.4.1 Analysis Procedures.......................................................................................................35 4.4.2 Response Parameters .....................................................................................................35

4.5 Discussion of Results ...............................................................................................................37 4.6 Concluding Remarks................................................................................................................42

5. PARAMETRIC STUDIES ..............................................................................................................43 5.1 Introduction..............................................................................................................................43 5.2 Parameters Considered.............................................................................................................43 5.3 Influence of the Panel Zone to Beam capacity ratio ................................................................44 5.4 Influence of the Beam Span.....................................................................................................53 5.5 Influence of the Beam Depth ...................................................................................................56 5.6 Influence of the Panel Zone Second Yield Distortion .............................................................60 5.7 Influence of Steel Strain Hardening........................................................................................63 5.8 Influence of the Gravity Load Level........................................................................................65

6. CONCLUSIONS AND FUTURE RESEARCH .............................................................................74 6.1 Summary and Conclusions ......................................................................................................74 6.2 Recommendations for Future Research ...................................................................................75

REFERENCES .....................................................................................................................................76 APPENDIX A.........................................................................................................................................1

A.1 OpenSees Input File ...........................................................................................................2

Index

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LIST OF FIGURES

Page

Figure 1.1. Panel Zone ................................................................................................................9

Figure 2.1. Timeline: panel zone development.........................................................................17

Figure 3.1.Moment distributions at joints.................................................................................18

Figure 3.2.Moment converted into Shear .................................................................................19

Figure 3.3.Analytical Models ...................................................................................................20

Figure 3.4.Geometrical parameters...........................................................................................21

Figure 3.5.Strength of the panel zone .......................................................................................22

Figure 3.6.Joint Models of the Panel Zone for Moment Resisting Frames ..............................23

Figure 4.1. Cruciform sub-assemblage. ....................................................................................28

Figure 4.2. Sub-assemblage geometrical properties and boundary conditions.........................29

Figure 4.3. Forces in the Panel Zone under lateral loading conditions.....................................30

Figure 4.4. Design criterion for the panel zone ........................................................................31

Figure 4.5. Design criterion for the panel zone. (a) Strong panel (b) Weak panel ...................32

Figure 4.6. Model Representation in OpenSees........................................................................33

Figure 4.7. Uniaxial Hardening Material ..................................................................................34

Figure 4.8. Panel Representation. a) Beam Column Joint Element (Lowes et al., 2004) b) Tri-

linear model adopted for the shear panel ..........................................................................35

Figure 4.9. Plastic Hinge Concept ............................................................................................37

Figure 4.10. Pushover Curve ....................................................................................................38

Figure 4.11. Deformed Shape 4% Drift ...................................................................................38

Figure 4.12. Contribution from Beam, Panel and Column to the drift .....................................39

Figure 4.13. Beam Elastic and Plastic Contribution to the drift ..............................................39

Figure 4.14. Plastic Hinge Rotation Beams ..............................................................................40

Index

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Figure 4.15. Normalized Plastic Hinge Length ........................................................................41

Figure 4.16. Curvature Ductility...............................................................................................41

Figure 4.17. Panel Distortion ....................................................................................................42

Figure 4.18. Panel Distortion Ductility.....................................................................................42

Figure 5.1. Influence of the Panel Zone to Beam capacity ratio in the Pushover Curve..........45

Figure 5.2. Contribution to Deformation: Panel Zone to Beam capacity ratio.........................46

Figure 5.3. Beam Contribution to Deformation: Panel Zone to Beam capacity ratio ..............47

Figure 5.4. Beam Plastic Contribution to Deformation: Panel Zone to Beam capacity ratio...48

Figure 5.5. Panel Contribution to Deformation: Panel Zone to Beam capacity ratio ...............49

Figure 5.6. Column Contribution to Deformation: Panel Zone to Beam capacity ratio ...........49

Figure 5.7. Beam Plastic Hinge Rotations: Panel Zone to Beam capacity ratio.......................50

Figure 5.8. Plastic Hinge Length: Panel Zone to Beam capacity ratio .....................................50

Figure 5.9. Curvature Ductility: Panel Zone to Beam capacity ratio........................................51

Figure 5.10. Panel Distortion: Panel Zone to Beam capacity ratio...........................................52

Figure 5.11. Panel Distortion Ductility: Panel Zone to Beam capacity ratio ...........................53

Figure 5.12. Pushover Curve: Beams Span ..............................................................................54

Figure 5.13. Plastic Hinge Rotation: Span to Beam Depth ratio ..............................................54

Figure 5.14. Curvature Ductility: Span to Beam Depth ratio ...................................................55

Figure 5.15. Panel Zone Distortion Ductility: Span to Beam Depth ratio ................................56

Figure 5.16. Pushover Curve: Beam Depth ..............................................................................57

Figure 5.17. Plastic Hinge Rotation: Beam Depth....................................................................58

Figure 5.18. Plastic Hinge Length: Beam Depth ......................................................................58

Figure 5.19. Curvatures: Beam Depth ......................................................................................59

Figure 5.20. Curvature Ductility: Beam Depth.........................................................................59

Figure 5.21. Panel Zone Distortion Ductility: Beam Depth .....................................................60

Figure 5.22. Pushover Curve: Second Yield Distortion ...........................................................61

Figure 5.23. Plastic Hinge Rotation: Second Yield Distortion.................................................61

Figure 5.24. Curvature Ductility: Second Yield Distortion......................................................62

Figure 5.25 Panel Zone Distortion Ductility: Second Yield Distortion....................................62

Figure 5.26. Pushover Curve: Strain Hardening.......................................................................63

Figure 5.27. Plastic Hinge Rotation: Strain Hardening ............................................................64

Figure 5.28. Curvature Ductility: Strain Hardening .................................................................64

Figure 5.29. Panel Zone Distortion Ductility: Strain Hardening ..............................................65

Index

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Figure 5.30. Multi-bay Structure ..............................................................................................65

Figure 5.31. Multi-bay Structure ..............................................................................................66

Figure 5.32. Pushover Curve: Gravity Load.............................................................................67

Figure 5.33. Curvatures at a drift level of 4%...........................................................................68

Figure 5.34. Plastic Hinge Rotations IntL: Gravity Load .........................................................69

Figure 5.35. Plastic Hinge Rotations IntR: Gravity Load.........................................................69

Figure 5.36. Curvature Ductility L2: Gravity Load (thick cref) ...............................................70

Figure 5.37. Curvature Ductility R2: Gravity Load..................................................................71

Figure 5.38. Distortion Ductility PZ1: Gravity Load ...............................................................71

Figure 5.39. Distortion Ductility PZ2-PZ3: Gravity Load .......................................................72

Figure 5.40. Distortion Ductility PZ4: Gravity Load ...............................................................73

Index

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LIST OF TABLES

Page

Table 4.1. Sub-assemblage Geometric Properties. ...................................................................30

Table 4.3. Panel Zone thickness for the control case................................................................33

Table 4.4. Output Parameters from the Analysis......................................................................35

Table 4.5. Response Parameters ...............................................................................................36

Table 5.1. Parameters considered in the parametric studies .....................................................43

Table 5.2. Summary Control Case Sub-assemblage.................................................................44

Table 5.3. Cases for Panel Zone to Beam Capacity ratio .........................................................44

Table 5.4. Cases for Span to Beam Depth ratio ........................................................................53

Table 5.5. Cases for Beam Depth .............................................................................................56

Table 5.6. Cases for Panel Second Yield Distortion.................................................................60

Table 5.7. Cases for Strain Hardening of Steel.........................................................................63

Table 5.8. Cases for Gravity Load level ...................................................................................66

Chapter 1. Introduction

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1. INTRODUCTION

1.1 General The response of a moment-resisting frame depends on the characteristics of its main components, namely the columns, the beams and the connections. There are several types of connection configurations such as flush end plate, extended end plate, welded flanges-bolted web or welded flanges-welded webs connections, among others. In the present study the connection type considered is welded flanges and welded webs in which the response is mainly governed by the panel zone. This component is defined as the column web portion delimited by the beam continuity plates and the column flanges, as shown in Figure 1.1.

Figure 1.1. Panel Zone

In the beginnings of the 1970s, the importance of the panel zone in the response of the frames was identified and, experimental and analytical studies were carried out to characterize this component behaviour. The panel was described to be an element mainly subjected to shear stresses and therefore its failure mode was governed by shear yielding. Tests demonstrated that the shear failure mode was stable and ductile under cyclic loading. These attractive features were taken into account in design regulations by the end of the 1980s which allowed the panel zone to be considered as a dissipative component.


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However, the 1994 Northridge earthquake resulted in severe damage in the connections of steel moment-resisting frames which had not been observed before. Extensive research was triggered which detected that excessive distortions in the panel zone played an important role in the development of weld failures in the connections. Since then research has been carried out to define new panel zone design criteria that can lead to both effective and reliable performance of panel zones during frame response. Different approaches have been proposed in recent seismic guidelines but until now a consistent approach has not been fully established and validated.

1.2 Objective This dissertation aims to provide a better understanding of the panel zone role in the seismic behaviour of steel moment-resisting frames. The influence of this component on the global and local seismic demands is examined through numerical studies carried out using idealized systems. The ultimate goal of the work is to suggest a design criterion for the panel zone that leads to a more optimized performance of the various components of a structure.

1.3 Dissertation Outline The dissertation is composed of seven chapters. In Chapter 2 a literature review on previous research done on panel zone is provided. The key experimental and numerical studies are described.

The panel zone behaviour under unbalanced loading is discussed in Chapter 3. The existing approaches to evaluate the stiffness and capacity of this component are introduced along with various modelling techniques available to represent this component in a numerical analysis. The chapter terminates with a review of design guidelines and code provisions for the design of the panel zone.

Chapter 4 describes a numerical investigation aiming to investigate the influence of the panel zone on the lateral response of an idealised cruciform system based on a balanced design for the panel zone. The nonlinear finite element program OpenSees, which is used to model the structure, is described as well as the procedures adopted in the analysis. The performance of the structure is then discussed based on several response parameters.

A parametric investigation to investigate the influence of several geometric, design and modelling on the performance of moment frames is presented Chapter 5. The selected parameters and the cases considered are firstly described. The results obtained are then compared with those obtained for the structure analysed in Chapter 4 which is used as a control case. The chapter ends with a discussion and some design considerations are made.

In Chapter 6 an application example is presented in order to validate the conclusions drawn in the previous chapters. The structure consists of a five-storey three-bay moment frame designed according Eurocode 3 but adopting different design criteria for the panel zone. The global performance of the structure and the local response of the various components is presented and a discussion of the results obtained is provided.


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Finally, Chapter 7 presents the conclusions of the work along with proposals for future research.

Chapter 2. Literature Review

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2. LITERATURE REVIEW

2.1 Introduction The following sections describe the main issues regarding panel zone performance in moment-resisting frames. An early stage into investigation of the topic and understanding of the mechanism is outlined. The experimental research is presented first, followed by a description of the main aspects of the behaviour of the panel zone in terms of resistance and energy dissipating capacity. The influence of lateral displacements caused by panel zone distortions is presented and analytical studies together with modelling proposals also described. Finally a suggestion made by researchers to design guidelines and code provisions ends this chapter.

2.2 Experimental studies to understand the Panel Zone role In the early 1970s recognition was made of the importance of beam to column connections in the behaviour of moment-resisting steel frames. The basic requirements for buildings were divided in two main topics: 1) to perform under serviceability conditions and 2) to minimize the possibility of failure of a structure when submitted to a low probability of occurrence of a seismic event.

To accomplish this, it was necessary to rely on the capacity of energy dissipation of the structure. In other words, the building was not expected to resist forces in the elastic range, since this would mean a high economic demand on the structural configuration. On the other hand using the inelastic range of the structure required a thorough understanding of the performance and hence motivated further research.

In the beginning of the 1970s, research was conducted to comprehend the inelastic behaviour of joints in moment-resisting frames [Fielding and Huang, 1971; Bertero et al., 1972]. In order to understand different loading regimes, several loading conditions were simulated on the tests, whereby gravity and cyclic seismic loads were applied to different sub-assemblages. In addition, the effect of axial loads on the performance of connections subjected to shear was also carried out.

Several years later, a number of test were performed by Popov [1985] in order to verify the extreme loading conditions on joints and to study the cyclic behaviour of large beam assemblies. Ten years after, Tsai et al. [1995] carried out further testing on similar joint sub-assemblies. The main objective was to study the performance of seismic steel beam-column


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moment joints. The research concluded about the significant influence of the panel zone in the joint behaviour and it has shown that the inelastic deformation capacity of the joint can be enhance if the panel zone is correctly proportioned. Accordingly, among the parameters studied in both researches was the design criteria used for the panel zone. The studies recommended involving the panel as a dissipative component by developing a yield mechanism simultaneously with the beam flexural yield mechanism.

The Northridge-California earthquake in 1994 triggered a large amount of research activity in the United States. Failure modes were studied in depth and design criteria were analysed under the light of the results. Failure of joint welds and premature fracture were observed and associated to excessive distortions in the panel zone. Several documents published in the following years [FEMA-267, FEMA-353, FEMA-355D], discussed the reasons for the poor behaviour of the connections and the factors affecting their performance. The concepts of seismic design in typical connections were considered as additional research subjects.

Additional testing was aimed to further understand the balance of energy dissipation between the panel zone and the beam by varying the panel zone capacity in terms of the moment capacity of the beam. Participation of the panel zone to the inelastic response contributed to the reduction of the demands on the beams in terms of deformation [Lee C.H. et al., 2005]. Thorough investigations to address the influence of different details for stiffening the column in steel moment-resisting connections under cyclic loading were also performed. For example, effectiveness of the doubler plate connection detail was addressed by Lee D. et al. [2005].

Analogous research was carried out in Europe by Dubina et al. [2001] and Ciutina and Dubina [2006] to understand the cyclic performance of beam-to-column joints. The panel zone was documented as a ductile component, capable of dissipating energy by allowing stable hysteretic loops. The studies intended to clarify the performance of moment-resisting connections, influenced by different reinforcing solutions to the panel zone region.

Analytical studies have been based on the experimental work presented in this section. In addition, the principal considerations regarding panel zone resistance, stiffness and analysis have been confronted against these experimental results, as presented in the subsequent sections.

2.3 Strength and Energy Dissipating Capacity of the Panel Zone Theoretical analysis of the yield condition of the web panel were carried out and verified against experimental tests. The typical load response from the panel was characterised by three stages. First, elastic shear response followed by yielding, according to the Von Mises criterion. Second, reserve in strength attributed to the surrounding elements of the panel. Finally, a post yield strength characterised by strain hardening of the steel.

The actions in the panel are summarized in terms of simplified models of constant shear distribution in the column web; this is done by assuming that the flexural moment of the beam is transmitted through the beam flanges mainly as a couple of forces, as presented by Fielding and Huang [1971] and Bertero et al. [1972]. The post yield range was considered to be stable and to sustain considerable load above the yield capacity. The panel was recognized as a


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dissipating energy component. Considerations of the elastic and inelastic range of the panel was done by an in depth experimental and clear analytical understanding of the load deformation behaviour of joints and the associated strain stress regime.

Initial suggestions were made by the researchers cited above about shear stiffening of the panel based on different criteria. Fielding and Huang [1971] proposed to base the stiffness according to the required rigidity of the connection. Bertero et al. [1972] suggested not making the panel very weak because the overall energy absorption capacity of connection could be reduced by not allowing other components to develop their strength. On the other hand, suggested that the panel zone should not be too strong in order to avoid loosing its inelastic dissipative capacity.

A discussion on the strength, stiffness and energy dissipation of joints was presented by Krawinkler [1978]. Importance was given to the capability of the joint to undergo severe inelastic strain reversal without loosing strength. An upper limit for the maximum strength and stiffness of a frame was established when all joints were designed for the maximum demands imposed by the elements framing into them. A discussion of the need for design criteria to balance out these parameters was hence given. A tri-linear model to represent this component in the analysis was proposed and suggestions about considering the second strength capacity attained by the surrounding elements to allow the joint to participate in energy dissipation through the inelastic range were stated. This publication strongly influenced subsequent guidelines in the topic as described in the following sections.

Panel zone design procedures started to be questioned, as a result of which an opinion paper by Englekirk [1999] was presented where the behaviour objectives of steel moment resisting frames compared to experimental results from eight subassemblies were discussed. The promotion of panel zone yielding was considered to result in poor frame performance. As a minimum objective the author proposed to support a criterion where the panel zone and framing beams yield simultaneously. Therefore, the capacity of the panel was suggested to be related to yield rather than to contributions from the surrounding elements or strain hardening; this hence, promoted reinforced panel zones. Induced kinks in the columns and problems in the weld of the beam flanges were suggested to be minimised by controlling excessive panel zone distortions through stiffening of the panel.

2.4 Stiffness and deformability of the Panel Zone From experimental test, Bertero et al. [1972] identified that the contribution to the top displacement of the sub-assemblage was highly influenced by the panel zone distortion. In the mid 1970s further analytical studies were carried out by Krawinkler et al. [1975] pointing out the importance of considering the influence of joint deformations in frames in terms of stiffness and energy absorption. Adequate control of shear deformations was promoted to attained stable hysteretic behaviour into the inelastic range. CHECK!

Further analytical studies stated the necessity of including the deformability of the joint in frame analysis. Suggestions about designing the panel to sustain the maximum strength developed in the beams, to avoid early deterioration of the lateral stiffness of the joint and the entire frame, were presented. To reduced the demands on the plastic hinge rotations of the


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beams, controlled deformations were allowed in the joint as long as the stiffness was not the principal design consideration of the joint. An important parameter identified was that large deformations of the panel zone could lead to local kinking in the column flanges, as already mentioned before.

Similarly, in an analytical study Popov [1987] critically reviewed experimental results to determine different contributions from the joint elements to the flexibility of the structure. The need to avoid considering the joints as rigid members was stated. A discussion of the flexibility of the joint when subjected to seismic loads was also carried out and an analytical modelling proposal presented. Moreover, necessity for further experimentation on large joints with different member geometries was suggested.

Analogously, after the Northridge earthquake, an analytical study was carried out by Schneider and Amidi [1998] to account for the effect of panel distortions on the behaviour of moment resisting frames. Results suggested that the base shear can be overestimated by 30% and the drift underestimated by 10% if the contributions from the panel distortions are not to be considered. The lateral strength of the frame can be also overestimated if the flexibility due to the panel zone is not incorporated. Recommendations about avoiding rigid eccentricities at the beam and column ends, to account for the finite dimension of the panel zone, were stated.

2.5 Numerical Studies Numerical studies were carried out by El-Tawil et al. [1999] in order to understand the effect of the inelastic behaviour of the panel zone on the possibility of fracture of the welds in steel connections. This was addressed by three-dimensional, nonlinear, finite-element models of different subassemblies based on the design criteria specified before the Northridge earthquake. A parametric study was presented where the principal geometric parameters were varied to estimate the participation to the overall performance of the connection.

Results showed that although weak panel zones controlled the beam plastic rotations, this could lead to high stress concentrations in the welds of the flanges resulting in brittle failures. According to the authors, the panel zone models capable of dissipating energy and contributing to the ductility of the connection. These results confirmed the experimental observations but it was suggested that special attention should be paid to control excessive deformations.

As part of a global study on buildings to enhance the elastic models utilised to design steel moment resisting frames, Foutch and Yun [2001] performed analysis on different 9-storey and 20-storey buildings designed accordingly to 1997 NEHRP provisions. Nonlinear behaviour was considered together with detailed modelling representations. The investigation involved the study of the centreline dimensions parameter and its influence to stiffness. Nonlinear springs for the beam connections and for the panel zones were used to simulate the inelastic response of the elements. The fracture of beam connections to simulate the pre-Northridge type of connection was also taken into account. Static pushover and dynamic analyses were carried out.


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The work has shown that the models that used centreline dimensions were more flexible and hence weaker than other models. This was considered to be conservative for the design of new buildings. The inclusion of connection fracture in the models resulted in a reduced drift capacity and significantly higher drift demands compared to the framing having ductile connections.

2.6 Recent Developments Motivated by the fact that the panel zone can control the performance of a structure, the need for realistic panel zone models to represent accurately the overall behaviour of frames was addressed by Kim and Engelhardt [2001],. Improvements to previous spring models were made to obtain better correspondence with experimental results. The monotonic loading used in the proposed model was based on a quadri-linear response, and it also included shear and bending deformations.

The same authors proposed a cyclic model, based on Dafalias bounding surface theory. The models do not predict the ultimate state of the panel zone, neither buckling nor fracture at the corners. Recommendations about further study for composite behaviour were suggested and extensive comparisons with experimental data were presented.

Importance to the modelling of the panel zone in steel and composite moment frames was addressed by Castro et al. [2005]. After reviewing existing analytical models to represent the panel zone a new approach was proposed to model composite joints. Validation of the proposal was done against detailed finite element models as well as against experimental data available. The work has shown that force distributions vary from composite joints to plain steel joints. The study was carried out for stress distributions which capture appropriately the distribution of plasticity.

An important conclusion from the same work was that the extent of the second range of the behaviour is directly related to the thickness of the column flange and differs from the initial proposal from Krawinkler [1978] who suggested the second yield occurring at four times the yield distortion. The aforementioned study highlighted the force regimes involved in steel and composite joints. The study also discussed the implementation in analytical frame modelling analyses.

2.7 Recommendations to Design Guidelines and Code Provisions To conclude the chapter, Figure 2.1 includes a timeline with relevant events for the evolution of the panel zone development. From experimental and analytical studies, suggestions have been made to regulations over the last decades.

When the post yielding range started to be considered stable and beneficial at the beginnings of the 1970s, the AISC design formula was considered to be conservative by Fielding and Huang [1971]. In the late 1970s Krawinkler [1978] presented a revision for the AISC design criteria in the light of the experimental studies available.

In the late 1980s and beginning of the 1990s, an important change in the design provisions was implemented for moment-resisting frames. As documented by Tsai and Popov [1990], the


17

new provisions motivated that yielding in the panel zones took place before or at the same time as beam yielding. This was encouraged by the investigations carried to-date showing the adequate behaviour of the panel zone under inelastic demands. The AISC Specification 1990 and the Uniform Building Code 1988 allowed the use of thinner doubler plates and in some cases neglected the in need, permitting more economic designs. However, this consideration implied the necessity of controlling frame deflections. Consideration for the panel zone contribution to the total drift of a structure was proposed by means of a simplified adjustment to the results from standard elastic analysis.

Different approaches have been proposed for the design of the panel zone; a diverse approach is presented in FEMA-350 [2000] seismic provisions. The main objective of the new criteria is to make the beams and the panels to yield simultaneously. The provisions were evaluated and discussed by Jun Jin and El-Tawil [2005], based on the experimental data available and the results from dynamic analyses. According to the limited results the authors considered, that the provisions may not be totally adequate since low levels of panel zone participation were identified.

Figure 2.1. Timeline: panel zone development

2.8 Concluding Remarks A general overview of previous research in the panel zone was presented in this chapter. The main experimental studies were presented. Subsequently, studies in the relevance of the stiffness of the panel zone in the overall lateral performance of frames were described. The main numerical studies were provided, along with recommended modelling and recent developments. Finally, the evolution of suggestions to design guidelines and code provisions were presented.

1990 2000 2007

Krawinkler et al. (1975)Influence of joint deformation in frames in terms of stiffness

and energy dissipation.

Fielding and Huang (1971)Theoretical analysis for yield condition verified against test.Failure mode due to yielding.

Bertero et al. (1972)Experimental investigations with gravity and cyclic loads. Panel

recognized as an energy dissipating component.

Krawinkler (1978)Proposal of analytical

tri-linear model.

Popov (1985)Tests to verify the extreme

loading conditions on joints.

UBC (1988)Panel Zone

Strength increased

Northridge earthquake (1994)Excessive distortions in

panel zones. Damage in welds.

AISC (2000)Supplement 2. Shear strength demand no longer estimated

from load combinations.

FEMA-350 (2000)Guidelines for seismic

design of moment-resisting frames

Dubina et al. (2001)European test for the cyclic performance of moment

resisting joints.

Lee C.H. et al. (2005)Tests to study the effects

of the panel zone and RBS in moment-resisting joints.

Lee D. et al. (2005)Tests to study the influence

of different details to reinforce moment-resisting joints. Effect of the panel zone and doubler

plates studied.

Ciutina and Dubina et al. (2006)European test to clarify the influence

of different reinforcing solutions to the panel zone in moment-resisting

connections.

1970 1980

Chapter 3. Panel Zone Behaviour and Design

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3. PANEL ZONE BEHAVIOUR AND DESIGN

3.1 Introduction In a moment-resisting frame the stiffness and resistance to lateral loads are developed through the transfer of bending moments between beams and columns, either by semi-rigid or rigid beam to column connections. The characteristics of the joint behaviour are therefore related to the column, beam and connection properties. As part of the connection the panel zone plays an important role in terms of strength, stiffness and ductility, for the overall behaviour of the frame.

The beam-column joints can fail for different causes according to Krawinkler et al. [1975]; among them column web crippling, column web buckling, column flange distortion, and shear yielding and buckling of the panel zone. In the following sections particular attention will be given to the shear failure mode. The panel zone is firstly described and, after that the methodologies used to represent analytically the strength and stiffness of the panel zone are discussed, in addition to the procedures to model the panel as part of a structural frame. Finally, a review of design guidelines and code specifications for the design of panel zones is conducted.

Figure 3.1.Moment distributions at joints.

Vcol

W W W

Vcol

EXTERNAL JOINT INTERNAL JOINT

Vertical LoadingUnbalanced Moment

Lateral LoadingUnbalanced Moment

Vertical LoadingBalanced Moment

Lateral LoadingUnbalanced Moment


19

3.2 Panel Zone under Shear The forces acting in the panel zone result from the force distribution applied to the joint. There are different types of forces caused by different loading conditions. Under vertical loading the moments in external joints are unbalanced, whereas the moments for internal joints are balanced, as it can be observed in Figure 3.1. When lateral loading is considered the moment distribution is unbalanced for both external and internal joints. Unbalanced moments at the joints are transmitted trough the connection components and equilibrated by the column.

An unbalanced moment produces a shear stress distribution in the panel zone where the higher stresses concentrate at the middle of the panel and reduce moderately towards the corners, according to Krawinkler et al. [1975]. A simplified methodology for the shear stress distribution is to assume a constant shear stress throughout the panel zone, implying that the bending moment is transmitted into the joint through a couple of forces concentrated at the centroid of the flanges of the beams, as presented in Figure 3.2. Although axial stresses and bending stresses are also present, the principal stress regime that develops in the panel is due to the shear imposed by the force pair.

Experimental tests performed on moment-resisting connections provided important information regarding the panel behaviour, [Fielding et al. 1971; Krawinkler et al., 1975; Popov, 1985; Tsai et al., 1995; Dubina et al. 2001]. Accordingly, the behaviour is typically characterised by three stages. In the elastic range, shear strains are predominant. Subsequently, yielding occurs and a significant reduction in stiffness is observed. In the second stage, additional strength in the panel develops due to the contribution of surrounding elements, i.e. column flanges and continuity plates. Finally in the third stage a considerable decrease in stiffness is observed accompanied by high strains. Inelastic deformations take place in a strain hardening regime before local buckling or other mode of failure occurs.

Figure 3.2.Moment converted into Shear

3.3 Representing Analytically Panel Zone Strength and Stiffness A representation of the experimental moment-distortion relation is presented in Figure 3.3, as well as different proposals for the analytical representation of the panel zone behaviour. Proposals regarding how the observed experimental behaviour should be modelled were

b bfpz

pz

pz

d =d - tM

M/d

M/d


20

suggested by several authors. Fielding and Huang [1971] proposed a bi-linear model. Few years later Krawinkler [1978] proposed a tri-linear model and, as a more recent suggestion, Kim and Engelhardt [2001] proposed a quadri-linear model. The models mainly agree for the elastic range, the main difference being in terms of the inelastic range. The model most widely used throughout the literature is the tri-linear model proposed by Krawinkler. In following paragraphs a description of the elastic and post-elastic ranges is provided.

Figure 3.3.Analytical Models

3.3.1 Elastic Range For the elastic range the commonly adopted expression can be derived from mechanics. Equation 3.1 expresses the shear stress as the product between the shear modulus GS of the steel material and the web panel distortion . Equation 3.2 expresses the shear stress as function of the moment M, the panel zone height dpz and the shear area Av. Therefore the moment resistance of the panel can be expressed as in Equation 3.3.

.SG= (3.1)

v

pz

v AdM

AV == (3.2)

... pzvS dAGM = (3.3)

The differences in the previous expression regard the definition of the shear area Av and the distance between the forces dpz. Fielding and Huang (1971) proposed Av= dc.twc, while Krawinkler at al. (1975) proposed Av=(dc-tcf)tcw. Figure 3.4 presents the convention and the two different alternatives for the shear area. Only when the thickness of the column flange is significant as in the case of deep columns, the differences between the two expressions

Experimental ResponsePanel Zone

Bi-Linear Model Fielding and Huang (1971)

Tri-linear ModelKrawinkler (1978)

Cuadri-linear ModelKim and Engelhardt (2001)

K

a) b)

c) d)

EL

KELKEL


21

become relevant. The distance between the equivalent forces is sometimes assumed to be dpz, however considerable differences are only expected for deep beams having thick flanges.

In order to find the moment in the panel that will cause yielding the Von Mises yield criterion is usually applied. The yield shear stress can be expressed as in Equation 3.4 when the effects of axial loads need to be accounted; Fy is the yield stress of the steel and Py the axial capacity of the column. The yield moment is presented in Equation 3.5.

2

13

=

y

yy P

PF (3.4)

ypzvpzy dAM .., = (3.5)

Comparisons of experimental and analytical predictions of the yield moment of the panel are adequate despite of the small differences mention above. The elastic rotational stiffness can then be derived as shown below:

.ELKM = (3.6)

. .EL S v bK G A d= (3.7)

Figure 3.4.Geometrical parameters

3.3.2 Post-elastic range The panel zone presents an important reserve of strength after yielding; this can be attributed mainly to the elements surrounding the panel. The column flanges provide strength due to their bending resistance and the beam webs together with the continuity plates provide in-

b r

d

t

t

b

d

tr

t

d =d -t

w =d -t

Section A-A

B

B

Section B-B

A A

A = d .tvA = (d -t )t v

Fielding and Huang (1971)

Krawinkler et al. (1975)

pz b bbf

bf

bw

bfpzc cf

cf

cw

c

cf c

c fc

cw

cw


22

plane stiffness. From experimental results Krawinkler (1978) proposed an analytical expression for the post-elastic stiffness KP-EL. An estimation of the post yield strength based assuming inelastic distortions of four times the yield distortion was also suggested. Figure 3.5 presents a graphical interpretation.

22

...04.110

...4cfcfS

cfcfSELP tbG

tbEK == (3.8)

To estimate the post yield strength the yield strength plus the additional strength must be calculated. The final expression for the post-elastic yield strength is presented in Equation 3.9. Once the post-elastic strength is reached and yielding has occurred, strain hardening of the material is considered with a KSH stiffness presented in Equation 3.10, where is a strain hardening parameter.

+= dbA

tbdbAM

v

fcfcyvELPy .

..12.31..

2

, (3.9)

ELSH KK .= (3.9)

The main differences from the previous tri-linear model and the quadri-linear model proposed by Kim and Engelhardt (2001) regard the inclusion of the shear and bending deformations modes. Participation of the column flanges thickness influencing the panel resistance in the elastic range and inelastic range was taking into account. When thick column flanges were considered, good agreement between experimental results and the model proposed were observed in contrast with other proposals. Cyclic conditions were also considered by the same authors as part of the model.

Figure 3.5.Strength of the panel zone

Tri-linear ModelKrawinkler

M

M

M

y, P-EL

y

KEL

4y y

KP-EL

KSH

3y


23

3.4 Modelling the Panel Zone The flexural strength of beam to column moment-resisting joints and its continuity is what provides lateral load capacity to a frame. Generally, in the analysis of frames the joint is considered to be rigid. No relative change in angle of rotation between the beam and the column centrelines is assumed to occur. There are some structural models that consider centreline dimensions for the elements and can be refined by introducing eccentricities to the joint; this can over predict the strength and stiffness of the structural frame.

For a reliable lateral load analysis, joint behaviour must be taken into account as the overall behaviour of the frame can be significantly influenced by the joint deformations. When subjected to earthquakes a structural frame can observe a reduction in stiffness if a proper joint design is not carried out. In order to state the elastic and inelastic behaviour of the panel, zone the stress-strain distribution and the load-deformation behaviour of joints must be understood and should be included in the structural model.

Different options for representation of the panel zone in moment- resisting frames have been proposed, namely, the scissors model and the frame model. The scissors model incorporates a rotational spring between the column and the beams, as shown in Figure 3.6(b). The rotational spring accounts for the relative deformation between the elements. Normally, rigid links are considered in the joint as extensions of the column and the beams.

The frame model which is presented in Figure 3.6(c), has evolved since the initial conception by Krawinkler et al (1975). Initially rigid links constituted the frame and rotational springs were located at each of the joints. At present, the model is typically considered as rigid links with a translational spring that accounts for the relative rotation between the members and vertical translation between the beams. The properties of the springs in the models can be easily derived from the expressions provided before in this chapter.

Figure 3.6.Joint Models of the Panel Zone for Moment Resisting Frames

3.5 Design Guidelines and Code Provisions The design philosophy of the main national guidelines and regulations for structural performance under seismic loading is to allow structures to deform and dissipate energy into the inelastic range. Therefore, structures are expected to observe large deformations in a ductile manner avoiding collapse. Yield mechanisms having stable deformation cycles capable of dissipating energy avoiding fracture and significant decrease in strength are

KTK

a) b) c)


24

desired. On the other hand, brittle failure modes which induce sudden reductions in strength, reduction in rotation capacity and cause fractures, should therefore be avoided.

At a given joint, the yield mechanism can develop in the column, the beam or the connection. To avoid collapse due to excessive story drifts, local ductility demands and a development of a soft storey mechanism, the column is aimed to remain elastic, thus invoking the weak beam-strong column mechanism as part of the capacity design criteria. Thus, the beam and connection yield mechanisms are the remaining dissipative components of interest in the seismic response of steel frames. Sharing of plasticity between the two elements is proposed in the recent literature.

As outlined in Chapter 2, the main research concerning joint behaviour under lateral loading was carried out at the beginning of the 1970s. Design regulations were based on the results obtained from experimental investigations and remained unaltered during the 1970s and great part of the 1980s. The main objective was to ensure that the panel zone would remain elastic under a given set of loading conditions, consequently not as a dissipative component. Only on the 1988 Uniform Building Code Regulation [UBC,1988] the shear strength of the panel zone was increased. This was motivated by the outstanding ductility performance and the post yield strength observed in the component. The main expressions established in national guidelines and regulations are presented below.

3.5.1 FEMA 350 Seismic Guidelines The 1994 Northridge earthquake in California triggered a number of experimental and analytical studies to further understand the behaviour of steel moment-resisting frame buildings. It was thought before the event that this type of structural configuration was considered among the most efficient earthquake-resistant type of structures. However, the 1994 earthquake evidenced the contrary, major connection failures were reported mostly by cracking of the beam bottom flange welds. As a result, different entities constituted the SAC Joint Venture to organize a systematic methodology for research on the subject. Among the objectives were the development of reliable guidelines and standards for the repair of damaged steel buildings, the design of new buildings and retrofit of existing steel buildings at risk.

The SAC Joint Venture then was sponsored by the Federal Emergency Management Agency (FEMA), in a cooperative agreement to perform problem focused studies of the seismic performance of steel moment frame buildings and connections of various configurations. The objective was to develop recommendations for professional practice and criteria for steel construction. The FEMA-350 Guidelines is one of the compiled publications aimed to provide recommended criteria for design; it is a document for organizations occupied in the development of building codes and standards for regulations in the design and construction of steel moment-frame structures that may be subject to the effects of earthquake ground shaking.

The recommended criteria for new steel moment-resisting buildings in FEMA-350, defines the strength of the panel zone such that yielding of the panel is initiated almost


25

simultaneously as the flexural yielding of the beams, thus generating two yield mechanisms at the same time. The required web panel thickness is given by:

( ) ( )bfbcycycb

cy

tddRFhdhMC

t

=

6.09.0 (3.10)

Where t is the equivalent thickness of the panel zone including doubler plates, CyMc accounts for the action including overstrength from the beams, h is the average story height, db is the beam depth, dc is the column depth, tfb is the beam flange thickness, Fyc is the yield stress of the material for the column and Ryc account for steel overstrength in the column.

3.5.2 AISC Seismic Provisions The American Institute of Steel Construction (AISC), is responsible for the American National Standard: Specification for Structural Steel Buildings and Seismic Provisions for Structural Steel Buildings. The objective of the Specification is to provide design criteria in a standardized document in agreement with practice development in design of steel buildings and other structures. The objective of the Seismic Provisions is to provide design and construction rules for structural steel and composite systems under high seismic demands.

The nominal shear strength Rn as well as the way to estimate the required shear strength Ru have been established by the specification and are related by the following expression Ru=vRn, where v is the resistance factor for the panel zone strength. The following expressions for panel zone nominal shear strength design are specified by AISC 360-05. When the effect of panel zone deformation on frame stability is not considered in the analysis:

For Pr0.40Pc

wcyn tdFR 6.0= (3.11)

For Pr>0.40Pc

=

c

rwcyn P

PtdFR 4.16.0 (3.12)

When frame stability, including plastic panel zone deformation is considered in the analysis:

For Pr0.75Pc

+=

wcb

cfcfwcyn tdd

tbtdFR

2.316.0 (3.13)

For Pr>0.75Pc


26

+=

c

r

wcb

cfcfwcyn P

Ptdd

tbtdFR 2.19.1

.316.0

2

(3.14)

Where Pr is the axial design capacity, Pc is equal to 0.6Py (Py is the axial yield strength of the column), Fyc is the column minimum specified yield stress, bcf is the column flange width, tcf the column flange thickness, db the beam depth, dc the column depth and tw the panel zone thickness. Equations 3.11-3.14 are based on Krawinkler (1978) proposal. Although slight modifications have occurred over time no significant modifications have been made.

On the other hand, the required shear strength demand of the panel zone under seismic loading specified by the AISC has evolved over the years. Two main approaches have been proposed, depending either on load combinations or on flexural strength at yielding of the connecting beams. The Specification is continuously under improvements and several editions have been published over the years. Recalling the Specifications of 1992, a concise revision of the main evolutions of the code referring to the panel zone required strength, follows.

(a) AISC 1992 Seismic Provisions. The provisions in 1992 attempted to be consistent with the UBC 1991, by determining the shear demand from the analysis using the appropriate load combinations. The resistance factor v for the panel zone design strength was equal to 0.75. However, there was a limiting value based on the flexural capacity the framing beams could develop, equal to 0.9bMp; where b is 0.9 and Mp is the beam plastic moment. This limiting value is referred as a capping value and its intention was to avoid exceeding realistic loading combination values.

(b) AISC 1997 Seismic Provisions. The provisions in 1997 were kept the same for estimating the shear demand in the panel. However, a structural overstrength magnification factor 0 was incorporated in the calculation of the earthquake demands. Moreover, the capped shear generated from the framing beams was modified to 0.8RyMp, where Ry accounts for yield strength above the minimum value. The intention with this capping was to account for the favourable effects of gravity loads in internal joints.

In 1999 a supplement was added to the provisions, where the main change was related with the capped shear demand of 0.8M*pb, where M*pb= (1.1RyMp+Mv). The additional moment Mv, resulted from the projection of the plastic hinge moments away from the column to the column face. A significant change was made in a supplement published in 2000, where the required strength was no longer estimated from load combinations. A minimum required shear strength Ru value was established from the summation of the moments at the column faces, determined by projecting the expected moments at the plastic hinges to the column faces, but removing the 0.8 factor. In addition, to relate beam and panel zone yielding, the resistance factor v was change from 0.75 to 1.0. In this Supplement the thickness of the panel is established from the methodology adopted for proportioning prequalified connections.


27

(c) AISC 2002 Seismic Provisions. The provisions in 2002 remained on the same line as AISC 2000, and the shear demand and the design shear strength remain unchanged. Nevertheless, a thickness condition was added to the panel zone as a requirement against local buckling of the column web.

( ) 90zz wdt + (3.15) Where t is the thickness of the column web or the doubler plates, dz is the panel zone depth between continuity plates and wz is the panel zone width between column flanges.

(d) AISC 2005 Seismic Provisions. The provisions in 2005 intended to merge the load and resistance factor design (LRFD) and the allowable stress design (ASD) design philosophies in one document, although no major change was considered for the panel zone compared to previous provision. The v factor for available strength of the panel zone remained 1.0. The required shear strength and the design shear strength remained as in AISC 2002 with minor modifications to notation.

3.5.3 Eurocode The Eurocode is a compilation of different building code regulations developed by the European Committee for Standardization. The Eurocode is organised in 10 different sections in which the objective of Eurocode 8: Design of Structures for Earthquake Resistance, is the design and construction of buildings and civil engineering works in seismic regions.

The shear resistance of column web panels should satisfy the following expression: Vwp,Ed/Vwp,Rd1.0, where Vwp,Ed is the shear force in the panel due to action effects taking into account the plastic resistance of the adjacent dissipative zones in beams or connections, and Vwp,Rd is the shear resistance in accordance to Eurocode 3 1-8 expressed as:

0

,, .3

9.0

M

vcwcyRdwp

AfV = (3.16)

Where fy,wc is the yield stress of the column web, Avc is the shear area of the column and M0 is usually assumed as 1.0 but is dependent on the national annex. If the column has web stiffeners or continuity plates, the codes allows the strength of the panel to be increased by:

s

RdfcplRdaddwp d

MV ,,,,

4= but s

RdstplRdfcplRdaddwp d

MMV ,,,,,,

22 + (3.17)

Where Mpl,fc,Rd is the design plastic moment resistance of a column flange, ds is the distance between centrelines of the stiffeners and Mpl,st,Rd is the design plastic moment resistance of a stiffener.

Chapter 4. Numerical Investigation

28

4. NUMERICAL INVESTIGATION

4.1 Introduction In this chapter an investigation is carried out to evaluate the influence of the panel zone design in structural frame response. This is achieved through the analysis of a cruciform sub-assemblage, which is representative of the behaviour of a moment-resisting frame. The properties of the structure are firstly described as well as the design criterion adopted for the panel zone. Following that, the numerical model of the structure is introduced and the procedures adopted in the analysis along with the response parameters are established. The results obtained are then presented and a discussion is made regarding the performance of the structure with particular emphasis on the influence of the panel zone.

Figure 4.1. Cruciform sub-assemblage.

b r

d

t

t

b

d

tr

t

d =d -t

w =d -t

Section A-A

B

B

Section B-B

A A

pz b bbf

bf

bw

bfpzc cf

cf

cw

c

cf


29

L/2

H/2

H/2

L/2-w /2L/2

L/2-w /2w

H/2-d /2

H/2-d /2

d

RLpz

pz

pz

pz pz pz

= V col HL

V col

V col

RR= V col HL

4.2 Cruciform Sub-Assemblage

4.2.1 Description In order to understand the panel zone role in the response of a structural frame, a simplified sub-assemblage is studied (Figure 4.2). The beam span (L) is assumed as 8.0m and the storey height (H) is assumed as 3.5m. The columns of the sub-assemblage span from the mid-height of the storeys and the beams from mid-length of the spans, where the contra-flexure points are generally located under lateral loading. The boundary conditions can then be established. The ends of the beams are assumed as vertically restrained, but able to rotate and to move horizontally. The bottom of the column is assumed vertically and horizontally restrained, but able to rotate. The top of the column is assumed free to displace. A summary of the simplified structure with the corresponding geometrical parameters and the boundary conditions are shown in Figure 4.2. The static equilibrium of the sub-assemblage is accomplished in terms of the external shear force in the column (Vcol) and the vertical reactions at the beam ends.

Figure 4.2. Sub-assemblage geometrical properties and boundary conditions.

For the design of the frame members, conventional procedures are used to determine the size of the columns and of the beams. The members are designed to sustain the demands from vertical and lateral loading, and to provide sufficient rigidity to the structure in order to fulfil drift limits. The typically adopted weak beam-strong column concept is employed for the column design To achieve this desirable energy dissipation mechanism, the column size was determined to be at least 1.3 times stronger than the plastic moment of the beams. The steel sections determined from the design with the respective dimensions and plastic moment relations, are presented in Table 4.1.

Having defined the beams and column sizes, the focus is now on the design of the connection, more precisely the web panel. In the following sections, the demands and criteria adopted in the design of the panel zone are described.


30

Table 4.1. Sub-assemblage Geometric Properties.

d bf tf tw Mpl mm mm mm mm kN.m

Steel Beam IPE400 400 180 13.5 8.6 340 Steel Column HEA340 330 300 16.5 9.5 484

4.2.2 Analytical Demands in the Panel Zone The demand in the panel zone is function of the moments in the beams and the shear in the column. The moment and shear force diagrams of the structure under lateral loading are illustrated in Figure 4.3(a). For the symmetric structure Mb,L=Mb,R and hence the moments acting at the boundaries of the panel zone can be expressed as follows.

, , ( 2 2)b L b R col pzHM M V L wL

= = (4.1)

Figure 4.3. Forces in the Panel Zone under lateral loading conditions

The forces at the boundary of the panel zone are summarized in Figure 4.3(b). The behaviour of the panel zone is mainly influenced by shear stresses. As shown by the shear force diagram, the shear force in the column is opposite in sign to the shear forces transferred through the beam flanges, therefore it reduces the demands. Thus the shear acting in the panel can be expressed as shown.

, ,b L b RPZ col

pz pz

M MV V

d d= + (4.2)

Vcol

Vcol

RL RR

Vcol

RRL R

Vcol

V M M

M /d

P

P

V col

pz

b,Lb,Lpz

V col

d b,R Vb,R

pzw

b,L M /d pzb,R

M /d pzb,L M /d pzb,R

a) b)


31

V

V

V

V

y, P-EL

y, pz

KEL

4y y

KP-EL

KSH

3y

PZ

(a) (b)

Capacity Demand

V =f(M )PZ b V =f(M )PZ b,PL

V y, pz =A . v y

=1

Mb=Mb,PL

The aim is to calculate the shear observed by the panel as function of the moments developed at the beams. Expressing the moment in the beams as Mb, the shear in the panel zone can be estimated as follows.

( 2 2)b b b

PZpz pz pz

M M M LVd d L w H

= + (4.3)

1 12( )PZ b pz pz

LV Md L w H

= (4.4)

4.2.3 Design Criterion for the Panel Zone Having defined the demands in the panel zone, a design criterion for the component needs to be established. For the structure under analysis, the panel is going to be proportioned such that yielding of this component initiates at the same load level that develops the plastic capacity of the connecting beams, as shown in Figure 4.4. However, the panel zone strength is defined at the first yield Vy,pz as marked by a circle in Figure 4.4(a) and not at the second yield as proposed by several design codes. This design criterion is referred hereafter as a balanced design.

Figure 4.4. Design criterion for the panel zone

The design criterion can be generalized by defining a capacity to demand ratio as follows:

,

,

y pz

PL PZ

VV

= >1 strong panel; 1, yielding in the beams occurs before the panel yields. Therefore

, ,1 12

( )PL PZ b PL pz pz

LV Md L w H

=


32

y

PZ

(a)

Capacity Demand

Vpz=A . v

>1

Mb =Mb,PL

V

V

V

V

y, P-EL

y, pz

KEL

4y y

KP-EL

KSH

3y

PZ

(b)

Mb =Mb,PL

ELASTIC RANGE

STRONG PANEL


33

Table 4.1. Panel Zone thickness for the control case

Parameter Value Panel thickness (tpz) 31.3 mm

Column web thickness (tcw) 9.5 mm Doubler plates thickness (tdp) 21.8 mm

In the next section a description of the numerical model of the structure is presented.

4.3 Numerical Modelling

4.3.1 OpenSees Finite Element Program for Non-linear Analysis The finite element program used in the numerical studies is Open System for Earthquake Engineering Simulation, OpenSees, developed by the University of California at Berkeley (http://www.berkeley.edu/OpenSees). The program was created for the sole purpose to be used for research projects. OpenSees is an object-oriented finite element analysis framework used to simulate structural and geotechnical scenarios in earthquake engineering.

4.3.2 OpenSees Model representation The sub-assemblage is represented in OpenSees using two different types of finite elements. The column and beams are represented by non-linear beam-column elements and the panel by a beam-column joint element, as shown in Figure 4.6.

Figure 4.6. Model Representation in OpenSees

(a) Nonlinear Beam Column element. This is a force-based element that considers the spread of plasticity across the section and along the member. The number of integration points is defined by the user and for this study five integration points chosen. Each integration point is characterised by a cross section and each section is defined by one or more uniaxial materials. A description of the Fibre Section Model is presented next.

Section A-A

L/2

Displacement Control

Non-linear beam column element

Fiber Sections

COLUMN

Beam columnjoint element

Rigid springs except shear panel

PANEL ZONE

Section B-B

A A

B

B

Non-linear beam column element

Fiber Sections

BEAM

i-node j-node

H/2

i-node

j-node

Integration Point

Bi-Linear Model Strain Hardening Steel

E

See Figure 4.7

S

ESH = S. E


34

Fibre Section Model. A fibre section enables to discretize a cross section in sub-regions denominated patches. The fibre section object is composed by different patch objects of simple geometrical shapes. For example, the flanges and the web of the I-sections are defined as rectangular patches. Each patch is described by a general geometric configuration and can be subdivided using the Fibre Command. The fibre command allows creating uniaxial fibre objects to be added to the section. A uniaxial material is then assigned to each fibre. Figure 4.6 presents the discretized fibres for the flanges and the webs of the column and the beam sections. A sub-routine was created to generate and discretize each steel section based on its geometrical properties.

The material model adopted for the steel in columns and beams is the Uniaxial Hardening Material. The properties considered are shown in Figure 4.7. The selected uniaxial material combines linear kinematic and isotropic hardening. The isotropic hardening is neglected and only kinematic hardening is considered. In this study the strain hardening parameter is assumed equal to 1%.

Figure 4.7. Uniaxial Hardening Material

(b) Beam Column Joint Element. This is used to create a joint element between the beams and the columns. As shown in Figure 4.8(a), the element is composed of 13 different components. As discussed, the main interest of the connection in the present research is to represent the panel zone behaviour, hence all the 12 translational springs are assumed as rigid. The parameter that will control the behaviour is the shear panel. The properties of the shear panel can be specified by a user defined moment-distortion relationship. In order to represent a tri-linear behaviour, a sub-routine combining two bilinear relationships in parallel was programmed. The properties assigned to the element are shown in Figure 4.8(b).

Hardening MaterialE

Fy

Fy

S

E s

ESH

Stress

Strain

ESFy

= 210000 MPa

= 275 MPa

E =SH E (H +H ) S iso kin

E +H +H S iso kin

Hiso = 0

H =kin E .S

1- = strain hardening parameter


35

M

b)

KEL

KSH

= G .A .d

= . K

K =P-EL4 E .b .t cfS cf

10

S v pz

2

EL

M

2

v pz)(1+ A .d

cfcf3.12.b .t pzv y= A . .d P-ELM pzv y= A . .d y, pzM

= strain hardeningparameter

y,P-ELM

y,pz

y 4 ya)

Figure 4.8. Panel Representation. a) Beam Column Joint Element (Lowes et al., 2004) b) Tri-linear model adopted for the shear panel

4.4 Analysis Procedures and Response Parameters

4.4.1 Analysis Procedures The structure is analysed in OpenSees by performing a nonlinear static (or pushover) analysis under displacement control. The control node is the top node, for which successive horizontal displacements of the order of one millimetre are applied to simulate the drift observed by the frame during a lateral loading condition. The target displacement for the sub-assemblage is calculated based on a storey drift of 4%.

The OpenSees software enables to record response parameters of interest; these recordings are stored in text files. The following response parameters are recorded for each step of the analysis: reactions at the boundary conditions, load factor, nodal displacements, strains at the extreme fibre of the I-sections and panel zone moments and distortions. Table 4.4 summarizes the recorded parameters.

Table 4.3. Output Parameters from the Analysis

Load factor Reactions RL, RR, RX

Nodal displacements x, y Strains at the Extreme Fibre I-section

Distortion of the panel zone

To be able to post-process this data the software Matlab is used. After loading the results these are manipulated and stored in an Excel spreadsheet and subsequently processed.

4.4.2 Response Parameters Having obtained the output parameters from the analysis, post-processing of the results is carried out to obtain additional response parameters for the sub-assemblage. These can be grouped into parameters describing the overall structure response, and parameters which are


36

. .

L

pl yL Lp

dx Lp

=

( )CS

pzcolCOL IxE

dHV..3

222

3=

related to the local response of the beams, columns and panel zones. A summary of all the response parameters is presented in Table 4.5 and the expressions adopted for the beam response are provided in Figure 4.9. For the panel zone, the contribution to the top displacement is function of the distortion and the geometrical configuration of the sub-assemblage as presented below.

( )( )( )

+=

pzpz

pzpzpzpzPZ wwL

dwdHwL222

.22224 (4.7)

Table 4.2. Response Parameters

Component Parameter Units Description

=+PZ+ COL [m] Top displacement Drift=/H [%] Top displacement over storey height Vcol [kN] Column Shear force

STRUCTURE

= /y Structure ductility

[mrad] Plastic hinge rotation

Lph/L Normalized plastic hinge length = /y Curvature ductility = /y Rotation ductility EL Cont=BEAM-ELiii/ [%] Elastic Contribution to top displacement PL Cont=BEAM-PLiv/ [%] Plastic Contribution to top displacement

BEAM

BEAM Cont=BEAMv/ [%] Beam Contribution to top displacement = EL+PL

[mrad] Distortion = /y Distortion ductility PZ [m] Panel Zone top displacement

PANEL

PZ Cont=PZvi/ [%] Panel Zone Contribution to top displacement

Column top displacement

COLUMN

COL Cont=COL/ [%] Column Contribution to top displacement


37

Figure 4.9. Plastic Hinge Concept

4.5 Discussion of Results The lateral performance of the sub-assemblage is now examined with the emphasis on the influence of the panel zone in the overall response of the structure and based on the response parameters described in the previous section.

The global response of the structure can be evaluated based on the pushover curve presented in Figure 4.10. The load factor applied to the structure to reach the objective displacement is referred in terms of Vcol. Three main points can be identified, namely, the initial yield of the beams, the point where the panel yields and the beams reach the plastic moment and finally, the point where the panel reaches the second yield. The load factor and the corresponding drift for each of these points are also provided in the plot.

Lph

x

MyMpl

y

L'

pl

=M /EIy

y

M : yield momentyM : plastic momentpl Moment Diagram

Curvatures

plBEAM-PL

BEAM-EL

Deflections

R

' _

0

. . . .phL L

BEAM EL y phx dx x L

= + ' _

'

. . . .ph

L

BEAM PL y phL L

x dx x L

=

'

0

. .L

BEAM x dx =


38

0

50

100

150

200

250

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0%

Drift

Vcol[kN]

Beam first yield

Panel zone yield and beam plastic moment

Panel zone second yield

[1.20%; 181kN]

[1.45%; 202kN]

[2.65%; 216kN]

Figure 4.10. Pushover Curve

Attention is now driven to the deformation of the structure. The scaled deformed shape for a 4% drift is presented in Figure 4.11. The contribution from the various components (beams, column and panel zone) to the flexibility of the structure is illustrated in Figure 4.12 for increasing levels of deformation of the system.

Figure 4.11. Deformed Shape 4% Drift

Before yielding takes place, the contribution to displacement is shared by the components as follows: the beams contribute 67.7%, followed by the column with 19.7% and then the panel with 12.6%. When yielding in the beams initiates, an increase in the contribution from these members occurs. However, when yielding of the panel takes place, the contribution from this component to the global deformation observes a gradual increase up to 30% (for 4% drift). This effect is obviously reflected in a reduction in terms of the contribution from the column

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00


39

0%

25%

50%

75%

100%

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0%

Drift

Con

trib

utio

n to

Def

orm

atio

n

100%

Beam

Column

Panel

and the beams. It becomes clear that panel yielding leads to an attenuation of the demand imposed on the beam. This will be further discussed and illustrated later in this section.

Figure 4.12. Contribution from Beam, Panel and Column to the drift

As presented in the previous section, the participation of the beams to the deformation of the structure can be divided into two terms namely, the elastic the plastic contributions which are illustrated in Figure 4.13. It is clear from the figure that the plastic contribution from the beam initiates when yielding takes place. The elastic contribution of the beam becomes less relevant as the plastic hinge develops in the beams. At approximately 3% drift the plastic contribution becomes more important then the elastic contribution. At the final displacement equivalent to 4% drift, the plastic and elastic contribution are 61% and 39%, respectively of the total contribution of the beam.

Figure 4.13. Beam Elastic and Plastic Contribution to the drift

It is worth noting that the total deformation of the structure at 4% drift results from 31% and 69% of elastic and plastic deformation of the components, respectively.

0%

25%

50%

75%

100%

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0%

Drift

Con

trib

utio

n to

Def

orm

atio

n

100%

Beam

Beam ELBeam PL


40

0

5

10

15

20

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0%

Drift

pl [mrad]

Having discussed the global response of the structure, the focus hereafter will be on the local response of the components. Regarding the beams, the plastic hinge rotation against drift is presented in Figure 4.14. As expected from the plastic contribution of the beams, the plastic hinge rotation increases as the deformation of the structure increases. Consistently with Figure 4.12, three different ranges can be observed. In the first range, the rate of increase in the rotations is larger compared to the rate after the panel yields. Similarly, the rate at which rotations increase after second yield of the panel is lower than the previous range. It is therefore clear the attenuating effect in terms of plastic demand that panel yielding provides to the beams.

Figure 4.14. Plastic Hinge Rotation Beams

The maximum plastic rotation of the beam at 4% drift is 16mrad. If plastic behaviour was only concentrated on the beams, plastic rotations of about 28mrad would be expected to develop in the beams for this level of drift. However, due to the development of inelasticity in the panel, the plastic beam rotations are clearly lower leading to a more desirable element response.

Another local response parameter involving the beam is the spread of plasticity along the member which is typically represented by the plastic hinge length Lph. Obviously, the plastic hinge length does not increase in steps, it rather spreads as a continuous function. However, the calculations are performed between integration points and hence the jumps in plastic hinge length visible in Figure 4.15. When the plastic moment in the beams is reached, the plastic hinge length is equal to 10% L, which is around 400mm, approximately the beam depth. For the final displacement the plastic hinge reache

Dissertation2007-DavilaArbona

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