seismic behavior of column-base plate connections …

SEISMIC BEHAVIOR OF COLUMN-BASE PLATE CONNECTIONS

BENDING ABOUT WEAK AXIS

by

Daeyong Lee

A dissertation submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy (Civil and Environmental Engineering)

in The University of Michigan 2001

Doctoral Committee: Professor Subhash C. Goel, Chairman Assistant Professor Božidar Stojadinović (UC Berkeley) Professor James K. Wight Professor Jwo Pan (MEAM)

ABSTRACT

SEISMIC BEHAVIOR OF COLUMN-BASE PLATE CONNECTIONS

BENDING ABOUT WEAK AXIS

by

Daeyong Lee

Chair: Subhash C. Goel

Column-base plate connection is one of the most important structural elements in

a steel structure, especially in a Moment Resisting Frame (MRF). The base plate connects

the column to the concrete foundation directly so that lateral forces due to wind or

seismic effects can be transferred through the base plate and anchor bolts to the

foundation. In spite of the importance of the column-base plate connection in steel MRFs,

there have been no unified seismic design provisions for this connection in the U.S.

In order to understand the complex force flow and stress distribution in the

column-base plate connection under large lateral displacements, a few experimental and

theoretical studies have been conducted after the Northridge earthquake in the U.S.

Recently, Drake and Elkin suggested a design procedure. They adopted an equivalent

rectangular bearing stress block, instead of a triangular shape, to apply the AISC LRFD

philosophy. However, their design method has not been verified analytically or

experimentally for either the strong or the weak axis bending case.

For the weak axis bending case, an analytical and experimental study was

undertaken by the author to evaluate the Drake and Elkin's design method (D&E method)

and to develop a more reliable design method. Two fairly typical types of the column-

base plate connection in the U.S. practice (i.e., 6-bolt type and 4-bolt type) were selected.

Using these selected two connection types, the D&E method was evaluated through

numerical and experimental studies. The results showed several limitations of the D&E

method and also pointed to some design considerations needed to develop a more rational

and reliable design method. Finally, based on the proposed new design force profile and

the concept of relative strength ratios among the connection elements, a new design

method was developed. Furthermore, two limit states of the column-base plate

connection were defined to prevent undesirable connection failures and to maximize

cyclic connection ductility.

© Reserved Rights All

Lee Daeyong 2001

To my parents and family

ii

ACKNOWLEDGMENTS

The author wishes to thank Professor Subhash C. Goel and Professor Božidar

Stojadinović for their invaluable guidance, advice, and encouragement throughout this

research work. The author also wishes to express his appreciation to Professor James K.

Wight and Professor Jwo Pan, members of his doctoral committee, for reviewing the

dissertation and offering valuable suggestions and comments.

This research was sponsored by the National Science Foundation under Grant No.

NSF-CMS 9810595. The author gratefully acknowledges the financial support.

Thanks are due to Robert Spence and Robert Fisher for their assistance during the

experimental phase of the research.

The author is indebted to his wife, Eunhee Kim, for her understanding and

encouragement during his study at The University of Michigan.

iii

TABLE OF CONTENTS

DEDICATION................................................................................................................... ii

ACKNOWLEDGMENTS ............................................................................................... iii

LIST OF TABLES ......................................................................................................... viii

LIST OF FIGURES ......................................................................................................... ix

LIST OF APPENDICES ............................................................................................... xiii

NOTATION.................................................................................................................... xiv

CHAPTER

1. INTRODUCTION...............................................................................................1

1.1 Background ..........................................................................................1 1.2 Literature Review .................................................................................5

1.2.1 Experimental Studies ........................................................5 1.2.2 Theoretical Studies............................................................9

1.3 Objectives of the Study ......................................................................10 1.4 Scope of the Study..............................................................................11 1.5 Organization of the Dissertation.........................................................13

2. SPECIMEN DESIGN AND PRE-TEST ANALYSES ..................................16

2.1 Outline of Drake and Elkin's Design Method ....................................17 2.1.1 Design Procedure for Base Plate Thickness ...................17 2.1.2 Design Procedure for Anchor Bolt Size..........................22

2.2 Design of Column-Base Plate Connection Assemblages...................24 2.2.1 Specified Compressive Strength of Grout, fc' .................25 2.2.2 Column............................................................................26 2.2.3 Base Plate........................................................................27 2.2.4 Anchor Bolts ...................................................................27 2.2.5 Weld Materials and Details.............................................29 2.2.6 Classification of Specimens............................................31

2.3 Pre-test Analyses ................................................................................33 2.3.1 Finite Element Analysis Models.....................................33 2.3.2 Finite Element Analysis Results .....................................38

2.3.2.1 Total Lateral Force .........................................38

iv

2.3.2.2 Total Tensile Bolt Force.................................39 2.3.2.3 Yielding in the Base Plate ..............................42 2.3.2.4 Bearing Stress Distribution on the

Grout...............................................................43

3. EXPERIMENTAL EVALUATION OF DRAKE AND ELKIN'S METHOD ..........................................................................................................45

3.1 Test Setup and Loading History.........................................................46 3.2 Gauge Location ..................................................................................48 3.3 Coupon Test Results...........................................................................51 3.4 Summary of Test Results ...................................................................52

3.4.1 Specimen 6-1 (SP 6-1) ....................................................53 3.4.2 Specimen 6-2 (SP 6-2) ....................................................55 3.4.3 Specimen 4-1 (SP 4-1) ....................................................57 3.4.4 Specimen 4-2 (SP 4-2) ....................................................59

3.5 Experimental Evaluation of Drake and Elkin's Method.....................62 3.5.1 Total Lateral Force..........................................................62 3.5.2 Total Tensile Bolt Force .................................................63 3.5.3 Effects of Different Number of Anchor Bolts ................65 3.5.4 Stiff Base Plate................................................................69

3.6 Effects of Different Weld Material and Weld Detail .........................73 3.6.1 Effects of Different Weld Material (Between SP

6-1 and SP 6-2) ...............................................................73 3.6.2 Effects of Fillet Weld Reinforcement over the

Groove Welds (Between SP 4-1 and SP 4-2) .................74

4. NUMERICAL PARAMETRIC STUDY ........................................................75

4.1 Classification of FEA Models ............................................................75 4.2 Effects of Anchor Bolt Stiffness ........................................................77

4.2.1 Total Lateral Force..........................................................78 4.2.2 Total Tensile Bolt Force .................................................80 4.2.3 Deformation of the Base Plate ........................................81 4.2.4 Variation of Yield Pattern in the Base Plate ...................84 4.2.5 Variation of Bearing Stress Distribution on the

Grout ...............................................................................87 4.2.6 Location of the Resultant Bearing Force ........................87

4.3 Effects of Base Plate Thickness .........................................................91 4.3.1 Total Lateral Force..........................................................92 4.3.2 Total Tensile Bolt Force .................................................94 4.3.3 Deformation of the Base Plate ........................................95 4.3.4 Variation of Yield Pattern in the Base Plate ...................99 4.3.5 Variation of Bearing Stress Distribution on the

Grout ...............................................................................99 4.3.6 Location of the Resultant Bearing Force ......................104

4.4 Effects of Grout Compressive Strength............................................105

v

5. LIMITATIONS OF DRAKE AND ELKIN'S METHOD...........................107

5.1 Unrealistic Application of Concrete Beam Design Methodology ....................................................................................107

5.2 Over-sensitive Design Procedure to q (or fc')...................................108 5.3 Inaccurate Location of Two Bending Lines .....................................111 5.4 No Explanation of Anchor Bolt Location Effects ............................111 5.5 No Use of Relative Strength Ratios .................................................112 5.6 Design of Stiff Base Plate ................................................................113

6. NEW DESIGN METHOD .............................................................................114

6.1 Three Geometric Ratios....................................................................114 6.1.1 Ratio of (bf / B) .............................................................115 6.1.2 Ratio of (a / B) ..............................................................116 6.1.3 Ratio of (a' / a) ..............................................................117

6.2 Three Strength Ratios.......................................................................117 6.2.1 Definition of Mp_column...................................................118 6.2.2 Definition of Mp_bolt ......................................................120 6.2.3 Definition of Mp_plate .....................................................121 6.2.4 Ratio of (Mp_bolt / Mp_column) ..........................................121 6.2.5 Ratio of (Mp_plate / Mp_column) .........................................122 6.2.6 Ratio of (Mp_bolt / Mp_plate) .............................................123

6.3 Desired Connection Behavior ..........................................................123 6.3.1 Target Location of Resultant Bearing Force.................124 6.3.2 Two Methodologies ......................................................125 6.3.3 Suggested Value for SR1 (= Mp_bolt / Mp_column) ...........127 6.3.4 Suggested Value for φbp ................................................127

6.4 New Design Force Profile ................................................................129 6.5 Basic Design Formulas.....................................................................131

6.5.1 Design of Base Plate Thickness....................................131 6.5.2 Design of Anchor Bolt Size ..........................................135

6.6 New Design of Base Plate Thickness and Anchor Bolt Size ...........136

7. TWO LIMIT STATES OF COLUMN-BASE PLATE CONNECTION...............................................................................................137

7.1 Limit State on the Tension Side (Numerical Approach)..................138 7.1.1 Basic Methodology .......................................................138 7.1.2 Limit State Check on the Tension Side

(Numerical Approach) ..................................................140 7.2 Limit State on the Tension Side (Theoretical Approach).................141

7.2.1 Global and Local Mechanisms......................................141 7.2.2 α and β ..........................................................................143 7.2.3 Minimum Base Plate Thickness ...................................145 7.2.4 Maximum Value of P, Pmax ...........................................146

vi

7.2.5 Limit State Check on the Tension Side (Theoretical Approach).................................................149

7.2.6 α versus (tp)min...............................................................150 7.3 Limit State on the Compression Side ...............................................150

7.3.1 Effective Bearing Area and Grout Bearing Strength .........................................................................151

7.3.2 Required Minimum Compressive Strength of the Grout .............................................................................153

7.3.3 Limit State Check on the Compression Side ................154 7.3.4 Confining Band.............................................................154

7.4 Comparison of Two Design Procedures...........................................155

8. SUMMARY AND CONCLUSIONS .............................................................157

8.1 Summary ..........................................................................................157 8.2 Conclusions ......................................................................................160 8.3 Suggestions for Future Study ...........................................................162

APPENDICES................................................................................................................163

BIBLIOGRAPHY..........................................................................................................184

vii

LIST OF TABLES

Table

2.1. Mechanical Properties of Two Weld Materials ............................................30

2.2. Classification of Specimens..........................................................................32

2.3. Mechanical Properties of Connection Elements ...........................................36

3.1. Coupon Test Results .....................................................................................52

4.1. Classification of FEA Models.......................................................................76

4.2. Selected Connections for the Study of Anchor Bolt Stiffness Effects..........78

4.3. Selected Connections for the Study of Base Plate Thickness Effects ..........91

4.4. Selected Connections for the Study of Grout Compressive Strength Effects .........................................................................................................105

6.1. Ry Values for Several Members (From AISC Seismic Provisions 97') ......119

6.2. Comparison of Connection Element Sizes .................................................136

7.1. Minimum Base Plate Thickness with Different Values of α......................150

viii

LIST OF FIGURES

Figure

1.1. Damage at a Column-Base Plate Connection .................................................2

1.2. Brittle Fracture through the Base Plate...........................................................2

1.3. Separation between Nut and Base Plate..........................................................3

1.4. Statistical Analysis Results of the Damage in Steel Structures ......................3

2.1. Plan View and Basic Dimensions of a Column-Base Plate Connection (6-Bolt Type) ................................................................................................18

2.2. Unknown Design Parameters in a Column-Base Plate Connection .............19

2.3. Effects of fc' on Base Plate Thickness (tp).....................................................25

2.4. Base Plate Planar Dimensions and Anchor Bolt Diameters .........................28

2.5. Anchoring System using Supplemental Anchor Plates (6-Bolt Type) .........29

2.6. Weld Detail of Column-Base Plate Connection Assemblages .....................31

2.7. FEA Model and its Boundary Conditions (6-Bolt Type) .............................34

2.8. Constitutive Relationships of Steel and Concrete Elements.........................35

2.9. Deformation of Column-Base Plate Connection Assemblages ....................37

2.10. Total Lateral Force versus Drift Responses..................................................39

2.11. Total Tensile Bolt Force versus Drift Responses .........................................40

2.12. Effects of Different Anchor Bolt Stiffness on Connection Behavior ...........41

2.13. Equivalent Mises Stress Contours on the Base Plate Surfaces (3.85 % Drift) .............................................................................................................43

2.14. Bearing Stress Distribution on the Grout (3.85 % Drift) ..............................44

3.1. Test Setup......................................................................................................46

ix

3.2. Loading History ............................................................................................47

3.3. Location of Strain Gauges and Displacement Transducers (6-Bolt Type).............................................................................................................49

3.4. Location of Strain Gauges and Displacement Transducers (4-Bolt Type).............................................................................................................49

3.5. Planar Location of Strain Gauges on the Anchor Bolts................................50

3.6. Location of Strain Gauges on Anchor Bolts and Gauge Protection (6-Bolt Type) .....................................................................................................50

3.7. Identification of Column Flanges (6-Bolt Type) ..........................................51

3.8. Moment-Rotation Response (SP 6-1) ...........................................................54

3.9. Initial Cracks in Welds at Column Flange Tips (SP 6-1) .............................54

3.10. Fracture of Column Flange "R1" Tip (SP 6-1) .............................................55



3.13. Fracture of Column Flange "L2" Tip (SP 6-2) .............................................57



3.16. Plastic Hinge Formation at the Bottom of the Column (SP 4-1) ..................59



3.19. Crack Initiation and Sudden Connection Failure (SP 4-2) ...........................61

3.20. Comparison of Total Lateral Forces .............................................................64

3.21. Comparison of Total Tensile Bolt Forces.....................................................66

3.22. Deformed Shape of the Base Plate along the Assumed Bending Line on the Tension Side (1.71 % Drift)...............................................................67

3.23. Grout Crushing in the 4-Bolt Type Connection (SP 4-1) .............................68

3.24. Strain Variation at the Center of the Assumed Bending Line (SP 6-1) ........70

x



4.1. Total Lateral Forces versus Drifts.................................................................79

4.2. Total Tensile Bolt Forces (3.85 % Drift) ......................................................80

4.3. Deformation of the Base Plate (6-Bolt Type, 3.85 % Drift).........................82


4.5. Equivalent Mises Stress Contours on the Base Plate Surface (6-Bolt Type, 3.85 % Drift).......................................................................................85

4.6. Equivalent Mises Stress Contours on the Base Plate Surface (4-Bolt Type, 3.85 % Drift).......................................................................................86

4.7. Bearing Stress Distribution on the Grout (6-Bolt Type, 3.85 % Drift).........88

4.8. Bearing Stress Distribution on the Grout (4-Bolt Type, 3.85 % Drift).........89

4.9. Overall Moment Arm L and Cantilever Lengths x and x' ............................90

4.10. Effects of Anchor Bolt Stiffness on Cantilever Length x' ............................90

4.11. Total Lateral Forces versus Drifts.................................................................93

4.12. Total Tensile Bolt Forces (3.85 % Drift) ......................................................94



4.15. Local Deformation of Outer Anchor Bolt (0.8 tpo, 3.85 % Drift) .................98

4.16.Local Stress Concentration in Outer Anchor Bolt (0.8 tpo, 3.85 % Drift)......................................................................................................................98

4.17. Equivalent Mises Stress Contours on the Base Plate Surface (6-Bolt Type, 3.85 % Drift).....................................................................................100

4.18. Equivalent Mises Stress Contours on the Base Plate Surface (4-Bolt Type, 3.85 % Drift).....................................................................................101

4.19. Bearing Stress Distribution on the Grout (6-Bolt Type, 3.85 % Drift).......102

4.20. Bearing Stress Distribution on the Grout (4-Bolt Type, 3.85 % Drift).......103

xi

4.21. Effects of Base Plate Thickness on Cantilever Length x' ...........................104

4.22. Variation of Cantilever Length x' on the Compression Side with Respect to fc' (6-Bolt Type, 3.85 % Drift) ..................................................106

5.1. Effects of q Value on the Location of Ru (= q·Y).......................................110

6.1. Two New Variables (a and a') Determining the Locations of Tu and Ru....115

6.2. Effects of Anchor Bolt Stiffness on the Ru Location (1.0 tpo) ....................126

6.3. Effects of Base Plate Thickness on the Ru Location (1.3 Ko).....................126

6.4. (Mp_bolt / Mp_column) versus (a' / a) ................................................................128

6.5. Comparison of Two Design Force Profiles ................................................130

6.6. Simplified Analysis Model (Simple Beam Model) ....................................132

6.7. Free Body Diagram.....................................................................................133

7.1. Limit Lines for Anchor Bolt Local Yielding ..............................................139

7.2. (Mp_bolt / Mp_column) versus (Mp_bolt / Mp_plate)max..........................................139

7.3. Global Mechanism......................................................................................142

7.4. Local Mechanism (For Each Anchor Bolt).................................................142

7.5. Detail around Anchor Bolt..........................................................................144

7.6. Simplified Local Mechanism......................................................................146

7.7. Two Internal Forces in Each Anchor Bolt ..................................................147

7.8. Stress Distribution across Anchor Bolt.......................................................148

7.9. Effective Bearing Area on the Grout ..........................................................152

7.10. Circular Shape Confining Band ..................................................................154

7.11. Comparison of Two Design Procedures .....................................................156

xii

LIST OF APPENDICES

Appendix

A. Column-Base Plate Connection Design (D&E Method) ............................164

B. Column-Base Plate Connection Design (New Method) .............................170

C. Minimum Base Plate Thickness (Numerical Approach). ...........................175

D. Minimum Base Plate Thickness (Theoretical Approach)...........................177

E. Required Minimum Compressive Strength of Grout..................................182

xiii

NOTATION

a distance between anchor bolts and base plate edge on the tension side

a' distance between resultant bearing force and base plate edge on the compression side

Ab nominal (gross) area of each anchor bolt

Ab_eff effective area of each anchor bolt

Ab_total total area of anchor bolts on the tension side

Ag_eff effective bearing area on the compression side

A1 area of the base plate concentrically bearing on the concrete (or grout)

A2 maximum area of the portion of the supporting surface that is geometrically similar to and concentric with the loaded area

bf column flange width

d overall column depth

db diameter of each anchor bolt including threaded part

db_eff effective diameter of each anchor bolt

dh diameter of oversized bolt hole

d1 distance between P1 and center of anchor bolt on the tension side (See Figure 7.4)

d2 distance between P2 and center of anchor bolt on the tension side (See Figure 7.4)

f anchor bolt distance from the centerline of column or base plate

fc' specified compressive strength of concrete (or grout)

xiv

fp concrete bearing stress capacity

Ft nominal tensile strength of anchor bolt

Fv nominal shear strength of anchor bolt

Fy specified minimum yield stress of beam

Fye expected yield stress of beam

Fy_bolt specified minimum yield stress of anchor bolt

Fy_column specified minimum yield stress of column

Fy_plate specified minimum yield stress of base plate

GR1 ratio of (bf / B)

GR2 ratio of (a / B)

GR3 ratio of (a' / a)

h distance between the location of maximum base plate design moment and the anchor bolts on the tension side

Ib_eff effective moment of inertia of each anchor bolt

Ko designed anchor bolt stiffness using Drake and Elkin's method

L distance between Tu and Ru

Lcolumn length of column

Ls distance between Tu and Ru when a = a' (= B - 2a)

m base plate bearing interface cantilever length perpendicular to moment direction

Mmax maximum design moment in base plate

Mn nominal flexural strength per unit width

Mp plastic bending moment per unit width

Mpl required base plate flexural strength per unit width

Mp_bolt ultimate moment capacity of anchor bolt in the connection

xv

(Mp_bolt)' ultimate moment capacity of anchor bolt in the connection when a = a'

Mp_column ultimate strength of column

Mp_plate ultimate strength of base plate

Mu required flexural strength (design moment)

n base plate bearing interface cantilever length parallel to moment direction

N base plate width

P equivalent reaction force in simplified local mechanism (See Figure 7.6)

Pmax maximum value of P

Pt_bolt tensile force limit of anchor bolt

P1 equivalent reaction force in anchor bolt (See Figure 7.4)

P2 equivalent reaction force in anchor bolt (See Figure 7.4)

q concrete bearing capacity per unit length

Rn nominal bearing strength

Ru resultant bearing force

Ry ratio of the expected yield stress to the specified minimum yield stress of beam

SR1 ratio of (Mp_bolt / Mp_column)

SR2 ratio of (Mp_plate / Mp_column)

SR3 ratio of (Mp_bolt / Mp_plate)

tf column flange thickness

tp required base plate thickness

tpo designed base plate thickness using Drake and Elkin's method

(tp)min minimum base plate thickness

tw column web thickness

xvi

Tu required total tensile strength of anchor bolts

Tub required tensile strength of each anchor bolt

Vu required total shear strength of anchor bolts

Vub required shear strength of each anchor bolt

W nut width across flats

Wu distributed loads on the base plate

x base plate tension interface cantilever length

x' base plate compression interface cantilever length

Y equivalent bearing length

Z plastic section modulus of beam

Zx_plate plastic section modulus of base plate

Zy_column plastic section modulus of column (about weak axis)

α ratio between P1 and P2

β equal to (d1 = d2)

φ resistance factor for anchor bolt

φb resistance factor for flexure

φbp resistance factor for flexure in base plate

φc resistance factor for bearing

#t number of anchor bolts resisting tensile force

#v number of anchor bolts resisting shear force

xvii

CHAPTER 1

INTRODUCTION

1.1 Background

Column-base plate connection is one of the most important structural elements in

a steel structure, especially in a Moment Resisting Frame (MRF). The base plate connects

the column to the concrete foundation directly so that lateral forces due to wind or

seismic effects can be transferred through the base plate and anchor bolts to the

foundation. In spite of the importance of the column-base plate connection in steel MRFs,

there are no unified seismic design provisions for this connection in the U.S.

In the U.S., most column-base plate connections resisting large moments have

been designed by using the AISC design guide series No. 1 (DeWolf and Ricker, 1990).

Unfortunately, these connections showed serious weaknesses during recent earthquakes.

Extensive damage to column-base plate connections has been reported since the

Northridge earthquake in 1994 (Northridge Reconnaissance Team, 1996). Many column-

base plate connections failed in several consistent patterns, such as brittle base plate

fracture, excessive bolt elongation, unexpected early bolt failure, concrete crushing, etc.

Typical damage patterns in these connections during the Northridge earthquake are

shown in Figures 1.1, 1.2, and 1.3. Furthermore, in Japan, similar damage types in the

column-base plate connections have also been reported since the 1995 Hyogo-ken Nanbu

(Kobe) earthquake. Based on the statistical results of the damage in steel structures

compiled after the Kobe earthquake, shown in Figure 1.4, Midorikawa (1997) noted

relatively high incidences of damage in the column-base plate connections designed by

1

2

Figure 1.1. Damage at a Column-Base Plate Connection

(Picture from Earthquake Spectra, EERI, Supplement C-2 to Vol.11, 1996, pp.29.)

Figure 1.2. Brittle Fracture through the Base Plate


3

Figure 1.3. Separation between Nut and Base Plate


Current Code

UnidentifiedPrevious Code

02468

1012

1416

18

(%)

Column BeamBrace Column

Base

Figure 1.4. Statistical Analysis Results of the Damage in Steel Structures

(Data from Midorikawa, 1997)

4

the current Japanese code as well as the previous code. The lessons from the above two

reports led to the need for improved understanding of column-base plate connection

behavior under seismic excitations and for development of more reliable design methods.

In order to understand the complex force flow and stress distribution in the

column-base plate connection under large lateral displacements, a few experimental and

theoretical studies have been conducted after the Northridge earthquake in the U.S.

Recently, Drake and Elkin (1999) suggested a design procedure. They adopted an

equivalent rectangular bearing stress block, instead of a triangular shape, to apply the

LRFD method. However, their design method has not been verified analytically or

experimentally for either the strong or the weak axis bending case.

An organized study has been conducted at The University of Michigan to evaluate

the Drake and Elkin's design method (D&E method) and to develop a more reliable

design method. Fahmy (1999) completed the first phase of the study for the case of the

strong axis bending. For the weak axis bending case, an analytical and experimental

study was undertaken by the author. Two fairly typical types of the column-base plate

connection in the U.S. practice (i.e., 6-bolt type and 4-bolt type) were selected. Using

these selected two connection types, the D&E method was evaluated through the

numerical and experimental studies. The results showed several limitations of the D&E

method and also pointed to some design considerations needed to develop a more rational

design method. Finally, based on the proposed new design force profile and the concept

of relative strength ratios among the connection elements, a new design method was

developed. Furthermore, two limit states of the column-base plate connection were

defined to prevent undesirable connection failures and to maximize cyclic connection

ductility.

5

1.2 Literature Review

In order to understand the column-base plate connection behavior under axial

loads and moments (i.e., combined loads) or the moments only, several experimental and

theoretical studies have been conducted in the past. Outlines and major findings of each

study are briefly summarized in the following:

1.2.1 Experimental Studies

DeWolf and Sarisley (1980) tested sixteen specimens to understand the effects of

axial loads and moments on the column-base plate connection behavior. The specimens

consisting of tube section columns were tested under varying eccentricity of the axial

loads. The main variables were eccentricity of the axial loads, anchor bolt size, and base

plate thickness. Three different failure modes were investigated: (1) concrete crushing at

small eccentricity of the axial loads, (2) anchor bolt yielding at large eccentricity of the

axial loads with a thick base plate, and (3) base plate yielding at large eccentricity of the

axial loads with a thin base plate. Based on the test results, three conclusions were drawn:

First, the distance between the anchor bolt on the tension side and the bearing zone is

shortened when the anchor bolt size is large in relation to the base plate dimensions.

Second, the effects of confinement in the concrete foundation should be included in the

design procedures when the concrete area is greater than the base plate area. Lastly,

increasing the base plate thickness beyond what is indicated by the design method can

lead to decreased connection capacity because of large bearing stresses on the

compression side.

Picard and Beaulieu (1985) tested fifteen specimens to study the behavior of

column-base plate connections under various loading conditions and to determine the

6

influence of axial loads in the connection rigidity. Three different column sections (i.e.,

M, W, and HSS) and two different anchor bolt types (i.e., 2-bolt type and 4-bolt type)

were selected for the experimental study. Two different loading conditions were applied:

(1) lateral loads only and (2) axial loads with different eccentricities. The test results

indicated that the axial loads applied on the column significantly increase the rotational

stiffness of the connection, and this rotational restraint in the connection is sufficient to

affect the frame responses. In addition, within several limitations, a theoretical model that

can predict the ultimate capacity of the connection was developed.

Thambiratnam and Paramasivam (1986) conducted experimental studies to

examine the behavior of base plates under the combined loads (i.e., axial loads and

moments). Twelve specimens consisting of tube section columns were tested. The

loading conditions were very similar to the DeWolf and Sarisley's. Two main variables

were considered: eccentricity of the axial loads and base plate thickness. Under small

eccentricity of the axial loads, the primary failure mode was concrete crushing. On the

other hand, base plate yielding was the primary failure mode under large eccentricity of

the axial loads. They reconfirmed that a thick base plate tends to ride up on edge because

of its high stiffness, and this may cause a premature connection failure due to large

bearing stresses on the compression side. They also observed that a thin base plate results

in early base plate yielding and thus, may not behave as predicted.

Sato and Kamagata (1988) performed an experimental study to understand force

flows among the connection elements in column-base plate connections. Under axial

loads and cyclic lateral loads, six specimens composed of four post-tensioned anchor

bolts and a stiff base plate were tested. Three main parameters were considered: base

plate size, column axial loads, and yield ratio of anchor bolt. Based on the test results, a

formula that can estimate the fixity and rotational capacity of the column-base plate

connection was developed. In addition, in order to study the effects of column base

hysteresis characteristics on the superstructure behavior, seismic response analyses were

7

conducted using three different framing systems designed by the Japanese seismic code.

Based on the analysis results, they noted that assuming the fixed condition of column-

base plate connections in the moment frame could result in underestimation of story drifts

and energy dissipation.

Astaneh et al. (1992) tested six column-base plate connection assemblages

consisting of W-shape columns to study their seismic behavior under axial loads and

cyclic lateral displacements. Four anchor bolts bent 90° at the bottom were used to

connect the base plate to the grout and foundation. Main variables were the amount of

axial loads and the thickness of base plate. Through the experimental study, they

observed that yielding in the base plate could be used as a good source of energy

dissipation for ductile connection behavior. They classified the base plate behavior into

one of three categories, i.e., a thin, intermediate, and thick base plate. Based on those

categories, they suggested three simplified base plate behavior models.

Targowski et al. (1993) conducted experimental and numerical studies to

understand the base plate behavior under pure bending conditions. For the experimental

study, a total of twelve connection assemblages consisting of six different column

sections (i.e., square, rectangular, circular, channel, and two different I-sections) and two

different base plate thicknesses (i.e., 6 mm and 10 mm) were prepared. Each connection

assemblage was connected to the concrete foundation using four anchor bolts. In order to

provide the limit loads of the connection, two possible failure mechanisms in the

connection were studied. For the numerical study, only square section columns were

considered. Based on the numerical analysis results, the performance of base plate under

pure bending condition was assessed. In addition, the contact force distribution between

the base plate and the concrete foundation was investigated.

Jaspart and Vandegans (1998) tested twelve column-base plate connections

consisting of I-shaped columns under combined loads (i.e., axial loads and moments).

Two anchor bolt types (i.e., 2-bolt type and 4-bolt type) were used for the test specimens,

8

and three main parameters (i.e., axial load, base plate thickness, and number of anchor

bolts) were considered. Through the experimental study, they observed that the bond

stresses between anchor bolt and concrete foundation vanish quickly at the beginning of

the loading. They also found that the contact zone on the compression side could change

with the increase of axial loads. Using the component method described in Annex J of

Eurocode 3, they developed a mechanical model that can estimate the moment-rotation

responses of a column-base plate connection.

Burda and Itani (1999) tested six one-half scale column-base plate connection

assemblages consisting of various base plate sizes and thicknesses. For the loading

condition, a constant axial load and lateral cyclic displacements were applied. They also

conducted nonlinear finite element analyses using the ADINA program to determine the

bearing stress distribution profile under the base plate. In addition, in order to study the

seismic responses of a selected four-story steel moment building, the DRAIN-3DX

program was used. Based on the numerical and experimental studies, a design procedure

that limits the inelastic behavior of the base plate was proposed.

Fahmy (1999) at The University of Michigan tested three column-base plate

connection assemblages under lateral cyclic displacements. Based on the test results and

nonlinear finite element analyses, he showed that weak column-strong connection

mechanism could maximize the post-yield deformation of the connection. In addition, a

concept of connection strength ratio was introduced to help the designers choose a

desired connection failure mode.

Adany et al. (2000) investigated the cyclic behavior of the column-base plate

connections consisting of the base plates directly connected to a steel base element. Total

six specimens, including one repaired specimen, were tested under cyclic lateral loads.

Three major findings from the experimental study are briefly summarized as: (1) The bolt

pre-tensioning has no outstanding effects on the cyclic behavior of the connection. (2)

The weld cracking affects significantly the cyclic moment resistance and the energy

9

absorption capacity of the connection. (3) The rigidity and the energy dissipation capacity

of the connection decrease whenever there is a significant bolt elongation.

1.2.2 Theoretical Studies

Ermopoulos and Stamatopoulos (1996A) proposed an analytical model which can

calculate the position of neutral axis and angle of rotation in the base plate under the

given axial loads and moments. Based on the level of concrete bearing stresses under the

base plate, column-base plate connections were classified in three types and in turn, three

analytical methods corresponding to each connection type were developed. In these

analytical models, the following main parameters were considered: (1) the size and

thickness of base plate, (2) the size, length, and location of anchor bolt, (3) material

properties of connection elements, (4) the geometry of concrete foundation, and (5) the

amount of axial loads. In order to verify the accuracy of their analysis models, the

analytical estimations were compared with the results of the tests conducted by Astaneh

et al. (1992). In addition, for more accurate frame analyses, they proposed a simple

expression of M-φ curves that provide an approximate degree of fixity in a column-base

plate connection.

Ermopoulos and Stamatopoulos (1996B) expanded their study to the cyclic

loading cases. An analytical model that can estimate the cyclic nonlinear responses of a

column-base plate connection was proposed.

Stojadinovic et al. (1998) studied the effects of semi-rigidity of the column-base

plate connection on the seismic responses of moment resisting frames. Push-over analysis

and time-history analysis were carried out using two different three-story buildings.

Based on the analysis results, two conclusions were drawn. First, the seismic behaviors of

the moment resisting frame consisting of fixed column-bases are representative for the

responses of the frames that have the realistic, semi-rigid, column-bases. Second, with a

10

reduction of column base stiffness and strength, an increase in rotation demand on the

first floor beams was observed through the push-over analyses. This phenomenon was

reconfirmed by the results of the time-history analyses.

Drake and Elkin (1999) recently suggested a design method for column-base plate

connections under combined bending and axial forces. In order to apply the LRFD

method for the design of base plate thickness, they adopted a rectangular bearing stress

block instead of a triangular shape. Depending on the eccentricity (i.e., the ratio between

axial force and bending moment), the connections were classified in four different cases.

For each case, the corresponding design procedure was developed. For the design of

anchor bolt size, however, they simply followed the AISC LRFD Specifications.

1.3 Objectives of the Study

As mentioned earlier in Section 1.1, for the column-base plate connections subject

to cyclic weak axis bending, the D&E method which is assumed to represent the current

design practice in the U.S. has not been verified analytically or experimentally. Thus, the

main effort in this study was concentrated on evaluating the D&E method numerically

and experimentally.

Through numerical pre-test analyses, complex force flow and stress distribution in

the connection were studied, and the D&E method was evaluated by comparing the

design estimations with the numerical analysis results. Through the experimental study,

the seismic nonlinear behavior of three major connection elements (i.e., column, anchor

bolts, and base plate) was investigated, and the D&E method was evaluated by

comparing the design estimations with the test results.

Based on the numerical pre-test analyses and experimental results, several

limitations of the D&E method were investigated and the effects of relative strength

ratios on the seismic behavior of the connection were emphasized. After an extensive

11

numerical parametric study, a more rational and reliable design method was developed

based on the proposed new design force profile and the concept of relative strength ratios

among the connection elements. Additionally, in order to prevent undesirable connection

failures, two limit states of the connection (i.e., one on the tension side and one on the

compression side) were defined.

Ductility is considered as one of the most desirable properties in seismic resistant

structures and their components including connections. The ductility of the column-base

plate connections in this study was also evaluated based on the test results.

Thus, the main objectives of the study were:

• To evaluate the current design practice in the U.S. numerically and experimentally.

• To understand realistic force flow and stress distribution in column-base plate

connections under weak axis bending.

• To investigate the seismic nonlinear behavior of three primary connection elements:

the column, the base plate, and the anchor bolts.

• To investigate the effects of relative strength ratios on the seismic behavior of the

connection.

• To examine the seismic ductility of the connection.

• To develop a more rational and reliable design method.

• To define two limit states of the connection.

1.4 Scope of the Study

The main focus of this study was placed on studying the seismic behavior of

exposed column-base plate connections in the case of the weak axis bending. Quasi-static

cyclic lateral displacements were applied at the tip of the column to cause cyclic bending

during the experimental studies. Under the given loading history, moment resisting

mechanisms and failure modes in the connection were investigated.

12

Using two typical connection types (i.e., 6-bolt type and 4-bolt type), numerical

and experimental studies were conducted. In order to investigate the effects of anchor

bolt size (stiffness) on the seismic behavior of the connection, different total areas of the

anchor bolts were used. The larger total area of the anchor bolts was used for the 4-bolt

type connection. Thus, in both numerical and experimental studies, the two main

variables were size (stiffness) and number of anchor bolts.

For the numerical pre-test analyses and parametric studies, a Finite Element

Analysis (FEA) tool was used. The ABAQUS program, a highly versatile FEA tool, was

selected for the study of nonlinear behavior of the three major connection elements and

for the modeling of several contact interfaces among the connection elements. In addition

to the above two main variables, one more variable was considered in the numerical

parametric study. The effects of base plate thickness, as well as the effects of size

(stiffness) and number of anchor bolts, on the seismic behavior of the connection were

investigated in depth through the numerical parametric study.

In order to evaluate the D&E method experimentally, a total of four column-base

plate connection assemblages, consisting of the same column and base plate planar sizes,

were fabricated and tested. Two specimens were prepared for the 6-bolt type connection

and the other two specimens were prepared for the 4-bolt type connection. Through the

experimental study, the effects of weld detail on the connection ductility as well as the

seismic nonlinear behavior of three major connection elements were investigated.

Based on the numerical and experimental studies, a new design method for

column-base plate connections under weak axis bending was formulated. This method is

based on the LRFD method, and is dependent on the relative strength ratios among the

connection elements.

13

1.5 Organization of the Dissertation

In Chapter 1, study background is introduced and literature reviews are briefly

summarized. Main objectives and scope of the study are also included in Chapter 1.

In Chapter 2, the D&E method is evaluated numerically through pre-test analyses.

For this purpose, two typical exposed column-base plate connection assemblages with

different total area and number of anchor bolts (i.e., 6-bolt type and 4-bolt type) were

designed by the D&E method. Based on the basic dimensions of the two designed

connections, an FEA model for each bolt type connection was prepared and analyzed.

Through comparisons between the FEA results and the design estimations given by the

D&E method, the current design practice is numerically evaluated and the effects of

relative strength ratios on the seismic behavior of the connection are emphasized.

In Chapter 3, the D&E method is evaluated experimentally. A total of four

column-base plate connection assemblages (i.e., two for the 6-bolt type and two for the 4-

bolt type) were fabricated and tested under the given cyclic loading history. Based on the

test results, the cyclic nonlinear behavior of the connection elements was carefully

investigated and several factors that may significantly affect the moment capacity and

cyclic ductility of the connection were revealed. Through the comparisons between the

test results and the design estimations provided by the D&E method, the current design

practice is experimentally evaluated and several limitations of the D&E method are

explored.

In Chapter 4, an extensive numerical parametric study to investigate the

contribution of relative strength ratios in the seismic behavior of the connection is

presented. Two main parameters (i.e., anchor bolt stiffness and base plate thickness) were

selected for the systematic investigation. For both bolt type connections (i.e., 6-bolt type

and 4-bolt type), the effects of anchor bolt stiffness and base plate thickness on the

14

seismic behavior of the connection were studied and several major observations are

summarized. Additionally, in order to examine the effects of grout strength on the

location of the resultant bearing force, three more FEA models consisting of different

grout compressive strengths were configured and analyzed. This study was conducted for

the 6-bolt type connection only. The FEA results are compared with the design

estimations provided by the D&E method, and the main differences are discussed.

In Chapter 5, a total of six limitations of the D&E method are summarized. The

numerical analysis results and major findings from the experimental study showed

several possible limitations of the D&E method in its basic assumptions and design

calculations. Six major limitations are discussed in this chapter.

In Chapter 6, a more rational and reliable design method is proposed based on the

new design force profile and the concept of relative strength ratios among the connection

elements. In order to help understand this new design method, a total of six ratios (i.e.,

three geometric ratios and three strength ratios) were defined and the desired seismic

behavior of the connection at its ultimate state was described effectively using those

ratios. Furthermore, several fundamental design formulas were derived based on the

proposed new design force profile. Using the proposed new design method, base plate

thickness and anchor bolt size were re-computed for the given column and base plate

planar sizes. The new element sizes are compared with those from the D&E method, and

the differences are discussed.

In Chapter 7, two limit states of the column-base plate connection are defined to

prevent undesirable connection failures and to maximize the cyclic ductility of the

connection. The first limit state of the connection was defined on the tension side based

on the local stresses around the anchor bolts. By checking the first limit state, the

minimum base plate thickness that can prevent local yielding in the anchor bolts is

provided numerically and theoretically. On the other hand, the second limit state of the

connection was defined on the compression side based on the proposed effective bearing

15

area on the grout. This second limit state of the connection provides the required

minimum compressive strength of the grout. Finally, the new design procedure which

includes checking the two limit states of the connection is briefly compared with the

Drake and Elkin's design procedure in the last part of this chapter.

In Chapter 8, several conclusions based on the study results are drawn and some

directions of future study are suggested.

CHAPTER 2

SPECIMEN DESIGN AND PRE-TEST ANALYSES

Numerical pre-test analyses are described in this chapter. For this study, two

exposed column-base plate connections consisting of different total area and number of

anchor bolts (i.e., 6-bolt type and 4-bolt type) are selected. Through the pre-test analyses,

the D&E method which is representing current design practice in the U.S. is evaluated

numerically.

In order to help understand the basic assumptions and design procedure of the

D&E method, the outline of this method is explained first. Based on the D&E method,

base plate thicknesses and anchor bolt sizes for the two selected bolt type connections

(i.e., 6-bolt type and 4-bolt type) are designed. In order to examine the effects of different

anchor bolt stiffness on the seismic response of the connection, a larger total area of

anchor bolts is used for the 4-bolt type connection.

Using the basic connection dimensions obtained by the D&E method, two FEA

models (i.e., one for the 6-bolt type and the other for the 4-bolt type) are configured

without consideration of weld detail. The ABAQUS program, a highly versatile FEA tool,

is used for the numerical analyses. In order to examine the effects of different stiffness

and location of anchor bolts on the seismic behavior of the connection, analysis results

for both bolt type connections are compared. In addition, these analysis results are

compared with the design estimates given by the D&E method to evaluate this design

method numerically. Through the numerical evaluations, several limitations of the D&E

method are revealed and the effects of relative strength ratios on the seismic behavior of

the connection are emphasized.

16

17

2.1 Outline of Drake and Elkin's Design Method

Two different approaches have been used for design of column-base plate

connections subject to axial loads and bending moments: working stress method and

ultimate strength method. The first design approach is based on the assumed behavior of

the connection at service loads, whereas the second approach is based on the assumed

behavior of the connection at ultimate loads. One of the main differences between these

two approaches is the assumed shape of bearing stress distribution on the compression

side of the connection. A triangular shape is assumed for the bearing stress distribution in

the working stress method. On the other hand, a rectangular block is assumed in the

ultimate strength method.

The D&E method follows the ultimate strength design method. Thus, the D&E

method is implicitly based on two basic assumptions. First, the nonlinear bearing stress

distribution can be simplified by an equivalent rectangular stress block. Second, the

anchor bolts on the tension side yield at the ultimate state of the connection.

In order to help understand the basic assumptions and subsequent design

procedures of the D&E method, outline of their design method is briefly presented in this

section. Highlights of the design procedure for base plate thickness and anchor bolt size

are explained in the following.

2.1.1 Design Procedure for Base Plate Thickness

In order to explain the design procedure for base plate thickness, plan view and

basic dimensions of a typical exposed 6-bolt type connection are presented in Figure 2.1.

18

N

m

m

0.95d

Y

B

0.8bfn n

f

x

AssumedBending Line

Figure 2.1. Plan View and Basic Dimensions of a Column-Base Plate Connection

(6-Bolt Type)

In Figure 2.1, the dotted lines indicate the location of base plate bending on the tension

and compression sides assumed in the D&E method. Dimensions in Figure 2.1 are:

B = base plate length, .in

.in

.

.in

.in

.in

.in

.in

N = base plate width,

bf = column flange width, in

d = overall column depth,

m = base plate bearing interface cantilever length perpendicular to moment

direction,

n = base plate bearing interface cantilever length parallel to moment direction,

f = anchor bolt distance from the centerline of column or base plate,

x = base plate tension interface cantilever length,

19

Y = equivalent bearing length, in .

Unknown design parameters in a column-base plate connection are briefly

profiled in Figure 2.2. In Figure 2.2, the concrete bearing capacity per unit length (q) and

the equivalent bearing length (Y) should be obtained first to calculate the required total

tensile strength of anchor bolts (Tu). In the D&E method, the Y value is calculated from

an assumed value of q expressed in terms of the specified compressive strength of

concrete (fc'). It should be noted that, in the D&E design procedure, the location of

resultant bearing force as well as its magnitude can be calculated if Y and q values are

given.

The assumed concrete bearing capacity per unit length (q) is

2'85.01

2

1

2 ≤⋅⋅⋅⋅=AAand

AANfq ccφ (2-1)

Y

q (Assumed)

Assumed Bending Line(Tension Side)

Assumed Bending Line(Compression Side)Mu

φVn

Tu

Vu

Figure 2.2. Unknown Design Parameters in a Column-Base Plate Connection

20

where:

φc = resistance factor for bearing, 0.6

fc' = specified compressive strength of concrete (or grout), ksi

A1 = area of the base plate concentrically bearing on the concrete (or grout), 2.in

A2 = maximum area of the portion of the supporting surface that is geometrically

similar to and concentric with the loaded area, 2.in

A significant point which should be mentioned is that the AISC LRFD Specifications

recommend 0.6 for φc, whereas the ACI 318-99 adopts 0.7 for the strength reduction

factor in case of bearing on concrete.

Two equilibrium equations can be formulated to solve for two unknowns:

equivalent bearing length (Y) and required total tensile strength of anchor bolts (Tu). In

order to maintain static equilibrium, the summation of moments taken at the anchor bolts

on the tension side of the connection must equal zero. Thus,

022

=−⎟⎠⎞

⎜⎝⎛ +−⋅⋅ uMfYBYq (2-2)

From the solutions of the quadratic Equation (2-2), the value of Y can be calculated as,

qMBfBfY u⋅

−⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛ +−−⎟

⎠⎞

⎜⎝⎛ +=

222

2

(2-3)

In addition, the summation of vertical forces must equal zero in order to maintain static

equilibrium, which gives:

21

0=⋅− YqTu (2-4)

From Equation (2-4), the value of Tu can be obtained as:

YqTu ⋅= (2-5)

After the value of Tu is formed from Equation (2-5), the required base plate

flexural strength per unit width (Mpl) can be calculated on both sides of the base plate

from the calculated two force resultants (i.e., Tu and q·Y). The larger value of Mpl, of

course, governs the design of base plate thickness. The expressions of Mpl on the tension

and compression sides are:

On the tension side

NxT

M upl

⋅= (2-6)

On the compression side

nYifnnfM ppl ≥⎟⎠⎞

⎜⎝⎛⋅⋅=

2 (2-7a)

nYifYnYfM ppl <⎟⎠⎞

⎜⎝⎛ −⋅⋅=

2 (2-7b)

In the above two equations, fp is concrete bearing stress capacity and can be expressed as

follows:

22

2'85.01

2

1

2 ≤⋅⋅⋅=AAand

AAff ccp φ (2-8)

Finally, based on the definition of the AISC LRFD Specifications for the yielding

limit state of a steel member, the required minimum thickness of the base plate can be

calculated as follows:

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⋅⋅=⋅=⋅≤4)( 2

_p

plateybpbnbpl

tFMMM φφφ (2-9)

plateyb

plp F

Mt

_

4⋅

⋅≥

φ (2-10)

where:

Mn = nominal flexural strength per unit width, k-in./in.

Mp = plastic bending moment per unit width, k-in./in.

φb = resistance factor for flexure, 0.9

Fy_plate = specified minimum yield stress of base plate, ksi

tp = required base plate thickness, in .

2.1.2 Design Procedure for Anchor Bolt Size

For the design of anchor bolts, the D&E method simply follows the AISC LRFD

Specifications. In the D&E method, the anchor bolt size is designed based on the

following two assumptions. First, all anchor bolts are considered effective in resisting the

23

design shear force (Vu). Second, the anchor bolts only on the tension side are considered

effective in resisting the design tensile force (Tu).

The AISC LRFD Specifications define shear and tensile force limit states of the

anchor bolt as follows:

For shear force

bvv

uub AF

VV ⋅⋅≤⎟⎟

⎠

⎞⎜⎜⎝

⎛= φ

# (2-11)

For tensile force

btt

uub AF

TT ⋅⋅≤⎟⎟

⎠

⎞⎜⎜⎝

⎛= φ

# (2-12)

where:

Vu = required total shear strength of anchor bolts, kips

Vub = required shear strength of each anchor bolt, kips

Tub = required tensile strength of each anchor bolt, kips

#v = number of anchor bolts resisting shear force, unitless

#t = number of anchor bolts resisting tensile force, unitless

φ = resistance factor for anchor bolt, 0.75

Fv = nominal shear strength of anchor bolt, ksi

Ft = nominal tensile strength of anchor bolt, ksi

Ab = nominal (gross) area of each anchor bolt, 2in.

24

From the above two expressions, the required minimum area and diameter of each

anchor bolt can be calculated using:

For shear force

v

ubb F

VA

⋅≥

75.0 (2-13)

v

ubb F

Vd

⋅⋅⎟⎠⎞

⎜⎝⎛≥

75.04π

(2-14)

For tensile force

t

ubb F

TA

⋅≥

75.0 (2-15)

t

ubb F

Td

⋅⋅⎟⎠⎞

⎜⎝⎛≥

75.04π

(2-16)

The larger anchor bolt diameter, of course, governs the final design value of the required

minimum anchor bolt size.

2.2 Design of Column-Base Plate Connection Assemblages

Based on the D&E method, base plate thickness and anchor bolt size are designed

for the two selected bolt type connections (i.e., 6-bolt type and 4-bolt type). The

schematic connection geometry and the design procedures are presented in Appendix A.

In this section, several specific design considerations are explained and designed each

25

connection element is described in detail. For the experimental study, two identical

specimens, except for weld detail, are also prepared in this section.

2.2.1 Specified Compressive Strength of Grout, fc'

For the design of base plate thickness and anchor bolt size in a column-base plate

connection, values of Y and Tu shown in Figure 2.2 should be calculated first. As

explained, in order to calculate the Y and Tu values, the D&E method uses the assumed

value of q in terms of the specified compressive strength of grout (fc'). However, due to

its significant effects on the entire design procedure, the value of fc' should be carefully

selected when the D&E method is applied. In order to show the sensitivity of the value of

fc' to base plate thickness (tp), Figure 2.3 is prepared.

If the value of fc' is less than 6 ksi, in Figure 2.3, tension side governs the design

procedure for base plate thickness. On the other hand, compression side governs if the

value of fc' is larger than 6 ksi. It should be noted that although the maximum variation of

2.15

2.2

2.25

2.3

2.35

2.4

2.45

4 5 6 7 8 9 10 11 12

Req

uire

d Bas

e Pla

te T

hick

ness

, tp

(in.)

Compressive Strength of Grout, fc' (Ksi)

Tension Side Governs

Compression Side Governs

Figure 2.3. Effects of fc' on Base Plate Thickness (tp)

26

base plate thickness is slightly more than 0.25 in., when the compression side governs the

design procedure under the given range of fc' values, this variation is large enough to

change the seismic behavior of the connection.

Based on experimental observations, it has been found that thinner base plates can

be a good source of energy dissipation and do provide for more ductile connection

behavior during earthquake excitation (Astaneh et al., 1992). Thus, in this study, 6 ksi is

selected for the fc' value to maximize the possibility of meeting a flexible base plate.

2.2.2 Column

A W12x96 section of ASTM A572 Grade 50 steel is selected for the 80 in. long

specimen column. The length of the column is decided based on a general assumption for

design of MRFs, i.e., bending moment is zero at mid-height of the column in the frames

which resist lateral loads only. Thus, the total story height is 160 in.

For the calculation of design moment (Mu), in this study, an expected yield stress

58 ksi is used instead of the specified minimum yield stress 50 ksi for a Grade 50 column

member to account for potential overstrength and strain hardening effects. This increase

is based on the Ry factor in 1997 AISC LRFD Seismic Provisions for design of beam-to-

column connections in moment frames. Using the expected yield stress value, design

moment (Mu) and design shear force (Vu) can be calculated as follows:

.3915).5.67()58()58( 3

_ ink in sik ZksiM columnyu −=⋅=⋅= (2-17)

kipsin

ink LM

Vcolumn

uu 94.48

.80.3915=

−== (2-18)

27

2.2.3 Base Plate

A 20 in. x 20 in. steel plate is chosen for the base plate planar size in this study.

Based on the D&E method, 2.25 in. thick ASTM A36 steel is selected for the base plate

thickness for both bolt type connections (i.e., 6-bolt type and 4-bolt type). The designed

base plate thickness (i.e., 2.25 in.) is denoted herein as "tpo" for convenient comparisons

in numerical parametric study in Chapter 4.

2.2.4 Anchor Bolts

ASTM A354 Grade BD rods, which have Fu_bolt = 150 ksi and Fy_bolt = 130 ksi, are

selected for the anchor bolts. The anchor bolt sizes for both bolt type connections (i.e., 6-

bolt type and 4-bolt type) are designed based on the AISC LRFD Specifications. The

entire design procedure is presented in the Appendix A. Mechanical properties of ASTM

A354 Grade BD rods are very similar to ASTM A490 bolts. Thus, nominal strengths of

ASTM A490 bolts are adopted herein for the design of anchor bolts.

As presented in the Appendix A, the designed minimum diameter of each anchor

bolt for the 6-bolt type connection is 1.107 in., whereas it is 1.356 in. for the 4-bolt type

connection. However, as indicated in Figure 2.4, 1.25 in. and 2.0 in. anchor bolt

diameters are selected for the 6-bolt and 4-bolt type connections, respectively. A 30 %

stiffer (i.e., 1.3 Ko) anchor bolts are selected for the 6-bolt type connection, whereas 120

% stiffer (i.e., 2.2 Ko) anchor bolts are selected for the 4-bolt type connection. In the

above expressions, "Ko" denotes the designed minimum stiffness of anchor bolts. Such

increases are intended to provide strong anchor bolts so as not to yield them at the limit

state of the connection during experimental study. The difference in anchor bolt stiffness

between the 6-bolt and 4-bolt type connections will facilitate the study of relative

28

2" 8"20"

2"

8"

20" 16"

2"8" 2" 8" 8" 2"20"

2"

8"

2"

20"

2"

Ø=1.25" Ø=2.0" 0.8 bf

AssumedBending Line

AssumedBending Line

(a) 6-Bolt Type (b) 4-Bolt Type

Figure 2.4. Base Plate Planar Dimensions and Anchor Bolt Diameters

strength ratio effects on the seismic behavior of the connection.

Over-sized bolt holes are designed to make it easy to place the connection

assemblages on their exact location. 1.5 in. (= 1.25 in. + 4/16 in.) diameter bolt holes are

prepared for the 6-bolt type connection, and 2.3125 in. (= 2.0 in. + 5/16 in.) diameter bolt

holes are prepared for the 4-bolt type connection. For the washers, the ASTM F436

circular washers with 3.0 in. nominal outside diameter are used only for the 6-bolt type

connection. Furthermore, the edge distance of each bolt hole, for both bolt type

connections, is fixed at 2.0 in. so that the ratio between bolt edge distance and base plate

length is equal to 0.1.

As shown in Figure 2.5, each anchor rod is fixed to the concrete foundation using

PL 22x4x1/2 ASTM A36 supplemental steel plates. The end of each anchor rod is

threaded so that this can fasten the base plate on the grout effectively. As shown in Figure

2.5, the effective length of each rod is 32 in.

29

FRONT

32

PL22x4x1/2

RIGHT

Figure 2.5. Anchoring System using Supplemental Anchor Plates (6-Bolt Type)

All nuts were hand-tightened right before each test was started. Thus, in the

numerical, experimental, and theoretical studies, the prestressing of anchor bolts was

neglected.

2.2.5 Weld Materials and Details

In order to connect the column to the base plate, two weld metals that satisfy the

minimum requirements specified by the SAC Joint Venture (1995) are selected in this

study. They are SuperArc L-50 (ER70S-3 based on the AWS classification) and NR-

311Ni (E70TG-K2 based on the AWS classification). Especially, the SuperArc L-50 is

one of the most common Gas Metal Arc Welding (GMAW) wires, or Metal Inert Gas

(MIG) wires, produced by the Lincoln Electric company. Mechanical properties of these

30

two weld materials are compared in Table 2.1. As shown in Figure 2.6, ER70S-3 is used

for the first pair of specimens (i.e., SP 6-1 and SP 4-1), whereas E70TG-K2 is used for

the second pair of specimens (i.e., SP 6-2 and SP 4-2). Through the experimental study in

Chapter 3, effects of these two different weld metals on the seismic behavior of the

connection will be investigated.

In reference to the weld detail suggested by Fahmy (1999), two types of welds are

applied: Partial Joint Penetration (PJP) groove welds are reinforced by fillet welds

rounding the boundary between column and base plate. This weld detail is schematically

described in Figure 2.6. Each column flange is welded to the base plate using the PJP

groove welds that have a 30° single bevel with 1/8 in. root face. The inside of each

column flange and the column web are reinforced using 1/4 in. fillet welds.

In order to prevent an early weld fracture at column flange tips, the outside of

column flange is reinforced using 3/16 in. fillet welds over the PJP groove welds, except

one specimen (i.e. SP 4-2). The hatched area in Figure 2.6 indicates these fillet weld

reinforcement at the outside of column flanges.

Table 2.1. Mechanical Properties of Two Weld Materials

Weld Materials Yield Strength

(ksi)

Tensile Strength

(ksi)

Charpy V-Notch

Toughness at -20°F (ft-lb)

ER70S-3

(SuperArc L-50)

63.7 76.2 65

E70TG-K2

(NR-311Ni)

69 86 35

31

ER70S-3(SP 6-1 & 4-1)

E70TG-K2(SP 6-2 & 4-2)

1/41/4

1/4

1/8

30�(SP 6-2 & 4-2)E70TG-K2

(SP 6-1 & 4-1)ER70S-3 ER70S-3

(SP 6-1 & 4-1)E70TG-K2

(SP 6-2 & 4-2)

3/16

WELD DETAIL

Figure 2.6. Weld Detail of Column-Base Plate Connection Assemblages

2.2.6 Classification of Specimens

A total of four column-base plate connection assemblages were designed for

experimental studies. Two specimens are for the 6-bolt type connection and the other two

specimens are for the 4-bolt type connection. As explained, the main differences between

these specimens are the total area (stiffness) and number of anchor bolts. As presented in

Table 2.2, 1.3 Ko is designed for the 6-bolt type connection, whereas 2.2 Ko is designed

for the 4-bolt type connection. For both bolt type connections, however, the same

thickness of the base plate (i.e., tpo) is used.

32

Table 2.2. Classification of Specimens

SP 6 SP 4

SP 6-1 SP 6-2 SP 4-1 SP 4-2

Number of Anchor Bolts 6 6 4 4

Anchor Bolt Stiffness 1.3 Ko 1.3 Ko 2.2 Ko 2.2 Ko

Base Plate Thickness tpo tpo tpo tpo

Weld Material ER70S-3

(SuperArc L-50)

E70TG-K2

(NR-311Ni)

ER70S-3

(SuperArc L-50)

E70TG-K2

(NR-311Ni)

3/16 in. Fillet Reinforcement

over PJP Groove Welds

(Outside of Column Flanges)

Yes

Yes

Yes

No

Effects of the two weld materials on the seismic behavior of the connection will

be investigated through the experimental study of two 6-bolt type connections. For this

study, the SP 6-1 is welded using ER70S-3 and the SP 6-2 is welded using E70TG-K2. In

addition, in order to investigate the effects of 3/16 in. fillet reinforcement over the groove

welds at the outside of column flanges, two different weld details are prepared for the 4-

bolt type specimens. The fillet reinforcement over the groove welds is applied on SP 4-1,

whereas no extra fillet reinforcement is used on SP 4-2.

33

2.3 Pre-test Analyses

Using the basic dimensions of the as-designed 6-bolt and 4-bolt type connection

assemblages, an FEA model for each bolt type connection is made without consideration

of weld detail. The FEA models are described first in this section. Using those two FEA

models, numerical pre-test analyses are conducted. Based on these analysis results, the

D&E method is evaluated numerically and the effects of relative strength ratios on the

seismic behavior of the connection are examined.

2.3.1 Finite Element Analysis Models

In order to investigate the responses of column-base plate connections under large

lateral displacements, two FEA models (i.e., one for the 6-bolt type connection and the

other for the 4-bolt type connection) are prepared and analyzed. The ABAQUS program

version 5.8 is used to study the nonlinear behavior of the connection and to model several

contact interfaces among the connection elements. The C3D8 (8 nodes linear brick

element), one of the most general three-dimensional solid elements in the ABAQUS

program, is chosen for the FEA modeling.

Because the connection geometry is symmetric for both bolt type connections,

only one half of each connection is modeled as shown in Figure 2.7. All concrete and

steel elements of a connection assemblage are included in the FEA model. Each anchor

bolt, which has the effective length equal to 32 in., is also included in the FEA model

with bottom end fixed directly to the concrete foundation.

It is very difficult to model the boundary conditions of the concrete foundation in

column-base plate connections. Even though the boundary conditions of the concrete

foundation in a test setup are much better controlled than the actual boundary conditions

34

in the field, it is still not easy to reflect them precisely in an analytical model. Therefore,

in this study, simplified boundary conditions are assumed in the FEA modeling. Concrete

foundation (74 in. x 74 in. x 35.75 in.) is assumed to be fixed to the ground at the bottom

only, as shown in Figure 2.7. All degrees of freedom at the bottom surface of the

foundation are constrained, whereas all degrees of freedom on the other sides of the

foundation are released. In addition, lateral braces are also included in the FEA model in

order to prevent twisting of the column under lateral large displacements.

Figure 2.7. FEA Model and its Boundary Conditions (6-Bolt Type)

35

1E

Fy

STRESS

STRAIN

fc=fc"[(2εc/εο)−(εc/εο) ]

εo=1.8fc"/Ec1

Ec

fc"=0.9fc'

STRESS, fc

STRAIN, εc0.0038

LINEAR0.15fc"

(a) Steel (b) Concrete

Figure 2.8. Constitutive Relationships of Steel and Concrete Elements

Constitutive relationships for steel elements are simplified by the elastic-perfectly

plastic bilinear model, as shown in Figure 2.8(a). For concrete elements, shown in Figure

2.8(b), the modified Hognestad stress-strain curve is used to model material nonlinearity.

The curvilinear portion in the modified Hognestad model is reformulated using ten linear

segments for the application of the ABAQUS program.

The principal mechanical properties for each connection element used in the FEA

model are summarized in Table 2.3. As mentioned, 58 ksi is assumed for the expected

yield stress of the column, considering potential overstrength and strain hardening effects.

One of the most difficult tasks in FEA modeling of column-base plate connections

are the contact interfaces among the connection elements. There are three major contact

interfaces: between the nut and the base plate upper surface, between the grout and the

base plate, and between the anchor rod and the concrete foundation. A small-sliding

formulation, one of three contact pair modeling tools in the ABAQUS program, is used in

order to model these contact interfaces. A friction coefficient of 0.5 is assumed for the

interfaces between nuts and base plate upper surface and between grout and base plate.

36

However, friction does not have to be considered for the interface between the anchor rod

and the concrete foundation based on experimental observations by Sato and Kamagata

(1988) and Jaspart and Vandegans (1998).

In order to show how FEA models are structured and how the contact pair

formulation roles in connection behavior, magnified deformations of the two as-designed

connection assemblages are presented in Figure 2.9.

Table 2.3. Mechanical Properties of Connection Elements

Connection Elements Yield Strength

or Compressive

Strength (ksi)

Young's

Modulus (ksi)

Poisson's Ratio

Column 58 29000 0.3

Base Plate 36 29000 0.3

Steel

Anchor Bolt 130 29000 0.3

Grout 6 4400 0.18 Concrete

Foundation 4 3600 0.18

37

(a) 6-Bolt Type

(b) 4-Bolt Type

Figure 2.9. Deformation of Column-Base Plate Connection Assemblages

38

2.3.2 Finite Element Analysis Results

Numerical pre-test analyses are conducted using the two FEA models (i.e., 6-bolt

type and 4-bolt type),. Through these pre-test analyses, the effects of different anchor bolt

stiffness and its location on the seismic behavior of the connection are investigated. In

this numerical study, 3.85 % drift is assumed as a drift limit state of the connection. At

this limit state, the following four connection response quantities are studied in depth:

total lateral force, total tensile bolt force, yield pattern in the base plate, and bearing stress

distribution on the grout. In order to evaluate the D&E method numerically, the analysis

results are also compared with the design estimations according to their design method.

These numerical evaluation results reveal several limitations of the D&E method and

emphasize the effects of relative strength ratios on the seismic behavior of the connection.

2.3.2.1 Total Lateral Force

In Figure 2.10, total lateral forces and the corresponding drifts of the two different

bolt type connections are plotted and compared each other. No significant differences in

both strength and stiffness are observed between the 6-bolt and 4-bolt type connections.

The analysis results, at the assumed limit state of the connection (i.e., 3.85 % drift), are

also compared with the design shear force (i.e., Vu = 48.94 kips) given by the D&E

method. As shown in Figure 2.10, the estimated design shear force shows a good

agreement to FEA results.

Based on the analysis results presented in Figure 2.10, three major findings are

summarized in the following. First, the flattening of two graphs, beyond 3.0 % drift, is a

result of assumed bilinear constitutive relationships for steel elements in the connection.

60

6-Bolt Type4-

0

10

0 1 2 3 4 5 6

20

30

40

50

Bolt Type

Tota

l Ll F

Kip

Drift (%)

ater

aor

ce (

s)

D&E

39

Figure 2.10. Total Lateral Force versus Drift Responses

Second, the rotational stiffness of the connection is affected by anchor bolt stiffness. For

instance, a stiffer anchor bolt case (4-bolt type connection) results in stiffer connection

responses. However, this effect is not significant as shown in Figure 2.10. Lastly,

connections designed by the D&E method develop the full moment capacity of the

column for both bolt type connections. In other words, the D&E method results in strong

connections such that a plastic hinge forms at the bottom of the column when the

connection reaches its ultimate state.

2.3.2.2 Total Tensile Bolt Force

Total tensile bolt forces and the corresponding drifts of the two connections are

compared in Figure 2.11. For both bolt type connections, the bolt forces are calculated

using two strain values measured on the outer surface of each anchor bolt in the plane of

Figure 2.11. Total Tensile Bolt Force versus Drift Responses

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6

6-Bolt Type4-Bolt Type

Tota

l Ten

sile

Bol

t For

ce (K

ips)

Drift (%)

D&E

40

bending. As shown in Figure 2.11, significant differences exist in total tensile bolt forces

between the 6-bolt and 4-bolt type connections. The analysis results at the assumed limit

state of the connection are also compared with the design tensile force (i.e., Tu = 244.8

kips) given by the D&E method.

Two major findings are summarized in the following. First, the flattening of two

graphs beyond 3.0 % drift does not mean that anchor bolts yield. Due to designing much

stronger anchor bolts in this study, anchor bolts are supposed not to yield even though the

connection reaches its limit state. Thus, the flattening of the graph indicates that some

other connection element, instead of the anchor bolts, has reached its own ultimate

capacity. Second, at the assumed limit state of the connection, two graphs show a

significant difference in maximum demand. This difference is mainly due to different

relative strength ratio between anchor bolts and base plate.

In order to explain the main reason of the difference in total tensile bolt forces

between the 6-bolt and 4-bolt type connections, the deformed shape of each bolt type

M6 = M4

L6 > L4

(T6 = R6) < (T4 = R4)

M6 M4

41


Figure 2.12. Effects of Different Anchor Bolt Stiffness on Connection Behavior

connection is compared in Figure 2.12. Because of stiffer anchor bolts, shown in Figure

2.12(b), the maximum vertical displacement of the base plate in the 4-bolt type

connection is smaller than that of the base plate in the 6-bolt type connection. Due to the

smaller deformation (or rotation) of the base plate in the 4-bolt type connection, the

length of overall moment arm (L4) between the anchor bolt on the tension side and the

location of resultant bearing force on the compression side becomes shorter. This

phenomenon requires the increase of the total tensile bolt force (T4) and the resultant

bearing force (R4) to resist the same amount of the moment (M6 = M4). Similarly, the

differences between the design estimation (i.e., Tu = 244.8 kips) and two FEA results at

the assumed limit state of the connection can be explained.

R4

L6 L4

T6 R6 T4

Based on these FEA results, relative strength ratios among the connection

elements, not considered in the D&E method, can affect significantly the seismic

behavior of the connection and change the failure mechanism of the connection. Hence,

the effects of relative strength ratios on the seismic behavior of the connection should be

considered in a more rational design method.

2.3.2.3 Yielding in the Base Plate

In order to investigate the yield distribution and pattern in the base plate at the

assumed limit state of the connection, the equivalent Mises stress contours for both bolt

42

type connections are presented in Figure 2.13. Due to the constraint of column flanges on

the top surface of the base plate, relatively large yields are observed on the bottom

surface of the base plate for both bolt type connections.

Interestingly, as shown in Figure 2.13, the base plates designed by the D&E

method do not fully yield across the whole width. Instead, only small yielded regions are

observed on the top and bottom surfaces of the base plate for both bolt type connections.

This indicates that the D&E method may be resulting in rather stiff base plates.

In the 6-bolt type connection, yielding in the base plate grew from the assumed bending

lines on both sides of the base plate (i.e., tension and compression sides). A rather large

amount of yield is observed on the compression side at the limit state of the connection.

In the 4-bolt type connection, however, a different yield shape is observed as shown in

Figures 2.13(b) and 2.13(d). The base plate yielding on the tension side shows a circular

shape instead of the straight line assumed in the D&E method. Moreover, relatively large

yields are observed on the tension side. Hence, the differences in yield distribution and

(a) 6-Bolt Type (Top) (b) 4-Bolt Type (Top)

(c) 6-Bolt Type (Bottom) (d) 4-Bolt Type (Bottom)

43

Figure 2.13. Equivalent Mises Stress Contours on the Base Plate Surfaces

(3.85 % Drift)

pattern between the 6-bolt and 4-bolt type connections must be recognized for a more

reliable design method.

2.3.2.4 Bearing Stress Distribution on the Grout

In the case of strong axis bending, bearing stresses on the grout tend to

concentrate on the middle of base plate width. Thus, the simplified rectangular stress

block adopted in the D&E method may be applied for design of column-base plate

connections under strong axis bending (Fahmy, 1999). However, due to much more

complex stress distribution along the base plate not only in the transversal direction but

also in the longitudinal direction, the concrete beam design methodology which is

adopted in the D&E method may not be applicable for design of column-base plate

connections under weak axis bending.

In order to investigate bearing stress distribution in the case of weak axis bending,

bearing stress contours for both bolt type connections are presented in Figure 2.14.

Interestingly, two different bolt type connections show remarkably different bearing

stress distribution. In the 4-bolt type connection, more stresses are concentrated at the

corners of the grout. This indicates that the 4-bolt type connection is more critical for

calculating the required compressive strength of the grout.

In the 6-bolt type connection, shown in Figure 2.14(a), the bearing stresses are

concentrated following the base plate edge line. It should be noted that high stress

concentrations on the grout edge can cause an unexpected grout crushing under small

lateral deformations (Thambiratnam and Paramasivam, 1986). Thus, designing more

44

flexible base plates may help to prevent undesirable grout crushing under the base plate

on the compression side.


Figure 2.14. Bearing Stress Distribution on the Grout (3.85 % Drift)

CHAPTER 3

EXPERIMENTAL EVALUATION OF DRAKE AND ELKIN'S METHOD

In Chapter 2, four column-base plate connections (i.e., two specimens for each

bolt type connection) were designed based on the D&E method and numerical pre-test

analyses were conducted. Using these four connections, the experimental study was

executed and the results are presented in this chapter. This study examines connection

behavior under weak axis bending and evaluates the D&E method experimentally. In

order to compare the experimental outputs to FEA results, strain gauges and displacement

transducers are installed on the surface of the base plate and anchor bolts.

Each connection assemblage is tested under a SAC Joint Venture quasi-static

loading history. Only one specimen (i.e., SP 4-1) completed all load cycles without

significant strength degradation. The test results of four specimens are compared each

other to investigate the effects of anchor bolt stiffness, anchor bolt number (or location),

and weld detail on the seismic behavior of the connection. From these comparisons,

several factors that may significantly affect the moment capacity and cyclic ductility of

the connection are discussed. Furthermore, experimental results are compared with the

pre-test FEA results presented in Chapter 2 as well as to the design estimations given by

the D&E method. Through these comparisons, the D&E method is evaluated and several

limitations of the D&E method are explored.

45

46

3.1 Test Setup and Loading History

As shown in Figure 3.1, a test setup is prepared for this experimental study so that

cyclic lateral displacements can be applied at the top of the column. An MTS hydraulic

actuator that can develop reversed cyclic loads up to 100 kips and displacements up to 10

in. (5 in. for each direction) is used for the tests.

A 2 in. thick layer of non-shrink grout is placed between the base plate and the

concrete foundation to plumb each specimen and to make a smooth contact interface. The

base plate is bolted using the anchor bolt system shown in Figure 2.5.

REACTION WALL

90"

74"

120"

4.25"

ACTUATOR 100Kips

22" 8"

LATERAL BRACE L5x5x0.5

BRACE POST 5x5x0.5

ANCHOR PLATE PL12x12x1.5

BRACE PLATE PL12x12x1

GROUT20x20x2

COLUMN (ASTM A572 Grade 50) W12x96

ACTUATOR PLATE (ASTM A36) PL16x20x2

BASE PLATE (ASTM A36) PL20x20x2.25

95"

66"

CONCRETE FOUNDATION 74x74x35.75 35.75" 35.75"

14"

84.25"

120"

Figure 3.1. Test Setup

47

The concrete foundation is fixed to the reaction floor by threaded rods and anchor

plates at the four corners of the foundation so as not to move vertically or horizontally

during the tests. In addition, in order to prevent out-of-plane deformations of the

specimen, the column is braced by a pair of lateral braces as shown in Figure 3.1. These

lateral braces are reinforced additionally by two threaded bars in the transverse direction.

The loading history, shown in Figure 3.2, used in the SAC Joint Venture steel

project (1995) is used for the experimental study. No axial load was applied to the

column. In Figure 3.2, drift is defined as the ratio between column lateral displacement

and its clear length. In order to observe the stiffness degradations of the connection

during the test, two small cycles (at 0.5 % drift level) are inserted between two large

inter-story drift cycles after the 1.0 % drift level.

-6

-4

-2

0

2

4

6

0 5 10 15 20 25 30 35 40

Drif

t (%

)

Cycles (No.)

(0.375%)(0.5%) (0.75%) (1%)

(0.5%)(0.5%)

(0.5%)

(1.5%)(2%)

(3%)

(4%)

(5%)

(0.5%)(0.5%)

Figure 3.2. Loading History

48

3.2 Gauge Location

In order to investigate the strain variation and post-yield strain distribution in

major connection elements, strain gauges are installed on the surface of the base plate and

anchor bolts. In particular, the measured strain values on the anchor bolts are used to

calculate the total tensile bolt forces during the test. YFLA-5 strain gauges, manufactured

by the TML Tokyo Sokki Kenkyujo Co., Ltd., are chosen in this experimental study. The

location of each strain gauge on the base plate is schematically presented in Figure 3.3(a)

for the 6-bolt type connection and in Figure 3.4(a) for the 4-bolt type connection. The

location of strain gauges on the anchor bolts is also shown in Figure 3.5 for both bolt type

connections.

The strain gauges on the anchor bolts are located in the middle of the 2 in. thick

grout layer. In order to protect these gauges from moisture while the grout is being cured,

N-1 (Moisture-proofing Material) manufactured by the TML Tokyo Sokki Kenkyujo Co.,

Ltd. is used to cover the strain gauges. Moreover, as shown in Figure 3.6, additional

protective rubber is placed on the strain gauges to protect them from the unexpected

contact forces during the test.

In order to investigate deformation of the base plate and elongation of each

anchor bolt, displacement transducers are installed. TRS 50 and TRS 100 position

transducers, manufactured by the Novotechnik, are used for the tests. The location of

each displacement transducer is shown in Figure 3.3(b) for the 6-bolt type connection and

in Figure 3.4(b) for the 4-bolt type connection. A total of nine displacement transducers

are installed for the 6-bolt type connection, whereas only eight displacement transducers

are installed for the 4-bolt type connection. In the 6-bolt type connection, one

displacement transducer is used to measure the lateral movement of the base plate, as

shown in Figure 3.3(b).

49

(a) Strain Gauges (b) Displacement Transducers

Figure 3.3. Location of Strain Gauges and Displacement Transducers (6-Bolt Type)

(a) Strain Gauges (b) Displacement Transducers

Figure 3.4. Location of Strain Gauges and Displacement Transducers (4-Bolt Type)

50


Figure 3.5. Planar Location of Strain Gauges on the Anchor Bolts

Figure 3.6. Location of Strain Gauges on Anchor Bolts and Gauge Protection

(6-Bolt Type)

51

3.3 Coupon Test Results

In order to estimate the actual moments transferred from the column to the

connection at its ultimate state, it is necessary to obtain the exact mechanical properties

of the column. For this, tensile coupon tests were conducted and the results are

summarized in this section. A total of four coupons are tested: two from SP 6-1 and two

from SP 4-1. For each specimen, two steel coupons are cut from the column flanges "L1"

and "R1" identified in Figure 3.7.

Based on the ASTM E-8 test specification, the tensile coupon tests are conducted

by the Edison Welding Institute using a UK 18 test machine. The test results are

summarized in Table 3.1. It should be noted that the expected column yield stress (58 ksi)

used in design calculations and numerical pre-test analyses is clearly over-estimated as

compared with the measured yield strength of the column.

L2

L1

R2

R1

Figure 3.7. Identification of Column Flanges (6-Bolt Type)

52

Table 3.1. Coupon Test Results

Coupon Coupon

Identification Width

(in.)

Thickness

(in.)

Temperature

(˚F)

Yield

Strength

(ksi)

Ultimate

Strength

(ksi)

L1 0.752 0.854 73 49.7 68.5 SP

6-1

R1 0.754 0.841 73 50.6 69.7

L1 0.755 0.854 73 51.5 69.5 SP

4-1

R1 0.754 0.862 73 49.2 68.3

3.4 Summary of Test Results

A total of four specimens (i.e., two for the 6-bolt type connection and two for the

4-bolt type connection) were tested under the given cyclic lateral displacements without

axial loads. Only one specimen (i.e., SP 4-1) completed the whole loading history

without significant strength degradations. The test results are summarized in this section.

In order to effectively show the global connection behavior during the test, moment-

rotation response of each specimen is plotted. In addition, initial cracks and the

corresponding drifts are schematically presented. The failure mode of each specimen is

also presented in this section.

53

3.4.1 Specimen 6-1 (SP 6-1)

As shown in Figure 3.8, SP 6-1 did not show a ductile connection behavior

through the whole loading history. The strength of SP 6-1 started to decrease after 2.0 %

drift cycles due to crack propagation in welds connecting the column to the base plate.

During the last two load cycles, SP 6-1 lost about half of its moment capacity.

In the case of weak axis bending, the first yielding in the connection is usually

observed at column flange tips due to high stress concentrations. Based on strain analysis

results, the first yielding in SP 6-1 was observed at the column flange tips in the drift

range between 0.75 % and 1.0 %.

Due to large cyclic strain gradient at column flange tips and boundary effects (Lee,

1997) at the boundary between column and base plate, the initial crack in the connection

is expected in the column flange tip regions. SP 6-1 was not an exception. As shown in

Figure 3.9, the initial crack in SP 6-1 was observed in the welds at the outside of the

column flange "R1" tip during the first load cycle of 1.5 % drift. This initial crack

propagated significantly after 2.0 % drift and completely fractured during the second load

cycle of 3.0 % drift, as shown in Figure 3.10.

Due to such relatively early fracture of the connection, yield distribution and

pattern in the base plate could not be fully investigated. Only small yielded regions were

observed on the surface of base plate near the column flange tips.

54

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Mom

ent (

Kip

-in.)

Rotation (Radian)

Figure 3.8. Moment-Rotation Response (SP 6-1)

R1

R2

L1

L2

1.5 %

1.5 %

1.5 %

Figure 3.9. Initial Cracks in Welds at Column Flange Tips (SP 6-1)

55

Figure 3.10. Fracture of Column Flange "R1" Tip (SP 6-1)

3.4.2 Specimen 6-2 (SP 6-2)

SP 6-2 showed very similar moment-rotation responses to the SP 6-1 up to 2.0 %

drift. As shown in Figure 3.11, no significant strength degradation was observed until this

specimen completed two load cycles at 3.0 % drift. However, SP 6-2 showed sudden

strength degradations right after 3.0 % drift (during the first load cycle of 4.0 % drift) and

lost most of its moment capacity during the second load cycle of 4.0 % drift.

The first yielding in SP 6-2 was also observed at the column flange tips in the

drift range between 0.75 % and 1.0 %. Most of the column flanges near the boundary

area fully yielded during the first load cycle of 3.0 % drift. However, only small yielded

regions were observed on the surface of the base plate even though the specimen

completed two load cycles of 3.0 % drift without strength degradation.

56

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Mom

ent (

Kip

-in.)

Rotation (Radian)


2.0%

1.5 %

1.5 %

1.0%

R1

R2

L1

L2

1.5 %


57

Figure 3.13. Fracture of Column Flange "L2" Tip (SP 6-2)

As shown in Figure 3.12, the initial crack in SP 6-2 was observed in the welds at

the inside of the column flange "L2" tip during the first load cycle of 1.0 % drift. This

crack grew continuously with increasing drift and a deep crack was observed at this

location during the first load cycle of 3.0 % drift, as shown in Figure 3.13. Column flange

"L2" significantly fractured during the first load cycle of 4.0 % drift.

3.4.3 Specimen 4-1 (SP 4-1)

As shown in Figure 3.14, SP 4-1 showed very ductile connection behavior

through the entire loading history. Only SP 4-1 reached the assumed limit state of the

connection (3.85 % drift) without significant strength degradations. The measured

moment capacity of SP 4-1 at the limit state (approximately 4000 kip-in.) was very close

to the design moment (Mu = 3915 kip-in.).

58

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Mom

ent (

Kip

-in.)

Rotation (Radian)


L2 R2

L1 R1

2.0%

1.5 %

2.0%


59

Figure 3.16. Plastic Hinge Formation at the Bottom of the Column (SP 4-1)

Even though SP 4-1 reached the assumed limit state of the connection, its base

plate did not fully yield across the whole width. Instead, only small yielded regions were

observed on the surface of the base plate. This indicates that the D&E method may be

resulting in rather stiff base plates. In other words, the column-base plate connections

designed by the D&E method may not behave as intended.

As shown in Figure 3.15, the initial crack in SP 4-1 was observed in the welds at

the outside of the column flange "L2" tip during the first load cycle of 1.5 % drift. This

crack did not propagate significantly by the end of the loading history. The plastic hinge

formed at the bottom of the column is presented in Figure 3.16.

3.4.4 Specimen 4-2 (SP 4-2)

SP 4-2 showed a sudden brittle failure at the early stage of the loading history.

The moment capacity of SP 4-2, shown in Figure 3.17, decreased markedly during the

60

first load cycle of 1.5 % drift. SP 4-2 lost most of its moment capacity during the first

load cycle of 2.0 % drift. Due to such early failure, SP 4-2 did not reach the limit state of

the connection.

As shown in Figure 3.18, the initial cracks in SP 4-2 were observed at column

flanges "R1" and "R2" during the first load cycle of 1.0 % drift. These cracks propagated

significantly with the increase of drift. As shown in Figure 3.19, a deep crack was

observed in the welds at the outside of column flange "R1" tip during the first load cycle

of 1.5 % drift. Finally, the column flange "R1" was completely fractured during the first

load cycle of 2.0 % drift.

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Mom

ent (

Kip

-in.)

Rotation (Radian)


61

1.0%

1.0%

1.5 % R1L1

R2L2


Figure 3.19. Crack Initiation and Sudden Connection Failure (SP 4-2)

62

3.5 Experimental Evaluation of Drake and Elkin's Method

The test results of four specimens were briefly summarized in the previous section.

In this section, based on the experimental analysis results, the D&E method is evaluated.

In order to examine global connection response, total lateral forces and total tensile bolt

forces for the four specimens are plotted and compared. The effects of different stiffness

and number (or location) of anchor bolts on the seismic behavior of the connection are

also investigated. In addition, in order to investigate the yield pattern in the base plate,

strain variations on the base plate surface are plotted and the maximum value is compared

with the expected yield strain. The experiment results are also compared with the pre-test

FEA results as well as with the design estimations given by the D&E method. Through

these comparisons, the D&E method is evaluated and several limitations of the D&E

method are identified in this section.

3.5.1 Total Lateral Force

In order to examine global connection behavior, total lateral forces of the four

specimens are compared each other. These results are also compared with the pre-test

FEA results and the design estimations given by the D&E method. Generally, it is not

easy to compare test results directly with numerical analysis results especially in a cyclic

displacement controlled tests. Thus, a total of twelve drift points are selected herein to

compare the test results with the FEA results. Especially, the test results at 3.85 % drift

(i.e., assumed drift limit state of the connection in this study) are considered as a

benchmark for experimental evaluation of the D&E method.

In Figure 3.20(a), total lateral forces and the corresponding drifts for the two 6-

bolt type specimens are compared with FEA results. In both specimens (SP 6-1 and SP 6-

63

2), initial stiffnesses show a good agreement with the FEA results up to 1.5 % drift, after

which the test results show significant strength degradations due to crack propagation in

the welds. Unfortunately, the test results of the 6-bolt type specimens at the assumed limit

state (i.e., 3.85 % drift) can not be compared with the FEA results and the design

estimation (Vu = 48.94 kips) due to early connection failures.

Total lateral forces and the corresponding drifts for the two 4-bolt type specimens

are plotted in Figure 3.20(b). The initial stiffnesses of the two 4-bolt type specimens

show slightly low as compared with those of the two 6-bolt type connections. However,

the differences are very small and ignorable in this study.

As shown in Figure 3.20(b), only the test results for SP 4-2 can be compared with

the FEA results and the design estimation (Vu = 48.94 kips) at the assumed limit state

(3.85 % drift). At this limit state, the measured total lateral force is clearly smaller than

the FEA prediction and the design estimate. The main reason of this difference can be

explained based on the tensile coupon test results shown in Table 3.1. As mentioned, an

over-estimated column yield stress (i.e., 58 ksi) was used for the design calculations and

FEA modeling. Consequently, the over-estimated column yield stress results in the over-

estimated FEA results and the over-estimated design shear force, as shown in Figure

3.20(b).

3.5.2 Total Tensile Bolt Force

Total tensile bolt forces of the four specimens are plotted and compared each

other in Figure 3.21. The test results are also compared with the pre-test FEA results and

the design estimations given by the D&E method. Bolt forces are calculated from two

strain values on the outer surface of each anchor bolt in the plane of bending.

64

0

10

20

30

40

50

60

0 1 2 3 4 5 6

FEA ResultsSP 6-1SP 6-2

Tota

l Lat

eral

For

ce (K

ips)

Drift (%)

D&E

(a) 6-Bolt Type

(b) 4-Bolt Type

Figure 3.20. Comparison of Total Lateral Forces

0

10

20

30

40

50

60

0 1 2 3 4 5 6


Tota

l Lat

eral

For

ce (K

ips)

Drift (%)

D&E

65

In Figure 3.21(a), total tensile bolt forces and the corresponding drifts for the two

6-bolt type specimens are compared with the FEA results. Due to the base plate

movement at the early stage of the loading history, the two graphs slightly shift in the

range between 0.2 % and 0.4 % drift. In both specimens (SP 6-1 and SP 6-2), the

measured total tensile bolt forces are in good agreement with the FEA results up to 1.5 %

drift, as shown in Figure 3.21(a).

In Figure 3.21(b), total tensile bolt forces and the corresponding drifts for the two

4-bolt type specimens are plotted and compared with the FEA results. The test results of

SP 4-1 show a very good agreement with the FEA results through the entire loading

history. However, as compared with the FEA results and the test results, the design

estimation (Tu = 244.8 kips) is significantly smaller at the assumed limit state (i.e., 3.85%

drift). As explained in Chapter 2, the main reason of this difference is originated from the

different anchor bolt stiffness: Variation of relative strength of anchor bolts and base

plate can result in different tensile bolt forces due to the change of the moment arm

between total tensile bolt force (Tu) and resultant bearing force (Ru).

3.5.3 Effects of Different Number of Anchor Bolts

In Chapter 2, it was shown that the different number (or location) of anchor bolts

could significantly affect the base plate yield pattern on the tension side and the bearing

stress distribution on the compression side. In order to investigate experimentally the

effects of different anchor bolt configuration, base plate deformations of SP 6-1 and SP

4-1 in the transverse direction are compared in this section. These deformations are also

compared with the FEA results.

66

(a) 6-Bolt Type

(b) 4-Bolt Type

Figure 3.21. Comparison of Total Tensile Bolt Forces

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6


Tota

l Ten

sile

Bol

t For

ce (K

ips)

Drift (%)

D&E

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6


Tota

l Ten

sile

Bol

t For

ce (K

ips)

Drift (%)

D&E

67

0.02

0.03

0.04

0.05

0.06

0.07

-10 -5 0 5 10

FEA ResultsSP 6-1

Ver

tical

Dis

plac

emen

t (in

.)

Base Plate Width (in.)

(a) 6-Bolt Type

0.02

0.03

0.04

0.05

0.06

0.07

-10 -5 0 5 10

FEA ResultsSP 4-1

Ver

tical

Dis

plac

emen

t (in

.)

Base Plate Width (in.)

(b) 4-Bolt Type

Figure 3.22. Deformed Shape of the Base Plate along the Assumed Bending Line on

the Tension Side (1.71% Drift)

68

In Figure 3.22, each base plate deformation along the assumed bending line on the

tension side is compared with the FEA results. For each specimen, the test results show a

good agreement with the FEA results. However, as shown in Figure 3.22, the test and

FEA results of SP 6-1 show significantly different base plate deformations as compared

with those of SP 4-1. The deformed base plate of SP 6-1, shown in Figure 3.22(a), is flat

or concave due to the restraint of the inner bolt in the connection, whereas the deformed

base plate of SP 4-1 is convex as shown in Figure 3.22(b).

The convex shape of the base plate in the 4-bolt type connection can increase the

bearing stresses at the corner of the grout due to the decrease of contact area between

base plate and grout. This phenomenon was already observed in pre-test FEA results.

Through the experimental study of SP 4-1, the high bearing stress concentrations at the

corner of the grout were reconfirmed. Due to such high stresses, a corner of the grout was

crushed during the first load cycle of 4.0 % drift as shown in Figure 3.23.

Figure 3.23. Grout Crushing in the 4-Bolt Type Connection (SP 4-1)

69

3.5.4 Stiff Base Plate

One of basic assumptions in the D&E method is that the base plate develops its

full moment capacity at the ultimate state of the connection. However, as shown in pre-

test FEA results, only small yielded regions were observed on the surface of the base

plate for both bolt type connections even though these connections reached the assumed

limit state (3.85 % drift). In this section, these numerical observations are reconfirmed

using the test results.

In order to investigate the yield pattern in the base plate, strain variations on the

base plate surface are plotted and the maximum value is compared with the expected

yield strain of the base plate (1240 microstrain). Due to high local stress concentrations,

significant yielding was observed on the base plate surface near the column flange tips in

SP 6-1, SP 6-2, and SP 4-1. However, these base plates did not fully yield along the

assumed bending lines as intended in the D&E method. In order to show the strain

variations at the center of the assumed bending line on the base plate surface, strain

measurements from SP 6-1, SP 6-2, and SP 4-1 are plotted in Figures 3.24, 3.25, and 3.26,

respectively. Based on experimental analysis results, the D&E method clearly results in

stiff base plates. This indicates that base plates designed by the D&E method may not

behave as intended.

70

-1500

-1000

-500

0

500

1000

1500

-6 -4 -2 0 2 4 6

Stra

in (m

icro

stra

in)

Drift (%)

Yield Strain

Yield Strain

Figure 3.24. Strain Variation at the Center of the Assumed Bending Line (SP 6-1)

71

-1500

-1000

-500

0

500

1000

1500

-6 -4 -2 0 2 4 6

Stra

in (m

icro

stra

in)

Drift (%)

Yield Strain

Yield Strain


72

-1500

-1000

-500

0

500

1000

1500

-6 -4 -2 0 2 4 6

Stra

in (m

icro

stra

in)

Drift (%)

Yield Strain

Yield Strain


73

3.6 Effects of Different Weld Material and Weld Detail

Based on the experimental observations, the effects of different weld material and

weld detail on the seismic connection ductility are examined in this section. In order to

investigate the effects of different weld material, test results of SP 6-1 and SP 6-2 are

compared. In addition, test results of SP 4-1 and SP 4-2 are compared in order to

investigate the effects of two different weld details on the seismic connection ductility.

3.6.1 Effects of Different Weld Material (Between SP 6-1 and SP 6-2)

Based on the global connection responses and experimental observations of SP 6-

1 and SP 6-2, the effects of different weld material on the seismic connection ductility are

examined. From Table 2.2, the only difference between SP 6-1 and SP 6-2 is the weld

material. SP 6-1 is welded using ER70S-3 (SuperArc L-50) electrode, whereas SP 6-2 is

welded using E70TG-K2 (NR-311Ni) electrode.

As already shown in Figure 3.9, initial crack in SP 6-1 was observed in the welds

at the outside of column flange "R1" tip during the first load cycle of 1.5 % drift. On the

other hand, initial crack in SP 6-2 was observed a little earlier than the SP 6-1 case, as

shown in Figure 3.12. However, up to 3.0 % drift, no significant differences were

observed in crack propagation and seismic behavior of the connection between those two

specimens. Therefore, based on the experimental observations, no significant differences

between ER70S-3 and E70TG-K2 electrodes were found.

74

3.6.2 Effects of Fillet Weld Reinforcement over the Groove Welds (Between SP 4-1

and SP 4-2)

In order to investigate the effects of 3/16 in. fillet weld reinforcement over the

groove welds at the outside of column flanges, as shown in Figure 2.6, crack propagation

and connection behavior of SP 4-1 and SP 4-2 are compared. As explained in Chapter 2,

the major difference between SP 4-1 and SP 4-2 is the existence of 3/16 in. fillet weld

reinforcement. SP 4-1 is reinforced by 3/16 in. fillet welds over the groove welds,

whereas only the suggested minimum welds are used for SP 4-2.

SP 4-1 and SP 4-2 showed very different seismic behavior of the connection. Due

to the lack of weld reinforcement at column flange tips, the initial crack in SP 4-2 was

observed at 1.0 % drift that is clearly earlier than the SP 4-1 case (1.5 % drift). As shown

in Figure 3.14, SP 4-1 showed very ductile connection behavior through the entire

loading history even though the initial crack was observed during the first load cycle of

1.5 % drift. On the other hand, SP 4-2 failed in a quite brittle manner at an early stage of

the loading history, as shown in Figure 3.17. These test results indicate that the fillet weld

reinforcement over the groove welds can help significantly develop the full moment

capacity in the connection. Therefore, for the weld detail of column-base plate

connections under weak axis bending, the fillet weld reinforcement over the groove

welds is recommended.

CHAPTER 4

NUMERICAL PARAMETRIC STUDY

Through the numerical pre-test analyses in Chapter 2 and the experimental study

in Chapter 3, the contribution of relative strength ratios in the seismic behavior of the

connection was discovered. An extensive numerical parametric study was conducted to

investigate more precisely the effects of relative strength ratio on the seismic behavior of

the connection, and the study results are presented in this chapter. Two main parameters

(i.e., anchor bolt stiffness and base plate thickness) are selected for this systematic

investigation of the relative strength ratio effects. For both bolt type connections (i.e., 6-

bolt type and 4-bolt type), the effects of anchor bolt stiffness and base plate thickness on

the seismic behavior of the connection are studied and several major observations are

summarized.

In addition, in order to examine the effects of grout strength on the location of the

resultant bearing force on the compression side, three more FEA models consisting of

different grout compressive strengths are prepared and analyzed. This study is conducted

for the 6-bolt type connection only. The FEA results are compared with the design

estimations given by the D&E method, and the principal differences are discussed in the

last part of this chapter.

4.1 Classification of FEA Models

A total of forty-three FEA models, including two FEA models used for the pre-

test analyses in Chapter 2, are prepared and analyzed for the numerical parametric study

75

76

in this chapter. Twenty FEA models are prepared for each bolt type connection to

investigate the effects of relative strength ratios on the seismic behavior of the connection.

In addition, three more FEA models are prepared only for the 6-bolt type connection to

examine the effects of grout strength on the location of the resultant bearing force on the

compression side.

All of the prepared FEA models are classified in Table 4.1. In this Table, "tpo" and

"Ko" denote, respectively, the designed base plate thickness and anchor bolt stiffness

according to the D&E method. In this parametric study, only stiffness values larger than

or equal to "Ko" are considered because the anchor bolts are intended not to yield even

though the connection reaches its limit state.

Table 4.1. Classification of FEA Models

Anchor Bolt Stiffness

6-Bolt Type 4-Bolt Type

1.0 Ko 1.3 Ko 1.7 Ko 2.2 Ko 1.0 Ko 1.3 Ko 1.7 Ko 2.2 Ko

0.8 tpo

0.9 tpo

fc'=6 ksi

(SP 6)

fc'=8 ksi

fc'=10 ksi

1.0 tpo

fc'=12 ksi

(SP 4)

1.1 tpo

Bas

e Pl

ate

Thic

knes

s

1.2 tpo

Remark: For all other blanks, the grout compressive strength (fc') is equal to 6 ksi.

77

For each bolt type connection, a total of four different anchor bolt stiffnesses (1.0

Ko, 1.3 Ko, 1.7 Ko, and 2.2 Ko) and a total of five different base plate thicknesses (0.8 tpo,

0.9 tpo, 1.0 tpo, 1.1 tpo and 1.2 tpo) are selected for the study of relative strength ratio

effects on the seismic behavior of the connection. In addition, a total of four different

grout compressive strengths (i.e., 6, 8, 10, and 12 ksi) are selected to examine the effects

of grout compressive strength on the location of the resultant bearing force on the

compression side.

4.2 Effects of Anchor Bolt Stiffness

In order to investigate the effects of relative strength ratios on the seismic

behavior of the connection, a total of twenty FEA models are prepared and analyzed for

each bolt type connection in this parametric study. However, in this section, only four

FEA models consisting of different anchor bolt stiffnesses are selected for each bolt type

connection to investigate the effects of anchor bolt stiffness on the seismic behavior of

the connection. The selected connection assemblages are marked on Table 4.2.

The effects of anchor bolt stiffness on the seismic behavior of the connection are

investigated by various methods. First, total lateral forces and total tensile bolt forces are

compared to examine the effects of anchor bolt stiffness on the global responses of the

connection at its limit state. Second, by comparing the deformation and yield pattern of

the base plate, the effects of anchor bolt stiffness on the base plate responses are

investigated. Third, the variation of bearing stress contours on the grout is examined to

investigate the effects of anchor bolt stiffness on the bearing stress distribution. Lastly,

locations of the resultant bearing force are calculated and these values are compared with

the design estimations given by the D&E method. Through these comparisons, sensitivity

of the resultant bearing force location to anchor bolt stiffness variation is investigated.

78

Table 4.2. Selected Connections for the Study of Anchor Bolt Stiffness Effects




0.8 tpo

0.9 tpo

fc'=6 ksi

(SP 6)

fc'=8 ksi

fc'=10 ksi

1.0 tpo

fc'=12 ksi

(SP 4)

1.1 tpo

Bas

e Pl

ate

Thic

knes

s

1.2 tpo



In order to investigate the effects of anchor bolt stiffness on global connection

response, such as initial rotational stiffness and moment capacity, the total lateral forces

of the selected eight connections (i.e., four for the 6-bolt type and four for the 4-bolt type)

are plotted and compared in Figure 4.1. Evidently, no significant differences are observed

in the global connection responses between the 6-bolt and 4-bolt type connections.

79

0

10

20

30

40

50

60

0 1 2 3 4 5 6

1.0 Ko1.3 Ko1.7 Ko2.2 Ko

Tota

l Lat

eral

For

ce (K

ips)

Drift (%)

(a) 6-Bolt Type

0

10

20

30

40

50

60

0 1 2 3 4 5 6

1.0 Ko1.3 Ko1.7 Ko2.2 Ko

Tota

l Lat

eral

For

ce (K

ips)

Drift (%)

(b) 4-Bolt Type

Figure 4.1. Total Lateral Forces versus Drifts

80

The FEA results, presented in Figure 4.1, provide two conclusions: First, initial

rotational stiffness of the connection is proportional to the anchor bolt stiffness for both

bolt type connections. However, within the given range of anchor bolt stiffnesses, the

variation is very small and may be neglected. Second, full moment capacity of the

column is developed in all eight models. This indicates that all of the selected base plate

thickness / anchor bolt stiffness combinations in this study are strong enough to develop a

strong connection / weak column mechanism.


For the selected eight connections, total tensile bolt forces are calculated at the

assumed limit state of the connection (3.85 % drift) to investigate the effects of anchor

bolt stiffness on total tensile bolt forces. The analysis results are plotted and compared in

Figure 4.2. As shown in Figure 4.2, no significant differences are observed in the total

240

250

260

270

280

290

300

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4


Tota

l Ten

sile

Bol

t For

ce (K

ips)

Anchor Bolt Stiffness (Ko)

Figure 4.2. Total Tensile Bolt Forces (3.85 % Drift)

81

tensile bolt forces between the 6-bolt and 4-bolt type connections.

For both bolt type connections, the stiffer anchor bolts result in a higher values of

the total tensile bolt force. This is due to shortening of the overall moment arm between

total tensile bolt force (Tu) and resultant bearing force (Ru) as explained in Chapter 2 and

Chapter 3. The analysis results, presented in Figure 4.2, reconfirm this fact.

4.2.3 Deformation of the Base Plate

In order to examine the seismic base plate responses with respect to different

anchor bolt stiffnesses, base plate deformations of the selected eight connections are

presented and compared in Figures 4.3 and 4.4. For both bolt type connections, due to

relatively large elongation of the anchor bolt, the largest base plate rotation is observed in

the case of 1.0 Ko.

In 6-bolt type connections, shown in Figure 4.3, the deformed shape of the base

plate on the tension side is almost flat in the transverse direction. This is due to the

restraint provided by the inner bolt on the tension side. On the other hand, as shown in

Figure 4.4, a convex shape of the base plate is observed in 4-bolt type connections. As

explained in Chapter 3, the convex shape of the base plate in the 4-bolt type connection

can increase the bearing stresses at the corner of the grout and result in undesirable grout

crushing before the connection reaches its ultimate state.

82

(a) 1.0 Ko

(b) 1.3 Ko

(c) 1.7 Ko

(d) 2.2 Ko

Figure 4.3. Deformation of the Base Plate (6-Bolt Type, 3.85 % Drift)

83

(a) 1.0 Ko

(b) 1.3 Ko

(c) 1.7 Ko

(d) 2.2 Ko


84

4.2.4 Variation of Yield Pattern in the Base Plate

In order to investigate the effects of anchor bolt stiffness on the variation of base

plate yield pattern, equivalent Mises stress contours on the base plate surface are

compared in Figures 4.5 and 4.6. For both bolt type connections, base plate yield pattern

is highly dependent on the relative strength ratio between the anchor bolts and the base

plate.

For the 6-bolt type connection, shown in Figure 4.5, relatively large yield of the

base plate is observed on the compression side in the case of 1.0 Ko. On the other hand,

relatively large yield of the base plate is observed on the tension side in the case of 2.2 Ko.

The main reason of the variation in major base plate yield area can be explained

effectively using the deformed shape of the base plate in the longitudinal direction. As

presented in Figure 4.3(a), smaller anchor bolt stiffness (1.0 Ko) results in the larger base

plate rotation. Due to very small base plate settlement on the grout, relatively large

curvature forms on the compression side of the base plate. This larger curvature, of

course, results in larger base plate yield area on the compression side. Similarly, larger

anchor bolt stiffness (2.2 Ko) results in larger base plate yield area on the tension side.

The FEA results of the 4-bolt type connection, shown in Figure 4.6, show the

similar variation in base plate yield pattern even though the 4-bolt type connection

develops a different yield shape (circular shape) on the tension side as compared with the

6-bolt type connection. Clearly large base plate yielded area is observed on the tension

side in the case of 2.2 Ko, as shown in Figure 4.6(d).

85

(a) 1.0 Ko

(b) 1.3 Ko

(c) 1.7 Ko

(d) 2.2 Ko

Figure 4.5. Equivalent Mises Stress Contours on the Base Plate Surface (6-Bolt

Type, 3.85 % Drift)

86

(a) 1.0 Ko

(b) 1.3 Ko

(c) 1.7 Ko

(d) 2.2 Ko


Type, 3.85 % Drift)

87

4.2.5 Variation of Bearing Stress Distribution on the Grout

In order to investigate the effects of anchor bolt stiffness on bearing stress

distribution, the variation of bearing stress contours on the grout is examined for each

bolt type connection. In Figures 4.7 and 4.8, the bearing stress contours for the eight

connections selected in Table 4.2 are presented and compared. As explained, due to the

convex shape of the base plate, relatively high bearing stresses are observed at the

corners of the grout in 4-bolt type connections.

For both bolt type connections, the contact (bearing) area between the base plate

and the grout in the longitudinal direction changes with different anchor bolt stiffnesses.

In the case of 1.0 Ko, the base plate deforms as a rigid plate so that the bearing area

decreases. Such decrease of bearing area results in an increase of bearing stresses on the

grout near base plate edges, as shown in Figures 4.7(a) and 4.8(a).

4.2.6 Location of the Resultant Bearing Force

The effects of anchor bolt stiffness on the location of resultant bearing force (Ru)

are investigated in this section. For this purpose, locations of Ru for the eight selected

connections are directly calculated from bearing stress distribution presented in the

previous section. Using a new variable, base plate compression interface cantilever length

x' shown in Figure 4.9, the calculated locations of Ru are plotted in Figure 4.10.

As shown in Figure 4.10, the increase of the anchor bolt stiffness results in a

decrease of the cantilever length x' for both bolt type connections. This analysis result

leads to a very important conclusion: undesirable grout crushing on the compression side,

due to high bearing stress concentrations, can be prevented by increasing anchor bolt size

(or stiffness).

88

(a) 1.0 Ko

(b) 1.3 Ko

(c) 1.7 Ko

(d) 2.2 Ko

Figure 4.7. Bearing Stress Distribution on the Grout (6-Bolt Type, 3.85 % Drift)

89

(a) 1.0 Ko

(b) 1.3 Ko

(c) 1.7 Ko

(d) 2.2 Ko


90

x x'

L


Assumed Bending Line(Compression Side)

Mu

Tu Ru

Figure 4.9. Overall Moment Arm L and Cantilever Lengths x and x'

2.8

3

3.2

3.4

3.6

3.8

4

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

x (Both Types)x' (6-Bolt Type)x' (4-Bolt Type)

Mom

ent A

rm fr

om A

ssum

ed B

endi

ng L

ine

(in.)


Figure 4.10. Effects of Anchor Bolt Stiffness on Cantilever Length x'

91

4.3 Effects of Base Plate Thickness

The effects of base plate thickness on the seismic behavior of the connection are

investigated in this section. For this purpose, three connection assemblages consisting of

different base plate thicknesses are selected for each bolt type connection. The selected

connection assemblages are marked on Table 4.3. In this parametric study, as shown in

Table 4.3, only 1.3 Ko is considered for anchor bolt stiffness of the selected six

connections.

Table 4.3. Selected Connections for the Study of Base Plate Thickness Effects




0.8 tpo

0.9 tpo

fc'=6 ksi

(SP 6)

fc'=8 ksi

fc'=10 ksi

1.0 tpo

fc'=12 ksi

(SP 4)

1.1 tpo

Bas

e Pl

ate

Thic

knes

s

1.2 tpo


92

For each bolt type connection, effects of base plate thickness on the seismic

behavior of the connection are investigated in depth based on the following six analysis

results: total lateral force, total tensile bolt force, base plate deformation, base plate yield

pattern, bearing stress distribution, and resultant bearing force location.


In order to investigate the effects of base plate thickness on global connection

behavior, total lateral forces of the selected six connections (three for the 6-bolt type and

three for the 4-bolt type) are plotted and compared in Figure 4.11. As shown in Figure

4.11, there is no significant difference in global connection responses between the 6-bolt

and 4-bolt type connections.

For both bolt type connections, lower strength and stiffness are observed in the

case of the thin base plate (0.8 tpo). The main reason of this strength and stiffness

reduction is early yielding in the base plate. On the other hand, the base plate designed by

the D&E method (1.0 tpo) and the thick base plate (1.2 tpo) do not show such reductions.

The FEA results, presented in Figure 4.11, provide one important conclusion: thinner

base plates result in strength and stiffness reduction of the connection such that a weak

connection / strong column mechanism can be developed.

93

0

10

20

30

40

50

60

0 1 2 3 4 5 6

0.8 tpo1.0 tpo1.2 tpo

Tota

l Lat

eral

For

ce (K

ips)

Drift (%)

(a) 6-Bolt Type

0

10

20

30

40

50

60

0 1 2 3 4 5 6

0.8 tpo1.0 tpo1.2 tpo

Tota

l Lat

eral

For

ce (K

ips)

Drift (%)

(b) 4-Bolt Type

Figure 4.11. Total Lateral Forces versus Drifts

94


For the selected six connections, total tensile bolt forces are calculated at the

assumed limit state of the connection (3.85 % drift) to investigate the effects of base plate

thickness on them. The analysis results are plotted and compared in Figure 4.12. As

shown in Figure 4.12, no significant differences exist in total tensile bolt forces between

the 6-bolt and 4-bolt type connections.

For both bolt type connections, a stiffer base plate results in a lower value of the

total tensile bolt force due to lengthening of the overall moment arm between total tensile

bolt force (Tu) and resultant bearing force (Ru). In the case of the thick base plate (1.2 tpo),

due to small base plate deformation, the overall moment arm between Tu and Ru is

lengthened. Therefore, in order to resist the same amount of moment (Mu), total tensile

bolt force Tu decreases with longer moment arm.

240

250

260

270

280

290

300

0.7 0.8 0.9 1 1.1 1.2 1.3


Tota

l Ten

sile

Bol

t For

ce (K

ips)

Base Plate Thickness (tpo)

Figure 4.12. Total Tensile Bolt Forces (3.85 % Drift)

95

4.3.3 Deformation of the Base Plate

The effects of base plate thickness on the seismic behavior of the connection are

investigated by comparing the base plate deformations at the assumed limit state of the

connection (3.85 % drift). Base plate deformations of the selected six connections are

presented and compared in Figures 4.13 and 4.14. In the cases of 1.0 Ko and 1.2 Ko, no

significant differences are observed between the 6-bolt and 4-bolt type connections,

except for the deformed shape of the base plate in the transverse direction. However, in

the case of 0.8 Ko, significant out-of-plane base plate deformation is observed in the 4-

bolt type connection due to the location of the anchor bolts, whereas the 6-bolt type

connection shows a quite in-plane base plate deformation.

For both bolt type connections, a significant difference in the base plate

deformations is observed between the 0.8 Ko case and the other two cases (1.0 Ko and 1.2

Ko). In the case of the 0.8 Ko, base plates deform outwardly on the tension side, as shown

in Figures 4.13(a) and 4.14(a). However, in the other two cases (1.0 Ko and 1.2 Ko), the

base plates deform inwardly. A significant point which should be mentioned is that

outward deformation of the base plate can cause unexpected local deformation of the

anchor bolts.

Based on experimental observations, it has been found that thinner base plates

could be a good source of energy dissipation and provide for more ductile connection

behavior during earthquake excitations (Astaneh et al., 1992). However, as shown in

Figures 4.13(a) and 4.14(a), a thin base plate can also cause high local stress

concentrations in the anchor bolts on the tension side. This can be clearly seen from the

deformed shape of the anchor bolts and the stress contours presented in Figures 4.15 and

4.16, respectively. Hence, minimum thickness of the base plate should be limited to

prevent possible anchor bolt failure due to such high stress concentrations.

96

(a) 0.8 tpo

(b) 1.0 tpo

(c) 1.2 tpo


97

(a) 0.8 tpo

(b) 1.0 tpo

(c) 1.2 tpo


98


Figure 4.15. Local Deformation of Outer Anchor Bolt (0.8 tpo, 3.85 % Drift)


Figure 4.16. Local Stress Concentration in Outer Anchor Bolt (0.8 tpo, 3.85 % Drift)

99

4.3.4 Variation of Yield Pattern in the Base Plate

In order to investigate the effects of base plate thickness on the variation of base

plate yield pattern, equivalent Mises stress contours on base plate top surface are

compared in Figures 4.17 and 4.18. For both bolt type connections, base plate yield

patterns are highly dependent on the relative strength ratio between the anchor bolts and

the base plate. As shown in Figures 4.17(a) and 4.18(a), relatively large yield of the base

plate is observed on the tension side in the case of 0.8 Ko. With the increase of base plate

thickness, however, the dominant yield region moves to the compression side.

4.3.5 Variation of Bearing Stress Distribution on the Grout

In order to investigate the effects of base plate thickness on the bearing stress

distribution, the variation of bearing stress contours on the grout is examined for each

bolt type connection. In Figures 4.19 and 4.20, bearing stress contours for the selected six

connections are presented and compared.

For both bolt type connections, high stress concentrations are observed under the

column flanges in the case of the thin base plate (0.8 tpo), whereas the thick base plate

case (1.2 tpo) shows high stress concentrations along the grout edge. Such significant

variation of bearing stress distribution is a result of different stiffnesses of the base plate.

In the case of a thin base plate, compressive forces concentrate on the grout under the

column flanges due to flexural base plate deformations. In the case of a thick base plate,

however, the base plate deforms as a rigid plate so that bearing stresses concentrate along

the edge of the grout. The FEA results, presented in Figures 4.19 and 4.20, enable one

important conclusion: designing thick base plates should be avoided because they may

cause undesirable grout crushing under the base plate edge on the compression side.

100

(a) 0.8 tpo

(b) 1.0 tpo

(c) 1.2 tpo


Type, 3.85 % Drift)

101

(a) 0.8 tpo

(b) 1.0 tpo

(c) 1.2 tpo


Type, 3.85 % Drift)

102

(a) 0.8 tpo

(b) 1.0 tpo

(c) 1.2 tpo


103

(a) 0.8 tpo

(b) 1.0 tpo

(c) 1.2 tpo


104

4.3.6 Location of the Resultant Bearing Force

The effects of base plate thickness on the location of the resultant bearing force

(Ru) are investigated in this section. For this purpose, the Ru locations for the selected six

connections are directly calculated from the bearing stress distribution presented in the

previous section. Using a new variable x', shown in Figure 4.9, the calculated locations of

Ru are plotted in Figure 4.21.

As shown in Figure 4.21, for both bolt type connections, the decrease of base

plate thickness results in a decrease of cantilever length x'. This analysis result indicates

that undesirable grout crushing on the compression side, due to high bearing stress

concentrations, can be prevented by decreasing base plate thickness.

2.8

3

3.2

3.4

3.6

3.8

4

0.7 0.8 0.9 1 1.1 1.2 1.3

x (Both Types)x' (6-Bolt Type)x' (4-Bolt Type)

Mom

ent A

rm fr

om A

ssum

ed B

endi

ng L

ine

(in.)


Figure 4.21. Effects of Base Plate Thickness on Cantilever Length x'

105

4.4 Effects of Grout Compressive Strength

In order to investigate the effects of grout strength on the location of resultant

bearing force (Ru), three additional FEA models consisting of different grout compressive

strengths are prepared and analyzed. A total of four selected connections are marked on

Table 4.4. As indicated in Table 4.4, this parametric study is conducted for the 6-bolt

type connection only.

Table 4.4. Selected Connections for the Study of Grout Compressive Strength

Effects




0.8 tpo

0.9 tpo

fc'=6 ksi

(SP 6)

fc'=8 ksi

fc'=10 ksi

1.0 tpo

fc'=12 ksi

(SP 4)

1.1 tpo

Bas

e Pl

ate

Thic

knes

s

1.2 tpo


106

As shown in Figure 2.3, the D&E design procedure appears quite sensitive to the

change of grout compressive strength (fc'). This is because the D&E method is highly

dependent on the assumed grout bearing capacity per unit length (q) and the equivalent

bearing length (Y). However, the FEA results, presented in Figure 4.22, show that the

cantilever length x' does not change significantly with the change of grout compressive

strength (fc').

2.5

3

3.5

4

4.5

5

5 6 7 8 9 10 11 12 13

Drake and Elkin's MethodFEA Results

Mom

ent A

rm fr

om A

ssum

ed B

endi

ng L

ine,

x' (

in.)

Compressive Strength of Grout, fc' (Ksi)

Figure 4.22. Variation of Cantilever Length x' on the Compression Side with

Respect to fc' (6-Bolt Type, 3.85 % Drift)

CHAPTER 5

LIMITATIONS OF DRAKE AND ELKIN'S METHOD

The pre-test FEA results in Chapter 2 revealed several possible limitations of the

D&E method in its basic assumptions and subsequent design calculations. These

limitations were confirmed through the experimental study in Chapter 3 and the

numerical parametric study in Chapter 4. A total of six limitations of the D&E method

are discussed in this chapter.

5.1 Unrealistic Application of Concrete Beam Design Methodology

As shown in Figure 2.2, the D&E method adopts an equivalent rectangular stress

block, which is generally used in concrete beam design, to calculate unknown design

parameters in a column-base plate connection. However, concrete beam design

methodology may not directly apply to the column-base plate connection design because

of the following two reasons. First, the base plate and grout is not monolithic so that the

traditional "plane sections remain plane" assumption made in the development of beam

theory does not hold. Second, due to small and unreliable bond stresses between anchor

rod and concrete (and grout), the "the strain in the reinforcement is equal to the strain in

the concrete at the same level" assumption cannot be used. Because of the above two

reasons, linear strain variation across the section cannot be used for calculation of neutral

axis location and bearing stress distribution.

The FEA results, shown in Figure 2.13, also show a clear limitation in the

application of concrete beam design methodology for the design of column-base plate

107

108

connections under weak axis bending. As shown in Figures 2.13(a) and 2.13(b), bearing

stress distributions in the longitudinal direction are not even close to uniform, which is

assumed in the D&E method, for both bolt type connections. Moreover, bearing stress

distributions in the transverse direction show more complex stress patterns in both

connections.

In conclusion, concrete beam design methodology cannot be directly applied for

design of column-base plate connections under weak axis bending. A more realistic

bearing stress block should be used for more reliable connection design. Alternatively,

another design methodology should be developed.

5.2 Over-sensitive Design Procedure to q (or fc')

The concrete bearing capacity per unit length (q), in terms of grout compressive

strength (fc') as presented in Equation 2-1, is the most important design parameter in the

D&E method. With an assumed value of the q, the D&E method calculates the required

total tensile strength of anchor bolts (Tu) and resultant bearing force (Ru=q·Y) using two

equilibrium equations, i.e., moment and vertical force equilibrium equations. Moreover,

base plate thickness is also highly dependent on the q value. This is because the required

base plate flexural strength per unit width (Mpl) on each side is calculated directly from

the two force resultants (i.e., Tu and Ru=q·Y, respectively).

In order to explain more effectively the role of concrete bearing capacity per unit

length q in the D&E method, two different cases (i.e., small q and large q) are compared

in Figure 5.1. As shown in Figure 5.1(b), due to the shortened equivalent bearing length

(Y), the larger q value results in longer L and x'. The lengthened L decreases the amount

of Tu and Ru needed to resist the same design moment (Mu). However, the variation is

very small and can be ignored. On the other hand, longer x' significantly increases base

plate thickness because Mpl on the compression side is very sensitive to the variation of x'.

109

Determining q is not easy because there is a clash between the AISC and ACI

recommendations for the strength reduction factor in case of bearing on concrete φc

which is a part of q as presented in Equation 2-1. As mentioned in Chapter 2, the AISC

LRFD Specifications recommends φc = 0.6, whereas the ACI 318-99 adopts φc = 0.7. The

D&E method is based on the AISC LRFD. Thus, 0.6 is adopted for φc in Equation 2-1.

However, the applicability of φc=0.6 for column-base plate connection design has not

been verified sufficiently. Hence, for more reliable connection design, the ultimate

bearing capacity of concrete (grout) in column-base plate connections should be

determined more accurately.

As explained, the base plate design in the D&E method appears quite sensitive to

the q (or fc') value. This is because q (or fc') values significantly change the location of the

resultant bearing force x'. As shown in Figure 2.3, within the given range of the fc' in this

study, the maximum variation of the base plate thickness is more than 0.25 in. This

variation is large enough to change the seismic behavior of the connection. In contrast,

the numerical parametric study shows a very different result. The FEA results, shown in

Figure 4.22, indicate that the x' does not change significantly with the change of fc'.

Hence, based on the FEA results, it can be concluded that the estimate of x' and the

subsequent design calculations using q (or fc') value in the D&E method may not be

realistic.

110



q (Small)

Mu

Tu

Lx'

Ru = qY

(a) Small q



Mu

Tu

Lx'

Ru = qY

q (Large)

(b) Large q

Figure 5.1. Effects of q Value on the Location of Ru (= q·Y)

111

5.3 Inaccurate Location of Two Bending Lines

As shown in Figure 2.1, the D&E method assumes a pair of bending lines (one on

the tension side and one on the compression side) for the design of base plate thickness in

both strong axis and weak axis bending. The assumed bending lines seem to be quite

applicable to the strong axis bending case because maximum curvature of the base plate

always occurs under the column flange. However, in the case of weak axis bending, it is

very difficult to estimate the locations of these two bending lines. This is because the

actual locations of the two critical lines can change depending on the geometry and

relative strength ratios among the connection elements. Moreover, each bending line may

not be located symmetrically in the weak axis bending case.

As shown in Figure 2.12, the FEA results also failed to find the representative

bending lines due to a nonuniform distribution of base plate yielding. However, for more

reliable connection design, locations of the maximum base plate curvature (i.e., critical

bending lines) must be provided. Thus, in the proposed new design method, these

locations will be estimated theoretically.

5.4 No Explanation of Anchor Bolt Location Effects

The D&E method does not recognize the differences in seismic behavior of the

connection between the 6-bolt and 4-bolt type connections. Both numerical and

experimental study, however, showed that anchor bolt location may significantly affect

the seismic behavior of the connection. Two major effects of different anchor bolt

locations are summarized in the following.

First, different anchor bolt location results in different base plate deformation on

the tension side. Such deformation causes different stress distribution in the base plate.

112

As shown in Figure 2.12, the 4-bolt type connection develops a circular shaped base plate

yield line on the tension side, whereas the 6-bolt type connection develops a linear shape.

A three-dimensional out-of-plane base plate deformation can develop in the 4-bolt type

connection. This problem can be more serious when the base plate is thin, as shown in

Figure 4.14(a).

Second, different anchor bolt location can affect the bearing stress distribution on

the compression side. As shown in Figure 2.13, due to the convex shape of the base plate,

relatively high bearing stresses are observed at the corners of the grout in the 4-bolt type

connection. The test results also confirmed the possibility of such high bearing stress

concentrations, as shown in Figure 3.23.

Unfortunately, the effects of out-of-plane base plate deformation in the 4-bolt type

connection on the design procedure were not examined in this study. However, the higher

bearing stresses at the corners of the grout in the 4-bolt type connection will be

considered in the proposed new design method.

5.5 No Use of Relative Strength Ratios

For the design of anchor bolts, the D&E method provides only the required

minimum anchor bolt size based on the AISC LRFD Specifications. However, in order to

prevent anchor bolt yielding in the column-base plate connection during earthquake

excitations, designers may want stronger anchor bolts than what the D&E method

provides. Unfortunately, in this case, the D&E method cannot be directly used for the

design of column-base plate connections because this method is developed based on the

assumption that "the anchor bolts on the tension side yield at the ultimate state of the

connection".

The concept of relative strength ratio can be used for design of column-base plate

connections which have stronger anchor bolts (i.e., anchor bolts larger than Ko). As

113

shown in Chapter 4, relative strength ratios among the connection elements can be used

as parameters to estimate connection behavior at its ultimate state. Thus, based on the

study results of the relative strength ratio effects, a more rational and reliable design

method will be developed in the following chapter.

5.6 Design of Stiff Base Plate

As explained in the Section 2.2.1, it is intended in this study to design the

minimum thickness of the base plate within the boundaries of the D&E method. However,

as shown in Figure 2.12, base plates designed by the D&E method did not fully yield

across the whole width for both bolt type connections. Instead, only limited yielded

regions were observed on the surface of the base plate. The experimental results, shown

in Figures 3.24, 3.25, and 3.26, reconfirmed the numerical observations. Hence, the D&E

method may be resulting in rather stiff base plates.

For ductile connection behavior, designing flexible base plates is very important

because of the following two reasons. First, a thick base plate may result in grout

crushing under the base plate edge on the compression side. Second, a thin base plate can

significantly dissipate earthquake input energy. However, in this case, minimum

thickness of the base plate should be limited because thin base plate may cause high local

stress concentrations in the anchor bolts on the tension side, as shown in Figures 4.15 and

4.16.

In conclusion, base plates designed by the D&E method did not fully yield along

the assumed two bending lines at the limit state of the connection. This indicates that

connections designed by the D&E method may not behave as intended. Therefore, for

ductile connection behavior, designing flexible base plates will be one of main goals in

the proposed new design method.

CHAPTER 6

NEW DESIGN METHOD

The limitations of the representative current design practice, as discussed in

Chapter 5, suggested the need for a more rational and reliable design method. Thus, the

primary objective of the study presented in this chapter is to develop a new design force

profile, which describes more realistically the actual force distribution in the connection.

Based on this new design force profile and the concept of relative strength ratios among

the connection elements, a new design method is proposed in this chapter.

In order to develop the new design method, a total of six parameters (i.e., three

geometric ratios and three strength ratios) are defined first and then, a desired connection

behavior at the ultimate state is described using these strength ratios for a given

connection geometry. Moreover, several basic design formulas are derived based on the

new design force profile. Finally, using the proposed new design method, the two

connections chosen for the study (i.e., 6-bolt type and 4-bolt type) are re-designed and the

new connection element sizes are compared with those obtained from the D&E method.

6.1 Three Geometric Ratios

Depending on the relative member sizes among the three major connection

elements (i.e., column, anchor bolts, and base plate), stress distribution and failure mode

in the connection can change. For the design, however, it is important to ensure the

consistent yield pattern and mechanism in the connection. Thus, two geometric ratios are

defined to provide reasonable geometric dimensions of the three major connection

114

115

elements. In addition, one more geometric ratio is defined for the location of the resultant

bearing force on the compression side.

6.1.1 Ratio of (bf / B)

The location of maximum curvature in the base plate can vary depending on the

base plate length for the given size and location of the other two major connection

elements, i.e., column and anchor bolts. For consistent base plate deformations at the

ultimate state of the connection, however, it is necessary to locate the maximum

curvature within some limited bandwidth in the base plate. This can be effectively

controlled by the relative member sizes between the column and the base plate. Thus, in

order to provide a reasonable range of base plate length for a given column size, the first

geometric ratio is defined as GR1 using two dimensional variables (i.e. bf and B) shown

in Figure 6.1.

L

B

Mu

Tu Ru

bf

a a'

Figure 6.1. Two New Variables (a and a') Determining the Locations of Tu and Ru

116

Bb

1GR f= (6-1)

The first geometric ratio (GR1) for the four specimens, used in the experimental study,

was (12.16 / 20) = 0.608. Based on the experimental observations and the numerical

analysis results, a range of 0.55 ~ 0.6 is suggested as the reasonable boundary of the GR1.

6.1.2 Ratio of (a / B)

The location of the anchor bolts in the longitudinal direction can change the

failure mode in the connection. For instance, if the edge distance of the anchor bolts is

too large, these anchor bolts can fracture in an undesirable manner, such as due to prying

action, before the connection reaches its ultimate state. The prying action can also cause

grout crushing on the tension side. Thus, in order to prevent the undesirable bolt failure

and grout crushing in the connection, the second geometric ratio is defined as GR2 in the

following:

Ba2GR = (6-2)

In the above expression, a is the distance of the anchor bolts from the base plate edge on

the tension side, as shown in Figure 6.1. For the experimental study, the specimens with

the second geometric ratio of GR2 = (2 / 20) = 0.1 were tested. Based on the

experimental observations, a value of 0.1 is suggested for the GR2.

117

6.1.3 Ratio of (a' / a)

As shown in Figure 4.9, in order to express the location of the resultant bearing

force (Ru), the cantilever length x' was used in Chapter 4. In the proposed new design

method, however, this cantilever length can no longer be used because the assumed

bending lines do not exist. In order to express the Ru location more effectively, a new

variable (a') is introduced in the new design method as shown in Figure 6.1. a' indicates

the distance between the Ru and the base plate edge on the compression side. Using the a,

introduced in previous section, location of the Ru can be expressed as:

aa3GR

'

= (6-3)

If GR3 is greater than 1.0, in the D&E method, the tension side governs the design

procedure of the base plate thickness due to larger cantilever length on the tension side.

On the other hand, the compression side governs the design procedure if GR3 is smaller

than 1.0. For the case, when GR3 is equal to 1.0, there is no need to check the design

moments of the base plate on both sides (i.e., tension and compression sides) because of

symmetry.

6.2 Three Strength Ratios

As already shown in the numerical and experimental study, seismic behavior of

the column-base plate connection is significantly affected by the relative strength ratios

among the connection elements. For a given connection geometry, the failure mechanism

and ductility of the connection can be governed by these strength ratios. However, due to

118

lack of understanding in this area, these strength ratios have not been defined in the

literature. Thus, in this section, three strength ratios are clearly defined based on the study

results. For this purpose, strengths of the three major connection elements (i.e., column,

anchor bolts, and base plate) are defined first and then, using these element strengths,

three strength ratios are defined.

6.2.1 Definition of Mp_column

For the required flexural strength Mu of a fully restrained beam-to-column

connection in moment resisting frames, the "AISC Seismic Provisions 97'" recommends

to use the lesser of the maximum moment delivered by the system or the following

expression:

ZFR1.1ZF1.1M yyyeu ⋅⋅⋅=⋅⋅= )( (6-4)

where:

Fye = expected yield stress of beam, ksi

Fy = specified minimum yield stress of beam, ksi

Ry = ratio of the expected yield stress to the specified minimum yield stress of

beam

Z = plastic section modulus of beam, 3in.

The recommended values of Ry for several member shapes and materials are summarized

in Table 6.1. The requirement of Equation (6-4) in the beam-to-column connection design

is intended to recognize potential overstrength and strain hardening effects in the

connection, so that the strong column / weak beam concept can be realized.

119

Table 6.1. Ry Values for Several Members (From AISC Seismic Provisions 97')

Member Classes Ry

ASTM A36 1.5

ASTM A572 Grade 42 1.3

Rolled Shapes

and Bars

Other Grades 1.1

Plate Plate 1.1

However, due to different intentions in the design, the strong column / weak beam

concept can not be directly applied for the column-base plate connection design. For the

column-base plate connection, it is desirable to design a flexible base plate instead of the

stiff base plate, because thinner base plates can be a good source of energy dissipation

and show more ductile connection behavior during earthquake loading (Astaneh et al.,

1992). The experimental study results, presented in Chapter 3, also confirmed that thick

base plates may cause the decrease of seismic connection ductility due to early fractures

in the welds.

In order to maximize the ductility of the connection, designing a flexible base

plate is also targeted in the proposed new design method. For this purpose, it is not

necessary to use the factor 1.1 for the column. Thus, based on the steel coupon test results

presented in Table 3.1, a more realistic expression for the strength of the column is

suggested in the following:

columnycolumnyycolumnp ZFRM ___ ⋅⋅= (6-5)

120

where:

Fy_column = specified minimum yield stress of column, ksi

Zy_column = plastic section modulus of column (about weak axis), 3in.

6.2.2 Definition of Mp_bolt

Coupling with the resultant bearing force (Ru), as shown in Figure 6.1, the total

tensile bolt force (Tu) resists the design moment (Mu) in the connection. Thus, ultimate

moment capacity of the anchor bolts can be defined as:

LAFLPM totalbtbolttboltp ⋅⋅⋅=⋅⋅= )( ___ φφ (6-6)

where:

φ = resistance factor for anchor bolt, 0.75

Pt_bolt = tensile force limit of anchor bolt, kips

Ft = nominal tensile strength of anchor bolt, ksi

Ab-total = total area of anchor bolts on the tension side, 2in.

L = distance between Tu and Ru, in.

It should be noted that the actual distance between the Tu and Ru can change depending

on the relative strength ratios among the connection elements. For the case, if a = a', the

distance between the Tu and Ru can be replaced by Ls expressed in the following:

aBLs ⋅−= 2 (6-7)

121

Consequently, the ultimate moment capacity of the anchor bolts, expressed in Equation

(6-6), can be replaced by,

)2()()()'( ___ aBAFLAFM totalbtstotalbtboltp ⋅−⋅⋅⋅=⋅⋅⋅= φφ (6-8)

6.2.3 Definition of Mp_plate

Referring to Equation (2-9), the ultimate strength of the base plate is defined as:

4)( 2

____p

plateybpplatexplateybpplatep

tNFZFM

⋅⋅⋅=⋅⋅= φφ (6-9)

where:

φbp = resistance factor for flexure in base plate

Fy_plate = specified minimum yield stress of base plate, ksi

Zx_plate = plastic section modulus of base plate, 3in.

In Equation (6-9), instead of φb = 0.9, a new value is suggested for the resistance factor

for flexure in base plate. Using the φbp in the new design method is intended to provide a

more flexible base plate, to help locate the Ru at the target location. The detailed

background for the suggested φbp value will be explained in Section 6.3.4.

6.2.4 Ratio of (Mp_bolt / Mp_column)

Using the defined strengths of the column and anchor bolts, the first strength ratio

is defined as:

122

columnp

boltp

MM

1SR_

_= (6-10)

At the ultimate state of the connection, the moment capacity developed by the Tu and Ru

should be larger than or equal to the design moment developed by the column. In other

words, the strength ratio of SR1 should be larger than or equal to 1.0. This simply

provides the minimum anchor bolt size for a given column size. In the new design

method, based on experimental observations, a new value is suggested for the SR1. The

background of this decision will be explained in detail in Section 6.3.3.

6.2.5 Ratio of (Mp_plate / Mp_column)

Using the defined strengths of the column and base plate, the second strength ratio

is defined as:

columnp

platep

MM

2SR_

_= (6-11)

With the use of extremely strong anchor bolts, the strength ratio of SR2 can significantly

affect the yield pattern in the connection. Thus, in this case, SR2 can be used as an

effective parameter that can control the failure mechanism of the connection. However,

with the use of conventional anchor bolt sizes, the role of SR2 in seismic behavior of the

connection becomes insignificant due to complex interactions among the connection

elements. For this reason, the effects of SR2 on the seismic behavior of the connection are

not investigated in depth in this study. Instead, the effects of SR2 can be examined

indirectly in the study of the other two ratio effects on the seismic connection behavior.

123

6.2.6 Ratio of (Mp_bolt / Mp_plate)

Using the defined strengths of the anchor bolts and base plate, the third strength

ratio is defined as:

platep

boltp

MM

3SR_

_= (6-12)

As mentioned in the Section 6.2.1, in order to maximize the seismic ductility of the

connection, designing a flexible base plate is targeted in the proposed new design method.

For this purpose, effort should be made on decreasing the base plate thickness. However,

for given anchor bolt strength and stiffness, decreasing the base plate thickness can raise

another problem in the connection design. As shown in Figures 4.15 and 4.16, too thin a

base plates may cause high local stress concentrations in the anchor bolts on the tension

side. Thus, in order to prevent the undesirable local stress concentrations in the anchor

bolts, the thickness of the base plate should not go below a certain minimum value. SR3

can be used to express the minimum base plate thickness for given anchor bolts.

6.3 Desired Connection Behavior

Using the geometric ratios and strength ratios as defined in the previous sections,

a desired connection behavior at its ultimate state is described in this section. First, in

order to prevent undesirable grout crushing under the base plate edge due to high stress

concentrations, an appropriate location of the resultant bearing force is proposed in terms

of a and a'. Two possible methodologies are introduced to locate the resultant bearing

force at the target location and the efficiencies of these two methodologies are compared

124

each other. Finally, based on the numerical parametric study results and experimental

observations, rational values for SR1 (= Mp_bolt / Mp_column) and φbp in the new design

method are suggested in order to maximize the seismic ductility of the connection.

6.3.1 Target Location of Resultant Bearing Force

Due to unpredictable interactions among the connection elements and complex

bearing stress distribution on the grout, finding the exact location of the resultant bearing

force (Ru) has been one of the most difficult parts in the column-base plate connection

design. In order to estimate the approximated location of the Ru, several assumptions

have been used in most of design methods. The D&E method is not an exception. In

order to calculate the amount and location of the Ru, as shown in Figure 2.2, the D&E

method assumes an equivalent rectangular stress block and concrete bearing capacity per

unit length (q). However, as shown in Figures 2.13 and 4.22, the assumptions used in the

D&E method do not seem to be very realistic.

Even though the exact location of Ru can be calculated, there remains another

potential problem. If the location of Ru is too close to the base plate edge on the

compression side, an undesirable grout crushing may occur under the base plate. In order

to prevent this undesirable grout crushing, Ru should be located away from the edge. For

this reason, a'=a is suggested for the target location of Ru in the proposed new design

method. Using a'=a for the target location of Ru, a simple analytical model for the base

plate design can be formulated.

125

6.3.2 Two Methodologies

As mentioned in the previous section, a'=a is suggested for the target location of

Ru at the ultimate state of the connection. Now, the question shifts to how Ru can be

located on the target location. Fortunately, the numerical parametric study results,

presented in Chapter 4, provide two possible methodologies: The first method is to

increase the anchor bolt size for a given base plate thickness, and the second method is to

decrease the base plate thickness for given anchor bolts.

In order to examine the effectiveness of the two methodologies, the sensitivities

of the anchor bolt stiffness and base plate thickness in the variation of Ru locations are

investigated. For this purpose, the FEA results, presented in Figures 4.10 and 4.21, are re-

plotted in Figures 6.2 and 6.3, respectively, using a new variable (a'/a). As shown in

Figure 6.2, for the given column and base plate, more than 120 % increase of the anchor

bolt stiffness is needed to cause a change of about 0.3 in the (a'/a) values. On the other

hand, as shown in Figure 6.3, only 40 % variation of the base plate thicknesses is

required to make about 0.5 change in the (a'/a) values for the given column and anchor

bolts. Based on these simple comparisons, it can be concluded that the control of the base

plate thickness provides a more effective way to locate the Ru at the target location.

Moreover, decreasing the base plate thickness is clearly more practical and economical

than increasing the anchor bolt size.

The proposed new design method adopts the above two methodologies. In order

to provide appropriate anchor bolt sizes, a value will be suggested for the SR1 (= Mp_bolt /

Mp_column) in Section 6.3.3 based on experimental observations. And then, in Section 6.3.4,

effort will be concentrated on decreasing the base plate thickness, based on the numerical

parametric study results, to maximize seismic ductility of the connection.

126

0.5

1

1.5

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4


Rat

io o

f ( a

' / a

)


Figure 6.2. Effects of Anchor Bolt Stiffness on the Ru Location (1.0 tpo)

0.5

1

1.5

0.7 0.8 0.9 1 1.1 1.2 1.3


Rat

io o

f ( a

' / a

)


Figure 6.3. Effects of Base Plate Thickness on the Ru Location (1.3 Ko)

127

6.3.3 Suggested Value for SR1 (= Mp_bolt / Mp_column)

An appropriate value for SR1 (= Mp_bolt / Mp_column) is suggested based on

experimental observations. As explained in Section 2.2.4, in order to prevent anchor bolt

yielding during the experimental study, larger anchor bolts than what the D&E method

provides were used for both bolt type connections (i.e., 6-bolt type and 4-bolt type).

SR1=1.3 is applied for the 6-bolt type connection, whereas SR1=2.2 is applied for the 4-

bolt type connection. As shown in Figure 6.2, strong anchor bolts clearly helped locate

the Ru at the target location. However, if the anchor bolt size is too large, it can raise

another problem such as practicality and constructibility. Thus, based on the experimental

observations, a value of 1.5 for SR1 is suggested.

6.3.4 Suggested Value for φbp

In the previous section, SR1=1.5 was suggested for the design of the anchor bolts

for a given column size. In this section, with SR1=1.5, the base plate thickness that can

locate the Ru at the target location is determined based on numerical parametric study

results. For this reason, the numerical parametric analysis results are re-plotted in Figure

6.4 using two variables, i.e., SR1 and (a'/a). The analysis results, shown in Figures 6.4(a)

and 6.4(b), indicate that Ru can be located at the target location by selecting 0.9 tpo base

plate when SR1=1.5. This means that a more flexible base plate, than what the D&E

method provides, is needed for the desired connection behavior at its ultimate state.

In order to design flexible base plates in the proposed new design method, a

different value for the resistance factor for flexure of base plate is suggested. In the D&E

method, 1.0 tpo base plate was designed using φb=0.9. However, as already shown in the

numerical and experimental study results, the base plate designed by the D&E method

128

0.5

1

1.5

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

0.8 tpo0.9 tpo1.0 tpo1.1 tpo1.2 tpo

Rat

io o

f ( a

' / a

)

Mp_bolt / Mp_column

(a) 6-Bolt Type

0.5

1

1.5

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

0.8 tpo0.9 tpo1.0 tpo1.1 tpo1.2 tpo

Rat

io o

f ( a

' / a

)

Mp_bolt / Mp_column

(b) 4-Bolt Type

Figure 6.4. (Mp_bolt / Mp_column) versus (a' / a)

129

was rather stiff and resulted in brittle fracture in the welds. Therefore, in order to design a

more flexible base plate, φbp=1.0 in Equation (6-9) is suggested for the new design

method.

6.4 New Design Force Profile

A new design force profile, which represents more realistically the actual force

distribution in the connection, is introduced in this section and this design force profile is

compared with the assumed force profile used in the D&E method. Three main

differences are discussed in the followings:

First, different assumptions are applied for the calculation of the Ru location. In

order to calculate the approximate location of the Ru, the D&E method assumes an

equivalent rectangular stress block and concrete bearing capacity per unit length (q). On

the other hand, in the new design method, the Ru location is simply assumed as a'=a by

adopting a strong anchor bolt (SR1=1.5) / flexible base plate (φbp=1.0) concept. This

a'=a assumption provides a simple analysis model for the base plate design.

Second, a more realistic force distribution on the base plate is suggested for the

new design method. In order to calculate the Tu and Ru, as shown in Figure 6.5(a), the

D&E method simply locates the design moment Mu at the bottom of the column without

consideration of the actual loading patterns on the base plate. In the new design method,

however, a more realistic force distribution is considered for the design of the base plate

thickness, as shown in Figure 6.5(b). In Figure 6.5(b), the distributed force Wu can be

expressed by,

)2(_ fcolumnyyu tFRW ⋅⋅⋅= (6-13)

where tf is column flange thickness.

130

Tu


φVn

Vu

Mu

Y

q (Assumed)


(a) Drake and Elkin's Design Method

(b) New Design Method

Vu

φVn

Tu Ru

Wu

P.H.

h

a a ≅ aExpected fromMp_bolt/Mp_column=1.5and φbp=1.0

Ls'

Figure 6.5. Comparison of Two Design Force Profiles

131

Third, for the calculation of the maximum curvature location in the base plate,

different approaches are applied. The D&E method simply assumes two bending lines

(one on the tension side and one on the compression side) for the maximum curvature

locations in the base plate. At these two locations, the required base plate flexural

strengths are calculated for the design of the base plate thickness. On the other hand, in

the new design method, the amount and location of the required base plate flexural

strengths can be calculated theoretically. In Figure 6.5(b), h indicates the location of the

maximum base plate design moment (i.e., plastic hinge location) from the anchor bolts on

the tension side.

6.5 Basic Design Formulas

The desired connection behavior at its ultimate state is described in Section 6.3,

and a more realistic design force profile is suggested for the new design method in

Section 6.4. Based on the suggested value for the SR1 (= Mp_bolt / Mp_column) and the new

design force profile, several formulas for the design of the base plate thickness and

anchor bolt size are derived in this section. Especially, for the design of the base plate

thickness, a simplified analysis model is developed.

6.5.1 Design of Base Plate Thickness

In order to design base plate thicknesses, in the new design method, a simplified

analysis model (simple beam model) is developed based on the new design force profile.

In this analysis model, as shown in Figure 6.6, the elongation of the anchor bolts on the

tension side is not considered by assuming a simple support at "A". This is because small

amount of the support settlement does not affect moment distribution in a simple beam.

132

Figure 6.6. Simplified Analysis Model (Simple Beam Model)

A BWu

Tu Ru

bf/2 bf/2

Ls

(Ls-bf)/2 (Ls-bf)/2

Using the simplified analysis model, as shown in Figure 6.6, several formulas for

the design of the base plate thickness are derived. As was shown in Figure 2.1, the D&E

method assumes two bending lines for the maximum curvature locations in the base plate.

However, using the simplified analysis model, the amount as well as the location of the

maximum design moment can be calculated theoretically for the new design method.

In order to calculate the two unknowns, Tu and Ru, in Figure 6.6, two equilibrium

equations are formulated in the following:

∑ =+⋅

−⋅

+−→= 022

0 ufufu

uy RbWbW

TF (6-14)

∑ =⎟⎟⎠

⎞⎜⎜⎝

⎛−

⋅−⎟⎟

⎠

⎞⎜⎜⎝

⎛+

⋅+⋅−→= 0

4224220 fsfufsfu

suB

bLbWbLbWLTM (6-15)

Solving the above two equilibrium equations, the Tu and Ru can be obtained as:

133

s

fuuu L

bWRT

⋅

⋅==

4

2

(6-16)

For the design of the base plate thickness, maximum design moment in the base

plate should be provided. Thus, a free body diagram is prepared in Figure 6.7 to calculate

the maximum moment in the beam. By taking the clockwise direction for the positive

moment, the moment variations in the beam can be expressed as:

22XXWX

bLTM u

fsu ⋅⋅−⎟⎟

⎠

⎞⎜⎜⎝

⎛+

−⋅=

)(22

2fs

uu

u bLT

XTXW

−⋅+⋅+⋅−= (6-17)

Using Equation (6-17), the moments in the beam can be calculated in the range of X =

0.0 ~ bf /2. Now, the location of the maximum design moment, in the range of X = 0.0 ~

bf /2, can be obtained by,

Figure 6.7. Free Body Diagram

+MWu

(Ls-bf)/2 X

Tu

134

0=+⋅−= uu TXWdXdM (6-18)

s

f

u

u

Lb

WT

X⋅

==4

2

(6-19)

Thus, the final location of the maximum design moment from the point "A" is

s

ssff

s

ffs

LLLbb

LbbL

h⋅

⋅+⋅⋅−=

⋅+

−=

422

42)( 222

(6-20)

Furthermore, from Equations (6-17) and (6-19), the maximum design moment in the

beam can be calculated by,

)(84442

22222

max fss

fu

s

f

s

fu

s

fu bLLbW

Lb

LbW

LbW

M −⋅⋅

⋅+

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅⋅

⋅

⋅+

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅⋅−=

)44(32

222

2

ssffs

fu LLbbL

bW ⋅+⋅⋅−⋅

⋅

⋅= (6-21)

Using the maximum design moment, presented in Equation (6-21), the required

minimum thickness of the base plate can be calculated by,

⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅⋅⋅=⋅≤=

4)(

2

__maxp

plateybpplatepbpu

tNFMMM φφ (6-22)

NFM

tplateybp

p ⋅⋅⋅

≥_

max4φ

(6-23)

135

As explained in Section 6.3.4, 1.0 is used for the φbp to design flexible base plates in the

new design method.

6.5.2 Design of Anchor Bolt Size

The size of the anchor bolts can be simply calculated using the suggested value

for the SR1 (= Mp_bolt / Mp_column) in Section 6.3.3. However, in this case, the Mp_bolt

should be replaced by the (Mp_bolt)' expressed in Equation (6-8) because a'=a is adopted

for the target location of the Ru in the proposed new design method. Thus,

5.1)()'(

__

_

_

_

_

_ =⋅⋅

⋅⋅⋅===

columnycolumnyy

stotalbt

columnp

boltp

columnp

boltp

ZFRLAF

MM

MM

1SRφ

(6-24)

From Equation (6-24), the required total area of the anchor bolts can be obtained from the

following equation,

st

columnycolumnyytotalb LF

ZFRA

⋅⋅

⋅⋅⋅=

φ__

_

5.1 (6-25)

Now, the required area and diameter of each anchor bolt can be calculated as follows:

t

totalbb

AA

#_= (6-26)

πb

bA

d⋅

=4

(6-27)

where #t is number of anchor bolts resisting tensile force.

136

Due to the choice of strong anchor bolts in the new design method, it is not

necessary to check the tensile strength or the shear strength of the anchor bolts. However,

for the reasonable design procedure, these strengths will be checked based on the AISC

LRFD Specifications.

6.6 New Design of Base Plate Thickness and Anchor Bolt Size

Using the design formulas as presented in Section 6.5, the base plate thickness

and anchor bolt size are re-designed for the given column and base plate planar sizes. The

complete design procedure is summarized in Appendix B.

In Table 6.2, the newly designed element sizes are compared with those obtained

from the D&E method. From the comparisons in Table 6.2, it can be concluded that the

proposed new design method clearly results in stronger anchor bolt and thinner base plate

as compared with those given by the D&E method.

Table 6.2 Comparison of Connection Element Sizes

D&E Method New Design Method Connection

Element 6-Bolt Type 4-Bolt Type 6-Bolt Type 4-Bolt Type

Column W12x96 W12x96 W12x96 W12x96

Base Plate

Thickness (tp, in.)

2.25 2.25 2.0 2.0

Anchor Bolt Size

(db, in.)

1.107

(1.25 - SP6)

1.356

(2.0 - SP4)

1.375 1.625

CHAPTER 7

TWO LIMIT STATES OF COLUMN-BASE PLATE CONNECTION

In order to prevent undesirable connection failures and to maximize cyclic

connection ductility, two limit states of the column-base plate connection are defined in

this chapter. The first limit state of the connection is defined on the tension side based on

the local stresses around the anchor bolts. The second limit state of the connection, on the

other hand, is defined on the compression side based on the proposed effective bearing

areas on the grout.

For the desired connection behavior at its ultimate state, designing a flexible base

plate is targeted in the proposed new design method. However, as explained in Chapter 4,

thinner base plates may cause increase of local stress concentrations in the anchor bolts

and, subsequently, may result in undesirable anchor bolt failure. Thus, in order to prevent

local stress concentration in the anchor bolts on the tension side, minimum thickness of

the base plate should be provided. Two different approaches (i.e., numerical and

theoretical approaches) are introduced in this chapter to provide the minimum base plate

thickness in the connection.

The compressive strength of the grout should be strong enough to resist the

bearing stresses transferred from the base plate under large cyclic moments. Thus, the

second limit state of the connection is defined on the compression side to provide the

required minimum compressive strength of the grout. Based on the numerical analysis

results presented in Chapter 4 and the experimental observations, effective bearing areas

are proposed to calculate the nominal bearing strength of the grout. By comparing this

137

138

nominal bearing strength with the resultant bearing force (Ru), the required minimum

compressive strength of the grout is determined.

Finally, the new design procedure which includes checking the two limit states of

the connection is briefly compared with the Drake and Elkin's design procedure in the

last part of this chapter.

7.1 Limit State on the Tension Side (Numerical Approach)

Designing a flexible base plate is targeted in the proposed new design method

because this can be used as a good source of energy dissipation and improve the cyclic

ductility of the connection. However, as shown in Figures 4.15 and 4.16, a thin base plate

may cause high local stress concentrations in the anchor bolts on the tension side. Hence,

minimum thickness of the base plate should be limited to prevent anchor bolt failure due

to such high stress concentrations. For this purpose, two equations (one for the 6-bolt

type and one for the 4-bolt type), which can provide the minimum base plate thickness,

are developed in this section based on the numerical parametric analysis results presented

in Chapter 4. Using these two equations, the minimum base plate thicknesses for both

bolt type connections are calculated and then, these thicknesses are compared with the

newly designed base plate thicknesses in Chapter 6.

7.1.1 Basic Methodology

In order to explain how the minimum base plate thickness is determined

numerically for given column and anchor bolt sizes, the numerical parametric analysis

results, presented in Chapter 4, are re-plotted schematically in Figure 7.1 using two

variables, i.e., (Mp_bolt / Mp_column) and (Mp_bolt / Mp_plate). For given (Mp_bolt / Mp_column)

values, the approximate starting points of the anchor bolt local yielding, expressed as

139

M p _ b o lt / M p _ co lu m n

Mp_

bolt /

Mp_

plat

e

1 .0 1 .3 1 .7 2 .2

A n ch o r B o ltL o ca l Y ie ldS ta rtin g P o in t

0 .8 tp o

1 .2 tp o

Anchor Bolt Local Yield Limit Lines

Figure 7.1. Limit Lines for Anchor Bolt Local Yielding

0

2

4

6

8

10

12

14

1 1.2 1.4 1.6 1.8 2 2.2


( Mp_

bolt

/ Mp_

plat

e ) m

ax

Mp_bolt / Mp_column

Figure 7.2. (Mp_bolt / Mp_column) versus (Mp_bolt / Mp_plate)max

140

(Mp_bolt / Mp_plate), can be determined. These points are marked in Figure 7.1. By

connecting these points, limit lines for the anchor bolt local yielding can be provided.

For both bolt type connections, approximate limit lines for the anchor bolt local

yielding are plotted in Figure 7.2. In the practical range of (Mp_bolt / Mp_column) = 1.0 ~ 1.7,

the results plotted in Figure 7.2 provide the following two equations which can limit the

minimum base plate thicknesses for given column and anchor bolt sizes.

9.00.5max_

_

_

_ +⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⎟

⎟⎠

⎞⎜⎜⎝

⎛

columnp

boltp

platep

boltp

MM

MM

6-Bolt Type (7-1a)

4.21.4max_

_

_

_ +⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⎟

⎟⎠

⎞⎜⎜⎝

⎛

columnp

boltp

platep

boltp

MM

MM

4-Bolt Type (7-1b)

From Equations (7-1a) and (7-1b), the value of (Mp_bolt / Mp_plate)max can be simply

calculated from the (Mp_bolt / Mp_column) = 1.5, which is adopted in the proposed new

design method. With a given anchor bolt size, the value of (Mp_bolt / Mp_plate)max directly

provides the minimum thickness of the base plate.

7.1.2 Limit State Check on the Tension Side (Numerical Approach)

Using Equations (7-1a) and (7-1b), the minimum base plate thicknesses which can

prevent local yielding in the anchor bolts are calculated for both bolt type connections.

These base plate thicknesses are compared with the newly designed base plate

thicknesses in Chapter 6. This procedure is summarized in Appendix C.

141

7.2 Limit State on the Tension Side (Theoretical Approach)

In the previous section, the minimum base plate thicknesses, which can prevent

anchor bolt local yielding on the tension side, were provided based on numerical

parametric analysis results. In this section, the minimum base plate thicknesses are

determined theoretically. For this purpose, a local mechanism, which represents actual

force flow around the anchor bolt on the tension side, is proposed based on numerical and

experimental study results. Using this local mechanism, an equation is formulated to limit

the minimum base plate thicknesses for both bolt type connections. Finally, the calculated

minimum base plate thicknesses are compared with the newly designed base plate

thicknesses from Chapter 6.

7.2.1 Global and Local Mechanisms

As shown in Figure 7.3, the anchor bolts on the tension side are assumed as a

hinge condition in the proposed new design method. This assumption, based on the

global mechanism of the connection, may be satisfactory for the design of the base plate

thickness. However, due to its simplicity, the analysis model (i.e., simple beam model)

cannot properly explain the actual force flow around the anchor bolts on the tension side.

Thus, based on numerical analysis results, the actual force flow around the anchor bolts is

investigated in depth and, finally, a representative local mechanism on the tension side of

the connection is developed, as shown in Figure 7.4. Using this local mechanism, an

equation, which can determine the minimum thickness of the base plate, will be derived

in Section 7.2.3.

142

Figure 7.3. Global Mechanism

P.H.

Mp_plate

Ru

Wu

Tu

h

hP.H.

d1 d2

P1 P2 Wu / #t

Mp_plate / #t

Figure 7.4. Local Mechanism (For Each Anchor Bolt)

143

In the proposed local mechanism, as shown in Figure 7.4, the portion of only one

anchor bolt is considered. Thus, Wu and Mp_plate are divided by the number of the anchor

bolts on the tension side (i.e., #t). In addition, the actual reaction forces, developed by the

contact between nut and base plate, are simplified as two force components (i.e., P1 and

P2) located at two different distances (i.e., d1 and d2) from the center of the anchor bolt.

These four variables will be replaced by more convenient expressions in Section 7.2.2.

7.2.2 α and β

For more convenient expressions, the two reaction forces (i.e., P1 and P2), shown

in Figure 7.4, are replaced by,

PP ⋅= α1 (7-2)

PP =2 (7-3)

In Equation (7-2), α is the ratio between P1 and P2. Based on the numerical parametric

analysis results, the value of α shows a variation between 0.65 and 0.70 when strong

anchor bolts (i.e., 1.3 Ko and 1.7 Ko) and flexible base plates (i.e., 0.8 tpo and 0.9 tpo) are

used. For the proposed local mechanism, α = 0.7 is adopted because larger α value

results in a more conservative checking limit for the minimum thickness of the base plate.

The background of this decision will be explained in detail in Section 7.2.6.

Based on numerical analysis results, d1 shows a little large value as compared

with d2 for both bolt type connections (6-bolt type and 4-bolt type). However, the amount

is very small and ignorable. Thus, in the proposed local mechanism, d1 and d2 are

assumed to have the same distance β, i.e.,

144

β== 21 dd (7-4)

A simple expression is proposed for β based on numerical analysis results and

experimental observations, i.e.,

82

3 ⎟⎠⎞

⎜⎝⎛ +

+⋅=

Wdd h

b

β (7-5)

where:

db = diameter of each anchor bolt including threaded part, in.

dh = diameter of oversized bolt hole, in.

W = nut width across flats, in.

αP P

β β

W

db

dh

Figure 7.5. Detail around Anchor Bolt

145

In Equation (7-5), the value of β (i.e., the location of P1 or P2 from the center of the

anchor bolt) is highly dependent on the size of the anchor bolt. Now, for a given detail

around the anchor bolt, shown in Figure 7.5, the location of P1 or P2 can be easily

provided from Equation (7-5).

7.2.3 Minimum Base Plate Thickness

Using two new variables, α and β, the proposed local mechanism is simply re-

configured in Figure 7.6. Based on the simplified local mechanism, shown in Figure 7.6,

the moment at the plastic hinge location can be determined as follows:

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅⋅⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛−−⋅++⋅⋅=

s

f

s

f

t

u

Lb

LbW

hPhPM42

14#

)()(22

ββα

{ } 2

4

32#)()(

s

f

t

u

L

bWPhh

⋅⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛−⋅−++⋅= ββα (7-6)

The moment M, expressed in Equation (7-6), should always be smaller than or equal to

the value of (Mp_plate / #t). Thus,

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⋅

⋅⋅⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛≤

t

pplateybp

t

platep tNF

MM

#4)(

#

2

__ φ (7-7)

Now, the applicable range of the base plate thickness, which can prevent local yielding in

the anchor bolt, can be given by,

{ }⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛−⋅−++⋅⋅

⋅⋅⋅

≥ 2

4

_

2

32#)()(

#4)(

s

f

t

u

plateybp

tp L

bWPhh

NFt ββα

φ (7-8)

146

Figure 7.6. Simplified Local Mechanism

h

β β

αP P

MWu / #t

(Ls-bf)/2 bf /4Ls

With the maximum value of P (i.e., Pmax) in the above expression, the minimum thickness

of the base plate can be provided in the following:

{ }⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛−⋅−++⋅⋅

⋅⋅⋅

= 2

4

max_

min 32#)()(

#4)(

s

f

t

u

plateybp

tp L

bWPhh

NFt ββα

φ (7-9)

7.2.4 Maximum Value of P, Pmax

The maximum value of P (i.e., Pmax) can be determined from the specified yield

stress limit of the anchor bolt. In order to explain this part, the force and moment resisting

mechanisms in the anchor bolt are briefly explained in Figure 7.7. The tensile force and

moment developed by P and αP, as shown in Figure 7.7, are resisted by Teach and Meach in

the anchor bolt. Using the defined two variables, α and β, the two internal forces (i.e.,

Teach and Meach) can be expressed by,

147

Figure 7.7. Two Internal Forces in Each Anchor Bolt

αP P

β β

Meach

Teach

PTeach ⋅+= )1( α (7-10)

PM each ⋅⋅−= βα )1( (7-11)

Now, in reference to Figure 7.8, the maximum tensile stresses due to the tensile

force (Teach) and the moment (Meach) in the anchor bolt can be written by,

effbeffb

each

AP

AT

__1

)1( ⋅+==

ασ (7-12)

effb

effb

effb

effbeach

I

dP

I

dM

_

_

_

_

2

2)1(

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅⋅−

=⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

=

βασ (7-13)

148

Figure 7.8. Stress Distribution across Anchor Bolt

where:

σ1 from Tensile Bolt Force Teach

σ2 from Moment Meach

db

db_eff

Anchor Bolt

Ab_eff = effective area of each anchor bolt = 4

75.02

bd⋅⋅π , 2in.

db_eff = effective diameter of each anchor bolt = π

effbA _4 ⋅, in.

Ib_eff = effective moment of inertia of each anchor bolt = 42

4_

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅ effbd

π, 4in.

In order to prevent anchor bolt yielding at its outer surface, the summation of σ1

and σ2 should be smaller than or equal to the specified yield stress of the anchor bolt, i.e.,

149

boltyeffb

effb

effb

FPI

d

A __

_

_21

2)1(

)1(≤⋅

⎪⎪

⎭

⎪⎪

⎬

⎫

⎪⎪

⎩

⎪⎪

⎨

⎧⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅−

++

=+

βαασσ (7-14)

The above expression provides the maximum value of P (i.e., Pmax) as given in the

following:

⎪⎪

⎭

⎪⎪

⎬

⎫

⎪⎪

⎩

⎪⎪

⎨

⎧⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅−

++

=

effb

effb

effb

bolty

I

d

A

FP

_

_

_

_max

2)1(

)1(βα

α

(7-15)

Finally, using the Pmax provided by Equation (7-15), the minimum base plate thickness,

which can prevent local yielding in the anchor bolt, can be determined from Equation (7-

9).

7.2.5 Limit State Check on the Tension Side (Theoretical Approach)

Using Equation (7-9), the minimum base plate thicknesses which can prevent

local yielding in the anchor bolts are calculated for both bolt type connections. These

base plate thicknesses are compared with the newly designed base plate thicknesses in

Chapter 6. This procedure is summarized in Appendix D.

150

7.2.6 α versus (tp)min

As was mentioned in Section 7.2.2, α = 0.7 is adopted for the proposed local

mechanism. This is because larger α value results in a more conservative checking limit

for the minimum thickness of the base plate. This fact can be easily confirmed based on

the simple sensitivity analysis results shown in Table 7.1. The calculated minimum base

plate thickness, as presented in Table 7.1, is proportional to the value of α for both bolt

type connections. Hence, within the given range of α = 0.65 ~ 0.7, the largest value of α

(i.e., 0.7) results in the most conservative checking limit for the minimum thickness of

the base plate.

Table 7.1 Minimum Base Plate Thickness with Different Values of α


α=0.65 α=0.68 α=0.70 α=0.65 α=0.68 α=0.70

(tp)min

1.8037

1.8808

1.9336

1.7060

1.7823

1.8345

7.3 Limit State on the Compression Side

Two different approaches (i.e., numerical and theoretical approaches) were

introduced in the previous two sections to provide the minimum base plate thickness

which can prevent local anchor bolt yielding on the tension side. In this section, another

151

limit state of the connection is defined on the compression side: The grout strength

should be strong enough to resist the bearing stresses transferred from the base plate.

From this limit state, the required minimum compressive strength of the grout (fc') is

determined. For this purpose, effective bearing areas are proposed to provide the nominal

bearing strength of the grout. By comparing this nominal bearing strength with the

resultant bearing force (Ru), the required minimum compressive strength of the grout (fc')

can be determined.

7.3.1 Effective Bearing Area and Grout Bearing Strength

Based on numerical analysis results and experimental observations, effective

bearing areas are proposed to provide the bearing strength of the grout in the connection.

These effective bearing areas are shown in Figure 7.9. For both bolt type connections, 2a

is determined for the length of the effective bearing area. However, as shown in Figure

7.9(b), the smaller width (i.e., 0.7 N) is assigned for the effective bearing area in the 4-

bolt type connection, so as to be on the conservative side. Now, the proposed effective

bearing areas for both bolt type connections can be expressed in the followings:

NaNaA effg ⋅⋅=⋅⋅⋅= 6.1)8.0()2(_ 6-Bolt Type (7-16a)

NaNaA effg ⋅⋅=⋅⋅⋅= 4.1)7.0()2(_ 4-Bolt Type (7-16b)

Using the proposed effective bearing areas and the grout bearing stress capacity,

expressed in Equation (2-8), the nominal bearing strength of the grout in the connection

can be given by,

152

(a) 6-Bolt Type

N

2a

0.4N

0.4N

2a

N

0.35N

0.35N

(b) 4-Bolt Type

Figure 7.9. Effective Bearing Area on the Grout

153

effgccnc AAAfR _

1

2'85.0 ⋅⋅⋅=⋅ φφ (7-17)

For more conservative design of the grout strength, φc = 0.6 is used in Equation (7-17)

instead of φc = 0.7 recommended by the ACI for the strength reduction factor in case of

bearing on concrete.

7.3.2 Required Minimum Compressive Strength of the Grout

By comparing the nominal bearing strength of the grout, expressed in Equation

(7-17), with the resultant bearing force (Ru), the required minimum fc' of the grout can be

determined as follows:

ncu RR ⋅≤ φ (7-18)

effgc

uc

AAA

Rf

_1

285.0'

⋅⋅⋅

≥

φ (7-19)

From the above expression, smaller effective bearing area (Ag_eff) clearly results in larger

value of the required minimum fc' of the grout. Thus, for a given connection geometry,

the 4-bolt type connection always requires the larger value of the required minimum fc' of

the grout as compared with the 6-bolt type connection.

154

7.3.3 Limit State Check on the Compression Side

Using Equations (7-16) and (7-19), the required minimum compressive strengths

of the grout are determined for both bolt type connections. This procedure is summarized

in Appendix E.

7.3.4 Confining Band

Using the nominal bearing strength of the grout, as given by Equation (7-17), and the

resultant bearing force (Ru), the required minimum fc' of the grout was determined in

Section 7.3.3. However, due to conservatism in calculating the values of Ag_eff and φc,

impractically high fc' of the grout can be required for its minimum value. For this reason,

increasing the bearing capacity of the grout may be needed in the proposed new design

Figure 7.10 Circular Shape Confining Band

155

method. In this section, a simple idea, which can effectively increase the bearing capacity

of the grout, is introduced without any verification. Using a confining band, which is

used for increasing the bearing capacity in slender bridge piers, the bearing capacity of

the grout can be effectively increased. A proposed circular shape confining band is

presented in Figure 7.10.

7.4 Comparison of Two Design Procedures

A new design method was proposed in Chapter 6, and two limit states of the

connection are introduced in the previous three sections of this chapter. Now, the

complete design procedure, which includes checking the two limit states of the

connection, is briefly compared with the Drake and Elkin's design procedure in Figure

7.11.

156

<Design Force Profile>

<Base Plate Thickness Design>

Vu

φVn

Tu Ru

Wu

P.H.

h

a a ≅ aLs Expected from

Mp_bolt/Mp_column=1.5and φbp=1.0

Tu


φVn

Vu

Mu

Y

q (Assumed)


'

minpp

plate_ybp

maxp

plate_yb

maxplp

ssffs

fumax

comppl

tensionplmaxpl

)t(tCheck

FM

tF

)M(t

)LLbb(L

bWM

)M(

)M(oflargerthe)M(

≥

⋅⋅

≥⋅

⋅≥

⋅+⋅⋅−⋅

⋅=

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

=

φφ44

4432

222

2

<Anchor Bolt Design>

⎭⎬⎫

⎩⎨⎧

≥

=

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⋅=

⋅=

≥

⋅⋅

⋅⋅⋅===

tensionb

shearbb

t

total_bb

t

ubtensionb

v

ubshearb

b

st

column_ycolumn_yytotal_b

t

uub

v

uub

)A()A(

oflargertheA

StrengthTensileandShearCheck

#A

A

F.T

)A(

F.V

)A(oflargertheA

LF.ZFR.

A#T

T,#V

V

750

750

75051

<Grout Strength>

eff_gc

uc

eff_gccncu

AAA

.

R'f

AAA

'f.RR

⋅⋅⋅

≥

⋅⋅⋅⋅=⋅≤

1

2

1

2

850

850

φ

φφ

(a) D&E Method (b) New Design Method

Figure 7.11 Comparison of Two Design Procedures

CHAPTER 8

SUMMARY AND CONCLUSIONS

8.1 Summary

The D&E method, representative current design practice of the column-base plate

connection in the U.S., was evaluated numerically and experimentally for the case of

weak axis bending. The results of the study showed several limitations of the D&E

method and emphasized the effects of the relative strength ratios on the seismic behavior

of the connection. In order to develop a more rational and reliable design method, a new

design force transfer mechanism was proposed based on numerical and experimental

study. Using this proposed new design force profile and the concept of relative strength

ratios, a new design procedure was developed. Furthermore, two limit states of the

column-base plate connection were defined to prevent undesirable connection failures

and to maximize connection ductility under cyclic loading.

For the study, two typical exposed column-base plate connections consisting of

different stiffness and number of anchor bolts (i.e., 6-bolt type and 4-bolt type) were

designed by using the D&E method. Using the basic connection dimensions, two FEA

models (i.e., one for the 6-bolt type connection and one for the 4-bolt type connection)

were configured without consideration of weld detail. Based on numerical pre-test

analysis results, the effects of different stiffness and number of anchor bolts on the

seismic behavior of the connection were investigated in depth. The numerical analysis

results of both bolt type connections were compared with the design estimations of the

D&E method to numerically evaluate their design method.

157

158

For the experimental evaluation of the D&E method, a total of four column-base

plate connection assemblages (i.e., two specimens for each bolt type connection) were

tested under reversed cyclic loading history. Only one specimen (i.e., SP 4-1) completed

all the load cycles without significant strength degradations. In the experimental study,

the effects of anchor bolt stiffness, anchor bolt location, and weld detail on the seismic

behavior of the connection were mainly investigated. The experimental results were

compared with the pre-test FEA results as well as with the design estimates from the

D&E method. Through these comparisons, the D&E method was evaluated and several

limitations of the D&E method were examined.

In order to investigate more precisely the relative strength ratio effects on the

seismic behavior of the connection, an intensive numerical parametric study was

conducted. For this purpose, a total of twenty FEA models, consisting of four different

anchor bolt stiffnesses (i.e., 1.0 Ko, 1.3 Ko, 1.7 Ko, and 2.2 Ko) and five different base

plate thicknesses (i.e., 0.8 tpo, 0.9 tpo, 1.0 tpo, 1.1 tpo and 1.2 tpo), were configured and

analyzed for each bolt type connection. The effects of anchor bolt stiffness and base plate

thickness on the seismic behavior of the connection were examined through the

numerical parametric study and several major observations were made. Additionally, in

order to examine the effects of grout strength variation on the location of the resultant

bearing force on the compression side, three more FEA models consisting of different

grout compressive strengths were prepared and analyzed.

Based on numerical and experimental evaluation results and major findings from

the experimental study, a total of six limitations of the D&E method were identified.

Those were:

• Application of concrete beam design methodology

• Oversensitivity to q (or fc')

• Location of the bending lines

• Anchor bolt location effects

159

• Relative strength ratio effects

• Effect of stiff base plate

The limitations of the representative current design practice indicated the need for

a more rational and reliable design method. For this reason, a new design force profile,

which describes more realistically the actual force distribution in the connection, was

proposed. Based on this new design force profile and the concept of strong anchor bolts

(SR1=1.5) / flexible base plate (φbp=1.0), a new design procedure was developed. Using

this new design procedure, the two connections chosen for the study (i.e., 6-bolt type and

4-bolt type) were re-designed and the new connection element sizes were compared with

those from the D&E method.

For the desired connection behavior at the ultimate state, designing a more

flexible base plate is targeted in the proposed new design method. However, thinner base

plates may cause increase of local stress concentrations in the anchor bolts and,

subsequently, may result in undesirable anchor bolt failure. Thus, in order to prevent

local yielding in the anchor bolts on the tension side, minimum thickness of the base plate

was provided by two different approaches (i.e., numerical and theoretical approaches).

Especially, for the theoretical approach, a representative local mechanism on the tension

side of the connection was introduced. The compressive strength of the grout should be

strong enough to resist the bearing stresses under the base plate. Thus, the second limit

state of the connection was defined on the compression side to provide the required

minimum compressive strength of the grout. Based on numerical analysis results and

experimental observations, effective bearing areas were proposed for each bolt type

connection to calculate the nominal bearing strength of the grout. By comparing this

nominal bearing strength with the resultant bearing force (Ru), the required minimum

compressive strength of the grout was determined.

160

8.2 Conclusions

Based on numerical and experimental studies, the main conclusions are drawn as

follows:

• For both bolt type connections, the base plates designed by the D&E method did not

fully yield along the assumed bending lines at the limit state of the connection. This

indicates that the connections designed by the D&E method may not behave as

expected.

• Due to violation of two basic assumptions and complexity of bearing stress

distribution in the transverse direction, it may not be realistic to directly apply the

concrete beam design methodology for the design of column-base plate connections.

• The design procedure of the D&E method is highly dependent on the assumed

concrete bearing capacity per unit length (q) which has not been fully verified.

• In the D&E method, the expected location of resultant bearing force is quite sensitive

to the variation of the grout compressive strength (fc'). However, the numerical

parametric study results show the opposite.

• Due to location of the anchor bolts, the 4-bolt type connection results in a circular

shaped base plate yield lines on the tension side and high bearing stresses at the

corner of the grout on the compression side.

• Due to relative strength ratios among the connection elements, the location of

resultant bearing force can vary. This can change the amount of the required total

tensile strength of the anchor bolts (Tu) as well as the resultant bearing force (Ru) and

can significantly affect the seismic behavior of the connection.

• The dominant failure mode of the tested connection assemblages was fracture of the

welds connecting the column to the base plate.

161

• In this limited experimental study, no significant differences were observed between

SuperArc L-50 (ER70S-3) and NR-311Ni (E70TG-K2) in terms of the seismic

connection ductility.

• Fillet weld reinforcement over the groove welds on the outside of column flanges can

significantly increase the seismic connection ductility in the case of the weak axis

bending.

• In order to develop a more rational and reliable design method, a new design force

path, which describes more realistically the actual force distribution in the connection,

was proposed.

• Based on the proposed new design force profile and the concept of strong anchor

bolts (SR1=1.5) / flexible base plate (φbp=1.0), a new design procedure was

developed.

• A thin base plate may cause high local stress concentrations in the anchor bolts on the

tension side. Thus, minimum thickness of the base plate should be limited to prevent

undesirable anchor bolt failure before the connection reaches its ultimate state. In this

study, the minimum base plate thickness was provided by two different approaches

(i.e., numerical and experimental approaches).

• The compressive strength of the grout should be strong enough to resist the bearing

stresses under the base plate. Thus, the required minimum compressive strength of the

grout should be determined. In this study, the required minimum compressive

strength of the grout was determined based on the proposed effective bearing areas.

162

8.3 Suggestions for Future Study

• For use in design practice, the proposed new design method must be verified

experimentally.

• The application of newly introduced design methodology, based on the relative

strength ratios, needs to be verified for the case of the strong axis bending.

• For practical reasons, the effects of axial load on the seismic behavior of the

connection should be included in the proposed new design procedure.

• For the design of column-base plate connections in braced frames, shear force

transferring mechanism in the connection should be investigated in depth.

APPENDICES

163

164

APPENDIX A

COLUMN-BASE PLATE CONNECTION DESIGN (D&E METHOD)

Using the D&E method, base plate thicknesses and anchor bolt sizes for both bolt

type connections (i.e., 6-bolt type and 4-bolt type) are designed. The whole design

procedures are summarized in the following:

Figure A.1. Schematic Connection Geometry

GROUT20x20x2

COLUMN (ASTM A572 Grade 50) W12x96

ANCHOR BOLTASTM A354 Grade BD

BASE PLATE (ASTM A36) PL20x20xtpCONCRETE FOUNDATION

74x74x35.75

A. Given Values

1. Column

50GradeA572 ASTM

( )3.5.67.,9.0.,16.12.,55.0.,7.129612 in Zint inb int in d xW y_columnffw =====

.80 in Lcolumn =

165

2. Base Plate

A36 ASTM

ptin inPL x.20x.20

3. Grout

ksi f c 6'=

.2x.20x.20 inin in

4. Anchor Bolt

Rod BDGradeA354 ASTM

B. Basic Dimensions and Design Loads

1. Basic Dimensions

.136.52

.)16.12(8.0.)20(28.0

in in in bBn f =

⋅−=

⋅−=

.8.)2(2

.)20(.)2(2

in in in in Bf =−=−=

.136.32

.)16.12(8.0.)8(2

8.0in in in

bfx f =

⋅−=

⋅−=

2. Design Loads

.3915).5.67()58()58( 3_

* ink in sik ZksiM columnyu −=⋅=⋅=

kips in

ink LM

Vcolumn

uu 94.48

.80.3915=

−==

* For the design of the column-base plate connection, 58 ksi is assumed for the expected

yield strength of the column considering the potential overstrength and strain hardening

effects in the connection.

166

C. Equivalent Bearing Length, Y and Required Total Tensile Bolt Strength, Tu

1. Equivalent Bearing Length

./2.611.)20()6(85.06.0'85.01

2 ink in ksi AANfq cc =⋅⋅⋅⋅=⋅⋅⋅⋅= φ

qMBfBfY u⋅

−⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛ +−−⎟

⎠⎞

⎜⎝⎛ +=

222

2

.)/2.61(.)3915(2

2.20.8

2.20.8

2

ink ink in in in in −⋅

−⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛ +−−⎟

⎠⎞

⎜⎝⎛ +=

.14.18 in in −=

.4 in =

2. Required Total Tensile Bolt Strength

kipsininkYqTu 8.244.)4(.)/2.61( =⋅=⋅=

D. Base Plate Design

1. Required Strength (per Unit Width)

ksiksiAAff ccp 06.31)6(85.06.0'85.0

1

2 =⋅⋅⋅=⋅⋅⋅= φ

On the Tension Side

./.4.38.)20(

.)136.3()8.244( ininkin

inkipsN

xTM u

pl −=⋅

=⋅

=

On the Compression Side (Y<n)

./.4.382

.4.136.5.)4()06.3(2

ininkinininksiYnYfM ppl −=⎟⎠⎞

⎜⎝⎛ −⋅⋅=⎟

⎠⎞

⎜⎝⎛ −⋅⋅=

2. Nominal Strength (per Unit Width)

167

4)( 2

_p

plateypn

tFMM ⋅==

3. Required Base Plate Thickness

On the Tension Side

.18.2)36(9.0

.)/.4.38(44

_

inksi

ininkFM

tplateyb

plp =

⋅−⋅

=⋅

⋅≥

φ

On the Compression Side (Y < n)

.18.2)36(9.0

.)/.4.38(44

_

inksi

ininkFM

tplateyb

plp =

⋅−⋅

=⋅

⋅≥

φ

Use tp = 2.25 in. tpo

E. Anchor Bolt Design

1. Required Strength of Each Anchor Bolt

For Shear Force

)6(15.86

94.48#

TypeBoltForkipskipsVV

v

uub −===

)4(24.124

94.48#


v

uub −===

For Tensile Force

)6(6.8138.244

#TypeBoltForkipskipsT

Tt

uub −===

)4(4.12228.244


Tt

uub −===

2. Nominal Strength of Each Anchor Bolt

168

Mechanical properties of the ASTM A354 Grade BD rods are very similar to

ASTM A490 bolts. Thus, nominal strength of the A490 bolt is adopted herein for the

design of the anchor bolt size.

For Shear Force

ksiFv 60=

For Tensile Force

ksiA

VF

b

ubt 1139.1147 ≤⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅−=

3. Required Diameter of Each Anchor Bolt

Assume Ft=113 ksi for the calculation of the required minimum bolt sizes.

For Shear Force

)6(.480.0)60(75.0

)15.8(475.0

4 TypeBoltForinksi

kipsF

Vd

v

ubb −=

⋅⋅⎟⎠⎞

⎜⎝⎛=

⋅⋅⎟⎠⎞

⎜⎝⎛≥

ππ

)4(.589.0)60(75.0

)24.12(475.0

4 TypeBoltForinksi

kipsF

Vd

v

ubb −=

⋅⋅⎟⎠⎞

⎜⎝⎛=

⋅⋅⎟⎠⎞

⎜⎝⎛≥

ππ

For Tensile Force

)6(.107.1)113(75.0

)6.81(475.0

4 TypeBoltForinksi

kipsF

Td

t

ubb −=

⋅⋅⎟⎠⎞

⎜⎝⎛=

⋅⋅⎟⎠⎞

⎜⎝⎛≥

ππ

)4(.356.1)113(75.0

)4.122(475.0

4 TypeBoltForinksi

kipsF

Td

t

ubb −=

⋅⋅⎟⎠⎞

⎜⎝⎛=

⋅⋅⎟⎠⎞

⎜⎝⎛≥

ππ

Required Minimum Anchor Bolt Sizes:

db = 1.107 in. for 6-bolt type and 1.356 in. for 4-bolt type

Determined Anchor Bolt Sizes in This Study:

db = 1.25 in. for 6-bolt type and 2.0 in. for 4-bolt type

4. Assumed Nominal Strength (113 ksi) for Tensile Force

169

For 6-Bolt Type

222

min .9625.04

.)107.1(4

)( inindA b

b =⋅

=⋅

=ππ

ksiksiin

kipsA

VF

b

ubt 1137.131

.9625.077.79.11479.1147 2 ≤=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅−=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅−=

rightwasdcalculatetoksiFsingU bt 113=∴

For 4-Bolt Type

222

min .4441.14

.)356.1(4

)( inindA b

b =⋅

=⋅

=ππ

ksiksiin

kipsA

VF

b

ubt 1137.131

.4441.165.119.11479.1147 2 ≤=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅−=⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅−=

rightwasdcalculatetoksiFsingU bt 113=∴

170

APPENDIX B

COLUMN-BASE PLATE CONNECTION DESIGN (NEW METHOD)

Using the proposed design method, base plate thicknesses and anchor bolt sizes

for both bolt type connections (i.e., 6-bolt type and 4-bolt type) are determined. The

whole design calculations are summarized in the following:

A. Given Values

1. Column

50GradeA572 ASTM

( )3.5.67.,9.0.,16.12.,55.0.,7.129612 in Zint inb int in d xW y_columnffw =====

.80 in Lcolumn =

2. Base Plate

A36 ASTM

3. Anchor Bolts


ksiFt 113=

B. Base Plate Planar Dimension and Anchor Bolt Location

1. Base Plate Planar Dimension

171

6.0.16.12===

Bin

Bb

1GR f (Suggested in Section 6.1.1)

in. in in B 20.27.206.0

.16.12≈==

Use B x N = 20 in. x 20 in.

2. Anchor Bolt Location

1.0.20===

in a

Ba2GR

.21.0.)20( in in a =⋅=

.16.)22(.)20(2 in inin aBLs =⋅−=⋅−=

C. Design Loads

.5.3712).5.67()50(1.1 3__ ink in sik ZFRM columnycolumnyyu −=⋅⋅=⋅⋅=

in./k in ksi tFRW fcolumnyyu 99.)9.02()50(1.1)2(_ =⋅⋅⋅=⋅⋅⋅=

kipsin

inin./k LbW

Ts

fuu 73.228

.)16(4.)16.12()99(

4

22

=⋅⋅

=⋅

⋅=

kips in

ink LM

Vcolumn

uu 41.46

.80.5.3712=

−==

D. Base Plate Design

1. Location of Maximum Design Moment

s

ssff

LLLbb

h⋅

⋅+⋅⋅−=

422 22

.)16(4.)16(2.)16(.)16.12(2.)16.12( 22

ininininin

⋅⋅+⋅⋅−

=

172

.23.4 in=

2. Maximum Design Moment for Base Plate Thickness

)44(32

222

2

max ssffs

fu LLbbL

bWM ⋅+⋅⋅−⋅

⋅

⋅=

{ }222

2

.)16(4.)16(.)16.12(4.)16.12(.)16(32

.)16.12(.)/99( ininininin

inink ⋅+⋅⋅−⋅⋅⋅

=

.4.703 ink −=

3. Required Minimum Base Plate Thickness

.977.1.)20()36(0.1

.)4.703(44

_

max ininksi

inkNF

Mt

plateybpp =

⋅⋅−⋅

=⋅⋅

⋅≥

φ

Use tp = 2.0 in.

E. Anchor Bolt Design

1. Total Anchor Bolt Area

5.1)()'( _

_

_ =⋅⋅⋅

==u

stotalbt

columnp

boltp

MLAF

MM

1SRφ

2_ .107.4

.)16()113(75.0.)5.3712(5.15.1

ininksi

inkLF

MA

st

utotalb =

⋅⋅−⋅

=⋅⋅

⋅=φ

2. Area of Each Anchor Bolt

)6(.369.13

.107.4#

22

_ TypeBoltForininAA

t

totalbb −===

)4(.0535.22

.107.4#

22

_ TypeBoltForininAA

t

totalbb −===

173

3. Diameter of Each Anchor Bolt

)6(.32.1).369.1(44 2

TypeBoltForininAd b

b −=⋅

=⋅

=ππ

)4(.62.1).0535.2(44 2

TypeBoltForininAd b

b −=⋅

=⋅

=ππ

Use db = 1.375 in.for 6-bolt type and 1.625 for 4-bolt type

F. Strength Check for Anchor Bolt

1. Required Strength of Each Anchor Bolt

For Shear Force

)6(74.76

41.46#


v

uub −===

)4(60.114

41.46#


v

uub −===

For Tensile Force

)6(25.76373.228


Tt

uub −===

)4(37.114273.228


Tt

uub −===

2. Nominal Strength of Each Anchor Bolt

For Shear Force

ksiFv 60=

For Tensile Force

ksiA

VF

b

ubt 1139.1147 ≤⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅−=

174

3. Required Diameter of Each Anchor Bolt

For Shear Force

)6(.468.0)60(75.0

)74.7(475.0

4 TypeBoltForinksi

kipsF

Vd

v

ubb −=

⋅⋅⎟⎠⎞

⎜⎝⎛=

⋅⋅⎟⎠⎞

⎜⎝⎛≥

ππ

)4(.573.0)60(75.0

)60.11(475.0

4 TypeBoltForinksi

kipsF

Vd

v

ubb −=

⋅⋅⎟⎠⎞

⎜⎝⎛=

⋅⋅⎟⎠⎞

⎜⎝⎛≥

ππ

For Tensile Force

)6(.070.1)113(75.0

)25.76(475.0

4 TypeBoltForinksi

kipsF

Td

t

ubb −=

⋅⋅⎟⎠⎞

⎜⎝⎛=

⋅⋅⎟⎠⎞

⎜⎝⎛≥

ππ

)4(.311.1)113(75.0)37.114(4

75.04 TypeBoltForin

ksikips

FT

dt

ubb −=

⋅⋅⎟⎠⎞

⎜⎝⎛=

⋅⋅⎟⎠⎞

⎜⎝⎛≥

ππ

The selected anchor bolt sizes (i.e., db=1.375 in. for the 6-bolt type and db=1.625 in. for

the 4-bolt type) satisfy the above requirements.

175

APPENDIX C

MINIMUM BASE PLATE THICKNESS (NUMERICAL APPROACH)

By comparing the minimum base plate thicknesses, calculated from Equations (7-

1a) and (7-1b), with the newly designed base plate thicknesses in Chapter 6, the limit

state of the connection on the tension side is checked for both bolt type connections.

These procedures are summarized in the following:

A. Given Values

5.1_

_ =⎟⎟⎠

⎞⎜⎜⎝

⎛

columnp

boltp

MM

.16 inLs =

1. Designed Base Plate

36AASTM

.2x.20x.20 inin inPL

2. Designed Anchor Bolt


ksiFt 113= 2

_ .107.4 inA totalb =

B. Minimum Base Plate Thickness Check

176

For 6-Bolt Type

4.89.0)5.1(0.59.00.5max_

_

_

_ =+⋅=+⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⎟

⎟⎠

⎞⎜⎜⎝

⎛

columnp

boltp

platep

boltp

MM

MM

stotalbtboltp LAFM ⋅⋅⋅= )( __ φ

.)16().107.4()113(75.0 2 ininksi ⋅⋅⋅=

.09.5569 ink −=

4)(

.99.6624.8

.09.5569)(2

min_min_

pplateybpplatep

tNFinkinkM

⋅⋅⋅=−=

−= φ

.9192.1.)20()36(0.1

.)99.662(4)(4)(

_

min_min in

inksiink

NFM

tplateybp

platepp =

⋅⋅−⋅

=⋅⋅

⋅=∴

φ

.).(.0.2)( min KOintt pp =<

For 4-Bolt Type

55.84.2)5.1(1.44.21.4max_

_

_

_ =+⋅=+⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=⎟

⎟⎠

⎞⎜⎜⎝

⎛

columnp

boltp

platep

boltp

MM

MM

stotalbtboltp LAFM ⋅⋅⋅= )( __ φ

.)16().107.4()113(75.0 2 ininksi ⋅⋅⋅=

.09.5569 ink −=

4)(

.36.65155.8

.09.5569)(2

min_min_

pplateybpplatep

tNFinkinkM

⋅⋅⋅=−=

−= φ

.9023.1.)20()36(0.1

.)36.651(4)(4)(

_

min_min in

inksiink

NFM

tplateybp

platepp =

⋅⋅−⋅

=⋅⋅

⋅=∴

φ


177

APPENDIX D

MINIMUM BASE PLATE THICKNESS (THEORETICAL APPROACH)

By comparing the minimum base plate thicknesses, calculated from Equation (7-

9), with the newly designed base plate thicknesses in Chapter 6, the limit state of the

connection on the tension side is checked for both bolt type connections. These

procedures are summarized in the following:

A. Given Values

in./k Wu 99=

.16.12 inb f =

.23.4 inh =

.16 inLs =

1. Designed Base Plate

36AASTM


2. Designed Anchor Bolt


ksiF bolty 130_ =

)6(.375.1 TypeBoltForindb −=

)4(.625.1 TypeBoltForindb −=

178

B. α and β

7.0=α

For 6-Bolt Type

.375.1 indb =

)(.6875.1.165.375.1 HoleBoltOversizedininindh =+=

.1875.2 inW =

.7578.08

2.1875.2.6875.1.)375.1(3

82

3in

inininWd

d hb

=⎟⎠⎞

⎜⎝⎛ +

+⋅=

⎟⎠⎞

⎜⎝⎛ +

+⋅=β

For 4-Bolt Type

.625.1 indb =

)(.9375.1.165.625.1 HoleBoltOversizedininindh =+=

.5625.2 inW =

.8906.08

2.5625.2.9375.1.)625.1(3

82

3in

inininWd

d hb

=⎟⎠⎞

⎜⎝⎛ +

+⋅=

⎟⎠⎞

⎜⎝⎛ +

+⋅=β

C. Pmax

For 6-Bolt Type

179

222

_ .1137.14

.)375.1(75.04

75.0 inindA b

effb =⋅

⋅=⋅

⋅=ππ

.1908.1).1137.1(44 2_

_ ininAd effb

effb =⋅

=⋅

=ππ

4

22_

_ .0987.042

.1908.1

42

in

ind

I

effb

effb =⎟⎠⎞

⎜⎝⎛⋅

=⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

=ππ

ksiPPin

PA effb

5264.1.1137.1)7.01()1(

2_

1 =⋅+

=⋅+

=ασ

PI

d

effb

effb

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅−

=_

_

2

2)1( βα

σ

Pin

inin⋅

⎟⎠⎞

⎜⎝⎛⋅⋅−

= 4.0987.02

.1908.1.)7578.0()7.01(

ksiP3714.1=

boltyF _21 ≤+σσ

ksiksiP 1308978.2 ≤

kipsP 86.44≤

kipsP 86.44max =∴

For 4-Bolt Type

2

22

_ .5555.14

.)625.1(75.04

75.0 inindA b

effb =⋅

⋅=⋅

⋅=ππ

.4073.1).5555.1(44 2_

_ ininAd effb

effb =⋅

=⋅

=ππ

4

22_

_ .1925.042

.4073.1

42

in

ind

I

effb

effb =⎟⎠⎞

⎜⎝⎛⋅

=⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

=ππ

ksiPPin

PA effb

0929.1.5555.1)7.01()1(

2_

1 =⋅+

=⋅+

=ασ

180

PI

d

effb

effb

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅−

=_

_

2

2)1( βα

σ

Pin

inin⋅

⎟⎠⎞

⎜⎝⎛⋅⋅−

= 4.1925.02

.4073.1.)8906.0()7.01(

ksiP9766.0=

boltyF _21 ≤+σσ

ksiksiP 1300695.2 ≤

kipsP 82.62≤

kipsP 82.62max =∴

D. Minimum Base Plate Thickness Check

For 6-Bolt Type

{ }⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅−++⋅⋅

⋅⋅⋅

=2

4

max_

min32#

)()(#4

)(s

f

t

u

plateybp

tp

L

bWPhh

NFt ββα

φ

{ }⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅⎟⎠⎞

⎜⎝⎛−⋅−++⋅⋅

⋅⋅⋅

=2

4

)16(32)16.12(

399)86.44()7578.023.4()7578.023.4(7.0

)20()36(0.1)3(4

.9336.1 in=


For 4-Bolt Type

{ }⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅−++⋅⋅

⋅⋅⋅

=2

4

max_

min32#

)()(#4

)(s

f

t

u

plateybp

tp

L

bWPhh

NFt ββα

φ

181

{ }⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅⎟⎠⎞

⎜⎝⎛−⋅−++⋅⋅

⋅⋅⋅

=2

4

)16(32)16.12(

299)82.62()8906.023.4()8906.023.4(7.0

)20()36(0.1)2(4

.8345.1 in=


182

APPENDIX E

REQUIRED MINIMUM COMPRESSIVE STRENGTH OF GROUT

By comparing the nominal bearing strength of the grout with the resultant bearing

force (Ru), required minimum compressive strengths of the grout are determined for both

bolt type connections. This procedure is summarized in the following:

A. Given Values

kipsTR uu 73.228==

1. Designed Base Pate

36AASTM


.2 ina =

B. Effective Bearing Area on Grout

For 6-Bolt Type

2

_ .64.)208.0(.)22()8.0()2( inininNaA effg =⋅⋅⋅=⋅⋅⋅=

For 4-Bolt Type

183

2_ .56.)207.0(.)22()7.0()2( inininNaA effg =⋅⋅⋅=⋅⋅⋅=

C. Required Minimum Compressive Strength of Grout

For 6-Bolt Type

ksiin

kips

AAA

Rf

effgc

uc 01.7

).64()1(85.06.073.228

85.0' 2

_1

2

=⋅⋅⋅

=

⋅⋅⋅

≥

φ

For 4-Bolt Type

ksiin

kips

AAA

Rf

effgc

uc 01.8

).56()1(85.06.073.228

85.0' 2

_1

2

=⋅⋅⋅

=

⋅⋅⋅

≥

φ

BIBLIOGRAPHY

184

185

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