,IIIi

d!~ !I;Ii .1I! t

1

'1. '<'.~i ~1

! nl11 1'1lit 1J

I ~ III~ f

II ~<.rlI I' 'III I ,I J

:.',111 ,1 i·,1I " ,, I' i

Illl l,i

l1,1' (

II III I, 'IIII)il \1 'I iH' UJ

NSF/ENG-85003

PB85-194363

~1~~l\;ltYlill~tl,fRl~S1~l!llfRI©1XJ ~ulLlJ[Q)m~

lQ)@!lJl[)rrtrru1l@B1I'i; @~ I\;!lgii ~i1l!BIurruGilwiliil®

TIC D UC:YCLJC E1HEHAVIO~

n~ e~ ~=Fg\l~~~ur ~~ tit tn~~~

8[: lU CD LECTmfQJ~~

byA. AzizinaminiJ.H. Bradburn

andJ.B. Radziminski

A REPORT OF AN INVESTIGATION CONDUCTED

by

THE DEPARTMENT OF CIVIL ENGINEERINGUNIVERSITY OF SOUTH CAROLINA

Supported by

EARTHQUAKE HAZARD MITIGATION PROGRAMDIVISION OF CIVIL AND ENVIRONMENTAL ENGINEERING

~~ATIONAL SCIENCE FOUNDATIONGrant No. CEE - 8115014

UNIVERSITY OF SOUTH CAROLINACOLUMBIA, SOUTH CAROLINA

MARCH,1985

50272 -101

REPORT DOCUMENTATION II. IIU'OItT NO.

PAGE NSF/ENG-85003I~

•• TItle and ..btltle

Static and Cyclic Behavior of Semi-Rigid Steel Beam-ColumnConnections

7. Auttlor(a)

A. Azizinamini, J.H. Bradburn, J.B. Radziminski,. "'rformi.,. Orsaniz.tioft Na.... and Add,,"s

University of South CarolinaDepartment of Civil EngineeringColumbia, SC 29208

12. $ponaorinc Oraanlzation N......nd Add,,",

Directorate for Engineering (ENG)National Science Foundation1800 G Street, N.W.Washington, DC 20550

15. Supplementary Not..

--------------_._---- _._----------II. Abstract (Umit: 200 _cia)

.. "'port Date

March 1985I.

L "'rform'nc O,.anization Iteot. No.

10. Pnlject/Tnk/Wortl Unit No.

11. Contract(C) or OranteG) No.

(C)

(0) CEE8115014

------------~1•.

. - .. -------..::-'.---I

~Results are presented of a study undertaken to investigate the behavior ofsemi-rigid beam-to-column connections subjected to static and cyclic loadings.Tests were conducted on bolted connections comprised of top and seat beam flangeangles and double web angles to evaluate cyclic performance under constantamplitude and variable amplitude displacements and to determine moment-rotationbehavior under static loading. ~the cyclic tests, the beam-column connectionsexhibited ductile behavior, with generally stable moment-rotation hysteresisloops being established at each controlled displacement ampl'i-tude. From theconstant amplitude cyclic tests, linear log-log equations were established.Empirical relationships established by the tests were applied to a linearcumulative damage model and the results of several variable amplitUde blockcyclic tests are compared with damage summations predicted by the model.Geometric parameters which affect connection performance were quantified by thestatic tests, and are compared with analytical models to predict initialstiffness and complete non-linear moment-rotation behavior of the connections.

17. Document AnalysiS a. Descriptors

Loads (forces)Cyclic loadsStatic loadsEquations

Mathematical modelsEarthquake resistant structuresDynamic structural analysis

Stee1 structuresColumns (supports)Beams (supports)

NTIS

Ie ANSI-Z39.11)

.. Sacurity c.... (T1tls .....)

... 'IMtrucfIOft. Oft It........

21. No. of~..

OI"TIONAL. FOIt.. 272 (4-77)(Formerl)' NTI5-3SlDepart....nt of Commerce

Final Report

STATIC AND CYCLIC BEHAVIOR

OF

by

A. Azizinamini,T .H. Bradburn

andJ.B. Radziminski

A Report of an Investigation Conductedby

The Civil Engineering DepartmentUniversity of South Carolina

Supported byEarthquake Hazard Mitigation Program

Division of Civil and Environmental EngineeringNational Science Foundation

Grant No. CEE-8ll5014

ONIVERSI't'Y OF SOUTH CAROLINACOLUMBIA, SOUTH CAROLINA

March, 1q85

Any opinions, findings, conclusions or recommendations expressedin this publication are those of the author(s) and do not necessarilyreflect the views of the National Science Foundation.

!e

ABSTRACI'

The purpose of the study has been to investigate the behavior of semi-rigid

beam to column connections subjected to static and cyclic loadings. Tests were

conducted on bolted connections comprised of top and seat beam flange angles,

and double web angles, to determine moment-rotation behavior under monotonic

(static) loading, and to evaluate cyclic performance under constant amplitude

and variable amplitude displacements. Fram the static tests, geometric

parameters which affect connection performance have been quantified, and

compared with analytical models formulated to predict the initial stiffness and

complete non-linear moment-rotation behavior of the connections.

In the cyclic tests, the beam-column connections e~~ibited ductile

behavior, with generally stable moment-rotation hysteresis loops being

established at each controlled displacement amplitude. The tests culminated in

the formation and subsequent propagation of fatigue cracks at the toe of the

fillet in one or more of the beam flange angles. Fram the constant amplitude

cyclic tests, linear log-log equations have been established relating fatigue

life to connection cyclic hysteretic energy absorption, and to a generalized

flange angle rotation parameter. The empirical relationships established by the

constant amplitude fatigue tests have been applied to a linear cumulative damage

model; the results of several variable amplitude block cyclic tests are

compared with damage summations predicted by the model.

! I

J

Page

I • IN'I'OODIJ'<:'I'IO~T•••••••••••••••••••••••••••••••••••••••••••••••••• •• 1

1.11.21.3

Background, Research Objectives •••••••••••••••••••••••••••• lScope of Investigation•....•...•..•.•..••••.••.•..•.•..•.•• 2AcJ<n()\YleClgernents ••••••••••••••••••••••••••••••••••••••••••• 5

II. DES~PTION OF TEST PROGRAM..•..•..••..•.••..•.•........•.•..•.. 7

2.12.22.3

Mater ials 7Description of Test Specimens ••••••••••••••••••••••••••••••?Testing Equipment and Test Procedures ••••••••••••••••••••• lO

2.3.12.3.2

Static Tests llCyclic Tests ••••••••••••••••••••••••••••••••••••••• 13

2.3.2.12.3.2.22.3.2.3

Low-to-High Amplitude Block Tests•••••••••14High-to-Low Amplitude Block Tests •••••••••15Constant Amplitude (Fatigue) Tests••••••••16

III. EXPERIMENTAL ~lESTIGATION •••••••••••••••••••••••••••••••••••••17

3.1 Static Tests .•....•.•...•.•.•.••••.•.••.••.••.•..•.••.•..•17

3.1.13.1.23.1.3

Scope of Investigation.•••••••••••••••••••••••••••• l?Test Results •..•••••••••••••••••••••••••••••••••••• 17Discussion of Test Results ••••••••••••••••••••••••• 20

3.1..• 3.13.1.3.2

Bolted Test Specimens ••••••••••••••••••••• 20Bolted-Welded ~est Specimens •••••••••••••• 29

3.1.4 Summary of Static Test Results ••••••••••••••••••••• 31

3.2 Cyclic Tests 33

3.2.13.2.2

3.2.3

Scope of Investigation••••••••••••••••••••••••••••• 33\Tariable Amplitude Block Tests ••••••••••••••••••••• 33

3.2.2.1 Test Results ...................•.......... 343.2.2.2 Discussion of Test Results •••••••••••••••• 36

Fatigue Tests 43

3.2.3.1 Test Results •.•••••••••••••••••••••••••••• 433.2.3.2 Discussion of Test Results •••••••••••••••• 46

N. ANALYTICAL INVESTIGATION••••••••••••••••••••••••••••••••••••••• 50

4.1 Static Tests 50

iii

4.1.1 Prediction of Moment-Rotation Behavior ••••••••••••• 50

4.1.1.14.1.1.24.1.1.3

Beam Model for Initial Stiffness•••••••••• 50Empirical Mbdel ••••••••••••••••••••••••••• 54Three Dimensional Finite ElementModel - Flange Angles ••••••••••••••••••••• 55

4.1.2 Discussion••••••••••••••••••.•••••••••••••••••••••• 56

4.2 Fatigue Tests ••••••••••••••••••••••••••••••••••••••••••••• 57

4.2.1 Fatigue Life Predictions ••••••••••••••••••••••••••• 57

4.3 Variable Amplitude Cyclic Tests •••••••••••••••••••••••••••60

4.3.1 Prediction of Damage Accumulation••••••••••••••••••60

v. St.Jr.1lV1ARY~ ~~US IOOS••••••••••••••••••••••••••••••••••••••••62

5.15.2

Static Tests••..•••.••.••••••.••.••.•••.•••.•••••.••••..••62Cy'clic Tests •••••••••••••••••••••••••••••••••••••••••••••• 65

5.2.15.2.2

Variable Amplitude Tests •••••••••••••••••••••••••••65Constant Amplitude (Fatigue) Tests•••••••••••••••••68

~~CES •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••71

1\P~IX A ~Tanenclature ••••••••••••••••••••••••••••••••••••••••••••••76

APPENDIX B Three Dimensional Finite Element Analysis ofDouble Angle Pull Test Specimens •••••••••••••••••••••••••• 81

'rABIES • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •94

FIQJRE..S •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••134

iv

LIST OF TABLES

Table Page

2.1 Mechanical Properties of Test Material ••••••••••••••••••••••95

2.2 Schedule of Bolted Test Specimens (3/4-InchDiameter Bolts) 96

2.3 Schedule of Bolted Test Specimens (7/8-InchDiameter Bolts) 97

2.4 Schedule of Bolted-Weldecl Test Specimens(7/8-Inch Diameter Bolts) •••••••••••••••••••••••••••••••••••99

3.1 St.nmtary of Static 'rest Results - Bolted Specimens(3/4-Inch Diameter Bolts) ••••••••••••••••••••••••••••••••••100

3.2 Summary of Static Test Results - Bolted Specimens(7/8-Inch Diameter Bolts) ••••••••••••••••••••••••••••••••••101

3.3 Summary of Static Test Results - Bolted-WeldedSpecilnens. • • • . • • • • • . . • • • • • . • • • • • • • • . • • • • • • • • • • • • • • • • • • • • • • •102

3.4 Summary of Cyclic Test Results - Specimen l4Cl ••••••••••••• l03

3.5 SUITIllary of Cyclic Test Results - Specimen l4C2 ••••.•••••••• l05

3.6 Summary of Cyclic Test Results - Specimen l4C3 ••••••••••••• l07

3.7 St.nmtary of Cyclic Test Results - Specimen l4C4 ••••••••••••• l09

3.8 Summary of Cyclic Test Results - Specimen 14Bl••••••••••••• lll

3.9 Summary of Cyclic Test Results - Specimen 8Cl••••••••.••••• 112

3.10 St.nmtary of Cyclic Test Results - Specimen 8C2 •••••••••••••• ll3

3.11 Summary of Cyclic 'rest Results - Specimen 8C3 •••••.••••••••1l4

3.12 Sunmary of Cyclic Test Results - Specimen 8Bl•••••••••••••• 1l5

3.13 Compilation of Constant Amplitude Cyclic(Fatigue) Test Results - All Test Specimens ••••••••••••••••116

3.14 Summary of Constant Amplitude Cyclic TestResults - Wl4X38 Specimens With 1/2-Inch ThickFlange Angles 117

v

3.15 Summary of Constant Amplitude Cyclic ~est

Results - W14X38 Specimens With 3/8-Inch ~hick

Flange .Angles 119

3.16 Summary of Constant Amplitude Cyclic ~est

Results - waX21 SPeCimens with 3/8-Inch ThickFlange Angles 121

3.17 Summary of Constant Amplitude Cyclic TestResults - waX21 Specimens With 5/16-Inch ThickFlange Angles 123

4.1 Comparison of Predicted Initial ConnectionStiffness with Test Results •••.•••••••••••••••••••••••••••• 124

4.2 Prediction of Cumulative Damage using FatigueRelationship Based on Nominal Chord RotationIndex - W14X38 Beam Sections •••••••••••••••••••••••••••••••125

4.3 Prediction of Cumulative Damage using FatigueRelationship Based on Nominal Chord RotationIndex - waX21 Beam Sections .....•........•......•••........ 127

4.4 Prediction of Cumulative Damage Using FatigueRelationship Based on HystereticEnergy - W14X38 Beam Sections ••••••••••••••••••••••••••••••129

4.5 Prediction of Cumulative Damage Using FatigueRelatonship Based on HystereticEnergy - W8X21 Beam Sections•••••••••••••••••••••••••••••••132

vi

LIST OF FIGURFS

Figure Page

2.1 General Configurations of Test Specimens •..••.••••••.•••••••• 135

2.2a Details of Connection for Wl4X38 Beam - BoltedSf'eC irnens •••••••••••••••••••••••••••••••••••••••••••••••••••• 136

2.2b Details of Connection for WEX21 Beam - BoltedSpecimens .........•..•......•.•.••.•...•.•..........•......•. 137

2.3 Details of Connection for ~_4X38 Beam - Bolted-Weld.ed SpeciInens .••..............•.••.•..•..••••......•....•• 138

2.4 Schematic of r~ding System for Test Beams ..••.••.••.•.•.•... 139

2.5 Beam Supports for ~est Specimens •...•.••..•...••.••.•..••.•.• 140

2.6 Lateral Support System for Test Specimens ••..•.••••••..•••... 141

2.7 Loading Frame and Test Set-Up•..•••...•••••••••••••••••••.••• 142

2.8 Close-Up of Test Connection•••..••••••••••••••••.•••••••••••• 142

2.9 Schematic of Testing and Recording F~ipment•••••••••••••••••143

2.10 LVDT Mounting Apparatus .........•....••...........••.•....... 144

2.11 Typical Time-Displacement Histories •..••...•••.......•.....•. 145

3.1 Comparison of Moment-Rotation Curves Obtainedfrom LVDT Measurements with Curve Obtained fromActuator Displacements •...•...•.•••.••••••.•.....•.•....••••. 146

3.2 Deformation Patterns in Beam-Column ConnectionElern.ents ......................................•..•........... 147

3.3 Flange Angle from Sf'eCimen 14S2 After Test ••...•.••••.•.•...• 148

3.4 Web Angles from Specimen 14S2 After Test•••....•............. 148

3.5 Effect of Flange Angle Thickness on Static Moment­Rotation Behavior - Wl4X38 Beam Connection (BoltDiameter = 3/4") 149

3.n Effect of Flange Angle Thickness on Static Moment­Rotation Behavior - Wl4X38 Beam Connection (BoltDiameter = 7/8") 150

vii

3.7a Effect of Bolt Diameter on Static Moment-RotationBehavior - Wl4X38 Beam Connection (Flange AngleThickness = 3/8 11

) •••••••••••••••••••••••••••••••••••••••••••• 151

3.7b Effect of Bolt Diameter on Static Moment-RotationBehavior - Wl4X38 Beam Connection (Flange AngleThickness = 1/2"} •......••.•..............•••.•......••..•... 152

3.8 Effect of Web Angle Thickness on Static Moment-Rotation Behavior - Wl4X38 Beam Connection••••••••••••••••••• 153

3.9 Effect of Web Angle Length on Static Moment-RotationBehavior - Wl4X38 BeamConnection••••••••••••••••••••••••••••154

3.10a Effect of Flange Angle Thickness on Static Mornent­Rotation Behavior - waX21 Beam Connection (BoltDiameter = 3/4", Angle Gage = 2") •••••••••••••••••••••••••••• 155

3.10b Effect of Flange Angle Thickness on Static Moment­Rotation Behavior --waX21 Beam Connection (BoltDiameter = 3/4", Angle Gage = 2 1/2") ••••••••••••••••••••••••156

3.11 Effect of Flange Angle Thickness on Static Moment­Rotation Behavior - waX21 Beam Connections (BoltDiameter = 7/8", Angle Gage = 2") ••••••••••••••••••••••••••••157

3.12a Effect of Bolt Diameter on Static Moment-RotationBehavior - waX21 Beam Connection (Flange Angle Thick-ness = 5/16") 158

3.12b Effect of Bolt Diameter on Static Moment-RotationBehavior - waX21 Beam Connection (Flange Angle Thick-ness = 3/8") 159

3.13a Effect of Flange Angle Gage on Static Mament­Rotation Behavior - waX21 Beam Connection (AngleThickness = 5/]_6") ••••••.•••••••.•••••••••••••••••••••••••.•• 160

3.13b Effect of Flange Angle Gage on Static Moment­Rotation Behavior - wax21 Beam Connection (AngleThickness == 3/8") •••••••••••••.•.••••••••••••••••••••••••••••161

3.14 Effect of Flange Angle Length on Static Moment-Rotation Behavior - waX21 Beam Connection••••••••••••••••••••162

3.15 Comparison of Static Moment-Rotation Behavior ofWl4X38 and waX21 Beam Connections ••••••••••••••••••••••••••••163

3.16 Effect of Flange Angle Thickness on Static Moment­Rotation Behavior of Wl.4X38 Beam Connections -Belted-Welded S~imens 164

viii

3.17a Flange Angle from Specimen 14Cl After Cyclic Test.....•...... 165

3.17b Flange and Web Angles from Specimen 14Cl AfterCyclic Test 166

3.18 Stable Hysteresis Loops for Specimen 14Cl•...•••.••.•.••.•... 167

3.19 Stable Hysteresis Loops for Specimen 14C2 ...••..•.••....••... 168

3.20 Stable Hysteresis Loops for Specimen 14C3 •••••.••.•....••.... 169

3.21 Stable Hysteresis Loops for Specimen 14C4 .......••...•......• 170

3.22 Stable Hysteresis Loops for Specimen 14Bl .•.•...•••...•...... 171

3.23 Stable Hysteresis Loops for Specimen 8Cl ..•••.•.•••..........172

3.24 Stable Hysteresis Loops for Specimen 8C2••......•...••.....•. 173

3.25 Stable Hysteresis Loops for Specimen 8C3 .....•........•.•...•174

3.26 Stable Hysteresis Loops for Specimen 8Bl ..•.•....•.....•.•... 175

3.27 Typical Moment-Rotation Hysteresis Loop -Cyclic Tests 176

3.28 Typical Time-Actuator Displacement Cycle........•............176

3.29 Configurations of Connection During One-Half Cycle 177

3.30 Select~ Hysteresis Loops for Specimen 14F3•......•.....•.... 178

3.31 Selected Hysteresis Loops for Specimen 14F2•................. 179

3.32 Selected Hysteresis Loops for Specimen 14Fl ..•.....•......•.•180

3.33 Selected Hysteresis Loops for Specimen 14F9 ••.•.....•...•.•.. 181

3.34 Selected Hysteresis Loops for Specimen 14F4 ...•.............. 182

3.35 Selected Hysteresis Loops for Specimen 14F7 .............•.... 183

3.36 Selected Hysteresis Loops for Specimen 14F5 .••....••......... 184

3.37 Selected Hysteresis Loops for Specimen 14F6 ........•...••.... 185

3.38 . Selected Hysteresis Loops for Specimen 14F8 •..........••....• 186

3.39 Selected Hysteresis Loops for Specimen 8F8 ...••..........•..• 187

3.40 Selected Hysteresis Loops for Specimen 8F7 188

ix

3.41 Selected Hysteresis Loops for Specimen 8Fl•••••••••••••••••••189

3.42 Selected Hysteresis Loops for Specimen 8F4 •••••••••••••••••••190

3.43 Selected Hysteresis Loops for Specimen 8F3 •••••••••••••••••••191

3.44 Selected Hysteresis Loops for Specimen 8F2•••••••••••••••••••192

3.45 Fatigue Crack Pattern for Specimen 14F9 ••••••••••••••••••••••193

3.46 Constant Amplitude Cyclic Test Behavior - Wl4X38Beam Connections (Flange Angle Thickness = 3/8"} •••••••••••••195

3.47 Constant Amplitude Cyclic Test Behavior - Wl4X38Beam Connections (Flange Angle ~hickness = 1/2"} ••••••••••••• 196

3.48 Constant Amplitude Cyclic Test Behavior - WBX21Beam Connections (Flange Angle Thickness = 5/16"} •••••••••••• 197

3.49 Constant Amplitude Cyclic Test Behavior - WBX21Beam Connections (Flange Angle Thickness = 3/8"} •••••••••••••198

4.1a Deflected Configuration for Flange Angle Model •••••••••••••••199

4.1b Deflected Configuration for Web Angle Model •••••••••••••••••• 200

4.2a Terminology for Idealized Beam Model of Flange Angle ••••••••• 201

4.2b Terminology for Idealized Beam Model of Web Angle •••.•••••••• 201

4.3a Segmental Beam Model for Flange Angle ••••••••••••••••••••••••202

4.3b Segmental Beam Model for Web Angle ••••••••••••••••••••••••••• 202

4.4 Comparison of Predicted Moment-Rotation Curve withTest Results for Specimen 14S1••••••••••••••••••••••••••••••• 203

4.5 Comparison of Predicted Moment-Rotation Curve withTest Results for Specimen 14S2••••••••••••••••••••••••••••••• 204

4.6 Comparison of Predicted Moment-Rotation Curve withTest Results for Specimen 14S4 ••••••••••••••••••••••••••••••• 205

4.7 Comparison of Predicted Moment-Rotation Curve withTest Results for Specimen 14S5 •••••••••••••••••••••••••••••••206

4.8 Comparison of Predicted Moment-Rotation Curve withTest Results for Specimens 14S6 and 1489 ••••••••••••••••••••• 207

4.9 Comparison of Predicted Moment-Rotation Curve withTest Results for Specimen 14S8 ••••••••••••••••••••••••••••••• 208

x

4.10 Comparison of Predicted Moment-Rotation Curve withTest Results for 8pecimen 881 ••.••••..•...••.•...•.....•.•.•• 209

4.11 Comparison of Predicted Moment-Rotation Curve withTest Results for Specimen 882 ••••.•.•...•..•.•..•••.•••••.••• 210

4.12 Comparison of Predicted Moment-Rotation Curve withTest Results for Specimen 883 .....•....•••.•••.•••••..••••... 211

4.13 Comparison of Predicted Moment-Rotation Curve withTest Results for 8pecimen 885 •••....••..•..•••.•..•..•...•..• 212

4.14 Comparison of Predicted Moment-Rotation Curve withTest Results for 8pecimen 886 •..•.••••••.••••..••.•..•..••.•• 213

4.15 Comparison of Predicted Moment-Rotation Curve withTest Results for 8pecimen 887 •.•........•....•.••.•..••••..•. 214

4.16 Comparison of Predicted Moment-Rotation Curve withTest Results for 8pecimen 888 •.••...•.•••.••.•.•..•••.•••.••. 215

4.17 Comparison of Predicted Moment-Rotation Curve withTest Results for 8pecimen 889 •.••••••..••.•••••••••.••••..••• 216

4.18 Comparison of Predicted Moment-Rotation Curve withTest Results for 8pecimen 8810 ••....•....••.•.•.•••........•. 217

4.19 Comparison of Total Fatigue Life with Nominal FlangeAngle Chord Rotation - All Constant Amplitude CyclicTests 218

4.20 Comparison of Total Fatigue Life with Average Areaof Individual Hysteresis Loop - All Constant AmplitudeCyclic Tests 219

xi

T. INTRODUC'rION

1.1 Background, Research Objectives

The satisfactory performance of ductile moment-resisting steel frame

building structures in an earthquake environment is dependent upon the ability

of "the beam-column connections to provide the rigid frame behavior and energy

absorption capacity necessary to withstand the seismically induced lateral

forces. Considerable experimental data have been generated on the

moment-rotation behavior of beam-column connections (1-45), the results of which

have demonstrated that the connections can contribute adequate strength and

ductility to ensure the required performance of the structural system.

Recently, studies have been reported (46-58) which consider the effect of

connection flexibility on the performance of building frames. The analytical

predictions of frame behavior are typically based on assumed non-linear

mathematical models of the beam-column connections. However, there is a

continuing need for additional experimental data to substantiate the

appropriateness of the mathematical models used to describe the behavior of

semi-rigid connections, includinq those utilizing both welded and bolted

connection elements. Such information is needed for modeling the

load-deformation behavior of complete building systems, and for possible

application to the retrofitting of existing structures as a means of improving

their resistance to lateral forces.

From cyclic tests of connections and subassemblages, it has been found that

the performance of steel frame building structures, under seismically induced

load histories, may be limited by low cycle fatigue of the connection elements.

Consequently, recent attention has been directed to the applicability of

cumulative damage models for predicting the cyclic response and eventual failure

of structural connections and frames subjected to earthquake type loadings (5,

59-62). Additional information, both experimental and analytical, is required

to determine the efficacy of such models in assessing the total time-history

performance of a complete building system.

The objective of the research program herein has been to experimentally

determine the moment-rotation performance of semi-rigid beam-column connections

under static (monotonic) and cyclic loadings. SPecifically, the effect varying

the stiffness of the various connection elements on the static response of the

connections, and on their hysteretic response under cyclic controlled displace­

ment loading, has been studied. Fran these tests, t.l1e significant material and

geometric parameters affecting the connection behavior are identified, and used

to formulate models of the non-linear connection moment-rotation response. The

constant amplitude and variable amplitude cyclic tests have served to identify

the mechanisms of distress under severe excursions of connection rotation, to

quantify hyseretic energy absorption capacity under cyclic loading, and to

establish bench-mark fatigue life relationships. A linear damage accumulation

model has been examined for for prediction of connection fatigue response under

variable amplitude loading.

1. 2 Scope of Investigation

In an initial investigation, NSF Grant No. 79-23520 (63), tests were

conducted of bolted beam to column connections comprised of top and seat beam

flange angles, and double web angles,to determine moment-rotation behavior under

monotonic (static) loading, and to measure energy absorption caPability under

cyclic loading. ASTM A36 steel was used for the members and connection

2

elements; the fasteners were 3/4-inch diameter, ASTM A325 high-strength bolts.

A pair of duplicate sPeCimens was tested simultaneously by framing simply

supported beam sections into a centrally-loaded stub column.

Two beam sizes, Wl4X38 and waX21, were used in the test program. For the

top and seat (flange) angles, the thickness, length, and gage (in the legs

attached to the column flange) were varied, together with beam depth, to effect

connections of varying stiffness. Var iations in the thickness and length of the

web angles were investigated also. The results of the static tests were used to

quantify the effect of the test variables on the non-linear moment- rotation

behavior 'of the connections, and to establish semi-empirical models of

connection response. The data were ccmpared, also, to predictions of

moment-rotation behavior using a two dimensional finite element model of the

connection.

The cyclic tests in the initial investigation consisted of subjecting ~he

connections to several stages of full reversal, controlled amplitude

displacements of progressively increasing magnitude. The connections exhibited

ductile behavior, with generally stable moment-rotation hystersis loops being

established at each displacement amplitude to the time that testing was

discontinued. The tests culminated in the formation and subsequent propagation

of fatigue cracks at the toe of the fillet in one or more of the beam flange

angles. The cvclic tests demonstrated that the effectiveness, under seismically

induced loading, of connections of the type studied may be limited by low-cycle

fatigue of the connection elements.

The scope of the current investigation (Grant No. CEE-8115014) extended

the initial study by including the static testing of additional bolted

connections utilizing a wider range of connection element stiffnesses. Because

major slip occurred in two of the earlier tests in which 3/4-inch diameter bolts

3

were used, 7/8-inch diameter, A325 bolts were used in all of the test specimens

in the present study. Slip was observed in one of the tests in which the

7/8-inch bolts were used.

The empirical equation developed in the initial study was found to offer

reasonable predictions of the static moment-rotation response of the connections

in the present series of tests; i.e., those using the 7/8-inch diameter bolts.

In addition, a three-dimensional finite element model has been generated to

represent one flange angle of the test connections; the load-displacement

relationship predicted by the model has been compared to the results of a double

angle pull test conducted as an extension of the test program.

As a consequence of the fatigue failures exhibited by the connection

elements in the initial test program, a series of constant amplitude cyclic

tests was conducted in the present study to establish bench-mark strain based

fatique life curves for bolted connections of varying stiffness. Fatigue lives

on the order of 101 to 103 cycles to failure were considered in this phase

4

of the study. Besides the constant amplitude tests, two specimens were

subjected to several blocks of full reversal, controlled displacements of

progressively decreasing magnitude for comparison with the low-to-high amplitude

block loadings examined in the initial study.

From the constant amplitude cyclic tests,a linear log-log relationship

between fatigue life and a generalized flange angle rotation parameter has been

established for the low cycle, strain based fatigue tests considered in the

investigation. A similar relationship, between fatigue life and hysteretic

energy absorbed per test cycle, has also been developed. The empirical

relationships established by the constant amplitude fatigue tests have been

applied to a linear fatigue damage accumulation model to predict the behavior of

the specimens subjected to the variable amplitude cyclic loadings. In addition,

the total hysteretic energy accumulated at the connections under both constant

amplitude and variable amplitude cyclic loading has been examined.

As a final phase of the present investigation, a pilot study was conducted

using connections canprised of top and seat angles welded to the beam flanges

and bolted to the supporting column, together with web angles also welded to the

beam and bolted to the column. The results of two static tests, using

connections framed to Wl4X38 beam sections, are reported.

1.3 Acknowledgements

The tests reported in this study are from an investigation conducted in the

Department of Civil Engineering at the University of South Carolina, Columbia,

South Carolina. The experimental data and analytical studies represent a

canpilation of the results obtained during both an initial investigation (Grant

No. 79-23520) and the present study (Grant No. CEE-8ll50l4) under support by

the National Science Foundation. Any opinions, findings, and conclusions or

recamnendations expressed in this document are those of the authors and do not

necessarily reflect the views of the National Science Foundation.

The investigations were conducted under the sUPervision of Dr. J.B.

Radziminski, professor, and Dr. J .H. Bradburn, Associate Professor, of the

Department of Civil Engineering. The latest test program and associated

research studies were conclucted by A. Azizinamini, with assistance from F.

Farley, J. Rabley, and W. Harper, Research Assistants in Civil Engineering.

Guidance concerning the scope of the investigation, provided by Dr. J .B.

Scalzi of the National Science Foundation, is gratefully acknowledged.

The authors wish to express their appreciation to H. Mullinax, G. Dowdy,

and B. Ward, laboratory technicians in the College of Engineering, for the

5

6

fabrication of the beam supports used in the testing program, for help in the

machining of the test numbers, and for the fabrication of instrumentation

support devices used in data acquisition. SPeCial thanks are extended to Ms.

K. Runyon for the careful typing of this final report.

7

II. DESCRIPI'ION OF TEST PROGRAM

2.1 Materials

'T'he mater ial for all of the test specimens, including beam sections, stub

columns, and framing angles, was specified to be AS'IM A36 steel, supplied by two

local fabricators. The mechanical properties obtained frcm selected coupon

specimens for material supplied by each of the fabricators is given in Table

2.1. For the all-bolted specimens, the beam-column connections were made using

either 3/4-inch diameter or 7/A-inch diameter ASTM A325 heavy hex high-strength

bolts, and A325 hardened washers. For the combined bolted-welded test

specimens, welding of the top and seat angles, and of the web angles, to the

beam sections was accanplished using AWS E70 electrodes. No tests of the

mechanical properties of the bolts or the filler metal were conducted.

2.2 Description of Test Specimens

The specimens consisted of a pair of beam sections attached to a centrally

positioned stub column using the particular flange and web angles to be

investigated in a given test. The connections contained top and seat angles

bolted to the flanges of the sUPJX)rting stub column, together with double web

angles bolted to the column flanges. For the all-bolted specimens, the flange

and web angles were connected to the beam sections using the same diameter bolts

as those used in the connection to the column flange. In the combined

bolted-welded specimens, t..he top and seat angles were attached to the beam

flanges by continuous longitudinal and transverse fillet welds (with returns on

the end of the beam); the double web angles were similarly welded to the web of

8

the beam.

TwO beam sizes, waX21 and Wl4X38, have been used throughout the testing

program. Each of these sections has a flange width to thickness ratio of 6.6,

typical of that encountered in building applications. For the Wl4X38 sections,

the overall test beam length was 20 feet, and for the waX21 sections, 12 feet,

so that the span-to-depth ratios were slightly less than 20 in each case. The

stub colt.nnn for the waX21 beams was a Wl2X58 section, and a 1"1l2X96 colLUnn

section was used with the Wl4X38 beams. Heavy colLUnn sections were selected to

eliminate colt.nnn panel zone distress as a contributing behavior factor, thereby

confining the moment-rotation interaction to the connection elements. It is

noted here that the same stub colt.nnn sections were used repeatedly throughout

the testing program without exhibiting any evidence of inelastic behavior. The

general configurations of typical test members using the 14-inch and 8-inch deep

beams are shown in Figures 2.la, and 2.lb, respectively.

The web angles were centered on the beam web and proportioned initially for

shears equal to 1-1/2 times the end reactions the member would experience at its

A.I.S.C. allowable uniform load as a simply supported beam with a span equal to

the length of the test beam (64). The lightest web angles used would thus be

adequate, also, for shear forces corresponding to the increased loads that would

be permitted if end connections had been used that were capable of developing

one-half the beam allowable moment at working load.

The top and bottom flange angles were of the same size in a particular test

specimen. Because the connections were to experience moment reversals, it was

felt that a symmetric arrangement would reduce the parameters influencing the

moment-rotation behavior, yet still represent a realistic design configuration.

For each of the two beam sizes, three different thicknesses of the top and

bottom angles were tested. Initial angle thicknesses were selected

9

approximmately equal to the flange thickness of the beam being supported. It

was reasoned that these sizes, together with the use of standard gages in the

legs of the angles attached to the column flange, would provide the bending

flexibility required of semi-rigid connection response. At the same time, the

connections would be eXPeCted to exhibit sufficient moment capacity (and energy

absorption capability) to contribute significantly to the resistance of a

structural frame subject to earthquake induced loads.

The details of the connection angles used to frame the W14X38 and waX21

beams to the stub columns are shown in Figures 2.2a and 2.2b, respectively

(all-bolted SPecimens), and in Figure 2.3 (ccmbined bolted-welded specimens).

For the W14X38 beam tests, 3/8-inch, 1/2-inch, and 5/8-inch thick top and seat

angles were used; these angles were of 5/16-inch, 3/8-inch, and 1/2-inch

thickness for the waX21 beam tests. For the 14-inch deep beams, the bolt

diameter (3/4-inch and 7/8-inch), and the length and thickness of the web angles

were varied for the static moment-rotation parameter studies. In addition, the

length of the flange angle, and the gage and bolt spacing on the leg attached to

the column flange were varied in one static test series of waX21 beam specimens.

Dimensions of the various connection elements are presented in the test specimen

schedules, Tables 2.2 and 2.3 (all-bolted specimens using 3/4-inch and 7/8-inch

diameter bolts, respectively), and ':t'able 2.4 (ccmbined bolted-welded test

specimens) •

Bolting of the connection elements was accomplished with an air wrench

using the standard turn-of-the-nut method. (64) A325 flat hardened washers were

used under the turned elements in all of the connections. The holes were all of

standard size, 13/16-inch diameter for the 3/4-inch diameter bolts, and

15/16-inch diameter for the 7/8-inch diameter bolts.

Welding was accomplished Ilsing the shielded metal-arc process by a local

10

steel fabricator in accordance with standard welding practice. All of the

connection angles were welded to the beam sections in the fabricator's shop;

the combined beam-connection assemblies were then delivered to the testing

laboratory for bolting to the stub coltnnn by project personneL

2.3 Testing Equipment and Test Procedures

A pair of duplicate SPecimens was tested simultaneously by framing the

beams into a centrally loaded stub coltnnn using the arrangement shown

schematically in Figure 2.4. The beam sections are supported at the ends by

roller-type seats located at the beam mid-depth, and designed to allow

longitudinal movement so that no direct axial forces would be introduced as the

SPecimen deflects. The height of the beam supports is adjustable to accornodate

the mounting of beams of different depth in the structural loading frame;

photographs of the supports are shown in Figure 2.5.

Adjustable roller-type guides were used to ensure vertical movement of the

stub column and, consequently, to prevent torsional displacements at the

beam-column interface. The guides are canprised of rollers mounted on channels

attached to the top and bottom of the stub coltnnn; the rollers ride against the

flanges of the actuator supporting columns of the main structural loading frame.

Photographs of the roller guides are shown in Figure 2.6. The rollers were

oiled and checked periodically to permit freedom of movement in the vertical

direction along the loading frame support coltnnns. Photographs of the complete

test set-up, including loading frame, beam supports, and roller guides are shown

in Figures 2.7 and 2.8.

A 55 kip, servo-controlled, hydraulically actuated ram was used to apply

load to the test members through the stub coltnnn, Figure 2.4. Local monitoring

11

of the actuator displacement was accomplished through an X-Y plotter. In

addition, the output data from the various measuring devices, described later,

were transferred directly to the College of Engineering VAX 11/780 computer

system for subsequent retrieval and graphic display; the basic elements of the

recording system are illustrated schematically in Figure 2.9.

using the test arrangement and loading system illustrated in Figure 2.4,

the connections were subjected to combined shear and bending memento For both

the static and cyclic tests the controlled input variable was the rate and

magnitude of actuator movement and, correspondingly, the displacement of the

stub column. Displacement control was imposed to avoid the possibility of

instantaneous collapse of the test member should complete separation occur in

any of the connection elements during testing.

2.3.1 Static Tests

For each of the all-bolted static test specimens, the beam sections were

first mounted in the end supports and then bolted to the stub collAI'll!l, which had

been blocked in the loading frame to effect a centered, level member. The

erection sequence proceeded as follows. For each beam size the actuator load

cell was initialized to a load equal in magnitude and opposite in sense to the

total weight of the specimen (beams plus stub column) less one-half the weight

of the beams. Having thus established the initial load cell reading, the

actuator was next attached to the top of the stub column. The bolts were then

loosely inserted in all of the connection elements. Power was supplied to the

actuator to maintain the specimen in a level position as the supporting blocks

were removed from beneath the stub column. The bolts in the legs of the angles

attached to the column flanges were then tightened, followed by tightening of

12

the remaining bolts in the angle-to-beam connections. At this point the load on

the specimen caused by fit-up (recorded by the load cell) was removed by

adjusting the position of the stub colunm. Thus, the average static manent at

the beam-colunm interface, resulting fran the erection operations, was

essentially null. This established the point of origin for the subsequent

load-displacement (and manent-rotation) plots; the static manents thereafter

calculated fran the load-cell output thus excluded the weight of the specimen

fran the measured manent-rotation response of the connection. (The same

installation and load initialization procedure was used for the bolted-welded

test specimens except, of course, that erection consisted only of bolting the

connection angles to the stub colunm, the angles having been previously shop

welded to the beam sections) •

It should be noted that, as a result of member configuration tolerances,

slight misalignment of the connection elements, and welding distortions, local

residual stresses were introduced during the erection operations. All sPeCimens

were prepared by area fabricators using standard shop practice, so that the

fit-up stresses would be of the order encountered during normal field erection.

For a select number of test sPeCimens, strain gages were mounted on both

faces of the leg of the top flange angle attached to the colunm to determine

local strains introduced during the bolting operation, and to monitor the

surface conditions as testing progressed. In addition, for all tests, LVID's

were mounted to each flange of the beam sections on eithe:r side of the stub

colunm, and seated against the flanges of the colunm. The device used to seat

the LVDI' probe and to accc::moClate the rotations develoPed during a test is

illustrated in Figure 2.10. 'T'he data fran a pair of LVDTs mounted on one beam

section were used to determine the angle of rotation of the connection as

testing progressed. The LVDT data were canpared, also, to rotations calculated

13

fran the actuator displacement readings.

Besides the direct strain measurements and L\nDT displacements, light gage

aluminum channel-shaped devices with attached strain gages were used to detect

slip between the top and botton flange angles and the elements to which they

were connected. These devices (slip monitors) were intended only to record the

presence of major slip, not the magnitude thereof.

After a SPecimen had been mounted in the loading frame and the

displacement-measuring devices attached, the test was undertaken using an

actuator displacement rate of 1.0 in./min. for the 14-inch deep beams, and 0.75

in./min. for the 8-inch beams (except for sPecimen 887, for which a rate of 1.0

in./min. was used). The upward (downward for SPecimen 884) movement of the

actuator (and stub column) was continuous, with load, displacement, L"\IDr, strain

gage, and slip indicator output each being sampled t\'X) times per second. In

addition, the actuator load and displacement were recorded locally on an X-Y

plotter to allow continuous visual monitoring of the system behavior. A test

was concluded when the actuator displacement reached 4 inches for the 20-foot

long Wl4X38 beam SPecimens, and 3 inches for the 12-foot long waX21 beams.

2.3.2 Cyclic Tests

The preparation and installation of the sPecimens in the cyclic tests was

the same as that used for the static loading, descr ibed above. Dur ing mounting

of a test member in the loading frame, the initial load setting was established

to exclude the contribution of the weight of the sPecimen to the static manent

at the connection in the manner described above for the static tests. In

addition, the same arrangement of L"\IDrs and slip monitors as in the static tests

was employed for measuring joint rotations and determining slip in the flange

14

angles, respectively.

2.3.2.1 Low-t~HighAmplitude Block Tests

For the low-to-high amplitude cyclic tests, Figure ?lla, an initial range

of actuator displacement of 0.4 inches (0.2-inch amplitude) was selected,

approximately 10 percent of the total displacement used in the static tests of

the 14-inch beams. The initial displacement amplitude was intended to produce a

hysteresis loop representing minimal non-linear response (estimated from the

corresponding static moment-rotation curves). In all tests, the full range of

controlled displacement was set to provide equal displacement amplitudes about

the initial horizontal beam position. Full reversal of displacement was chosen

to provide the symmetry required for comparison of test data from beams of

different depths, and to awroximate the reversals that might be exhibited under

extreme conditions during seismic loading.

For the specimens tested in the initial study (using 3/4-inch diameter

bolts), the first displacement cycle in each test was applied sinusoidally using

a frequency of 0.10 Hz. This relatively slow rate of actuator move..ment was

selected to allow visual monitoring of the load- displacement relationship, to

ensure that the strain and displacement measuring devices were recording

properly, and to check the alignment of the lateral support devices. Additional

individual cycles were then applied using a frequency of 0.10 Hz or 0.25 Hz

until a stable hysteresis loop was established~ usually this occurred within a

few cycles after the initial cycle had been run. To complete the sequence, ten

additional cycles were applied continuously at a frequency of 0.25 Hz, so that a

total of 12 to 15 complete cycles were normally imposed at one displacement

amplitude. The displacement range was then increased to 0.8 inches and the

15

above procedure repeated~ Le., several individual cycles followed by a

continuous run of 10 cycles at 0•25 Hz. Each sequence was followed by an

increase of 0.4 inches in the displacement range and the process repeated,

resulting in displacement-time histories typified by the block arrangement

illustrated in Figure 2.lla.

For the specimens tested in the current investigation (using 7/8-inch

diameter bolts), a constant test frequency of 0.25 Hz was used at each

displacement amplitude. Otherwise, testing followed the same procedure as that

described in the previous paragraph for specimens tested in the initial study.

2.3.2.2 High-to-Low Amplitude Block ~ests

The high-to-low amplitude cyclic tests, Figure 2.Hc, were intended to

follow basically the reverse time-displacement histories as those imposed in the

low-to-high amplitude tests, for specimens of duplicate geometry. However, for

one of the specimens tested under these conditions, BBl, fatigue cracking was

not as extensive, at the conclusion of the intended block history, as that

exhibited by the corresponding low-to-high test specimen, 8e3. Thus, to

complete the testing of specimen 8Bl, the displacement amplitude was again

increased to the same magnitude, 1.2 inches, as that of the first block of

cycles in the sequence. The fatigue crack then grew considerably larger during

the first cycle of the higher amplitude, and the test was stopped.

7he other specimen tested under the high-to-low amplitude history, l4Bl,

exhibited appreciable fatigue cracking during the first block of imposed cycles~

the cracks continued to grow, albeit at a reduced rate, during the remainder of

the test. Testing of specimen l4Bl was concluded after five blocks of loading

at decreasing displacement amplitudes (compared to nine plus blocks sustained by

16

its campanion specimen, 14C3), due to the presence of extensive cracking in two

of the beam flange angles.

2.3.2.3 Constant Amplitude (Fatigue) Tests

The constant displacement amplitude cyclic (fatigue) tests, Figure 2.llb,

were conducted at a frequency of 0.25 Hz (with some exceptions, as noted in the

tables in which the fatigue test data are reported). For several of the

sPeCimens, a number of "half" cycles (displacement excursions from the null

position to the rnaximium displacement amplitude and return) were applied before

proceeding with the full reversal test cycles. This was done to apply several

initial cycles of tensile strain to the top flange angles in an effort to

promote the initiation of fatigue cracking first in those angles, so that the

subsequent crack propagation could be easily monitored with the sPeCimens

mounted in the testing machine. It should be noted that fatigue cracking did

initiate first in the top flange angles to which the half cycles had been

applied before continuing with the full reversal cycles.

All of the cyclic tests were terminated when observed fatigue cracking had

progressed partially across the face(s) of one or more of the flange angles at

the toe of the fillet (see following discussions of test results). No test was

extended to the point of complete fracture of a connection element.

17

III. EXPERIMENTAL INVESTIGATION

3.1. Static Tests

3.1.1 Scope of Investigation

Eighteen all-bolted specimens were tested in the static test

investigations, eleven in the initial study (63), and seven in the current

program. In acldition, two combined bolted-welded members were tested in the

latter investigation. 'T'he purpose of this phase of the study was twofold: (1)

to quantify the static moment-rotation behavior of the semi-rigid beam-column

connections; and (2) to identify and measure the effect of various geanetric

parameters on the connection behavior. The static tests were intended, also, to

serve as a frame of reference against which the cyclic hysteresis behavior of

the connections could be compared.

The geometric variables that were altered in the parametric study included:

the depth of the beam sections (W8X21 and 1:"1l4X38 sections), the thickness and

length of the top and bottom beam flange angles, the gage and spacing of belts

in the leg of the flange angles connected to the column flange, t-he bolt

diameter (3/4-inch and 7/8-inch), and the thickness and length of the web

angles.

3.1.2 Test Results

Summaries of the test results for the static test investigations are

presented in Table 3.1 (boltecl sPeCimens, 3/4-inch diameter bolts), Table 3.2

(bolted specimens, 7/8-inch diameter bolts), and Table 3.3 (bolted-welded

specimens) •

18

Details of the corresponding specimen geometries are reported in

Tables 2.2, 2.3, and 2.4, respectively.

Tables 3.1-3.3 include the initial stiffness of the connections (initial

slope of the moment-rotation curve). The slope was measured tangent to the

moment-rotation (M-<p) curve at the origin as the derivative of a second degree

polynomial fit through the first several data points. The tables also list:

(1) the slope and intercept moment of a secant line from the origin and

intersecting the M-<p curve at a rotation of 4.0XlO-3 radians; and (2) the

moment, and the slope tangent to the M-¢ curve at 24X10-3 radians, a rotation

achieved in all of the static tests. Although the latter slope offers a measure

of the degradation of connection stiffness as the applied moment increases, it

should not be interpreted as a constant or final slope for a specific

connection. In some tests, the connections continue to "soften" as the moment

increased, never actually reaching a constant M-<p slope at the conclusion of

loading. The tangent slope at the rotation of 24XlO-3 radians does, however,

allow comparisons to be made among the various connections at a canmon point, as

well as quantifying the degree of connection softening in a particular test.

Similarly, the secant slope offers an additional indication of the early

stiffness of the connection. In same respects the secant slope may be more

representative than the initial tangent slope, because the latter is highly

sensitive to any irregularities in the first few data points fram which it was

calculated.

The maments reported in Tables 3.1-3.3 (and the figures to follow) were

calculated directly from the actuator load cell readings. To obtain the

corresponding <p values, initially the displacements measured by the LVDTs

mounted to each flange of the beam were converted to relative rotations between

the flange of the stub column and the end of the beam. The rotations were also

19

independently calculated using the actuator displacement and the beam span by

considering rigid body movement of each beam segment and correcting for elastic

curvature from bending of the beam. Because of the high stiffness of the stub

column, and the transfer of load in fr iction between the connecting elements

(except for the slip encountered in three tests) the beam did rotate essentially

as a rigid body with respect to the column flange, which was maintained in a

vertical position by the lateral support system.

A typical comparison of the M-~ relationship obtained from LVDT data with

the results obtained from the displacement measurements is shown in Figure 3.1.

The curves labeled East and West represent the data from individual pairs of

LVDI's mounted to the flanges of each of the two beam segments framing into the

central stub column. It can be seen from Figure 3.1 that the LVDI' data obtained

fran each of the two connections in the test member were very close, and

consistent with the M-~ curve calculated using the actuator displacements.

Consequently, the data reported in Tables 3.1-3.3, and plotted in the figures to

follow, use rotations calculated fran actuator displacements~ the results may

thus be considered to represent an "average" of the behavior exhibited by the

connections attached to each face of the stub column.

For each of the static tests, the beams were observed to rotate, with

respect to the stub column, by pivoting about a point near the surface of the

beam compression flange, as illustrated in Figures 3.2a (bolted specimens) and

3.2b (bolted-welded specimens). The heel of the tension flange angle was

observed to "curl around" the end of the beam flange in the all-bolted specimens

(Figure 3.2a) ~ however, this deformation pattern was less pronounced in the

bolted-welded specimens (Figure 3.2b), as the weld return served to restrain the

movement of the heel of the angle. It should be noted that the beam set-back

was 1/2-inch for all of the test specimens (Figures 2.2,2.3).

20

Photographs of typical deformation patterns observed in the connection

flange and web angles are shown in Figures 3.3 and 3.4, respectively. With the

exception of specimens 1482, 882, and 8810, post-test inspection revealed no

apparent inelastic deformation in either the flanges or the web of the beams.

8imilarly, no distress was evident in the stub columns, because, as discussed

previously, intentionally heavy sections were selected to confine the study to

the response of the beams and their connection elements.

In the testing of specimen 1482, major slip first occurred when

approximately one-half the final actuator displacement had been reached. After

the specimen had been dismantled, the holes in both legs of the tension flange

angle and in the beam flange were elongated, as were the holes in the beam web.

The plastically deformed steel formed a protruding lip on the bearing surface of

each of the elements exhibiting the elongated holes. Post-test inspection of

specimens 882 and 8810 indicated patterns of distress in the connection elements

similar to those observed in specimen 1482.

At the conclusion of each of the static tests, there was no rupture nor

were there any cracks observed by visual inspection in any of the fasteners or

connection elements.

3.1.3 Discussion of Static Test Results

3.1.3.1 Bolted Test Specimens

The moment-rotation curves for the tests reported in Tables 3.1 and 3.2 are

plotted in Figures 3.5 through 3.15. The figures provide canparisons of the

initial stiffness and non-linear connection behavior for test members in which

individual geometric parameters were altered. General observations with respect

21

to these test results are discussed in the following paragraphs.

From practical design considerations, one of the most apparent means of

increasing the initial stiffness and total moment transfer capability in a

connection of the tyPe studied is to increase the thickness of the angles

attached to the top and bottom flanges of the supported beam. This flange

dimension was, therefore, the principal variable investigated in both the static

and cyclic test series.

Figure 3.5 presents the moment-rotation curves for two Wl4X38 beam

SPeCimens fastened with 3/4-inch diameter bolts, one (14S1) with flange angles

of 3/8-inch thickness, and the other (14S2) with 1/2-inch thick flange angles.

Both the initial stiffness and the moment developed at comparable rotations are

greater for SPeCimen 1482. For example, at a rotation of 24XlO-3 radians,

sPeCimen 14S2 developed a connection moment of about 950 k-in., or almost 1-1/2

times the 668 k-in. manent of sPeCimen 1481. The rotation of 24XIO-3 radians

has been used for purposes of comparison among the test members in Tables

3.1-3.3 and in this discussion because it was a number easily reached in all of

the static tests. The rotation corresponds to a deflection of approximately

2-3/4 inches for the 14-inch beam tests, or approximately four times the

mid-SPan deflection a Wl4X38 beam, 20 feet long, would exhibit as a simply

supported member at its A.I.S.C. allowable uniform load (assuming full lateral

support) • For the 8-inch beam tests, a rotation of 24XlO-3 radians

corresponds to a deflection of about 1.6 inches, four times the deflection, at

allowable load, of a l2-foot long simply supported beam using the waX2l

sections. These deflections were considered to be reasonably representative of

a severe ductility demand, even under seismic loading conditions.

SPecimen 1482 exhibited major slip in the leg of the tension flange angle

bolted to the beam (and in the legs of the web angles attached to the beam web)

22

at a rotation of approximately 12XIO-3 radians, followed by slip in the leg of

the flange angle bolted to the column face at approximately 20XIO-3 radians.

For the static tests, in which the rate of actuator movement was the controlled

input variable, slip as indicated in Figure 3.5 corresponds to a gradual drop in

moment until bear ing is achieved in the connected elements. With bear ing

established, the stiffness of the connection prior to slip is regained, with no

anticipated permanent degradation in the capacity of the connection (barr ing

premature bolt shear failure or tear-out in th~ connected parts) •

The effect of flange angle thickness on the moment-rotation behavior of

Wl4X38 beam connections using 7/8-inch diameter bolts is sho~m in Figure 3.6.

As with the members fastened with 3/4-inch diameter bolts, the initial stiffness

and the moment developed at comparable rotations increased with increasing

flange angle thickness. The initial slope of the moment-rotation curve was

247XI03 k-in./radian for specimen 1485 (3/fl-inch thick angles), 286XI03 and

258XI03 k-in./radian for specimens 1486 and 1489, respectively (1/2-inch thick

angles), and 579XI03 k-in./radian for specimen 1488 (S/8-inch thick angles).

8imilarly, at a rotation of 24XIO-3 radians, the connection moment increased

fran 736 k-in. for specimen 1485 (3/8-inch thick angles) to an average of 1038

k-in. for the two specimens with 1/2-inch thick flange angles, and 1561 k-in.

for specimen 148S, with SIS-inch thick angles. It should be noted also that in

contrast to specimen 1482, which was fabricated using 3/4-inch diameter bolts,

no slip was exhibited by the 14-inch beam specimens fastened with the 7/8-inch

diameter bolts.

The effect of bolt diameter on the static moment-rotation behavior of the

14-inch beam specimens is illustrated in Figures 3.7a (specimens with 3/8-in.

thick flange angles) and 3.7b (specimens with 1/2-inch thick flange angles).

Comparison of Figures 3.7a and 3.7b (and Tables 3.1, 3.2) shows that the initial

23

stiffnesses of the connections (initial slope of the M-ep curve) are

approximately the same for specimens with flange angles having the same

thickness. Beyond the initial portions of the M-ep curves, however, the

connections fastened with 7/S-inch diameter bolts developed moderately larger

moments, at comparable rotations, than those fabricated using the 3/4-inch

moment of approximately 1040 k-in.

diameter bolts. For example, specimens 1486 and 14S9 developed an average

-1 .at 24XIO - radIans, compared to a rnoment

of 947 k-in. for specimen 1482. (Although specimen 14S2 exhibited major slip,

a projection of the M-ep curve that might be expected had slip not occurred would

still fall below those of 1486 and 1489). Similarly, specimen 1485 developed a

moment of 763 k-in. at a rotation of 24XIO-3 radians, about 14 percent higher

than the moment for specimen 1481 at that rotation, 668 k-in.

The closeness of the initial slopes for the 14-inch beam specimens fastened

with the 7/8-inch and 3/4-inch diameter bolts was not anticipated, as it was

expected that the connections with the 7/S-inch diameter bolts would initially

be stiffer, by developing an increased clamping force between the connected

elements, by having a smaller clear distance between the bolt head (and washer)

and the toe of the fillet in the angle, and by having a smaller clear distance

between the two bolts on the column gage line. No explanation is offered at

this time for the difference between the anticipated and observed effect of bolt

diameter on initial connection stiffness for the 14-inch beam specimens (and for

Lhe 8-inch beam specimens, as discussed subsequently).

In contrast to the influence of flange angle thickness on the

moment-rotation behavior of the 14-inch beam specimens, moderate changes in the

size of the web angles did not as significantly affect the connection

performance. Figures 3.8 and 3.9 show the effect of web angle thickness and

lenqth, respectively, on the M-ep relationships for Wl4X38 sections with 3/8-inch

24

thick flange angles. For example, increasing the thickness of the web angle by

50 percent, from 1/4-inch to 3/8-inch (specimens 1481 and 1484), produced a

corresponding increase in moment, at a rotation of 24XIO-3 radians, of

approximately 25 percent, fran 668 k-in. to 822 k-in. An apparently lesser

influence on post-elastic moment capacity was exhibited by a change in the

length of the web angles, as comparison of specimens 1481 and 1483, Figure 3.9,

indicates. At a rotation of 24XIO-3 radians, specimen 1483, with web angles

having a length of 5-1/2 inches, developed a moment of 652 k-in., some 17 k-in.

less than the 668 k-in. moment of specimen 1481, which had the standard 8-1/2

inch long web angles. It should be noted that specimen 1483 had the only

non-symmetrical connection in the test series, with the legs of the web angles

attached to the beam column stub each using two bolts placed in the upper two

holes of the standard detail, Figure 2.2a. In this location, with the web

angles closer to the beam tension flange, they would be expected to contr ibute

differently to the moment transfer capability of the connection than if they had

been positioned at mid-depth, closer to the pivot point of the connection. The

arrangement used is of practical imPortance, however, in that it represents a

normal positioning of web angles designed for shear transfer in beams using

simple (flexible) framing.

The influence of flange angle thickness on moment-rotation behavior was

examined also for the W8X21 beam specimens, the results of which are shown in

Figures 3.10a, 3.10b, and 3.11. Figure 3.10a presents a comparison of the

M- <P curves for specimen 881, with a flange angle thickness of 5/16-inch, and

specimen 882, with 3/8-inch thick flange angles. The gage in the legs of the

flange angles attached to the stub column was 2 inches, and the angle length was

6 inches in both of these specimens.

25

The bolt diameter was 3/4 inches.

Although comparison of the initial portion of the moment-rotation relationships

indicated a considerably stiffer connection for specimen 882 relative to that of

881 (123.4XI03 k-in./radian vs. 66.7XI03 k-in./radian), and a

correspondingly greater moment transfer capability, specimen 882 exhibited major

slip in the connection elements at a rotation of approximately l6XIO-3

radians. Unlike specimen 1482, in which slip also occurred, specimen 882 did

not regain nor approach the stiffness it had maintained prior to slip. The

stiffness continued to degrade with continued loading, the slope of the

M-<jJ curve reducing to only 1.5XI03 k-in./radian at a rotation of 24XIO-3

radians. As there were no cracks nor other geometric irregularities observed in

the connection elements of specimen 882, either during testing or upon post-test

visual inspection, no explanation is offered for the singular behavior of this

specimen.

In Figure 3.10b, the moment-rotation curves for specimens 886 (5/16-inch

flange angle thickness) and 887 (3/8-inch angle thickness) are compared. In

these specimens, the bolt diameter was 3/4 inches, the gage in the legs of the

flange angles attached to the column was 2-1/2 inches, and the angle length was

fi inches. As with the 14-inch deep beam tests, both the intitial stiffness and

the moments develOPed at common rotations were greater for the waX21 beam

connection having the heavier flange angles. For example, the 1/16-inch

increase in flange angle thickness of specimen 887 over that of specimen 886

As no slip occurred in

effected a greater than 50 percent increase in moment

k-in.) at a connection rotation of 24XIO-3 radians.

(381 k-in. vs. 244

either of these two tests, the comparative behavior of the two specimens, shown

in Figure 3.10b, may be considered representative of similar connections framing

the 8-inch deep beams.

26

Figure 3.11 presents a comparison of the M-¢ curves for specimens 8S8

(5/16-inch thick flange angles), 8S9 (3/R-inch thick angles), and 8S10 (1/2-inch

thick angles). For each of these specimens the bolt diameter was 7/8 inches,

the gage in the legs of the flange angles attached to the column was 2 inches,

and the angle length was 6 inches. Again, the initial connection stiffness and

the moments at comparable rotations increased with increasing flange angle

thickness. At 24XIO-3 radians, the connection moment developed in specimen

8S8 was 380 k-in., increasing to 423 k-in. in specimen 8S9, and 634 k-in. for

specimen 8S10. It may be noted, also, that specimen 8810 exhibited major slip

at 5.3XIO-3 radians; this specimen had the thickest flange angles, 1/2 inch,

of all the waX21 beam members. (It was also the only specimen fastened with

7/8-inch diameter bolts that exhibited slip in either the static or cyclic test

series.) Specimen 8810 was similar to 1482 in that it was able to regain, after

slip, the stiffness it held just prior to the occurrence of the slip (c.L,

Figures 3.5 and 3.11).

The effect of bolt diameter on the moment-rotation behavior of the 8 inch

beam specimens is illustrated in Figures 3.12a (specimens with 5/16-inch thick

flange angles) and 3.Bb (specimens with 3/8-inch thick flange angles). As with

the 14-inch beam specimens discussed previously, there were no consistent,

significant differences in the initial stiffnesses of the specimens fabricated

using the two bolt sizes. In fact, the initial slope of the M-¢ curve for

specimen 882, with 3/4-inch diameter bolts (123.4XI03 k-in./radian), is

greater than that of specimen 889, l04XI03 k-in./radian, which had 7/8-inch

bolts as the fasteners. It should be noted, again, that the behavior of

SPecimen 882 is sanewhat of an ananaly, in that it was the only specimen, of all

of those tested under either static or cyclic loading, that did not regain a

positive slope to the moment-rotation curve after slip occurred. Thus,

27

comparison of the moments developed at either 4XIO-3 or 24XIO-3 radians

cannot be significant for these two specimens. Additional data, including tests

of specimens with a greater range of flange angle thicknesses, are needed before

the relative effect of bolt diameter on connection behavior can be better

quantified.

The effect of varying the gage in the leg of the flange angle attached to

the column flange was examined in the W8X21 beam test ser ies. wi t.l1 an angle

thickness of 3/8 inch, gages of 2, 2-1/2, and 4-1/2 inches were used in

specimens 882, 887, and 884, respectively. The bolt diameter was 3/4 inches for

each of these specimens. To accornnodate the 4-1/2 inch gage in specimen 884, a

6X6X3/8 angle was used in place of the smaller 6X3-1/2X3/8 and 6X4X3/8 angles

used in the other two specimens. Specimens 881 and 886, with flange angles of

5/16-inch thickness, had gages of 2 inches and 2-1/2 inches, respectively.

Complete details of the dimensions for these specimens are presented in Table

2.2.

The static test results for these five specimens are summarized in Table

3.1. For the two members having 5/l6-inch thick flange angles, t.l1e

moment-rotation curves are plotted in Figure 3.13a; the curves for the three

specimens with flange angles of 3/8-inch thickness are compared in Figure 3.13b.

As expected, changes in flange angle gage had a pronounced effect on both the

initial slope of the M-~ curve, and on the moment capacity of the connection at

large displacements. For example, with the 3/8-inch thick flange angles, the

initial connection stiffness decreased fran 123.4XI03 k-in./radian to

3 k-in./radian the angle gage was changed fran 2 inches to 4-1/215.3XIO as

inches (specimens 882 and 884). Specimen 887, with a gage of 2-1/2 inches,

exhibited an initial M-~ slope of 48.0X103 k-in./radian, intermediate in

stiffness between those of the other two members. At a rotation of 24XIO-3.

28

radians, specimen 8S7 achieved a mcrnent of approximately 380 k-in., more than

twice the 165 k-in. mcrnent of specimen 884 at that rotation. It should be

noted again, that specimen 8S2 sustained slip at about l6XlO-3 radians, after

which its moment-rotation curve reduced to a slope of only 1.5Xl03

k-in./radian at a rotation of 24XlO-3 radians. This behavior is not

considered indicative of the performance eXPeCted of the connection had slip not

occurred; consequently, canparison of specimen 882 with the other two members

at large displacements is not appropriate.

The two connections with 5/16-inch flange angles exhibited the same

relative response as those with 3/8-inch angles; Le., decreasing the gage

results in an increase in initial connection stiffness and subsequent mcrnent

capacity at large displacements. For specimen 8Sl (2-inch gage), the initial

slope of the M-¢ curve was 66.7Xl03 k-in./radian, almost double the 39.5Xl03

k-in./radian slope for specimen 886 with a 2-1/2 inch gage. Similarly, at a

connection rotation of 24XlO-3 radians, specimen 881 developed a mcrnent of 329

k-in., significantly higher than the 244 k-in. manent in specimen 886.

For the waX2l beam sections, the effect of changing the length of the

flange angle was examined. As indicated in Table 2.2, with all other connection

dimensions remaining the same, a flange angle length of 6 inches was used for

specimen 8Sl, and a length of 8 inches used for specimen 8S3. The one-third

increase in flange angle length resulted in a corresponding increase of about

one-third in the initial connection stiffness (104.7Xl03 k-in./radian vs.

66.7Xl03 k-in./radian), and the development of higher manents at large

displacements (422 k-in. vs. 329 k-in. at a rotation of 24XIO-3 radians).

The canplete manent rotation curves for specimens 881 and 8S3 are plotted in

Figure 3.14.

Finally, in Figure 3.15, a comparison is made between a Wl4X38 section

29

specimen (14S1) and a W8X21 specimen (8S5) in which the dimensions of all of the

connection elements were the same except for the lengL~ of the web angle (8-1/2

inches for 14S1, and 5-1/2 inches for 885). As seen fran the M-<P curves of

Figure 3.15 and the data recorded in Table 3.1, the initial slope of the

moment-rotation curve is increased significantly, fran 76.7XI03 k-in./radian

to 195.0XI03 k-in./radian, for the Wl4X38 specimen in comparison to the W8X21

member. Similarly, the manent developed at 24XlO-3 radians was 668 k-in. for

specimen 14S1, about double the 3~7 k-in. mcment of specimen 8S5. The increase

in initial connection stiffness and manent development capability are to be

expected, as the deeper beam section provides, at comparable rotations, a larger

displacement of the tension flange angle (and larger force in the angle)

together with a larger mcment arm from the positiorr of the tension flange angle

to the pivot point of the connection in the vicinity of the compression flange.

3.1.3.2 Bolted-Welded Test Specimens

The manent-rotation curves for the two bolted-welded test specimens are

shown in Figure 3.16. Numerical values for the initial slope, secant slope at

4.0XIO-3, and slope at 24XIO-3 radians are presented in Table 3.3, together

with the mcment developed at both 4.0XIO-3 and 24XIO-3 radians. As

expected, specimen 14WS2, fabricated using 1/2-inch thick flange angles,

exhibited the larger initial stiffness, and developed larger manents at

comparable rotations than did specimen 14WSl, which had 3/8-inch thick flange

angles.

Comparison of the data in Table 3.3 for the bolted-welded specimens with

the test results for comparable all-bolted specimens 14S5 (3/8-inch flange angle

thickness; 7/8-inch bolt diameter), and specimens 1486 and 14S9 (1/2-inch thick

30

angles, 7/8-inch bolt diameter) indicates that the initial stiffnesses of the

bolted-welded specimens are somewhat higher than those of the all-bolted

specimens (Table 3.2). This may be attributed to the greater restraint against

movement of the heel of the angle at the end of the beam flange in the welded

elements, as illustrated in Figure 3.2. The weld return, together with the

continuous longitudinal fillet welds connecting the top and seat angles to the

beam flange, did not permit the angles the freedom to curl around the beam end

(as in the all-bolted specimens) in accamnodating the rotations between the end

of the beam and the flange of the column. The greater restraint thus i.mpJsed by

the welded connection resulted in a larger initial stiffness for those specimens

in comparison to the all-bolted members, where greater relative movement was

more easily achieved.

In addition to the higher initial stiffnesses, the bolted-welded specimens

developed moderately larger moments than those in the bolted specimens at

comparable rotations. For example, specimen 14SW2 developed a moment at 1235

k.-in. at 24XIO-3 radians, almost 20 percent larger than the approximately

1040 k.-in. average moment for specimens 1486 and 1489. Similarly, specimen

14sv.n developed 923 k.-in. at 24XIO-3 radians, canpared to 763 k.-in. for

specimen 1485 at that rotation. However, because only two specimens fabricated

in the bolted-welded configuration were tested in this study, the above

observations should be considered preliminary, and not necessarily indicative of

the relative performance of the welded specimens with respect to the all-bolted

specimens when a more complete range of section depths, and flange and web angle

sizes are considered. 8uch tests have been proposed as part of the continuation

of the current investigation.

The surrnnaryof the static tests in the following section, 3.1.4, refers to

the behavioL of all-bolted test specimens; generalizations regarding the

31

performance of the combined bolted-welded specimens were not considered

appropriate from the limited data available at this time.

3.1.4 Summary of Static Test Results

For all of the specimens tested in the static test series, the connections

exhibited a moment-rotation response which becomes non-linear relatively early

in the loading sequence. This non-linearity is contributed to, in part, by

local yielding and eventual plastic hinge formation at each toe of the fillet in

the flange angle attached to the tension flange of the beam. Another hinge

develops in the vicinity of the bolt line in the leg of the flange angle

attached to the column, together with progressive plastic hinging in the

outstanding legs of the -web angles. It is of interest to note, however, that

each of the connections develOPed a moment greater than two times the capacity

that would be predicted by simple plastic hinging mechanisms in the leg of the

tension flange angle attached to the column flange and in the legs of the web

angles; further analysis of this post-elastic connection response is presented

below.

Inspection of Figures 3.5 through 3.15 shows that each of the test

specimens (with the exception of specimen 882) was able to develop increasing

moments through the full range of rotations imposed during the test. In fact, a

nearly constant or slightly decreasing positive M-~ slope was observed during

the latter stages of loading for these static test specimens. It is believed

that this nearly constant stiffness at large deformations can be attributed to,

in part, to material strain hardening, and to the con~equences of significant

changes in the geometries of the connecting angles. The increasing deflection

of the tension flange angle at large connection rotations produces a continuous

32

change in the internal force distribution in the legs of the angle, with axial

tension becaning an increasingly larger factor (relative to bending) as the

angle progressively "flattens out." A gradual transition fran a predaninantly

flexural to a combined flexural-axial response in the tension flange angle, with

the accanpanying strain hardening, can thus be expected to contr ibute to the

ability of the connection to achieve a considerably greater moment capacity than

that predicted by a simple plastic hinge mechanism, as noted above.

Fran the static tests, was been found that the geanetric parameters that

most significantly affect the static moment-rotation performance of the

semi-rigid connections investigated were: the depth of the beam section to

which the connection elements were framed: the thickness of the flange angles:

and the gage in the leg of the flange angles attached to the column flange.

Although the data are inconclusive, it appears that bolt diameter has a minimal

effect on the initial stiffness of the connections: however, increasing the

bolt diameter effects a corresponding increase in moment capacity at large

rotations (beyond about 4XIO-3 radians). Variations in the length of the

flange angles, and in the length and thickness of the web angles, had a less

pronounced effect on connection response than the other -parameters listed above.

Analytical mJdels proposed in the initial investigation (63) to predict the

initial stiffness of the semi-rigid connections have been applied to the

specimens tested in the current study. Canparisons of the predicted stiffnesses

with the experimental data fran the static test investigations are presented in

Section 4.1. Further, using the results of the parametric study, a

semi-empirical analytical model has been developed to generate complete

non-linear moment-rotation curves for the connections:

phase of the study are reported also in Section 4.1.

the results of this

33

3.2 Cyclic Tests

3.2.1 Scope of Investigation

The purpose of this phase of the investigation was twofold: (1) fran the

variable amplitude cyclic tests, to quantify the cyclic moment-rotation behavior

of the semi-rigid beam-column connections; and (2) fran the constant amplitude

cyclic tests, to obtain base-line fatigue data for connections of varying

stiffness. The objectives of the variable amplitude tests have been to

determine energy absorption capabilities under complete reversal of moment, and

to qualitatively describe the characteristics of the attendant hysteresis loops.

From the constant amplitude tests, fatigue life relationships have been

developed for application to appropriate cumulative damage models for predicting

total fatigue lives of connections subjected to variable amplitude displacement

histories. The fatigue tests have served, also, to provide additional data fran

which the total energy absorption capacities of connections of varying stiffness

could be evaluated.

The intent of the cyclic tests was to examine the connection response to

moment reversals, not the behavior of a complete subassemblage under seismic

loading. Consequently, the rate of loading in the cyclic tests was

"quasi-static," and was not intended to suggest that the loading would be the

direct result of actual earthquake induced ground motions.

3.2.2 Variable Amplitude Block Tests

Seven specimens were tested under the law-to-high amplitude block

displacement histories; the geometric parameters that were varied in this test

34

series included the beam depth (Wl4X38 and W8X2l sections), the flange angle

thickness, and the bolt diameter. Two specimens were tested under high-to-low

amplitude block histories; one was an 8-inch beam connection, the other was a

W14X38 beam connection. Details of the test specimens are reported in Tables

2.2 and 2.3; the testing procedures are described in Section 2.3.2.

3.2.2.1 Test Results

As discussed previously, all of the cyclic test specimens were subjected to

complete displacement reversal to facilitate comparison of the hysteresis loops

generated for beams of different depth. The tests were terminated when observed

fatigue cracking had progressed partially across the faces of the flange angles.

No test was extended to the point of ccmplete rupture of a connection element.

No slip was observed during the cyclic tests.

Figure 3.17a shows front and rear views of a top flange angle fram specimen

14Cl after the test was stopped.. It can be seen that cracking had progressed

over most of the width at the toe of the fillet in the leg bolted to the column

flange. (It should be noted that, for the majority of the cyclic test

specimens, fatigue cracking initiated, in one or more of the flange angles, at

the toe of the fillet in the leg bolted to the beam flange; otherwise, the

appearance of the crack patterns is similar to that shown in Figure 3.17a).

After disassembly of test specimen 14Cl (and several of the other cyclic

test specimens), it was discovered that significant cracking had progressed in

the vicinity of the bolt hole under the washer. Although the formation of

fatigue cracks had an observable effect on the load-displacement hysteresis

loops, the decrease in maximum load was usually a small percentage of the

maximum load for the stabilized

35

The permanent distortions shown in the flange and web angles of specimen l4Cl,

Figure 3.17b, give an indication of the large deformations experienced by the

connection angles during the cyclic tests.

As mentioned previously, the specimens were intended to simulate, within

reason, actual connections in situ. During the erection procedure, it would be

natural to seat the beam on the botton flange angle for support, thereby

aligning the bottan angle as required at the expense of the top angle. As a

consequence, the top angle would be subjected to the greater initial strains

resulting fran any lack of fit during the bolting procedure. This same erection

sequence was followed in the test program, and is believed to explain the

tendency of the top angle to form the first cracks in most of the cyclic tests.

Also, the hysteresis loops tended to exhibit signs of stiffness degradation

first in the negative mcm.ent region, corresponding to tension in the top flange

angle.

Summaries of the cyclic test results are presented in Tables 3.4 through

3.8 for the Wl4X38 beam specimens, and in Tables 3.9 through 3.12 for the

connections framed to the waX2l sections. Complete hysteresis loop traces at

each displacement amplitude for each of the nine test specimens are shown in

Figures 3.18 through 3.26. The tables include the actuator displacement

amplitude, the number of cycles imposed at each arnpli tude and test frequency,

and the cumulative number of test cycles. For each displacement amplitude, the

range of rotation (peak-to-peak) and the range of mcm.ent is given for the

hysteresis loops. ~he area enclosed by a single hysteresis loop is given as

well as the cumulative loop area. For the specimens tested in the initial study

(14CI, 14C2, SCI, 8C2) the areas of the hysteresis loops, other than for the

single cycles reported in the tables, were calculated as the average of the

first and last loop areas at a particular displacement amplitude and test

frequency.

36

For those specimens investigated in the present study (14C3, 14C4,

l4Bl, BC3, 8Bl), the areas of all of the hysteresis loops at each displacement

arnpli tude were taken to be the same as the single reported area for purposes of

calculating cumulative hysteretic energy.

3.2.2.2 Discussion of Test Results

In the variable amplitude cyclic test series, stable hysteresis loops were

maintained,for the l4-inch beam specimens, within a few cycles after a change in

amplitude was imposed relative to the preceding displacement under the

block-type loading. For several of the 8-inch deep beam connections, a

continual, though small, softening (loss of rnanent) was noted for each

progressive cycle at a constant displacement amplitude: however, the succeeding

hysteresis loops were otherwise similar in appearance. As seen in Figures 3.18

through 3.26, the rncment-rotation behavior of the connections was characterized

by hysteresis loops of continually decreasing slope for relatively small

displacements ·in the non-linear range. In contrast, the loops exhibited a

moderate "pinching" effect at larger amplitudes, the degree of pinching being

more pronounced in the Wl4X38 beam connections than in the W8X21 members. This

increase in stiffness observed toward the tip of each hysteresis hoop may be

attributed, in large measure, to the changing geometry of the connection during

each half cycle of loading:

subsequently.

this behavior is explained in greater detail

As noted earlier, each of the variable amplitude cyclic tests culminated in

the formation and subsequent propagation of fatigue cracks originating at the

toe of the fillet in one or more of the beam flange angles. The cracks

generally initiated in the region of greatest restraint against displacement:

37

Le., in the region between the bolt in the leg of the flange angle attached to

the column and the first bolt fran the end of the beam in the leg attached to

the beam flange. The tests were terminated when cracking had progressed at

least partially across the face of the angle at the fillet; no tests were

extended to the point of rupture of a connection element. The connections

maintained ductile behavior during the full extent of the cyclic tests, and

exhibited only modest loss of maximum manent fran. the time fatigue cracking was

noticed to the termination of a test. No slip was observed dur ing the cyclic

tests, nor was there any local buckling of the connection elements.

Discussion of Manent-Rotation Hysteresis Loops

The shape of the hysteresis loops for the cyclic test specimens can be

described in terms of the changes in the geometry of the connection as the

moment is reversed. Consider one half of a typical loop, shown as a solid line

in Figure 3.27. Point 1 in Figure 3.27 corresponds to one extreme of the

actuator movement (Point 1 in Figure 3.28, actuator displacement vs. time) •

The portion of the moment-rotation curve that is generated as the actuator moves

fran Point 1 to Point 3 can be divided into three regions based on the

configuration of the connection; these regions are labeled I, II, and III in

Figure 3.27.

The initial loading of the connection in a cycle, culminating in the

attainment of maximum negative moment, causes the connection to assume the

configuration shown in Figure 3.29a. In this configuration the beam is pivoting

about a point near BFA, the current canpression flange angle. The remaining

connection angles are pulled away fran the column flange, generating the tension

forces which establish the correspOnding resisting moment at the beam-column

38

interface. With the oottan angle in full bearing on the column flange, the

stiffness of the connection is now at a relative rnaxbnum. The completion of

this initial loading is indicated as Point I in Figure 3.27.

Reversal of the direction of actuator movement, with the specbnen in the

configuration shown in Figure 3.29a effects a period of essentially elastic

unloading at a slope comparable to the initial slope of a statically loaded

connection. This is identified as Region I in Figure 3.27.

Region II is a transition stage. During this time, the geanetry of the

connection is undergoing significant change. The compression force in BFA,

which bears on the column face in Region I, decreases and eventually converts to

a tension force as the mement is reversed; hence, the angle moves away fran the

column face (see Figure 3.29b).

The force in the top flange angle, TFA, changes fran tension to compression

in Region II, causing that angle to move toward the column face. As a result,

the center of rotation of the connection moves (reflecting the redistribution of

forces taking place) and eventually maintains a position near the top of the

beam. During the time when ooth flange angles are temporarily bent away fran

the column face, the connection stiffness is at a minimum. The stiffness of

Region II is not a constant for all loading histories. The initiation of yield

in the flange angles is affected by the presence of residual stresses (and,

later, fatigue cracks) . The response of the connection in Region II is

analogous to a rigid beam on an elastic-plastic foundation, where the foundation

is represented by springs with changing stiffnesses. ~he relative stiffnesses

of the springs depends on the magnitude of the connection rotation at the

previous reversal of memento As a result of this behavior, it is hypothesized

that unloading fran the central range of Region II will not be at a slope equal

to that of Region I. Rather, the slope will lie between the limits established

39

fran the Region I response ann the Region II slope immediately preceding

unloading. (This has not been experimentally tested in the present

investigation.) The end of Region II is reached when angle TFA has folded back

upon the column face in compression. The behavior of the connection in Region

II occurs only in cyclic loading, and hence cannot be canpared to a monotonic

static test.

Region III can be considered geometrically the reverse of the configuration

existing in Region I. As shown in Figure 3.29c, the compression angle in

bearing against the column face is now TFA, whereas flange angle BFA and t.he web

angles are now pried in tension fran the column. The center of rotation is

again stationary, located near the top flange of the beam. The change in

stiffness as the configuration changes fran that of Figure 3.29b to the one in

Figure 3.29c can be determined by noting the difference in the slope of the

moment-rotation curve. The magnitude of this change depends on the connection

details, as discussed belCM.

Canparing the change in slope between Regions II and III in sPecimens 14Cl

and 14C2, for example, (Figures 3.18 and 3.19, resPectively), it can be seen

that the change is more pronounced in specimen 14Cl. This difference can be

attributed to the thicker flange angles of sPecimen 14C2, the web angles and

belt diameter being identical for the two sPecimens. Assuming the angles behave

as beams, an analogy may be drawn between a span-to-depth ratio for a beam and

the ratio of an "effective" gage length, g - db' to the thickness of the

angle, t, for the leg of the flange angle mounted to the column flange. For

specimen 14Cl, (g - db)/t is 4.7 and, for sPecimen l4C2, 3.5, indicating a

stiffer beam in bending for the flange angles of sPecimen 14C2. During the

transition phase of Region II the stiffer flange angles of sPecimen 14C2 offer

more resistance to movement than the flange angles of sPecimen 14Cl. ThUs, when

40

the canpression flange angle goes into bear ing , the change in stiffness is

greater in specimen 14Cl than the corresponding change in stiffness of specimen

14C2. The same observations may be drawn by ca:nparing the relative response of

the other three 14-inch beam specimens, 14C3, 14C4, and 14Bl. Specimens 14C3

and 14Bl, with {g - db)/t ratios of 3.25, exhibited very little evidence of

pinching of the hysteresis loops, while 14C4, with a {g - db)/t ratio of 4.3,

exhibited perhaps a bit more praninent pinching than the other two members.

(The pinching effect in specimen 14C4 was still considerably less pronounced

than that of 14Cl, however, as comparison of Figures 3.18 and 3.21 indicates).

By canparing the manent-rotation curves of specimens BCl, 8C2, 8C3, and

8Bl, the observations of the previous paragraph are again applicable. Specimen

BCl, with a {g - db)/t ratio of 4.0, exhibited a more praninent change in

slope fran Region II to Region III than that of specimen 8C2, with a (g ­

~)/t ratio of 3.3, or specimens 8C3 and 8Bl, with identical ratios of 3.0.

In fact, the latter three specimens are distinguished as having exhibited almost

no consistent pinching behavior at all, even at large displacements.

Connection Hysteretic Energy Capacity

The "average" hysteresis loop area at each displacement amplitude, and the

total hysteretic energy accumulated at the termination of testing, is presented

in Tables 3.4 through 3.12 for the nine variable amplitude test specimens. In

general, for the low-to-hiqh amplitude block tests, it was found that, with the

exception of the first cycle following an increase in displacement amplitude,

the hysteretic energy absorbed per cycle remained reasonably constant at each

amplitude. Further, the ductile behavior of the connections was evident by the

increase in hysteresis loop area with each succeeding increase in displacement

amplitude (and connection rotation) through the full range of testing, even with

41

pinching evident at the larger amplitudes.

As a consequence of the general stability of the connections at large

rotations, and of the ductility of the connection elements, it is reasonable

that the overall energy absorption capacities of like connections would increase

directly with the depth of the beam sections to which they are attached. This

is demonstrated, for example, by canparing the data for specimens l4Cl and 8C2,

both of which contained 3/8-inch thick flange angles and were fastened with

3/4-inch diameter bolts. For specimen 14Cl, the total accumulated hysteresis

loop area was 520 k-in., more than twice the 243 k-in. achieved by specimen

8C2.

The hysteretic energy absorption performance of the specimens framed to a

particular beam section, however, exhibited limited consistency. For example,

specimen 14C4, fabricated with 3/8-inch thick angles and 7/8-inch diameter

bolts, develOPed only 345 k-in. of hysteretic energy, well below the 520 k-in.

of specimen 14Cl (3/8-inch flange angles, 3/4-inch bolts). It may be noted that

fatigue cracking was observed during the block of cycles applied at a

displacement amplitude of 1.6 inches for specimen 14C4; these cracks thereafter

propagated continuously, and the test was discontinued after nine cycles were

applied at a displacement amplitude of 1.8 inches. In contrast, fatigue

cracking was not observed in specimen 14CI until the twelfth cycle at a 2.0-inch

displacement amplitude, enabling the latter member to accumulate considerable

hysteretic energy at the large loop areas corresponding to that displacement.

Comparison of the behavior of specimens 14Cl and 14C4 serves to illustrate

the sensitivity of total hysteretic energy absorption capacity to the formation

and rate of propagation of fatigue cracks in the connection elements,

particularly the flange angles. Fatigue crack initiation, in turn, is

influenced by such factors as surface irregularities formed during the rolling

42

or fabrication of the connection angles, residual stresses introduced during the

erection process, and concentrations of stress resulting fram the restraint

against movement in the area adjacent to the bolts in each leg of the flange

angle. Further illustration of the dependency of energy absorption on fatigue

behavior is obtained by canparison of specimens 14C3 and 14Bl. Geanetrica1ly

the same, specimen 14C3 was tested under low-to-high arnpli tude loading, with

displacement amplitudes increasing in blocks fram 0.2 to 2.0 inches, and

accumulated a 683 k-in. total hysteresis loop area. A fatigue crack was

detected dur ing the 1.6 inch displacement amplitude block, and progressed at a

moderate rate until the test was stopped during cycling at an amplitude of 2.0

inches. Specimen 14B1, in a high-to-low amplitude test, exhibited fatigue

cracking during the first block of cycles at a displacement amplitude of 1.8

inches; these cracks continued to grow, although at decreased rates, as the

displacements were lowered progressively to 1.0 inches. At this point, a large

crack had extended to the limit permitted in the other tests, and cycling of

specimen 14B1 was discontinued. The total hysteretic energy achieved was 514

k-in., about 75 percent of that for the canpanion member, 14C3.

The influence of fatigue crack propagation on hysteretic energy absorption

is further demonstrated by canparison of the behavior of specimen 14B1 with that

of specimen 8B1. Although fatigue cracks were first detected in specimen 8B1

during the first block of cycles at its largest displacement amplitude, 1.2

inches, crack retardation (temporary cessation of crack growth) was observed at

succeeding1y smaller displacement amplitudes. At 0.2 inches, the crack lengths

were still within the limits permitted in the cyclic test series; the amplitude

was then increased again to 1. 2 inches, and the crack extended rapidly during

the first cycle at that amplitude. The total hysteretic eneregy accumulated by

43

specimen 8Bl was 216 k-in., greater than that for its companion specimen, 8e3,

(186 k-in.), which was tested under low-to-high amplitude block loading.

The consequences of fatigue crack acceleration or retardation on energy

absorption capacity during variable amplitude cyclic loading are evident from

the above comparisons. The differences in the crack growth rates between the

low-to-high and the high-to-low amplitude tests also serve to illustrate the

dependence of cyclic performance (and, correspondingly, damage accLUnulation

models) on sequencing history as well as on amplitude of load or displacement.

ThUS, a linear damage rule of the form proposed by Miner (65), although simple

to apply, cannot be expected to offer a consistently accurate prediction of

damage accLUnulation for displacement histories more typical of a seismic event;

this is discussed further in Section 4.3.

3.2.3 Fatigue Tests

Sixteen specimens were tested under constant amplitude cyclic (fatigue)

displacement histories. The geometric parameters that were varied in this test

series were the beam depth (W14X38 and W8X2l sections) and the flange angle

thickness (3/8 inch and 1/2 inch for the l4-inch beam specimens, 5/16 inch and

3/8 inch for the weX2l specimens). The bolt diameter was 7/8 inch for all

specimens in this test series. Details of the test specimens are reported in

Table 2.3; the testing procedures are described in Section 2.3.2.

3.2.3.1 Test Results

A compilation of the fatigue test results for the sixteen specimens is

44

presented in Table 3.13. The table includes the nominal chord rotation, the

fatigue life, and the total accumulated hysteresis loop area for the specimens.

The fatigue data for each of the specimens (except 8F6) , including range of

rotation, range of moment, and individual hysteresis loop area at selected

percentages of the total fatigue life are presented in Tables 3.14 through 3.17.

No hysteresis loop areas are available for specimen 8F6 because of a malfunction

in the data recording equipment.

As discussed in Section 2.3.2.3, several of the fatigue test specimens were

subjected to a number of initial "half" cycles before continuing with the full

reversal displacements, in order to induce first cracking in the top flange

angles, where inspection was easiest. Cracking did initiate in the top angles

for these specimens, with the origin of cracking at the toe of the fillet,

usually in the leg of the angles mounted to the beam flange. Fatigue "failure"

was defined as the number of cycles at which the longest fatigue crack had

extended over approximately three-fourths of the width of the flange angle. For

some of the test specimens, this crack had grown through the thickness of the

flange angle at one or more points by the time it had reached its limit length.

Complete hysteresis loop traces at selected cycles are shown in Figures

3.30 through 3.44 for the fifteen fatigue specimens for which data are

available. For a few of the 1CM amplitude tests (e.g., specimens l4F8, 14F4,

and 8F2) the hysteresis loop traces shown in the figures appear somewhat erratic

and non-coincidental. ~his is attributed to the sensitivity of the recorded

data to slight self adjustments in the testing apparatus at 1CM actuator loads

corresponding to reversals in the direction of actuator movement. The irregular

appearance of the tops of the hysteresis loops results from the limited number

of digitized data points that could be recorded by each channel of the recording

equipment, particularly in those specimens in which elastic displacements were

4S

prevalent. In general, however, it can be seen that the hysteretic response in

specimens l4F3, 14F4, and 8F2 was reasonably consistent, with only small

inelastic displacements evident during each cycle, and little degradation of

moment carrying capability even toward the end of a test when fatigue cracking

. was quite extensive.

For the specimens tested at large displacement amplitudes, and which

exhibited fatigue failures at the lower lives in the test program, it is

apparent that the hysteresis loops were quite stable throughout each test, and

that only nominal loss of moment occurred for the complete connection even

toward the end of a test. Specimen 8F7, shown in Figure 3.40, typifies the

response observed in the large displacement constant amplitude tests. The

hysteresis loops are large and quite stable, with minor pinching evident toward

the end of the loop. Note also the gradual, though rather nominal, loss of

moment exhibited by the specimen toward the end of the test (Nf = 67 cycles).

This behavior was exhibited by the fatigue test specimens in spite of the fact

that fatigue cracks had progressed to some depth through the thickness of the

flange angle at the time they had reached the limit length at the surface.

Because the crack was extending rapidly along the surface at the time testing

was stopPed, however, it was felt that the recorded fatigue life was very close

to the total number of cycles that could be tolerated before complete rupture of

one of the flange angles. The fatigue cracks were generally first visually

detected as a series of fine hairline cracks which coincided with slight

irregularities in the surface of the flange angle at the toe of the fillet. As

cycling progressed, these individual cracks would eventually coalesce into a

single crack, which then propagated more rapidly along the surface (and through

the thickness, as the increasing width of the opening at the surface would

indicate).

46

The appearance of the fatigue cracks in specimen 14F9 at 126, 136, 158, and

214 cycles is shown in Figure 3.45. Note the irregularity of the crack front,

typical of that observed in all of the cyclic test specimens. Although cycle

126 is reported as the time at which a fatigue crack \vas first observed in

specimen 14F9, the actual onset of visible cracking probably occurred slightly

earlier, as the previous time the test had been stopPed to examine for cracks

was at 105 cycles. It should be noted, also, that the testing of specimen 14F9

was stopPed at 230 cycles, at which time the c;ack shown in Figure 3.45 had a

total surface length of about six inches.

3.2.3.2 Discussion of Test Results

The test data for the four sets of fatigue tests are plotted in Figures

3.46 through 3.49. Figures 3.46 and 3.47 present the data for the 1i.L4X38 beam

specimens fabricated with flange angles of 3/8-inch and 1/2-inch thickness,

respectively. ~he data in Figures 3.48 and 3.49 represent the W8X21 beam

specimens with flange angle thicknesses of 5/16 inch and 3/8 inch, respectively.

In the figures, the total fatigue lives (number of complete cycles of

displacement, as identified in Figure 3.28) are plotted as a function of the

total nominal range of rotation in an individual cycle, the range of rotation

being calculated directly from the controlled actuator displacements. For each

of the four sets of tests, the data generally are seen to follow a linear

log-log relationship for the range of fatigue lives obtained. Using standard

regression analysis, Manson-Coffin (66-68) type fatigue life relationships, with

two empirically determined constants, have been generated for each of the four

individual sets of data, and are shown in the figures.

In order to develop a single expression capable of predicting constant

47

amplitude fatigue lives for specimens with varying geometries, a

non-dimensionalized nominal flange angle chord rotation index was calculated for

each of the sixteen specimens tested in this phase of the study. This chord

rotation index may be considered representative, proportionally, of t..he surface

strain in the tension flange angle of the test specimen at a particular .

displacement amplitude. The numerical values of the chord rotation index, R,

are reported in Table 3.13 for each of the test specimens. The applicability of

a relationship between R and Nf as a model for predicting constant amplitude

cyclic life expectancies is discussed in Section 4.2, where an analysis of the

cyclic test data is apresented. The efficacy of using such a fatigue life

relationship as a baseline for cumulative damage assessment under variable

amplitude displacement excursions is explored also in Section IV.

Tables 3.14 through 3.17 include the total hysteretic energy (summation of

moment-rotation hysteresis loop areas) accumulated by each of the specimens

during fatigue testing. Typical of structural elements subjected to

strain-based, low-cycle fatigue loading, the total accumulated hysteretic energy

for a specific type of connection was not found to be constant over the range of

fatigue lives considered in the investigation. From examination of the data in

Tables 3.14 through 3.17, there appears to be a general trend toward increasing

total hysteretic energy accumulation at the longer fatigue lifes corresponding

to the smaller jJer cycle loop areas. For example, with the W8X21 specimens

containing 3/8-inch thick flange angles (~able 3.16), the total hysteretic

energy increases fran 116.6 k-in. for specimen 8Fl (tested at a loS-inch

actuator displacement amplitude, and exhibiting a fatigue life of 10 cycles) to

approximately 308 k-in. for specimen 8F2 (which was tested as a displacement

amplitude of 0.5 inches, and had a fatigue life of 560 cycles). This trend is

not consistent, however, as the somewhat erratic pattern of energy accumulation

48

in the 14-inch beam fatigue test specimens indicates (Tables 3.14, 3.15). It is

apparent that additional data are required, covering a greater variety of

specimen geometries, and for tests conducted over a broader range of fatigue

lives, before any correlation between total energy absorption capacity and

fatigue performance can be attempted. It may be noted here, however, that a

linear log-log relationship between energy absorbed per cycle and fatigue life

expectancy has been established for the specimens tested in this study; such a

relationship offers promise as a means of predicting fatigue lives under

constant amplitude testing, and as a baseline for use in damage accumulation

models involving variable amplitude test excursions. The results of this

analytical phase of the study are examined in Section IV.

As one element of the constant amplitude cyclic test program, it was

intended that the separate stages of crack- initiation and propagation be studied

during each fatigue test. This turned out to be a rather formidable task

because, as noted earlier, the fatigue cracks first appeared as a series of

fine, hairline cracks separated from one another both along the width of the

flange angle and in elevation from the toe of the fillet in the angle. These

individual cracks would grow, at varying rates, until they eventually coalesced

into a single, irregular crack similar in appearance to the one shown in Figure

3.45d. Beyond that point, the crack, usually not symmetrically positioned on

the face of the flange angle, would extend quite rapidly to the limit length

established for that test specimen. It was quite difficult, then, to define a

representative crack growth history from among the several individual cracks

that first appeared on the specimen surface.

~he crack growth rate through the thickness of the affected flange angle

was also difficult to determine. To obtain depth measurements, the fatigue test

was stopped periodically with the top flange angle in the full tension position.

49

A O.C01-inch thick feeler gage was then inserted in the open crack to try to

probe to the crack root.* The results of these measurements have been analyzed

in a separate study (69), using a fracture mechanics crack growth model to

predict the growth pattern. The results of that investigation are not reported

here because it was felt that too few measurements were made to offer meaningful

interpretations of the correlation between through-thickness crack growth and

the observable surface crack growth behavior. Additional studies in this area

have been proposed for consideration in a subsequent study.

*Because of the complex geometries of the test members and the loadingapparatus, other potential non-destructive crack size measurement techniques,such as ultrasonic insPection, were not attempted.

50

IV. ANALYTICAL INVESTIGATION

4.1 Static Tests

In the initial study (n3) a number of analytical models were investigated

for their ability to predict the moment-rotation characteristics of semi-rigid

beam-to-column connections. It was determined that the initial stiffness of the

connection could be reasonably predicted by a simple model which models the legs

of the connecting angles as an assembly of beams. In addition, it was

determined that the complete moment-rotation curve was best predicted by an

empirical model which incorporates the physical and material characteristics of

the connection as parameters. These models were utilized in this study in an

attempt to predict the behavior of the specimens tested in the investigation.

In addition to these models, a three dimensional finite element model using

solid isopararnetric elements was developed in an attempt to predict the

moment-rotation curve for a typical connection.

4.1.1 Prediction of Moment-Rotation Behavior

4.1.1.1 Beam Model for Initial Stiffness

The initial stiffness of the connections under study is assumed to

correspond to the physical behavior indicated by Figure 4.1a: namely, that the

center of rotation of the connection is located at the point of contact of the

bottom flange of the beam with the compression flange angle at the end of the

beam. Also, it is assumed that the material is linearly elastic and that

displacements are small. Fram these assumptions, the horizontal displacement of

the heel of the top flange angle, X, (Figure 4.1a) is:

x

where:

= q,d (4.1)

Sl

q, = rotation of end of beam with respect to column. face

It is assumed that the vertical leg of the flange angle can be represented

by "stiff" beams and "flexible" beams as shown in Figures 4.la, 4.2a, and Figure

4.3, where:

A = assumed beam length, flange angle leg adjacent to column. face

~ = mcment at end A of beam AB

~A = mcment at end B of beam AB

F = shear force in beam (naninal bolt force)

It is assumed that the outstanding legs of the web angles can also be

represented by "stiff" beams and "flexible" beams, as shown in Figures 4.lb, and

4.2b and Figure 4.4, where:

AC

= assumed beam length, web angle leg adjacent to column. face

Pc = pitch, center-to-center spacing of bolts in legs of web angle

t.i = d i <p(i=I,2,3), displacement of heel of web angle for beam i

d. = distance fran assumed center of rotation to beam i1

52

01 = d/2 + (n-l)p /2

d2 = (n-2)d/2

d3 = d/2 - (n-l)p /2

F. = shear force in beam i1

(M_). = rncment at end C of beam i-,_D 1

(~). = rncment at end D of beam i1

Neglecting the bending rncment in the compression flange angle at the

assumed center of rotation, and including both flexural and shear deformation,

the total resisting moment of the connection is

M (4.2)

Mf = rncment contributed by flange angle

MC

= rncment contributed by web angle

where

MC(stiff) = rncment contributed by stiff portion of web angle

53

MC(flexible) = moment contributed by flexible portion of web angle

Considering equilibrium of the beam shown in Figure 4.2a and using ~he

slape deflection equations, it can be shown (71) that

Similarly considering the beams in Figure 4.2b:

M (flexible) =c

(4.3)

where:

Al = b t1

= t

1..2 B t 2 = t

1..3

= b t3 = tc c

1..4 = B t 4 = tc c

AS = B t s tc c

12E1.1 21

1.r. = 2 , = IT Pi t i1A .GA. 1

Sl 1

PI = (no. of bolts) x dw

P2 L-p1

P3 = dw

P4 1/2[L -d -(n-l)p ]c w c

Ps = Pc - dw

2A . = -3 p. t.

Sl 1 1i = 1,2,3,4,5

54

del = [2d+(n-l)p +L +d J/4c c w

de2 = [2d-(n-l)p -L -d2J/4c c

dfl = d/2+(n-2)p /2c

df2 = (n-2) (d-pc)/2

n = number of bolts in beam web (2 or 3)

Equations 4.1 through 4.4 were evaluated for the specimens of this

investigation which were tested statically. These equations were evaluated for

both inclusion and exclusion of shear deformation: the results are compared in

Table 4.1 with the corresponding test data. The test results presented in this

table are taken fran Tables 3.1 and 3.2, which include results fran both the

initial investigation and the current study.

4.1.1.2 Empirical Model

In the initial study (63) an empirical model was develOPed to predict the

moment-rotation behavior of semi-rigid beam to column connections of the type

investigated herein. The resulting equation is:

(4.5)

where

= rotation of beam with respect to column

M = manent developed by beam to column connection

K

55

and:

= t

= d

= I,

= b+t/2

= -1.12808769

= -1.2870455

= -.41454097

= -.69412158

= 1.34994572

=

=

=

.2232429 X 10-4

.1850728 X 10- 7

.3188976 X 10-11

Comparisons of Equation 4.5 with the results of the test investigations are

presented in Figures 4.4 through 4.18.

4.1.1.3 Three Dimensional Finite Element Model =Flange Angles

Observations fran all of the static tests inClicated that a major portion of

the connection Cleformation take place in the tension flange angle.

Consequently, both analytical and experimental studies were carried out to

determine its deformational characteristics. Pull tests were conducted to

56

determine experimentally the behavior of the flange angle (see Appendix B.l) and

a three dimensional finite element model of the flange angle was generated to

analytically determine its behavior (see Appendix B.3). The moment-rotation

characteristics for both the experimental and ana1ytical studies were determined

from the force-displacement relationships by assuming that the moment is

calculated by multiplying the force in the angle by the depth of the beam, and

that the rotation is calculated by dividing the flange angle displacement by the

depth of the beam. A canparison of the pull test data with the finite element

results is presented in Appendix B; a more detailed report of this study is

given in Reference 69.

4.1.2 Discussion

Comparison of the test results with the predicted initial slopes, Table

4.1, indicates that slopes predicted by Equations 4.1 to 4.4 are reasonable,

although not precise. The ccmparison also indicates that, in general, the

predicted values are too low for the thinner angles and too high for the thicker

angles for specimens using both the 3/4-inch diameter bolts and 7/8-inch

diameter bolts. It also appears that inclusion of shear deformation in the

prediction equations produces results that are generally more accurate.

Results obtained from the three-dimensional finite element analysis (see

Figure B.lO) for predicting the full moment-rotation curves were encouraging.

The program and model developed in this investigation produced results far more

accurate than the two-dimensional or three-dimensional models developed in the

initial investigation (63). This appears to indicate that material

nonlinearities are more significant than geometric nonlinearities in the

behavior of the flange angle. In addition, it appears that solid elements are

necessary to accurately model the behavior of the flange angles. Although the

S7

finite element analysis developed in this study is much more efficient than that

of the initial study, the effort required to predict the full moment-rotation

characteristics of the connections is still prohibitively large for design

purposes.

Results presented in Figures 4.4 to 4.18 indicqte that the empirical model,

F~ation 4.5, is a good predictor of the overall moment-rotation characteristics

of connections of the tyPe studied in this investigation. The equation is

simple and suitable for incorporation into computer programs for design purposes

or nonlinear analysis of frames with semi-rigid connections.

4.2 Fatigue Tests

4.2.1 Fatigue Life Predictions

This study employed the low cycle fatigue concept to generate baseline

fatigue data in terms of two different parameters. In low cycle fatigue, the

baseline fatigue data are usually expressed in terms of plastic strain. For

most metals, the plot of plastic strain versus the number of cycles to failure

produces a linear relationship on a log-log plot. This observation led Coffin

(f;6, 67) and Manson (68) to propose the following equation:

I:::.E .. c--E. EfCNf )

2

whereI:::.E plastic strainp =-2-

i fatigue ductilityE f =

Nf = total number of cycles to failure

c = fatigue ductility exponent

A number of researchers have concluded that if the strain at critical

58

locations in the structure could be measured, these measurements, together with

Miner's Rule (65), baseline fatigue data, and an appropriate cycle counting

method, could be used to make a reasonably good prediction of the life of

structural canponents under random loading. Methods like that of Neuber's Rule

(70) could be used to estimate local behavior if the external load is known for

siIllTJle specimens. However, for complex systems such as connections, predicting

strain at critical locations is not an easy task.

In order to establish baseline fatigue data in this study, four sets of

constant amplitude tests were conducted, as discussed in Section III. Then, in

order to develop a single expression for predicting fatigue lives for specimens

of varying geometry, a parameter, R, representative of the degree of deformation

in the tension flange angle, was considered. The parameter R, called the

"naninal flange angle chord rotation index," is defined as

where:

R = 2 [ (d+t)tan<pJg-d /2-tw

(4.6)

d = beam depth

t = flange angle thickness

= rotation of end of beam with respect to column face

d = diameter of washerw

59

g = gage in the flange angle; distance frcm the heel ofthe angle to the center of the bolt hole in the legof the flange angle attached to the column face

Referring to Figure 4.l(a) we can write

tan<j>

tana

x'" d+t

X

::: 7'"(g-_-:'"t-w/-r;2~--:-t""-)

(4.7)

(4.8)

Since one complete reversal goes through the relative beam to column

rotation twice, the total chord rotation index, R, is found as

R = 2tan a

Equations 4.7 to 4.9 are then combined to give Equation 4.6.

(4.9)

Figure 4.lq shows a plot of R versus the number of cycles to failure on a

log-log scale for the constant amplitude cyclic tests. The least squares fit of

a straight line through the data resulted in the following equation, which

relates R to the number of cycles to failure, Nf :

Nf

::: 1.868(R)-3.2531 (4.10)

At high displacement amplitudes, plastic strain is the predominant cause of

energy dissipation in semi-rigid connections. In this study the amount of

dissipated energy is approximated as the area of the hysteresis loop under the

60

moment-rotation curve. TO examine the effect of energy dissipation on fatigue

life, the energy per cycle at approximately midlife, E, was plotted against the

number of cycles to failure for all of the constant displacement amplitude

cyclic tests on a log-log scale, as shown in Figure 4.20. This figure indicates

that a linear relationship exists for each beam depth. Using a least squares

fit, the follCMing equations were obtained for beams of 14-inch depth and 8-inch

depth, respectively:

Nf

= 844.9(E)-1.20

Nf

= 298.65(E)-1.2639

where:

Nf = number of cycles to failure1 fatigue life for constant

displacement amplitude cyclic test

E = energy per cycle1 area of single hysteresis loop

The parameter E becanes an alternative to the parameter R, so that the

equations of Figure 4.20 could be considered as baseline fatigue relationships

which could be used with Miner's Rule to calculate the life of a specimen under

randan loading.

4.3 Variable ~litude Cyclic Tests

4.3.1 Prediction of Damage Accumulation

61

To predict the cumulative damage for the specbnens tested under the

low-to-high amplitude and high-to-low amplitude cyclic loadings, the chord

rotation index, R, was calculated as described above for each test displacement.

E,quation 4.10 was then used to predict the number of cycles to failure, Nf ,

and the cumulative damage ratio, n/Nf' was calculated using the number of

applied cycles, n, obtained fran the test data. The results of this analysis

are presented in Tables 4.2 and 4.3.

Cumulative damage in the variable amplitude cyclic tests was also predicted

using energy dissipation. The average hysteresis loop area, obtained fran the

tests, was chosen to represent the dissipated energy, E, and F,quations 4.11 and

4.12 were then used to predict the number of cycles to failure, Nf • The

cumulative damage was then calculated. The results of this analysis are

presented in Tables 4.4 and 4.5.

Comparison of Tables 4.3 and 4.4 with Tables 4.5 and 4.6 indicates that

slightly better predictions of cumulative damage are obtained using energy

dissipation, E, to predict fatigue life. Predictions based on the chord

rotation index, R, are seen to be smaller than those obtained using E.

Additional tests are needed, however, to further refine the proposed fatigue

life relationships, for application to a linear cumulative damage model, as

above, or to other models appropriate to the prediction of fatigue behavior

under randan loading conditions. Such tests have been proposed as an extension

of the present investigation.

62

V. SUMMARY AND CONCLUSIOOS

5.1. Static Tests

In an initial investigation (63) and in the current study, a combined total

of 18 bolted beam to column connections were tested under mo~otonic loading to

generate static moment-rotation relationships. The connections consisted of top

and seat angles bolted to the flanges of beam sections and a supporting stub

column, together with double web angles bolted to the beam web and colurnn

flange. AS'IM A36 steel was used for the members and connection elements; the

fasteners were ASTM A325 high-strength bolts. Eight of the test connections

were framed to Wl4X38 beam sections; of these, four were fastened with 3/4-inch

diameter bolts, the remaininq four with 7/8-inch diameter bolts. Ten

connections were framed to waX21 beam sections; seven of these were fabricated

using 3/4-inch diameter bolts, the remainder with 7/8-inch diameter bolts. For

the top and seat flange angles, the thickness, length, and gage (in the leg

attached to the column flange) were varied, together with the beam depth and

bolt diameter, to effect connections of varying stiffness. The thickness and

length of the web angles were varied also.

In all of the static tests, the connections exhibited a moment-rotation

response that became non-linear relatively early in the loading sequence. This

is attributed, primarily, to local yielding and eventual plastic hinge formation

at each toe of the fillet in the angle attached to the tension flange of the

beam. Another hinge developed in the vicinity of the bolt line in the leg of

the flange angle attached to the colurnn, together with progressive plastic

hinging in the outstanding legs of the web angles. Two of the specimens

63

fastened with 3/4-inch diameter bolts, 882 and 1482, and one specimen fastened

with 7/8-inch bolts, 8810, exhibited slip in the connection angles during

testing. These were the stiffer connections for each beam size, developing the

larger moments (and, correspondingly, larger bolt shear forces) in each test

group.

With the exception of specimens 882, 8810, and 1482, all of the test

connections were able to develop continually increasing moments through the full

range of rotations imposed during the tests. (The maximum rotations

corresponded to deflections exceeding four times the deflection, at allowable

load, of simply supported beams having the same section and span as those in the

test program). During the latter period of loading, a nearly constant or only

very gradually decreasing positive slope of the moment-rotation curve was

exhibited by each of the specimens (except 882). This nearly constant stiffness

at large deformations has been attributed to material strain hardening, and to

the consequences of progressive changes in the geanetr ies of the connecting

angles. The increasing deflection of the tension flange angle at large

connection rotations produces a continuous change in the internal force

distribution in the legs of the angle, with axial tension becaning an increasing

factor as the angle progressively "flattens out." The gradual transition fran a

predaninately flexural response to a canbined flexural-axial response, with the

accanpanying strain hardening, can thus account for the ability of the

connections to achieve considerably greater moment capacities, by a factor of at

least two, than those predicted by a simple flexural plastic hinge mechanism.

Fran the static tests, it has been found that the geometric parameters that

most significantly affect the static moment-rotation performance of the

semi-rigid connections investigated are: the depth of the beam section to which

the connection elements are framed; the thickness of the flange angles; and

64

the gage in the leg of the flange angles attached to the column flange.

Although the data are inconclusive, it appears that bolt diameter has a minimal

effect on the initial stiffness of the connections; however, increasing the

bolt diameter effects a corresponding increase in moment capacity at large

rotations (beyond about 4XIO-3 radians). Variations in the length of the

flange angles, and in the length and thickness of the web angles, had a less

pronounced effect on connection response than the other parameters.

An analytical model developed to predict the initial stiffness of the

semi-rigid connections has been found to correlate reasonably well with the test

results for the specimens considered in the investigation. The model represents

the legs of the connection angles as an assembly of "stiff" and "flexible" beam

elements, the stiff elements associated with the segments of the angles confined

by the connecting bolts, and the flexible elements representinq those segments

between the bolt lines and at each end of the angles.

Using the results of the parametric test program, an empirical model has

been generated to predict the complete non-linear moment-rotation behavior of

the test connections. With the exception of the stiffest connections in both

the Wl4X38 and waX21 test series, this model offers reasonable approximations to

the rnament-rotation curves of the connections up to the limits of rotation

examined in the test program. For the stiffest connections of each beam size,

the model underestimates the moments developed at the larger connection

rotations.

In a pilot study, tests were conducted of two specimens comprised of flange

and web angles welded to Wl4X38 beam sections and bolted to the flanges of the

supporting stub column. AWS E70 electrodes were used for the angle to beam

welds; 7/8-inch diameter A325 bolts were used in the attachment of the angles

to the stub column. For specimens of canparable geanetry, the combined

65

bolted-welded connections exhibited higher initial stiffnesses than the

corresponding all-bolted specimens. This was attributed to the greater

restraint against movement of the heel of the angle at the end of the beam

flanges occasioned by the presence of the weld return on the top and seat

angles. In addition to the higher initial stiffness, the bolted-welded

specimens developed moderately larger moments than those in the all-bolted

specimens at comparable rotations. These results are considered preliminary,

however, and not necessarily indicative of expected relative performances when a

more complete range of section depths, and flange and web angle sizes are

considered. Such tests have been proposed as Part of a continuation of the

current investigation.

5.2 Cyclic Tests

5.2.1 Variable Amplitude Block Tests

Nine specimens, with geometries comparable to those of the static test

ser ies connections, were tested under var iable amplitude cyclic loadings. Five

of the specimens were framed to the Wl4X38 beam sections, the remaining four to

the waX2l beams. The other geometric parameters that were varied were the bolt

diameter and the thickness of the top and seat flange angles.

Seven of the specimens were tested under low-to-high amplitude block

displacement histories~ the other two were subjected to high-to-low amplitude

block loadings. The tests were conducted using full reversal of displacement to

generate data indicative of the displacement extremes to which the connections

could be subjected under seismic loading. The test procedure consisted of

cycling sinusoidally between controlled limits of displacement, while monitoring

66

the range in mcment and the local displacements (rotations) developed during

each cycle. The displacement-time histor ies followed a sequential block loading

pattern, with a total of 12-15 cycles applied in each block before the amplitude

was altered (increased in the low-to-hiqh amplitude tests, decreased in the

high-to-low amplitude tests).

Stable hysteresis loops were established, for the l4-inch test specimens,

within a few cycles after an increase in amplitude was llnposed relative to the

preceding displacement under the low-to-high amplitude block loading pattern.

For several of the 8-inch deep beam connections, a continual, though small,

softening (loss of mcment) was noted for each progressive cycle at a constant

amplitude; however, the succeeding hysteresis loops were otherwise similar in

appearance.

For each of the test specimens, the mcment-rotation behavior was

characterized by loops of continually decreasing slope for relatively small

displacements in the non-linear range. In contrast, the hysteresis loops

exhibited a moderate "pinching" effect at larger amplitudes, the degree of

pinching being more pronounced in the Wl4X38 beam connections than in the waX2l

members. This increase in connection stiffness observed tOYlard the tip of each

hysteresis loop may be attributed, in large measure, to the changing geometry of

the connection during each half cycle of loading. As rotation progresses,

following a reversal in the direction of the mcment at the connection, there is

a period when both flange angles are drawn away fran the column. With the

connection in this configuration, the slope of' the mcment-rotation curve

decreases as rotation proceeds. Eventually, the vertical leg of the compression

flange angle folds back into full bear ing on the column flange, with the

connection exhibiting a concurrent increase in relative stiffness (pinching of

the M-</> curve).

67

Each of the cyclic tests culminated in the formation and subsequent

propagation of fatigue cracks at the toe of the fillet in one or more of the

beam flange angles. The tests were terminated when cracking had progressed at

least partially across the face of the angle at the fillet; no tests were

extended to the point of rupture of a connection element. The connections

maintained ductile behavior during the full extent of the cyclic tests, and

exhibited only modest loss of maximum moment from the time fatigue cracking was

noticed to the termination of the test. No slip was observed during the cyclic

tests, nor was there any local buckling of the connection elements.

In general, for the low-to-high amplitude block tests, it was found that,

with the exception of the first cycle following an increase in displacement

amplitude, the hysteretic energy absorbed per cycle remained reasonably constant

at each amplitude. Further, the ductile behavior of the connections was evident

by the increase in hysteresis loop area with each succeeding increase in

displacement amplitude, even with pinching evident at the larger amplitudes.

As a result of the general stability of the connections at large rotations,

and of the ductility of the connection elements, it was found that the overall

energy absorption of like connections increased directly with the depth of the

beam sections to which they were attached. The hysteretic energy absorption

performance of sPeCimens framed to a particular beam section, however, exhibited

limited consistency. This was attributed largely to the sensitivity of total

energy absorption capacity to the time of formation, and rate of propagation of

fatigue cracks in the connection elements, particularly the top and seat flange

angles. Fatigue crack initiation, in turn, is influenced by such factors as

surface irregularities formed during the rolling or fabrication of the

connection angles, residual stresses introduced during the erection process, and

stress concentrations at the toe of the fillet in each leg of the angles.

5.2.2 Constant Amplitude (Fatigue) Tests

68

Sixteen specimens were tested under constant displacement amplitude cyclic

loading. Nine of the specimens were framed to the Wl4X38 beam sections, the

remaining seven framed to the W8X2l beams. For each of the beam sizes, two

thicknesses of the top and seat flange angles were used in the test members.

The bolt diameter was 7/8 inch for all specimens in this test series. With the

exception of several specimens which were initially subjected to a number of

half cycles (null position to maximum displacement and return), the constant

amplitude tests were conducted using full reversal of controlled displacement.

The displacement amplitudes chosen resulted in fatigue lives ranging from nine

to approximately 3500 cycles to "failure" (failure was defined as the number of

cycles at which the longest fatigue crack had extended over approximately

three-fourths of the width of the flange angle).

As with the variable amplitude tests, the specimens tested in the constant

displacement amplitude series exhibited fatigue cracking that initated at the

toe of the fillet in one or more of the beam flange angles. Again, the observed

hysteresis loops remained quite stable throughout each test, with only nominal

loss of moment evident even toward the end of a test, when fatigue cracks had

progressed to some depth through the thickness of the flange angle.

For each of the four test sets in the constant amplitude series (two

thicknesses of flange angle framed to both Wl4X38 and v"18X2l beam sections), it

was found that a linear log-log relationship exists between the cyclic range of

rotation in the connection and the resultant total fatigue life. To develop a

single expression capable of predicting constant amplitude fatigue lives for

specimens of varying geometry, a nominal chord rotation index, R, indicative of

the magnitude of the surface strain in the tension flange angle, was determined

69

for each of the sixteen test specimens in the series. For the combined data, a

linear lo:j-log expression was generated relating the chord rotation index, R, to

the total number of cycles to failure, Nf :

Nf

= 1.868(R)-3.2531

At large displacement amplitudes, plastic strain is the predominant means

of energy dissipation in the semi-rigid connections. In this study, the amount

of dissipated energy is approximated as the area of the hysteresis loops under

the moment-rotation curve. To examine the effect of energy dissipation on

fatigue life, the energy per cvcle, E, measured at approximately mia-life, was

compared to the number of cycles to failure for each of the constant amplitude

test specimens. Again, a linear expression, on a log-log scale, was found to

provide a reasonably good relationship between energy per cycle and total

fatigue life, for each of the beams sizes individually:

Nf

844.9(E)-1.20

Nf

298.65(E)-1.2639

(14-inch beam section)

(8-inch beam section)

The low cycle, constant amplitude fatigue relationships between Nf and R

or E were then applied to Miner's linear damage accumulation model in an attempt

to predict the behavior of the specimens subjected to the variable amplitude

cyclic displacements. Cumulative damage summations for both tne low-to-hiqh

amplitude and the high-to-low amplitude block cyclic tests ranged from 0.4279 to

1. 2848 • In general , slightly better predictions of cumulative damage were

obtained usinq energy dissipation, E, to predict fatigue life, than were

obtained fram the fatigue relationship based on the chord rotation index.

Additional data, leading to more refined fatigue life relationships, are needed

to Dmprove variable amplitude

other cumulative damage models;

of the present investigation.

70

fatigue life predictions using Miner's Rule or

such tests have been proposed as a continuation

REFERENCES

1. Takanashi, K., and Ohi, K., "Shaking Table Tests on 3-Story Bracedand Unbraced Steel Frames," Proc. of the Eighth World Conference onEarthquake Engineering, Vol. VI, San Francisco, CA, U.S.A., ,July 1984.

2. Plugge, H.B., and Walpole, W.R., "The Tenacity of Bolted Beam End­Plate to Column Connections Under Simulated Seismic Loading."Report 83-2, Dept. of Civil Engineering, University of Canterbury,Christchurch, New Zealand, September 1983.

3. Kato, B., "Beam-to-f'..-olumn Research in Japan," Journal of theStructural Division, ASCE, Vol. 108, No. ST2, Proc. Paper IF,852,February 1982.

4. Krawinkler, H. and Pooov, E.P., "Seismic Behavior of McrnentConnections and Joints," ,Journal of the Structural Division, ASCE,Vol. 108, No. ST2, Proc. Paper 16865, February 1982.

5. Popov, E.P., "Seismic Steel Framing Systems for 'T'all Buildings,"Engineering Journal, AISC, 3rd Quarter, ~Tol. 19, No.3, 1982.

6. Rentschler, G.P., Chen, W. F., and Driscoll, G.C., "Beam-to-ColumnWeb Connection Details," ,Journal of the Structural Division, ASCE,Vol. 108, No. ST2, Proc. Paper 16880, February 1982.

7. Whittaker, D., and Walpole, W.R., "Bolted End Plate Connections forSeismically Designed Steel Frames," Report 82-11, Dept. of CivilEngineering, University of Canterbury, Christchurch, New Zealand,June 1982.

8. Witteveen, J., Startk, J.W.B., Bijlaard, F.S.K., and zoetemiejer,P., "Welded and Bolted Beam-to-Column Connections," Journal of theStructural Division, ASCR, Vol. 108, No.ST2, Proc. Paper 16873,February 1982.

9. Bijlaard, F.S.K., "Requirements for Welded and Bolted Beam-to-ColumnConnections in Non-Sway Frames," ed. Howlett, ,T .H., ,Jenkins, W.M.,and Stainshy, R., ,Joints in Structural Steelwork, Proceedings of theInternational Conference, Teesside Polytechnic, Middlesbrough,England, April 1981.

10. Chen, W.F., and Patel, K. 'IT., "Static Behavior of Beam-to-ColumnMcrnent Connections," Journal of the Structural Division, ASCE,Vol. 107, No. ST9, Proc. Paper 16512, September 1981.

11. Johnstone, N.D., and Walpole, W.R., "Bolted End Plate Beam toConnections Under Earthquake Type Loadings," Report 81-7, Dept. ofCivil Engineering, University of Canterbury, Christchurch, NewZealand, September 1981.

71

12. Grundy, P., Thanas, ToR., and Bennetts, D., "Beam-to-Colrnnn ManentConnections," ,Journal of the structural Division, ASCE, Vol. 106,No. STl, Proc. Paper 15108, January 1980.

13. Popov, E.P., "An Update on Eccentric Seismic Bracing," EngineeringJournal, AISC, 3rd Quarter, Vol. 17, No.3, 1980.

14. Rentschler, G.P., Chen, W.F., and Driscoll, G.C., "Tests ofBeam-to-Colrnnn Web Manent Connections," Journal of the StructuralDivision, ASCE, Vol. 106, No. ST5, Proc. Paper 15386, May 1980.

15. Krishnamurthy, N., .Juang, H.-'T'., and .Jeffrey, "Analytical M- ~

Curves for End-plate Connections., Journal of the StructuralDivision, ASCE, Vol. 105, No. STl, Proc. Paper 14294, January 1979.

16. Roeder, C.W., and Popov, E.P., "Eccentrically Braced Steel Framesfor Earthquakes," Journal of the Structural Division, ASCE, Vol. 105,No. 8'l'11, Proc. Paper 14982, November 1979.

17. Krawinkler, H., "Shear in Bearn-Colrnnn Joints in Seismic Design ofSteel Frames, Engineering Journal, AISC, 3rd Quarter, Vol. 15,No.3, 1978.

18. Krishnamurthy, N. "A Fresh Look at Bolted End-Plate Behavior andDesign," Engineering Journal, AISC, 2nd Quarter, vol. 15,No.2, 1978.

19. Roeder, C.W., Popov, E.P., "Eccentrically Braced Steel Frames forEarthquakes," Journal of the Structural Division, ASCE, vol. 104,No. ST3, Proc. Paper 13619, March 1978.

20 • Krawinkler, H., Bertero, V.V., and popov, E. P., "InelasticBehavior of Steel Beam-to-Colrnnn Subassemblages, "ReJ:X)rt No.UCB/EERC 71-7, University of California, Berkeley, California,lq77.

21. Parfitt,.1., Jr., and Chen, W.F., "Tests of Welded SteelBeam-to-Column Manent Connections, ".Journal of the StructuralDivision, ASCE, Vol. 102, No. ST1, Proc. Paper 11854, January1976.

22. Hanson, R.D., "Characteristics of Steel Members and Connections,"Proc. of the U.S. Nat. Conference on Earthquake Engineering,EERI, Ann Arbor, Michigan, June 1975.

23. Popov, E.P., Bertero, V.V. and Chandramouli, S., "HystereticBehavior of Steel Columns," Report No. TJCB/EBRC 75-11, Universityof California, Berkeley, California, September 1975.

24 • 'l'arpy, T.S., and Lindsey, S.D., "~rimental 'rest Results onEnd-Plate Manent Connections," Report No. CE-AISE-l, CivilEngineering Department, Vanderbilt University, 1975.

72

25. Bertero, V.V., Krawinkler, H. and Popov, E.P., "Further Studies onSeismic Behavior of Steel Bearn-Column Subassemblies," Report No.UBC/EERC 73-27, University of California, Berkeley, California,December 1973.

26. Carpenter, L.D., and Ly, L.-W., "Reversed and Repeated Load Testsof Full-Scale Steel Frames," Bulletin No. 24, AlSI, April 1973.

27. Popov, R.P., and Bertero, V.V., "Cyclic Loading of Steel Beams andConnections," Journal of the Structural Division, ASCE, VoL 99,No. ST6, Prac. Paper 9790, June 1973.

28 • Bertero, V.V., Popov, E.P ., and Krawinkler, H., "Bearn-ColumnSubassemblages Under Repeated roading," Journal of the StructuralDivision, ASCE, VoL 98, Prac. Paper 8915, May 1972.

29. popov, E.P., and Stephen, R.M., "Cyclic Loading of Full-Sized SteelConnections," Bulletin No. 21, ArSI, February 1972.

30. Krawinkler, H., Bertero, V.V., and Popov, E.P., "Inelastic Behaviorof Steel Beam-to-Column Subassemblies," Report No. UBC/EERC 71-7,University of C~lifornia, Berkley, California, October 1971.

31. Ostrander, J .R., "An Experimental Investigation of End PlateConnections," Master's Thesis, University of Saskatchewan,Saskatoon, Saskatchewan, Canada, 1970.

32. Bertero, V.V., "Seismic Behavior of Steel Beam-to-Column ConnectionSUbassemblages," Prac. of the Fourth World Conference on EarthquakeEngineering, \Tol. II, Santiago, Chile, January 1969.

33. Naka, T., Kato, B., Watabe, M., and Nakao, M., "Research on theBehavior of Steel Beam-to-Column Connections on EarthquakeEngineering," Prac. of the Fourth World Conference on EarthquakeEngineering, Vol. II, Santiago, Chile, January 1969.

34. popov, E.P., and Pinkney, R.B., "Reliability of Steel Beam-to­Column Connections Under Cyclic Loading," Prac. of the FourthWorld Conference on Earthquake Engineering, VoL II, santiago, Chile,,January 1969.

35. Popov, E.P., and Pinkney, R.B., "Cyclic Yield Reversal in SteelBuilding Connections," ,Journal of the Structural Division, ASCE,Vol. 95, No. ST3, Prac. Paper 6441, M~rch 1969.

36. Galambos, T.V., "Deformation and Energy Absorption Capacity of SteelStructures in the Inelastic Range," Bulletin No.8, AlSI, March 1968.

37. Hanson, R.D., "Canparison of Static and Dynamic Hysteresis Curves,"Journal of the Engineering Mechanics Division, ASCE, VoL 92,No. EMS, Prac. Paper 4949, October 1966.

38. Douty, R.T., and McGuire, W., "High Strength Bolted Manent

73

Connections," Journal of the Structural Division, ASCE, Vol. 91,No. ST2, Prac. Paper 4298, April 1965.

39. Beedle, L.S., and Christopher, R., "Tests of Steel ManentConnections," Engineering Journal, AISe, 3rd Quarter, Vol. 1,No.3, October 1964.

40. Naka, T., Kato, B., Watabe, M., Tanaka, A., and Sasaki, T.,"Research on the Behavior of Steel Beam-to-Column ConnectionsSubjected to Lateral Force," Report No.3, Trans. of theArchitectural Inst. of Japan, Vol. 103, October 1964.

41. Pray, R.F., and Jensen, C.D., "Welded Top Plate Beam-ColumnConnections," Welding Journal, Vol. 35, No.7, July 1956.

42. Brandes, J .L., and Mains, R.M., "Report of Tests of Welded Top­plate and Seat Connections," 'J:'he Welding Journal, Vol. 24, No.3,March 1944.

43. Johnson, B.G., and Deits, G.R., "Tests of Miscellaneous WeldedBuilding Connections,'· Welding Journal, ,January 1942.

44 • Rathbun, J.C., "Elastic Properties of Riveted Connections,"Transactions, ASCE, Vol. 101, 1936.

45. "Second RelX)rt of the Steel Structures Research Camnittee," GreatBritain, Dept. Sci. Ind. Res., London, 1934.

46. Chen, C.K., "Seismic Analysis of Building Frames With SemirigidConnections,'· Prac. of the Eighth World Conference on EarthquakeEngineering, Vol. V, San Francisco, CA, U.S.A., July 1984.

47. Stelmack, T.W., "Analytical and Experimental Response of Flexibly­Connected Steel Frames,'· ReI?Ort to AISI Under Project No. 199,Dept. of Civil, Environmental, and Architectural Engineering,University of Colorado, Boulder, Colorado, February 1983.

48. Wales, M.W., and Rossow, E.C., "Coupled Manent-Axial ForceBehavior in Bolted Joints," Journal of the Structural Division,ASCE, Vol 109, No.5, May 1983.

49. Ackroyd, M.H., and Gerstle, K.H., "Behavior of Type 2 Steel Frames,Journal of the Structural Division, A..SCE, Vol. 108, No. ST7, Prac.Paper 17207, July 1982.

so. Marley, M.H., "Analysis and Tests of Flexibility-Connected SteelFrames,'· ReI?Ort to AISI Under Project No. 199, Dept of Civil,Environmental, and Architectural Engineering, University of Colorado,Boulder, Colorado, March 1982.

51. Moncarz, P.D., and Gerstle, K.H., "Steel Frames With NonlineaarConnections," Journal of the Structural Division, ASCE, Vol. 107,No. ST8, Prac. Paper 16440, August 1981.

74

52. Graves, R.W., Biggs, J .M., and Irvine, H.M., "The Effect ofConnection Flexibility on the Seismic Response of Welded OpenSteel Frames," Pub. No. R80-25, School of Engineering,Massachusetts Institute of Technology, Cambr idge, Mass., June1980.

53. Ackroyd, M., and Gerstle, K., "Strength and Stiffness of Type 2Steel Frames," Report Prepared for the American Iron and SteelInstitute Undner Projet No. 199, Department of Civil, Environmentaland Architectural Engineering, University of Colorado, Boulder,Colorado, July 1977.

54. American Iron and Steel Institute, "Type 2 Construction With WindManent Connections: A Return to Simplicity," AISI, Washington,D.C., 1976.

55. Kahl, T.L., "Flexibility-Connected Steel Frames," Report Preparedfor the American Iron and Steel Institute Under Project No. 199,Department of Civil, Environmental, and Architectural Engineering,University of Colorado, Boulder, Colorado, December 1976.

56. Frye, M.J., and Morris, G.A., "Analysis of Flexibility-ConnectedSteel Frames," Canadian Journal of Civil Engineering, Vol. 2, 1975.

57. Ronstad, K.M., and Sabramanian, C.V., "Analysis of Frames WithPartial Connection Rigidity," ~Tournal of the Structural Division,ASCE, Vol. 96, No. STll, Proc. Paper 7664, November 1970.

58. Monforton, G.R., and Wu,T.S., "Matrix Analysis of Semi-RigidlyConnected Frames," Journal of Structural Division, ASCE, Vol. 89,No. ST6, Proc. Paper 3713, December 1963.

59. Kaneta, K., Kohzu, 1., and Nishizawa, H., "Cumulative Damage ofWelded Beam-tO-Column Connections in Steel Structures Subjected toDestructive Earthquakes," Proc. of the Eighth World Conference onEarthquake Engineering, Vol. VI, San Francisco, CA, U.S.A., July1984.

60. Krawinkler, H., "Damage Assessment in Steel Structures Subjectedto Severe Earthquakes," Proc. of the Eighth World Conference onEart..hquake Engineering, Vol. IV, San Francisco, CA, U.S.A.,July 1984.

61. Nash, W.A., Chon, V.T., and Hutchinson, C.E., "Cumulative DamageEffects in Seismic Structures," Proc. of the Fifth World Conferenceon Earthquake Engineering, Vol. 2, Rane, Italy, June 1974.

62. Suidan, M.T., and Eubanks, R.A., "Cumulative Fatigue Damage inSeismic Structures," Journal of the Structural Division, ASCE,Vol. 99, No. ST5, Proc. Paper 9749, May 1973.

63. Altman, W.G., .Jr., Azizinamini, A., Bradburn, J.H., and

7'f CI../

Radziminski, .T .B., "Manent-Rotation Characteristics of Semi-RiqidSteel Beam-ColLUm Connections," Structural Research Studies, ­Department of Civil Engineering, University of South Carolina,Columbia, S.C., June 1982.

64. American Institute of Steel Construction, Manual of SteelConstruction, Eighth Edition, AISC, Inc., Chicago, Illinois,1980.

65. Miner, M.A., "CLUTIulative Damage in Fatigue," Transactions,ASME, Vol. 12, No.3, September 1945.

66. Tavernelli, J.F., and Coffin, L.F., Jr., "Experimental Supportfor Generalized F.quation Predicting LoN Cycle Fatigue,"Transactions, ASME, J. Basic Engr., Vol. 84, NO.4, December1962.

67. Coffin, L.F., ,Jr., "A study of the Effects of Cyclic ThermalStresses on a Ductile Metal," Transactions, ASME, Vol. 76,1954.

68. Manson, S.S., "Behavior of Materials Under Conditions of ThermalStress," NACA TN 2933, 1954.

69. Azizinamini, A., "Cyclic Characteristics of Bolted Semi-RigidSteel Beam to COlLUm Connections," Ph.D. Dissertation,University of South Carolina, Columbia, S.C., 1985.

70. Neuber, H., "Theory of Stress Concentration for Shear-Strainedprismatic Bodies with Arbitrary Non-Linear Stress-Strain Law,"Journal of Applied Mechanics, Transactions, ASME, Vol. 83, 1961.

71. Azizinamini, A., "Monotonic Response of Semi-Rigid Steel Beamto Collmm Connections," M.S. Thesis, University of SouthCarolina, Columbia, S.C., ,July 1982.

75

APPENDIX A

NOOENCLATURE

76

77

APPENDIX A

NCMENCLATURE

Symbol

A = cross-sectional area·of flange angle, t X L

B = B' - t/2

B' = overall length of leg of flange angle adjacent to column face

Bc = B'c - tci2

B' c = overall length of leg of web angle adjacent to column face

C. = coefficients in empirical equation of static M- ~ curve1

D = d + t/2

E = Modulus of Elasticity of steel, 29000 ksi

E = energy per cycle; area of single hysteresis loop

F = shear force in beam representative of angle leg

G = shear modulus of steel

K

Lc

M

Mc

= PlcxlP a2 --- P an2 n

= overall length of flange angle

= overall length of web angle

= resisting moment transferred from beam to column through connection

= moment in beam representing connection angle

= moment contribution of web angles

= moment in connection at elastic limit

= moment contribution of flange angle

= yield moment of connection

= fatigue life for constant displacement amplitude cyclic test

= parameters affecting relationship between M and ~

Symbol

R

S

z

a

b

g

k

n

n

p

= ncminal flange angle chord rotation index, 2 [ (d;:1w7~t<j> ]

= elastic section modulus

= plastic section modulus

= g - k

= g - dtl2 - t/2

= gc - dtl2 - tcl2

= depth of beam

= diameter of bolt

= diameter of bolt hole

= diameter of washer

= gage in flange angle; fram heel of angle to center of bolt holein leg adjacent to colt.nnn face

= gage in web angle; fram heel of angle to center ofbolt hole

= distance from heal of angle to toe of fillet, flange angle

= distance fram heel of angle to toe of fillet, web angle

= number of applied constant amplitude displacement cycles

= number of bolts in beam web

= pitch, center-to-center spacing of bolts in leg of flange angleadjacent to colt.nnn face

= pitch, center-to-center spacinq of bolts in each leg of web angle

78

t = thickness of flange angle

t c = thickness of web angle

ai = exponents in empirical equation of static M-<j> curve

y = length of flange angle used in finite element analysis

~ = displacement of heel of flange angle

Symbol

E:Y

A

Ac

(Jy

<P

= strain at initial yieldng in connection angles

= length of beam representative of flange angle leg adjacent tocolumn face

= length of beam representative of web angle leg adjacent tocolumn face

= stress at initial yielding in connection angles

= .rotation of end of beam with resPect to column face

79

80

lp

L

rr •

, I j

-, . -,ftt») I (t»)-

j --" ./,,., c::l

n:l.0 en.I-

~

•.:.t:. -I-'

,- Be In/- ..... {t: '\~@\ ®J- j_/ '--

I I u0-

I@' -,,+j I (f) J- U

--l.... '.-..I t.. 9c I

-0

J"u

0--I@~ I@ _ ,....... ;,/ ,_I

tcJU: B1

~C

,.- "',"." ~~ ~J}ii.:"):"_)'??_-'%"'If""'C:(;"/;'_" __~':J_,,,,', .;,2...§i__ 0'.'I, ~"~~"-""'~""""""""" __ '~;~""'_---'-"~----1

FIG. A1 NOMENCLATURE FOR CONNECTION ELEMENTS

APPENDIX B

THREE DIMENSIONAL FINITE E.LEMEN'r

Ar-.1ALYSIS OF roUBLE ANGLE puu.

TEST SPECIMENS

81

82

APPENDIX B

B.I Pull Tests

The main objective of the pull tests was to investigate the behavior of the

flange angle only. A total of two pull tests was conducted. The general

configuration of these sPec~ens is shown in Figure B.I.

Flange angle thicknesses of 1/2-inch and 3/8-inch were investigated. An

lluposed displacement rate of 0.624 inch/minute was applied to the sPec~ens

through the actuator ram, which was attached to the center plate, as shown in

Figure B.I. Figure B.2 shows the load vs. the average displacement obtained

fran the nlDI's attached to the two flange angles for SPec~ens with a flange

angle thickness of 1/2-inch. For the purpose of analysis, the exper~entally

obtained load-deforrnation curve was approximated by the smooth curve. It should

be noted that Figure B.2 depicts the load-deforrnation curve for two flange

angles attached as shown in Figure B.I. The assumption was made that the

actuator load was evenly carried by the two flange angles, allowing for the load

displacement curve for one flange angle to be obtained as shown in Figure B.4.

Figure B.3 shows the actuator load vs. the average of the two LVIYl'

displacements for SPec~ens with 3/B-inch thick flange angles, together with a

smooth approx~ated curve for the purpose of analysis. Because of actuator load

limitations, the test was discontinued when a load of approximately 50 kips had

been applied to the spec~en. Again, the assumption was made that each flange

angle carries half the actuator load, to obtain the load-displacement curve for

one flange angle as in Figure B.4.

B.2 SPeC~ens With Top and Bottan Flange Angles

In addition to the pulltests , tests were conducted of two sPecimens

83

canprised of top and seat angles attached to Wl4X38 beam sections. The purpose

of these tests was to study the ability of the results of the pull tests, and of

a finite element analysis (discussed in Section B.3), to predict the

moment-rotation characteristics of a connection with top and seat flange angles

only. The test configuration for the specimens with top and bottom flange

angles was identical to the specimens tested in the present investigation,

Figure 2.2a, except that the web angles were omitted.

The results of tests for moment-rotation obtained for specimens with

1/2-inch thick flange angles and 3/8-inch flange angles are shawn in Figures B.9

and B.lO, respectively.

B.3 Three Dimensional Finite Element Analysis

The finite element analysis program used in the analytical study is

described in Reference 69. The model used in the analysis was developed. from a

portion of the flange angle, as shawn in Figure B.5, by considering approximate

boundary conditions and conditions of symmetry. Instead of modeling the entire

length of the horizontal leg, only 1.75 inches of the 1/2-inch thick flange

angle, and 1.625 inch of the 3/8-inch thick flange angle was modeled, since test

observations indicated no appreciable deformation in the remainder of the

horizontal leg.

A model was generated for both the 1/2-inch thick and 3/8-inch thick

angles, each model consisting of 150 twenty-node isoparametric elements

producing a total of 993 nodes, as shown in Figure B.6. For simplicity, the

bolt hole in the vertical leg was modeled as a square with an area equivalent to

that of a circular hole having a l5/l6-inch diameter.

Symmetry conditions were imposed on Face A by restraining displacements in

the Y direction on this face. Bolt head restraint was simulated by restraining

84

all displacements for nodes at the intersection of the bolt hole and the front

face of the angle. Displacements in the Z direction were restrained along line

B-B and displacements in the X direction were restrained along line A-A.

Loading on the !rodel was created by imposing uniform displacement of Face B

in the X direction, as shown in Figure B.7, in small increments.

The stress-strain relation used in the analysis was obtained by conducting

tension tests on sample coupons of flange angles used in the pull tests. The

results were approximated by the bi-linear relationship indicated by Figure B.8.

Canparisons of the rncment-rotation diagrams obtained fran the pull tests,

the finite element analysis, and the connection tests are shown for 1/2-inch and

3/B-inch thick flange angles in Figures B.9 and B.IO, respectively, for a 14X38

beam section. For the 1/2-inch thick flange angles, the initial slopes fran the

finite element analysis, pull test, and connection test are 430,000, 365,000,

and 840,000 k.-in./radian, respectively, while for the 3/8-inch thick flange

angles, the slopes were 209,000, 338,000, and 135,000 k.-in./radian,

respectively.

FIG. 8.1 GENERAL CONFIGURATION OF PULL TEST SPECIMEN

85

86

o·ill

lJ')

I

O n?U'l. \,-,,_ .u

TEST RESULT

APPROXIMATED -...

'\I

·CO:::r

c, ,

-. I i

I-J__ . CJ C50 - . nOlO 0 . 004 0 o. 0090 0 . 0 140 C. C~ ,90AVERAGE OF LVDT DISPLACEMENTS, INCHES

·o:::r

o

·CO

~c...... .~("\J

.. (T)Cl<o-l

0:::

~C< .~::T~("\J

FIG. 8.2 LOAD DEFORMATION CHARACTERISTICS OF PULL TESTSPECIMEN (FLANGE ANGLE THICKNESS OF %-INCH)

87

·CDLJ")

c·CO

::r -

·~l

~c...... .~0J

" (Y")a<:::(o......l

0:::

~C

~ ::fl'U0J<:::(

c:lCD-;<-1 I

I

I!

c

c

APPROXIMATED

TEST RESULT

C.CJOO,,

" "'10.' i I' I!.......' .. ~-,-:

I0.060

In flQOU.'..J'-J~

AVERAGE OF LVDT DISPLACEMENTS, INCHES

FIG. 8.3 LOAD DEFORMATION CHARACTERISTICS OF PULL TESTSPECIMEN (FLANGE ANGLE THICKNESS OF %-INCH)

88

o,

OJN

0» 120

a...-_ 1/2 INCH FLANGE ANGLE

3/8 INCH FLANGE ANGLE__~

o

a

AiI

I01'1

CD I II !

I !c I j

'11

="11o I'-i:tSr-----,-I-----r-(----,.-1-------;!r-------ri------,c .0.000 0.020 0.040 0.060 O.OSG O.ICO

,:::r

(/)c........~o

AVERAGE OF LVDT DISPLACEMENTS, INCHES

FIG. 804 LOAD DEFORMATION CHARACTERISTICS OFPULL TEST SPECIMENS.

89

o

o.....

o­_"'-::a.

-~-C5.--...-

FIG. 8.5 PORTION OF THE FLANGE ANGLE MODELED FOR FINITEELEMENT ANALYSIS

t.O o

y

.-----B

FACE

A~

.~co1S

.~co1S

I\\S

.31Q

.I\\

S.

~ (Y)

z

~ (Y)

(Y)

00

LO

N .......

LO

LO

N .......

·25

·5·2

5·5

FIG

.8

.6F

INIT

EE

LE

ME

NT

MO

DE

LO

FF

LA

NG

EA

NG

LE

FO

R%

AN

D%

INC

HT

HIC

KF

LA

NG

EA

NG

LE

for

flg

.an

gle

thic

knes

s

91z

FIG. B.7 LOADING DIRECTION FOR FINITE ELEMENT MODEL

(J

e:

FIG. B.8 STRESS-STRAIN DIAGRAM OBTAINED FROM COUPON TESTUSED IN FINITE ELEMENT ANALYSIS OF FLANGE ANGLE

92

·oo::r-·o

o('\l

·ooo-·

! :1~ .-: iI.1J '- I:E: C-lo c..:J I:E I

a I A

~~. I. !III M-d, TOP AND BOTTOM SEAT~l ANGLE ONLY,t=1/2 INCH

I 'I /....__---7L-------M-;r,PULL TEST,t=1/2 INCH(; 1.C II· I I / M-j}',FINITE ELEMENT ANALYSISC (1/ t=1/2-INCH

~11~I .I

.~------"----"""'------;l----"'-------'-------'l

c:b~o 4.0 8.0 12.0 15.0 20.0 24.0ROTATION, RADIANS (xlOOO)

FIG. B.9 COMPARISON OF MOMENT-ROTATION CURVES FORCONNECTION WITH TOP AND BOTTOM FLANGE ANGLE ONLY, T= %-inch

93

·aoC'

Cl

M-%,TOP AND BOTTOM SEAT--------~

f ANGLE ONLY,t=3/8-INCHJ

/----------+i-----M-~,PULL TEST,t=3/8-INCHI

I'.. M-i, FINITE ELEMENT ANALYSISI ~=3/8-INCH

~ II1 ; II '

~ IiI~l/

I':I:1j

·aClto

caa1..1;

0

·Vl 0W Cl:c ~uz......

Ic......... C::.:::t- oZw C:E ("T")0:;;;;:

-: (1 ,-.. ....I ....... '_

,

20.01 0 ,.,~ .U

......----r-----,------r------r------,------a .O.ll

ROTATION, RADIANS (xlOOO)

FIG. 8.10 COMPARISON OF MOMENT-ROTATION CURVES FORCONNECTION WITH TOP AND BOTTOM FLANGE ONLY, T=3Ja-INCH

TABLES

94

TABLE 2.1

MECHANICAL PROPERTIES OF TEST MATERIAL

Mechanical Properties *

Yield Stress Ultimate Strength Elongation in 2-inchDesignation (ksi) (ksi) Gage Length (percent)

ASTM A36 42.8 69.9 23.8

42.9 67.9 22.9

39.3 68.0 32.5

37.6 67.9 31.9

53** 80** - -

36.5 71.9 31.3

43.7 69.9 31.3

40.0 64.0 34.4

38.0 66.0 37.5

* Top five entries represent stock used in fabrication of specimens ininitial study (with 3/4" dia. bolts); bottom four entries representstock used in fabrication of specimens in current study (with 7/8" dia.bolts, welds).

** Flange angle material, specimen 14S2.

95

TABL

E2

.2

SCH

EDU

LEOF

BOLT

EDTE

STSP

ECIM

ENS

3/4

-IN

CHD

IAM

ETER

BOLT

S

Top

and

Bot

tom

Fla

ng

eA

ngle

s**

Web

Ang

les

**S

peci

men

Typ

eo

fB

eam

Ang

leL

engt

hG

age

inL

egB

olt

Sp

acin

gin

Leg

Ang

leL

eng

th,

Num

ber

Tes

t*

Sec

tio

n"L

"on

Col

umn

onC

olum

nF

lan

ge,

"L"

(in

ches

Fla

ng

e"g

""p

"c

(in

ches

)(i

nch

es)

(in

ches

)1

----

----

._--

---~

__._

-'.

--

-_.-

----

----

_.,

-_._

_._.-

--

.-_~_'----'-'-.----'--

--'-

'--

-~_---------_._._.

'--._

---

14

Sl

Sta

tic

W14

X38

L6X

4X3/

88

2~

5~

~L4X3~X~

8~

14S2

Sta

tic

W14

X38

L6X4x~

82~

5~

2L4X3~X~

8~

14S3

Sta

tic

W14

X38

L6X

4X3/

88

2!z

5~

2L4X3!zX~

51t

~

14S4

Sta

tic

W14

X38

L6X

4X3/

88

2!z

5~

2L4

X3!

zX3/

88!

z

8S1

Sta

tic

W8X

21L6X3~X5/16

62

3~

2L4X3~X~

5~

8S2

Sta

tic

W8X

21L6X3~X3/8

62

3~

2L4X3!zX~

5~

8S3

Sta

tic

W8X

21L6X3~X5/16

82

3~

2L4X3!zX~

5~

I

8S4

Sta

tic

W8X

21L

6X6X

3/8

64~

3~

2L4X3~X~

5~

I I8S

5S

tati

cW

8X21

L6X

4X3/

88

2!z

5~

2L4X3~X~

5~

8S6

Sta

tic

W8X

21L

6X4X

5/16

62!

z3~

2L4X3~X~

5~

I8S

7S

tati

cW

8X21

L6X

4X3/

86

2~

3!z

2L4X3~X~

5~

14C

1C

ycli

c-L

HW

14X

38L

6X4X

3/8

82~

5~

2L4X3!zX~

8~

14C

2C

ycl

ic-L

HW

14X

38L6

X4!

z8

2~

5!z

2L4X3~X~

8!z

8C1

Cyc

lic-

LH

W8X

21L6X3~X5/16

62

3~

2L4X3~X~

5~

8C2

Cy

clic

-LH

W8X

21L6X3~X3/8

62

3~

2L4X3~X~

5~

j

*C

ycl

ic-

LH:

Low

toh

igh

amp

litu

de

blo

cklo

adin

g,

Fig

.2

.11

aC

ycl

ic-

CF:

Co

nst

ant

amp

litu

de

(fati

gu

e)

load

ing

,F

ig.

2.1

1b

Cy

clic

-H

L:H

igh

tolo

wam

pli

tud

eb

lock

load

ing

,F

ig.

2.1

1c

**S

eeN

om

encl

atu

re,

App

endi

xA

tTw

ob

olt

sat

3-i

nch

spac

ing

,m

ount

edon

top

two

ho

les

onst

ub

colu

mn,

Fig

.2

.2a

<.0

0\

TABL

E2

.3

SCH

EDU

LEOF

BOLT

EDTE

STSP

ECIM

ENS

7/8

-IN

CHD

IAM

ETER

BOLT

S

Top

and

Bot

tom

Fla

ng

eA

ngle

s**

Web

Ang

les

**S

peci

men

Typ

eo

fB

eam

Ang

leL

engt

hG

age

inL

egB

olt

Sp

acin

gin

Leg

Ang

leL

eng

th,

Num

ber

Tes

t*

Sec

tio

n"L

"on

Col

umn

onC

olum

nF

lan

ge,

"L"

(in

ches

Fla

ng

e"g

""p

"c

(in

ches

)(i

nch

es)

(in

ches

)

l4S

5S

tati

cW

14X

38L

6X4X

3/8

82~

5~

2L4X3~X~

8~

l4S

6S

tati

cW

14X

38L6X4X~

82~

5~

2L4X3~X~

8~

14S8

Sta

tic

W14

X38

L6X

4X5/

88

2~

5~

2L4X3~X~

8~

14S9

Sta

tic

W14

X38

L6X4X~

82~

5~

2L4X3~X~

8~

14F1

Cy

clic

-CF

W14

X38

L6X

4X3/

88

2~

5~

2L4X3~X~

8~

14F2

Cy

clic

-CF

W14

X38

L6X

4X3/

88

2~

5~

2L4X3~X~

8~

14F3

Cy

clic

-CF

W14

X38

L6X

4X3/

88

2~

5~

2L4X3~X~

8~

14F4

Cy

clic

-CF

W14

X38

L6X

4X3/

88

2~

5~

2L4X3~X~

8~

14F5

Cy

clic

-CF

W14

X38

L6X4X~

82~

5~

2L4X3~X~

8~

14F6

Cyc

1ic-

CF

W14

X38

L6X4X~

82~

5~

2L4X3~X~

8~

14F7

Cy

clic

-CF

W14

X38

L6X4~

82~

5~

2L4X3~X~

8~

14F8

Cy

clic

-CF

W14

X38

L6X4~

82~

5~

2L4X3~X~

8~

14F9

Cy

clic

-CF

W14

X38

L6X

4X3/

88

2~

5~

2L4X3~X~

8~

14C

3C

yc1i

c-L

HW

14X

38L6X4X~

82~

5~

2L4X3~X~

8~

14C

4C

ycli

c-L

HW

14X

38L

6X4X

3/8

82~

5~

2L4X3~X~

8~

J

*C

ycl

ic-

LH:

Low

toh

igh

amp

litu

de

blo

cklo

adin

g,

Fig

.2

.11

aC

ycl

ic-

CF:

Co

nst

ant

amp

litu

de

(fati

gu

e)

load

ing

,F

ig.

2.1

1b

Cy

clic

-H

L:H

igh

tolo

wam

pli

tud

eb

lock

load

ing

,F

ig.

2.1

1c

**S

eeN

om

encl

atu

re,

App

endi

xA

\D --J

TABL

E2

.3(C

ON

TIN

UED

)

SCH

EDU

LEOF

BOLT

EDTE

STSP

ECIM

ENS

7/8

-IN

CHD

IAM

ETER

BOLT

S

Top

and

Bot

tom

Fla

ng

eA

ngle

s**

Web

Ang

les

**S

peci

men

Typ

eo

fB

eam

Ang

leL

engt

hG

age

inL

egB

olt

Sp

acin

gin

Leg

Ang

leL

eng

th,

Num

ber

Tes

t*

Sec

tio

n"L

"on

Col

umn

onC

olum

nF

lan

ge,

"L"

(in

ches

Fla

ng

e"g

""p

"c

(in

ches

)(i

nch

es)

(in

ches

)

14B

1C

ycli

c-H

LW

14X

38L6X4X~

82~

5~

2L4X3~X~

8~

8S8

Sta

tic

W8X

21L6X3~X5/16

62

3~

2L4X3~X~

5~

8S9

Sta

tic

W8X

21L6X3~X3/8

62

3~

2L4X3~X~

5~

8S10

Sta

tic

W8X

21L6X3~X~

62

3~

2L4X3~X~

5~

8F1

Cy

clic

-CF

W8X

21L6X3~X3/8

62

3~

2L4X3~X~

5~

8F2

Cy

clic

-CF

W8X

21L6X3~X3/8

62

3~

2L4X3~X~

5~

8F3

Cy

clic

-CF

W8X

21L6X3~X3/8

62

3~

2L4X3~X~

5~

8F4

Cy

clic

-CF

W8X

21L6X3~X3/8

6·2

3~

2L4X3~X~

5~

8F6

Cy

clic

-CF

W8X

21L6X3~X5/16

62

3~

2L4X3~X~

5~

8F7

Cy

clic

-CF

W8X

21L6X3~X5/16

62

3~

2L4X3~X~

5~

8F8

Cy

clic

-CF

W8X

21L6X3~X5/16

62

3~

2L4X3~X~

5~

8C3

Cyc

lic-

LH

W8X

21L6X3~X3/8

62

3~

2L4X3~X~

5~

8Bl

Cyc

lic-

HL

W8X

21L6X3~X3/8

62

3~

2L4X3~X~

5~

J

*C

ycl

ic-

LH:

Low

toh

igh

amp

litu

de

blo

cklo

adin

g,

Fig

.2

.11

aC

ycl

ic-

CF:

Co

nst

ant

amp

litu

de

(fati

gu

e)

load

ing

,F

ig.

2.1

1b

Cy

clic

-H

L:H

igh

tolo

wam

pli

tud

eb

lock

load

ing

,F

ig.

2.1

1c

**S

eeN

omen

clat

ure,

App

endi

xA

\D 00

TABL

E2

.4

SCHE

DULE

OFBO

LTED

-WEL

DED

TEST

SPEC

IMEN

S7/

8-IN

CH

DIA

MET

ERBO

LTS

Top

and

Bot

tom

Fla

nge

Ang

les*

Web

Ang

les*

Bol

tS

paci

ngG

age

inLe

gin

Leg

onL

engt

hL

engt

hO

nC

olF

lang

eC

olum

nF

lang

eW

eld

"L"

Wel

dS

peci

men

Typ

eo

fB

eam

"L"

"g"

"p"

size

csi

ze

Num

ber

Tes

tS

ecti

on

Ang

le(i

nch

es)

(in

ches

)(i

nch

es)

(in

ches

)A

ngle

(in

ches

)(i

nch

es)

14W

SIS

tati

cW

14X

38L6

X4X

3/8

82~

5~

5/1

62L4X3~X~

8~

3/16

14W

S2S

tati

cW

14X

38L6X4X~

82~

5~

5/1

62L4X3~X~

8~

3/1

6

*See

Nom

encl

atur

e,A

ppen

dix

AF

orw

eld

deta

ils,

see

Fig

.2

.3

\0 \0

TABL

E3

.1

SUM

MAR

YOF

STA

TIC

TEST

RESU

LTS

-BO

LTED

SPEC

IMEN

S3/

4-IN

CH

DIA

MET

ERBO

LTS

Spe

cim

enIn

itia

lS

lop

eo~

Slo

pe

of

Sec

ant

Lin

eto

Mom

ent

at

Slo

pe

of

M-¢

Cur

veM

om2n

tat

Num

ber

M-¢

Cur

ve·1

-¢C

urve

at

4.0X

lO-3

rad

ian

s4.

0XlO

-3ra

dia

ns

at24X10~3radians

24X

10-

rad

ian

sR

emar

ks(k

-in

./ra

dia

n)

(k-i

n./

rad

ian

)(k

-in

.)(k

-in

./ra

dia

n)

(k-i

n.)

14S1

195.

0X10

+3

108.

7X20

+3

435

5.8X

10+

368

8

14S2

29

5.0

151.

860

71

2.6

(947

)M

ajor

sli

pat

12X

10-3

&20

X10

-3ra

dia

ns

14S3

U5

.98

8.8

355

7.2

652

14S4

221.

91

24

.049

68

.382

2

8S1

66

.74

4.3

177

4.1

329

8S2

12

3.4

69

.027

61

.5(3

84)

Maj

orsli

pat

16X

10-3

rad

ian

s8S

31

04

.76

4.3

257

4.0

422

8S4

15

.31

4.4

57

.52

.216

5

8C5

76

.74

7.9

191.

52

.733

7

8S6

39

.53

0.0

120

3.2

244

8S7

48

.04

0.8

163

3.2

381

....... o o

TABL

E3

.2

SUM

MAR

YOF

STA

TIC

TEST

RESU

LTS

-BO

LTED

SPEC

IMEN

S(7

/8-I

NC

HD

IAM

ETER

BOLT

S)

Init

ial

Slo

peo

fS

lop

eo

fS

ecan

tL

ine

toM

omen

tat

Slo

pe

ofM-~

Cur

veM

omen

tat

Spe

cim

enM-~

Cur

veM-~

Cur

vean

d4.

0X10

-3ra

dia

ns

4.0X

lO-3

rad

ian

sat

24X

10-3

rad

ian

s?4

XlO

-3ra

dia

ns

Num

ber

(k-i

n./

rad

ian

)(k

-in

./ra

dia

n)

(k-i

n.)

(k-i

n.j

rad

ian

)(k

-in

.)R

emar

ks

14S5

247X

10+

311

7.4X

10+

346

710

.8X

10+

376

3

14S6

286

14

6.9

589

10

.310

53

14S8

579

256.

910

271

5.0

1561

14S9

258

154.

162

49

.310

24

8S8

704

4.4

183

3.8

380

8S9

104

54

.522

64

.442

3

8S10

427

10

4.1

434

6.9

(634

)M

ajor

s!ip

at

5.3X

10-

.ra

dia

ns

..... a .....

TABL

E3

.3

SUM

MAR

YOF

STA

TIC

TEST

RESU

LTS

-BO

LTED

-WEL

DED

SPEC

IMEN

S

Init

ial

Slo

pe

of

Slo

pe

of

Sec

ant

L~~e

toMome~3

at

Slo

pe

of_~-~

Cur

veMom~~t

at

Spe

cim

enM-~

Cur

veM-~

Cur

veat

4.0X

10ra

dia

ns

4.0X

lOra

dia

ns

at

24X

I0ra

dia

ns

24X

I0ra

dia

ns

Num

ber

(k-i

n.j

rad

ian

)(k

-in

.jra

dia

n)

(k-i

n.)

(k-i

n.j

rad

ian

)(k

-in

.)

14W

SI20

0Xl0

+3

119.

4Xl0

+3

486

12

.192

3

14H

S245

61

88

.577

31

1.5

1235

"

I-'

o N

TA

BLE

3.4

SUM

MAR

YO

FC

YC

LIC

TEST

RES

ULT

S-

SPEC

IMEN

14C

1

Act

uat

or

Fre

qu

ency

Num

ber

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eC

um

ula

tiv

eD

isp

lace

men

t(H

z)

of

Ro

tati

on

Mom

ent

aS

ing

leA

rea

of

Num

ber

Rem

arks

Am

pli

tud

eC

ycl

es(r

ad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(in

ches

)X

1000

)L

oop*

Loo

ps(k

ip-i

nch

es)

(kip

-in

ch

es)

0.2

.05

4-

--

-4

No

Dat

a.1

12

.20

43

5.8

00

51

2.0

844

1.5

00

6.5

12

.10

42

8.5

00

710

2.3

44

39

.20

017

0.4

.11

4.7

57

45

.0.2

96

.29

618

14

.87

73

8.5

.12

3.4

19

191

4.8

974

1.5

.11

1.5

30

20.2

51

4.9

17

42

.5.0

69

.59

921

14

.77

73

7.1

.06

4.6

63

22I

105

.04

751.

7.0

69

1.3

53

32,-

0.6

.11

7.8

49

31

.3.7

34

2.0

87

331

7.7

79

34

.9.4

19

2.5

06

341

7.8

59

33

.2.3

20

2.8

26

35.2

51

7.7

89

24

.9.2

83

3.1

09

361

7.8

89

22

.0.2

79

3.3

88

37I

108

.08

93

2.2

.28

26

.20

847

0.8

.11

11

.10

1068

1.6

08

7.8

16

481

10

.99

1046

.99

88

.81

449

11

0.8

610

31.8

24

9.6

38

50.2

51

10

.95

1032

.81

21

0.4

50

511

11

.03

1034

.83

11

1.2

81

5210

11

.23

1042

.82

91

9.5

71

621

.0.1

11

4.4

411

422

.45

22

.02

163

11

4.3

211

051

.91

22

3.9

33

641

14

.37

1102

1.8

75

25

.80

865

.25

11

4.4

910

951

.81

82

7.6

26

661

14

.28

1094

1.8

32

9.4

56

6710

14

.70

1109

1.7

84

7.2

56

77*

Fo

rm

ult

iple

cy

cle

s,th

eare

ao

fon

elo

op

isco

mpu

ted

asth

eav

erag

eo

fth

efi

rst

and

last

loo

pare

as.

Co

nti

nu

ed-

..... o 0-l

TABL

E3

.4(C

ON

TIN

UED

)

SUM

MAR

YO

FC

YC

LIC

TEST

RES

ULT

S-

SPEC

IMEN

14C

1

A.c

tuat

or

Fre

qu

ency

Num

ber

R:m

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eC

um

ula

tiv

e

111s

p.1a

cem

ent

(Hz)

of

Ro

tati

on

Mom

ent

aS

ing

leA

rea

of

Num

ber

Rem

arks

Am

pli

tuc1

cC

ycl

es(r

adL

ans

(kip

-in

ch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(in

ch

es)

X1

00

0)

Loo

p*L

oops

(kip

-in

ch

es)

(kiD

-in

ch

es)

1.2

.11

17

.73

1185

3.7

47

51

.00

378

11

7.6

411

463

.37

25

4.3

879

11

7.7

811

423

.39

57

.77

80.2

51

17

.67

1139

3.2

78

61

.04

811

17

.70

1140

3.2

41

64

.28

821

01

7.9

411

403

.19

39

6.2

192

1.4

.11

21

.12

1207

5.4

80

10

1.6

993

12

1.1

711

835

.23

01

06

.994

12

1.3

611

735

.23

21

12

.295

.25

12

1.2

211

715

.09

11

7.2

961

21

.18

1169

5.0

33

12

2.3

9710

21.

7311

704

.98

17

2.1

107

1.6

.11

24

.51

1276

7.0

92

17

9.2

108

12

4.6

512

506

.70

41

85

.910

91

24

.68

1238

6.5

77

19

2.5

110

12

4.8

312

306

.59

41

99

.011

1.2

51

24

.52

1217

6.5

82

05

.611

21

24

.60

1219

6.5

37

21

2.2

113

102

5.1

112

176

.50

727

7.2

123

1.8

.11

28

.30

1261

9.0

28

6.2

124

12

8.4

212

328

.91

22

95

.112

51

28

.31

1213

8.7

34

30

3.9

126

.25

12

8.1

712

138

.61

53

12

.512

71

28

.22

1203

8.6

03

21

.112

810

28

.55

1206

8.4

15

40

5.2

138

2.0

.11

31

.81

1257

11

.04

16

.213

91

31

.76

1225

10

.87

42

7.1

140

13

2.1

712

201

0.7

75

43

7.9

141

.25

1--

----

----

----

----

--h

alf

cy

cle

13

1.8

511

931

0.5

54

48

.414

21

31

.90

1198

10

.47

44

58

.914

36

32

.46

1197

10

.26

52

0.5

149

crac

ksdetected~th

cy

cle

..... o -!'o-

py

pp

ga

lOO

pare

as.

TAB

LE3

.5

SUHM

ARY

OF

CY

CLI

CTE

STR

ESU

LTS

-SP

ECIM

EN14

C2

Act

uat

or

Fre

.que

ncy

Num

ber

Ran

Re

of

Ran

geo

fA

rea

of

Cu

mu

lati

ve

Cu

mu

lati

ve

njspJa~ement

(Hz)

of

Ro

tati

on

Mom

ent

aS

ing

leA

rea

of

Num

ber

Rem

arks

Am

pli

tud

eC

ycl

es(r

ad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(in

ch

es)

X1

00

0)

Loo

p*L

oops

(kip

-in

ch

es)

(kip

-tn

ch

es)

--

0.2

.11

2.1

64

72

.30

1.2

51

2.1

24

78

.10

21

2.0

94

74

.20

310

2.3

74

88

.70

013

.4.1

14

.47

85

0.7

.23

8.2

38

14.2

51

4.4

58

31

.1.1

52

.39

015

14

.54

85

7.0

.13

5.5

25

1610

4.4

3**

.211

**2

.63

526

.6.1

17

.07

1132

.72

53

.36

027

Inv

erte

dcy

c1e*

**.2

51

7.0

1143

.40

43

.76

428

Inv

erte

dcy

cle

17

.111

39.3

10

4.0

74

29In

ver

ted

cycl

e10

7.3

111

54.3

04

7.1

14

39.8

.11

10

.12

1357

1.4

69

8.5

83

401

9.9

513

45.8

78

9.4

61

41In

ver

ted

cycl

e1

9.8

713

451

.03

81

0.4

99

42In

ver

ted

cycl

e.2

51

10

.08

1334

.74

81

1.2

4743

19

.82

1331

.92

81

2.1

75

4410

10

.09

1332

.91

92

1.3

65

541

.0.1

11

3.1

214

902

.80

92

4.1

74

55.2

51

12

.98

1477

2.4

37

26

.61

156

11

3.2

614

662

.26

22

8.8

73

5710

13

.43

1465

2.1

97

50

.84

367

.1

.2.1

11

6.2

815

714

.56

35

5.4

06

68.2

51

16

.31

1548

4.2

37

59

.64

369

11

6.1

815

414

.10

16

3.7

44

7010

16

.70

1536

4.0

12

10

3.8

680

*For

mu

ltip

lecy

cle

s,th

eare

ao

fon

elo

op

isco

mpu

ted

asth

eav

erag

eo

fth

efi

rst

and

last

loo

pare

as•.

**

Qu

esti

on

able

data

.**

*Loa

dcy

cle

inv

ert

ed

from

norm

alsi

ne

wav

e,F

ig.

3.2

8.

.....C

on

tin

ued

-g

TABL

E3

.5(C

ON

TIN

UED

)

S~~RY

OF

CY

CLI

CTE

STR

ESU

LTS

-SP

ECIM

EN14

C2

Act

uat

or

Fre

qu

ency

Num

ber

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eC

um

ula

tiv

eD

isp

lace

men

t(H

z)

of

Ro

tati

on

Mom

ent

aS

ing

leA

rea

of

Num

ber

Rem

arks

Am

pl:I

.tude

Cy

cles

(rad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(in

ch

es)

X1

00

0)

Loo

p*L

oops

(kip

-in

ch

es)

-(k

ip-i

nch

es)

1.4

.11

19

.79

1637

6.8

37

nO

.70

81.2

51

19

.96

1608

6.4

81

11

7.1

882

11

9.8

015

906

.38

91

23

.57

830

.5.1

16

.92

66

0.4

.45

11

24

.02

84In

specti

on

for

crac

ks

0.5

16

.83

662

.23

41

24

.26

851

.4.1

11

9.8

015

796

.20

61

30

.46

861

19

.89

1577

6.4

28

13

6.8

987

12

0.1

515

604

.59

51

41

.49

88In

vert

ed

cyc1

e**

11

9.9

515

596

.36

31

47

.85

89In

ver

ted

cycl

e.2

510

20

.21

1562

6.2

42

10

.25

99In

vert

ed

cycl

e1

.6.1

12

3.3

916

537

.93

32

18

.18

100

12

3.5

216

229

.06

92

27

.25

101

.25

12

3.4

416

158

.79

23

6.0

410

21

23

.30

1613

8.7

49

24

4.7

910

310

23

.78

1606

8.5

59

33

0.3

811

31

.8.1

12

6.7

816

701

1.4

873

41

.87

114

.25

12

6.8

616

471

1.2

963

53

.16

115

12

7.0

516

361

1.1

13

36

4.2

811

610

27

.20

1633

10

.77

747

2.0

512

6C

rack

det

ecte

d2

.0.1

13

0.4

816

871

4.0

32

48

6.0

812

71

30

.37

1659

13

.87

14

99

.95

128

13

0.5

416

431

3.7

22

51

3.6

712

91

30

.60

1623

13

.52

95

27

.20

130

*For

mu

ltip

lecy

cle

s,th

eare

ao

fon

elo

op

isco

mpu

ted

asth

eav

erag

eo

fth

efi

rst

and

last

loo

pare

as.

**L

oad

cycl

ein

vert

ed

from

no

rmal

sin

ew

ave,

Fig

.3

.28

.

f-'

o ()\

TABL

E3

.6

SUM

MAR

YO

FC

YC

LIC

TEST

RES

ULT

S-

SPEC

IMEN

14C

3

Act

uat

or

Fre

qu

ency

Num

ber

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eC

um

ula

tiv

eR

emar

ksD

isp

lace

men

t(H

z)o

fR

ota

tio

nM

omen

ta

Sin

gle

Are

ao

fN

umbe

rA

mp

litu

de

Cy

cles

(rad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(in

ches

)x

10

00

)L

oop

Loo

ps*

(kip

-in

ch

es)

(kip

-in

ch

es)

0.2

.25

2-

--

--

-.0

64

21

2.2

54

86

.5.0

32

.09

63

9-

--

--

-.3

84

120

.4.2

52

--

--

--

.56

714

14

.293

5.0

92

.659

1511

--

--

--

1.6

66

260

.6.2

52

--

--

--

2.8

06

281

6.7

1272

.57

03

,37

629

9-

--

--

-8

.50

638

0.8

.25

2-

--

--

-1

1.7

840

19

.715

031

.63

71

3.4

241

9-

--

--

-2

8.1

550

1.0

.25

2-

--

--

-3

5.1

252

112

.816

663

.48

43

8.6

053

9-

--

--

-6

9.9

662

1.2

.25

2-

--

--

-8

2.5

564

11

6.0

1740

6.2

97

88

.85

659

--

--

--

14

5.5

741

.4.2

53

--

--

--

172

.477

11

9.0

1825

8.9

54

18

1.2

799

--

--

--

26

1.9

871

.6.2

52

--

--

--

28

6.0

891

22

.419

091

2.0

15

29

8.0

909

--

--

--

40

6.1

99C

rack

dete

cte

d

*A

tea

chd

isp

lace

men

tam

pli

tud

e,th

eare

ao

fall

hy

stere

sis

loo

ps

isas

sum

edco

nst

an

t.

Co

nti

nu

ed-

I-'

o ---J

TABL

E3

.6(C

ON

TIN

UED

)

SUM

MAR

YOF

CYCL

ICTE

STRE

SULT

S-

SPEC

IMEN

14C

3

Act

uat

or

Fre

qu

ency

Nw

nber

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eC

um

ula

tiv

eR

emar

ksD

isp

lace

men

t(H

z)o

fR

ota

tio

nM

omen

ta

Sin

gle

Are

ao

fN

umbe

rA

mp

litu

de

Cy

cles

(rad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(in

ches

)x

10

00

)L

oop

Loo

ps*

(kip

-in

ch

es)

(kip

-in

ch

es)

1.8

.25

4-

--

--

-4

66

.010

31

26

.119

091

4.9

67

48

0.9

104

9-

--

--

-6

15

.611

32

.0.2

52

--

--

--

64

9.1

115

13

0.3

1780

16

.73

26

65

.811

61

--

--

--

68

2.6

117

Lar

ge

crac

ks

-all

flan

ge

an

gle

s

*A

tea

chd

isp

lace

men

tam

pli

tud

e,th

eare

ao

fall

hy

stere

sis

loo

ps

isas

sum

edco

nst

an

t.I-

'o 0

0

TABL

E3

.7

SUM

MAR

YO

FC

YC

LIC

TEST

RES

ULT

S-

SPEC

IMEN

14C

4

Act

uat

or

Fre

qu

ency

Num

ber

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eC

um

ula

tiv

eR

emar

ksD

isp

lace

men

t(H

z)o

fR

ota

tio

nM

omen

ta

Sin

gle

Are

ao

fN

umbe

rA

mp

litu

de

Cy

cles

(rad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(in

ches

)x

1000

)L

oop

Loo

ps*

(kip

-in

ch

es)

(kip

-in

ch

es)

0.2

.25

2-

--

--

-.0

40

21

2.6

356

.02

0.0

60

39

--

--

--

.24

012

0.4

.25

2-

--

--

-.4

47

141

5.1

657

.10

3.5

50

159

--

--

--

1.4

81

240

.6.2

52

--

--

--

2.2

92

261

7.8

902

.40

52

.69

727

9-

--

--

-6

.34

636

0.8

.25

2-

--

--

-8

.39

738

11

0.9

1072

1.0

26

9.4

23

399

--

--

--

18

.65

481

.0.2

52

--

--

--

22

.84

501

14

.211

912

.09

32

4.9

351

9-

--

--

-4

3.7

660

1.2

.25

2-

--

--

-5

1.0

562

11

7.4

1268

3.6

44

54

.70

639

--

--

--

87

.49

721

.4.2

52

--

--

--

98

.79

741

20

.912

915

.65

01

04

.475

9-

--

--

-1

55

.384

1.6

.25

2-

--

--

-1

71

.386

12

4.7

1318

7.9

86

17

9.2

879

--

--

--

25

1.1

96C

rack

dete

cte

d

I*

At

each

dis

pla

cem

ent

amp

litu

de,

the

are

ao

fall

hy

stere

sis

loo

ps

isas

sum

edco

nst

an

t.

Co

nti

nu

ed-

i--< o <.0

TABL

E3

.7(C

ON

TIN

UED

)

SUM

MAR

YO

FC

YC

LIC

TEST

RES

ULT

S-

SPEC

IMEN

14C

4

Act

uat

or

Fre

qu

ency

Num

ber

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eC

um

ula

tiv

eR

emar

ksD

isp

lace

men

t(H

z)o

fR

ota

tio

nM

omen

ta

Sin

gle

Are

ao

fN

umbe

rA

mp

litu

de

Cy

cles

(rad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(in

ches

)x

10

00

)L

oop

Loo

ps*

(kip

-in

ch

es)

(kip

-in

ch

es)

1.8

.25

2-

--

--

-27

2.0

981

27

.913

111

0.4

42

28

2.4

996

--

--

--

345-

.110

5L

arg

ecr

ack

-te

st

sto

pp

ed

t I

*A

tea

chd

isp

lace

men

tam

pli

tud

e,th

eare

ao

fall

hy

stere

sis

loo

ps

isas

sum

edco

nst

an

t......

......

.o

TABL

E3

.8

SUM

MAR

YOF

CY

CLI

CTE

STR

ESU

LTS

-SP

ECIM

EN14

Bl

Act

uat

or

Fre

qu

ency

Num

ber

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eC

um

ula

tiv

eR

emar

ksD

isp

lace

men

t(H

z)o

fR

ota

tio

nM

omen

ta

Sin

gle

Are

ao

fN

umbe

rA

mp

litu

de

Cy

cles

(rad

ian

s(k

ip-i

nch

es)

Hys

teri

C's:

!s

Hy

stere

sis

of

Cy

cles

(in

ches

)x

10

00

)L

oop

Loo

ps*

(kip

-in

ch

es)

(kip

-in

ch

es)

1.8

.25

2-

--

--

-3

2.1

62

12

6.0

1863

16

.07

84

8.2

33

9-

--

--

-1

92

.912

Cra

ckd

ete

cte

d1

.6.2

52

--

--

--

21

4.4

141

23

.516

481

0.7

11

22

5.1

159

--

--

--

32

1.5

241

.4.2

52

--

--

--

33

6.8

261

20

.414

727

.64

23

44

.427

Ex

ten

siv

ecra

ck

s-9

--

--

--

41

3.2

36tw

oflan~e

an~les

1.2

.25

2-

--

--

-4

23

.538

11

7.5

1299

5.1

63

42

8.7

399

--

--

--

47

5.1

481

.0.2

52

--

--

--

48

1.6

SO1

14

.411

013

.24

14

84

.851

9-

--

--

-5

14

.060

Lar

ge

cra

ck

-test

sto

pp

ed

*A

tea

chd

isp

lace

men

tam

pli

tud

e,th

eare

ao

fall

hy

stere

sis

loo

ps

isas

sum

edco

nst

an

t......

......

......

.

TABL

E3

.9

SUM

MAR

YO

FC

YC

LIC

TEST

RES

ULT

S-

SPEC

IMEH

8C1

Actu

ato

rF

rpq

uen

cyN

umhe

rH

ange

of

Ran

Re

of

Are

ao

fC

um

ula

tiv

eC

um

ula

tiv

e[H

spL

acen

tent

(Hz

)o

fH

ota

tio

nM

omen

t*

aS

ing

leA

rea

of

Num

ber

Rem

arks

Am

pli

tud

eC

ycl

es(r

ad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

lin

rhes)

X1

00

0)

Loo

p**

Loo

ps(k

ip-i

nch

es)

(kJp

-in

ch

es)

---

0.2

.11

4.3

323

1.2

.045

.045

1.2

510

4.2

72

33

.8.0

37

.415

11

.4.1

19

.11

39

9.7

.37

0.7

8512

18

.96

39

4.9

.247

1.0

32

13.2

510

9.5

44

22

.2.1

622

.65

223

.6.1

11

3.8

14

95

.91

.08

93

.74

124

11

3.9

84

88

.4.8

714

.61

225

11

4.1

14

85

.3.8

215

.43

326

.25

101

4.5

04

84

.0.7

741

3.1

73

36.8

.11

20

.22

53

8.6

2.3

03

15

.47

637

11

9.8

05

23

.52

.29

91

7.7

75

381

19

.98

50

0.2

2.3

42

20

.11

739

12

0.1

84

95

.92

.41

72

2.5

34

40.2

510

20

.54

90

.12

.36

146

.144

501

.0.1

12

6.0

351

1.6

4.1

88

50

.33

251

12

6.3

65

16

.24

.22

25

4.5

54

521

26

.23

49

0.8

4.1

54

58

.70

853

12

7.2

04

90

.94

.43

16

3.1

39

54.2

510

28

.00

49

9.7

4.2

83

10

5.9

69

641

.2.1

13

2.3

55

21

.36

.13

01

12

.10

651

32

.71

51

3.9

6.3

20

11

8.4

266

.25

53

2.8

25

05

.76

.11

81

49

.01

715

32

.55

48

0.5

6.0

04

17

9.0

376

1.4

.11

38

.94

49

8.2

7.9

23

18

6.9

577

13

9.0

54

78

.67.

626

19

4.5

878

--

--

--

Hal

fcy

cle

,ab

rup

tcra

ck

form

atio

n*E

xtre

me

valu

es

rep

ort

ed

.**

For

mu

ltip

lecy

cle

s,th

eare

ao

fon

elo

op

isco

mpu

ted

asth

eav

erag

eo

fth

efi

rst

and

last

loo

pare

as.

f-'

f-'

N

TABL

E3

.10

SUM

HARY

OF

CY

CU

CTE

STR

ESU

LTS

-SP

ECIM

EN8C

2--

Act

uat

or

Fre

qu

ency

Num

ber

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eC

um

ula

tiv

eD

isp

lace

men

t(H

z)

of

Ro

tati

on

Mom

ent*

aS

ing

leA

rea

of

Num

her

Rem

arks

Am

plit

ud

eC

ycl

es(r

ad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(i.n

ches

)X

1000

)L

oop*

*L

oops

(kjp

-in

ch

es)

(kip

-in

ch

es)

0.2

.11

4.1

32

52

.2.0

62

.06

21

.25

104

.39

26

8.9

.31

73

.23

211

.4.1

18

.39

43

9.3

.45

43

.68

612

18

.05

45

4.0

.307

3.9

93

13.2

510

8.4

94

53

.8.2

54

6.5

33

23.6

.11

13

.43

56

4.3

1.4

38

7.9

71

241

13

.29

55

6.0

1.2

72

9.2

43

25.2

510

13

.85

55

4.5

1.2

65

21

.89

35.8

.11

19

.00

60

5.2

3.1

12

25

.01

361

19

.12

60

1.5

3.0

39

28

.04

371

18

.80

58

9.6

2.8

86

30

.93

38.2

510

19

.89

59

2.9

2.9

03

59

.96

48L

O.1

12

5.0

26

16

.05

.20

26

5.1

649

12

5.3

26

19

.45

.22

70

.38

50.2

510

25

.75

61

1.1

4.9

56

11

9.9

601

.2.1

13

0.7

86

35

.07

.26

51

27

.261

13

1.1

26

37

.17

.30

31

34

.562

.25

103

2.1

76

50

.27

.06

32

05

.172

Cra

cks

det

ecte

d-b

tm.

ang

le1

.4.1

13

7.2

96

63

.79

.70

42

14

.873

13

6.8

96

59

.19

.64

72

24

.574

.25

23

7.2

16

53

.29

.44

92

43

.476

Cra

cks

dete

cte

d-t

op

ang1e~

*Ext

rem

ev

alu

esre

po

rted

**

Fo

rm

ult

iple

cy

cle

s,th

eare

ao

fon

elo

op

isco

mpu

ted

asth

eav

erag

eo

fth

efi

rst

and

last

loo

pare

as.

I-"

I-"

Vl

TABL

E3.

11

SUM

MAR

YOF

CYCL

ICTE

STRE

SULT

S-

SPEC

IMEN

8C3

Actu

ato

rF

req

uen

cyN

umbe

rR

ange

of

Ran

geo

fA

rea

of

Cu

mu

lati

ve

Cu

mu

lati

ve

Rem

arks

Dis

pla

cem

ent

(Hz)

of

Ro

tati

on

Mom

ent

aS

ing

leA

rea

of

Num

ber

Am

pli

tud

eC

ycl

es(r

ad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(in

ch

es)

x10

00)

Loo

pL

oops

*(k

ip-i

nch

es)

(kip

-in

ch

es)

0.2

.25

2-

--

--

-.0

40

21

3.5

31

6.8

.02

0.0

60

39

--

--

--

.24

012

0.4

.25

2-

--

--

-.7

30

141

7.6

54

1.6

.245

.97

515

9-

--

--

-3

.18

024

0.6

.25

2-

--

--

-5

.28

026

11

2.1

68

1.4

1.0

50

6.3

29

279

--

--

--

15

.78

360

.8.2

52

--

--

--

21

.11

381

17

.37

35

.42

.66

62

3.7

739

9-

--

--

-4

7.7

748

1.0

.25

2-

--

--

-5

7.8

450

12

3.9

76

4.8

5.0

37

62

.88

519

--

--

--

10

8.2

60C

rack

sd

ete

cte

d1

.2.2

52

--

--

--

12

3.9

621

29

.87

50

.37

.83

51

31

.763

7-

--

--

-1

86

.570

Lar

ge

crac

ks

-te

st

sto

pp

ed

*A

tea

chd

isp

lace

men

tam

pli

tud

e,th

eare

ao

fall

hy

stere

sis

loo

ps

isas

sum

edco

nst

an

t.I-

'I-

' """

TABL

E3

.12

SUM

MAR

YOF

CY

CLI

CTE

STR

ESU

LTS

-SP

ECIM

EN8B

l

IA

ctu

ato

rF

req

uen

cyN

umbe

rR

ange

of

Ran

geo

fA

rea

of

Cu

mu

lati

ve

Cu

mu

lati

ve

Rem

arks

Dis

pla

cem

ent

(Hz)

of

Ro

tati

on

Mom

ent

aS

ing

leA

rea

of

Num

ber

Am

pli

tud

eC

ycl

es(r

ad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

of

Cy

cles

(in

ch

es)

x10

00)

Loo

pL

oops

*(k

ip-i

nch

es)

(kip

-in

ch

es)

1.2

.25

2-

--

--

-1

6.4

62

12

9.9

77

5.5

8.2

28

24

.63

39

--

--

--

93

.74

12C

rack

sd

ete

cte

d1

.0.2

52

--

--

--

10

3.7

141

24

.96

60

.44

.96

11

13

.615

9-

--

--

-1

58

.324

0.8

.25

2-

--

--

-1

63

.726

11

9.7

572

.52

.69

41

66

.427

9-

--

--

-1

90

.636

0.6

.25

2-

--

--

-1

93

.038

11

4.2

46

1.5

1.1

96

19

4.2

399

--

--

--

20

5.0

480

.4.2

52

--

--

--

20

5.6

501

9.2

34

3.5

.34

72

06

.051

9-

--

--

-2

09

.160

0.2

.25

2-

--

--

-2

09

.262

14

.61

95

.2.0

29

20

9.2

639

--

--

--

20

9.5

721

.2.2

51

30

.76

68

.26

.62

32

16

.173

Lar

ge

crac

k-

ltest

sto

pp

ed

I

*A

tea

chd

isp

lace

men

tam

pli

tud

e,th

eare

ao

fall

hy

stere

sis

loo

ps

isas

sum

edco

nst

an

t......

......

.ti

l

TABL

E3

.13

COM

PILA

TIO

NOF

CONS

TANT

AM

PLIT

UD

ECY

CLIC

(FA

TIG

UE)

TEST

RESU

LTS

ALL

TEST

SPEC

IMEN

S Fat

igu

eT

est

Res

ult

s

Th

ick

nes

sA

ctu

ato

rN

omin

alN

omin

alT

ota

lA

ccum

ulat

edo

fF

lan

ge

Dis

pla

cem

ent

Ran

geo

fF

lan

ge

Ang

leF

atig

ue

Hy

ster

esis

Spe

cim

enB

eam

Ang

leA

mpl

itud

eR

otat

ion*

Cho

rdR

ota

tio

nL

ife

Loo

pA

rea

Num

ber

Sec

tio

n(i

nch

es)

(in

ches

)(r

adia

nsX

lOO

O)

Ind

ex,

R**

Cyc

le(k

ip-i

nch

es)

14F3

W14

X38

3/8

2.8

49

.10

.56

99

232.

0514

F2W

14X

383

/82

.03

5.1

00

40

758

'V80

014

F1W

14X

383

/81

.62

8.1

0.3

25

725

89

.41

14F9

W14

X38

3/8

1.0

17

.50

.20

323

05

15

.76

14F4

W14

X38

3/8

0.5

8.8

0.1

02

3450

763.

5714

F7W

14X

38!z

2.5

43

.90

.57

026

64

8.8

214

F5W

14X

38!,;

1.5

26

.30

.34

159

51

5.8

42

14F6

W14

X38

!z1

.01

7.5

0.2

27

316

92

4.0

014

F8W

14X

38!,;

0.7

12

.30

.16

010

3191

1.30

2

8F8

W8X

215

/16

1.5

45

.50

.48

116

15

3.9

88F

7W

8X21

5/1

61

.03

0.3

0.3

20

6223

1.87

8F6

W8X

215

/16

0.7

21

.20

.22

417

3N

od

ata

8F1

W8X

213

/81

.54

5.5

0.5

25

101

16

.57

8F4

W8X

213

/81

.03

0.3

0.3

50

5626

3.46

8F3

W8X

213

/80

.72

1.2

0.2

45

147

257.

768F

2W

8X21

3/8

0.5

15

.20

.17

556

030

7.99

*T

wic

eactu

ato

rd

isp

lace

men

tam

pli

tud

ed

ivid

edby

dis

tan

ce

from

sup

po

rtto

colu

mn

face

.

**R

=2

[(d

+t)

tan<

l>]

Lg

-dw

/2-t

See

No

men

clat

ure

,A

ppen

dix

A.

I--'

I--'

0\

Co

nti

nu

ed-

TABL

E3

.14

SUM

MAR

YO

FCO

NST

AN

TA

MPL

ITU

DE

CY

CLI

CTE

STR

ESU

LTS

W14

X38

SPECI~ffiNS

WIT

H~-INCH

THIC

KFL

AN

GE

AN

GLE

S

Spe

cim

enA

ctu

ato

rF

req

uen

cyC

ycl

eP

erce

nt

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eR

emar

ksN

umbe

rD

isp

lace

men

t(H

z)N

umbe

ro

fT

ota

lR

ota

tio

nM

omen

ta

Sin

gle

Are

ao

fA

mpl

itud

eF

atig

ue

(rad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

(in

ches

)L

ife

x1

00

0)

Loo

pL

oops

*(k

ip-i

nch

es)

(kip

-in

ch

es)

14F7

2.5

0.0

25

13

.81

9.0

1601

1.8

30

1.8

3C

ycl

es1

,2-

0.0

25

31

1.5

38

.420

543

5.2

64

38

.92

half

cycl

es0

.25

72

6.9

38

.618

772

7.1

39

15

9.6

70

.10

124

6.2

38

.918

522

6.0

63

29

2.1

4C

ycl

e20

-0

.10

186

9.2

39

.218

292

5.6

39

44

7.0

3cr

ack

sd

e-0

.10

259

6.2

39

.218

062

4.9

75

62

3.8

5te

cte

d0

.10

2610

0-

--

--

-6

48

.82

End

of

test

14F5

1.5

0.2

56

10

.22

1.5

1729

8.9

68

53

.81

122

0.3

21

.717

038

.83

21

07

.14

183

0.5

21

.616

928

.87

41

60

.28

244

0.7

21

.816

748

.55

02

12

.39

I30

50

.82

1.7

1663

8.8

98

26

4.9

1C

ycl

e33

-36

61

.02

1.8

1648

8.5

33

31

7.0

2cr

ack

de-

l I42

71

.22

1.7

1653

8.7

28

36

8.9

0te

cte

d48

81

.42

1.6

1637

8.7

18

42

1.2

354

91

.52

1.9

1678

8.5

66

47

3.0

159

100

--

--

--

51

5.8

4E

ndo

fte

st

*F

or

cy

cle

sb

etw

een

tho

sere

po

rted

,th

ear

eao

fa

sin

gle

hy

stere

sis

loo

pis

calc

ula

ted

asth

eav

erag

eo

fth

ep

rece

din

gan

dsu

ccee

din

gre

po

rted

loo

pare

as.

..... ..... '-l

TABL

E3

.14

(CO

NTI

NU

ED)

SUM

MAR

YO

FCO

NST

AN

TA

MPL

ITU

DE

CY

CLI

CTE

STR

ESU

LTS

W14

X38

SPEC

IMEN

SW

ITH

~-INCH

THIC

KFL

AN

GE

AN

GLE

S

Spe

cim

enA

ctu

ato

rF

req

uen

cyC

ycl

eP

erce

nt

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eR

emar

ksN

umbe

rD

isp

lace

men

t(H

z)N

umbe

ro

fT

ota

lR

ota

tio

nM

omen

ta

Sin

gle

Are

ao

fA

mp

litu

de

Fat

igu

e(r

ad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

(in

ches

)L

ife

x10

00)

Loo

pL

oops

*(k

ip-i

nch

es)

(kip

-in

ch

es)

14F6

1.0

0.2

51

0.3

6.2

1051

2.1

80

2.1

8C

ycl

es1

-10

,13

4.1

13

.115

712

.99

63

0.7

9h

alf

cy

cle

s18

5.7

12

.915

682

.84

94

5.3

320

06

3.3

13

.115

372

.90

95

69

.33

Cy

cle

199

-26

78

4.5

13

.414

343

.17

97

73

.42

crac

ks

de-

287

90

.81

3.7

1318

3.0

93

83

6.0

9te

cte

d29

79

4.0

14

.113

133

.15

58

67

.36

307

97

.21

4.1

1265

2.9

27

89

7.6

631

610

0-

--

--

-9

24

.00

End

of

test

14F8

0.7

0.2

51

0.1

1.1

795

0.1

65

0.1

7C

ycl

es1

-25

,27

2.6

8.3

.13

420

.82

35

.77

half

cycl

es31

3.0

8.4

1327

0.8

27

9.0

736

3.5

8.5

1308

0.8

79

13

.36

838

.18

.612

800

.88

15

4.7

248

14

6.7

8.3

1200

0.8

96

40

8.3

680

67

8.2

8.4

1197

0.8

78

69

6.6

2C

ycl

e79

5-

906

87

.98

.512

020

.89

37

85

.18

crac

ks

de-

956

92

.78

.811

731

.05

28

33

.88

tecte

d10

3110

08

.911

741

.01

39

11

.30

End

of

test

*F

or

cycl

esbe

twee

nth

ose

rep

ort

ed

,th

eare

ao

fa

sin

gle

hy

stere

sis

loo

pis

calc

ula

ted

asth

eav

erag

eo

fth

ep

rece

din

gan

dsu

ccee

din

gre

po

rted

loo

pare

as.

I-'

I-'

00

TABL

E3

.15

SUM

MAR

YOF

CON

STA

NT

AM

PLIT

UD

EC

YC

LIC

TEST

RESU

LTS

W14

X38

SPEC

IMEN

SW

ITH

3/8-

INC

HTH

ICK

FLA

NG

EA

NG

LES

Spe

cim

enA

ctu

ato

rF

req

uen

cyC

ycl

eP

erce

nt

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eR

emar

ksN

umbe

rD

isp

lace

men

t(H

z)

Num

ber

of

To

tal

Ro

tati

on

Mom

ent

aS

ing

leA

rea

of

Am

plit

ude

Fat

igu

e(r

ad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

(in

ches

)L

ife

x10

00)

Loo

pL

oops

*(k

ip-i

nch

es)

(kip

-in

ch

es)

14F

32

.80

.25

11

1.1

44

.616

483

1.4

83

1.4

82

22

.24

4.6

1538

26

.92

58

.40

33

3.3

45

.215

082

5.9

78

4.3

74

44

.44

5.3

1470

25

.50

10

9.8

75

55

.64

5.7

1454

25

.15

13

4.9

96

66

.74

5.5

1449

24

.67

15

9.6

6S

udde

ncr

ack

77

7.8

45

.614

352

4.3

91

84

.05

form

atio

nin

88

8.9

45

.414

092

4.0

02

08

.05

9th

cycl

e9

100

--

--

--

23

2.0

6E

ndo

fte

st

14F2

2.0

0.2

51

1.7

30

.715

101

9.3

81

9.3

85

8.6

31

.513

151

4.6

28

5.0

010

17

.23

1.8

1267

13

.94

15

6.0

620

34

.53

1.9

1210

13

.47

29

2.8

725

43

.13

2.0

1176

13

.13

35

9.2

030

51

.73

1.9

1166

13

.20

42

5.0

658

100

--

--

--

'U80

0E

ndo

fte

st

14F1

1.6

0.2

54

5.6

24

.511

729

.14

36

.56

I13

18

.12

3.9

1000

8.6

41

16

.32

233

1.9

24

.29

91

.58

.38

201.

3233

45

.82

5.2

1008

8.2

62

84

.43

435

9.7

25

.799

57

.87

36

4.8

8C

ycl

e43

-53

73

.62

5,4

904

7.7

94

43

.14

crac

ks

de-

638

7.5

24

.790

17

.67

52

0.3

8te

cte

d72

100

--

--

--

58

9,4

1E

ndo

fte

st

*F

or

cy

cle

sb

etw

een

tho

sere

po

rted

,th

eare

ao

fa

sin

gle

hy

stere

sis

loo

pis

calc

ula

ted

asth

eav

erag

eo

fth

ep

rece

din

gan

dsu

ccee

din

gre

po

rted

loo

pare

as.

Co

nti

nu

ed-

I-'

I-'

\D

TABL

E3

.15

(CO

NTI

NU

ED)

SUM

MAR

YO

FCO

NST

AN

TA

MPL

ITU

DE

CY

CLI

CTE

STRE

SULT

SW

14X

38SP

ECIM

ENS

WIT

H3/

8-IN

CH

THIC

KFL

AN

GE

AN

GLE

S

Spe

cim

enA

ctu

ato

rIF

req

uen

cyC

ycl

eP

erce

nt

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eR

emar

ksN

umbe

rD

isp

lace

men

t(H

z)N

umbe

ro

fT

ota

lR

ota

tio

nM

omen

ta

Sin

gle

Are

ao

fA

mp

litu

de

Fat

igu

e(r

ad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

(in

ches

)L

ife

x10

00)

Loo

pL

oops

*(k

ip-i

nch

es)

(kip

-in

ch

es)

14F

91

.00

.02

51

-11

4.8

--

--

--

--

No

dat

a**

0.2

523

10

.01

4.3

1169

2.0

52

24

.62

Cy

cles

12

-23

462

0.0

14

.611

242

.18

97

3.4

6as

sum

edeq

ual

662

8.7

14

.611

252

.29

51

18

.36

are

a86

37

.41

4.5

1109

2.3

82

16

5.1

710

64

6.1

14

.510

682

.37

52

12

.74

Cy

cle

126

-13

86

0.0

14

.510

632

.49

72

90

.75

crac

ks

de-

159

69

.11

4.8

1056

2.4

76

34

2.7

6te

cte

d17

57

6.1

14

.910

382

.48

23

82

.62

205

89

.11

4.8

1012

2.4

28

45

6.2

422

59

7.8

15

.096

42

.36

55

04

.14

227

98

.71

5.1

949

2.3

19

50

8.8

023

0-

--

--

--

-5

15

.76

End

of

test

14F4

0.5

0.2

51

0.0

37

.060

30

.43

90

.44

30

.09

6.8

630

0.2

39

1.0

210

12

.96

.862

20

.17

52

1.2

725

17

.26

.861

20

.16

54

6.7

780

12

3.2

7.0

622

0.2

11

15

0.1

982

62

3.9

7.2

633

0.2

24

15

5.6

314

514

2.1

7.0

623

0.1

88

28

4.3

621

016

0.9

7.2

638

0.2

49

42

6.4

2C

ycl

e26

80-

2876

83

.47

.161

70

.25

66

22

.11

crac

kd

e-29

768

6.3

7.1

613

0.2

35

64

6.8

5te

cte

d32

769

5.0

7.1

607

0.2

51

71

9.5

634

019

8.6

7.4

607

0.2

54

75

1.1

234

5010

0-

--

--

-7

63

,57

End

of

test

- *F

or

cycl

esbe

twee

nth

ose

rep

ort

ed

,th

eare

ao

fa

sin

gle

hy

stere

sis

loo

pis

calc

ula

ted

asth

eav

erag

eo

fth

ep

rece

din

gan

dsu

ccee

din

gre

po

rted

loo

pare

as.

**C

ycl

es1-

11ar

eh

alf

cycl

es-

nod

ata

reco

rded

.

I-'

N a

Co

nti

nu

ed-

TABL

E3

.16

SUM

MAR

YOF

CON

STA

NT

AM

PLIT

UD

EC

YC

LIC

TEST

RES

ULT

SW

8X21

SPEC

IMEN

SW

ITH

3/8-

INC

HTH

ICK

FLA

NG

EA

NG

LES

Spe

cim

enA

ctu

ato

rF

req

uen

cyC

ycl

eP

erce

nt

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eR

emar

ksN

umbe

rD

isp

lace

men

t(H

z)N

umbe

ro

fT

ota

lR

ota

tio

nM

omen

ta

Sin

gle

Are

ao

fA

mp

litu

de

Fat

igu

e(r

ad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

(in

ches

)L

ife

x10

00)

Loo

p·L

oops

*(k

ip-i

nch

es)

(kip

-in

ch

es)

8F1

1.5

0.0

25

11

0.0

17

.469

96

.49

96

.50

Cy

cles

1,2

-0

.25

33

0.0

37..6

89

1.2

13

.80

92

6.8

1h

alf

cycl

es5

50

.03

8.7

82

4.4

13

.12

15

3.3

97

70

.03

9.3

.7

91

.61

2.5

81

78

.82

Cy

cle

9-l

arg

e('

rack

so

bse

rved

1010

0-

--

--

-1

16

.57

End

of

test

8F4

1.0

0.0

25

11

.8-

--

--

-N

od

ata

-cy

-0

.25

71

2.5

24

.96

54

.45

.19

62

5.9

8cle

s1

,2

111

9.6

24

.46

21

.54

.99

94

6.2

7h

alf

cycl

es16

28

.62

4.8

61

5.4

4.8

84

70

.92

213

7.5

24

.661

14

.93

49

5.4

925

44

.62

4.9

60

5.1

4.9

09

11

5.1

6C

ycl

e3

0-c

rack

s31

55

.42

4.4

591

4.7

72

14

4.1

4d

ete

cte

d36

64

.32

4.9

60

4.9

4.9

04

16

8.4

041

73

.22

4.9

59

9.6

4.8

31

19

2.7

045

80

.42

4.9

593

4.8

68

21

1.6

651

91

.12

5.0

59

0.3

4.8

18

24

0.2

455

98

.22

5.2

57

5.1

4.5

71

25

8.8

956

100

--

--

--

26

3.4

6E

ndo

fte

st

*F

or

cycl

esbe

twee

nth

ose

rep

ort

ed

,th

ear

eao

fa

sin

gle

hy

stere

sis

loo

pis

calc

ula

ted

asth

eav

erag

eo

fth

ep

rece

din

gan

dsu

ccee

din

gre

po

rted

loo

pare

as.

I-'

N I-'

TABL

E3

.16

(CO

NTI

NU

ED)

SUM

MAR

YO

FCO

NST

AN

TA

MPL

ITU

DE

CY

CLI

CTE

STR

ESU

LTS

----

--

-----.-

------

--

------

-------

---._~

--._

---

Spe

cim

enA

ctu

ato

rF

req

uen

cyC

ycl

eP

erce

nt

Ran

geo

f.

Ran

geo

fA

rea

of

Cu

mu

lati

ve

Rem

arks

Num

ber

Dis

pla

cem

ent

(Hz)

Num

ber

of

To

tal

Ro

tati

on

Mom

ent

aS

ing

leA

rea

of

Am

pli

tud

eF

atig

ue

(rad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

(in

ches

)L

ife

x10

00)

Loo

pL

oops

*(kip~inches)

(kip

-in

ch

es)

8F3

0.7

0.2

51

0.7

7.5

462

1.1

54

1.1

5C

ycl

es1

-57

4.8

15

.56

88

.81

.92

29

.61

half

cy

cle

s15

10

.21

5.1

65

2.8

1.7

382

4.1

629

19

.71

5.7

64

0.7

1.7

00

48

.21

432

9.3

14

.76

02

.91

.80

47

2.7

957

38

.81

6.0

60

5.9

1.7

389

7.5

571

48

.31

5.8

601

1.7

141

21

.70

Cy

cle

86-

996

7.3

16

.16

03

.71

.78

51

70

.72

crac

kd

ete

cte

d11

37

6.9

16

.15

96

.61

.83

21

96

.07

126

85

.71

6.4

577

.91

.815

21

9.7

614

19

5.9

16

.35

73

.41

.82

82

47

.09

145

98

.61

6.6

56

5.6

1.7

62

25

4.2

414

710

0-

--

--

-2

57

.76

End

of

test

8F2

0.5

0.2

51

0.1

84

.833

40

.36

40

.36

Cy

cles

1-1

0-

213

.89

.95

81

.30

.60

61

0.3

1h

alf

cy

cle

s57

10

.29

.95

78

.50

.42

72

8.8

111

32

0.2

10

,45

59

.50

.48

85

4.4

622

54

0.2

10

,45

46

.70

.50

11

09

.85

Cy

cle

280

-28

15

0.2

10

.95

34

.20

.60

51

40

.87

crac

ks

de-

341

60

.91

0.7

53

2.5

0.6

70

17

9.1

5te

cte

d39

37

0.2

10

.85

22

.80

.61

32

12

.48

449

80

.21

0.9

59

8.6

0.6

04

24

6.5

550

59

0.2

10

.947

7.9

0.5

60

27

9.1

255

99

9.8

11

.54

37

.80

,49

13

07

.47

560

100

11

.443

00

.51

93

07

.99

End

of

test

*F

or

cycl

esb

etw

een

tho

sere

po

rted

,th

eare

ao

fa

sin

gle

hy

stere

sis

loo

pis

calc

ula

ted

asth

eav

erag

eo

fth

ep

rece

din

gan

dsu

ccee

din

gre

po

rted

loo

pare

as.

f-'

N N

TABL

E3

.17

SUM

MAR

YOF

CON

STA

NT

AM

PLIT

UD

EC

YC

LIC

TEST

RES

ULT

SW

8X21

SPEC

IMEN

SW

ITH

5/16

-IN

CH

THIC

KFL

AN

GE

AN

GLE

S

Spe

cim

enA

ctu

ato

rF

req

uen

cyC

ycl

eP

erce

nt

Ran

geo

fR

ange

of

Are

ao

fC

um

ula

tiv

eR

emar

ksN

umbe

rD

isp

lace

men

t(H

z)N

umbe

ro

fT

ota

lR

ota

tio

nM

omen

ta

Sin

gle

Are

ao

fA

mpl

itud

eF

atig

ue

(rad

ian

s(k

ip-i

nch

es)

Hy

stere

sis

Hy

stere

sis

(in

ches

)L

ife

x10

00)

Loo

p*L

oops

(kip

-in

ch

es)

8F8

1.5

0.0

25

16

.32

1.2

57

8.8

6.3

81

6.3

8C

ycl

eI-

half

0.2

53

18

.83

9.1

724

10

.95

02

8.2

8cy

cle

63

7.5

39

.77

03

.21

0.0

87

59

.40

Cy

cle

8-c

rack

s9

56

.33

9.7

69

0.5

9.7

89

89

.07

dete

cte

d13

81

.33

9.9

65

5.4

9.3

39

127

.10

159

3.8

40

.86

10

.98

.88

51

45

.10

1610

0-

--

--

-1

53

.98

End

of

test

8F7

1.0

0.2

51

1.6

2.0

47

3.0

2.7

46

2.7

5C

ycl

es1

-5-h

alf

91

4.5

24

.66

31

.74

.06

52

9.9

9cy

cle

s19

30

.62

5.6

61

7.1

3.9

89

70

.22

315

0.0

25

.46

09

.43

.92

21

17

.65

Cy

cle

30

-43

69

.42

5.4

59

5.9

3.8

25

16

4.0

9cr

ack

sd

e-56

90

.32

5.7

52

9.3

3.6

08

21

2.2

9te

cte

d61

98

.42

6.9

49

6.0

3.0

90

22

8.7

867

100

--

--

--

23

1.8

7E

ndo

fte

st

8F6

0.7

0.2

51

-16

9-

--

--

--

--

-N

od

ata*

*17

09

8.3

17

.54

31

.81

.37

7-

-C

ycl

e9

5-

171

98

,81

7.3

41

7.8

1.1

82

--

crac

ks

de-

172

99

.41

7.7

43

0.3

1.2

51

--

tecte

d17

310

0-

--

--

--

-E

ndo

fte

st

*F

or

cycl

esbe

twee

nth

ose

rep

ort

ed

,th

ear

eao

fa

sin

gle

hy

stere

sis

loo

pis

calc

ula

ted

asth

eav

erag

eo

fth

ep

rece

din

gan

dsu

ccee

din

gre

po

rted

loo

pare

as.

**M

alfu

nct

ion

of

reco

rdin

gsy

stem

.

f-'

N VI

TABLE 4.1

COMPARISON OF PREDICTED INITIAL CONNECTION STIFFNESSWITH TEST RESULTS

Initial Slope (k. -in. jradian)

Predicted

Specimen Including ExcludingNumber Test Shear Shear

14S1 195,000 152,900 172 ,00014S2 295,000 328,700 409,80014S3 115,900 150,000 169,50014S4 221,900 212,200 240,90014S5 247,000 191,000 217,00014S6 286,000 408,800 518,90014S8 579,000 748,000 1,093,00014S9 258,000 408,800 518,9008S1 66,700 62,100 72,3008S2 123,400 103,200 129,000883 104,700 63,300 73,5008S4 15,300 12,500 13,0008S5 76,700 52,900 59,700886 39,500 31,700 34,5008S7 48,000 51,400 58,2008S8 70,000 80,100 94,5008S9 104,000 132,700 169,4008S10 427,000 292,600 453,500

124

TABL

E4

.2PR

EDIC

TIO

NO

FCU

MU

LATI

VE

DAM

AGE

USI

NG

FATI

GU

ER

ELA

TIO

NSH

IPBA

SED

ONN

OM

INA

LCH

ORD

RO

TATI

ON

IND

EXW

14X

38BE

AMSP

ECIM

ENS

.......

N VI

Co

nti

nu

ed-

~_._----

No

min

al------

Nom

inal

--.-

--.

.A

ctu

ato

rN

onnn

alD

isp

lace

men

tR

ange

of

Fla

ng

eA

ngle

Ap

pli

edC

ycl

es,

n,

Pre

dic

ted

Co

nst

ant

Spe

cim

enA

mp

litu

de

Ro

tatj

on

,4>

Cho

rdR

ota

tio

nat

Dis

pla

cem

ent

Nn

pli

tud

cF

atig

ue

n/N

fE

n/N

fN

umbe

r(i

nch

es)

(rad

iun

sx

1000

).

Ind

ex,

R*

Am

pli

tud

eL

ife,

Nf**

------

1-----------

--14

C1

0.2

3.5

0.0

37

178

4,9

49

0.0

00

20

.00

02

0.4

7.0

0.0

74

158

,91

00

.00

17

0.0

01

90

.61

0.5

0.1

11

152

,38

30

.00

63

0.0

08

20

.81

4.0

0.1

48

1593

50

.01

60

0.0

24

21

.01

7.5

0.1

85

1545

20

.03

32

0.0

57

41

.22

1.1

0.2

22

1525

00

.06

00

0.1

17

41

.42

4.6

0.2

59

1515

10

.09

93

0.2

16

71

.62

8.1

0.2

96

1698

0.1

63

30

.38

00

1.8

31

.60

.33

215

67

.50

.22

22

0.6

02

22

.03

5.1

0.3

69

1248

0.2

50

00

.85

22

14C

20

.23

.50

.04

113

60

,83

20

.00

02

0.0

00

20

.47

.00

.08

213

6,3

80

0.0

02

00

.00

22

0.5

8.8

0.1

03

23

,03

90

.00

07

0.0

02

90

.61

0.5

0.1

23

131

,70

60

.00

76

0.0

10

50

.81

4.0

0.1

64

1566

90

.02

24

0.0

32

91

.01

7.5

0.2

05

1332

40

.04

01

0.0

73

01

.22

1.1

0.2

46

1317

90

.07

26

0.1

45

61

.42

4.6

0.2

87

1710

80

.15

74

0.3

03

01

.62

8.1

0.3

28

1470

0.2

00

00

.50

30

1.8

31

.60

.36

91

348

0.2

70

80

.77

38

2.0

35

.10

.41

04

340

.11

76

0.8

91

4

----

---_

._-.

__..---------------------

----

-

[(d

+t)

tan

ep]*R

=2

g-d

/2-t

w

**Fr

omE

qu

atio

n:

N f=

.1.8

68

(R)-

3.2

53

1(s

eeF

ig.

4.1

9)

TABL

E4

.2(C

ON

TIN

UED

)PR

EDIC

TIO

NO

FCU

lvlL

JLAT

IVE

DM-tA

GEU

SIN

GFA

TIG

UE

REL

ATl

ON

SIH

PBA

SED

ONN

OM

INA

LCH

ORD

ROTA

TIO

NIN

DEX

W14

X38

BEAM

SPEC

IMEN

S

--.---------~.

Nom

inal

Nom

-inal

Nom

inal

Act

uat

or

Dis

pla

cem

ent

Ran

geo

fF

lan

ge

Ang

leA

pp

lied

Cy

cles

,n

,P

red

icte

dC

on

stan

tS

peci

men

Am

pli

tud

eR

ota

tio

n,

4>C

hord

Ro

tati

on

at

Dis

pla

cem

ent

Am

pli

tud

eF

atig

ue

n/N

fI:

n/N

fN

umhe

r(i

nch

es)

(rad

ian

sx

1000

)In

dex

,R*

Am

pli

tud

eL

ife

N**

,f

-f--.

14C

30

.23

.50

.04

612

41

,83

70

.00

03

0.0

00

30

.47

.00

.09

114

4,5

47

0.0

03

10

.00

34

0.6

10

.50

.13

712

1,2

01

0.0

10

00

.01

34

0.8

14

.00

.18

212

477

0.02

520

.03

86

1.0

17

.50

.22

712

232

0.0

51

70

.09

03

1.2

21

.10

.27

312

128

0.0

93

80.

1841

1.4

24

.60

.31

913

770

.16

88

0.3

52

91

.62

8.1

0.3

64

1250

0.2

40

00

.59

29

1.8

31

.60

.41

014

340

.41

18

1.00

472

.03

5.1

0.4

55

424

0.1

66

71

.17

14

14C

40

.23

.50

.04

112

60

,83

20

.00

02

0.00

020

.47

.00

.08

112

6,6

40

0.0

01

80

.00

20

0.6

10

.50

.12

212

1,7

52

0.0

06

80

.00

88

0.8

14

.00

.16

312

683

0.0

17

60.

0264

1.0

17

.50

.20

312

334

0.0

35

90

.06

23

1.2

21

.10

.24

412

184

0.06

520.

1275

1.4

24

.60

.28

412

112

0.10

710

.23

46

1.6

28

.10

.32

512

720

.16

67

0.4

01

31

.83

1.6

0.3

66

949

0.1

83

70.

5850

14B

11

.83

1.6

0.4

10

1234

0.3

52

90

.35

29

1.6

28

.10

.36

412

500

.24

00

0.5

92

91

.42

4.6

0.3

19

1277

0.1

55

80.

7487

1.2

21

.10

.27

312

128

0.0

93

80

.84

25

1.0

17

.50.

227

1223

20

.05

17

0.89

42

----

--_

.._-_

._-'

---_

.I

--

-----_

._--

*R=

2[(

d+

t)ta

n<P

]g

-d/2

-tJ

w

**Fr

omE

qu

atio

n:

Nf

=1

.86

8(R

)-3

.25

31

(see

Fig

.4

.19

)

..... N 0\

·TA

BLE

4.3

PRED

ICTI

ON

OF

CUM

ULA

TIV

EDA

MAG

EU

SIN

GFA

TIG

UE

RE

LA

TIO

NSm

pBA

SED

ONN

OM

INA

LCH

ORD

ROTA

TIO

NIN

DEX

W8X

21BE

AMSP

ECIM

ENS

----

Nom

inal

-N

omin

alN

omin

alA

ctu

ato

rD

isp

lace

men

tR

ange

of

Fla

ng

eA

ngle

Ap

pli

edC

ycl

es,

n,

Pre

dic

ted

Co

nst

ant

Spe

cim

enA

mp

litu

de

Ro

tati

on

,iJl

Cho

rdR

ota

tio

nat

Dis

pla

cem

ent

Nn

pli

tud

eF

atig

ue

n/N

fE

n/N

fN

umbe

r(i

nch

es)

(rad

ian

sx

1000

)In

dex

,R

*A

mp

litu

de

Lif

e,

Nf*

*

f--._

--

8C1

0.2

6.1

0.0

56

1122

,062

0.0

00

50.

0005

0.4

12

.10

.11

112

2,3

83

0.0

05

00

.00

55

0.6

18

.20

.16

713

631

0.0

20

60

.02

61

0.8

24

.20

.22

214

250

0.0

56

00

.08

21

1.0

30

.30

.27

814

120

0.1

16

70

.19

88

1.2

36

.40

.33

312

670

.17

91

0.3

79

91

.44

2.4

0.3

89

240

0.0

50

00

.42

79

8C2

0.2

6.1

0.0

60

111

7,6

27

0.0

00

60

.00

06

0.4

12

.10

.12

012

1,8

48

0.0

06

50

.00

71

0.6

18

.20

.18

012

494

0.0

24

30

.03

14

0.8

24

.20

.24

013

194

0.0

67

00

.09

84

1.0

30

.30

.30

012

940

.12

77

0.2

26

11

.23

6.4

0.3

60

1252

0.2

30

80

.45

69

1.4

42

.40

.42

04

31

.50

.12

70

0.5

83

98C

30

.26

.10

.07

012

10

,67

60

.00

11

0.0

01

10

.41

2.1

0.1

40

121

,12

00

.01

07

0.0

11

80

.61

8.2

0.2

10

1229

90

.04

01

0.0

51

90

.82

4.2

0.2

80

1211

70

.10

26

0.1

54

51

.03

0.3

0.3

50

1257

0.2

10

50

.36

50

1.2

36

.40

.42

010

31

.50

.31

75

0.68

25

1__

__

---------

---

*R=

2[(

d+

t)ta

n~J

g-d

/2-t

w

**Fr

omE

qu

atio

n:

Nf

=1

.86

8(R

)-3

.25

31

(see

Fig

.4

.19

)C

on

tin

ued

-f-

'N ---

.l

TABL

E4

.3(C

ON

TIN

UED

)PR

EDIC

TIO

NO

FCU

MU

LATI

VE

DANA

GEU

SIN

GFA

TIG

UE

REL

ATl

ON

SIIlP

BASE

DON

NO

MIN

AL

CHOR

DRO

TATI

ON

IND

EXW

8X21

BEAM

SPEC

IMEN

S

Nan

dn

alN

omin

alan

geA

ngle

Ap

pli

edC

ycl

es,

n,

Pre

dic

ted

Co

nst

ant

rdR

ota

tio

nat

Dis

pla

cem

ent

Am

pli

tud

eF

ati

gu

en/

Nf

En/N

fn

dcx

,R*

Am

pli

tud

eL

ife

N**

,f

----

-_._

_.0

.42

012

31

.50

.38

10

0.3

81

00

.35

012

570

.21

05

0.5

91

50

.28

012

117

0.1

02

60.

6941

0.2

10

1229

90

.04

01

0.7

34

10

.14

012

1,1

20

0.0

10

70

.74

49

0.0

70

121

0,6

76

0.0

01

10

.74

60

0.4

20

13

1.5

0.0

31

70

.77

77

-_

__

__

__

__

l-.

FIC

ho I

36

.43

0.3

24

.21

8.2

12

.16

.13

6.4

----

No

min

af­

Ran

geo

fR

ota

tio

n,

tp(r

ad

ian

sx

1000

)

---_

._--

---

"'--

-

1.2

1.0

0.8

0.6

0.4

0.2

1.2

Act

uat

or

Dis

pla

cem

ent

Am

pli

tud

e(i

nch

es)

8B1

Spe

cim

enN

umbe

r

*R=

2[(

d+

t)ta

n~l

g-d

/2-t

Jw

**Fr

omE

qu

atio

n:

Nf

=1

.86

8(R

)-3

.25

31

(see

Fig

.4

.19

)

.......

N ex>

TABL

E4

.4pn

ED

ICT

ION

OF

CU~IULATIVF.

DAM

AGE

USI

NG

FATI

GU

ER

ELA

TIO

NSH

IPBA

SED

ONH

YST

ERET

ICEN

ERG

Y

W14

X38

BEAM

SPEC

IMEN

S ----

----

------------

._-

----

Act

uat

or

Ave

rage

Num

ber

of

Pre

djc

ted

Co

nst

ant

Dis

pla

cem

ent

Hy

stere

sis

Loo

pA

pp

lied

Cy

cles

,n

,A

mp

litu

de

Fat

igu

eS

peci

men

Am

pli

tud

eA

rea

at

Dis

pla

cem

ent

Lif

e,

Nf*

n/N

fr.

n/N

fN

umbe

r(i

nch

es)

(kip

-in

ch

es)

AlI

lpli

tud

e

1--

-------

14C

10

.2-

17-

--

0.4

0.0

915

15

,19

5.0

010

.001

00

.60

.32

153

,31

7.0

045

.005

50

.80

.89

1597

2.0

154

.020

91

.01

.35

1540

4.0

371

.058

01

.23

.26

1520

5.07~2

.131

21

.45

.06

1512

1.1

240

.255

21

.66

.57

1688

.181

8.4

370

1.8

8.5

315

64

.5.2

326

.669

62

.01

0.4

812

50

.5.2

376

.907

2

14C

20

.2-

13-

--

0.4

0.1

813

6,6

14

.002

0.0

020

0.5

0.3

42

3,0

83

.000

7.0

027

0.6

0.3

413

3,0

83

.004

2.0

069

0.8

0.9

515

899

.016

7.0

236

1.0

2.2

713

316

.041

1.0

647

1.2

4.0

813

156

.083

3.1

480

1.4

6.2

217

94.1

809

.328

91

.68

.58

1464

.218

8.5

477

1.8

10

.90

1348

.270

8.8

185

2.0

13

.79

436

.111

1.9

296

._

--------

*Fro

mE

qu

atio

n:

-1.2

0N

f=

84

4.9

(E)

(see

Fig

.4

.20

)

Co

nti

nu

ed-

t-'

N l.O

TABL

E4

.4(C

ON

TIN

UED

)PR

EDIC

TIO

NOF

CUM

ULA

TIV

EDA

MAG

EU

SIN

GFA

TIG

UE

REL

ATI

ON

SIIIP

BASE

DON

HY

STER

ETIC

ENER

GY

W14

X38

BEAM

SPEC

IMEN

S

-------

Act

uat

or

Ave

rage

Num

ber

of

Pre

dic

ted

Co

nst

ant

Dis

pla

cem

ent

Hy

stere

sis

Loo

pA

pp

lied

Cy

cles

,n

,A

mpl

itud

eF

atig

ue

Spe

cim

enA

mpl

itud

eA

rea

at

Dis

pla

cem

ent

Lif

e,

Nfl:

n/N

fIn

/Nf

Num

ber

(in

ches

)(k

ip-i

nch

es)

AmpI

iti

lde

-14

C3

0.2

0.0

312

56

,78

8.0

002

.000

20

.40

.09

1415

,195

.000

9.0

011

0.6

0.5

712

1,6

59

.007

2.0

083

0.8

1.6

412

467

.025

7.0

340

1.0

3.4

812

189

.063

5.0

975

1.2

6.3

012

92

.5.1

297

.227

21

.48

.95

1361

.213

1.4

403

1.6

12

.02

124

2.5

.282

4.7

227

1.8

14

.97

1433

.424

21

.14

69

2.0

16

.73

429

.137

91

.284

814

C4

0.2

0.0

212

92

,37

8.0

001

.000

10

.40

.10

1213~391

.000

9.0

010

0.6

0.4

112

2,4

63

.004

9.0

058

0.8

1.03

1281

5.0

147

.020

61

.02

.09

1234

9.0

344

.OS5

01

.23

.64

1217

9.0

670

.122

01

.45

.65

1210

6.1

132

.235

21

.67

.99

126

9.5

.172

7.4

079

1.8

10

.44

95

0.S

.178

2.5

861

1--

.---

~---_._-

-

-120

*Fro

mE

qu

atio

n:

Nf

=8

44

.9(E

).

(see

Fig

.4

.20

)C

on

tin

ued

-.....

.C.

N o

TABL

E4

.4(C

ON

TIN

UED

)PR

EDIC

TIO

NOF

CUM

ULAT

IVE

DAM

AGE

USI

NG

FATI

GU

ER

ELA

TIO

NSH

IPBA

SED

ONH

YST

ERET

ICEN

ERGY

W14

X38

BEAM

SPEC

IMEN

S

Act

uat

or

Ave

rage

Num

ber

of

Dis

plac

emen

tH

yst

eres

isL

oop

App

lied

Cy

cles

,n

,S

peci

men

Am

plit

ude

Are

aat

Dis

plac

emen

tN

umbe

r(i

nch

es)

(kip

-in

ches

)A

mpl

itud

e

14B

11

.816

.08

121

.610

.71

121

.47.

6412

1.2

5.1

612

1.0

3.2

412

Pre

dic

ted

Co

nst

ant

Am

plit

ude

Fat

igu

eL

ife,

N/

30 49 73.5

11

820

6

n/N

f

.400

0.2

449

.163

3.1

017

.058

3

En/

Nf

.400

0.6

449

.808

2.9

099

.968

2

*Fro

mE

qu

atio

n:

N f=

84

4.9

(E)-

1.2

0(s

eeF

ig.

4.2

0)

to-'

tN to-'

TABL

E4

.5PR

EDIC

TIO

NOF

CUM

ULA

TIV

EDA

MAG

EU

SIN

GFA

TIG

UE

REL

ATI

ON

SHIP

BASE

DON

HY

STER

ETIC

ENER

GYW

8X21

BEAM

SPEC

IMEN

S

---

--

Act

uat

or

Ave

rage

Num

bcT

of

Pre

dic

ted

Co

nst

ant

Dis

pla

cem

ent

Hy

stere

sis

Loo

pA

pp

lied

Cy

cles

,n

,A

mpl

itud

eF

atig

ue

Spe

cim

enA

mpl

itud

eA

rea

at

Dis

pla

cem

ent

Lif

e,

N/

n/N

fE

n/N

fN

umbe

r(i

nch

es)

(kip

-in

ches

)A

mpl

itu

de

----

8C1

0.2

0.0

41

117

,465

.000

6.0

006

0.4

0.1

912

2,4

37

.004

9.0

055

0.6

0.8

11

339

0.0

333

.038

80

.82

.36

14.1

01.1

386

.177

41

.04

.27

144

7.5

.294

7.4

721

1.2

6.0

912

30.4

000

.872

11

.47

.77

22

2.5

.088

9.9

610

8C2

0.2

0.2

911

1,4

29

.007

7.0

077

0.4

0.2

812

1,4

93

.008

0.0

157

0.6

1.2

812

219

.054

8.0

705

0.8

2.9

313

76

.5.1

699

.240

41

.05

.00

1239

.307

7.5

481

1.2

7.1

012

25.4

800

1.0

281

1.4

9.5

64

17.2

353

1.2

634

-------

----

---

------

--------

*Fro

mE

qu

atio

n:

Nf

=2

98

.65

(E)-

1.2

63

9(s

eeF

ig.

4.2

0)

Co

nti

nu

ed-

~ U'I

N

TABL

E4

.5(C

ON

TIN

UED

)PR

EDIC

TIO

NOF

CUM

ULA

TIV

EDA

MAG

EU

SIN

GFA

TIG

UE

REL

ATI

ON

SHIP

BASE

DON

HY

STER

ETIC

ENER

GYW

8X21

BEAM

SPEC

IMEN

S

----

--A

ctu

ato

rA

vera

geN

umbe

ro

fP

red

icte

dC

on

stan

tD

isp

lace

men

tH

yst

ere

sis

Loo

pA

pp

lied

Cy

cles

,n

,A

mpl

itu

de

Fat

igu

eS

peci

men

Am

plit

ude

Are

aat

Dis

pla

cem

ent

Lif

e,

Nr*

n/N

fE

n/N

fN

umbe

r(i

nch

es)

(kip

-in

ches

)A

mpl

itud

e

8C3

0.2

0.0

212

41,9

43.0

003

.000

30

.40

.25

121

,72

3.0

070

.007

30

.61

.05

1228

1.0

427

.050

00

.82

.67

1286

.139

5.1

895

1.0

5.0

412

38

.5.3

117

.501

21

.27

.84

1022

.454

6.9

558

8Bl

1.2

8.2

312

20

.5.5

854

.585

41

.04

.96

123

9.5

.303

8.8

892

0.8

2.6

912

85

.5.1

404

1.0

296

0.6

1.2

012

237

.050

61.

0802

0.4

0.3

512

1,1

26

.010

71.

0909

0.2

0.0

312

25,1

24.0

005

1.0

914

1.2

6.6

21

27

.5.0

364

1.12

78

1---

----

--~-

*Fro

mE

qu

atio

n:

-1.

2639

Nf

=29

8.65

(E)

(see

Fig

.4

.20

).....

.tN tN

FlGURE..S

134

135

Holes for Attachmentto Load Actuator

Stub Column

+

Web Angle

W 14 X 38•••

20'-0'"

Hole for Mountingto Support Frame

,Ir

+

a. W 14 X 38 BEAM-TEST SPECIMEN

W 12 X 58

+ ~ '7 W 8 X 21 [ [;J W8 X 21 ~

-

12'-0"

• 1'" ....

b. W 8 X 21 BEAM TEST SPECIMEN

+

..

FIG. 2.1 GENERAL CONFIGURATIONS OF TEST SPECIMENS

N " o .... , .- X <D 0)

X N s

I £3

/4"

Pla

te2

1/4

"2

1/2

"

L-6

X4

X0

'-8

"th

ickn

ess

varia

ble

2L

-4X

31

/2X

0'-

81

12

"----

-thic

kn

ess

vari

ab

le

W14

X3

8

'\

L-6

X4

X0

'-8

"th

ickn

ess

vari

ab

le

2"

<0 " v

1'-

0-1

18

"~

r5

1/2

"-.-

.,I

....31/2'~

,4

II

FIG

.2.

2aD

ET

AIL

SO

FC

ON

NE

CT

ION

FO

RW

14X

38B

EA

M-

BO

LT

ED

SP

EC

IME

NS

I-'

0-l

0\

I ft3

/4"

Pla

te2

1/4

"2

1/2

"r

10

Irt<

;;~~i

•I

"II

II

II

II

II

I~

I,

III

~'I

II""

I"I,

II

I"~ .tb

.k

l~

~

25

/S"

~'r.

~..t

n-

t-"I"

"Y

r-

!!~'I

I

:I

~"~

II

YT

"I

, ",

II

:I

II

I, 'i I,

... ~(")

..: ro > , ex> "­ III

N v "- -~W

8X

21

L,si

zeva

ria

ble

2L

-4X

31

/2X

1/4

X0

'-5

1/2

"

\L,

sire

vari

ab

le

N "- - x ex> ll) X No .... " .... 3::

2"

FIG

.2

.2b

DE

TA

ILS

OF

CO

NN

EC

TIO

NF

OR

W8X

21B

EA

M-

BO

LT

ED

SP

EC

IME

NS

i-'

VI

-..]

L-6X

4XO

'B"

3/.'

Pla

te

1'-o

Va"

ri

5W

'i

lII

,.,

II~,..

"II

...II I.

1F~,.. Ir

,~

...\,1

1

r,,, 'I

I

r,."

~l

"'I'

"

~

21

9/3

2"

•.01

;iN " \l

!!Ir

1'''

,"

l!

~ N

'<t

to ,.... '­ ,.... M M

typ

typ

typ

typ

6% typ

51,6

2L-4

X3'

hX%

XO

'-BV

2'

W14

X38

5/1

6L-

6X4X

O'B

"

thic

kne

ssva

ria

ble

---II'~~I

14Y,

"

I <t.

3:~I o ,.... ,.... , to 0> X C\J ,....

FIG

.2.

3D

ET

AIL

SO

FC

ON

NE

CT

ION

FO

RW

14X

38B

EA

M-

BO

LT

ED

­W

EL

DE

DS

PE

CIM

EN

Sf-

'(.

N

00

~~

.......09;lQ.;:,

(f) enE 2ttl ,Q) <aJ 'O.

WOJ~en

... w0 ~....ttl c:;:,.... 0(,J« u..~ a 2

"C Wttl ~.3 en

>-enC)z0<0....JU.0U

(J) ~Q) <"C;:, 2

<-' w... :c~(5 U0:: en

.qN

C)

U.

139

FIG. 2.5 BEAM SUPPORTS FOR TEST SPECI MENS

140

141

·FIG. 2.6 LATERAL SUPPORT SYSTEM FOR TEST "SPECrMENS'

FIG. 2.8 CLOSE-UP OF TEST CONNECTIONJ

142

Dis

plac

emen

tor

Load

Contro.~l-+-,~

with

Dig

ital

ir

i

Rea

dout -}

XVP

lott

er

MTS

Con

trol

XVP

lott

er(L

oad

vs.

Dis

plac

emen

t}to

Mic

roco

mpu

ter

55-k

ipH

ydra

ulic

Act

uato

rw

ithLV

DTan

dL

oadc

ell

Tes

tSp

ecim

en

Str

ain

Gag

ean

dLV

DTD

ata

toC

ompu

ter

20C

hann

elV

olta

geC

ondi

tion

eran

dA

mpl

ifie

r Mot

orol

a68

00M

icro

com

pute

rw

ith32

Cha

nnel

Ana

log

toD

igit

alC

onve

rsio

n

Dig

ital

Dat

ato

VAX

for

Stor

age

and

Proc

essi

ng

IF

IG.

2.9

:S

CH

EM

ATI

CO

FT

ES

TIN

GA

ND

RE

CO

RD

ING

I'E

QU

IPM

EN

TVA

X11

/780

l-'

.p,.

<oN

144

Bar Attaching LVOTto Beam Flanges

11 "114-4---~

]x}--_c:::::t==/LVDT

W 14 X 381===:==:==:1==:==:==:==:==:======1 Position of W 8 X 21

with respect to LVOT s

W 8 X 21

Bar f9r Attachment

to Stub Column

Position of W 14 X 38

with respect to LVOT s

"CXl

CXl "-"- ...-N

Plastic

"15/16

3/16"

Flexible Rod

Threaded Holefor LVOT Probe

11116

FIG. 2.10 LVDT MOUNTING APPARATUS

...o...,tll::l...,

.(.)

«

a. LOW-HIGH AMPLITUDE

b. caNSTANT AMPLITUDE

145

...o«l::l.....(.)

«

c. HIGH-LOW AMPLITUDE

FIG. 2.11 TYPICAL TIME-DISPLACEMENT HISTORIES

146

---J- LVDT Data~est Connection

/

Specimen 14S411

//IfjI)

o

"'"N

oN(V)

oeoeo

...~"- ."

iO

iL{)1

en!<D'.c t(.)1ci·-'0'eo

: ~ "'". "';-1

C<DOE0","

~

".J

o<.0

oeo

oo 4 8

)

12, • I

16 20 24-Rotation, radians (X1000)""'

-'28

I

32I

36,

40 .

FIG. 3.1 COMPARISON OF MOMENT-ROTATION CURVES OBTAINED FROMLVDT MEASUREMENTS WITH CURVE OBTAINED FROM ACTUATOR

DISPLACEMENTS

I CL I

a.A

LL

-SO

LT

ED

CO

NN

EC

TIO

N

I Q. I

b.S

OL

TE

D-W

EL

DE

DC

ON

NE

CT

ION

FIG

.3.2

DE

FO

RM

AT

ION

PA

TT

ER

NS

INB

EA

M-C

OL

UM

NC

ON

NE

CT

ION

EL

EM

EN

TS

>-.•

+:>­

-....J

148

I FIG. 3.3 FLANGE ANGLE FROM SPECIMEN 14S2AFTER TEST---_._~...•.• -. ~,. ----

-FI-G~-3.4 WEB ANGLES FROM SPECIMEN 14S2 AFTER TEST

149

ooo.

~.,....----------------------------------tooo~

oooc

1452t = ~/I

coo0)

oocCD

Bo lt Di ameter: 3/4"

Connection Details

Flange Angles: thickness variablegage on col. = 2~'1

length = 0 1 -8/1

Web Angles: 2L-4x3~x~XOI_8~/I

·0rn 'wo

..c: 0(.)C'­C..,a.~c:::..;-0COWillEo~o

ooLn

ooo::r

ooc(Y)

oooC'J

ooo

1451t = 3/8"

12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00Rotation, radians (X1000)

o01'.---,.----r---"""T""----'j---,....--""'T"""------r'--~r__--~--..,...J

4.00 B.OO

FIG. 3.5 EFFECT OF FLANGE ANGLE THICKNESS ON STATICMOMENT-ROTATION BEHAVIOR - W14X38 BEAM CONNEC­TION (BOLT DIAMETER = %")

150

40.036.0

1455t=3/8"

32.0

1456t=!Z"

1458t=5/8"

-- 14S9t=!z'

7/8"

2L-4X3!zX~XO'-8!z"

thickness variablegage on col. = 2!z"length = 01 -8"

28.0

Connection Details

Web Angles:

Bolt Diameter:

Flange Angles:

16.0 20.0 24.0Rotation, radians (X1000)

12.08.0

0

00::t'C\I

0

00C\IC\I

0

000C\I

0

00co......

0

00lD......

0

0C::t'

en ......Gl

.J::.() 0CI 0

.9- 0~ C\I......iGl oE .00:20

0......

0

00co

0

00LD

0

00::t'

0

00C\I

0

0 0 . 0 4.0

FIG.3.6 EFFECT OF FLANGE ANGLE THICKNESS ON STATIC MOMENT­ROTATION BEHAVIOR - W14X38 BEAM CONNECTION (BOLTDIAMETER = 7/s")

151

1455d =7/8"b

Connection Details

Web Angles: 2L-4X3!zX~XOI_8!z"

40.036.032.028.0

1451d -3/4"b-

Flange Angles: L-6X4X3/8XO I-8"

Bolt Diameter: variable

12. 0 16. 0 20. 0 24. 0Rotation, radians (X1000)

0

0CDm

0

0CDCD

0

00CD

0

0C'JC'

0

0=t'CD

0

0CDt..n

(/)Q).c )

uco" co,e- =t'~-C:o

~c:i00~=t'

0

0C'J(r)

0

0=t'(\J

0

0CD......

0

0CD

0

0 0 . 0 4.0 8.0

FIG.3.7a EFFECT OF BOLT DIAMETER ON STATIGMOMENT-ROTATIONBEHAVIOR - W14X38 BEAM CONNECTION (FLANGE ANGLETHICKNESS = %")

152

oo

~-r--------------------------------.....,ooo~

......

o

ooo......

o

oom

14S6/ db=7/8"

--14S9d =7/8"b

14S2d =3/4"b

oooco

ooot"-

en(])

.s:::ucO

'...e.0:;2f6-c(])

Eoo .~oo

en

ooo;:t'

ooo(Y]

Connection Details

Flange Angles: L-6X4~XOI_8"

oooN

Web Angles: 2L-4X3~X~4XOI_8~"

Bolt Diameter: variableooo~

40.036.032.028.024.020.016.012.08.04.0

O--.-__..,...__...,.__.....,. ~__.,.-__..,....__"""T'"__-r__--, ,.....0 0. 0

Rotation, radians (X1000)

FIG.3.7b EFFECT OF BOLT DIAMETER ON STATIC MOMENT-ROTATIONBEHAVIOR - W14X38 BEAM CONNECTION (FLANGE ANGLETHICKNESS = 112")

153

o

~-------------------------------------,m

oococo

1454t = 3/811

C

oooco

oo~

lD

1451t = k ll

C 4

.0

~c..c: lD()Lnc

"

.e. c~ .

_ 0

-coa3 :::rEo

:2: 0

oo~

oo~

\\JConnection Details

oClD

o

oCO

Flange Angles: L-6x4x3/8xO'-8 11

Web Angles: thickness variablegage on col. = 2~1I

length = OI-8~1I

BoIt Di ameter: 3/4"

12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00- ,.~ __ ..,Rotation, radians (X1000)

8.004.00

0-A-__....,. .,....__~__~~__...,....__-.,. .,....__~__-., .,......o·

FIG. 3.8 EFFECT OF WEB ANGLE THICKNESS ON STATICMOMENT-ROTATION BEHAVIOR - W14X38 BEAM CONNECTION

154

C

ogsr-----------------------------------"C

Ccoco

C

oCco

1451Lc = 8~1I

C

C:::TLO

1453L =5k: 1I

c 2

CCIl •Q)C

..c: LO()IF,C..,C-.- C~ .+..: CCCl'JQ) :::T

Eo~c

CC:::T

C

C:::T0J

C

CLO

C

Cco

Connection Details

Flange Angles: L-6x4x3/8xO I -8 11

Web Angles: thickness = ~II

gage on col. = 2~1I

length variable

Bolt Diameter: 3/4 11

12.00 1G. 00 20.00 24.00 28.00 32.00 36.00 40.00Rotation, radians (X1000)

8.00

Cc-tfl----r---r----,-----r---oor----r---,...---..,....----,.-----l4.00

FIG. 3.9 EFFECT OF WEB ANGLE LENGTH ON STATIC MOMENT-ROTATIONBEHAVIOR - W14X38 BEAM CONNECTION

155

e

fi5 __-------------------------------_---,::r

eo::r::r

eoo::r

eoill(Y)

me(]) ,.cO()cocN'Tc..~e~.. oC::r(])N

Eo~e

ooN

eolD

852t=3/8 11

eoN

eoco

e

e::r

Connection Details

Flange Angles: thickness variablegage on col. = 211

length = 01 -6 11

Web Angles: 2L-4x3~x~XOI-5~1I

Bolt Diameter: 3/4 11

12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00Rotation, radians (X1000)

c· tI---.......--......,.---r----~--_.,...--.....,.---.,....--_,_--...,..---r__Jc. 4.

l

DO

FIG.3.10a EFFECT OF FLANGE: ANGLE THICKNESS ON STATIC MOMENT­ROTATION BEHAVIOR - W8X21 BEAM CONNECTION (BOLTDIAMETER = %", ANGLE GAGE = 2")

156

o

26 -----------------------------------.~

oo~

~

ooo~

ooc:J(Y")

8S7t = 3/8"

ooC'J(Y")

(flO

~cu aJcC'J"T i

c.,~o

~Oc~(l)C'JEo~o

8S6t = 5/16"

ooC'J

oolD

C­

oC'J

ooaJ

oo~

Connection Details

Flange Angles: thickness variablegage on col. = 2~"

length = 0 1 -6"

Web Angles: 2L-4x3~x~XOI-5~"

Bolt Diameter: 3/4"

12.00 16.00 20.00 24.00 28.00 32.00 3G.00 40.00Rotation, radians (X1000)

8.004.000-J.-_-........-----,----r----....,....----r---r-----r-----r----,---,.....o

FIG.3.1Gb EFFECT OF FLANGE ANGLE THICKNESS ON STATIC MOMENT­ROTATION BEHAVIOR - W8X21 BEAM CONNECTION (BOLTDIAMETER = %", ANGLE GAGE = 2%")

157

a

atoOl

a

aCDCD

a

aaCD

a0Nl'

0

0 8S10::rto tIll

-~

0

ato

CIl lJlQ)

.cuc 0Ia. 0~ CD

::riQ)

E 00

::2 00::r

o

oN(Y]

859t=3/8"

8S8t=5/16 11

o

o::rN

o

oLD

o

oCD

o

Connection Details

Flange Angles: thickness variablegage on col. = 2"length = 01 -6"

Web Angles: 2L-4X3~X~XOI_5~"

Bolt Diameter: 7/8"

c0.0 4.0 8.0 ]2.0 ]6.0 20.0 24.0

Rotation, radians (X1000)28.0 32.0 36.0 40.0

FIG.3.11 EFFECT OF FLANGE ANGLE THICKNESS ON STATIC MOMENT­ROTATION BEHAVIOR - W8X21 BEAM CONNECTIONS (BOLTDIAMETER = ~8", ANGLE GAGE = 2")

158

Connection Details

Web Angles: 2L-4X3~X~XO'5~"

Flange Angles: L-6X3~X5/l6XO'-6"

40.036.032.028.024,0

858d =7/8"b

851d =3/4"b

20.0

Bolt Diameter: variable

16.0]2.0

0

0CD.:!'

0

0.:!'.:!'

0

00.:!'

0

0LO(YJ

(::)

0C'J(YJ

0

0CDC'J

(flQ)..cuc 0I

0a.~

.:!'C'J

CQ)

E 00~ 0

0C'J

0

0LO~

0

0C'J~

0

0CD

0

0.:!'

0

0 0,0 4.0 8,0

Rotation, radians (X1000)

FIG.3.12a EFFECT OF BOLT DIAMETER ON STATIC MOMENT-ROTATIONBEHAVIOR - W8X21 BEAM CONNECTION (FLANGE ANGLETHICKNESS =5/16")

159

Connection Details

Flange Angles: L-6X3~X3/8XO'-6"

40.0

8S9d =7/8"b

36.032.02B.024.020.0

Web Angles: 2L-4X3~X~XO'-5~"

Bolt Diameter: variable

16.012.0

0

0(Xl:::r

0

0:::r:::r

0

00:::r

8S2d =3/4 11

0 b0lDrr)

0

0C'Jrr)

0

0(XlC'J

tilCD.c() 0CI 0a. :::r

::.::: C'J

-CCD 0E0 0~ 0

C'J

0

0lD~

0

0C'J~

0

0(Xl

0

0:::r

0

0 0 . 0 4.0 B.O

Rotation. radians (X1000)

FIG.3.12b EFFECT OF BOLT DIAMETER ON STATIC MOMENT-ROTATIONBEHAVIOR - W8X21 BEAM CONNECTION (FLANGE ANGLETHICKNESS = %")

160

~

~

3l----------------------------------~

::r::r

=

oo[.:J(r]

ooN(r]

en 0Q) •..co(.) OJ.~ NI'a.:~C- .coQ):::r

ENo~

cooN

co[.:J

c

oN~,

ooOJ

oo:::r

Connection Details

Flange Angles: thickness = 5/16"gage on col. variablelength = 0'-6"

Web Angles: 2L-4x3!:ix~xO'-5!:i"

Bolt Diameter: 3/4"

oo-:'fl·---,.---...,----r---.....,---..,......---,---.....,.---,---..,....--....,.....

4.00 8~00 12.00 16.00 20.00 24.DO 28.00 32.00 36.00 40.00Rotation, radians (X1000)

FIG. 3.13a EFFECT OF FLANGE ANGLE GAGE ON STATICMOMENT-ROTATION BEHAVIOR - W8X21 BEAM CONNECTION

(ANGLE THICKNESS - 5/16")

161

oo

~T-----------------------------------.

oo::r::r

ooo::r

oo<..0(T)

852g,= 2"

ooN(T)

854g = 4~"

Web Angles: 2L-4x3~x~XOI_5~"

Connection Details

Flange Angles: thickness = 3/8"gage on col. variablelength = 0'-6"

Bolt Diameter: 3/4"

ooN

oen •Q)O~OJ

UNc::

"

a..~O

"";0c::::rQ)N

Eo~O

o

o::r

ootD

Gc..N

oo .....----r"----r----....,...--.....,---~----r"'---,...---...,..------.......

4.00 8.00 12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00Rotation, radians (X1000)

ooOJ

FIG. 3.13b EFFECT OF FLANGE ANGLE GAGE ON STATICMOMENT-ROTATION BEHAVIOR - W8X21 BEAM CONNECTION

.. _--~ ---- -- - .- _..._---

(ANGLE THICKNESS = %")

162

c:;

o

~r-""':""""---------------------------------oc:;:::r:::r

c:;

oo:::r

c:;

ol.:J(Y]

c:;

8S1L = 611

C

c:;c:;0J

c:;

ol.:J

c:;

c:;0J

c:;

c:;co

c:;

o:::r

Connection Details

Flange Angles: thickness = 5/16"gage on col. = 211

length variable

Web Angles: 2L-4x3~x~XOI_5~1I

Bolt Diameter: 3/4 11

40.0036.0032.0028.002ll.00

J12. 00 16. 00 20. 00

Rotation, radians (X1000)

8.00ll.OO

c:;

o ..---T"---r---""'i""----,---"'i"""----r---~---,---.....,----r--!

FIG. 3.14 EFFECT OF FLANGE ANGLE LENGTH ON STATICMOMENT-ROTATION BEHAVIOR - W8X21 BEAM CONNECTION

163

cc&ir-----------------------------------..cccoCD

C

GCCC!

co0J

"

14S1W14x38

o

CJ::rlD

-Cill C­O) ,

~8c: Ln

"

0.,

~:c

tIcO)CG

E: ::r0;

2 ccc::r

8S5W8X21

c

o0J(Y")

cc::r0J

cClD

coCD

Connection Details

Flange Angles: thickness = 3/8"gage on col. = 2~"

length = 0'-8"

Web Angles: 2L-4x3~x~

Bolt Diameter: 3/4"

12.00 16.00 20.00 24.00 2B.OO 32.00 36.00 40.00Rotation, radians (X1000) -.,

cc ....--"""'i'"........-.....,.----r---""i'""--..,..--.....,r---.,.....---r---~---,...J

4,00 B,OO

FIG. 3.15 COMPARISON OF STATIC MOMENT-ROTATION BEHAVIOROF W14X38 and W8X21 BEAM CONNECTIONS

0

000l~

0

00N~

0

00~

0

000~

0

00IT)

0

00CO

(J)0(I)

.cu 0c 0I C"-o.~

C 0

(I) 0E 00 lD~

0

00lf1

0

00~

0

000l

0

00N

0

00~

164

14WS2t=~"

14WSlt=3/8"

Connection Details

Flange Angles: thickness variablegage on col. = 2~"

length = 0'-8"

Web Angles: 2L-4X3~X~XO'-8~"

Bolt Diameter: 7/8/1

Weld Size: 5/16" (flange angles)3/16" (web angles)

o~-.....,---,-.--.,...----r---,...--.,.-----"--"""'T"""--""'----"'..J

4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0 40.0

Rotation, radians (X1000)

FIG. 3.16 EFFECT OF FLANGE ANGLE THICKNESS ON STATICMOMENT-ROTATION BEHAVIOR OF W14 X 38 BEAM CONNECTIONS ­

BOLTED-WELDED SPECIMENS

165

b. REAR VIEWi......-.,~_ .. _

FIG. 3.17a FLANGE ANGLE FROM SPECIMEN 14CI AFTER CYCLIC TEST

166

b. WEB ANGLES - END VIEW .J

FIG. 3.17b FLANGE AND WEB ANGLES FROM SPECIMEN 14CI AFTERCYCLIC TEST

167

n

1510

Connection Details

Flange Angles: thickness = 3/811

gage on col. = 2~1I

length = 0'-8 11-500

-300

-200

-400

600

,cn\, 700wi.cUC

-15

-600 Web Angles: 2L-4x3~x~XO'_8~1I

Bolt Diameter: 3/4"

FIG. 3.18 STABLE HYSTERESIS LOOPS FOR SPECIMEN 14C1

-300

-400

15

~Rotation 'Radians (X1000) ]L_~_~ ...._.~J. ..- ~

Connection Details

-500

-600

Flange Angles: thickness = ~II

-700 gage on col. = 2~1I

length = 0'-8 11

-800 Web Angles: 2L-4x3~x!.ixOI_8~1I

11""'1

168

i(f) 900Q).c ,01

'·~I 800'OJ--4,-:<=..-Jr ",

;~i 700,gt:2J 600I.'

-15

Bolt Diameter: 3/4 11

'-------

-15l--__--'-_

169

'"Q)

: ~ 1200

_" 1000cQ)

E

~ l80D

I 600

15

Rotation. radians (X1000)

Connection Details!.. -600

Flange Angles: thickness = !z"gage on col. = 2!z"

_ -800 length = 0'-8"

Web Angles: 2L-4X3!zX\XO I -8!z"-1000

Bolt Diameter: 7/8"

-1200

FIG. 3.20 STABLE HYSTERESIS LOOPS FOR SPECIMEN 14C3

170

tflQ)

.r:::.uc:Ia.~

800

700

1612

Rotation, radians (X1000)

/ / /I / ,

I / /

/ I /1//1

500

400

600iQ)

Eo:2

-8-12

i- -300Ji,I}- -400i

:- -500 Connection Detail s/

/ -600 Flange Angles: thickness = 3/8"r gage on col. = 2~"

I length = 0'-8"I- -700 Web Angles:

I2L-4X3~X~XO'-8~"

Bolt Diameter: 7/8"L. -800

FIG. 3.21 STABLE HYSTERESIS LOOPS FOR SPECIMEN 14C4

171

Connection Details

Bolt Diameter: 7/8"

Web Angles: 2L-4X31zX~XO'-81z"

12

Rotation, radians (X1000)

8

Fl ange Angl es : thi ckness = 1z"gage on col. = 21z"length = 0 1 -8"

r -400

~ -600

~ -800

I\ -1000

L -1200

(J)ell

.r::.uci r1200

~ r 1000~ I

~ 800Iir 600

I

-8-12L.--------lL-..,..<~__,.?____7"~L---,,.L_--___+_---~

FIG. 3.22 STABLE HYSTERESIS LOOPS FOR SPECIMEN 1481

172

'enQ)

J::(..) 300c:

'Rotation' Radians (X1000) -:JL' ... ~

-200Connection Details

Flange Angles: thickness = 5/16"gage on col. = 2"length = 0 1 -6"

-300 \~eb Angl es: 2L-4x3~x~xO'-5~"

Bolt Diameter: 3/4'1

Iciili Q) !..c ::~; 300

-200

-300

173

Connection Details

Flange Angles: thickness = 3/8"gage on col. = 2"length = 0'-6"

Web Angles: 2L-4x3~x~XOI_5~"

Bolt Diameter: 3/4"

1612

//

Rotation, radians (X1000)

8

174

(J) ~ 400(j)..c()c,Q.

:::.:::

7-c(j)

E0::? 300

-12

-200 Connection Details

Flange Angles: thickness = 3/8 11

gage on col. = 211

length = 01 -6 11

-300 Web Angles: 2L-4X3!zX~XOI_5!z1l

L Bolt Diameter: 7/8 11

-400

-161_.. --1..' _

FIG. 3.25 STABLE HYSTERESIS LOOPS FOR SPECIMEN 8C3

175

-400 80It Di ameter: 7/8 11

-300 Fl ange Angl es: thi ckness = 3/8"gage on col. = 2"length = 0'-6"

15

Rotation, radians (X1000)

10

Connection Details

Web Angles: 2L-4X3!zX~XO'-5!z"

-200

enQ) r 400.cu first blockcI ! of cyclesa.

j::2....;-c last cycleQ)

E0 300:2:

-10-15

/II~r;

FIG. 3.26 STABLE HYSTERESIS LOOPS FOR SPECIMEN 8B1

MOMENT

3

REGION III

REGION II

//0,4

//

//

//

/

FIG.3.27 TYPICAL MOMENT-ROTATION HYSTERESIS LOOP- CYCLICTESTS

ACTUATOR

DISPLACEMENT

°__----__------411...4-- TIME

3

FIG. 3.28 TYPICAL TIME-ACTUATOR DISPLACEMENT CYCLE

rTF

AI

l__I

L-~

___-

.,I

----_c=)

I

IJ

I()

II

II

I

'--

BFA

I

3.

RE

GIO

NI

CO

NF

IGU

RA

TIO

N.b

.R

EG

ION

IIC

ON

FIG

UR

AT

ION

c.R

EG

ION

III

CO

NF

IGU

RA

TIO

N,

FIG

.3.

29C

ON

FIG

UR

AT

ION

SO

FC

ON

NE

CT

ION

DU

RIN

GO

NE

-HA

LF

CY

CL

E

......

'-I

'-I

Bolt Diameter: 7/8"

Flange Angles: L-6X4X3/8XO'-8"r- -700 gage on co1. = 2!z"i

I Web Angl es: 2L-4X3!zX~XOI -8!z"r -800

24

Rotation, radians (X1000)

Connection Details

8

-500

-400

300

200

100

;- -600

178

If) I(l)..c:u 800cIa.~

- 700c(l)

E0~ I

l- 600III!h 00

-24

FIG. 3.30 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 14F3

Rotation, radians (X1000)

-15

179

(/) 800 ____1<ll..c

\(,)C )

I / 5Cl. 700 //20:;;::

- I ---c - --10<llE r 6000 25~

I

30II

~ 5

~r 400 ~-

~

15

-400

LConnection Details

-500 Flange Angles: L-6X4X3/8XO'-8"I! gage on col. = 2!z'1

r -600 vJeb Angl es: 2L-4X31zX~XOI_81z"!

L -700 Bolt Diameter: 7/8"

FIG. 3.31 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 14F2

20

180

-300

Rotation, radians (Xi 000)

1 -64

Connection Details

Flange Angles: L-6X4X3/8XO ' -8"gage on col. = 2~"

Iveb Angles: 2L-4X3~X~XO'-8~"

8 12-~_ _I._--,4-,'--I..__ ....,.J.~ •. • ..J

-500

-400

-12

v-600 Bolt Diameter: 7/8"

FIG. 3.32 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 14F1

181

600 Bolt Diameter: 7/8"

Connection Details

8

Rotation, radians (X1000)

Web Angles: 2L-4X3~X~XO'_8~"

Flange Angles: L-6X4X3/8XO'-8"gage on col. = 2~"

500

400

(f) 700OJ.c 12()cIa. 600~

~cOJE 5000:2

i 185II

~ 400i 225I -I

~ 300j;iI

-4-8

FIG. 3.33 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 14F9

182

4

Connection Details

Rotation, radians (X1000)

2

Flange Angles: L-6X4X3/8XO'-8"gage on col. = 2!z"

-200

-100

- -300

!r400

~ ~ 300

~ I

I~ 200,I

j

I,ri

825, 1500,2125, 3000

'------'----+--+1I'----Mil__-----------'------'

-4

I Web Angles: 2L-4X3!zX~XO'_8V'

,~_I -400 Bolt Diameter: 7/8"

FIG. 3.34 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 14F4

183

-600

Connection Details

Rotation, radians (X1000)

8

-800Flange Angles: L-6X4X!.zXO I -8"

gage on col. = 21 IIYz

-1000Web Angles: 2L-4X3!.zX~XOI_8!.z"

-1200 Bolt Di ameter: 7/8"

UlOJ..cu

~ 1200cIa.~ 3...:c 1000OJE0~ !

~ 800I!

24---L--f----+--------l---H~--l..--. ----l

-16-24

FIG. 3.35 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 14F7

-12 -8

184

(/)Q).c(,) 1200cIa.

:::l::... 1000cQ)

E0~

800

600

12

Rotation, radians (X1000)

- -400

~ -600Connection Details

-800 Flange Angles: L-6X4X!zXO I-8"gage on col. = 2!z"

-1000 Web Angles: 2L-4X3!zX~XOI_8!z"

-1200 Bolt Di ameter: 7/8'1

FIG. 3.36 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 14F5

86

Rotation, radians (Xi000)

4

Connection Details

Web Angles: 2L-4X3!zX~XOI_8!z"

Fl ange Angl es: L-6X4X!zXO 1_8"gage on col. = 2!z"

Bolt Diameter: 7/8"

~ -700

- -300

- -400

- -600

- -500

l -800

185

If) 900Q)or;uCI

800Q.

~-cQ)

E 7000~

600

500

400

-4'-- --L -¥1~------+--___T'_-_r__r_.L...?Si'-----L-------i----------------l

-6

FIG. 3.37 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 14F6

186

RotatioR, radians (X1000)

64

Web Angles: 2L-4X3!zX~XOI_8!z1l

- -300I

Connection Details

- -500 Fl ange Angl es: L-6X4X!zXO I -8 11

gage on col. = 2!z"

- -400

Bolt Diameter: 7/8 11

- -700

enQ) r700.c0cIa. I~ L 600- I 481c !Q)

l 500E0 81

::2:I 1007!

:.. 400

300

16

-4-6

FIG. 3.38 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 14F8

-24 -16 -8

187

(f)

OJ

r

400..c'U

....... 13cI

Q.

~

.....cOJE0

300~ 15 -~

16L.

Rotation, radians (X1000)

-200

Connection Details-300 Flange Angles: L-6X3~X5/16XO'-6"

gage on col. = 2"

Web Angles: 2L-4X3~X~XO'-5~"

Bolt Diameter: 7/8 11

-400

FIG. 3.39 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 8F8

__.-L1 --1.-_-12 -8

188

en 400<J)

.s:::.ucIa.

:;2

C ____ 31<J)

E 3200:::2:

240

12

Rotation, radians (X1000)

Connection Details

-240 Flange Angles: L-6X3~X5/l6XO'-6"gage on col. = 2"

Web Angles: 2L-4X3~X~XO'-5~"

Bolt Diameter: 7/8 11

- -320

FIG. 3.40 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 8F7

189

24-.I

L-6X3~X3/8XO'-611

gage on col. = 211

Rotation, radians (X1000)

Connection Details

8L

Flange Angles:-300

- -400

(j)Q)

..cu

1500cI ,0-

5~ IC ~ 400 7Q)

E I0 !~ !

i~

-16-24

vJeb Angl es : 2L-4X3~X~XO I -5~1I

L -500 Bolt Di ameter: 7/8"

FIG. 3.41 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 8F1

190

- -320

Connection Details

-160

12I

L-6X3!zX3/8XO I -6 11

gage on col. = 211

8

2L-4X3!zX~XOI_5!z1l

7/8 11

Rotation, radians (X1000)

... L •....

Web Angles:

BoIt Di ameter:

Flange Angles:-240

<f)Q).c

320 19,27,43()cI

a.35Q

.....-cQ)

E0~

240

-8,

L....- -L_ .,Q.+.-_._..L.--_.. ".-12

FIG. 3.42 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 8F4

8-12 -8

191(/)(1)

.cu r400c:.,

70..

~-c: 1(1)

! 87E 460 I::;E

f- 300II 143II,I

I200r-

!!,

12-/--.l-- --L- ,j

Rotation, radians (X1000)

-200

Connection Details

Flange Angles: L-6X3~X3/8XO'-6"

-300 gage on col. = 2"

Web Angles: 2L-4X3~X~XOI_5~"

Bolt Diameter: 7/8",L -400

FIG. 3.43 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 8F3

64

Rotation, radians (X1000)

1-4---;--- 558

Connection Details

2

Web Angles: 2L-4X3~X~XO'-5~"

Flange Angles: L-6X3~X3/8XO'-6"

gage on col. = 2"

BoIt Di ameter: 7/8"

-80

I

I~ -160

Ii

I1- -240

I

l-320

192

(f)Q).c 320ucIa. 61::.::

...,-cQ)

E 4010~

240

-8 -6L.__.____ +-.1 _

FIG. 3.44 SELECTED HYSTERESIS LOOPS FOR SPECIMEN 8F2

193

a. CRACK PATTERN AT 126 CYCLES

b. CRACK PATTERN AT 136 CYCLES

FIG. 3.45 FATIGUE CRACK PATTERN FOR SPECIMEN 14F9

194

c. CRACK PATTERN AT 158 CYCLES

d. CRACK PATTERN AT 214 CYCLES

FIG. 3.45 FATIGUE CRACK PATTERN FOR SPECIMEN 14F9

II

II

-

--:0-~ /

----

-~'0

..2~

=0.

1050

(Nf

)-0.

3089

-- I---

---

0--

--- ----

-r---. --- ~~

- -T

est

Spec

imen

Beam

Sec

tion

W14

X38

Flan

geA

ngle

sL6

X4X

3/8

-Bo

1t

Diam

eter

7/8"

I

80 60

040

0 0 ,.... x (f)

C til

-0 ~ -e-

20N C 0 ro 0 a: '0 OJ

10O

JC ti

l a:8

Cii c E

60 z

4 24

68

1020

4060

8010

0

Cyc

les

toF

ailu

re,

Nf

200

400

600

800

1000

2000

4000

......~ U

l

FIG

.3.

46C

ON

ST

AN

TA

MP

LIT

UD

EC

YC

LIC

TE

ST

BE

HA

VIO

R-

W14

X38

BE

AM

CO

NN

EC

TIO

NS

(FL

AN

GE

AN

GL

ET

HIC

KN

ES

S=

3Ja"

)

4000

2000

800

1000

600

400

200

8010

060

40

IJ

II

II

JI

II

I

'--

--

__

0 ~~

I-

~-

c

/ ~~

/~~

2~=

0.12

07(N

f)-

0.33

72-

~r--

- ~I-

.......

-

I-T

est

Spec

imen

-

-Be

amS

ecti

on\~14X38

-Fl

ange

Ang

les

L6X4X~

BoIt

Diam

eter

7/8"

-

II

II

II

II

II

II

I,

I4

20

68

80 60

0 0 0 ,.-

40x (J

) c co "0 ~ e C\I c- o ro ....

200 c: ...... 0 Q)

OJ

C co c: ~ c E 0 z0

Cyc

les

toF

ailu

re,

Nf

FIG

.3.

47C

ON

ST

AN

TA

MP

LIT

UD

EC

YC

LIC

TE

ST

BE

HA

VIO

R-W

14

X3

8B

EA

MC

ON

NE

CT

ION

S(F

LA

NG

EA

NG

LE

TH

ICK

NE

SS

=%

")

......

1.0

0\

400

200

8010

060

4020

810

64

IJ

I,

II

II

II

I

--

- -----.~

--

:---

l-

I----

---r----

- ~-

2~=

0.11

16(N

f)-

0.32

05r-

- ~-....

.........

--

--

, , -T

est

Spec

imen

-i-

Beam

Sec

tion

W8X

2l-

Flan

geA

ngle

sL6

X3!

:iX5/

l6-

BoIt

Diar

nete

rs7/

8 -I

II

II

II

II

II

II

I

80

8

o Q)

OJ

C l1:l

a: co c E ~0

a; o20

a:c o

60

6 4 2

o o o x40

CfJ c .~ u ~ -e-,

C\J

Cyc

les

toF

ailu

re,

Nf

I-'

l.O ---J

FIG

.3.

48C

ON

ST

AN

TA

MP

LIT

UD

EC

YC

LIC

TE

ST

BE

HA

VIO

R-

W8X

21B

EA

MC

ON

NE

CT

ION

S(F

LA

NG

EA

NG

LE

TH

ICK

NE

SS

=5

/16

")

8 6 4

0 0 0 X en c2

III

"0 III .... -e C

\J C 0 +" III <5 cr: a Q)

OJ

C III cr: <a c E 0 z

JI

,I

,

)

--~-

r---

)

~---

----

LO.0

885(Nf

)-~-

r-- r

--1-

-0--

-0

-------r

---o.

t--.

.-

I--.r--

-v 8 6

Tes

tSp

ecim

en-

4Be

amS

ecti

on1~8X2J

Flan

geA

ngle

sL6

X3!

zX3/

8

BoIt

Oia

met

er7/

8"

2.

..

I

Llh

g1

0?O

406

010

020

040

06)

08C

o1

JOO

2000

4000

Cyc

les

toF

ailu

re.

NI

FIG

.3.4

9C

ON

ST

AN

TA

MP

LIT

UD

EC

YC

LIC

TE

ST

BE

HA

VIO

R-

W8X

21B

EA

MC

ON

NE

CT

ION

S(F

LA

NG

EA

NG

LE

TH

ICK

NE

SS

=%

")

..... '-0

00

I~

I

x

•••

199

Vertical Leq of TensionFlanqe Angle

~-4--- WSection Beam

~ Compression Flange Angle

FIG. 4.1a DEFLECTED CONFIGURATION FOR FLANGE ANGLE MODEL

200

H--- WEB ANGLEt c

WEB OFWSECTION

.L"~~' . -, ~

FIG. 4.1 b DEFLECTED CONFIGURATION FOR WEB ANGLE MODELI

F___L____

\\\

\\

B \

201

FIG. 4.2a TERMINOLOGY FOR IDEALIZED BEAM MODEL OF FLANGEANGLE

fl (MCO ) .---- -- 1

F. C1

-1--~ID \(Moe) JJit·~H

f':,.1

FIG. 4.2b TERMINOLOGY FOR IDEALIZED BEAM MODEL OF WEBANGLE

202

"flexible" beam

c. BEAM MODEL1FOR FLEXIBLE'BEAM

B

1b

b, BEAM MODELFOR STIFF BEAM

I _ I I~-L/d' \0;\ \

,- /1 '/-

1-'I J I I

\' r-jlI

"stiff" beam

B

a. SUBDIVISION OF FLANGEANG-LE'TN"To BEAMS'- .

--'--------- _.. _"---'---------- ...._- ------- - ~--- - -~---

FIG.4.3a SEGMENTAL BEAM MODEL FOFfFLANGE ANGLE

.r-+>Vl

~~

-c. -BEAM MODELFOR FLEXIBLE BEAM

-" ., - ..

b. BEAM MODEL FORSTIFF BEAM

=

E<0OJ.0

I----+-

..-~

E<0OJ.0

=

OJ..-.0.r-XOJ

-',-----_.--_._----- ~ -- ---- -,-,

a. SUBDIVISION OF WEB:

ANGLE INTO BEAMS·

20~

co

~-.-----------------------------------..

coeoeo

coo(XJ

coNC'

c

",0::Till

c(/) ,(1)0£:illgUl"

a.~O

_"0Ceo(1)::T

Eo~c

o

co"J(T)

o

Predicted

Connection Details

Flange Angles: L-6x4x3/8xO'-8 11

gage on col. = 2~1I

Web Angles: 2L-4x3~x~XOI_8~1I

Test

oceo

Bo lt Di ameter: 3/4 11

co-+---...,.---.,....--..,....--.....,---..,.-----r---.,...--..,....--.....,---~

4.00 8.00 12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00RotatTb nO: "raaTarls(X1'666)"-~,

--i

"FIG.4.4 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 14S1

204

oo

~.,....----------------------------coo~

cooo

oooOl

coO.co

Test

o(J) ,

Q) 0J::OU f'C

"

Q.

:;2C::_" 0C 0Q) LD

Eo~o

ooLf1

coo:::J'

coo('Il

ccoN

coo

Connection Details

Flange Angles: L-6x4x~XOI_8"

gage on col. = 2~"

Web Angles: 2L-4x3~x~XOI_8~"

Bolt Diameter: 3/4"

oo ....---.,.---.,....---,...--~,.....--..,-----r---.,....----r----,.....--.........

4.00 8.00 12.00 15 ']0 20.00 24.00 28.00 32.00 36.00 - 40.00

Rotation, radians (X1000)

~ _ __ .•. ..1

FIG. 4.5 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 14S2

205

eE6.,..... --,01

eeCDCD

ccoCD

ceNC'

cc""j'

w

cCIl •<!lie-Cw~LnI'0..

~c

"":0C:COQ) i::!'EiO!~c

cc;j<

cCN(Y'")

co::!'N

eoCD~

eeco

Predicted

Test

Connection Details

Flange Angles: L-6x4x3/8xO ' -8"gage on col. = 2~"

Web Angles: 2L-4x3~x3/8xO"-8~"

Bolt Diameter: 3/4"

~~·---4"T.-0-0--81. -nO---1,12

.-0-0--161 .-0-0--2'0-.-0-0--2"T4-.-00--218-.0-0--312 .-0....0-~36r:-.....O"':'0--:-!~

Rotation. radians (X1000)

FIG. 4.6 COMPARISON OF PREDICTED MOMENT-ROTATION CURVBWITH TEST RESULTS FOR SPECIMEN 14S4

206

0

0illm

0

0CDCD

0 Test00eo

0 Predicted00Jr--

0

0~

ill

C

0illen

CIlQ)

.r:.u 0CI 0a. eo~ ~

.....-CQ)

0E0 0~ 0

~

0

00J(Y")

0

0 Connection Detail s~

0J

Flange Angles: L-6X4X3/8XO ' _II

0 gage on co1. = 21 II"20ill

Web Angles: 2L-4X3!zX~XO'_8!z1l

0 Bolt Diameter: 7/8 11

0CD

o+---~--"""--~---"'--"""--"""----'I"""---,.....--.,....--..,...-I

4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0 40.0

Rotation, radians (X1000)

FIG. 4.7 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 14S5

207

0

00N

0

00 Test, 1456

Test, 14590

000~

0

00 Predictedm

0

00co

0

00

en r--Q)

.J::(,)CI 0a. .

.- 0:::e: 0- illCQ)

E0 0

::2: 00U1

0

00::l'

0

0 Connection Detail s0rrl

Flange Angles: L-6X4X!zXO I-8"0 gage on col. = 21

""200

Web Angles: 2L-4X3!zX~XOI_8!z1lN

0 Bolt Di ameter: 7/8 11

00~

o

4.0 a.o 12.0 16.0 20.0 24.0 28.0 32.0 36.0 40.0

Rotation, radians (X1000)

FIG. 4.8 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMENS 14S6 AND 14S9

0

00::rN

0

00NN

0

00'.:::lN

0

Cl0

0

00CD

0

00::r

rnQ) 0

.!::.U 0C 0I Na.

:;2

- CCQ)

0E 00 0~ -.

c0cCO

c00CD

0

C0::r

r:-c00N

208

Test

Predicted

Connection Details

Fl ange Angl es: L-6X4X5/8XO 1_8'1gage on col. = 2!z"

Web Angles: 2L-4X3!zX~XO'_8!z"

Bolt Diameter: 7/8"

o ....__...,. ~__~ ,.....__...,..__.....,. .,..-__...,.. ,.....__-,....-a

4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0 40.0

Rotation, radians (X1000)

FIG. 4.9 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 14S8

209

c§5.,... -,=r'

co=r'::r

c

cc=r'

cCill(Y]

co(\J(Y]

Predicted

c(/) .Q) 0.ceo() (\JCIa.~c::_" cc ::rQ) C'J

Eo~c

co(\J

colD

co(\J

c

oeo

oo::r

Connection Details

Flange Angles: L-6x~x5/l6xOI-611gage on col. = 2"

Web Angles: 2L-4x3~x~XOI-5~"

Bolt Diameter: 3/4"

40.0036.0032.0028.0024.001.~

12.00 16.00 20.00Rotation, radians (X1000)

8.004.0004-----r'---.,.....---r-----,---"'T"""---r---~--""'T"--.....,:__---r-'o

FIG. 4.10 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 8S1

. 210

oo

~-------------------------------------.

o

o~

:::r

Predicted

ooo:::r Test

ooLOrn

ooNrn

(flO(1) •.!::Ou aJeNI

0.,

:;20. .CO(1)~

ENo~ o

ooLO

ooN~

Connection Details

Flange Angles: L-6x3~x3/8xOI_6"

gage on col. = 211

Web Angles: 2L-4x3~x~XOI_5~1I

oom

Bolt Diameter: 3/4 11

oo:::r

J2.00 J6.00 20.00 24.00 28.00 32.00 36.00 40.00Rotation, radians (X1000)

8.004.00

o-l!l---.....,.---.,.....--..,..--~r----~----r---.,.---..,..---r----~o·

FIG. 4.1/1" COMPARISON OF PREDICTED MOMENT-ROTATl'bN CURVEWITH TEST RESULTS FOR SPECIMEN 8S2

211

c0CO::1'

C

C::1'::1'

0

0c::r

0

0UJ(rl

0

0N(rl

---'0

0CO

III N(1)

.c(.)c: 0

"

e.O;,;;:: ::r

N-c:(1)

E 0

0 c~ 0

N

C

0(D

C

0N

coOJ

co::r

Test

Predicted

Connection Details

Flange Angles: L-6x3~x5/l6xOI-8"

gage on col. = 2"

Web Angles: 2L-4x3~x~XOI_5~"

Bolt Diameter: 3/4"

40.00

t..__

cc-+----,.---..,.---.....,.---..,.---.....,.----r-----,---....,..----,~--...,.....

4.00 8.00 12.00 16.00 20.00 24.00 28.00 32.00 36.00Rotation, radians (X1000)

FIG. 4.12 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 8S3

212

c __---------------------------------.......o::r::t'

coo::r

Test

Connection Details

Predicted

Web Angles: 2L-4x3!zx~XOI_5~1I

Flange Angles: L-6x4x3/8xO'-8 11

gage on col. = 2~1I

BoIt Di ameter: 3/4 11

coco

coillrrJ

co::r

co("\J

coNrrJ

coill

coco

CIl.N~iu.!:: c

I •

0.0

~R1

12.00 15.00 20.00 24.n[) 28.00 32.00 l[.On 40.00Rotatiori,-raclians (X1 000) ..,

8.004.00c4----.,.---.,.....--~--__.,~--_r_--___r_---or_--__r_--__.,---..,.....c

FIG. 4.-13 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 8S5

_.~.~ .1....

213

o

25-r-------------------------------------.::1'

cC::1'::1'

coo::1'

cCill(T)

coN(T)

w O<1)0.!::COgN"I;Q.l:;Zc"";0C::1'(J)N

E.0'~ic

coC"\l

coill

coN

coco

oo::1'

Predicted

Connection Details

Flange Angles: L-6x4x5/l6xO ' -6 11

gage on col. = 2~1I

Web Angles: 2L-4x3~x~XOI_5~1I

BoIt Di ameter: 3/4 11

o0--l!J-----r---~---r---r----,..--__r---_r_--_r-;...-.-r__--..,....J

4.00 8.00 ]2.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00Rotation, radians (X1000)

FIG. 4.14 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 8S6

--'...-.._-

214

c

55 __--------------------------------.......--,:::r

co.-:1':::r

coC.-:1' Test

coLD(Y]

Predicted

Connection Details

cC/) •

Q)O..ceoUNc:Ia.~c::"";0c::::rQ)C'J

Eo~C

ooC'J

ooLD

ooeo

oo:::r

Flange Angles:

Web Angles:

BaH Diameter:

L-6x4x3/8xO I -6 11

gage on col. = 2~1I

2L-4x3~x~XOI_5~1I

3/4 11

12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00---- -

Rotation, radians (X1000)8.004.00

O ....__--r' .,....__..,..__~---.,...--...,.---_r__--..,..--__,---.,..-IO·

-~--=-

FIG. 4.15 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 8S7

0

0CO:::r

0

0:::r:::r

0

00:::r

0

0ill(Y")

0

0('J(Y")

0

0CO

en ('JQ).ctlc 0Ic.. 0~ :::r

('J

CQ)

E 00:2: 0

0('J

0

0ill-c

0

0('J-

0

0CO

0

0:::r

215

Test

Predlcted

Connection Details

Flange Angles: L-6X3~X5/l6XOI-6"

gage on col. = 2"

Web Angles: 2L-4X3~X~XOI_5!z"

Bolt Diameter: 7/8"

o --+---...,..----,.---.,..---..,....----r"---,....--..,....---.,..-----.,---..,.....I4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0 40.0

Rotation, radians (X1000)

FIG. 4.16 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 8S8

216

0

0CO~

0 Predicted0 Test~

::1'

0

00~

0

0LO(l)

0

0N(l)

0

(fJ 0Ql co~ NuCIa.

::.:::0

- 0c ~

Ql N

E0~ 0

00N

0

0LO~

Connection Detail s0

0 Flange Angles: L-6X3~X3/8XO'-6"N~ gage on col. = 2"

0 Web Angles: 2L-4X3~X~XO'-5~"0()J Bolt Diameter: 7/8"

0

a~

40.036.032.028.024.020.016.012.08.04.0O+---r---r----"T"'"--...,..----r---or---..,...--...,.---~--..,.....J0 0: 0

Rotation, radians (X1000)

FIG. 4.17 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 8S9

217

Flange Angles: L-6X3~X~XO'_6"

gage on col. = 2"

40.036.032.028.024.0

Test

Connection Details

Predicted

Web Angles: 2L-4X3~X~XO'_5~"

Bolt Diameter: 7/8"

t6.812.0

aatD01

aaOJOJ

aaaOJ

aaNl'

aa:::rtD

a

en aOJ tD

..c::. LI1(,)

CI

Do a~ a- OJc :::rOJE0~ a

aa:::r

aaNCl1

0

a:::rN

0

atD~

a0co

d

0 0 . 0 4.0 8.0

Rotation, radians (X1000)

FIG. 4.18 COMPARISON OF PREDICTED MOMENT-ROTATION CURVEWITH TEST RESULTS FOR SPECIMEN 8S10

4000

2000

400

600

800

1000

200

6080

100

4020

810

6

II

I--,

IT

,.

I,

--

r--..

.0

<~

0-

~'"

1~68(R

)-3.25

31~

~'U-.r-.

..-

~~

I--k>

-.""~~

br--

- r-----

--

r---

- ~

Spec

imen

Type

Sym

po1

W14

X38

,t

=3/

8"0

~Jl4X

38,

t=

1/2"

0

W8X

21,

t=

5/16

11jj.

W8X

21,

t=

3/8"

0I

0.2

0.4

0.6

0.8

0.02

_ 4

0.04

0.06o.

1

0.0

8

II

I.-.

.-J

N 0..

r-.

-e-

.jJ

CI

rtl

N.j

J...

..... ::=

......

..-0

+-'

I+ -0

Ol

Cyc

les

toF

ailu

re,

Nf

FIG

.4.

19C

OM

PA

RIS

ON

OF

TO

TA

LF

AT

IGU

EL

IFE

WIT

HN

OM

INA

LF

LA

NG

EA

NG

LE

CH

OR

DR

OT

AT

ION

-A

LL

CO

NS

TA

NT

AM

PL

ITU

DE

CY

CL

ICT

ES

TS

N I--'

00

100Iii

iii

iIiiiii

iiiiiiIii

IIii

100,

000

10,0

0010

00

,N f

=84

4.9(

E)-

1.20

100

o

~

N f~2

98.65(

E)-1.2

639~

Spec

imen

Sym

bol

W14

X38

,t

=3/

811

0

W14

X38

,t

=1/

211

0

W8X

21,

t=

5/16

116

-

W8X

21,

t=

3/8"

0

II

II 10

101

Ih.

.:""

I/

II

1

C I Q.

~ Wro

-Q

)Q

)...

.

u«

>.

Q.

U0

....0

Q)

--l

Q.

CIl

>.

"00O

JQ

)...

.....

Q)

Q)

C.-

W~ I Q

)

OJ

ttl .... Q) > ~.

Cyc

les

toF

ailu

re,

Nf

FIG

.4.

20C

OM

PA

RIS

ON

OF

TO

TA

LF

AT

IGU

EL

IFE

WIT

HA

VE

RA

GE

AR

EA

OF

IND

IVID

UA

LH

YS

TE

RE

SIS

LO

OP

-A

LL

CO

NS

TA

NT

AM

PL

ITU

DE

CY

CL

ET

ES

TS

N f-'

1.0