Experimental and Analytical Performance Evaluation
of Welded Steel Moment Connections
to Box or Deep W-shape Columns
by
Taejin Kim
B.S. (Seoul National University, Korea) 1990
M.S. (Seoul National University, Korea) 1994
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophy
in
Engineering-Civil and Environmental Engineering
in the
GRADUATE DIVISION
of the
UNIVERSITY OF CALIFORNIA, BERKELEY
Committee in charge:
Professor Bozidar Stojadinovic, Chair
Professor Andrew S. Whittaker
Professor Stephen A. Mahin
Professor Paul A. Vojta
Spring 2003
The dissertation of Taejin Kim is approved:
______________________________________________________________________
Chair
Date
______________________________________________________________________
Date
______________________________________________________________________
Date
______________________________________________________________________
Date
University of California, Berkeley
Spring 2003
Experimental and Analytical Performance Evaluation
of Welded Steel Moment Connections
to Box or Deep W-shape Columns
Copyright 2003
by
Taejin Kim
Abstract
Experimental and Analytical Performance Evaluation of Welded Steel
Moment Connections to Box or Deep W-shape Columns
by
Taejin Kim
Doctor of Philosophy in Civil and Environmental Engineering
University of California, Berkeley
Professor Bozidar Stojadinovic, Chair
In modern construction heavy W-shape beams, deep W-shape columns, and column
shapes other than the traditional W-shape are often preferred as components of welded steel
moment frames because moment-resisting frames designed with such components can provide
better drift control and may be somewhat more economical. Practical design guidelines, published
in a series of FEMA documents, starting with the seminal FEMA-350 design guide for new steel
moment-frame construction, both gave designers new tool to design special steel moment frames
and provided a portfolio of new connection solutions. However, FEMA-350 connections are prequalified only for W12 and W14 columns. There is not enough test data upon which to base a
performance evaluation or develop retrofit solutions for the connections to box or to deep Wshape columns. The main objectives of this study are to investigate the seismic performance,
identify the key design variables, and present design recommendations for such connections.
To achieve the objectives three phases of work were conducted. First, three factors that
influence the ductility of welded steel moment connection were identified. They are: brittle
fracture, inelastic instability, and residual rotation capacity. The effect of these factors on the
1
performance of moment connections were investigated and strategies to evaluate the severity of
these effects were proposed. Second, steel moment connections in a building built before the
1994 Northridge earthquake were selected to evaluate the pre-Northridge type moment-resisting
connections to box or deep W-shape columns. Standard pre-qualification tests were conducted for
the connection specimens. The observed performance of these pre-Northridge connections was
poor. In parallel with the test program the connections were analyzed using nonlinear finite
element models. These analytical models were used to augment and interpret the test results.
Third, key design variables were identified: column shapes, continuity plates, column plates, and
loading directions for box column connections; and column boundary conditions, connection
types, and beam lateral bracing for deep W-shape column connection. A series of parametric
finite element studies for these design variables were conducted to formulate design
recommendations.
_____________________________________________
Professor Bozidar Stojadinovic
Dissertation Committee Chair
2
To my parents
i
Table of Contents
List of Figures ................................................................................................................................. iv
List of Tables ................................................................................................................................... x
Acknowledgements ......................................................................................................................... xi
Chapter 1.
Introduction............................................................................................................ 1
1.1
Background..................................................................................................................... 1
1.2
Objective and Scope of Research ................................................................................... 2
1.3
Organization of Thesis ................................................................................................... 3
Chapter 2.
Factors Influencing Connection Ductility.............................................................. 4
2.1
Introduction .................................................................................................................... 4
2.2
Brittle Fracture................................................................................................................ 6
2.2.1
Metallurgical characteristic of fracture.................................................................. 6
2.2.2
Effects of deformation restraint on fracture........................................................... 8
2.2.3
Fracture assessment of welded connections ........................................................ 16
2.2.4
Model of connection fracture strength ................................................................. 25
2.3
Inelastic Instability ....................................................................................................... 27
2.3.1
Behavior of plate reinforced connections ............................................................ 28
2.3.2
Local buckling ..................................................................................................... 32
2.3.3
Lateral-torsional buckling .................................................................................... 36
2.3.4
Model of strength degradation ............................................................................. 37
2.4
Residual Rotation Capacity .......................................................................................... 40
2.4.1
Shear tab damage ................................................................................................. 40
2.4.2
Post-fracture behavior of moment connections ................................................... 41
2.4.3
Model for residual strength .................................................................................. 45
Chapter 3.
Preliminary Investigation and Experimental Program ......................................... 66
3.1
Introduction .................................................................................................................. 66
3.2
Preliminary Investigation ............................................................................................. 67
3.2.1
Building description............................................................................................. 67
3.2.2
Selection of sample connections .......................................................................... 67
3.2.3
On-site investigation of connection details .......................................................... 69
3.2.4
In-situ material properties .................................................................................... 69
3.3
Test Specimen Details and Fabrication ........................................................................ 71
3.3.1
Specimen details .................................................................................................. 71
3.3.2
Specimen supply and fabrication ......................................................................... 72
3.3.3
Mechanical properties of materials ...................................................................... 72
3.4
Experiment Set-up ........................................................................................................ 74
3.4.1
Test fixture ........................................................................................................... 74
3.4.2
Instrumentation and data acquisition ................................................................... 75
3.4.3
Loading protocol .................................................................................................. 77
Chapter 4.
Finite Element Analysis ....................................................................................... 92
4.1
Introduction .................................................................................................................. 92
4.2
Finite Elements ............................................................................................................. 93
4.2.1
Solid elements ...................................................................................................... 93
4.2.2
Shell elements ...................................................................................................... 94
4.2.3
Mechanical properties of materials ...................................................................... 96
4.3
Analytical Models ........................................................................................................ 97
4.3.1
Solid element models ........................................................................................... 97
4.3.2
Shell element models ......................................................................................... 100
ii
4.3.3
Applied loading.................................................................................................. 102
4.4
Analysis Procedures ................................................................................................... 102
4.4.1
Material nonlinear analysis ................................................................................ 102
4.4.2
Geometric nonlinear analysis............................................................................. 103
Chapter 5.
Performance Evaluation of Box Column Connections ...................................... 112
5.1
Introduction ................................................................................................................ 112
5.2
Performance of Pre-Northridge Connections ............................................................. 112
5.2.1
Cyclic response of Specimen EC01 ................................................................... 113
5.2.2
Cyclic response of Specimen EC02 ................................................................... 116
5.2.3
Numerical simulation of the tests ...................................................................... 118
5.3
Evaluation of Response Data...................................................................................... 122
5.3.1
Analysis parameters ........................................................................................... 122
5.3.2
Welded joint....................................................................................................... 124
5.3.3
Post-fracture connection stiffness ...................................................................... 135
5.3.4
Column shape .................................................................................................... 136
5.3.5
Continuity plate strength .................................................................................... 136
5.3.6
Column flange stiffness ..................................................................................... 138
5.3.7
Bi-axial loading.................................................................................................. 141
5.4
Design Guidelines for Box Column Connections ...................................................... 142
5.4.1
Continuity plate design ...................................................................................... 143
5.4.2
Column plate design .......................................................................................... 143
5.4.3
Connection upgrade ........................................................................................... 144
Chapter 6.
Performance Evaluation of Deep W-shape Column Connections ..................... 197
6.1
Introduction ................................................................................................................ 197
6.2
Performance of Pre-Northridge Connection ............................................................... 197
6.2.1
Cyclic response of Specimen EC03 ................................................................... 198
6.2.2
Numerical simulation of the test ........................................................................ 200
6.3
Evaluation of Response Data...................................................................................... 202
6.3.1
Analysis parameters ........................................................................................... 203
6.3.2
Welded joints ..................................................................................................... 206
6.3.3
Post-fracture connection stiffness ...................................................................... 210
6.3.4
Column boundary condition .............................................................................. 211
6.3.5
Connection type ................................................................................................. 212
6.3.6
Beam lateral bracing .......................................................................................... 214
6.4
Design Guidelines for Deep W-shape Column Connections ..................................... 218
6.4.1
Beam lateral bracing .......................................................................................... 219
6.4.2
Connection upgrade ........................................................................................... 219
Chapter 7.
Summary and Conclusions ................................................................................ 244
7.1
Summary..................................................................................................................... 244
7.2
Conclusions ................................................................................................................ 245
References .................................................................................................................................... 252
iii
List of Figures
Figure 2-1: Moment-drift responses in welded steel moment connections ................................... 48
Figure 2-2: Various scales used to asses the potential for brittle fracture ..................................... 49
Figure 2-3: Effect of the deformation restraint in beam-column connections ............................... 50
Figure 2-4: End effects in the beam flange connection region ...................................................... 51
Figure 2-5: Effect of fillet size on local stress disturbance ............................................................ 52
Figure 2-6: End effect mesh convergence study ............................................................................ 52
Figure 2-7: Fracture paths in the beam flange joint ....................................................................... 53
Figure 2-8: Initiation of cleavage in front of a macroscopic crack (Anderson 1995) .................... 53
Figure 2-9: Pressure Index in the flanges in Models UCB-RC00 and UCB-RC03 at 0.5-percent
story drift (Kim et al. 2000a) .................................................................................... 54
Figure 2-10: Rupture Index in the flanges in Models UCB-RC00 and UCB-RC03 at 2.0-percent
story drift (Kim et al. 2000a) .................................................................................... 54
Figure 2-11: Microcrack forming region in beam cross section .................................................... 55
Figure 2-12: Stress demands in SAC PN2 specimen and comparison to stress at fracture for other
tests (Schafer et al. 2000) .......................................................................................... 55
Figure 2-13: Moment versus drift angle for Specimen UCB-RC03 (Kim et al. 2000a) ................ 56
Figure 2-14: Local buckling of Specimen UCB-RC03 after the cycle to 3-percent story drift (Kim
et al. 2000a) ............................................................................................................... 56
Figure 2-15: Peak compressive strains on beam flanges at 3-percent story drift, UCB-RC03 (Kim
et al. 2000a) ............................................................................................................... 57
Figure 2-16: Moment-drift relations and buckling amplitudes for Model UCB-RC03 (Kim et al.
2000a) ....................................................................................................................... 57
Figure 2-17: Buckle shape of beam cross section at each story drift angle, UCB-RC03 (Kim et al.
2000a) ....................................................................................................................... 58
Figure 2-18: Moment versus drift angle for Models SH-RC00, SH-RC03, and SOL-RC03 (Kim et
al. 2000a)................................................................................................................... 58
Figure 2-19: Plastic hinge location, length, and beam plastic rotation .......................................... 59
Figure 2-20: Local buckling patterns of beam flanges................................................................... 59
Figure 2-21: Lateral-torsional buckling model for the beam ......................................................... 60
Figure 2-22: Strength degradation model due to local buckling .................................................... 60
Figure 2-23: Amplitude of FLB versus connection strength ......................................................... 61
Figure 2-24: Types of shear tab damages after FEMA 352 (2000c).............................................. 61
Figure 2-25: Load versus drift of a simple connection, Specimen 7B (Liu 2000)......................... 62
Figure 2-26: Moment-rotation response of an unreinforced connection, Specimen 7.2
(Stojadinovic et al. 2000) .......................................................................................... 62
Figure 2-27: Finite element model for post-fracture analysis ........................................................ 63
Figure 2-28: Moment-rotation response of post-fracture connections ........................................... 63
Figure 2-29: Displacement cycles of θb = 0.01 rad. and the gap size ............................................ 64
Figure 2-30: Cyclic response of the post-fracture connection ....................................................... 64
Figure 2-31: Load transfer at θb = 0.005 rad. and force distribution for shear tab design ............. 65
Figure 3-1: Plan view of typical floor showing locations of test specimens.................................. 78
Figure 3-2: Frame elevation at line A ............................................................................................ 78
Figure 3-3: Connection detail between beam bottom flange and w-shape column ....................... 79
Figure 3-4: Connection detail between beam bottom flange and box column............................... 79
Figure 3-5: Construction detail for Specimen EC01 ...................................................................... 80
Figure 3-6: Construction detail for Specimen EC02 ...................................................................... 80
Figure 3-7: Construction detail for Specimen EC03 ...................................................................... 81
iv
Figure 3-8: Downhand welding for CJP welds in the beam bottom flange ................................... 81
Figure 3-9: Original drawing for box column details (Design Documents 1990) ......................... 82
Figure 3-10: Fabrication of horizontal continuity plates into a box column.................................. 82
Figure 3-11: Modified details for the continuity plates in box columns ........................................ 83
Figure 3-12: Plan view of test fixture for Specimen EC01 ............................................................ 83
Figure 3-13: Anchorage detail between the column-end and the clevis ........................................ 84
Figure 3-14: Anchorage detail for the actuator .............................................................................. 84
Figure 3-15: Lateral-brace frames for Specimen EC02 ................................................................. 85
Figure 3-16: Photograph of test fixture for Specimen EC01 ......................................................... 85
Figure 3-17: Plan view of test fixture for Specimen EC02 ............................................................ 86
Figure 3-18: Photograph of test fixture for Specimen EC02 ......................................................... 86
Figure 3-19: Plan view of test fixture for Specimen EC03 ............................................................ 87
Figure 3-20: Photograph of test fixture for Specimen EC03 ......................................................... 87
Figure 3-21: Instrumentation for Specimen EC01 ......................................................................... 88
Figure 3-22: Instrumentation for Specimen EC02 ......................................................................... 89
Figure 3-23: Instrumentation for Specimen EC03 ......................................................................... 90
Figure 3-24: Instrumentation on the clevis .................................................................................... 91
Figure 3-25: Cyclic displacement history by SAC ........................................................................ 91
Figure 4-1: ABAQUS Solid elements (HKS 2002) ..................................................................... 104
Figure 4-2: Schematic of shell offset (HKS 2002) ...................................................................... 104
Figure 4-3: Assumed stress-strain relationship in ABAQUS ...................................................... 105
Figure 4-4: ABAQUS Type SOL model of Specimen EC01 ...................................................... 105
Figure 4-5: ABAQUS Type SOL model of Specimen EC02 ...................................................... 106
Figure 4-6: ABAQUS Type SOL model of Specimen EC03 ...................................................... 106
Figure 4-7: Element meshing for beam of Type SOL model of Specimen EC01 ....................... 107
Figure 4-8: Element meshing for column of Type SOL model of Specimen EC01 .................... 107
Figure 4-9: ABAQUS Type SH model of Specimen EC01 ......................................................... 108
Figure 4-10: ABAQUS Type SH model of Specimen EC02 ....................................................... 108
Figure 4-11: ABAQUS Type SH model of Specimen EC03 ....................................................... 109
Figure 4-12: Newton iteration for nonlinear problems (HKS 2002)............................................ 109
Figure 4-13: First mode shape for Type SH model of Specimen EC01 ...................................... 110
Figure 4-14: First mode shape for Type SH model of Specimen EC02 ...................................... 110
Figure 4-15: Mode First mode shape for Type SH model of Specimen EC03 ............................ 111
Figure 4-16: Modified Riks algorithm (HKS 2002) .................................................................... 111
Figure 5-1: Beam top flange yield during the 0.75-percent drift cycle: Specimen EC01 ............ 145
Figure 5-2: Beam bottom flange yield during the 0.75-percent drift cycle: Specimen EC01...... 145
Figure 5-3: Crack in CJP weld of beam top flange: Specimen EC01 .......................................... 146
Figure 5-4: Beam top flange fracture during the 1-percent drift cycle: Specimen EC01 ............ 146
Figure 5-5: Fracture surface of beam top flange: Specimen EC01 .............................................. 147
Figure 5-6: Fracture of shear tab fillet weld: Specimen EC01..................................................... 147
Figure 5-7: Gap under the backing bar during the 1-percent drift cycle: Specimen EC01 .......... 148
Figure 5-8: Beam bottom flange fracture during the second 1-percent drift cycle: Specimen EC01
................................................................................................................................. 148
Figure 5-9: Fracture surface of beam bottom flange: Specimen EC01 ........................................ 149
Figure 5-10: Shear tab tearing after beam bottom flange fracture: Specimen EC01 ................... 149
Figure 5-11: Shear tab fracture during the 4-percent drift cycle: Specimen EC01 ...................... 150
Figure 5-12: Complete separation of the shear tab: Specimen EC01 .......................................... 150
Figure 5-13: Moment at the column face versus story drift angle for Specimen EC01............... 151
Figure 5-14: Moment at the column face versus panel zone plastic rotation for Specimen EC01
................................................................................................................................. 151
Figure 5-15: Beam top flange tensile strain profiles: Specimen EC01 ........................................ 152
v
Figure 5-16: Beam web shear strain profiles: Specimen EC01 ................................................... 152
Figure 5-17: Whitewash flaking during the 0.375-percent drift cycle: Specimen EC02 ............. 153
Figure 5-18: Beam top flange fracture during the 0.75-percent drift cycle: Specimen EC02 ..... 153
Figure 5-19: Fracture surface of beam top flange: Specimen EC02 ............................................ 154
Figure 5-20: Beam bottom flange fracture during the 0.75-percent drift cycle: Specimen EC02154
Figure 5-21: Fracture surface of beam bottom flange: Specimen EC02 ...................................... 155
Figure 5-22: Shear tab tearing during 2-percent drift cycle: Specimen EC02 ............................. 155
Figure 5-23: Shear tab deformation during the 2-percent drift cycle: Specimen EC02 ............... 156
Figure 5-24: Shear tab fracture during the 3-percent drift cycle: Specimen EC02 ...................... 156
Figure 5-25: Moment at the column face versus story drift angle for Specimen EC02............... 157
Figure 5-26: Moment at the column face versus panel zone plastic rotation for Specimen EC02
................................................................................................................................. 157
Figure 5-27: Beam top flange tensile strain profiles: Specimen EC02 ........................................ 158
Figure 5-28: Beam web shear strain profiles: Specimen EC02 ................................................... 158
Figure 5-29: Moment-drift relations for analysis and experiment in Model SH-EC01 and
Specimen EC01 ....................................................................................................... 159
Figure 5-30: Moment-drift relations for analysis and experiment in Model SH-EC02 and
Specimen EC02 ....................................................................................................... 159
Figure 5-31: Von Mises stress distribution in the panel zone and the beam web at the 0.5-percent
drift in Model SH-EC01 .......................................................................................... 160
Figure 5-32: Von Mises stress distribution in the panel zone and the beam web at the 0.5-percent
drift in Model SH-EC02 .......................................................................................... 160
Figure 5-33: Axial stress distribution along the top continuity plate and the beam top flange at the
0.5-percent drift in Model SH-EC01 ....................................................................... 161
Figure 5-34: Axial stress distribution along the top continuity plate and beam top flange at the
0.5-percent drift in Model SH-EC02 ....................................................................... 161
Figure 5-35: Data report line on the beam top flange and the beam web .................................... 162
Figure 5-36: Stress and fracture indices along the upper surface of beam top flange at the 0.5percent story drift in Model SH-EC01 .................................................................... 163
Figure 5-37: Stress and fracture indices along the upper surface of beam top flange at the 0.5percent story drift in Model SH-EC02 .................................................................... 164
Figure 5-38: Design variables of box column connections.......................................................... 165
Figure 5-39: Data report planes for response indices .................................................................. 165
Figure 5-40: Maximum Principal Index in SOL-EC01 beam flange at column face, Plane A .... 166
Figure 5-41: Mises Index in SOL-EC01 beam flange at column face, Plane A .......................... 166
Figure 5-42: Pressure Index in SOL-EC01 beam flange at column face, Plane A ...................... 167
Figure 5-43: Triaxiality Index in SOL-EC01 beam flange at column face, Plane A ................... 167
Figure 5-44: Rupture Index in SOL-EC01 beam flange at column face, Plane A ....................... 168
Figure 5-45: Maximum Principal Index in SOL-EC01 beam flange at weld access hole, Plane B
................................................................................................................................. 168
Figure 5-46: Mises Index in SOL-EC01 beam flange at weld access hole, Plane B ................... 169
Figure 5-47: Pressure Index in SOL-EC01 beam flange at weld access hole, Plane B ............... 169
Figure 5-48: Triaxiality Index in SOL-EC01 beam flange at weld access hole, Plane B ............ 170
Figure 5-49: Rupture Index in SOL-EC01 beam flange at weld access hole, Plane B ................ 170
Figure 5-50: Maximum Principal Index in SOL-EC02 beam flange at column face, Plane A .... 171
Figure 5-51: Mises Index in SOL-EC02 beam flange at column face, Plane A .......................... 171
Figure 5-52: Pressure Index in SOL-EC02 beam flange at column face, Plane A ...................... 172
Figure 5-53: Triaxiality Index in SOL-EC02 beam flange at column face, Plane A ................... 172
Figure 5-54: Rupture Index in SOL-EC02 beam flange at column face, Plane A ....................... 173
Figure 5-55: Maximum Principal Index in SOL-EC02 beam flange at weld access hole, Plane B
................................................................................................................................. 173
vi
Figure 5-56: Mises Index in SOL-EC02 beam flange at weld access hole, Plane B ................... 174
Figure 5-57: Pressure Index in SOL-EC02 beam flange at weld access hole, Plane B ............... 174
Figure 5-58: Triaxiality Index in SOL-EC02 beam flange at weld access hole, Plane B ............ 175
Figure 5-59: Rupture Index in SOL-EC02 beam flange at weld access hole, Plane B ................ 175
Figure 5-60: Normalized maximum principal stress (MPI) distribution on the interface of the
beam flange in Model SOL-EC01 at 0.78-percent drift .......................................... 176
Figure 5-61: Equivalent plastic strain (PEEQ) distribution on the interface of the beam flange in
Model SOL-EC01 at 0.78-percent drift .................................................................. 176
Figure 5-62: Normalized hydrostatic stress (PI) distribution on the interface of the beam flange in
Model SOL-EC01 at 0.78-percent drift .................................................................. 177
Figure 5-63: Normalized maximum principal stress (MPI) distribution on the interface of the
beam flange in Model SOL-EC02 at 0.59-percent drift .......................................... 177
Figure 5-64: Equivalent plastic strain (PEEQ) distribution on the interface of the beam flange in
Model SOL-EC02 at 0.59-percent drift .................................................................. 178
Figure 5-65: Normalized hydrostatic stress (PI) distribution on the interface of the beam flange in
Model SOL-EC02 at 0.59-percent drift .................................................................. 178
Figure 5-66: Microcracking and crack propagation in the CJP welds for the top beam flange in
Specimen EC01 at 0.78-percent drift ...................................................................... 179
Figure 5-67: Principal stress vectors and fracture path on the bottom surface elements in the beam
flange in Model SOL-EC01 at 0.78-percent drift ................................................... 179
Figure 5-68: Maximum Principal Index and initial crack size in CJP welds of Specimen EC01 at
0.78-percent drift..................................................................................................... 180
Figure 5-69: Model of stress intensity solution for a semi-elliptical surface flaw in a flat plate for
a ≤ c (Anderson 1995).......................................................................................... 180
Figure 5-70: Normal stress (σ11/ σy) distribution on the interface of the beam flange in Model
SOL-EC01 at 0.78-percent drift .............................................................................. 181
Figure 5-71: Stress intensity solution for brittle fracture of CJP welds in Specimen EC01 ........ 181
Figure 5-72: Maximum principal stress vectors in the box column section and its continuity plate
at 2-percent drift: SOL-EC01 .................................................................................. 182
Figure 5-73: Distribution of Maximum Principal Index in the CJP weld between the continuity
plate and the column side plate in Model SOL-EC01 at 2-percent drift ................. 182
Figure 5-74: Connection stiffness in Specimen EC01 ................................................................. 183
Figure 5-75: Connection stiffness in Specimen EC02 ................................................................. 183
Figure 5-76: Maximum principal stress vectors in the top continuity plate at 2-percent drift:
Model SH-EC01 ...................................................................................................... 184
Figure 5-77: Maximum principal stress vectors in the top continuity plate at 2-percent drift:
Model WF-CN14 .................................................................................................... 184
Figure 5-78: Maximum principal stress vectors in the top continuity plate at 2-percent drift:
Model SH-EC02 ...................................................................................................... 185
Figure 5-79: Comparison of global responses in Models SH-EC01, BX-CP00, BX-CP05, BXCP07, and BX-CP10 ............................................................................................... 186
Figure 5-80: Comparison of global responses in Models WF-CP14, WF-CP05, WF-CP00, and
SH-EC01 ................................................................................................................. 186
Figure 5-81: Equivalent plastic strain distribution in the continuity plate and beam top flange in
Model BX-CP07 at 3-percent drift.......................................................................... 187
Figure 5-82: Equivalent plastic strain distribution in the continuity plate and beam top flange in
Model BX-CP10 at 3-percent drift.......................................................................... 187
Figure 5-83: Equivalent plastic strain distribution in the continuity plate and beam bottom flange
in Model BX-CP07 at 3-percent drift...................................................................... 188
Figure 5-84: Equivalent plastic strain distribution on the continuity plate and beam bottom flange
in Model BX-CP10 at 3-percent drift...................................................................... 188
vii
Figure 5-85: Out-of-plane deformation of the column flange and equivalent plastic strain
distribution in the beam top flange in Model BX-CP00 at 3-percent drift.............. 189
Figure 5-86: Definition of beam flange rotation and out-of-plane deform shape of the column
flange in Model BX-CP00 at 3-percent drift........................................................... 189
Figure 5-87: Definition of beam web rotation and out-of-plane deform shape of the column flange
in Model SH-EC01 at 3-percent drift ...................................................................... 190
Figure 5-88: Comparison of beam flange rotations in Models SH-EC01, BX-CP07, BX-CP00,
and WF-CP14.......................................................................................................... 190
Figure 5-89: Comparison of beam web rotations in Models SH-EC01, BX-CP07, BX-CP00, and
WF-CP14 ................................................................................................................ 191
Figure 5-90: Comparison of global responses in Models SH-EC01, BX-CF08, BX-CF20, and
WF-CP14 ................................................................................................................ 191
Figure 5-91: Comparison of beam flange rotations in Models SH-EC01, BX-CF08, BX-CF20,
and WF-CP14.......................................................................................................... 192
Figure 5-92: Comparison of beam web rotations in Models SH-EC01, BX-CF08, BX-CF20, and
WF-CP14 ................................................................................................................ 192
Figure 5-93: Equivalent plastic strain (PEEQ) distribution on a plastic hinge formed in the box
column connection (Model SH-EC01) at 3-percent drift ........................................ 193
Figure 5-94: Equivalent plastic strain (PEEQ) distribution on a plastic hinge formed in the Wshape column connection (Model WF-CP14) at 3-percent drift ............................. 193
Figure 5-95: Model BX-BI05 ...................................................................................................... 194
Figure 5-96: Normalized tensile stress (σ22/Fy) distribution at 3-percent drift along the column
web in Model BX-CP05: Uni-directional loading .................................................. 195
Figure 5-97: Normalized tensile stress (σ22/Fy) distribution at 3-percent drift along the column
web in Model BX-BI05: Bi-axial loading............................................................... 195
Figure 5-98: Maximum principal stress vectors on the top continuity plate at 3-percent drift, BXBI05......................................................................................................................... 196
Figure 5-99: Normal stress (σ22) distribution along the PJP weld line of column plates ............. 196
Figure 6-1: Whitewash flaking during the 0.375-percent drift cycle ........................................... 220
Figure 6-2: Crack in top CJP weld during the 0.5-percent drift cycles........................................ 220
Figure 6-3: Beam top flange fracture during the 0.75-percent drift cycle ................................... 221
Figure 6-4: Fracture surface of the beam top flange .................................................................... 221
Figure 6-5: Beam top flange local buckling during the 1-percent drift cycle .............................. 222
Figure 6-6: Beam bottom flange fracture during the 1.5-percent drift cycle ............................... 222
Figure 6-7: Fracture surface of the beam bottom flange .............................................................. 223
Figure 6-8: Bolt failure during the 3-percent drift ....................................................................... 223
Figure 6-9: Moment at the column face versus story drift angle ................................................. 224
Figure 6-10: Moment at the column face versus panel zone plastic rotation............................... 224
Figure 6-11: Beam top flange tensile strain profiles .................................................................... 225
Figure 6-12: Beam web shear strain profiles ............................................................................... 225
Figure 6-13: Moment-drift relations for analysis and experiment in Model SH-EC03 ............... 226
Figure 6-14: Von Mises stress distribution in the panel zone and the beam web at the 0.5-percent
story drift in Model SH-EC03 ................................................................................. 226
Figure 6-15: Normal stress distribution along the top continuity plate and beam top flange at the
0.5-percent story drift in Model SH-EC03 .............................................................. 227
Figure 6-16: Stress and fracture indices along the upper surface of beam top flange at the 0.5percent story drift in Model SH-EC03 .................................................................... 228
Figure 6-17: Out-of-plane deformation of a beam column connection ....................................... 229
Figure 6-18: Model DC-UR00 ..................................................................................................... 229
Figure 6-19: Sub-assemblage for connection model.................................................................... 230
Figure 6-20: Meshing details of post-Northridge connection models ......................................... 230
viii
Figure 6-21: Maximum Principal Index in Model SOL-EC03 beam flange at column face, Plane
A.............................................................................................................................. 231
Figure 6-22: Mises Index in Model SOL-EC03 beam flange at column face, Plane A ............... 231
Figure 6-23: Pressure Index in Model SOL-EC03 beam flange at column face, Plane A ........... 232
Figure 6-24: Triaxiality Index in Model SOL-EC03 beam flange at column face, Plane A ....... 232
Figure 6-25: Rupture Index in Model SOL-EC03 beam flange at column face, Plane A ........... 233
Figure 6-26: Maximum Principal Index in Model SOL-EC03 beam flange at weld access hole,
Plane B .................................................................................................................... 233
Figure 6-27: Mises Index in Model SOL-EC03 beam flange at weld access hole, Plane B ........ 234
Figure 6-28: Pressure Index in Model SOL-EC03 beam flange at weld access hole, Plane B .... 234
Figure 6-29: Triaxiality Index in Model SOL-EC03 beam flange at weld access hole, Plane B 235
Figure 6-30: Rupture Index in Model SOL-EC03 beam flange at weld access hole, Plane B .... 235
Figure 6-31: Normalized maximum principal stress (MPI) distribution on the interface of the
beam flange in Model SOL-EC03 at 0.58-percent story drift ................................. 236
Figure 6-32: Equivalent plastic strain (PEEQ) distribution on the interface of the beam flange in
Model SOL-EC03 at 0.58-percent story drift ......................................................... 236
Figure 6-33: Normalized hydrostatic stress (PI) distribution on the interface of the beam flange in
Model SOL-EC03 at 0.58-percent story drift ......................................................... 237
Figure 6-34: Connection stiffness in Specimen EC03 ................................................................. 237
Figure 6-35: Comparison of global responses in Models DC-UR00, DC-URWP, and DC-URFH
................................................................................................................................. 238
Figure 6-36: Comparison of twist angles in Models DC-UR00, DC-URWP, and DC-URFH along
the column height at 4-percent story drift ............................................................... 238
Figure 6-37: Comparison of global responses in Models DC-UR00, DC-RB00, DC-FF00, and
DC-CP00 ................................................................................................................. 239
Figure 6-38: Comparison of out-of-plane displacements in Models DC-UR00, DC-RB00, DCFF00, and DC-CP00 at 4-percent story drift ........................................................... 239
Figure 6-39: Connection detail of lateral beam braces in Building CT-15 (Design Documents
1990) ....................................................................................................................... 240
Figure 6-40: Lateral braces in Model DC-CP10 .......................................................................... 240
Figure 6-41: Comparison of global responses in Models DC-CP00, DC-CP10, DC-CPBR, and
DC-CPNH ............................................................................................................... 241
Figure 6-42: Comparison of column twist at the level of the beam bottom flange in Models DCCP00, DC-CP10, DC-CPBR, and DC-CPNH ......................................................... 241
Figure 6-43: Comparison of lateral reaction at the brace point in Models DC-CP00, DC-CP10,
DC-CPBR, and DC-CPNH ..................................................................................... 242
Figure 6-44: Comparison of lateral reaction and member forces in Brace 1 and Brace 2 ........... 242
Figure 6-45: Computation of the brace force contribution by vertical deflection of beam ......... 243
ix
List of Tables
Table 2-1: Minimum acceptable interstory drift angle capacities (FEMA 2000a) .......................... 5
Table 2-2: Extreme values of fracture indices on beam tension flange ......................................... 24
Table 2-3: Maximum measured buckling amplitudes of reinforced connections .......................... 29
Table 2-4: Normalized amplitudes for each buckling mode, UCB-RC03 (Kim et al. 2000a) ....... 30
Table 2-5: Shear tab damage indices, reproduced from FEMA-352 (FEMA 2000c) .................... 41
Table 2-6: Summary of unreinforced connection tests .................................................................. 44
Table 2-7: Boundary conditions for post-fracture behavior modeling........................................... 45
Table 3-1: Information on prototype connections.......................................................................... 68
Table 3-2: Grades of steel in connection components ................................................................... 70
Table 3-3: Target values of yield and tensile strength for test specimens ..................................... 70
Table 3-4: Dimensions of test specimens ...................................................................................... 71
Table 3-5: Mill test report data for W-shape sections of the specimens ........................................ 73
Table 3-6: Coupon test data for W-shape sections of the specimens ............................................. 73
Table 3-7: Instrumentation of test specimens ................................................................................ 76
Table 4-1: Material properties used for ABAQUS models............................................................ 96
Table 5-1 Distribution of shear force in beam flanges and beam web at 0.5-percent drift .......... 120
Table 5-2: Analytical models for the box column connection ..................................................... 123
Table 5-3: Maximum values of response indices in Model SOL-EC01 ...................................... 128
Table 5-4: Maximum values of response indices in Model SOL-EC02 ...................................... 130
Table 6-1: Distribution of shear force in beam flanges and beam web at 0.5-percent story drift 201
Table 6-2: Analytical models for the deep column connection ................................................... 204
Table 6-3: Maximum values of response indices in Model SOL-EC03 ...................................... 208
Table 6-4: Summary information of stress and strain states for Specimens EC01, EC02, and EC03
................................................................................................................................. 209
Table 6-5: Torque reactions at 4-percent story drift .................................................................... 212
Table 6-6: Contribution of each displacement component in the brace force ............................. 217
Table 6-7: Contribution of each displacement component in the member force of diagonal bracing
................................................................................................................................. 218
x
Acknowledgements
It was a great fortune in my life to have opportunities to meet so competent and
passionate professors, interesting projects, and nice colleagues during my graduate studies at
Berkeley.
I would like to express my deepest gratitude to Professor Bozidar Stojadinovic, my
advisor and chair, and Professor Andrew Whittaker, my co-advisor, for their continuous support
and assistance with the development of this work. I would like to extend my gratitude to
Professor Vitelmo Bertero for his guidance through the SAC project. I would also like to thank
Professors Stephen Mahin and Paul Vojta for their review of my work, and Professor James Kelly
for serving as the committee member in my qualifying examination.
The work described in this thesis was funded in part by the California Department of
Transportation and the SAC Joint Venture through contracts with the Pacific Earthquake
Engineering Research (PEER) Center, University of California at Berkeley. These financial
supports are gratefully acknowledged.
The test specimens were fabricated and shipped to the University by Gayle
Manufacturing Company, Woodland California, at cost. Fabrication inspection services and
testing services were provided at cost to the University by SIGNET Testing Services. The
research described in this thesis could not have been undertaken without this generous support.
Many individuals made significant contributions to this research program and the
author’s studies at Berkeley. Special thanks are due to Messrs Fadel Alameddine, Bill Davis,
Michael Foy and Greg Case of Caltrans, Mr. Rick Wilkinson and Mr. Ross Duncan of the Gayle
Manufacturing Company; Mr. Michael Everson of SIGNET Testing Services, Messrs Don Clyde,
Wesley Neighbour, David Maclam of PEER Center and UC Berkeley students Giwhan Jung and
Eduardo Rios. Dr. Shakhzod Takhirov and Dr. Amir Gilani deserve my gratitude for their advice
and hard work during the SAC project.
xi
I am grateful to Dr. Sung-Gul Hong, Professor of Seoul National University, for his
valuable advice and help on my dissertation work while he was a visiting scholar at UC Berkeley.
I am also grateful to Kyungkoo Lee for fruitful discussion on connection buckling. I would like to
thank Professor Sung-Mok Hong, my advisor and mentor at Seoul National University, and Mr.
Jong-Ho Kim, President of Chang & Minwoo Structural Consultants, for their constant care and
encouragement on my study.
The dissertation is dedicated to my parents. I am indebted to my parents for their endless
love and support. Without their love, this work would not be possible to finish. Thanks mother
and father. I wish to extend my deep appreciation to my mother-in-law for her care and pray for
me and my family.
Finally, I wish to express my utmost appreciation to my wife and sons. My wife Junga
should have all credit for her sacrifice, patience, inspiration, and love for me and my work. I will
never be able to thank her enough. My two sons, Jaewon and Jaeho, are the greatest achievement
in my life. I wish I be a good father for them.
xii
Chapter 1. Introduction
1.1 Background
Moment-connections in more than 200 steel moment-frame buildings were damaged
during the 1994 Northridge earthquake (Whittaker et al. 1998). A comprehensive research effort
funded by the Federal Emergency Management Agency (FEMA) through the SAC Joint Venture
after that earthquake contributed greatly to the understanding of the seismic vulnerability of
special steel moment frames. In addition, practical design guidelines (FEMA 2000a-f), published
in a series of FEMA documents, starting with the seminal FEMA-350 design guide (FEMA
2000a) for new steel construction, gave designers new tools for design of special steel moment
frames and a portfolio of new connection solutions. Satisfactory seismic behavior of the new
connections was proven in a comprehensive series of pre-qualification tests. Such tests are now
mandatory for every new connection that falls outside the parameter space tested to date.
The principal characteristic of the pre-qualified connection parameter space is the size
and shape of the columns. FEMA-350 connections are pre-qualified only for W12 and W14
columns. While such pre-qualification range covers a majority of new moment-resisting frames
designed today, some designers have opted to use deep columns, featuring heavy W-shapes
ranging between 21 and 36 inches in depth. Moment-resisting frames designed with such columns
offer better control of drift and are somewhat more economical (Shen et al. 2002). Specialpurpose pre-qualification tests were done on a small number of deep-column connections,
featuring exclusively the RBS (dog-bone) connection (Chi and Uang 2002; Stojadinovic 2001).
Similar to the deep W-shape columns, box columns were not considered within the SAC
Joint Venture Steel Project because they were not very common in US design practice at the time
1
(Linderman and Anderson 1990). However, changes in special moment-resisting frame design
practice in recent years have seen increased use of box columns. Box columns offer two principal
advantages over W-shape columns (Anderson and Linderman 1991). First, box columns can be
designed to have similar strength and stiffness about each horizontal axis. Second, box columns
are closed cross sections, making their torsion stiffness and resistance much higher than those of
W-shape columns. The box column is the column-of-choice in Japanese steel building design
practice (AIJ 1997; Nakashima et al. 2000). However, detailing of the connections and design of
Japanese box columns are sufficiently different from U.S. practice to make a separate
investigation of U.S. box-column connection behavior necessary.
1.2 Objective and Scope of Research
The main objectives of this study are to investigate the seismic performance, identify the
key design variables, and to present design recommendations for welded steel moment
connections to box or deep W-shape columns. To evaluate pre-Northridge moment connections to
box or deep W-shape columns, steel moment connections in a building built before the 1994
Northridge earthquake were selected for study. To achieve the above objectives, nine tasks were
undertaken as follows:
1. Identify and understand the factors that influence the ductility of welded steel moment
connections.
2. Select representative sample connections and undertake a preliminary investigation of
connection details and in-situ material properties.
3. Design and construct sample moment connections.
4. Prepare nonlinear finite element analysis models for each of the specimens.
5. Test the sample moment-resisting connections.
6. Collect, reduce, and analyze the test data.
2
7. Undertake numerical analysis of mathematical models of the test specimens and other
models for parametric studies.
8. Evaluate the experimental and analytical data.
9. Prepare design recommendations for moment connections of steel W-shape beams to
box or deep W-shape columns.
1.3 Organization of Thesis
This thesis is divided into seven chapters and a list of references. Chapter 2 describes
three factors that can influence the ductility of welded steel moment connections, namely, brittle
fracture, inelastic instability, and residual rotation capacity. Chapter 3 presents an overview of
preliminary investigation, the design of three test specimens, the test fixture, material data, a list
of the transducers, and loading protocols for the connection test. Chapter 4 provides information
on the nonlinear finite element models and analysis procedures to predict and evaluate the
response of test specimens and analytical models for parametric study. Chapter 5 summarizes the
results of tests and numerical simulations on the box-column connection specimens. An
evaluation of the response sensitivity data for the key box-column design variables is also
presented in this chapter. Chapter 6 summarizes the results of the test and the numerical
simulations on the deep-column connection specimen. An evaluation of the response sensitivity
data for the key deep-column design variables is also presented in Chapter 6. Chapter 7 presents
summary and conclusions for connections to box or deep columns. References are listed
following Chapter 7.
3
Chapter 2. Factors Influencing Connection
Ductility
2.1 Introduction
Lateral load resisting systems constructed in high seismic regions require sufficient
rigidity to eliminate damage in small but frequent events and an ability to deform in a ductile
manner to safely sustain large but infrequent events. Welded steel moment-resisting frames
(WSMF) can achieve such objectives. The perception that WSMF is a highly ductile system is
based on the ductile nature of steel. Since carbon steel can deform beyond the elastic limit,
structural steel design codes allow for load redistribution in the WSMFs (Bruneau et al. 1998).
Ductility is a quantitative measure of the capacity of the structure to sustain inelastic
deformation without significant loss of strength. It is defined as a ratio of the imposed (ultimate)
deformation to the yield deformation, greater than one.
Figure 2-1 shows moment-drift response curves in welded steel moment connections.
Depending on the ductility of the connection, three moment-drift curves are possible. The
connection of high ductility can increase its strength as the inelastic deformation increases.
Failure occurs when the maximum strain reaches the rupture strain at the critical location in the
member (Bertero and Popov 1965).
In case of limited ductility, the strength of the connection decreases after attaining the
peak strength, Mm (Gioncu and Mazzolani 2002). Strength degradation of the connection is
caused by plastic local buckling of the connected beam. Under a moment gradient, flange local
buckling (FLB) triggers web local buckling (WLB) and lateral-torsional bucking (LTB). As the
drift increases, amplitudes of each buckling mode grow. Eventually, ductile tearing develops in
4
the beam flange k-line or the flange edges and propagates into the whole beam section. If the
connection fractures before developing its full plastic strength capacity, it is considered to have
reduced ductility (Gioncu and Mazzolani 2002).
In general, fractures of beam flanges or weldments do not lead to failure to support
gravity loads. The fractured connection can still carry the gravity load as long as the shear tab can
sustain the vertical reaction forces from the beam (Gross 1998). At the ultimate performance level,
residual strength and residual rotation capacity are crucial to maintain overall structural integrity.
The residual strength is defined by the remaining moment capacity after flange fractures (Luco
and Cornell 2000) and the residual rotation capacity is the ultimate rotation capacity in the
fractured connection.
In general, the connection showing highly ductile behavior can have larger rotation
capacity than that of low ductility. Table 2-1 present acceptance criteria in terms of interstory
drift angle limits of two performance levels for each moment-frame type: Ordinary Moment
Frame (OMF) and Special Moment Frame (SMF) systems (FEMA 2000a). The drift angle for the
performance level of lateral load strength degradation is denoted θSD. This corresponds to the
interstory drift angle at which either fracture of the connection occurs or the strength of the
connection degrades to less than the nominal plastic capacity, Mp = Fy·Z, where Fy is the
specified yield strength. The drift angle associated with the ultimate performance level, θU, is
defined as the interstory drift angle at which connection damage is so severe that the connection
cannot sustain gravity loading (FEMA 2000a).
Table 2-1: Minimum acceptable interstory drift angle capacities (FEMA 2000a)
Structural system
Strength degradation,
θSD (radians)
Ultimate,
θU (radians)
OMF
0.02
0.03
SMF
0.04
0.06
5
Rotation capacity of welded steel moment connections can be improved by controlling
factors that reduce the ductility of the connection. These factors are: 1) brittle fracture, 2) inelastic
stability, and 3) residual rotation capacity. The remainder of this chapter provides a general
discussion about such factors.
2.2 Brittle Fracture
This section provides a general discussion on brittle fracture in welded steel moment
connection. The following subsection describes metallurgical aspect of fracture in ferritic steels
and weldments. Effects of deformation restraint on fracture are discussed in the Subsections 2.2.2.
Subsection 2.2.3 presents the methods of fracture assessment of welded connections including
fracture mechanics parameters and fracture indices. The remainder of this section describes a
model that can evaluate the fracture strength of the connection where no apparent initial crack
exists.
2.2.1 Metallurgical characteristic of fracture
Fracture is a process of forming free surfaces within a body by breaking the cohesive
bonds of microparticles and the accumulation of microcracks (Anderson 1995). In a macroscopic
view, two types of fracture can be defined. Fracture is called brittle when a crack propagates
instantaneously, accompanied by no or little plastification. Fracture is termed ductile when the
material sustains substantial plastic strain with high energy absorption before fracture (Barsom
and Rolfe 1999).
Fracture of ferritic steels
Ferritic steel has a body centered cubic (BCC) crystal structure, which undergoes a
ductile to brittle transition with decreasing temperature. A BCC metal is susceptible to cleavage
6
fracture at low temperature due to a small number of active slip systems. In the case of face
centered cubic (FCC) metals, cleavage fracture may not occur at any temperature because enough
active slip systems exist in FCC metals such that ductile behavior of the material can occur
(Anderson 1995).
In a microscopic view, brittle fracture is associated with cleavage, which is the crack
propagation corresponding to a series of separation of atomic bonds along the crystallographic
plane (Callister 2001). Cracking of brittle particles, such as carbides, causes cleavage fracture.
When the stress around the particles becomes larger than fracture stress, the crack propagates into
the matrix, causing cleavage fracture.
Ductile fracture results from the nucleation of microvoids followed by their growth and
coalescence through the plastic instability. Nucleation of microvoids is caused by either interface
decohesion between inclusions and the matrix. The decohesion stress is defined as a combination
of hydrostatic stress and effective (von Mises) stress. Note that the nucleation strain decreases as
the hydrostatic stress increases (Anderson 1995). Therefore, microvoids can be created more
rapidly in triaxial stress state. After the voids form around a particle, they will grow and
eventually coalesce in the presence of further plastic strain and hydrostatic stress. A crack
propagates through the growth and coalescence of the microvoids, but ultimate failure in the
ductile fracture process occurs by cleavage (Anderson 1995). As the crack grows by ductile
tearing, more material is sampled. Cleavage takes place as soon as the growing crack samples a
critical particle.
Fracture of weldments
A weldment has a highly heterogeneous microstructure resulting from both a cooling
mechanism and welding process (Fisher et al. 1995; Panontin et al. 1998). In general, the fracture
toughness of weld metal is better than that of parent metal because the equivalent carbon content
is low and the grain structure is fine due to the high cooling rate. Fracture toughness of a
7
weldment is lowest near the region close to a weld nugget that has been heated to high
temperature but below the melting point of the base metal (Fisher et al. 1995). A crack can
initiate if a weld defect has a critical size. The region in the parent metal affected by welding heat
is called as the heat-affected-zone (HAZ). Metallurgical transformations occur in this region. The
welding process can make HAZ brittle by forming hard martensite microstructures and by
increasing grain size. In the weldments with low fracture toughness the HAZ may have equal or
greater toughness than the weld metal (Fisher et al. 1995).
2.2.2 Effects of deformation restraint on fracture
Since resistance of ferritic steel to cleavage is much higher than that due to dislocation,
yielding prevails before the fracture stress is attained. However, when dislocation or slippage in
the microstructure of steel is restrained, the stress in the material can increase beyond the yield
strength for the unrestrained case. Thus, fracture can occur before yielding (Barsom 2002).
Dislocation movement in the crystal structure of steel can be restrained by low
temperature, high strain rate, and high triaxial stress state. Temperature affects the generation of
active slip systems on planes of crystal structures (Anderson 1995). Lowering the temperature
reduces the number of active slip systems (Anderson 1995). When the strain changes rapidly, the
dislocation will be suppressed or delayed. It is well known that microvoid nucleation and its
growth are promoted by high triaxial state of tensile stress (Lemaitre 1996). If a microcrack
forming from the coalescence of microvoids reaches a critical size, unstable crack propagation
will begin.
Deformation restraint and additional tensile loading (e.g. tension in column flange, and
residual stress due to welding) in other than the principal loading direction in the welded joint
induce triaxial states of stress. The degree of restraint depends on the geometry configuration,
loading type, and material properties. Sometimes, it is also affected by the residual stress that is
induced during the process of manufacture or fabrication of the structure (Panontin et al. 1998).
8
Simple analytical models are presented in Figure 2-2 to investigate the effect of
deformation restraint on the behavior of welded connections. Influences of such restraint on the
global connection behavior were discussed in detail by Lee el al. (1997). Lee et al. found that the
stress and strain distribution in the beam-to-column connection do not follow the traditional
assumption of the classical beam theory because of boundary effects. The effects of geometric
singularity and deformation restraint on the brittle fracture in a welded joint are discussed in the
following subsections.
Deformation restraint for a mesoscale element
The degree of restraint cannot be easily determined using simple models because it
depends on many factors, especially when complex geometry and material properties are
involved. Nevertheless, a simple model using a mesoscale element is employed in Figure 2-2d to
investigate the effect of deformation restraint. The cubic shown in this figure corresponds to a
Representative Volume Element (RVE). The RVE is the smallest material volume such that it
does not have high gradients of strain evident on the element scale, but large enough to represent
the process occurring at the micro scale in the material. The principles of continuum mechanics
can be applied to the RVE without explicitly considering microstructure mechanisms. The order
of magnitude of RVE for metals is 0.1 mm3 (Lemaitre 1996).
It is assumed that the deformation in the lateral directions (2- and 3- axes) is fully
restrained (ε2 = ε3 = 0), while the deformation to the loading direction (1- axis) is allowed. This
constraint is too restrictive in practical conditions because the flexibility of surrounding material
may reduce the degree of the deformation restraint. The constitutive equation for a linear
isotropic material is expressed as follows:
ε ij
=
1 +ν
ν
σ ij − σ kk δ ij
E
E
( 2-1 )
9
where ν is Poisson’s ratio (= 0.3 for steel), E is Young’s modulus (= 2×105 MPa or 29,000 ksi for
steel), and δij is Kronecker delta (= 1 when i = j; = 0 when i ≠ j). Using the constraint assumed
above and the symmetry condition (σ22 = σ
33
= σLAT) in the RVE, the three dimensional
constitutive equation can be reduced to the following one dimensional equation:
ε1 =
σ1
( 2-2 )
E1
where ε1 is a normal strain in 1-direction and σ1 is an applied stress: E1 is the equivalent Young’s
modulus in 1-direction defined as follows:
E1 =
1 −ν
E
(1 +ν )(1 − 2ν )
( 2-3 )
Note that when Poisson’s ratio ν is zero, E1 is equal to E, the elastic modulus of unrestrained
material.
The contraction stress in a lateral direction, σLAT, can be computed using the following
equation:
σ LAT =
ν
1 −ν
σ1
( 2-4 )
Thus, the normal strain in 1-direction, ε1, can be represented in terms of the normal strain ( ε1 =
σ1/E) for unrestrained case as follows:
ε=
1
σ1
=
E1
(1 +ν )(1 − 2ν ) σ=
(1 +ν )(1 − 2ν ) ε
1
1
E
(1 −ν )
(1 −ν )
( 2-5 )
The hydrostatic stress, σm, is defined as the negative of one-third of the first invariant
(trace) of the stress tensor (σij). Figure 2-3a shows the relationship between the Poisson’s ratio
and the stress and strain quantities under the deformation restraint; ε1 is normalized by ε1 . Stress
quantities are normalized by σ1. As Poisson ratio ν increases, ε1 decreases while σLAT and σm
increase. If ν is zero, the effect of restraint will disappear.
10
The maximum shear-stress theory suggests that yielding begins whenever the maximum
shear stress reaches a certain critical value τcr, which depends on the material itself (Popov and
Balan 1998). From the result of a uniaxial tensile test, the critical value can be determined as
follows:
τ max ≡ τ cr=
1
(σ y − 0)
2 τy
= σ y /=
2
( 2-6 )
where σy is yield strength determined from the uniaxial tensile test.
The yield stress under the restrained condition, σcr, can be computed as follows:
σ
1
 1 −ν 
τ max = (σ 1 − σ LAT ) =τ cr = y ⇒ σ cr =
σ y
2
2
 1 − 2ν 
( 2-7 )
Figure 2-3b compares the Mohr circles upon yielding for the materials with the ν = 0 and
ν = 0.3. The axial stress is normalized by σy while the shear stress is normalized by the shear
yield strength, τy. When the stress applied to a restrained RVE has the magnitude of σy, the
material with ν = 0 yield s, b u t the material with ν = 0.3 does not yield because the maximum
shear stress decreases while the lateral stress increases (circle A in Figure 2-3b). For the material
with ν = 0.3 to yield under deformation restraint, the applied stress should be increased further
beyond σy (circle B in Figure 2-3b). Note that 1.75 σy is the maximum yield stress that can be
achieved in the restrained condition if no additional tensile loading in other than the principal
loading direction (1-axis). When the addition tensile loading in the other direction is applied, the
yield stress can increase to more than 1.75 σy.
From the macroscale (structural element) view, it is difficult or sometimes impossible to
obtain a simple governing equation for a deformation restraint condition because of the variation
in the rigidity of surrounding materials, geometric configuration, and multi directional loading. In
such cases, nonlinear numerical analysis using finite element method is useful to study the local
behavior of a material under various degrees of restraint.
11
End effects in welded joints
In welded steel moment connections, the stress state near the weldment joining the beam
flange and column flange is more complex than in the beam flange far from the joint. The
complex stress states in the joint are caused by several factors, including welding induced
residual stresses, shear stresses across the beam flange thickness, and kinking of the beam and
column flanges.
The End effect (Timoshenko and Goodier 1982), a stress singularity in the reentrant
corner of the joint, also affects the stress state in the joint. Because the end effect in the reentrant
corner of the beam flange joint is too localized to be considered in global connection behavior
analyses, it has rarely been dealt with in design of steel structures. The high localized stress state
induced by the end effect, however, cannot be overlooked from the point of view of fracture,
since the mechanisms of fracture depend on the local stress state as well as the global demands in
the joint.
Finite element models were prepared to investigate the local stress distribution caused by
the end effect and its sensitivity to both of the mesh size and the sharpness of the reentrant corner.
The middle section of a beam flange was considered to be restrained sufficiently to prevent any
deformation in the direction of beam flange width (3-direction). 2-D plane strain elements were
selected to model such region, as shown in Figure 2-2b and Figure 2-2c. Two types of models
were considered in the analyses; a linear elastic model and an elastic–perfectly plastic model. The
magnitude of the applied stress (σapp) was identical to the uniaxial yield strength of the material.
Poisson’s ratio was set to 0.3. Zero displacement was specified at the material boundary at the
joint. Material properties, geometries, and applied loadings are symmetric with respect to the
mid-plane of the beam flange. Thus, only the upper half of the beam flange was modeled by
applying the symmetry condition on the mid-plane.
12
Analysis results for a linear elastic model having the mesh size of 1/32tf are presented in
Figure 2-4, where tf is the flange thickness. The distributions of normal stress (σ11), contraction
stress (σ22) in the direction of beam thickness, and hydrostatic stress (σm) near the displacement
boundary are shown in this figure. The degree of localization of the normal stress is high at the
reentrant corner of the beam flange. Theoretically, normal stress becomes infinite as the radius of
the reentrant corner approaches zero (Benthem 1963):
=
σ re c ρ − a ,
ρ → 0,
0 < re a < 1
( 2-8 )
where σ is a stress along the boundary, ρ is the distance from the reentrant corner, re a is the real
part of the exponent which determines the characteristic of the singularity, c is the coefficient
which determines the strength of the singularity. In the finite element analysis, stresses are
extrapolated from the values at the element integration points, which are located far from the
element nodes. Thus, the computed stress concentration factor (K = σmax/σapp) is only 1.6 (Figure
2-4a) rather than infinity which is predicted by the singularity theory.
The contraction stresses in 2-direction are presented in Figure 2-4b. Stress σ22 on the
flange surface is small because of the traction free boundary condition on the surface. Stress σ22
has maximum at the mid-plane. The degree of restraint in 3-direction is infinite (no deformation)
and no external loading is applied in this direction. Thus, the distribution pattern of σ33 is similar
to σ11: σ33 is high where σ11 is high.
The hydrostatic stress σm (Figure 2-4c) has maximum value at the reentrant corner of the
flange and rapidly decays in the longitudinal direction (1-direction), but it is relatively constant
along the direction of the flange thickness (2-direction).
The end effect will be dramatically reduced when the reentrant corner of the flange has
some roundness that is achieved using a fillet. Various radii of fillet in the reentrant corner were
considered to study the local stress state. Figure 2-5 shows a relationship between the radius of
fillets and the stress concentration factor. One linear elastic model, having 64 elements along the
13
beam flange thickness was used for the analysis. The fillet pushes the location of the critical
stress far from the boundary and reduces the stress concentration. When the radius of the fillet is
less than a quarter of the flange thickness, the stress concentration is high. If the radius of the
fillet is increased to greater than the flange thickness, the stress concentration becomes negligible.
Anderson et al. (2002) conducted tests for pre-Northridge moment connections upgraded with
weld overlays of notch tough weld metal. Such weld overlays moved the stress concentration
region away from the column face as discussed above and improved the rotation capacity of
connections. For small size specimens, the plastic rotation exceeded 3-percent radian while the
specimen of intermediate size failed in the parent material. In both cases, no fracture in CJP welds
(Miller 1995) of overly welds was observed.
The mesh sensitivity and the material model effect were investigated as shown in Figure
2-6. The number of elements along the beam flange thickness increases from 4, 8, 16, 32, 64, to
128 elements. For the linear elastic material, the stress concentration factor increases
continuously, as the number of elements increases. For the elastic-perfectly plastic material, the
stress concentration factor converges to 1.4. Considering the fact that the steel can yield and
infinite sharp crack does not exist, it follows that the finite element meshes for local stress
analysis in welded connection do not need to be excessively refined. A moderate mesh size of
approximately 16 elements per flange thickness is sufficient to accurately analyze the connection.
Cleavage mechanism in welded joints
Figure 2-7 shows the hydrostatic stress distribution across the lower half of the beam
flange and the maximum principal stresses in the elements in the neighborhood of the boundary.
The high tensile pressure (hydrostatic stress) at the boundary increases the potential for brittle
fracture by limiting the plastic strain in the material at the boundary (Dexter and Melendrez 2000).
There are two fracture paths in this region; Path A in the weld and Path B in the column flange.
Any initial defect of a critical size in the weld may cause fracture along Path A if the fracture
14
toughness of weld metal is not high enough. Otherwise, fracture along Path B will occur. Path B
is related to the column damage type C1 and C2 defined in FEMA 351 (FEMA 2000b). Type C1
damage has a small crack in the column flange thickness at the joint of beam flange. Type C2
damage is similar to Type C1 but the crack extends along the column flange with a curved failure
surface.
The reentrant corner of the beam flange may act as a stress riser if the radius of fillet is
small enough to cause end effects. The crack plane in the reentrant corner forms an angle of 135°
to the bottom face of the beam flange. Cleavage tends to propagate perpendicular to the direction
of the maximum principal stress. The fracture path follows the plane where the driving force is
maximized rather than the original crack plane (Anderson 1995). Thus, cracks may form and
propagate along Path B. When the column flange is subjected to high axial tensile stresses, the
cracks will penetrate deep into the column flange, because the axis of principal stress rotates
closer to the crack plane. The possibility of brittle fracture in the column flange also increases due
to high degree of triaxiality induced by tensile stress in the column flange.
Cleavage is a process of breaking bonds between atoms in the microstructure (Anderson
1995). When the stress at the atomic level exceeds the cohesive strength of the material, cleavage
fracture will occur. The theoretical debonding stress of material is approximately E/π (= 0.3E)
(Anderson 1995). A cleavage initiation model for metal is presented in Figure 2-8. Macroscopic
cracks act as geometric discontinuities for applied stresses and cause stress amplification. These
are the so called stress risers. Weld root flaws, notches, or sometimes ductile tearing (Kuwamura
and Yamamoto 1997) are stress risers in welded steel connections. If the crack has an elliptical
shape and is oriented perpendicular to the loading direction, the stress concentration factor Kt at
the crack tip can be expressed as follows (Anderson 1995):
Kt
=
σ local
a
= 2 1
σ app
ρ
( 2-9 )
15
where σlocal (= 2σapp [a1/ρ]1/2 ) is the maximum stress at point O, σapp is the magnitude of the
applied stress, a1 is the length of an edge crack, and ρ is the radius of curvature of the crack tip.
As reported by Kaufmann et al. (1997), the initial flaw depth (corresponding to a1) in samples of
fractured moment connections ranged from 0.8 mm to 10 mm (0.03 in. to 0.4 in.). To initiate the
cleavage at the applied stress level equal to the uniaxial yield strength (σapp = σy = Eεy = 0.002E),
the required maximum sharpness (crack tip radius ρ) is 2 μm (0.00007 in.):
K t ,cr = σ debond / σ app =
0.3E
a
a
= 150 = 2 1 → ρcr = 12
0.002 E
75
ρ
( 2-10 )
In general, stress risers in welded connections may not have such a sharp crack tip. To
understand the cleavage in metal, microcracking due to the high triaxiality needs to be considered.
The triaxiality ahead of the crack tip can elevate the stress for void nucleation and its growth
(McClintock 1963) by restricting the plastic flow in the metal. Microcracks are formed during the
process of void nucleation and growth around the inclusions or the second phase particles, such as
carbide. Under a high triaxial stress state, these microcracks will remain sharp, thus they can
trigger cleavage fracture when the stress concentration is high enough for the elevated stress to
overcome the cohesive strength of the material.
2.2.3 Fracture assessment of welded connections
Whether or not brittle fracture occurs in welded connection depends on the material
properties, initial crack size, geometric configurations, loading type, and weld residual stress
distribution. Fracture mechanics analysis can be effective to analyze such complex factors.
Welded steel structures without apparent initial defects also have experienced brittle
fracture driven by stress concentration (Kuwamura 1998; Tide 1998). In this case, a fracture
mechanics approach using an inherent crack cannot be used to evaluate the fracture strength of
the structure. Therefore, a local criterion for the crack initiation process is required. A fracture
index is an indicator of stress and strain state in the critical region. Without performing complex
16
fracture mechanics analysis, a fracture index can indicate fracture-critical locations.
Micromechanisms of fracture may be included without difficulty. For these reasons, it is useful to
use a fracture index in the evaluation of a welded connection.
Fracture mechanics parameters
Parameters commonly used in fracture mechanics analysis are the stress intensity factor
(K), the energy release rate (G), and the crack tip opening displacement (CTOD). K defines
singular field of stress ahead of a crack tip (Anderson 1995). Once K is computed, it is possible to
solve for all components of stress and strain in the singularity dominated zone. G is the rate of
change in potential energy associated with crack area (Anderson 1995). It is calculated from the
derivative of the potential energy. CTOD is a measure of the crack tip blunting due to plastic
deformation. The degree of crack blunting is related to toughness of the material. If the geometric
configuration and material property distribution in the connection are not simple, the analytical
solution by fracture mechanics may not be available. In this case, a numerical analysis using the
J-integral is useful. Once J is computed, K, G, and CTOD at a critical location can be determined
using their predetermined relationships to J.
Before the Northridge earthquake, the fracture mechanics approach was not used for
design of steel building structures. Brittle failures identified during the investigation of
connections damaged after the Northridge earthquake made it necessary to consider fracture
mechanics.
Popov et al. (1998) conducted 3-D elastic-plastic analysis using solid elements on preNorthridge connections. They noticed that significantly triaxial stress states exist in the welded
beam-to-column connection because of deformation restraint. Backing bars were modeled to be
fully bonded to the beam flange, but the interface between the backing bar and the column flange
was assumed not to be fused. Crack like discontinuities (gaps) at the backing bar interface were
considered, but weld defects were not included in their analysis. KI at the bottom backing bar was
17
found to be larger than that at the top backing bar. When KI reached a critical value, KIc, unstable
crack propagation occurred. Removing the backing bar or closing the gap by a continuous fillet
weld was recommended to reduce the deleterious effect of the backing bar.
Joh and Chen (1999) proposed a method that can assess the probability of brittle fracture.
Their method was based on linear elastic fracture mechanics (LEFM), and they conducted elastic
analysis using solid element models. A representative crack was assumed to be located across the
entire width of the beam flange. This artificial crack included all factors adverse to the connection
strength, such as a crack-like defect, welding induced residual stresses, and HAZ. The maximum
energy release rate in front of the edge crack at the brittle fracture load, Ge, was used as the
fracture toughness parameter. Joh and Chen collected data on crack-like defect size from the
connections damaged by the earthquake as well as the fractured sections from beam-column
connection tests. A statistical distribution of brittle fracture moments, Mf, was computed using the
distribution of defect sizes, while statistical distribution of plastic moments, Mp, was determined
using the distribution of the yield strength of the beam flange material. From the distribution of
the moments for each fracture mode, the probability of brittle fracture was computed as;
P(brittle fracture)= P ( M f − M p ≤ 0)
( 2-11 )
Zhang and Dong (2000) studied the influence of welding-induced residual stresses on
brittle fracture in welded beam-to-column connections. A 2-D plain strain element model was
used to simulate the multi-pass weld beads. A residual stress analysis was conducted by using a
sequentially coupled thermal and mechanical procedure. Upon completion of the residual stress
analysis, two sizes (0.5 and 2.5 mm) of weld defects were introduced in the weld root. In each
case, energy release rate G was computed, converted to the stress intensity factor KI, and
compared to the fracture toughness KIc of the weldment.
Zhang and Dong found that the transverse residual stresses peaked at the notch tip
between the backing bar and column flange. The presence of high tensile residual stresses
18
significantly increased the energy release rate. A smaller defect had an even higher fracture
driving force if residual effects were considered. Fracture driving force for a larger defect was
larger if the residual effects were not considered. For a small defect, removing the backing bar
reduced the fracture driving force by 5 to 8 percent.
Chi et al. (2000) performed a detailed finite element analysis to study the fracture
toughness demands in the welded steel connection. The authors defined the fracture toughness
demands using elastic stress intensity factor, KI, and the inelastic crack tip opening displacement,
CTOD. They found the following: CTOD demands were much smaller for overmatched weld
metals; the stress intensity factor was proportional to the root defect size and was unaffected by
the backing bar thickness; adding a reinforcing fillet weld or removing the backing bar reduced
toughness demands; weld root or backing bar notch effects at the underside of the top flange were
much smaller than those at the underside of the bottom flange; toughness demands on the face of
flange directly above the backing bar were much higher than the average values in the beam
flange estimated using beam theory; and fracture toughness demand for a weak panel zone was
much higher than that for a strong panel zone because of localized column flange kinking
adjacent to the beam flange weld.
Matos and Dodds (2000) introduced a semi-elliptical crack into fracture mechanics
analysis of the linear elastic model for a pull-plate specimen (Kaufmann and Fisher 1995). A
through-crack configuration has been commonly used in fracture mechanics analysis because it
requires less mesh generation than any other crack configuration. It is also convenient for a 2-D
model to analyze the connection with the uniform through crack. However, the depth of weld
defects in the middle of the bottom flange is generally larger than the depth of a defect at another
location due the interruption of the welding of the bottom flange at the web. Thus the assumption
of a uniform through crack may lead to incorrect conclusions on fracture strength.
Matos and Dodds investigated the effects of welding-induced residual stresses using the
eigenstrain approach. Stress intensity factor KI was computed in the form of non-dimensional
19
geometry factors for geometrically similar configurations. They concluded the following: fracture
demand by the residual stress alone was approximately one-third of the available fracture
toughness for the connection fabricated using E70T-4 electrodes; the fracture demand for
through-width uniform crack condition was larger than that for the semi-elliptical crack in the
root pass. They proposed the use of a grooved backing bar to eliminate the cost of removing the
backing bar.
Matos and Dodds (2001) developed a probabilistic micro-mechanical model to describe
the cleavage fracture process. Brittle fracture (cleavage) in ferritic steels is related to a micromechanical fracture process. Ferritic steels experiences ductile rather than brittle fracture if the
temperature is higher than the ductile-to-brittle transition temperature and the strain rate is not too
high. However, under a high triaxial stress state, plastic deformation near the connection region is
restrained, but microvoid nucleation and growth are promoted. If the microstress around any
microcrack reaches the debonding stress of the material, cleavage will occur. Thus, the
microprocess of cleavage in fracture mechanics analysis of brittle fracture of ferritic steels must
be considered. Matos and Dodds conducted large-scale 3-D finite element analyses of the full
connections to compute the crack-front stress fields, which capture local variations in the fracture
parameters and constraint. Their combined model provided a quantitative estimate for the
cumulative probability of cleavage fracture in a connection.
Fracture indices
Instead of the fracture mechanics approach described in the above, four normalized stress
and strain quantities and two fracture indices are used in this study to identify the potential sites
of brittle and ductile fracture. These are: Pressure Index, Mises Index, Maximum Stress Index,
and PEEQ Index (normalized stress and strain quantities); Triaxiality Index and Rupture Index
(fracture indices). Most of these indices were used by El-Tawil et al. (1998) in their finite element
studies of the strength and ductility of fully restrained steel beam-column connections. The
20
Maximum Principal Index was not used in their study. Information on each of these indices
follows.
Pressure Index: The Pressure Index (PI) is defined as the ratio of the hydrostatic stress
(σm) divided by the yield stress (σy), where the hydrostatic stress is:
1
3
1
3
σm =
− trace(σ ij ) =
− σ ii
( 2-12 )
where i and j represent the global directions (1, 2, 3). A large tensile (negative) hydrostatic stress
is often accompanied by large principal stresses and generally implies a greater potential for
either brittle or ductile fracture. In the presence of a crack or defect, large tensile hydrostatic
stress can produce large stress intensity factors at the tip of the crack or defect, and increase the
likelihood of brittle facture. A large tensile hydrostatic stress can also lead to rapid damage
accumulation in metals due to micro-void nucleation, growth, and coalescence (ductile fracture)
and a substantial reduction in component ductility (Hancock and Mackenzie 1976; Thomason
1990).
Mises Index: The Mises Index (MI) is defined as von Mises stress (σeff) divided by the
yield stress (σy). Von Mises stress is defined as the second invariant of the deviatoric stress tensor:
σ eff =
3
S S
2 ij ij
( 2-13 )
where Sij are the deviatoric stress components calculated as S=
σ ij + σ mδ ij using tensor notation.
ij
This index provides information about the intensity of the deviatoric stress tensor, responsible for
deformations that do not change volume.
Maximum Principal Index: The Maximum Principal Index (MPI) is defined as the
maximum principal stress (σ1 or σmax) divided by the yield stress (σy), where the maximum
principal stress is defined as the algebraically largest normal extreme of the stress tensor (σij). It is
one of roots for the following equation:
21
σ ij − λδ ij =
0
( 2-14 )
The maximum stress, σmax is invariant with respect to a rotation of the axes at a point. No shear
stress exists on the principal planes defined by σmax. This index is used to define the boundary of
an initial crack induced by triaxiality.
PEEQ Index: The equivalent plastic strain index (PEEQI) is defined as the equivalent
plastic strain (PEEQ in ABAQUS) divided by the yield strain (σy/E). The equivalent plastic strain
is the second invariant of the plastic strain tensor and is calculated as:
PEEQ =
2 p p
ε ε
3 ij ij
( 2-15 )
where ε ijp are the plastic strain components. This index is a measure of ductility at the local level
(El-Tawil et al. 1998).
Triaxiality Index: The Triaxiality Index (TI) is defined as the hydrostatic stress (σm)
divided by von Mises stress (σeff):
TI =
σm
( 2-16 )
σ eff
Lemaitre (1996) describes the important effect that this index has on the ductile rupture
of metals. He noted that the measured ductility at fracture decreases as the Triaxiality Index
increases. El-Tawil et al. (1998) report that: 1) values of Triaxiality Index between 0.75 and 1.5
can cause large reductions in the rupture strain of metals, and 2) values of Triaxiality Index
greater than 1.5 can trigger brittle fracture. Schafer et al. (2000) investigated triaxiality and
maximum principal stress demands on fractured notched round bars, small-scale tension
specimens and a full-scale moment-resisting connection. They defined two triaxiality-related
indices applicable to a ductile metal using the von Mises yield criteria. Triaxiality demands were
calculated using a 3-D (material) nonlinear finite element analysis. They found that the fracture
location is consistent with the location of high triaxiality demands. Based on analysis of the test,
22
they proposed that fracture of welded steel moment connections may be governed by triaxiality
even when high toughness parent and weld metals are used.
Rupture Index: The definition of the Rupture Index (RI) used in this study is identical to
that adopted by El-Tawil et al. (1998), namely:
PEEQ
=
RI a=
εr
PEEQ

σ
exp 1.5 m
 σ eff

( 2-17 )




where a is a material constant, ε r is the rupture strain, and the other terms are as defined above.
In this equation, hydrostatic compression is positive. The strain at ductile fracture (rupture) given
by Hancock and Mackenzie (1976) and adopted by El-Tawil et al. is

ε r = a exp 1.5


σm 

( 2-18 )
σ eff 

Hydrostatic compression increases the rupture strain while hydrostatic tension decreases the
rupture strain. El-Tawil et al. note that Equation 2-17 can be used to compare the likelihood of
ductile fracture either in a single specimen at several critical locations or between different
specimens.
Lu et al. (2000) used the equivalent plastic strain index (PEEQI) to identify the critical
location in the weld access hole and to evaluate nine weld access hole configurations. The
effective plastic strain (PEEQ), von Mises stress, hydrostatic stress, and rupture index (RI) were
calculated at the critical locations to evaluate the effect of panel zone stiffness on the performance
of moment-resisting connections.
Application – effects of connection reinforcement
Kim et al. (2000a) conducted 3-D nonlinear finite element analysis to determine if the
stress and strain conditions in reinforced connections were substantially better than those in
unreinforced (pre-Northridge) connections. To address this, a finite element model of an
23
unreinforced connection, termed UCB-RC00, was prepared and analyzed. Analysis results on the
cover-plate connection test specimen UCB-RC03 are presented here for comparison. For details
see Kim et al. (2000a).
The largest fracture index values were computed at points in beam cross section planes at
the face of the column and at the end of the reinforcement plate. Table 2-2 presents a summary of
fracture index values in the two finite element models at 0.5-, 1-, and 2-percent story drift. At 0.5and 1-percent story drifts, the maximum values of Triaxiality Index and Rupture Index are greater
in the beam flange of UCB-RC00 than in the beam flange of UCB-RC03. At 2-percent story drift,
the maximum value of Rupture Index is recorded in the beam flange of UCB-RC00 at the face of
the column.
Table 2-2: Extreme values of fracture indices on beam tension flange
Story
drift
Model
UCB-RC00
Location
Column face
UCB-RC03
Column face
Nose of plate
Index
TI
RI
TI
RI
TI
RI
0.5 %
-0.93
0.0017
-0.82
0
-0.61
0
1.0 %
-0.88
0.0170
-0.83
0.0042
-0.68
0.0012
2.0 %
-0.77
0.0990
-0.84
0.0250
-0.69
0.0260
The plotted data in Figure 2-9 and Figure 2-10 are for the surface of one half of the beam
flange at the face of the column. The maximum values of stress and strain along this line were not
necessarily the maximum values in the finite element models, but this line was chosen to facilitate
a comparison of results for different models. Figure 2-9 presents the distributions of Pressure
Index on UCB-RC00 and UCB-RC03 FE models at 0.5-percent story drift when the connection
behavior is elastic. The abscissa represents a distance from the beam centerline. The Pressure
Index of UCB-RC00 FE model was much higher than in UCB-RC03. This result indicates that
reinforcing the connection reduces the driving force for brittle fracture. Figure 2-10 presents the
24
distributions of Rupture Index in the UCB-RC00 and UCB-RC03 models at 2-percent story drift.
After yielding of beam flange, the peak Rupture Index in UCB-RC00 was almost 0.1 while the
corresponding value in UCB-RC03 was only 0.023. Putting aside issues related to defect size and
location, the values of fracture indices reported above clearly indicate that the addition of
reinforcement plates to a steel moment-resisting connection substantially reduces the likelihood
of brittle and ductile fracture at modest levels of story drift.
2.2.4 Model of connection fracture strength
As long as all pertinent data are given, fracture mechanics analysis employing numerical
methods will provide an accurate estimate of the potential for brittle failure. However most of the
data required for a fracture mechanics analysis will likely not be available for design. For
example, the distribution and size of initial cracks is a matter of construction, not a matter of
design. A fracture mechanics approach can not be implemented without knowing the distribution
and size of the initial cracks. Furthermore, it is possible that fracture will occur without apparent
initial cracks. In this case, an assumption for the initial crack must be made for fracture
mechanics analysis.
Careful detailing, fabrication, and inspection of the connection can substantially eliminate
the defects in welded connections (Barsom 2002), but such practices do not change the force flow
causing the stress concentration in the critical connection region. Proper design of the connection
is required to reduce the degree of stress concentration (Mohr 2002). Unfortunately, there are no
design criteria based on stress concentration levels or brittle fracture potential, because it has been
assumed that the locally concentrated stresses can spread into the neighboring regions by yielding.
Critical stress for microcracking
A procedure that can evaluate the (brittle) fracture strength of the connection where no
apparent initial defect exists in the fracture critical region (e.g. CJP weld in the beam top flange
25
or bottom flange where backing bar was removed and weld defects were repaired) is proposed
below. It is assumed that a crack will appear in the region where the maximum principal tensile
stress σmax is larger than the critical stress for microcracking, σmax,f (see Figure 2-11). Stress σmax,f
includes the effects of stress triaxiality, residual stress, and material yielding.
Schafer et al. (2000) reported maximum principal stresses at fracture from coupon and
connection tests as shown in Figure 2-12: σmax reported in this figure is a maximum stress value in
the cross section when fracture occurred; σu is a uniaxial tensile strength of material and is
corresponding to the maximum stress that can be sustained by a structure in uniaxial tension. If
this is stress applied and maintained, fracture will result (Callister 2001). The ratio σmax/σu from
coupon tests ranged from 1.2 to 1.6. In the coupon, the maximum principal stress develops along
the circumference rather that at one point. Thus, as soon as the maximum principal stress reaches
a critical value, brittle fracture occurs in a coupon. The ratio σmax/σu has a value of approximately
1.3 (Test 7 and Test 13 plots in Figure 2-12) for small-scale tension specimens designed to
simulate beam flange-to-column flange connections (Kaufmann and Fisher 1995). In contrast to
the notched round bars, the largest value at a point in a typical moment connection cannot
represent the stress state at failure. This indicates that microcracking initiated at values of σmax,f
less than 1.3 σmax.
A critical stress for microcracking, σmax,f, must be defined to evaluate the fracture strength
of connections. Randomness of microstructure, welding residual stress, and material yielding will
cause a large variation in σmax,f. A probabilistic approach using the Weibull stress model may
provide a better answer.
Evaluation procedure for connection fracture strength
The proposed procedure to determine the connection strength to brittle fracture without
an apparent initial defect is presented as follows:
1. Prepare FE model using 3-D solid elements.
26
2. Define a critical stress for microcracking, σmax,f, from experimental data for connections
having similar materials and configurations (use σu as σmax,f if data is not available).
3. Increase the displacement in the FE model to the expected story drift.
4. For each increment of tip displacement, report the stress distribution at the fracture
critical region.
5. Define a initial crack from the contour of maximum principal stress and σmax,f (see
Figure 2-11).
6. Compute stress intensity factor KI at the crack tip using fracture mechanics analysis.
7. Compare KI with fracture toughness KIc for the material.
8. If KI < KIc then repeat 2, 3, 4, 5, 6, and 7 for next increment of tip displacement.
9. When KI > KIc, report corresponding displacement and resistance as the fracture drift
and strength.
10. If KI < KIc, up to the target story drift for ductile behavior, brittle fracture should not
occur in the pre-defined fracture critical region.
Pre-qualification tests are required for any new connection design. The use of the
proposed connection fracture strength model allows for the efficient use of finite element analysis
to optimize a connection design before undertaking pre-qualification tests.
2.3 Inelastic Instability
The potential of brittle fracture is greatly reduced in post-Northridge connections by
limiting stress concentration in the critical locations. However, post-Northridge connections
suffer relatively rapid strength degradation after plastic hinge is formed in the beam. Such
strength degradation is related to the onset of inelastic instability of the beam.
This section provides a general discussion on inelastic instability in welded steel moment
connection. The following subsection describes the response of plate reinforced connections, one
27
of post-Northridge connections, tested at University of California at Berkeley in 1999 as the
Phase II of SAC Steel Project. Researches on the lateral buckling and lateral-torsional buckling
of beams conducted by Lay (1965a, 1965b), Lay and Galambos (1965, 1967) are summarized in
Subsections 2.3.2 and 2.3.3, respectively. The remainder of this section describes the model that
can evaluate strength degradation in the moment connection using the amplitude of flange local
buckling.
2.3.1 Behavior of plate reinforced connections
Cyclic responses
Figure 2-13 shows the cyclic response of a cover-plated connection, UCB-RC03 (Kim et
al. 2000a). Moment at the column face is normalized using the plastic moment of the beam. Beam
flange outside of the cover plate started to yield during the cycles to 1-percent story drift. Minor
flange local buckling was observed during the cycle to 1.5-percent story drift. Amplitudes of the
flange local buckling increased during the cycle to 2-percent story drift. Web local buckling
initiated at the second negative cycle to 3-percent story drift. The beam strength dropped after
local web buckling. The amplitude of the flange and web local buckling greatly increased and
beam twisting due to lateral-torsional buckling was observed during the cycle to 4-percent story
drift. Figure 2-14 shows a view of the flange buckle at the end of the cover plate following the
displacement cycles to 3-percent interstory drift. One edge of the beam flange buckled upward
and the other side of the beam flange buckled down. The maximum amplitude of the flange
buckling was measured as 56 mm (2.2 in.) and the buckle length was 500 mm (20 in.). This test
specimen UCB-RC03 failed during the second negative cycle to 5-percent story drift due to
tearing in the bottom flange k-line that was a result of sever flange local buckling and web local
buckling.
28
The amplitudes of flange local buckling (FLB) and web local buckling (WLB) measured
during tests of 6 reinforced connection specimens are summarized in Table 2-3. The amplitudes
of both buckling modes are normalized with respect to the beam flange thickness. Buckling
amplitude of the connections rapidly increased during the displacement cycles to 3-percent and 4percent interstory drift.
Table 2-3: Maximum measured buckling amplitudes of reinforced connections
2 % drift
3 % drift – 1st cycle
3 % drift– 2nd cycle
4 % drift
FLB2
WLB2
FLB2
WLB2
FLB2
WLB2
FLB2
WLB2
UCB-RC011
0.45
-3
1.04
-
2.91
-
4.48
-
UCB-RC021
0.07
-
0.52
0.30
-
-
-
-
UCB-RC031
-
-
1.18
1.18
3.29
-
5.60
2.99
UCB-RC041
0.30
0.18
1.79
2.34
-
-
-
-
UCB-RC051
1.18
-
2.24
2.06
-
-
4.48
-
UCB-RC061
-
-
-
-
4.85
-
5.97
-
1.
2.
For details see Kim et al. (2000a).
Normalized using beam flange thickness, tf = 17 mm (0.67 in.).
3. Not available.
Figure 2-15 shows the maximum axial strains measured using the strain gages attached to
the outer surfaces of top and bottom flange of Specimen UCB-RC03. These strain gages were
placed at the location 51 mm (2 in.) away from the end of cover plates. The strain distribution
measured using these strain gages shows the effect of FLB on the flange forces. Points (1+, 1-, 2+,
and 2-) in Figure 2-13 are the peak loading points for positive and negative loading cycles to 3percent drift, respectively. Positive loading caused tension in the top flange and compression in
the bottom flange. Only strains in the compression flange are reported in Figure 2-15. At the first
positive displacement cycle, distribution of compressive strain in the bottom flange was relatively
uniform. Simultaneously, strength degradation in the moment-rotation curve was negligible
(Figure 2-13). During the next negative cycle, the top flange started to buckle and its strain
29
distribution was no longer uniform. Strength degradation at this displacement cycle was obvious
because the top flange already experienced high plastic deformation during the previous halfcycle. The degree of the strain concentration in the middle of beam flanges increased during the
next full displacement cycle. While the amplitude of FLB increases, the amount of flange force
transmitted through the edges of the flanges decreases.
Strength degradation of connections
Figure 2-16 shows the relation between the moment at column face and the interstory
drift angle obtained by finite element analysis in Model UCB-RC03 using shell elements (Kim et
al. 2000a). The moment is normalized with respect to the nominal plastic moment of the beam.
Shown on this figure are points A through E that represent different stages in the response of the
model. Point A corresponds to the elastic response. Point B corresponds to first strength
degradation point after attaining maximum resistance. Points C, D, and E correspond the moment
at 3-, 4-, and 5-percent story drift, respectively. Figure 2-17 presents the deformed shape of the
beam cross section at each of these five points at a location, 184 mm (7.25 in.) from the end of
the cover plate. Note that the locations of maximum flange and web local buckling amplitudes, as
well as lateral-torsional buckling amplitude are not necessarily at the same cross section.
Table 2-4: Normalized amplitudes for each buckling mode, UCB-RC03 (Kim et al. 2000a)
Point
Drift
angle %
FLB1
WLB1
LTB1
A
1
0.01
0.01
0.01
B
2
0.39
0.62
0.37
C
3
2.52
1.53
1.40
D
4
3.39
2.75
1.97
E
5
4.04
3.17
2.19
1. Normalized using beam flange thickness, tf = 17 mm (0.67 in.).
30
All sections in the plastic hinge region were examined and maximum buckling amplitude
values were reported in Table 2-4. Thus, Table 2-4 lists the maximum amplitudes of local
buckling and lateral torsion buckling at each of the five points in Figure 2-16. The amplitudes are
normalized with respect to the beam flange thickness for comparison. LTB was measured using
the distance from the original location of the centerline of the beam flange to its deformed
location.
The amplitudes of each buckling mode are also plotted in Figure 2-16. They are
converted using the equation below to investigate the relationship between the buckling
amplitudes and the strength degradation of the connection.
M col M m δ M m − M E
=
−
Mp
M p δE
Mp
( 2-19 )
In this equation, Mm is a maximum moment in the response curve, ME is a moment at
point E, and δE is the amplitude of each buckling mode at point E (corresponding to 4 percent
drift). As shown in Figure 2-16, the rate of strength loss in the connection is best matched with
the rate of increase in buckling amplitude of flange local buckling. Thus, the amplitude of FLB
may be used to predict connection strength degradation.
Figure 2-18 shows the moment-drift relations for Model UCB-RC03 and Model UCBRC00 calculated using shell element FE models (SH). The response in Model UCB-RC03
calculated using the solid element model (SOL) is also presented to show connection behavior
when lateral deformation is fully restrained. Moments at column face for each model are
normalized with respect to the nominal plastic moment of the beam. In the case when lateral
deformation is fully restrained (SOL-RC03), connection strength increases as the drift increases.
This represents the behavior of highly ductile connection discussed in the Section 2.1. However,
note that the solid element model was incapable of reproduction buckling because of its perfectly
symmetric initial geometry (no initial imperfections), while the shell finite element model was
designed to analyze buckling using the Riks solution procedure, as will be explained in Chapter 4.
31
Model RC00 attains its peak resistance at an interstory drift of approximately 2.7-percent
while Model RC03 attains its peak resistance at a drift of approximately 1.9-percent. The
interstory drift angles corresponding to strength degradation to the nominal strength of the
connection (Mp) were 2.6-percent radian for SH-RC03 and 3-percent radian for SH-RC00,
indicating that apparent strength degradation is more rapid in a reinforced connection. Note that
brittle fracture of the connections was not considered in these analyses. In fact, tests have shown
that specimens with the same geometry as RC00 (FEMA-350 WUF-B connection) and welds
using E70T-4 weld metal fracture at drifts between 1-percent and 1.5-percent. Similar specimens
made using notch-tough weld metal fracture at drifts between 2-percent and 3-percent
(Stojadinovic 2000). Thus, finite element analysis including fracture element is required for more
refined results.
Disregarding the fracture in the connection, the behavior of reinforced connections shows
higher strength degradation rate than that of unreinforced connection. There is a possible
explanation for this phenomenon. As shown in Figure 2-19, beam plastic rotation demand θp is
higher in reinforced connections. And the plastic hinge length Lr is smaller than in unreinforced
connections. To achieve the same plastic rotation θp the amplitude of buckling must increase,
while Lr must decrease. On the other hand, the amplitude of buckling is related to the torsional
stiffness of the boundary. The torsional stiffness of the boundary (column flange) of the
unreinforced connection is much higher than that (beam flange plus cover plate) of the reinforced
connection. Therefore, the strength degradation of the reinforced connection will be more rapid
than that of an unreinforced connection.
2.3.2 Local buckling
A steel member is composed of steel plate elements. When the slenderness of each
component plate is smaller than member slenderness, the member may buckle locally before it
buckles globally. Design codes such as AISC Seismic Provisions (AISC 2002) specify the
32
limiting slenderness ratios for each cross-section component. Local slenderness rations are
prescribed to prevent elastic local buckling. The section that satisfies such slenderness criteria is a
compact section. However, when the section is used as a component in seismic moment-resisting
frames, a plastic hinge may form in it. Thus, local instability of a section will eventually occur
due to reduction in stiffness caused by yielding even if the section satisfies the criteria for a
compact section.
Flange local buckling
Flange local buckling is the principal mechanism leading the process of instability in
steel moment-resisting connection for typical US shapes. The length of yielded plastic hinge
region will be defined by the moment distribution along the beam span. After the moment in the
beam at the beam-column connection reaches plastic moment Mp, the yielded region extends
along the beam away from the connection because of strain hardening of steel. If the yielded
region is long enough to develop a full wavelength of the flange buckle, inelastic local buckling
of the beam flange will initiate (Lay 1965b).
If the compressed flange is not connected to the web or the stiffness of the web is small,
the flange will buckle symmetrically, as shown in Figure 2-20a. However, the vertical movement
of the beam flange is restrained by the web, especially if the web is compact. Thus, the beam
flange will twist about an axis parallel to the longitudinal axis of the beam (Figure 2-20b). The
problem of asymmetric beam flange buckling can be solved as torsional buckling of a column
(Bruneau et al. 1998). When beam flange twisting is restrained by rotational stiffness of the web
at the section k-line, the governing equation is represented as following:
d 4β
d 2β
E st C w
+ (σI p − G st J ) 2 = kβ
dz 4
dz
( 2-20 )
where β is the twisting angle of the member, Cw (= 7b3f t3f /2304) is the warping constant of the
compression flange, Ip (= bf3 tf /12) is the polar moment of inertia of the flange, J (= bf t3f /3) is
33
the St. Venant torsional constant for the flange, Est is the strain-hardening modulus in
compression, Gst is the strain-hardening modulus in shear, and σ is the applied compressive stress.
Rotational stiffness of the web at the flange-web joint, k, can be determined from Equation 2-20.
The following equation was obtained after assuming that the tension flange does not rotate and
that lateral deflections of the flanges are identical (Lay 1965b):
 4G st
k=
 d − 2t f
 t w3
G st t w
 =
 12 3(d − 2t f )
( 2-21 )
where d is the depth of the beam, tw is the web thickness, and tf is the flange thickness. When
beam flange local buckling starts, lateral deflection of the compression flange is minor and the
tension flange does not move laterally. The flanges do not rotate, either, as shown in Figure 2-17b.
Thus, Lay’s assumptions about beam flange local buckling are valid at the onset of buckling. The
particular solution of Equation 2-20 can be computed by substituting β = C sin (nπz/l) into
Equation 2-20 as follows:
 nπ 
 nπ 
E st C w 
 =k
 + (G st J − σI p )
 l 
 l 
4
2
( 2-22 )
This can be rearranged to obtain the critical flange local buckling stress σcr:
 l 
 nπ 
σ cr I p = E st C w   + G st J + k  
 nπ 
 l 
2
2
( 2-23 )
The half-wave length l/n that may trigger flange buckling can be determined by
differentiating the critical stress with respect to l/n, that is by setting ∂σcr/∂(l/n) = 0 (Bruneau et al.
1998):
tf
E C
l
= π 4 st w = 0.713
n
k
tw
4
Aw
bf
Af
( 2-24 )
where n is a buckling mode number, Aw (= [d-2tf]tw) is a web area, and Af (= bftf) is a flange area.
Local flange buckling under a moment gradient will commence when the yielded length extends
enough to accommodate full buckling wave length 2l of the flange as follows:
34
 tf   A 
2l = 1.42b f   4  w 


 tw   Af 
( 2-25 )
Web local buckling
A beam web may buckle without flange local buckling if the slenderness ratio (h/tw) of
the web is high. The elastic buckling stress of a plate simply supported along two opposite sides
perpendicular to the direction of loading and having various edge conditions along the other two
sides under pure bending is given by following equation (Salmon and Johnson 1995):
Fcr = k
π 2D
h 2t
=k
π 2E
12(1 − µ 2 )(h / t ) 2
( 2-26 )
where k depends on the boundary conditions along the edges and the aspect ratio of the plate. The
minimum value of k in the case of a pined boundary along the edges is 23.9 and the minimum
value of k in the case of a fixed boundary is 39.6. The limiting width-thickness ratio (λr = h/tw ≤
5.70(E/Fy)1/2, ksi) for buckling of wide flange beam webs specified in AISC-LRFD manual was
determined using this equation (Salmon and Johnson 1995) such that Fcr < Fy. In the case of
compact-section beams bend-buckling will not occur because the limiting width-thickness ratio
(λp = h/tw ≤ 3.76(E/Fy)1/2, ksi) of the web for compact sections is smaller than that for non
compact sections. If the web buckles but the flange does not buckle, the bending strength
reduction of the section will not be significant. Basler and Thurlimann (1961) proposed an
effective section that disregards the buckled region of the web. Then section moment strength can
be determined by a conventional flexural strength formula using this effective section. Following
Basler’s effective section method, the maximum strength degradation will be proportional to
(Zsection – Zweb)/ Zsection. For a W30×99 beam section maximum degradation is 34 percent.
The out-of-plane deformation of the compact-section web is due to the rotation of the
joint between the web and the compressed flange triggered by flange local buckling. Rotation of
35
the beam web-flange joint depends on the amplitude of flange local buckling, while the amplitude
of web buckling is related to the out-of-plane stiffness of the web. Two local buckling modes
interact with each other (Kemp 1996). Thus, if one of the buckling modes is controlled, then local
buckling response of the beam will be improved (Kim et al. 2000b).
2.3.3 Lateral-torsional buckling
Lateral-torsional buckling may trigger local buckling of the beam when uniform moment
is applied. Whether the lateral-torsional buckling or local buckling prevails at the initiation of
inelastic instability depends on the yielded length associated with lateral-torsional buckling and
that associated with local buckling.
Lay and Galambos (1967) considered the compressed half of the beam as an isolated
fictitious column, as shown Figure 2-21. Lateral buckling, then, is equivalent to column buckling
subjected to compression stresses stemming from beam bending. The buckling equation for the
fictitious column may be expressed as follows:

 1

− cot[λb π (1 − τ )] 
 λb π + S 
tan(λb πτ / c )
1 
 λb π
 =
0 ( 2-27 )
+

tan( λb π (1 − τ ))
 1

c
 λb π + S 
− tan[ λb π (1 − τ )] 
 λb π
 

where c is the ratio of lateral bending stiffness in the yielded region to its elastic values, S is the
value of end-restraint, τ is the ratio of the yielded length to the beam length, and λb is the
nondimensional beam slenderness factor defined as:
λb =
Lb
ry π
σy
( 2-28 )
E
The relation between λb and τ can be found for a given value of S from Equation 2-27.
From this relation, the critical value of τ for lateral-torsional buckling can be determined. The
critical values of τ for lateral-torsional buckling and local buckling are termed as τLTB and τLB,
36
respectively. The minimum yielded length for local buckling (Equation 2-25) can be rewritten as
follows:
 t f  Aw
4
 tw  Af
τ LB L=
2=
l 1.42b f 
b
( 2-29 )
If the value of τLTB is larger than that of τLB (τLTB > τLB), lateral buckling will initiate
instability. When local buckling occurs in a beam under moment gradient, lateral stiffness of the
beam will be reduced as the amplitude of the local buckling increases. That is, the beam
slenderness factor, λb, becomes larger, because the radius of gyration about y axis, ry, of the
effective width (see Figure 2-22 and subsection 2.3.4) of the compressed beam flange is smaller
than that of the unbuckled compressed beam flange. Consequently, lateral-torsional buckling will
start when the yielded length of the beam, τLb reaches the value τLTBLb for the effective section.
2.3.4 Model of strength degradation
Many researchers have focused on the initiation of local and lateral-torsional buckling
rather than post-buckling behavior of beam-column connections. The post-buckling behavior
such as strength degradation and low cycle fatigue can greatly affect the rotation capacity and
ductility in a beam-column connection. A proposed strength degradation model due to local
bucking is presented in Figure 2-22. Consider the yield mechanism for a beam flange in the
buckled zone of a beam flange shown in Figure 2-22a. Under a moment gradient, flange local
buckling starts when the yielded length extends to the full wave length of buckling. Once the
flange buckles, plastic strains tend to concentrate at the location where the buckling amplitude
peaks (Point A). A plastic hinge will form at that point in the flange. Assuming a symmetric
buckled shape and flange axial forces, it founds that a shear force cannot develop in the flange
because of equilibrium at Point A. Therefore, additional plastic hinges begin to form at the
boundary of the yield region (Point B in this model). The maximum amplitude of flange local
37
buckling is labeled δFLB. Then, the axial force Pp,f corresponding to a buckling amplitude δFLB can
be computed as follows:
Pp , f =
2M p , f
( 2-30 )
δ FLB
where Mp,f is a plastic moment of the beam flange. Note that flange axial force decreases as the
amplitude of flange local buckling increases. Since FLB occurs when the beam flange yields, the
axial force in the flange cannot be larger than the axial yield strength Py,f of beam flange. If δFLB is
so small that the axial force computed from the above equation exceeds the axial yield strength of
the flange, it means that there in no strength degradation due to FLB. In such a case, the beam
flange force is equal to the axial yield strength of the flange. The threshold amplitude of flange
local buckling δFLB,th is that at which strength degradation of the beam flange force initiates. It can
be computed as follows:
Py , f = σ y t f
P, f =
2M p , f
δ FLB
=
2σ y Z f
δ FLB
=
σ yt 2
f
2δ FLB
≡ Py , f = σ y t f
( 2-31 )
δ FLB ,th = t f / 2
where σy is the yield strength of the beam flange and tf is the beam flange thickness. Following
above equation flange axial force drops as shown in Equation 2-30 when the amplitude of flange
local buckling, δFLB, exceeds 0.5tf. Since the threshold amplitude of FLB is proportional to beam
flange thickness, increasing the beam flange thickness can prevent early strength degradation due
to FLB.
The stress distribution in the beam plastic hinge, shown in Figure 2-22b assumes that the
axial stress on the cross section of the beam is uniform before any geometric instability occurs.
When the amplitude of buckling exceeds the threshold of flange local buckling, the stress
distribution will be changed by the P-δ effect described above. Figure 2-22c presents the buckled
shape of the beam and the axial stress distribution on the cross section. Several assumptions were
38
made: a rigid joint exists between the flange and the web; rotation hinge is at the neutral axis; and
fully plastic condition exists in the beam flanges and the web.
The threshold of WLB was found to be much higher than that for flange local buckling
using finite element analysis described in Subsection 2.3.1. It was also found that the distribution
of membrane forces transmitted through the web is relatively uniform along the web height. The
web, a stiffened element, can effectively transmit the membrane force though the buckled section
due to its restraint at the boundary. Thus WLB may not cause strength degradation as long as the
amplitude of WLB is not significant. However, the flange, an unstiffened element, has no such
restraint at its edges and will likely not transmit the membrane force along the buckled edge.
Thus, for the moderate range of buckling amplitudes, FLB will be the governing buckling mode
for strength degradation in the connection. For this study, a model considering FLB only is used
to identify the relation between strength degradation and buckling amplitude.
Figure 2-23 shows the relation between the amplitude of FLB and the moments computed
using the proposed model. A beam in Model UCB-RC03 described in Subsection 2.3.1 is selected
for the calculation. Data from the finite element analysis for Model UCB-RC03 is also presented
in this figure. To facilitate the comparison, moments at the column face are extrapolated from the
moments computed using the proposed model assuming the plastic hinge is located at the edge of
cover plates. The strength degradation computed from the proposed model agrees well with that
computed using a finite element model, especially in the moderate FLB amplitude range. For low
amplitudes of FLB, the moment based on the proposed model is higher than that computed by
finite element analysis because the beam flange may not be fully yielded at this level of buckling,
as is assumed in the model. At high amplitudes of FLB, the strength of the connection computed
from the proposed model is lower than that calculated using finite element analysis. As the
amplitude of buckling increases, web local buckling starts to affect the connection strength. Thus,
at higher buckling amplitudes, strength reduction due to WLB should be considered. For this
39
purpose, several models using 3-D plastic mechanisms in beam sections have been proposed
(Gioncu and Mazzolani 2002; Lee and Stojadinovic 2003).
2.4 Residual Rotation Capacity
Even after flange fractures, the connection between the beam and the column can sustain
gravity loads and lateral moments through the load-carrying capacity of the shear tab connection
(Gross 1998). From the view point of the global stability of a building structure, it is important to
provide sufficient rotation capacity to the shear tab connection. This section provides a general
discussion on residual rotation capacity of welded steel moment connections. The following
subsection describes shear tab damage during the Northridge earthquake and its classification.
Information on post-fracture behavior of simple connection tests and moment connection tests is
provided in Subsection 2.4.2. The remainder of this section describes the results of cyclic analysis
of a fractured beam section and proposes a model that could be used for design of each
component in shear tab connection.
2.4.1 Shear tab damage
A shear tab is designed to transmit the vertical reaction from the beam to the column. The
major consideration in the design of shear tabs is not the moment but the shear force. The welds
(or bolts) attaching the shear tab to the column are designed for the shear Ru and the eccentric
moment Rua where a is the distance from the face of the column to the centroid of the bolt group
(AISC 2001). As long as the shear tab is designed to have enough resistance for the largest
expected shear force, shear tab failure should not occur in beam-to-column connections. However,
extensive damage in shear tabs of moment connections was observed when the beam flange or its
weld experienced fracture during the 1994 Northridge earthquake.
40
Six types of damage to the shear tab, defined in FEMA-352 document (FEMA 2000c) are
presented in Figure 2-24 and Table 2-5. The damage indices in this table indicate the degree of
impact by such damage on the global frame behavior and the local gravity load carrying capacity
of each connection. As the index increases, the impact of the connection damage type is more
severe. For example, the connection capacity is not significantly reduced by cracking of the
supplemental weld, while the connection cannot carry gravity loads after a full-length fracture of
the shear tab weld to the column. Complete separation of the shear tab connection may cause
partial collapse of the floor it supports and a significant reduction in the structural integrity of the
building.
Table 2-5: Shear tab damage indices, reproduced from FEMA-352 (FEMA 2000c)
Type
Description
Index dj
S1
Partial crack at weld to column
2
S2
Crack in supplemental weld
1
S3
Fracture through tab at bolt holes
4
S4
Yielding or buckling of tab
3
S5
Damaged bolts
2
S6
Full length fracture of weld to column
4
2.4.2 Post-fracture behavior of moment connections
Simple connection tests
Liu (2000) and Astaneh performed a total of sixteen full-scale tests on simple
connections including pre-1980’s shear tab details, stiffened seat, supplement seat angles, and
top-and-bottom angle connection with a concrete floor slab. They used the measured cyclic
responses to develop moment-rotation models of typical shear tab and supplemental seat angle
connections. Most of beam sizes in those tests were relatively small (between W18 and W24)
41
comparing the beam size used in the conventional US moment connections (between W30 and
W36). Specimen 7B fabricated using a W33×118 beam was the only connection that used a beam
size comparable to those in typical moment connection. Eight φ-22 mm (0.875 in.) bolts and a 9.5
mm (0.375 in.) thick shear tab were used to connect the beam and the column. The gap between
the beam flange end and the column flange was 25 mm (1 in.).
Figure 2-25 shows the load versus drift response of Specimen 7B. Due to the presence of
the concrete slab, yielding and deformation of the shear tab at the lower bolts were observed first
at drifts between the 0.75-percent and 3-percent. After the concrete around the column was
crushed at a drift angle of 4-percent radian, deformation and yielding of the shear tab near the top
bolts was observed at the drift angle of 5-percent radian. Minor fracture at the bottom of the tab
was also found at this drift angle. As the bottom beam flange began to bind on the column flange
at the drift angle of 6-percent radian, the top bolt fractured. During the next cycle of 6-percent
radian, the next two top bolts fractured and the bottom bolt fell off. Bolt failures occurred
continuously through the cycles to 7- and 8-percent radian, until only three center bolts remained
(Liu 2000).
It is evident that binding of the beam flange on the column flange is an adverse factor that
reduces the ductility of the shear tab while increasing the strength and stiffness of the connection.
Such binding leads the failure of the shear tab connection by cascading bolt failures, and may
cause a loss of gravity shear capacity.
Moment connection tests
The ultimate state at failure of steel moment connections has not been studied in detail
because many connection tests were stopped after losing the moment capacity of the connection
due to fracture of the beam flanges. One of the reasons for not conducting the test to complete
failure was to protect the test set-up from damage caused by complete separation of the test
specimens.
42
Information on the post-fracture behavior in selected connection tests is summarized in
Table 2-6. As shown in this table, the connections had some degree of residual strength even
though both flanges fractured. The source of this resistance is the moment arm between the
compression flange and the group of bolts in the shear tab. Common failure modes were shear tab
tearing at the edge of the tab and bolt shear failure. Shear tab thickness may affect the governing
failure mode in the shear tab connection. For example, Uang and Bondad (1996) used thin shear
tabs (t = 9.5 mm) for their test specimens, while Stojadinovic et al. (2000) used thick shear tabs (t
= 23.9 mm). Uang’s test specimens suffered damage in the shear tab right after flange fracture.
However, bolts failed in the tests by Stojadinovic et al.
Figure 2-26 shows the moment-rotation response of Specimen 7.2 tested by Stojadinovic
et al. (2000). The connection of this test specimen employed post-Northridge details. All field
welds in the connection were made using E71T-8 weld metal that was a sufficiently high notchtoughness rating. A relatively thick plate was used for the shear tab while supplement welds were
not used. The bottom flange of the beam fractured during the displacement cycle to 3-percent
radian while the top flange survived till the displacement cycle to 5-percent radian. Bolts at the
bottom of the shear tab failed during the next displacement cycle (4-percent radian) after the
cycle in which the bottom flange fractured (3-percent radian). Beam flange binding was observed
during the negative cycles to 4- and 5-percent radian. The drift at binding increased as the number
of cycle increased, indicating the gap was enlarged by the permanent deformation of the beam
flange, the shear tab and bolt fracture.
43
Uang and
Bondad
(1996)
Shuey,
Engelhardt,
and Sabol
(1996)
Stojadinovic,
Goel, Lee,
Margarian,
and Choi
(2000)
1.
2.
3.
4.
5.
Residual
strength5, %
0.03
N.A.
50
RN1
0.02
Tearing at bottom edge
of the tab and weld
31
PN12
0.022
N.A
23
0.015
N.A
30
Supplement
welds, mm
57
Number of
bolts3
N.A.
Shear tab,
mm
0.02
Beam1
Shear tab
failure
Popov,
Blondet,
Stepanov,
and
Stojadinovic
(1996)
Beam flange
fracture, θb
Whittaker,
Bertero, and
Gilani
(1996)
Specimen ID
Researcher
Table 2-6: Summary of unreinforced connection tests
PN2
PN3
PN22
W30×99
W36×150
12.7
15.9
8
7.9
10
7.9
PN3
0.022
UCSD1
0.02
UCSD2
W30×99
9.5
8
7.9
0.03
UCSD3
0.03
UTA-1
0.0075
W36×150
15.9
10
7.9
UTA-2
0.015
UTA-3
0.015
7.1
W36×150
7.2
tw+8
=
23.9
10
Tearing of the shear
tab and fracture of
three bolts
Tearing at bottom edge
of the tab and weld
Tearing at tab edges
(θb = 0.02)
Tearing of tab edges
(θb = 0.02)
Tearing of tab edges
(θb = 0.0075)
Net section fracture
and vertical fillet weld
fracture (θb = 0.015)
Tearing at bottom edge
of the tab and weld (θb
= 0.015)
Three bolts failure (θb
= 0.002)
Fracture of the bottom
edge of the shear tab
65
N.A
N.A
N.A
48
37
N.A
0.028
Bolt failure
29
0.028
Bolt failure
25
0
Steel grade: ASTM A36 except note 2.
Steel grade: ASTM A572 Grade 50
ASTM A325, φ 22 mm bolts.
θb = δact/Lbeam, where δact is the displacement at the actuator and Lbeam is the beam length between the
centerline of the actuator and the face of the column.
The ratio between the residual strength and peak resistance of the displacement cycle on the
fracture.
44
2.4.3 Model for residual strength
Post-fracture analysis for moment connections
A finite element model is prepared to study the post-fracture behavior of welded steel
moment connections. As show in Figure 2-27, a column is not explicitly modeled but it is
considered as a rigid boundary. A572 Grade 50 steel is used for the W33x118 beam, and A36
steel is used for the 15.9 mm thick shear tab. The beam length is 2,060 mm (81 in.). The beam
size and length are selected as the same as the beam in the test specimen being reported in
Chapter 5. Fracture of beam flanges at the weld joint is modeled by manipulating the boundary
condition at the beam-column interface as shown in Table 2-7. Upward monotonic loading is
applied, so that top flange is in compression and bottom flange is in tension.
Table 2-7: Boundary conditions for post-fracture behavior modeling
No-fracture (NF)
Bottom flange
fracture (BF)
Top and bottom
flange fracture
(TBF)
Shear tab only (ST)
Top flange
Shear tab
Bottom flange
U1 = U2 = U3 =0
θ1 = θ2 = θ3 = 0
U1 = U2 = U3 =0
θ1 = θ2 = θ3 = 0
U1 = U2 = U3 =0
θ1 = θ2 = θ3 = 0
U1 = U2 = U3 =0
θ1 = θ2 = θ3 = 0
U1 = U2 = U3 =0
θ1 = θ2 = θ3 = 0
U1 = U2 = 0
U1 = U2 = U3 =0
θ1 = θ2 = θ3 = 0
NA
NA
U1 = U2 = U3 =0
θ1 = θ2 = θ3 = 0
NA
NA
Figure 2-28 presents relations of moment and rotation at the boundary for each analyzed
case. Moments are normalized using maximum moment in the no-fracture case. Rotations are
computed by dividing the beam tip displacement by the beam length. After a beam flange
fractures, connection strength is reduced to about 60 percent of maximum moment capacity. BF
and TBF cases show similar behavior up to a beam rotation of 1.5-percent radians. Beyond 1.5percent radians, the difference between the moment in the BF and TBF cases increases. The
strength of a fractured connection is two times larger than that of the shear tab itself.
45
Cyclic responses of the fractured connection are analyzed using a 1-percent radian
rotation cycle sequence. The applied displacement cycle and the changes in the size of the gap
between the bottom beam flange and the boundary are plotted in Figure 2-29. Even though the
amplitude of the displacement cycle is constant, the gap between the bottom flange and the
column face increases as the number of cycle increases. Because fracture and binding are
modeled using boundary conditions, negative gap size values appear as shown in this figure.
Under the downward loading, the movement of the end of the beam flange is limited to model the
contact between the beam flange and the column face. As loading direction changes, such
restraint to the movement is released. Thus the shortened bottom beam flange due to compression
recovers its elastic deformation, showing a negative gap size. However, the global response of the
model as shown in Figure 2-30 is not significantly affected. It shows a sharp load drop in the
response of the connection instead of a gradual load drop observed in the tests. The increases in
the stiffness after the beam flange contacts the column face are also shown.
Estimate of residual connection strength
Figure 2-31a shows the equivalent plastic strain (PEEQ) and principal stress distribution
at the interface between the beam and the boundary. High plastic strains exist at the bottom edge
of the shear tab. This may lead to shear tab tearing. The direction of the principal stress indicates
that flexural stress governs in the compression flange and the bottom part of the shear tab while
shear stress governs in the upper part of the shear tab. Distribution of principal stress in the
bottom part of the shear tab is uniform due to yielding. This observation leads to a simplified
stress distribution shown in Figure 2-31b. It is assumed that the upper part of the shear tab is
taking only the shear force, while the bottom part of the shear tab and the compression flange
carry the axial force from the moment couple. The procedure for composite simple connection
suggested by Liu (2000) can be applied to compute residual moment capacity of the moment
connections as follows:
46
1. Determine how many bolts are required to carry the given shear force and assign these
bolts as shear element beginning with the top bolt.
2. Assuming that the remaining bolts carry the tensile stress from the bending moment,
determine the ultimate axial stress distribution along the shear tab such that bolts and a
tab plate do not fail, following the design specification in AISC-LRFD (AISC 2001).
3. From the above tensile stress distribution, compute the tension force Ptens applied to the
shear tab.
4. Compute the ultimate compressive strength of the beam flange. If the flange
slenderness ratio is larger than the critical value at initiation of flange local buckling,
use Pcomp = Fy ·Af, where Fy is nominal yield strength of the beam flange and Af is the
flange area.
5. The smaller of Ptens or Pcomp governs. If Pcomp governs, find a new distribution of tensile
axial stress distribution along the shear tab to equilibrate Pcomp and Ptens.
6. Compute the moment capacity.
Shear tab and bolts should be designed to resist the force distribution discussed above if
residual strength and rotation capacity are required from a connection. However, plastic strain
accumulation due cyclic loading will cause shear tab tearing even if the components are designed
to have sufficient strength capacity. The use of slotted holes for shear tab bolts is recommend in
the case when ductile behavior of the shear tab connection is required (FEMA 2000a).
47
Local buckling
Rupture
High ductility
Moment at the column face
Mu
Mm
Mp
Mf
My
Fracture
Limited ductility
Yielding
Ductile fracture propagation
Reduced ductility
Shear tab failure
Residual strength
Mrf
Mr
θy θSDf
θm
θSDb
θUf
θUb
Story drift angle
Figure 2-1: Moment-drift responses in welded steel moment connections
48
Column
CJP welds
Beam
P, δ
Beam bottom flange joint
(a) Steel moment-resisting connection
Rigid boundary
Beam web (neglected)
σapp, tensile stress
bf
Plane strain element model
(b) Beam bottom flange
σapp, tensile stress
tf
Representative volume element
(c) Plain strain model of beam flange
σ2
σ1 = σapp
σ3
ε1
(d) Representative volume element (RVE)
Figure 2-2: Various scales used to asses the potential for brittle fracture
49
1
1.5
Normalized stress, σ / σ 1
0.8
Normalized strain, ε1 / (σ 1 /E)
Contraction stress, σ LAT
Tensile pressure, σ m
Normal strain, ε1
0.6
0.4
0.2
0
0
0.1
0.2
0.3
Poisson`s ratio, ν
1
0.4
0.5
(a) Contraction stress, pressure, and normal strain versus the Poisson’s ratio
τ
τy
ν=0
ν = 0.3
1
B
A
σ1
σLAT
1
1.75
σ
σy
-1
(b) Mohr’s circle of extreme stresses on RVE
Figure 2-3: Effect of the deformation restraint in beam-column connections
50
Reentrant corner
tf
(a) Normal stress (σ11) distribution
tf
(b) Contraction stress (σ22) distribution
tf
(c) Hydrostatic stress (σm) distribution
Figure 2-4: End effects in the beam flange connection region
51
2
Nomalized maximum axial stress (σ 11 /σ app )
r
1.8
σapp
tf
1.6
1.4
1.2
1
0
0.2
0.4
0.6
Normalized radius of fillet (r/tf)
0.8
1
Figure 2-5: Effect of fillet size on local stress disturbance
Nomalized maximum axial stress (σ 11 /σ app )
2.4
Elastic mode l
Plastic mode l
2.2
2
1.8
1.6
1.4
1.2
1
4
20
100
80
60
40
Number of elements along the flange thickness
Figure 2-6: End effect mesh convergence study
52
120 128
135°
A
β
B
CJP weld
Weld
defect
Figure 2-7: Fracture paths in the beam flange joint
σyy
σapp
a1
Microcrack
ρ
r
O
2a2
Macroscopic crack
σlocal
Figure 2-8: Initiation of cleavage in front of a macroscopic crack (Anderson 1995)
53
-1
UCB-RC00
-0.9
UCB-RC03
-0.8
Pressure Index
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0
1
2
3
4
5
6
Distance from beam flange centerline (in.)
Figure 2-9: Pressure Index in the flanges in Models UCB-RC00 and UCB-RC03 at 0.5-percent
story drift (Kim et al. 2000a)
0.1
UCB-RC00
0.09
UCB-RC03
0.08
Rupture Index
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
1
2
3
4
5
6
Distance from beam flange centerline (in.)
Figure 2-10: Rupture Index in the flanges in Models UCB-RC00 and UCB-RC03 at 2.0-percent
story drift (Kim et al. 2000a)
54
Web
σmax,f
Flange
a
2b
Figure 2-11: Microcrack forming region in beam cross section
Figure 2-12: Stress demands in SAC PN2 specimen and comparison to stress at fracture for other
tests (Schafer et al. 2000)
55
2+
1.5
1+
Moment at column face, M col/Mp
1
0.5
0
-0.5
-1
-1.5
-6
1-4
22
0
-2
Story drift angle, % radian
4
6
Figure 2-13: Moment versus drift angle for Specimen UCB-RC03 (Kim et al. 2000a)
Amplitude of
FLB
Buckled length
Axial strain
gages
Figure 2-14: Local buckling of Specimen UCB-RC03 after the cycle to 3-percent story drift (Kim
et al. 2000a)
56
Top surface of beam top flange
1-, 2-
ε / εy
-10
0
-5
1st cycle
Cover plates
2nd cycle
Bottom surface of beam bottom flange
1+, 2+
Figure 2-15: Peak compressive strains on beam flanges at 3-percent story drift, UCB-RC03 (Kim
et al. 2000a)
1.4
B
Moment at column face, M col/Mp
1.2
A
1
C
0.8
D
E
0.6
0.4
Mm δ Mm − ME
−
M p δE
Mp
0.2
0
0
1
2
3
4
Story drift angle, % radian
FLB
WLB
LTB
5
6
Figure 2-16: Moment-drift relations and buckling amplitudes for Model UCB-RC03 (Kim et al.
2000a)
57
A: 1 % rad.
B: 2 % rad.
C: 3 % rad.
D: 4 % rad.
E: 5 % rad.
Figure 2-17: Buckle shape of beam cross section at each story drift angle, UCB-RC03 (Kim et al.
2000a)
1.4
SH-RC03
Moment at column face, M col/Mp
1.2
1
SOL-RC03
SH-RC00
0.8
0.6
0.4
0.2
0
0
1
2
3
4
Story drift angle, % radian
5
6
Figure 2-18: Moment versus drift angle for Models SH-RC00, SH-RC03, and SOL-RC03 (Kim et
al. 2000a)
58
Lb
Lb
P
P
Lr
Mp
Mp
My
My
M
M
Lpr
Lp
Δp
Δp
θp
θpr
(a) Unreinforced connection
(b) Plate reinforced connection
Figure 2-19: Plastic hinge location, length, and beam plastic rotation
Slotted hole
or
slender web
Compact
section
C
C
T
T
(a) Symmetric flange buckling
(b) Asymmetric flange buckling
Figure 2-20: Local buckling patterns of beam flanges
59
δwlb
Lbeam
δflb
Local buckling
τLb1
Lb1
Lb2
Mmax
My
δltb
δltb
Lateral buckling
(a) Lateral buckling model by Lay and Galambos (1967) (b) Buckling modes and amplitudes
Figure 2-21: Lateral-torsional buckling model for the beam
A
Pp,f
Mp,f
Mp,f
B
2l
A
δFLB
Mp,f
Pp,f
Pp,f
B
Mp,f
h1
NA
h
σy,c
D
h
E
NA
σy,t
σy,t
σy,t
(b) Before buckling
σy,c
h2
h3
B
bE
(a) Plastic mechanism in the flange buckle zone
σy,c
σy,c
C
σy,c
σy,c
Mp
Mp,f
Pp,f
σy,t
σy,t
(c) After buckling
σy,t
(d) Effective section
Figure 2-22: Strength degradation model due to local buckling
60
Normalized moment at column face, M/Mp
1.4
Strength degradation model
Finite element analysis
1.2
1
0.8
0.6
0.4
0.2
0
0
0.5
4
3.5
3
2.5
2
1.5
1
Normalized amplitudes of flange local buckling, δFLB/tf
4.5
5
Figure 2-23: Amplitude of FLB versus connection strength
S6
S3
S1
S5
S2
S4
Fracture of CJP weld or beam flange
Figure 2-24: Types of shear tab damages after FEMA 352 (2000c)
61
Figure 2-25: Load versus drift of a simple connection, Specimen 7B (Liu 2000)
Binding of the bottom
beam flange on the
column flange
Bolts failure
Bottom flange
fracture
Figure 2-26: Moment-rotation response of an unreinforced connection, Specimen 7.2
(Stojadinovic et al. 2000)
62
B.C for top flange
Ptip
B.C for shear tab
Lbeam
B.C for bottom flange
Figure 2-27: Finite element model for post-fracture analysis
Normalized moment with
max Mnf
1
No fracture (NF)
0.8
Bottom flange fracture (BF)
0.6
Top and bottom flanges fracture (TBF)
0.4
Shear tab only (ST)
0.2
0
0
0.5
1
1.5
2
Beam rotation, % rad.
2.5
Figure 2-28: Moment-rotation response of post-fracture connections
63
3
1
Tip displacement
0.8
0.4
0.2
0
Gap size
-0.2
-0.4
-0.6
-0.8
-1
0
2
4
6
Step time
8
10
12
Figure 2-29: Displacement cycles of θb = 0.01 rad. and the gap size
1
0.8
0.6
Normalized moment
Normalized amplitude
0.6
0.4
0.2
Release contact
0
-0.2
-0.4
-0.6
Binding of the bottom
beam flange on the
boundary
-0.8
-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Beam rotation, % rad.
0.6
0.8
Figure 2-30: Cyclic response of the post-fracture connection
64
1
Pcomp
Vshear
darm
Ptens
(a) PEEQ and σmax
(b) Force distribution
Figure 2-31: Load transfer at θb = 0.005 rad. and force distribution for shear tab design
65
Chapter 3. Preliminary Investigation and
Experimental Program
3.1 Introduction
The California Department of Transportation (Caltrans) is reviewing the seismic
vulnerability of its building inventory. Building CT-15, one of the first buildings to be evaluated,
is located in Northern California. A realistic evaluation of this building's earthquake resistance is
key to the implementation of a retrofit strategy that minimizes personnel and facility relocation
and construction costs.
A number of the connections in the (existing) CT-15 building make use of deep W-shape
columns or box columns and pre-Northridge Welded Unreinforced Flange-Bolted Web (WUF-B)
connections: connections of a type for which there is no test data upon which to base a
performance evaluation or develop retrofit solutions. As such, a reliable seismic evaluation of the
building was not possible in the absence of test-derived performance data for its critical
components.
A preliminary investigation was performed through the collection of data from the
construction documents and an on-site inspection of sample connections. Based on this
investigation, prototype connections were selected and three test specimens were designed and
fabricated. A test fixture was designed and fabricated to accommodate the test specimens and to
replicate filed conditions to the degree possible.
66
3.2 Preliminary Investigation
3.2.1 Building description
The lateral-load resisting system in Building CT-15 comprises special steel momentresisting frames on lines 1, 6, 7, 12, A and H of the structural grid. Figure 3-1 provides
information for a typical floor of the building and identifies the grids and the moment-resisting
frames. Corner columns are shared among perimeter frames 1, 12, A and H. The shared columns
are steel box columns designed to withstand bi-directional earthquake action, while the columns
in the North-South frames are so-called deep (W-shape) columns.
The frame elevation at line A is shown in Figure 3-2. The building is fifteen stories tall
with ten stories of offices (Tower 6 – 15) above four stories of parking (Garage 2 – 5) and a lobby
(Ground) above a single basement level. A single story penthouse for mechanical equipment is
located above the roof of the building. The building was most likely designed following the
seismic provisions of the 1988 Uniform Building Code (ICBO 1988) and constructed in the early
1990s, well before the 1994 Northridge earthquake. The typical beam-column connection in the
moment-resisting frames is a Welded Unreinforced Flange-Bolted Web (WUF-B) moment
connection that was widely used in California in the 1980s and early 1990s.
3.2.2 Selection of sample connections
Three beam-column connections were selected for detailed physical and numerical
investigation to aid decision regarding the retrofit of Building CT-15. None of the three
connections was similar to those pre-Northridge connections tested as part of the SAC Phase I
(FEMA 1995, 1997) and Phase II (FEMA 2000a) projects. The three prototype connections were:
1. A moment connection between a box column, BC 18x18x257, and a W33x118 beam:
part of a corner column-connection at Levels 7 through 10.
67
2. A moment connection between a box column, BC 31.5x13x464, and a WTM36x12x232
beam: part of center column-connection at Level 2.
3. A moment-connection between a W36x210 beam and a (deep) WTM 27x14x281column:
part of perimeter column-connection at Levels 7 through 8.
More information on the three prototype connections is presented in Table 3-1 below.
Figure 3-1 and Figure 3-2 show the locations of each of the prototype connections in the building.
Table 3-1: Information on prototype connections
Prototype EC01
Prototype EC02
Prototype EC03
Location in building
All four corners of the
structure
Two center spans
along the perimeter of
the core, in the NorthSouth direction
Twelve joints in the
North-South and EastWest directions
Floor level
7 through 10
2
7 through 8
Earthquake loading
direction
North-South
East-West
North-South
North-South
East-West
Span length
4.572 m (15 ft.)
9.144 m (30 ft.)
9.144 m (30 ft.)
Floor-to-floor height
4.166 m above and
below
3.454 m above and
5.480 m below
4.166 m above and
below
These prototype connections are representative samples of the non-traditional momentresisting connections in the building. Realizing that many more specimens were needed to
represent all size combinations of beam-column connections in the building, the author and
Professor Whittaker and Stojadinovic chose large beam and column sizes for the sample test
specimens, recognizing that the smaller sizes of beams and columns would likely deliver greater
rotation capacities than the larger sizes. Such approach is consistent with the connection prequalification strategy presented in FEMA 350 and with the trend observed by Roeder (2002a,
2002b) that pre-Northridge steel moment connections featuring smaller beams have a larger
rotation capacity.
68
3.2.3 On-site investigation of connection details
Two typical connections in Building CT-15 were inspected: a connection similar to EC03
between a deep W-shape column and a W-shape beam at the 5th floor in Frame 6; and a
connection similar to EC02 between a deep box column and a deep W-shape beam at the first
basement level in Frame 7 (see Figure 3-1 and Figure 3-2). These connections were inspected so
that the research team could replicate, to the degree possible, the in-service beam-column
connection details. Inspection of these connections revealed the following:
1. The CJP welding practice used in this building was consistent with that adopted in the
late 1980s and early 1990s, namely, that flange CJP weld, backing bars, and runoff tabs
were left in place (see Figure 3-3).
2. The weld access hole is smaller than that specified in FEMA-350, but larger than typical
pre-Northridge access holes: the edges of the access hole were machined smooth rather
than flame-cut; and the access hole radius cut was located so that transition from the
flange to the web occurs at an angle of approximately 45 degrees (see Figure 3-3).
3. The PJP welds (Miller 1995) connecting the plates that form the box column are
consistent with the details specified in the design drawings (see Figure 3-4).
Findings 1 and 2 were expected on the basis of the review of the construction documents.
Furthermore, the smooth shape and the size of the access hole are favorable in terms of achieving
modest plastic rotation in the connection.
3.2.4 In-situ material properties
The pre-test parametric analysis using ABAQUS (HKS 2002) showed that small changes
in material properties did not substantially influence the rotation capacities of the test specimens.
Based on this finding, the research team searched for test-specimen materials (section, plate, and
weld metal) with similar, but not necessarily identical mill test data and other material
69
characteristics as the material used in the building. The material search was based on the grades
of steel identified in the contract documents for the components of the three prototype
connections listed above: see Table 3-2 for details. Identification of target material properties was
based on review of mill test reports (MTRs) for the components of the three specimens and the
relationships identified by the SAC Joint Venture between MTR data and coupon test data for
steels of different types and vintages.
Table 3-3 lists the target values of yield and tensile strength for the components of the
three test specimens.
Table 3-2: Grades of steel in connection components
Prototype EC01
Prototype EC02
Prototype EC03
Beam
ASTM A572, Gr. 50
ASTM A572, Gr. 50
ASTM A572, Gr. 50
Column
ASTM A572, Gr. 50
ASTM A572, Gr. 50
ASTM A572, Gr. 50
Table 3-3: Target values of yield and tensile strength for test specimens
Specimen EC01
Specimen EC02
Specimen EC03
σ y (MPa)
σ u (MPa)
σ y (MPa)
σ u (MPa)
σ y (MPa)
σ u (MPa)
Beam flange
374
516
377
535
373
515
Beam web
374
516
377
535
373
515
Column flange
NA1
NA
NA
NA
394
553
Column web
NA
NA
NA
NA
394
553
1. NA = Not applicable.
The type of weld metal used in the beam-column connections could not be identified
conclusively. Anecdotal evidence from the Gayle Manufacturing Company suggests that E70T-4
weld metal was used for these connections: the common practice at the time this building was
constructed. This weld metal has poor notch toughness, with no minimum CVN value. As such,
E70T-4 was used to join the key components in the test specimens.
70
3.3 Test Specimen Details and Fabrication
3.3.1 Specimen details
The test specimens were designed using information from the Building CT-15
construction drawings, specifications, mill certificate data, and a site investigation. The column
height of each specimen was selected to match the typical story height in the building (4.166 m).
The lengths of the beams were set equal to half of the span of the corresponding beam in the
building, subject to a maximum span of 8.23 m (27 feet). This limitation (producing a maximum
beam length from the centerline of the column to the centerline of the actuator of 4.114 m) was
set because the maximum stroke of the actuator was 508 mm: accepting a longer beam span
would have limited the drift angle that could be imposed on the test specimens. Summary
information on each specimen is presented in Table 3-4. Figure 3-5, Figure 3-6, and Figure 3-7
present the connection details for Specimens EC01, EC02, and EC03, respectively.
Table 3-4: Dimensions of test specimens
Specimen EC01
Beam length (mm)
1
Specimen EC02
Specimen EC03
2,286
4,114
4,114
W33×118
W36×232
W36×210
Shear tab thickness (mm)
16
16
16
Fillet weld on shear tab (mm)
11
0
0
4,166
4,166
4,166
BC18×18×257
W27×281
25
BC31.5×13×464
70 (flange)
32 (web)
25
NA
NA
10
9
9
9
Beam size
Column height (mm)
Column size
Box column plate thickness
(mm)
Continuity plate thickness (mm)
Doubler plate thickness (mm)
Number of bolts in web tab
connection3
1.
2.
3.
29
Distance from column centerline to actuator centerline.
NA = Not applicable.
A490SC bolts, diameter = 29 mm.
71
NA2
17
3.3.2 Specimen supply and fabrication
Gayle Manufacturing Company fabricated the three test specimens to designs prepared
by the research team. To simulate the field condition, CJP welds connecting the beam flanges and
the column flanges were made in the downhand (or vertical; Ricker 1988) position as shown in
Figure 3-8. The construction details for the beam-column connections were essentially identical
to those adopted for the original construction except for the method used to weld the continuity
plates inside the box columns. This alteration was necessary because the welding equipment used
by Gayle Manufacturing Company for such connections differs from that used by the original
fabricator of the box columns. In the original connections, the continuity plate inside the box (see
Figure 3-9) was welded using access openings and a long electrode (electro slag welding; Miller
1995). For test specimens EC01 and EC02, the continuity plates were welded to the inside of the
box column on three sides and to the outside of the box column on one side (see Figure 3-10). All
welds were CJP welds. The exterior weld was placed on the face of the column remote from the
beam (see Figure 3-11). ABAQUS analysis showed the effect of this change to be negligible in
terms of strains in the connection.
3.3.3 Mechanical properties of materials
The continuity plates, doubler plates, W-shape beams, and W-shape columns were
fabricated from ASTM A572 Grade 50 steel; shear tabs were fabricated from ASTM A36 steel.
These materials matched those used in the subject building reasonably well. Lincoln E70T-4 filler
metal was specified for all CJP beam-to-column welds in the test connections.
Mill test report (MTR) data for the components of the specimens are summarized in
Table 3-5. Coupons were extracted from the four W-shapes (W33×118, W36×232, W30×210,
and W27×281) from remnants of the sections following fabrication. Two tensile samples were
taken from the flange sections and two tensile samples were taken from the web sections of each
72
wide flange beam. Steel coupon tests were conducted in accordance with ASTM A370. Average
values of yield and tensile strength from the coupon tests are summarized in Table 3-6.
Table 3-5: Mill test report data for W-shape sections of the specimens
Yield strength
Member
W33×118
W36×232
W36×210
W27×281
Tensile strength
Location
MPa
ksi
MPa
ksi
Flange
418
60.7
525
76.3
Web
418
60.7
525
76.3
Flange
392
57.0
520
75.5
Web
392
57.0
520
75.5
Flange
389
56.6
529
76.8
Web
389
56.6
529
76.8
Flange
375
54.5
503
73.0
Web
375
54.5
503
73.0
Beam
Beam
Beam
Column
Table 3-6: Coupon test data for W-shape sections of the specimens
Yield strength
Member
W33×118
W36×232
W36×210
W27×281
Tensile strength
Location
MPa
ksi
MPa
ksi
Flange
426
61.8
527
76.4
Web
479
69.5
549
79.6
Flange
374
54.2
521
75.6
Web
422
61.2
522
75.7
Flange
383
55.6
519
75.3
Web
402
58.3
522
75.7
Flange
356
51.6
506
73.4
Web
392
56.9
505
73.3
Beam
Beam
Beam
Column
73
3.4 Experiment Set-up
3.4.1 Test fixture
Figure 3-12 shows a plan view of the test fixture for Specimen EC01. This fixture was
designed to accommodate all three specimens in horizontal plane, 577 mm above the strong floor.
The columns were anchored at each end with machined pinned connections developed for a
previous connection-testing project (Whittaker et al. 2002). These pins were installed in large-size
clevises attached to steel reaction blocks that were welded to 31 mm thick steel plates placed on
the strong floor. Minor modifications and strengthening of the reaction blocks was undertaken for
the purpose of this project. The reaction plates were stressed to the strong floor. Figure 3-13
shows the column-end anchorage.
The free end of the beam was attached to two 2224-kN, 508-mm stroke actuators
installed in the custom-made reaction boxes. These reaction boxes were also stressed to the strong
floor. Figure 3-14 shows the anchorage detail for the actuator.
The test fixture included two lateral-restraint frames that served to replicate the restraint
conditions in the field. Arrows in Figure 3-15 identify the two frames installed for Specimen
EC02. The lateral-restraint frames were designed to resist over 10 percent of the maximum
expected axial strength of the beam flange among the test specimens. HSS 5×5×1/4” tube was
used for the lateral-restraint frame near the actuator and HSS 6×6×5/8” tube was used for the
lateral-restraint frame in the middle of the beam.
Figure 3-12 and Figure 3-16, Figure 3-17 and Figure 3-18, and Figure 3-19 and Figure
3-20 present a plan view of the test fixture and a photograph of the test specimen, for EC01,
EC02, and EC03, respectively.
74
3.4.2 Instrumentation and data acquisition
The instrumentation for the three specimens consisted of: two load cells in-line with the
actuator measuring axial force; an NVTC (Novotechnic linear potentiometer) at the beam end
measuring the imposed displacement; uniaxial and rosette strain gages to measure local strains;
displacement transducers placed on the panel zone and column measuring deformations;
displacement transducers placed on the bottom of column measuring the twist of the column;
displacement transducers on the beam flange measuring the amplitude of flange local buckling;
uniaxial and rosette strain gages measuring the brace force; displacement transducers placed on
the strong floor measuring the reaction frame slip; and displacement transducers placed on the
clevis measuring the gap and slip between the clevis plate and column end plate.
The instrumentation scheme for Specimen EC01 consisted of 71 channels. A total of 79 channels
were used for Specimens EC02 and EC03. Table 3-7 presents the channel number, instrument
type, and response quantity for each of the transducers. Figure 3-21, Figure 3-22, and Figure 3-23
present information on the instrumentation of EC01, EC02, and EC03, respectively. Figure 3-24
is a photograph of the instrumentation on the clevis measuring the slip between the clevis plate
and the column end plate.
The test control and the data acquisition system were run by a PC Windows-based control
and acquisition program called Automated Testing System (ATS) developed by SHRP
Equipment Corporation of Walnut Creek, California. The ATS system was used to monitor and
control the displacement and force feedback signals. Pacific Inc. signal conditioners were used to
amplify the transducer signals and to filter out the frequencies above 100 Hz from the analog
signal.
75
Table 3-7: Instrumentation of test specimens
No
Transducer
1
dcdt1
2
Response
No
Transducer
Panel zone deformation
39
sg13
Beam flange strain
dcdt2
Panel zone deformation
40
sg14
Beam flange strain
3
dcdt3
Column deformation
41
sg15
Beam flange strain
4
dcdt4
Column deformation
42
sg16
Beam flange strain
5
nvtc1
Column twist
43
sg17
Beam flange strain
6
nvtc2
Column twist
44
sg18
Beam flange strain
7
nvtc3
Column twist
45
sg19
Beam flange strain
8
nvtc4
Column twist
46
sg20
Beam flange strain
9
wp1
Beam flange buckling
47
br1
Brace shear
10
wp2
Beam flange buckling
48
br2
Brace shear
11
wp3
Beam flange buckling
49
br3
Brace shear
12
wp4
Beam flange buckling
50
br4
Brace shear
13
r1_r
Panel zone shear
51
bsg1
Brace strain
14
r1_s
Panel zone strain
52
bsg2
Brace strain
15
r2_r
Panel zone shear
53
bsg3
Brace strain
16
r2_s
Panel zone strain
54
bsg4
Brace strain
17
r3_r
Panel zone shear
55
br5**
Brace shear
18
r3_s
Panel zone strain
56
br6**
Brace shear
19
r4_r
Beam web shear
57
br7**
Brace shear
20
r4_s
Beam web strain
58
br8**
Brace shear
21
r5_r
Beam web shear
59
bsg5**
Brace strain
22
r5_s
Beam web strain
60
bsg6**
Brace strain
23
r6_r
Beam web shear
61
bsg7**
Brace strain
24
r6_s
Beam web strain
62
bsg8**
Brace strain
25
r7_r
Beam web shear
63
sg21
Column flange strain
26
r7_s
Beam web strain
64
sg22
Column flange strain
27
sg1
Column flange strain
65
lc1
Actuator 1 force
28
sg2
Column flange strain
66
lc2
Actuator 2 force
29
sg3
Column flange strain
67
dcdt01
Actuator 1 displacement
30
sg4
Column flange strain
68
dcdt02
Actuator 2 displacement
31
sg5
Column flange strain
69
wp01
Actuator 1 displacement
76
Response
No
Transducer
32
sg6
29
Response
No
Transducer
Response
Column flange strain
70
wp02
Actuator 2 displacement
sg3*
Continuity plate strain
71
nvtc01
Beam tip displacement
30
sg4*
Continuity plate strain
72
wp03
Beam tip displacement
31
sg5*
Continuity plate strain
73
nvtc5
Reaction frame slip
32
sg6*
Continuity plate strain
74
nvtc6
Reaction frame slip
33
sg7
Beam flange strain
75
nvtc7
Reaction frame slip
34
sg8
Beam flange strain
76
dcdt5
Clevis gap
35
sg9
Beam flange strain
77
dcdt6
Clevis gap
36
sg10
Beam flange strain
78
dcdt7
Clevis slip
37
sg11
Beam flange strain
79
dcdt8
Pin slip in slot hole
38
sg12
Beam flange strain
* for Specimen EC03, ** for Specimen EC02 and Specimen EC03
3.4.3 Loading protocol
Figure 3-25 shows the cyclic displacement history in the testing program following the
AISC prequalification test procedure (AISC 2002) used. This history is identical to that
developed by Krawinkler (1998) for the SAC Joint Venture. Story drift was used as the control
variable. The cyclic history consisted of symmetric and stepwise-increasing displacements (ATC
1992; SAC 1997) that were imposed by the actuators at the end of the beam. The complete
displacement history consisted of thirty-four cycles; six cycles at a target drift angle of 0.375percent, 0.500-percent, and 0.750-percent, four cycles at a target drift angle of 1.0-percent, and
two cycles at a target drift angles of 1.5-percent, 2.0-percent, 3.0-percent, 4.0-percent, and 5.0percent. Testing using this displacement history continued until the beam completely separated
from the column.
77
1
6
7
12
A
EC01
W
52.730 m (173 feet)
EC02
N
9.144 m
E
EC03
9.144 m
7.010 m
S
7.010 m
9.144 m
13.411 m
4.572 m
H
86.563 m (284 feet)
Figure 3-1: Plan view of typical floor showing locations of test specimens
EC01
Column splice
EC03
EC02 in Frame 6 and 7
Figure 3-2: Frame elevation at line A
78
60.312 m
EC01
Mech./Roof
Tower 15
Tower 14
Tower 13
Tower 12
Tower 11
Tower 10
Tower 9
Tower 8
Tower 7
Tower 6
Garage 5
Garage 4
Garage 3
Garage 2
Ground
Basement
EC03
4.877 m
Fire proofing
Weld access hole
Column flange
CJP weld
Beam bottom flange
Weld end dam
Runoff tab
Figure 3-3: Connection detail between beam bottom flange and w-shape column
Column plate
Weld access hole
Weld end dam
Beam bottom flange
Backing bar
PP weld
Fire proofing
Figure 3-4: Connection detail between beam bottom flange and box column
79
unit: inches
Figure 3-5: Construction detail for Specimen EC01
unit: inches
Figure 3-6: Construction detail for Specimen EC02
80
unit: inches
Figure 3-7: Construction detail for Specimen EC03
Figure 3-8: Downhand welding for CJP welds in the beam bottom flange
81
Figure 3-9: Original drawing for box column details (Design Documents 1990)
Figure 3-10: Fabrication of horizontal continuity plates into a box column
82
unit: inches
2,286
737
Figure 3-11: Modified details for the continuity plates in box columns
4,166
unit: mm
Figure 3-12: Plan view of test fixture for Specimen EC01
83
Clevis and pin
Test specimen
column
Reaction block
Strong floor
Williams rod (φ = 1-3/8”)
Figure 3-13: Anchorage detail between the column-end and the clevis
Actuator
Reaction box
Strong floor
Williams rod (φ = 1-3/8”)
Figure 3-14: Anchorage detail for the actuator
84
Lateral-brace frames
Figure 3-15: Lateral-brace frames for Specimen EC02
Figure 3-16: Photograph of test fixture for Specimen EC01
85
737
4,114
4,166
unit: mm
Figure 3-17: Plan view of test fixture for Specimen EC02
Figure 3-18: Photograph of test fixture for Specimen EC02
86
737
4,114
4,166
unit: mm
Figure 3-19: Plan view of test fixture for Specimen EC03
Figure 3-20: Photograph of test fixture for Specimen EC03
87
LVDT
SG4
SG
SG11
SG
a. Displacement transducers
SG21
SG
SG22
SG18
b. Strain gages
Figure 3-21: Instrumentation for Specimen EC01
88
a. Displacement transducers
RO
RO
b. Strain gages
Figure 3-22: Instrumentation for Specimen EC02
89
NVTC1, NVTC2
LVDT
DCDT3
DCDT
DCDT4
DCDT
a. Displacement transducers
b. Strain gages
Figure 3-23: Instrumentation for Specimen EC03
90
Figure 3-24: Instrumentation on the clevis
5.0
Story drift angle, % radians
4.0
3.0
2.0
1.0
0
-1.0
-2.0
-3.0
-4.0
-5.0
0
6
22 24 26 28 30 32
18
12
Number of cycles
Figure 3-25: Cyclic displacement history by SAC
91
Chapter 4. Finite Element Analysis
4.1 Introduction
Finite element analysis can provide considerable insight into the likely behavior of
complex connections such as those discussed in this thesis. However, such analysis has
significant limitations because material imperfections, geometric imperfections, residual stresses
and strains, and flaws or defects cannot be modeled a priori. Such limitations can substantially
impact the global behavior of a rigid steel connection. Further, finite element analysis using a
cyclic loading history similar to that adopted in the SAC testing program (e.g., Kim et al. 2000a,
2002a, 2002b) and for the tests described in Chapter 3, Chapter 5, and Chapter 6 is both time
consuming and computationally intensive.
Work conducted with funding from the SAC Joint Venture (e.g., El-Tawil et al. 1998;
Kim et al. 2000a) showed that global and most local test specimen responses under cyclic loading
could be computed reasonably accurately using finite element models subjected to monotonic
loading. In addition, finite element analysis can be used to both better understand states of stress
and strain in connections and to compare behaviors between connections of differing
configurations. Such information cannot be cost-effectively gathered from full-scale testing. As
such, analysis of finite element models under monotonic loading was used exclusively in this
research program to support the experimental studies and advance the knowledge of the response
of large-size beams connected to box columns or deep W-shape columns.
Version 6.3 of the general purpose finite element program ABAQUS (HKS 2002) was
used to model the three prototype beam-column connections described in Chapter 3; EC01, EC02,
and EC03. The primary objectives of the preliminary analyses were to 1) identify zones of high
92
stress and strain in the test specimens, 2) understand the likely sequence of yielding in the test
specimens, 3) investigate the effect of variation of material properties of the specimens with
respect to the prototype connections, and 4) design the instrumentation for the test specimens.
These preliminary models were prepared and analyzed prior to fabrication of the test specimens.
Expected material properties were used because mill and coupon data were unavailable at that
time. At the completion of testing program, coupons were extracted from the four W-shapes, and
accurate estimates of the beam and column material properties were established. The three finite
element models were updated and reanalyzed. Only summary information on the reanalysis work
is presented in this chapter. Detailed analytical results are presented in the following chapters.
4.2 Finite Elements
4.2.1 Solid elements
Solid elements are volume elements that approximate the behavior of a continuum in
three dimensions. They were used in this study to investigate the local stress and strain
distributions in the connection regions of the test specimens.
Three dimensional solid elements include tetrahedral elements, wedge (triangular prism),
and hexahedron (brick) elements (see Figure 4-1). Because of the nature of the formulation, the
tetrahedral elements are overly stiff and exhibit volumetric locking in incompressible problems.
Extremely fine meshes are required for reliable solutions. Therefore such elements should not be
used in the region where the strain must be predicted accurately. The hexahedron elements are
isoparametric elements and they are more accurate if not distorted. When well-shaped
isoparametric elements are used in the critical region, accurate results can be expected without
losing computational efficiency (HKS 2002).
93
Because first-order (linear) interpolation is more economical computationally than
second-order (quadratic) interpolation for similar levels of accuracy, first-order interpolation was
used in this study.
The beam flanges near the column face are subjected to local bending and high plastic
strain. First-order, fully integrated elements used in such regions may suffer from both shear and
volumetric locking. Reduced integration can decrease the number of internal constraints
introduced by an element, and will generally work well in such cases. However, the element
stiffness matrix formed by the reduced integration will be rank-deficient so that the element
usually exhibits the singular hourglass modes. Since the first-order, reduced-integration elements
have only one integration point, it is possible for them to distort in such a way that the strains
calculated at the integration point are all zero which leads to uncontrolled mesh distortion.
ABAQUS provides hourglass control features but such features must be used with reasonably
fine meshes. Hourglassing can also be minimized by distributing point loads and boundary
conditions over a number of adjacent nodes (HKS 2002).
Eight-node, Three-dimensional, first order, reduced integrated brick elements (C3D8R
elements in ABAQUS) were used to discretize the solid-element (Type SOL) models for the test
specimens, EC01, EC02, and EC03. El-Tawil et al. (1998) reported that these brick elements
performed well in the convergence studies.
4.2.2 Shell elements
Shell elements are a particular form of a three-dimensional solid with a small thickness
compared with other dimensions. Under such an assumption, the two dimensional shape of the
shell can be treated as a three-dimensional element. The choice of three-dimensional shell
elements instead of traditional solid elements was made to gain computational efficiency without
sacrificing accuracy. They were used to analyze global and selected local response quantities of
the specimens.
94
The shell elements used in this study are ABAQUS S4R5 4-node reduced integration
shell elements that enable large deformation/small strain analysis. Such elements have been
employed successfully in prior investigations of steel connections (Lee et al. 1997; El-Tawil et al.
1998; Kim et al. 2000a).
The reference surface of the shell is defined by the shell element’s nodes and the righthand-rule definition of the shell surface normal. The reference surface is typically coincident with
the mid-surface of the shell. However, many situations arise in which it is more convenient to
define the reference surface as offset from the shell mid-surface (see Figure 4-2). For example,
when the thickness of the beam flange and column plate is changed, the whole model must be
updated to accommodate such local changes. An offset was therefore introduced in the definition
of beam flanges, continuity plates, column flanges, and column plates of the box column by using
the OFFSET parameters in the *SHELL SECTION options in the ABAQUS. The outer surface of
such components was considered as the reference surface for modeling using shell elements. The
degrees of freedom for the shell are thus associated with this reference surface. All kinematic
quantities, including the element’s area, are calculated at the reference surface. Any loading in the
plane of the reference surface will, therefore, cause both membrane forces and bending moments
when a nonzero offset value is used. Large offset values coupled with the presence of high
curvature may also lead to a surface integration error, affecting the stiffness for the shell section
(HKS 2002). However, such stiffness changes were not detected in this study.
95
Table 4-1: Material properties used for ABAQUS models
Yield Point1
Component
W33×118
beam flange2
W33×118
beam web2
W36×232
beam flange2
W36×232
beam web2
W36×210
beam flange2
W36×210
beam web2
W27×281
col. flange 2
W27×281
col. web 2
Box column
plates3
Continuity
plates3
Doubler
plate3
1.
2.
3.
Ultimate Point1
Rupture Point1
Stress
(MPa)
σy
Strain
(%)
εy
Stress
(MPa)
σu
Strain
(%)
εu
Stress
(MPa)
σr
Strain
(%)
εr
426
0.21
527
12
483
39
479
0.24
549
12
483
39
374
0.19
521
12
483
39
422
0.21
522
12
483
39
383
0.19
519
12
483
39
402
0.20
522
12
483
39
356
0.18
506
12
483
39
392
0.20
505
12
483
39
365
0.18
496
12
448
39
365
0.18
496
12
448
39
392
0.20
505
12
483
39
See Figure 4-3 for details.
Data from coupon tests.
Assumed values based on previous studies conducted by the author.
4.2.3 Mechanical properties of materials
Data from the tests of coupons extracted from the W-shape beam and column of the
specimens were used to establish the stress-strain relationships for the beam and column finite
elements. For all materials, Young modulus was set equal to 200,000 MPa (29,000 ksi), Poisson’s
ratio was set equal to 0.3, and isotropic strain hardening was assumed for monotonic loading.
Table 4-1 presents the material properties adopted for the analytical studies reported in this
chapter. A tri-linear stress-strain relationship was assumed for each of the components identified
in Table 4-1. Figure 4-3 shows the assumed tri-linear stress-strain relationship.
96
4.3 Analytical Models
Solid model (Type SOL) models were prepared for each test specimen. The beam,
column, and plates in these connections were discretized using three-dimensional sold elements.
These solid models were used to study the stress and strain distributions in the connections at
different levels of story drift, and to evaluate selected indices at different levels of story drift.
However, the solid models were not used to capture local and global instabilities such as flangeand web-local buckling, and lateral-torsional buckling. Because flange and web local buckling in
the beams were expected at story drift angles greater than 2-percent radian, the results of the
analyses using the solid models are not presented for story drift angles greater than 2-percent
radian.
Shell-element (Type SH) models were prepared to study local and global instabilities in
the connections because such models are computationally more efficient than solid-element
models for this purpose. Type SH models were prepared for each test specimen. The beam,
column, and plates in theses connections were discretized using three-dimensional shell elements.
Effects of global instabilities were included in these models.
4.3.1 Solid element models
Geometric modeling
The coordination system, finite element meshes and boundary conditions of the solid
element models for each test specimens are presented in Figure 4-4, Figure 4-5, and Figure 4-6,
respectively. The global coordinate system (X, Y, Z) was used as the reference frame for each
local coordination system, loading, and boundary conditions. The X-direction coincides with the
longitudinal axis of the beam; the Z-direction coincides with the longitudinal axis of the column.
The out-of-plane Y-direction is defined by the right-hand screw rule.
97
To reduce the computational effort, only one quarter of each specimen was modeled,
taking advantage of symmetry and asymmetry in the model. These models take advantage of
symmetry about the Z-X plane (y=0) and anti-symmetry about the X-Y plane of the specimen. In
the quarter model, only half of the height and width of the column and half of the depth and width
of the beam were modeled. The discussion below is for the quarter model only.
The symmetric boundary condition about the Z-X plane (YSYMM in ABAQUS) constrains
the displacement along the Y-axis and rotations (first derivative of the displacement) about the Zand X-axes to be zero. The anti-symmetric boundary condition about the X-Y plane (ZASYMM in
ABAQUS) constrains the displacements along the X-axis and Y-axis and rotations about the Zaxis to be zero. Figure 4-7 and Figure 4-8 show element meshes for the quarter model of
Specimen EC01 in the (X, Y, Z) coordinate system. The constraints on the Z-X and X-Y planes are
also shown in this figure.
A line of nodes at the end of the column was defined as the displacement boundary
condition which replicates the pin in the actual test setup described in the previous chapter. This
boundary point was restrained against translation only (i.e., Ux = Uy = Uz = 0). Use of the point
boundary condition and rigid plate described in the next section was not considered for the solid
element models because of numerical problems.
Restraint of lateral movement of the beam and column flanges was provided for the Type
SOL models by virtue of the fact that displacements of the beam web centerline in the y-direction
of the beam were restrained and equal to zero.
Finite element meshes
Details on the meshing the solid element model for Specimen EC01 are shown in Figure
4-7 and Figure 4-8 and are described in this section. Since the connection models have different
sizes and configurations, separate models were constructed for Specimens EC02 and EC03.
Summary information for the EC01 model follows.
98
The size of the finite element mesh varied over the length and height of the EC01 model.
A fine mesh was used near the connection of the beam to the column and at the corner of box
column. A coarser mesh was used elsewhere. Most of the solid elements were right-angle prisms.
The smallest element dimension was 4.7 mm (0.19 in.). The largest element dimension was 140
mm (5.5 in.) at the end of the beam.
Beam flanges were modeled using 4 layers of elements through the flange depth and 11
elements across the flange half-width. This choice of element size was based on the studies of ElTawil et al. (1998). The beam web was modeled using 1 element through the (half) thickness and
18 elements along the (half) height (from the upper of the bottom flange). Four-node (tetrahedron)
elements were used to model the shape of the weld access (cope) hole.
The CJP groove welds joining the beam to the column and the CJP groove welds joining
the continuity plates to the column flange and web plate were not modeled explicitly. The
backing bars and weld end dams were not modeled. Instead, the response indices used in this
study were calibrated to account for the potentially adverse effects of the notch created by the
backing bar, as suggested by Chi et al. (2000). The web of the beam was directly connected to the
column flange and the shear tab and bolts were not modeled. This modeling decision was justified
because the effect of the shear tab and its bolts on the behavior of the connection before beam
flange fracture is not large (Kim et al. 2000a). A significantly more complex finite element model
would be needed to model connection behavior after beam flange fracture because deformations
of the shear tab and the bolts become very large.
The column flange plate near the beam was discretized into 7 elements across its (half)
width and 4 elements through its thickness. The column flange plate remote from the beam was
discretized into 2 elements across its (half) width and 2 elements through its thickness. The
column web plate was modeled using 2 elements through its thickness and 20 elements along its
depth. The continuity plates in the column opposite the beam flange were modeled using 5 layers
of elements per plate for the solid model of Specimen EC01 (the number of layers varied for
99
different models). Four-node (tetrahedron) elements were used to model the shape of the cope
hole in the continuity plates.
The doubler plate was included in the solid model of Specimen EC03 by adding one layer
of elements over the depth of the column web with a thickness equal to one-half the thickness of
the doubler plate.
4.3.2 Shell element models
Geometric modeling
Two coordinate systems, global and local, were used to model the connections as shown
Figure 4-9, Figure 4-10, and Figure 4-11, respectively. The global coordinate system (X, Y, Z)
was used as the reference system for each local coordinate system, loading, and boundary
conditions. The local coordinate system (1, 2, 3) was defined to model the geometry and local
stress and strain distributions in the thee-dimensional shell elements. The 1-direction coincides
with longitudinal axis of the beam or column; the 3-direction coincides with the normal to the
surface of shell element. The 2-direction is defined by the right-hand screw rule.
To investigate geometry changes in the test specimens at large drifts, the boundary
condition in the model should replicate the test conditions. Because it was not possible to model
such boundary conditions with quarter models, complete models using shell elements were
prepared.
The test setup (see Chapter 3) had a circular hole with a pin and a slotted hole with a pin
to replicate the assumed inflection point boundary conditions at mid-height of the column. Pointwise defined boundary conditions, a pin for the circular hole and a roller for the slotted hole,
coupled with a rigid end-plate model were used in the finite element model. The actual clevis and
end-plate configuration of the column ends did not influence the behavior of the specimen and
were not modeled. The rigid end-plate was used to avoid artificial, but potentially large, local
100
strains in this end-region of the model. Lateral movement of the flanges of the beam was
prevented near the free end of the beam by replicating the lateral restraint provided by a frame
placed near the actuators in the finite element model. For the shell element models of Specimens
EC02 and EC03, lateral restraints of the beam flange in the middle of beam span were provided to
model the beam lateral bracing used in the tests (see Chapter 3).
Finite element meshes
The coordination systems, finite element meshes and boundary conditions of the shell
element models for each test specimen are presented in Figure 4-9, Figure 4-10, and Figure 4-11.
The beam, column, and plates in these connections were discretized using shell elements and
joined by sharing the nodes at common locations.
A two-dimensional structured meshing technique was used to generate the mesh in
regions of the finite element model characterized by complex geometry and complex strain and
stress states: the groove-weld connection of the beam flanges to the column, the k-line of beam
web or column web, and the corners of the box column have a relatively fine mesh. A structured
mesh is defined by seeding an edge, a process that prescribes a number of elements or a bias of
their distribution along a given edge line in the model. The smallest element dimension was 17
mm (0.67 in.) in the connection region, while the largest element dimension was 150 mm (6 in.)
at the end of the beam and the column. Mesh convergence studies by El-Tawil et al. (1998)
showed that the use of six S4R5 elements across the width of the beam flange produced similar
results when compared to meshes with 8 or 12 elements across the width of the beam flange.
Given the data from El-Tawil’s study and the objectives of this project, the beam flanges were
modeled using 8 elements across their widths. The mesh for the continuity plates matched the
meshes used for the beam flanges and column web. The thickness of the column web elements in
the panel zone in Model EC03 was increased to account for the presence of the doubler plate. The
weld access hole was also included in the shell-element models by adjusting the geometry of the
101
finite element mesh. However, the CJP groove welds joining the beam to the column and the CJP
groove welds joining the continuity plates to the column flange and web were not modeled
explicitly. The backing bars and weld end dams were not modeled. The web of the beam was
directly connected to the column flange and the shear tab and bolts were not modeled.
4.3.3 Applied loading
A displacement history was imposed at the free end of the beam using the displacementcontrol feature in ABAQUS and applying displacement in the plane of the beam web. The
corresponding history of the applied load was back-calculated from the support-reaction histories.
Monotonic loading was applied to the same displacement magnitude as the cyclic loading
tests. The maximum beam tip displacements corresponded to 2-percent and 5-percent radian of
inter-story drift angle for the Type SOL and Type SH models, respectively. For Type SOL
models, tip upward load (positive z direction) was applied so that the beam bottom flange was
subjected to tension force. A tip-down load (negative z direction) was applied for Type SH
models so that the beam bottom flange was in compression.
4.4 Analysis Procedures
4.4.1 Material nonlinear analysis
ABAQUS uses Newton’s method to solve the equilibrium equations associated with
material nonlinearity. Since the material response is dependent on the response history during the
previous time step, the solution is obtained incrementally, with iteration to obtain equilibrium
within each increment (see Figure 4-12). The increments should be small enough to capture the
history-dependent effects.
102
4.4.2 Geometric nonlinear analysis
Geometric nonlinearity can substantially affect the load-displacement relationship for
steel structural components. To evaluate these effects, eigenvalue analysis was used to: 1)
compute the critical buckling load of the specimen, and 2) characterize the buckled mode shapes
of the specimen. Meshing studies in the vicinity of the buckled zone are typically required to
ensure that the estimate of the buckling load has converged. Such studies were performed as part
of this study. Following refinements of the mesh to attain convergence of the buckling load,
imperfections were introduced in the refined mesh at locations determined from the elastic
eigenvalue analysis. The distribution of geometric imperfections in the models matched the linear
combination of the first and second buckled mode shapes of the loaded connection configuration.
The first buckled mode shapes of Specimens EC01, EC02, and EC03 are shown in Figure 4-13,
Figure 4-14, and Figure 4-15, respectively. The maximum imperfection magnitude was set at
approximately 5 percent of the flange thickness. The studies by El-Tawil et al. (1998) showed
that the results were not particularly sensitive to the magnitude of the imperfection.
The second stage of the analysis involved the calculation of a load-displacement response
curve for the specimen under a monotonically applied displacement at the tip of the beam. The
stiffness of the model approaches zero when peak load capacity of the specimen is reached. Such
zero-stiffness condition may result in an unbounded displacement increment in a typical NewtonRaphson numerical integration procedure. Therefore, a modified Riks algorithm (HKS 2002) was
used to handle such instabilities. This method assumes that the global instability can be controlled
by using the load magnitude as an additional unknown (see Figure 4-16). This method has also
been used in numerous studies (Lee et al. 1997; Kim et al. 2000a) and it has yielded satisfactory
results.
103
Figure 4-1: ABAQUS Solid elements (HKS 2002)
Figure 4-2: Schematic of shell offset (HKS 2002)
104
σu
Stress (MPa)
σr
σy
εy
εu
Strain (mm/mm)
εr
Figure 4-3: Assumed stress-strain relationship in ABAQUS
P, Δ
UX = UY = UZ = 0
Figure 4-4: ABAQUS Type SOL model of Specimen EC01
105
P, Δ
UX = UY = UZ = 0
Figure 4-5: ABAQUS Type SOL model of Specimen EC02
P, Δ
UX = UY = UZ = 0
Figure 4-6: ABAQUS Type SOL model of Specimen EC03
106
Symmetric plane
Anti-symmetric plane
UY = 0
∂U X
∂X
∂U Z
∂Z
=0
=0
Beam web
Weld access hole
Beam flange
(a) Beam cross section
(b) Beam elevation
Figure 4-7: Element meshing for beam of Type SOL model of Specimen EC01
Anti-symmetric plane
Symmetric plane
UX = 0
UY = 0
∂U Z
∂Z
=0
Column
web plate
Continuity
plate
Cope hole
Column
flange plate
(a) Column cross section
(b) Column elevation
Figure 4-8: Element meshing for column of Type SOL model of Specimen EC01
107
UX = UY = RZ = 0
1
3
2
3
2
UY = 0
1
Z
P, Δ
Y
UX = UY = UZ = RZ = 0
X
Figure 4-9: ABAQUS Type SH model of Specimen EC01
UX = UY = RZ = 0
1
3
2
3
2
1
UY = 0
Z
Y
X
UX = UY = UZ = RZ = 0
Figure 4-10: ABAQUS Type SH model of Specimen EC02
108
P, Δ
UX = UY = RZ = 0
1
3
2
3
2
1
UY = 0
Z
Y
X
UX = UY = UZ = RZ = 0
Figure 4-11: ABAQUS Type SH model of Specimen EC03
Figure 4-12: Newton iteration for nonlinear problems (HKS 2002)
109
P, Δ
Z
Y
X
Figure 4-13: First mode shape for Type SH model of Specimen EC01
Z
Y
X
Figure 4-14: First mode shape for Type SH model of Specimen EC02
110
Z
Y
X
Figure 4-15: Mode First mode shape for Type SH model of Specimen EC03
Figure 4-16: Modified Riks algorithm (HKS 2002)
111
Chapter 5. Performance Evaluation of Box
Column Connections
5.1 Introduction
The following section reports the results of the tests on and the numerical simulations of
two box column connection specimens (EC01 and EC02) fabricated using pre-Northridge
connection detail. Global and local response information is presented in Section 5.2. The
remainder of this chapter provides an evaluation of the experimental and analytical data. In
particular, the results of the parametric study on key box column connection design variables are
presented in Section 5.3. Section 5.4 provides preliminary design guidelines for box column
connections.
5.2 Performance of Pre-Northridge Connections
Two full-scale steel beam-column connections (Specimens EC01 and EC02) were tested
in the Structural Research Laboratory at the Pacific Earthquake Engineering Research (PEER)
Center at the University of California, Berkeley. Specimen EC01 was tested between July 10 and
July 16, 2002; Specimen EC02 was tested on July 29 and 30, 2002.
The data acquired during each of the two tests was reduced using data reduction
procedures implemented in the MATLAB (Mathworks. 1999) computing environment. The data
was filtered to eliminated noise and then zero corrected. Drift in the strain gage channels was
eliminated as appropriate.
Selected global and local response data for each of the two specimens are presented in
this section. Global response data in the form of moment-story drift angle and moment-panel
112
zone plastic rotation relations are presented. Moment-beam plastic rotations are not plotted
because the specimens fractured before specimen yielding. The reference moment presented for
each specimen is the moment at the face of the column, which was calculated by multiplying the
actuator force by the distance between the centerline of the actuator and the face of the column.
Story drift angle was computed by dividing the beam tip displacement by the distance between
the displacement measuring point and the centerline of the column. The procedures used for the
calculation of column, panel zone, and beam deformations from the transducer measurements are
similar to those used in the SAC Steel Project. Details can be found in Whittaker et al. (1996).
Local responses in the beam and column flanges and webs are reported in terms of strains.
In the following presentations, the strains are normalized with respect to an assumed yield strain
of 0.002. The normalized strain for each drift cycle is computed when the force attains its peak.
5.2.1 Cyclic response of Specimen EC01
Specimen EC01 was tested using the loading protocol presented in Section 3.4.3. An
actuator displacement of 23 mm corresponded to a story drift angle of 1 percent in the specimen.
Whitewash paint was applied to the specimen prior to testing to aid in the visual identification of
damage and yielding in the components of the connection.
Specimen response
Yielding of the top and bottom flanges of the beam was observed during the first
displacement excursion to a drift angle of 0.75-percent. Figure 5-1 and Figure 5-2 are
photographs of the top and bottom flanges of the beam at this drift angle, respectively, showing
the flaking of the whitewash paint.
Three cracks in the CJP weld of the beam top flange to the column flange formed just
prior to fracture of the top flange. Figure 5-3 shows the locations of these three cracks. They
propagated rapidly following initiation, (this took approximately 0.03 seconds, measured by
113
video image data recorded during the test), and joined, leading to top flange fracture. The beam
top flange of Specimen EC01 fractured at the story drift angle of 0.76-percent during the first
displacement excursion to a story drift angle of 1-percent. Figure 5-4 and Figure 5-5 are
photographs of the fractured top flange. Fracture of the top flange was followed by fracture of the
supplemental fillet weld to the web shear tab: see Figure 5-6. Figure 5-7 shows the gap that
formed between the backing bar and the beam bottom flange in the cycle following the fracture of
the beam top flange. The gap resulted by deformation of the beam bottom flange associated with
shear force transfer from the beam to the column. More information on this subject can be found
in Kim et al. (2002a). A highly strained region of the beam bottom flange near the weld end dam
is also identified in Figure 5-7.
The beam bottom flange fractured at a story drift angle of 0.91-percent during the second
displacement excursion to a story drift angle of 1-percent. The fracture initiated from the highly
strained region identified in Figure 5-7. Figure 5-8 and Figure 5-9 are photographs of the
fractured bottom flange. Following fracture of the beam bottom flange, a tear developed in the
shear tab as shown in Figure 5-10. This tear propagated slowly in subsequent cycles. The test was
terminated when the shear tab fractured along a line through the bolts during the first excursion to
a story drift angle of 4-percent. Figure 5-11 and Figure 5-12 are photographs of the fractured web
shear tab.
Global response
The relation between moment (at the column face) and story drift angle for Specimen
EC01 is presented in Figure 5-13. The positive (tension in the top flange and compression in
bottom flange) maximum moment at the column face before the first fracture was 2,026 kN-m
(17,934 kip-in), which is 86 percent of the plastic moment based on the nominal yield strength of
345 MPa (50 ksi) or 71 percent of the plastic moment based on the MTR yield strength of 418
MPa (61 ksi). The negative (compression in the top flange and tension in the bottom flange) peak
114
moment before the bottom flange fractured was 2,294 kN-m (20,300 kips-in), which is 98 percent
of the plastic moment based on the nominal yield strength of 345 MPa (50 ksi) or 81 percent of
the plastic moment based on the MTR yield strength of 418 MPa (61 ksi).
The peak moment resisted by the shear tab after both flanges had fractured was 995 kNm (8,804 kip-in), which is 42 percent of the plastic moment of the connection based on the
nominal yield strength, and 3 times larger than the plastic moment of the shear tab alone based on
a nominal yield strength for the tab steel of 248 MPa (36 ksi). This large residual strength is
developed by the couple between the compressive force transferred across the fractured beam
flange and a resultant tensile force carried by the bolts of the shear tab.
The relation between the moment and the plastic deformation in the panel zone is
presented in Figure 5-14. The stiffness of a box column was extremely high and the panel-zone
and column deformations were very small.
Local response
Figure 5-15 shows the maximum tensile strain profiles on the beam top flange during the
each drift cycle. This strain distribution was recorded by strain gages attached on the top surface
of the top flange along a line at a distance of 51 mm (2 in.) from the column face during the
positive loading half-cycle (producing tension in the top flange). The strain was normalized by an
assumed yield strain of 0.002, typical for Grade 50 steel. The strains were highest at the edges of
the beam flange and lowest in the middle of the beam flange above the web. This result was
expected because there is no column web in the box column to provide restraint for the beam
flange. Instead, such restraint is provided by the box column side plates and affects the edges of
the beam flange.
The shear strain profiles in the beam web produced by positive loading half-cycle are
shown in Figure 5-16. The shear strains were recorded using three rosette strain gages attached to
the web along a line at a distance of 178 mm (7 in.) from the column face. The shear strains are
115
higher near the flanges and lower at the mid-height of the web. This result was also expected and
replicates results of previous studies (Lee et al. 1997; Kim et al. 2000a). Note that the magnitude
of the shear strain is much lower than the yield shear strain.
5.2.2 Cyclic response of Specimen EC02
Specimen EC02 was tested using the loading protocol presented in Section 3.4.3. An
actuator displacement of 41 mm corresponded to a story drift angle of 1 percent in the specimen.
Whitewash paint was applied to the specimen prior to testing to aid in the visual identification of
damage and yielding in the components of the connection.
Specimen response
Yielding of the bottom flange of the beam was observed during the first displacement
excursion to a drift angle of 0.375-percent: see Figure 5-17 for details. Yielding of the beam top
flange was not observed prior to top flange fracture.
The beam top flange of Specimen EC02 fractured at the story drift angle of 0.59-percent
during the first displacement excursion to a story drift angle of 0.75-percent. Figure 5-18 and
Figure 5-19 are photographs of the fractured top flange. The beam bottom flange fractured at a
story drift angle of 0.68-percent during the following negative displacement excursion to a story
drift angle of 0.75-percent. Figure 5-20 and Figure 5-21 are photographs of the fractured bottom
flange. A tear developed in the shear tab, as shown in Figure 5-22, during the displacement
excursions to a story drift angle of 2-percent. This tear propagated slowly in subsequent cycles.
The test was terminated when the shear tab fractured along a line through the bolts during the first
excursion to a story drift angle of 3-percent. Figure 5-23 and Figure 5-24 are photographs of the
web tab at story drift angles of 2- and 3-percent, respectively.
116
Global response
The relation between moment (at the column face) and story drift angle for Specimen
EC02 is presented in Figure 5-25. The positive (tension in the top flange and compression in
bottom flange) maximum moment at the column face before the first fracture was 3,473 kN-m
(30,736 kip-in), which is 66 percent of the plastic moment based on the nominal yield strength of
345 MPa (50 ksi) or 58 percent of the plastic moment based on the MTR yield strength of 393
MPa (57 ksi). The negative (compression in the top flange and tension in the bottom flange) peak
moment before the bottom flange fractured was 3,897 kN-m (34,489 kip-in), which is 74 percent
of the plastic moment based on the nominal yield strength of 345 MPa (50 ksi) or 65 percent of
the plastic moment based on the MTR yield strength of 393 MPa (57 ksi).
The peak moment resisted by the shear tab after both flanges had fractured was 1,173 kNm (10,382 kip-in), which is 22 percent of the plastic moment of the connection based on the
nominal yield strength, and 3.5 times larger than the plastic moment of the shear tab alone based
on a nominal yield strength for the tab steel of 248 MPa (36 ksi). This large residual flexural
strength is developed by the couple between the compressive force transferred across the
fractured beam flange and a resultant tensile force carried by the bolts of the shear tab. The peak
shear force in the tab following fracture of both flanges was 318 kN (71 kips): 29 percent of the
nominal shear strength of the tab.
The relation between the moment and the plastic deformation in the panel zone is
presented in Figure 5-26. The stiffness of a box column was extremely high and the panel-zone
and column deformations were very small.
Local response
Figure 5-27 shows the maximum tensile strain profiles on the beam top flange during the
each drift cycle. This strain distribution was recorded by strain gages attached on the top surface
117
of the top flange along a line at a distance of 51 mm (2 in.) from the column face during the
positive loading half-cycle (producing tension in the top flange). The strain was normalized by an
assumed yield strain of 0.002. The strains were highest at the edges of the beam flange and lowest
in the middle of the beam flange above the web, an observation identical to that for EC01.
However, the strain distribution across the width of the beam flange was more uniform that for
EC01 because the out-of-plane stiffness of the column flange plate was much higher in EC02: the
thickness of the EC02 flange plate was 70 mm, compared to 29 mm for EC01, while the width of
the EC02 flange was 330 mm, compared to 457 mm for EC01.
The shear strain profiles in the beam web produced by positive loading half-cycle are
shown in Figure 5-28. The shear strains were recorded using three rosette strain gages attached to
the web along a line at a distance of 178 mm (7 in.) from the column face. The shear strains are
higher near the flanges and lower at the mid-height of the web, an observation identical to that
mad for EC01.
5.2.3 Numerical simulation of the tests
Two numerical models for the tested specimens were prepared after the tests, details are
provided in Chapter 4. These finite element models were analyzed by applying monotonic
loading as discussed in Section 4.3.3. The expected global response of the test specimens and the
states in stress and strain in the critical regions of the models are presented in this section.
Global response
The beam moment-story drift angle responses of finite element models of Specimens
EC01 and EC02 (Models SH-EC01 and SH-EC02) are presented in Figure 5-29 and Figure 5-30,
respectively. The cyclic responses of each test specimen are also shown for the purpose of
comparison. Yielding, characterized by a change in model stiffness, starts at approximately 1percent story drift angle for all analytical models. The response of the models and the tested
118
specimens is virtually identical in the elastic (pre-yield) range, suggesting that the finite element
model is quite accurate in this loading range. While the specimens experienced brittle failure in
the elastic range of their response, the finite element model continued with inelastic response
because fracture was not modeled. The peak resistances in finite element models were attained at
slightly more than 3-percent story drift. Beyond this drift angle, local buckling of beam flanges
and the web results in a loss of strength and stiffness. Such response of the finite element model
is consistent with the response of pre-qualified new connections proposed in the FEMA-350
design guidelines. However, note that the fracture and post-fracture behavior of the tested
specimens cannot be predicted by the finite element analysis having without using fracture
modeling element. For this reason, local responses of each analytical model are reported at a story
drift angle of 0.5-percent in the following sections: the story drift angle associated with fracture
of the test specimens.
Shear transfer
Figure 5-31 and Figure 5-32 show the distribution of von Mises stress in the beam web
and the panel zone at 0.5-percent story drift angle in Models SH-EC01 and SH-EC02,
respectively. Both the tested specimens and the finite element models were still elastic at this drift
level. The values of von Mises stresses are large (and similar to those recorded in the beam flange)
near the weld access hole.
It is well documented that the transfer of shear force from the beam to the column in steel
moment-resisting connections does not follow elementary beam theory because of the effect of
connection boundary conditions (Lee et al. 1997). In general, beam flanges transfer significant
amounts of shear to the column, compared to approximately 2-percent predicted by the beam
theory. The percentage of the shear force transfer through the beam flanges depends on the beam
geometry and the boundary conditions imposed by the column. Table 5-1 shows the distribution
of shear force in the web and both flanges of the beam at four cross-sections located at increasing
119
distance from the column face. The shear force transferred to the column via the beam flanges is
quite high: 11 percent in Model SH-EC01 and 62 percent in Model SH-EC02 at a cross-section
10 mm (0.4 in) away from the column face. For the reference, shear force at the same location in
Model SH-EC03 (see Table 6-1) is 38 percent. Changes in the percentage of shear force transfer
through the beam web with increasing the distance from the column face were the minimal in
Model SH-EC01, because the degree of restraint provided by the column flange is small. The
increase in flange shear in Model SH-EC02 is due to the large thickness of the column flange
plate: column flange plate in Model SH-EC02 was 70 mm (2.75 in.) thick, while comparable
dimensions in Models SH-EC01 and SH-EC03 were 29 mm (1.125 in) and 49 mm (1.93 in.),
respectively. Such column flange thickness produces a large degree of restraint in the joint
between the beam flange and column flange in Model SH-EC02 and causes a significant increase
in shear force flow from the beam web to the beam flanges. In addition to producing a complex
state of stress in the flanges, such shear forces cause local bending of the flanges in the access
hole region. Note that the distribution of the shear force in the beam cross section follows the
beam theory at a cross section 460 mm (18.4 in), or one-half of beam depth, away from the
column face. Thus, only the connection region of the beam is affected by the connection
boundary conditions.
Table 5-1 Distribution of shear force in beam flanges and beam web at 0.5-percent drift
Distance from column face (mm)
SH Model
10
25
180
460
% shear in web
89
93
97
98
% shear in flanges
11
7
3
2
% shear in web
32
36
98
99
% shear in flanges
68
64
2
1
EC01
EC02
120
Local response
The distributions of axial stress S11 (the 1-direction lies along the longitudinal axis of the
beam) on the upper surface of the beam top flanges and top surface of the continuity plates in
Models SH-EC01 and SH-EC02 are presented in Figure 5-33 and Figure 5-34, respectively, at
0.5-percent story drift angle. The highly stressed regions in the analytical models correspond to
the location of the cracks observed just before fracture of beam flanges in the tests. The
maximum stresses in Model SH-EC01 are located in the middle and the edges of beam flange.
The stress concentration at the edges of the beam flange is caused by the column web plates
located in the edge of the box column. In comparison, the stress in the connection to the W-shape
column (such as Model SH-EC03 in Chapter 6) is maximized in the middle of beam flange while
the stresses at the flange edges are relatively small. Such a stress distribution is a consequence of
the location of the column web. The bending stiffness of the column flange in Model SH-EC02 is
so large that the stresses were almost uniformly distributed along the beam flange width. Note
that the beam flange of Specimen EC02 fractured without developing any hairline cracks.
The fracture indices for Models SH-EC01 and SH-EC02 along the upper surface of the
beam top flange, along the lines defined in Figure 5-35 are presented in Figure 5-36 and Figure
5-37, respectively. Line A is located along the CJP welds on the beam flange, Line B is defined at
the edge of the weld access hole, Line C is located 25 mm from the edge of a shear tab plate, and
Line D is 460 mm away from the column face. The fracture index data are reported for the top
surface of the beam flange. Note that the maximum values of stress and strain along the chosen
lines are not necessarily the maximum values in the connection. Nevertheless, these lines are
chosen to facilitate a comparison of results for different specimens.
In both models the Mises Index (MI) increases as the reporting line is closer to the
column flange. The maximum value of Mises Index is approximately 1, suggesting that yielding
will occur. The maximum values of Mises Index in Model SH-EC01 are located at the edges of
121
beam flanges, while the maximum values in Model SH-EC02 is uniform across the width of the
beam flange.
The Pressure Index (PI) shows high values near the column flange for all models. Note
that hydrostatic stress was defined as positive in compression, thus giving the values of Pressure
Index in the tension flange negative signs. The absolute values of Pressure Index are smaller than
0.5 and larger than 0.1 for all models. The maximum value of Pressure Index in Model SH-EC01
is located at the edges of beam flanges while the maximum for Model SH-EC02 is located in the
middle of the beam flange.
The maximum value of the Triaxiality Index in all models is approximately 0.47. The
values of Triaxiality Index in Models SH-EC01 and SH-EC02 with a box column are slightly
higher than those in Model SH-EC03 (Section 6.2.2) with a W-shape column.
5.3 Evaluation of Response Data
This section serves to integrate the results of experimental studies of Section 5.2 and the
findings from the theoretical studies in Chapter 2. The following section describes the key design
variables unique to the box column connections. Vulnerability to brittle fracture of the welded
joints in the box column connection is discussed in the Section 5.3.2. An evaluation on postfracture connection stiffness is presented in Section 5.3.3. Sections 5.3.4 through 5.3.7 present
and evaluate the response of the analytical models in terms of design variables, namely, column
shape (Section 5.3.4), continuity plate strength (Section 5.3.5), column flange stiffness (Section
5.3.6), and bi-axial loading (Section 5.3.7).
5.3.1 Analysis parameters
Performance of a box column connection is influenced by a number of design variables.
Column shape, continuity plate strength, column flange stiffness, and bi-axial loading (Figure
122
5-38) are unique features for the box column connection. These design variables may affect the
global response of the box column connection while they do not significantly change the global
response of the W-shape column connection (Kim et al. 2002c). Analytical models are developed
from Model SH-EC01 as the base. All the geometric and material properties for the analytical
models are identical with that in Model SH-EC01 except the four design variables varied
parametrically as shown in Table 5-2.
Table 5-2: Analytical models for the box column connection
Analysis parameters
Model
Continuity
plate1
SH_EC01
1.351 tbf
BX_CP00
None
BX_CP05
0.5 tbf
BX_CP07
0.625 tbf
BX_CP10
1.0 tbf
BX_CF08
BX_CF20
Column flange2
4.
5.
Column4
1.0 tcf
Uniaxial
BC18×18×257
0.75 tcf
1.351 tbf
2.0 tcf
BX_BI14
1.
2.
3.
Loading5
Biaxial3
BX_BI05
0.5 tbf
WF_CP14
1.351 tbf
WF_CP05
0.5 tbf
WF_CP00
none
1.0 tcf
Uniaxial
W14×257
tbf = 19 mm (0.74 in.) for W33×118.
tcf = 29 mm (1.125 in.) for BC18×18×257; tcf = 48 mm (1.89 in.) for W14×257.
Biaxial bending of the column coming from simultaneous action in perpendicular moment-resisting
frames.
Web thickness of W14×257 increases from tcw = 30 mm (1.18 in.) to tcw = 57 mm (2.25 in.).
Beam length from the beam tip to the column face is set to 2,057 mm (81 in.).
123
5.3.2 Welded joint
The likely location of brittle fracture in the test specimens were identified in the
numerical simulation study (Section 5.2). The location of the cracks observed just before fracture
of beam flanges in the tests coincides with the highly stressed region identified in the numerical
simulations. However, because of the limitations in shell element formulation, such models used
in the numerical simulations cannot provide sufficient information on the local stress and stain
distribution along the beam flange thickness necessary to evaluate the fracture vulnerability of the
welded joints. Thus, the solid element models described in Section 4.2, SOL-EC01 and SOLEC02, are employed to investigate the cause of brittle fracture of the tested specimens.
For each connection discussed in this section, response data are presented at three levels
of inter-story drift: 0.5-percent (elastic response); 0.78-percent for SOL-EC01, 0.59-percent for
SOL-EC02 (the drift levels corresponding to brittle fracture in both tests); and 2-percent (inelastic
response of the numerical models). Data are not presented for story drifts greater than 2-percent
because geometric instabilities at such high story drift render the solid element models inaccurate.
The response of each of the solid element models is described below using fracture
indices presented in Section 2.2.3. ABAQUS data are reported for the cross section of the beam
flange defined in Figure 5-39. Plane A is the vertical plane of the beam flange at the face of the
column. Plane B is the vertical plane at the toe of the weld access hole. This solid element model
has several layers within the beam flange thickness. The number of the layers depends on the
beam flange thickness. The beam flange in Model SOL-EC01 has 5 layers (4 elements) through
the thickness and that in Model SOL-EC02 has 7 layers (6 elements) through the thickness.
Numbering of the layers that define the surfaces of the elements, starts from the bottom surface of
the beam flange and increases sequentially through the flange thickness.
124
Fracture indices of SOL-EC01
Figure 5-40, Figure 5-41, and Figure 5-42 present the distributions of Maximum Principal
Index (MPI), Mises Index (MI), and Pressure Index (PI), respectively, across the width of the
beam flange at the face of the column (Plane A) at story drifts of 0.5- and 2-percent. The
distributions of Pressure Index and Mises Index are related to that of Maximum Principal Index.
That is, the locations of peak values of each index coincide and the distribution pattern of the
index values along beam flange thickness is similar. The indices on the bottom surface (Layer 1)
show three peaks, in the middle and both edges of the beam flange. The difference between the
values in opposite surfaces (Layer 1 and Layer 5) becomes small near the edges of the beam
flange while it does not decrease much in the middle of the beam flange.
At 0.5-percent story drift, all the values of Maximum Principal Index in Layer 1 (Figure
5-40a) exceed the uniaxial yield strength (MI = 1) of the beam flange while those on other layers
are still less than the yield strength except the region near the edge of the beam flange. At 2percent story drift, the values of Maximum Principal Index in Layers 1, 2, and 3 (Figure 5-40b)
exceed the uniaxial tensile strength (note that σu/σy = 1.24 for Specimen EC01). As discussed in
Chapter 2, microcracking may occur when the maximum principal stress is larger than the
uniaxial tensile strength.
At 0.5-percent story drift, the values of Mises Index on the majority of the area of Plane
A (Figure 5-41a) are smaller than the initial yield point on the von Mises yield surface, while the
values of Mises Index at 2-percent story drift are larger than the initial yield point except in the
upper layers (Layer 4 and Layer 5) near the middle of beam flange (Figure 5-41b).
At 0.5-percent story drift, the peak value of Pressure Index in Layer 1 (Figure 5-42a) in
the middle of the beam flange was slightly smaller than that on both edges of the beam flange,
showing the same trend as Maximum Principal Index. However, the peak value of Pressure Index
on the same layer (Figure 5-42b) in the middle of the beam flange becomes larger than that of the
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edges of the beam flange at 2-percent story drift. The Maximum Principal Index in the middle of
the beam flange is still smaller than that at the edges of the beam flange. Yielding of beam flange
edges reduces the degree of deformation restraint (see Chapter 2) while the elastic portion inside
the beam flange is still restraining further yielding in the middle of the beam flange.
Figure 5-43 presents the distributions of Triaxiality Index (TI) across the width of the
beam flange at the face of the column (Plane A) at story drifts of 0.5- and 2-percent. At 0.5percent story drift, the values of Triaxiality Index are maximized in the middle layer (Layer 3)
while the layer does not yield (MI < 1). Thus, brittle propagation likely occurs in this plane if the
material is not notch-tough and an initial crack is induced in the extreme fiber (Layer 1) by the
high principal stress. At 2-percent story drift, the values of Triaxiality Index are maximized in the
bottom surface (Layer 1) and their magnitudes are similar to those at 0.5-percent story drift.
Because most values of Mises Index at this drift exceed 1, brittle fracture is not likely to occur.
Figure 5-44 presents the distributions of Rupture Index (RI) across the width of the beam
flange at the face of the column (Plane A) at story drift of 0.5- and 2-percent. At 0.5-percent story
drift, localized yielding occurs at the both edges of the beam flange but the magnitude of Rupture
Index is small as Plane A is still in elastic state. At 2-percent story drift, peak values of Rupture
Index in the both edges of the beam flange in Layer 1 are larger than the peak in the middle of the
beam flange. Because of high Rupture Index values in the edge of the beam flange, ductile
fracture can initiate from this location.
Figure 5-45, Figure 5-46, and Figure 5-47 present the distributions of Maximum
Principal Index, Mises Index, and Pressure Index, respectively, across the width of the beam
flange at the toe of the weld access hole (Plane B) at story drifts of 0.5- and 2-percent. The
distributions of Pressure Index and Mises Index relate to that of Maximum Principal Index. That
is, the location of peak value coincides and the distribution pattern of these indices along the
beam flange thickness is similar. The indices on the top surface (Layer 5) attain peak values in the
middle of the beam flange. As drift increases, the difference between the values in the surface
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layers (Layer 1 and Layer 5) becomes small near the edges of the beam flange while it does not
decrease much in the middle of the beam flange.
At 0.5-percent story drift, the values of Maximum Principal Index in Plane B (Figure
5-45a) are maximized at the top surface in the middle of the beam flange and minimized at the
bottom surface in the same location. The difference between the maximum and minimum values
is quite large, indicating the high local bending occurs in the middle beam flange. At 2-percent
story drift, the difference becomes small but the magnitude increases more than uniaxial yield
strength (Figure 5-45b). Significant portion of beam flange is subjected to tensile principal
stresses larger than the uniaxial tensile strength.
At 0.5-percent story drift, the values of Mises Index in Plane B (Figure 5-46a) are less
than the initial yield point in the von Mises yield surface while those at 2-percent story drift are
greater than the initial yield point (Figure 5-46b). Entire area of Plane B is subjected to yielding at
2-percent story drift.
At 0.5-percent story drift, the values of Pressure Index in Plane B (Figure 5-47a) are
maximized in the middle of the top surface (Layer 5). The distribution of Pressure Index in Plane
B at 2-percent story drift (Figure 5-47b) is similar to that of Maximum Principal Index at the
same drift since the distribution of Mises Index is constant due to yielding.
Figure 5-48 presents the distributions of Triaxiality Index (TI) across the width of the
beam flange at the toe of the weld access hole (Plane B) at story drifts of 0.5- and 2-percent. The
values of Triaxiality Index are maximized in the middle of the top surface (Layer 5) at both story
drift levels. The high triaxiality in this region is caused by the deformation restraint provided by
the beam web.
Figure 5-49 presents the distributions of Rupture Index (RI) across the width of the beam
flange at the face of the column (Plane B) at story drifts of 0.5- and 2-percent. No Rupture Index
is recorded at 0.5-percent story drift. At 2-percent story drift, the values of Rupture Index are
maximized in the middle of top flange surface (Layer 5).
127
Table 5-3 presents the summary of the response indices in Model SOL-EC01 at 0.5- and
2-percent story drift levels. The maximum values of Maximum Principal Index, Mises Index,
Pressure Index, Triaxiality Index, and Rupture Index at the column face (Plane A) are larger than
those at the toe of the weld access hole (Plane B). In the test specimen EC01, Plane A is the
location of CJP welds where E70T-4 electrodes were used. It is well known that the CJP welds
using E70T-4 electrodes have low fracture toughness (FEMA 2000a). Because the fracture
strength at Plane A is much lower than that at Plane B, and values of Maximum Principal Index
and Triaxiality Index are higher at Plane A than at Plane B, brittle crack propagation initiated at
the column face during the test. Two cracks at the edges of the beam were observed before flange
fractured (Figure 5-3). Since the values of Mises Index at these locations approach the yield point
at 0.5-percent story drift, and the values of Rupture Index are maximized at the same location, the
cracks developed at the edge of the beam flange are identified as ductile cracks (Kuwamura 1997).
Rapid crack propagation initiated from the crack in the middle of the beam flange. This crack
connected to the edge cracks at a later stage of its propagation. After the crack connected with
each other, the entire cross section of beam flange fractured.
Table 5-3: Maximum values of response indices in Model SOL-EC01
Column face (Plane A)
Toe of the weld access hole (Plane B)
Drift
MPI
MI
PI
TI
RI
MPI
MI
PI
TI
RI
0.5 %
1.42
1.13
-0.66
-0.75
0.002
1.24
0.99
-0.59
-0.61
0
2.0 %
1.66
1.23
-0.89
-0.75
0.22
1.55
1.23
-0.79
-0.64
0.19
Fracture indices of SOL-EC02
Figure 5-50, Figure 5-51, and Figure 5-52 present the distributions of Maximum Principal
Index, Mises Index, and Pressure Index, respectively, across the width of the beam flange at the
face of the column (Plane A) at story drifts of 0.5- and 2-percent. The distributions of Maximum
128
Principal Index, Mises Index, and Pressure Index on the bottom surface (Layer 1) at 0.5-percent
story drift are uniform, while those at 2-percent story drift form a wave along the width of the
beam flange. The difference between the largest value and the smallest value of each index value
is largest in the middle of the flange due to high local bending of the flange.
The values of Maximum Principal Index in Layer 1 at 0.5-percent story drift are close to
the uniaxial tensile strength (note that σu/σy = 1.39 for Specimen EC02). Maximum Principal
Index values in the bottom three layers (Layers 1, 2, and 3) at 2-percent story drift exceed the
uniaxial tensile strength. The values of Mises Index in Layer 1 at 0.5-percent story drift are close
to the uniaxial yield strength (σy) while Mises Index values in the other layers are less than σy.
The distribution of Mises Index at 2-percent story drift indicates that both edges of the flange
yield while the half of the flange thickness in the middle of the beam flange is still elastic. The
values of Pressure Index on Plane A in Model SOL-EC02 are higher than those on the same plane
in Model SOL-EC01 because the thicker column flange of Specimen EC02 restrains the
deformation of the beam flange at the interface.
Figure 5-53 presents the distribution of the Triaxiality Index across the width of the beam
flange at the face of the column (Plane A) at story drifts of 0.5- and 2-percent. The value of
Triaxiality Index is largest in the middle of the beam flange on the top surface (Layer 7). The
maximum value at this location is -2, which can results in brittle behavior (El-Tawil et al. 1998).
However such high value of Triaxiality Index does not automatically lead to brittle fracture. For
brittle fracture to occur, high principal stress as well as an initial crack is required at the location
of high triaxiality. As soon as a crack grows into the region of high triaxiality, crack propagation
will be brittle rather than ductile.
Figure 5-54 presents the distribution of Rupture Index across the width of the beam
flange at the face of the column (Plane A) at story drifts of 0.5- and 2-percent. Small yielding at
both corners of the edges of the beam flange occurs at 0.5-percent story drift. At 2-percent story
drift, the values of Rupture Index are maximized at both edges of the beam flange on the bottom
129
surface (Layer 1) but the magnitudes of those peaks are smaller than those in Model SOL-EC01.
This difference is related to the thickness of the beam flange: a thick beam flange reduces the
magnitude of Rupture Index.
Figure 5-55, Figure 5-56, Figure 5-57, Figure 5-58, and Figure 5-59 present the
distributions of Maximum Principal Index, Mises Index, Pressure Index, Triaxiality Index, and
Rupture Index, respectively, across the width of the beam flange at the toe of the weld access hole
(Plane B) at story drifts of 0.5- and 2-percent. Except the values of Mises Index at 0.5-percent
story drift, all the values of indices are maximized on the top surface in the middle of the beam
flange. The value of Mises Index at 0.5-percent story drift is largest on the bottom surface (Layer
1) at both edges of the beam flange.
Table 5-4 presents the summary of the response indices in Model SOL-EC02 at 0.5- and
2-percent story drift levels. The maximum values of Maximum Principal Index, Mises Index,
Pressure Index, Triaxiality Index, and Rupture Index at the column face (Plane A) are larger than
those at the toe of the weld access hole (Plane B). In the test specimen EC02, Plane A is the
location of CJP welds of E70T-4 electrodes having low toughness. Since the fracture resistance is
lower while the stress and stain demands are higher at Plane A than at Plane B, brittle fracture is
likely to occur at the column face of the beam flange.
Table 5-4: Maximum values of response indices in Model SOL-EC02
Column face (Plane A)
Toe of the weld access hole (Plane B)
Drift
MPI
MI
PI
TI
RI
MPI
MI
PI
TI
RI
0.5 %
1.35
1.01
-0.69
-2.01
0.005
0.94
0.93
-0.44
-0.60
0
2.0 %
1.65
1.17
-0.98
-1.49
0.16
1.58
1.16
-0.84
-0.73
0.15
130
Local response at fracture
The sizes of members and lengths of beams in Specimens EC01 and EC02 differed. Thus,
stress and strain states in these specimens at a given drift may not be the same making it difficult
to do a comparison. For the purpose of comparison between two specimens, story drift angles at
the first brittle fracture of each specimen are selected as the reference points. The fracture drift of
Specimen EC01 was 0.78-percent radian and that of Specimen EC02 was 0.59-percent radian.
Figure 5-60, Figure 5-61, and Figure 5-62 show the contours of Maximum Principal
Index, equivalent plastic strain, and Pressure Index of Specimen EC01, respectively, at the story
drift of 0.78-percent. The Maximum Principal Index is 1.53 (corresponding to 654 MPa or 94.8
ksi) at Point A, 1.48 (629 MPa or 91.2 ksi) at Point B, and 1.44 (614 MPa or 89.0 ksi) at Point C.
The equivalent plastic strain is 0.003 at Point A and 0.0054 at Point C. The equivalent plastic
strain in the beam flange edge (near Point B) ranges from 0.002 to 0.005, showing moderate
yielding. The Pressure Index is -0.75 (-319 MPa or -46.3 ksi) at Point D, -0.69 (-295 MPa or 42.8 ksi) at Point E, and -0.70 (-298 MPa or -43.2 ksi) at Point F. The values of Triaxiality Index
at those points (Points D, E, and F) are -0.70, -0.70, and -0.62, respectively, indicating that
triaxiality of the middle of beam flange is slightly higher than that at the beam edge.
The high values of the maximum principal stress at the extreme fiber of the beam flange
caused the cracks that had been developed before fracture: see Figure 5-3. Because both edges of
the beam flange yield while the center region of the beam flange is still elastic at the story drift of
0.78-percent radian, the cracks in both edges of the beam flange propagate in a ductile manner
(slow crack growth) while the crack in the beam flange center propagates in brittle fashion (rapid
crack growth without any energy dissipation).
Figure 5-63, Figure 5-64, and Figure 5-65 show the contours of Maximum Principal
Index, equivalent plastic strain, and Pressure Index of Specimen EC02, respectively, at the story
drift of 0.59-percent. Maximum Principal Index is 1.46 (corresponding to 546 MPa or 79.2 ksi) at
131
Point A, 1.43 (535 MPa or 77.6 ksi) at Point B, and 1.36 (507 MPa or 73.6 ksi) at Point C. The
equivalent plastic strain is 0.001 at Point A and 0.0034 at Point C. The Pressure Index is -0.81 (304 MPa or -44.1 ksi) at Point D, -0.70 (-261 MPa or -37.9 ksi) at Point E, and -0.66 (-247 MPa
or -35.9 ksi) at Point F. The values of Triaxiality Index at those points (Points D, E, and F) are 0.94, -0.75, and -0.66, respectively.
The values of Triaxiality Index in Model SOL-EC02 are higher than those in Model
SOL-EC01 while the values of Rupture Index in Model SOL-EC02 are smaller than those in
Model SOL-EC01. Thus cracks developed at the edges of the beam flange of Specimen EC02
propagate rapidly. The cracks could not been observed during the test because the interval from
nucleation to crack propagation was so short and the video image recorded at 33 frames per
second was not sufficiently fast to record brittle crack propagation. However, a metallic
“pinging” noise (Stojadinovic et al. 2000) coming from the specimen three seconds before flange
facture indicates formation of microcracks in the CJP weld. The maximum principal stress at the
expected crack location of Specimen EC02 is lower than that of Specimen EC01. Because the
same weld metal was used for both specimens, the level of the maximum principal stress might
be the same to develop microcracking. If the variance in material properties of both welds is
small, the difference of the maximum principal stress at fracture can be explained by the residual
stress caused by welding process (Dong and Zhang 1999). Because the volume of weld metal for
CJP weld in the Specimen EC02 is much larger than that in Specimen EC01, higher residual
stresses could exist in CJP welds of Specimen EC02. Such residual stress may elevate the level of
maximum principal stress in Specimen EC02 compared to that in Specimen EC01.
Evaluation of fracture strength
Finite element analysis using solid element model can be used to identify the location of
initial microcracking and direction of crack propagation as discussed in above. However such
models can not predict the critical size of the microcracks and the critical level of fracture stress
132
because exact material properties and crack geometry are unknown. To determine the fracture
strength of Specimen EC01, an inverse analysis procedure is used instead of the procedure
described in Section 2.2.4.
Figure 5-66 shows photographs taken before and after flange fracture in Specimen EC02
at 0.78-percent story drift. Before fracture, three cracks formed at both edges and center of the top
surface of the CJP weld joining the beam top flange and the column flange plate. The length of
the center crack (2c) was 108 mm (4.24 in.). The center crack propagated rapidly to the edge
cracks as shown Figure 5-66b.
Figure 5-67 presents the maximum principal stress vectors in the beam flange of Model
SOL-EC01 at 0.78-percent story drift. The fracture path observed during the test is inserted into
this figure. Because the weld end dam used in the reentrant corner between the side of the beam
flange and the column plate reinforced the beam flange near the column face, the crack in the
edges of the beam moved far from the column face. The direction of initial cracks and crack
propagation is perpendicular to that of the maximum principal stress vectors.
Initial crack size is determined from the measured crack length (2c) and the associated
maximum principal stress distribution as shown in Figure 5-68. The microcracking critical
Maximum Principal Index (MPIcr = σmax,f/σy ) can be determined from the contours in this figure
by reading the value of Maximum Principal Index at the edge of the crack. It is equal to 1.482
(corresponding to 631 MPa or 91.6 ksi). Crack depth a can be determined from the crossing point
of a contour line corresponding to the microcracking critical MPI (= 1.482) and it is found to be
2.35 mm (0.093 in.). The crack shape is assumed to be semi-elliptical with short radius equal to a
and long radius equal to c (Dong and Zhang 1999).
Numerical analysis using elements capable of modeling singularities can determine the
stress intensity factor, KI, in the crack tip by evaluating the J-integral. However, this procedure
requires a significant effort to model the crack. For this study, an analytical solution for semielliptical surface flaw is used to find the stress intensity factor. As long as the crack shape is
133
regular, the result from this analytical solution will apply. Figure 5-69 presents the model used to
find the stress intensity factor for a semi-elliptical surface flaw in a flat plate, in this figure, a ≤ c,
W is the half of the plate width, t is the plate thickness, and σm and σb is the applied stresses. The
stress intensity factor, KI, can be computed using equation:
=
K I (σ m + H σ b )
πa  a a a

F  , , ,φ 
Q t c W 
( 5-1 )
where, H is a correction factor for bending stress, Q is a shape factor, φ is angle from the surface
of the crack as shown and F is a function of the location along the crack tip. Details about each
factor used in this equation can be found in Anderson (1995).
The membrane stress, σm, and the bending stress, σb, are computed from the normal stress
(σ11) distribution on the interface of the beam flange and the column flange computed using a
finite element model as shown in Figure 5-70.
Figure 5-71 presents the solution of stress intensity factors along the crack tip. The value
of stress intensity factor (KI) is maximized at Point B on the crack tip as shown in Figure 5-69
and it is 53.9 ksi/in1/2. The minimum value of KI is 18.3 ksi/in1/2 and it is located at Points A and
C on the crack tip. Chi et al. (2000) reported that the fracture toughness, KIc, of E70T-4 weld
metal ranges between 40 and 60 ksi/in1/2. Therefore brittle fracture of this weld occurred due to
the low toughness of weld metal. If high toughness weld metals e.g. E70TG-K2 with KIc = 105 ~
160 ksi/in1/2 (Chi et al. 2000) were used, brittle fracture is postponed and may be avoided
(Barsom and Pellegrino 2002). Thus, connection rotation capacity can be increased.
CJP welds for continuity plates
The box columns of Specimens EC01 and EC02 are built-up sections, which are
fabricated by welding the component plates. Partial joint penetration (PJP) welds were used to
join the column plates. Interior continuity plates were joined to the column plates by CJP welds.
In contrast to a W-shape column, forces in the box column are transmitted through the CJP welds
134
of the continuity plates and the PJP welds of the column plates. Thus, it is possible for a weld to
fracture if the applied stress is high while the fracture toughness of the weld metal is low.
Figure 5-72 shows the distribution of maximum principal stress vectors in the box
column of Model SOL-EC01 at 2-percent story drift. Most of flange forces are transmitted
through the CJP welds joining the continuity plate and the column flange. The transmitted forces
are distributed along the depth of the column side plates. The distribution of Maximum Principal
Index along Section A in Figure 5-72 is shown in Figure 5-73. The largest value of Maximum
Principal Index on the interface between the CJP weld and the column flange plate is 1.21, which
is less than the microcracking critical Maximum Principal Index 1.482. Thus, microcracking may
not occur in the CJP weld at this story drift.
5.3.3 Post-fracture connection stiffness
Flange fracture affects connection stiffness as well as connection strength. Figure 5-74
and Figure 5-75 present a classification of the connection stiffness (AISC 2001). Momentrotation curves from each test and numerical simulations are also plotted in these figures.
Moments are computed at a column centerline and normalized by beam stiffness (Kb =
EIbeam/Lfloor), where Lfloor is a floor span and it is twice of the beam span in a connection subassemblage. The ratio of connection stiffness to beam stiffness was defined as α = KsLfloor/EIbeam
in AISC LRFD Manual (AISC 2001), where Ks is a secant stiffness of a connection for the
serviceability limit state. It is reasonable to classify connection as fully restrained when α > 20
while to classify it as simple when α < 2 (AISC 2001; Leon 1994). Because the relative end
transverse displacement stiffness of a fixed beam is 4 times larger (12EI/L3) than that of a
cantilever beam (3EI/L3), a correction factor, 4, is applied for the connection sub-assemblage in
this study. Nominal beam plastic moments are also shown in those figures.
Before flange fracture, the connection stiffness ratio (4α) is 11 in Specimen EC01 and 18
in Specimen EC02. Considering the AISC LRFD criterion does not include the effects of column
135
deformation, Specimen EC02 should be regarded as a fully-restrained (FR) connection. Specimen
EC01 will be classified as a partially-restrained (PR) connection following the above criterion but
it is close to a fully-restrained connection. After flange fracture, connection stiffness ratio ranges
from 2 to 7 in Specimen EC01 and is approximately equal to 2 in Specimen EC02. Therefore, the
connection should be considered as simple connections following the above criterion.
The bending stiffness of column flange affects the pre-fracture connection stiffness while
it does not influence the post-fracture connection stiffness because the stiffness of the flangefractured connection is much smaller than that of the column flange plate.
5.3.4 Column shape
Figure 5-76, Figure 5-77, and Figure 5-78 show the distribution of the maximum
principal stress vectors on the top continuity plate in Models SH-EC01, WF-CN14, and SH-EC02,
respectively, at 2-percent story drift. In box column connections, most of the beam flange forces
are transmitted to the column side plates through the continuity plate (Models SH-EC01 and SHEC02). In W-shape column connections, most of the beam flange forces are transmitted to the
column web (Model WF-CN14). When the ratio of the column flange and the beam flange widths
is small, the forces are transmitted to the corner of the box column (Model SH-EC02). When the
ratio is large (i.e. column is wider than the beam) the forces in the continuity plates are uniformly
distributed along the depth of column side plate (Model SH-EC01).
5.3.5 Continuity plate strength
Because the continuity plates transmit the beam flange force to the column, it affects the
global response as well as the local response of the box column connection. The effect of
continuity plate strength is studied by comparing the response of five identical models with
different thickness of the continuity plate. Figure 5-79 presents the relationships between moment
at the column face versus story drift angle in Models SH-EC01, BX-CP00, BX-CP05, BX-CP07,
136
and BX-CP10. Moments are normalized using the nominal plastic moment of the beam. The
difference between the global responses in Models SH-EC01 and BX-CP10 is negligible. For the
connection models with thin continuity plates (Models BX-CP05 and BX-CP07), global response
depends on the thickness of the continuity plate. As the thickness of the continuity plate decreases,
the resistance of the connection also decreases. The maximum resistance of the connection
without continuity plates (BX-CP00) is only 58-percent of peak resistance in Model SH-EC01.
Global response of a W-shape column connection is substantially different from the
response of a box column connection because of the force transfer mechanism in the continuity
plate. Figure 5-80 presents the relationships between moment at the column face versus story drift
angle in W-shape column connections, Models WF-CP14, WF-CP05, and WF-CP00. The
response in Model SH-EC01 is also plotted for the purpose of comparison. Moments are
normalized using the nominal plastic moment of the beam. Global responses of W-shape column
connection models are not affected by the thickness of the continuity plate.
The beam moment-couple tension force in the top flange transmitted to the continuity
plates can cause the plates to yield when the plate thickness is small compared to the beam flange
thickness. Figure 5-81 and Figure 5-82 present the distributions of equivalent plastic strain in the
top continuity plate and the top beam flange in Model BX-CP07 and Model BX-CP10,
respectively, at 3-percent story drift. The beam top flange is in tension while the bottom flange is
in compression as described in Section 4.3. The maximum value of PEEQ in the continuity plate
in Model BX-CP07 is 50 percent larger than that in Model BX-CP10 while yielded area in the
beam flange in Model BX-CP07 is smaller than that in Model BX-CP10. Note that PEEQ
indicates that degree of plastic strain. Thus, when the thickness of the continuity plate is smaller
than the beam flange thickness, plastic hinge will occur not only in the beam flange but also in
the continuity plate.
The compressed flange force transmitted to the bottom continuity plate can also cause the
plate to yield in compression. As discussed in Chapter 2, when the yielded area of the plate is
137
large enough to accommodate a buckling wave length, plate local buckling will occur. Figure
5-83 and Figure 5-84 show views of deformed shapes of bottom continuity plates in Model BXCP07 and Model BX-CP10, respectively, at 3-percent story drift. The distribution of equivalent
plastic strain on the continuity plate, beam bottom flange, beam web, and column web plate are
also shown in these figures. The beam flange and continuity plate are in compression. The
column web plate and flange plate near the beam are removed in this figure for the better view of
the continuity plate inside the box column. Local buckling of the continuity plate in Model BXCP07 is clearly shown in Figure 5-83 while such buckling does not occur in the continuity plate
in Model BX-CP10. Instead beam flange local buckling occurs in Model BX-CP10 as shown in
Figure 5-84. For a box column connection with thin continuity plates, beam flange local buckling
may not occur due to plate buckling.
Yielding and local buckling of the continuity plate are possible causes of strength loss in
Models BX-CP05 and BX-CP07 (see Figure 5-79). Another serious consequence of continuity
plate buckling is that such damage occurs inside the box column and, thus, cannot be easily
inspected and repaired (Chen et al. 1991). Therefore, thickness of continuity plates should be
large enough to prevent both yielding and local buckling.
5.3.6 Column flange stiffness
Yielding and local buckling of continuity plates in box column connection reduce the inplane stiffness of the continuity plate. In consequence, a significant portion of the beam flange
force will be transmitted to the column web plate through the column flange plate facing the
beam. If the continuity plate stiffness reduces significantly, the response of the box column
connection will be similar to that of the box column connection without a continuity plate.
Furthermore, a box column connection without continuity plate is preferred by many engineers
because it can save the efforts to fabricate the continuity plates. The strength of such connection
138
depends on the out-of-plane stiffness and flexural strength of the column flange plate connected
to the beam.
Figure 5-85 and Figure 5-86 show deformed shapes in Model BX-CP00 at 3-percent
story drift. The contour of equivalent plastic strains is also shown in Figure 5-85. Yielding of the
beam flange is confined in the small region at the column face. An angle of beam flange rotation,
θflange, is defined by dividing the relative displacement of two reference points, one on each beam
flange, by the beam depth as shown in Figure 5-86. This angle indicates the degree of column
flange plate rotation. To find the precise rotation due to out-of-plane movement of the column
flange plate, column rotation due to column bending and panel zone deformation should be
excluded. However, the magnitude of the excluded rotation is so small compared to θflange that it is
not considered in this comparison study. Another definition, beam web rotation, θweb, is made to
consider the local deformation of the column flange plate as shown in Figure 5-87.
Figure 5-88 and Figure 5-89 the relationships between beam flange rotation angle versus
story drift angle in Models SH-EC01, BX-CP07, BX-CP00, and WF-CP14. Beam flange rotation
in Model BX-CP00 is the same as the story drift, indicating that rotation in the box column
connection is primarily due to column flange deformation. If the continuity plate is used, the
beam flange rotation changes depending on the in-plane stiffness of the continuity plate. When a
thick continuity plate is used, the beam flange rotation becomes small as that in the W-shape
column connection (Model WF-CP14). Local bending of the column plate causes the beam web
rotation. Beam flange rotations in the box column connections affect the global responses in the
connections while the beam web rotations in the connections are identical as shown in Figure
5-89. Large rotations in the beam web indicate that flexural forces carried by the beam web are
insignificant while most flexural forces are transmitted through the beam flanges.
Beam flange rotation and web rotation and global response in the box column connection
are affected by the out-of-plane stiffness of the column flange (JSSC 1997). Figure 5-90, Figure
5-91, and Figure 5-92 present the relationships between moment at the column face, beam flange
139
rotation angle, and beam web rotation angle, respectively, versus story drift angle in Models SHEC01, BX-CF08, BX-CF20, and WF-CP14. Moments are normalized using the nominal plastic
moment of the beam. A thicker column flange plate (in Model BX-CP20) increases the moment
resistance while it reduces the beam flange and web rotations comparable to those in W-shape
column connections (Model WF-CP14). In contrast, a thin column flange plate (in Model BXCP08) decreases the moment resistance while it increases the beam flange and web rotations.
In Models WF-CP14 and BX-CF20, peak moment resistance is reached at between 2- and
2.5-percent story drift, followed by its rapid deterioration due to flange and web local buckling. In
contrast, the peak resistance in Model SH-EC01 is reached at the drift larger than 3-percent and
the post-peak connection strength degradation rate is markedly slower. However such strength
degradation is not observed in Model BX-CF08. As discussed in Chapter 2, rapid strength
degradation of the moment resistance in W-shape column connections is usually related to the
amplitude of beam flange local buckling as well as web local buckling and lateral torsional
buckling. However, web local buckling is affected by the stiffness of the web support. Because
the location of column side plates, column plates in box column connections are more flexible
than that of column flange in W-shape column connections. Such support flexibility leads to a
redistribution of beam stresses from the web to the flange. Reduction of web stresses results in a
delay of web local buckling and less yielding of the web. Instead, flange local buckling occurs
without web instability, and the assumption that the beam web near the column is fully yielded
can not be applied to box column connections.
Figure 5-93 and Figure 5-94 show PEEQ contours at 3-percent story drift level for the
box column connection (Model SH-EC01) and the W-shape column connection (Model WFCP14), respectively. Column plate yields in the vicinity of the beam weld access hole in the box
column connection. In contrast, the column flange of the W-shape column connection does not
yield. Consequently, the plastic hinge in a box column connection forms partially inside the box
column, moving the theoretical center of rotation of the beam closer to the column, compared to
140
W-shape column connections in which the beam plastic hinge is confined to the beam. More
importantly, local yielding of the column can cause a weak-column-strong-beam condition
(Anderson and Lindermann 1991; Chen and Chen 1993).
Out-of-plane bending of the plate of the box column facing the beam causes strength loss
in the connection and may lead to tearing of column plate. Many researchers have focused on
developing methods to determine the column plate thickness needed to prevent yielding (Chen
and Chen 1993). Yield line analysis proposed by Blodgett (1966) is the major starting point of
these studies (Anderson and Linderman 1991; Mortia et al 1989, 1998; Yamamoto et al. 1989).
Further investigation is needed to verify the effectiveness of these methods under cyclic
connection loading.
5.3.7 Bi-axial loading
In the US design practice, box sections are used when two orthogonal moment-resisting
frames share a corner column (Tsai and Popov 1993). To investigate the performance of a box
column connection under bi-axial loading, a model with two beams connected to perpendicular
column sides was made (Figure 5-95). In contrast to uniaxial loading, several combinations of
uniaxial loading protocols are possible in the bi-axial loading case. A realistic loading protocol
should be determined from the global response demand analysis of target structure (MacRae and
Tagawa 2001). A conservative combination loading protocol is used in this study: that is, the
amplitude and direction of loadings for each of the beams are the same.
Figure 5-96 and Figure 5-97 show contours of normal stress (σ22) along the inner face
(negative direction of the normal vector of shell elements: see below) of the column plate in
Model BX-CP05 and Model BX-BI05, respectively, at 3-percent story drift. Stresses are
normalized using yield strength of the beam flange. Note that local coordinates for column plates
are defined such that 1-direction coincides with the longitudinal axis of the column, the 3direction coincides with the normal vector toward the outside of the box column, and the 2141
direction is defined by the right-hand-screw rule and is parallel to the longitudinal axis of each
beam. High tensile stresses exist in the corner of box columns near the beam. The magnitudes of
the stresses in each model are similar while the distributions of the stresses are quite different.
Under uniaxial loading, the normal stresses are concentrated in the small region of the column
web plate near the corner of the box column. Under biaxial loading, the stresses are uniformly
distributed along the corner.
Figure 5-98 presents the distribution of maximum principal stress vectors on the top
continuity plate in Model BX-BI05 at 3-percent story drift. The distribution in the corner of the
plate (Region A) is quite different from that for uniaxial loading: see Figure 5-76.
Figure 5-99 shows the normal stress (σ22) distribution along the line A-B at interface
between the edge of the column plate and the PJP welds in Models SH-EC01, BX-CP05, and BXBI05 at 3-percent story drift. This corner undergoes local bending. Due to the bi-axial loading, the
tensile stress at Point A in Model BX-BI05 is higher than that in Model BX-CP05. As the
thickness of the continuity plate increases, the level of the stress at Points A and B drops
dramatically as in Model SH-EC01. A large in-plane stiffness of the continuity plate can prevent
excessive deformation and local bending of the corner of the box column.
5.4 Design Guidelines for Box Column Connections
This section outlines design and upgrade guidelines for welded steel moment connections
to box columns with internal continuity plates. These preliminary design and upgrade guidelines
are based on the results of experimental and analytical investigations presented in this study. Thus,
these guidelines may not be applicable to the connection comprising member size and materials
other than the ones used in tests conducted in this study. Design guidelines for fully restrained
(FR) moment connection specification in FEMA-350 documents (FEMA 2000a) and AISC
Seismic Provisions (AISC 2002) take precedence over these recommendations. The following
142
two subsections provide additional guidelines for design and joining of continuity plates and
column plates, respectively. The remainder of this section discusses upgrading design strategy for
pre-Northridge box column connections.
5.4.1 Continuity plate design
The column continuity plates should be designed to remain linearly elastic for the stress
demands from the connected beam flanges. The thickness of the continuity plate tcp should be no
less than that of the largest flange thickness of the beams connected to the column tbf,max:
tcp ≥ tbf ,max
( 5-2 )
The continuity plates shall be welded to the column plates where frame girders are
connected using CJP welds. Weld metal meeting FEMA-350 requirements for notch toughness
shall be used for these CJP welds.
5.4.2 Column plate design
Frame design governs the size of the column cross section. The goal of such design is to
achieve strong-column-weak-beam frame response. FEMA-350 guidelines regarding relative
beam and column strength at the connection should be followed.
The effect of column plate flexibility on the column stiffness and on the local responses
in the connection should be considered. Thin column plate may yield and deform excessively
under the force transmitted from the beam web. It is assumed that continuity plates exist such that
all of the beam flange force is transmitted directly to such plates. More research is needed to
establish a design method for determining adequate column plate thickness.
The column plates shall be joined by CJP or PJP welds. When the PJP welds are used, a
minimum 8 mm (5/16 in.) supplement fillet welds reinforcing the unfused root of the PJP welds
shall be used in the reentrant corner in the box column, at least the half of column cross section
depth above and below the beam. Weld metal used to weld the column cross section must satisfy
143
the notch toughness requirements specified in FEMA-350 document (FEMA 2000a) and AISC
Seismic Provisions (AISC 2002).
5.4.3 Connection upgrade
Welded Unreinforced Flange-Welded Web, Reduced Beam Section, and Cover Plate
connection may be used for the box column connection upgrade. Use of external reinforcing
diaphragms at the level of column continuity plates should be considered (Tsai et al. 1992;
Shanmugam and Ting 1995; Tanaka 2003).
For box column connections, flexibility of the column flange governs the choice of
connection upgrade design. If column flange plate is flexible, connection that results in
substantial force transfer in the plane of the beam web (such as Hunch and Free Flange
connections) should not be used.
144
Figure 5-1: Beam top flange yield during the 0.75-percent drift cycle: Specimen EC01
Figure 5-2: Beam bottom flange yield during the 0.75-percent drift cycle: Specimen EC01
145
Figure 5-3: Crack in CJP weld of beam top flange: Specimen EC01
Weld end dam
Figure 5-4: Beam top flange fracture during the 1-percent drift cycle: Specimen EC01
146
Figure 5-5: Fracture surface of beam top flange: Specimen EC01
Figure 5-6: Fracture of shear tab fillet weld: Specimen EC01
147
Gap between the
backing bar and
flange
High local strain
demand
Figure 5-7: Gap under the backing bar during the 1-percent drift cycle: Specimen EC01
Figure 5-8: Beam bottom flange fracture during the second 1-percent drift cycle: Specimen EC01
148
Figure 5-9: Fracture surface of beam bottom flange: Specimen EC01
Figure 5-10: Shear tab tearing after beam bottom flange fracture: Specimen EC01
149
Figure 5-11: Shear tab fracture during the 4-percent drift cycle: Specimen EC01
Figure 5-12: Complete separation of the shear tab: Specimen EC01
150
Moment at the column face (×1000 k-in)
40
30
Top flange fracture
20
Shear tab failure
10
0
Bottom flange
fracture
-10
-20
Gap between backing bar and bottom flange
-30
-40
-5
-4
-3
0
1
2
-2
-1
Story drift ange (% radian)
3
4
5
Figure 5-13: Moment at the column face versus story drift angle for Specimen EC01
Moment at the column face (×1000 k-in)
40
30
20
10
0
-10
-20
-30
-40
-5
-4
-3
-2
-1
0
1
2
3
Panel zone plastic rotation (% radian)
4
5
Figure 5-14: Moment at the column face versus panel zone plastic rotation for Specimen EC01
151
1
0.375% drift
0.500% drift
Nomalized distance from beam web
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.2
0.4
0.6
0.8
1
1.2
Normalized peak strain profile on top flange (ε /ε y)
1.4
Figure 5-15: Beam top flange tensile strain profiles: Specimen EC01
Nomalized distance from beam mid-depth
1
0.375% drift
0.500% drift
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.2
0.4
0.6
0.8
1
1.2
Normalized peak shear strain profile in web (γ/γy)
Figure 5-16: Beam web shear strain profiles: Specimen EC01
152
1.4
Figure 5-17: Whitewash flaking during the 0.375-percent drift cycle: Specimen EC02
Figure 5-18: Beam top flange fracture during the 0.75-percent drift cycle: Specimen EC02
153
Figure 5-19: Fracture surface of beam top flange: Specimen EC02
Figure 5-20: Beam bottom flange fracture during the 0.75-percent drift cycle: Specimen EC02
154
Figure 5-21: Fracture surface of beam bottom flange: Specimen EC02
Figure 5-22: Shear tab tearing during 2-percent drift cycle: Specimen EC02
155
Figure 5-23: Shear tab deformation during the 2-percent drift cycle: Specimen EC02
Figure 5-24: Shear tab fracture during the 3-percent drift cycle: Specimen EC02
156
40
Moment at the column face (×1000 k-in)
Top flange fracture
30
20
Shear tab failure
10
0
-10
-20
-30
-40
-5
Bottom flange fracture
-4
-3
0
1
2
-2
-1
Story drift angle (% radian)
3
4
5
Figure 5-25: Moment at the column face versus story drift angle for Specimen EC02
Moment at the column face (×1000 k-in)
40
30
20
10
0
-10
-20
-30
-40
-5
-4
-3
-2
-1
0
1
2
Panel zone plastic rotation (% rad)
3
4
5
Figure 5-26: Moment at the column face versus panel zone plastic rotation for Specimen EC02
157
1
0.375% drift
0.500% drift
Nomalized distance from beam web
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.2
0.4
0.6
0.8
1
1.2
Normalized peak strain profile on top flange (ε /ε y)
1.4
Figure 5-27: Beam top flange tensile strain profiles: Specimen EC02
Nomalized distance from beam mid-depth
1
0.375% drift
0.500% drift
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.2
0.4
0.6
0.8
1
1.2
Normalized peak shear strain profile in web (γ/γy)
Figure 5-28: Beam web shear strain profiles: Specimen EC02
158
1.4
Moment at the column face (×1000 k-in)
60
Analysis
Experiment
50
40
30
20
10
0
0
0.5
1
1.5
2
2.5
3
3.5
Story drift angle (% radian)
4
4.5
5
Figure 5-29: Moment-drift relations for analysis and experiment in Model SH-EC01 and
Specimen EC01
Moment at the column face (×1000 k-in)
60
Analysis
Experiment
50
40
30
20
10
0
0
0.5
1
1.5
2
2.5
3
3.5
Story drift angle (% radian)
4
4.5
5
Figure 5-30: Moment-drift relations for analysis and experiment in Model SH-EC02 and
Specimen EC02
159
Column
Beam
(ksi)
z
y
x
Figure 5-31: Von Mises stress distribution in the panel zone and the beam web at the 0.5-percent
drift in Model SH-EC01
Column
Beam
(ksi)
z
y
x
Figure 5-32: Von Mises stress distribution in the panel zone and the beam web at the 0.5-percent
drift in Model SH-EC02
160
(ksi)
Column
Beam
z
y
x
Figure 5-33: Axial stress distribution along the top continuity plate and the beam top flange at the
0.5-percent drift in Model SH-EC01
(ksi)
Column
Beam
z
y
x
Figure 5-34: Axial stress distribution along the top continuity plate and beam top flange at the
0.5-percent drift in Model SH-EC02
161
0
25
180
Unit: mm
460
Beam
Line D
Line C
Line A
Line B
Column
Figure 5-35: Data report line on the beam top flange and the beam web
162
1
0.8
Line
Line
Line
Line
A
B
C
D
Line
Line
Line
Line
A
B
C
D
Line
Line
Line
Line
A
B
C
D
0.6
0.4
0.2
0
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
a. Mises Index
-0.5
-0.4
-0.3
-0.2
-0.1
0
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
b. Pressure Index
-0.5
-0.4
-0.3
-0.2
-0.1
0
-1
-0.8 -0.6 -0.4 -0.2
0
0.2 0.4 0.6 0.8
Normalized distance from beam web centerline
1
c. Triaxiality Index
Figure 5-36: Stress and fracture indices along the upper surface of beam top flange at the 0.5percent story drift in Model SH-EC01
163
1
0.8
Line
Line
Line
Line
A
B
C
D
Line
Line
Line
Line
A
B
C
D
Line
Line
Line
Line
A
B
C
D
0.6
0.4
0.2
0
-1
0.2
0
-0.8 -0.6 -0.4 -0.2
a. Mises Index
0.4
0.6
0.8
1
-0.5
-0.4
-0.3
-0.2
-0.1
0
-1
0.2 0.4
0
-0.8 -0.6 -0.4 -0.2
b. Pressure Index
0.6
0.8
1
-0.5
-0.4
-0.3
-0.2
-0.1
0
-1
0.2 0.4 0.6 0.8
0
-0.8 -0.6 -0.4 -0.2
Normalized distance from beam web centerline
1
c. Triaxiality Index
Figure 5-37: Stress and fracture indices along the upper surface of beam top flange at the 0.5percent story drift in Model SH-EC02
`
164
tcp
Column shape
tcf
Bi-axial
loading
Figure 5-38: Design variables of box column connections
Layer 5
Layer 4
Layer 3
Layer 2
Layer 1
Plane A
Plane B
Figure 5-39: Data report planes for response indices
165
1.6
1.6
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0.5
0
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-40: Maximum Principal Index in SOL-EC01 beam flange at column face, Plane A
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0.5
0
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-41: Mises Index in SOL-EC01 beam flange at column face, Plane A
166
-1
-1
-0.8
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
-0.8
-0.6
-0.6
-0.4
-0.4
-0.2
-0.2
0
0
-0.5
0.5
0
Normalized distance, y/bf
-0.5
(a) 0.5% drift
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-42: Pressure Index in SOL-EC01 beam flange at column face, Plane A
-2
-2
-1.5
-1.5
-1
-1
-0.5
-0.5
0
0
-0.5
0.5
0
Normalized distance, y/bf
-0.5
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-43: Triaxiality Index in SOL-EC01 beam flange at column face, Plane A
167
0.2
0.15
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
0.2
0.15
0.1
0.1
0.05
0.05
0
-0.5
0
-0.5
0.5
0
Normalized distance, y/bf
(a) 0.5% drift
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-44: Rupture Index in SOL-EC01 beam flange at column face, Plane A
1.6
1.6
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0
0.5
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
0
0.5
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-45: Maximum Principal Index in SOL-EC01 beam flange at weld access hole, Plane B
168
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0.5
0
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-46: Mises Index in SOL-EC01 beam flange at weld access hole, Plane B
-1
-0.8
-1
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
-0.8
-0.6
-0.6
-0.4
-0.4
-0.2
-0.2
0
0
-0.5
0.5
0
Normalized distance, y/bf
-0.5
(a) 0.5% drift
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-47: Pressure Index in SOL-EC01 beam flange at weld access hole, Plane B
169
-2
-2
-1.5
-1.5
-1
-1
-0.5
-0.5
0
0
-0.5
0.5
0
Normalized distance, y/bf
-0.5
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-48: Triaxiality Index in SOL-EC01 beam flange at weld access hole, Plane B
0.2
0.15
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
0.2
0.15
0.1
0.1
0.05
0.05
0
-0.5
0
-0.5
0
0.5
Normalized distance, y/bf
(a) 0.5% drift
0
0.5
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-49: Rupture Index in SOL-EC01 beam flange at weld access hole, Plane B
170
1.6
1.6
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0.5
0
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-50: Maximum Principal Index in SOL-EC02 beam flange at column face, Plane A
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0
0.5
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0
0.5
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-51: Mises Index in SOL-EC02 beam flange at column face, Plane A
171
-1
-1
-0.8
-0.8
-0.6
-0.6
-0.4
-0.4
-0.2
-0.2
0
0
-0.5
0.5
0
Normalized distance, y/bf
-0.5
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-52: Pressure Index in SOL-EC02 beam flange at column face, Plane A
-2
-2
-1.5
-1.5
-1
-1
-0.5
-0.5
0
0
-0.5
0.5
0
Normalized distance, y/bf
-0.5
(a) 0.5% drift
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-53: Triaxiality Index in SOL-EC02 beam flange at column face, Plane A
172
0.2
0.15
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.2
0.15
0.1
0.1
0.05
0.05
0
-0.5
0
-0.5
0.5
0
Normalized distance, y/bf
(a) 0.5% drift
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-54: Rupture Index in SOL-EC02 beam flange at column face, Plane A
1.6
1.6
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0
0.5
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0
0.5
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-55: Maximum Principal Index in SOL-EC02 beam flange at weld access hole, Plane B
173
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0.5
0
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-56: Mises Index in SOL-EC02 beam flange at weld access hole, Plane B
-1
-0.8
-0.6
-1
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
-0.8
-0.6
-0.4
-0.4
-0.2
-0.2
0
0
-0.5
0
0.5
Normalized distance, y/bf
-0.5
(a) 0.5% drift
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-57: Pressure Index in SOL-EC02 beam flange at weld access hole, Plane B
174
-2
-2
-1.5
-1.5
-1
-1
-0.5
-0.5
0
0
-0.5
0.5
0
Normalized distance, y/bf
-0.5
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-58: Triaxiality Index in SOL-EC02 beam flange at weld access hole, Plane B
0.2
0.15
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.2
0.15
0.1
0.1
0.05
0.05
0
-0.5
0
-0.5
0
0.5
Normalized distance, y/bf
(a) 0.5% drift
0
0.5
Normalized distance, y/bf
(b) 2.0% drift
Figure 5-59: Rupture Index in SOL-EC02 beam flange at weld access hole, Plane B
175
C
B
A
Figure 5-60: Normalized maximum principal stress (MPI) distribution on the interface of the
beam flange in Model SOL-EC01 at 0.78-percent drift
C
A
Figure 5-61: Equivalent plastic strain (PEEQ) distribution on the interface of the beam flange in
Model SOL-EC01 at 0.78-percent drift
176
F
E
D
Figure 5-62: Normalized hydrostatic stress (PI) distribution on the interface of the beam flange in
Model SOL-EC01 at 0.78-percent drift
C
B
A
Figure 5-63: Normalized maximum principal stress (MPI) distribution on the interface of the
beam flange in Model SOL-EC02 at 0.59-percent drift
177
C
A
Figure 5-64: Equivalent plastic strain (PEEQ) distribution on the interface of the beam flange in
Model SOL-EC02 at 0.59-percent drift
F
E
D
Figure 5-65: Normalized hydrostatic stress (PI) distribution on the interface of the beam flange in
Model SOL-EC02 at 0.59-percent drift
178
Weld end dam
Edge cracks
Center crack
2c
Crack propagation
Top surface of
beam top flange
Column
flange
(a) Before fracture
(b) After fracture
Figure 5-66: Microcracking and crack propagation in the CJP welds for the top beam flange in
Specimen EC01 at 0.78-percent drift
Symmetric plane
Beam web
Center crack
Beam flange
Box column
Edge crack
Fracture path
Weld end dam
Figure 5-67: Principal stress vectors and fracture path on the bottom surface elements in the beam
flange in Model SOL-EC01 at 0.78-percent drift
179
(MPI)
Beam web
Beam flange
W = bf /2
t = tbf
Beam web centerline
a
c
2c = measured crack length
a = computed crack depth
bf = beam flange width
tbf = beam flange thickness
Figure 5-68: Maximum Principal Index and initial crack size in CJP welds of Specimen EC01 at
0.78-percent drift
σm
σb
σm = Membrane (tensile) stress
σb = Bending stress
=
σb
Mt
=
, where I
2I
Wt 3
6
a
2c
B
t
2W
t
φ
C
2c
a
A
Figure 5-69: Model of stress intensity solution for a semi-elliptical surface flaw in a flat plate for
a ≤ c (Anderson 1995)
180
σ11/ σy
σ11/ σy
Bottom surface of beam flange
y/bf
Beam web
Top surface of beam flange
z/tbf
Figure 5-70: Normal stress (σ11/ σy) distribution on the interface of the beam flange in Model
SOL-EC01 at 0.78-percent drift
60
B
Stress intensity factor, K I (ksi/in1/2 )
50
KIc for E70T-4
weld metal
(Chi et al. 2000)
40
30
20
C
A
10
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Angle from the surface, φ/π
0.8
0.9
1
Figure 5-71: Stress intensity solution for brittle fracture of CJP welds in Specimen EC01
181
Column flange plate
CJP weld
Center line
A
Beam web
Beam flange
Continuity plate
Cope hole
Column web plate
PP weld
Figure 5-72: Maximum principal stress vectors in the box column section and its continuity plate
at 2-percent drift: SOL-EC01
Column side plate
PP weld
Column flange plate
Continuity plate
Cope hole
Figure 5-73: Distribution of Maximum Principal Index in the CJP weld between the continuity
plate and the column side plate in Model SOL-EC01 at 2-percent drift
182
25
20
Model SH-EC01
Specimen EC01
FR
PR
4MLfloor/EIbeam (%)
15
10
5
Simple
0
-5
Simple
-10
4 M p ,beam L floor
-15
PR
-20
-25
-4
-3
FR
-2
(%)
EI beam
1
0
-1
Story drift angle (% radian)
4
3
2
Figure 5-74: Connection stiffness in Specimen EC01
25
20
Model SH-EC02
Specimen EC02
FR
4MLfloor/EIbeam (%)
15
PR
10
5
Simple
0
-5
Simple
4 M p ,beam L floor
-10
(%)
EI beam
PR
-15
-20
-25
-4
FR
-3
-2
-1
0
1
Story drift angle (% radian)
2
Figure 5-75: Connection stiffness in Specimen EC02
183
3
4
Box column (BC18×18×257)
Beam top flange (W33×118)
Figure 5-76: Maximum principal stress vectors in the top continuity plate at 2-percent drift:
Model SH-EC01
W-shape column (W14×257)
Beam top flange (W33×118)
Figure 5-77: Maximum principal stress vectors in the top continuity plate at 2-percent drift:
Model WF-CN14
184
Box column (BC31.5×13×464)
Beam top flange (W36×232)
Figure 5-78: Maximum principal stress vectors in the top continuity plate at 2-percent drift:
Model SH-EC02
185
1.4
Moment at the column face (M col/Mp )
1.2
1
0.8
0.6
SH-EC01 (tcp = 1.35 tbf)
BX-CP00 (tcp = 0)
BX-CP05 (tcp = 0.5 tbf)
BX-CP07 (tcp = 0.625 tbf)
BX-CP10 (tcp = 1.0 tbf)
0.4
0.2
0
0
0.5
1
1.5
3.5
3
2.5
2
Story drift angle (% radian)
4
4.5
5
Figure 5-79: Comparison of global responses in Models SH-EC01, BX-CP00, BX-CP05, BXCP07, and BX-CP10
1.4
Moment at the column face (M col/Mp )
1.2
1
0.8
0.6
0.4
WF-CP14 (tcp = 1.35 tbf)
WF-CP05 (tcp = 0.5 tbf)
WF-CP00 (tcp = 0)
SH-EC01 (tcp = 1.35 tbf)
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
Story drift angle (% radian)
4
4.5
5
Figure 5-80: Comparison of global responses in Models WF-CP14, WF-CP05, WF-CP00, and
SH-EC01
186
Box column (BC18×18×257)
Beam top flange (W33×118)
Continuity plate (tcp = 0.625 tbf)
Figure 5-81: Equivalent plastic strain distribution in the continuity plate and beam top flange in
Model BX-CP07 at 3-percent drift
Box column (BC18×18×257)
Beam top flange (W33×118)
Continuity plate (tcp = 1.0 tbf)
Figure 5-82: Equivalent plastic strain distribution in the continuity plate and beam top flange in
Model BX-CP10 at 3-percent drift
187
Continuity plate
local buckling
Beam web
Beam bottom flange
Box column (BC18×18×257)
Figure 5-83: Equivalent plastic strain distribution in the continuity plate and beam bottom flange
in Model BX-CP07 at 3-percent drift
Beam flange
local buckling
Beam web
Beam bottom flange
Box column (BC18×18×257)
Figure 5-84: Equivalent plastic strain distribution on the continuity plate and beam bottom flange
in Model BX-CP10 at 3-percent drift
188
Box column (BC18×18×257)
Beam top flange (W33×118)
No continuity plate
δtf
Figure 5-85: Out-of-plane deformation of the column flange and equivalent plastic strain
distribution in the beam top flange in Model BX-CP00 at 3-percent drift
Box column (BC18×18×257)
Db
δtf
Beam web (W33×118)
δbf
θ flange =
δ tf + δ bf
Db
Figure 5-86: Definition of beam flange rotation and out-of-plane deform shape of the column
flange in Model BX-CP00 at 3-percent drift
189
Box column (BC18×18×257)
Beam web (W33×118)
θweb
Figure 5-87: Definition of beam web rotation and out-of-plane deform shape of the column flange
in Model SH-EC01 at 3-percent drift
5
SH-EC01
BX-CP07
BX-CP00
WF-CP14
Beam flange rotation (% radian)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
Story drift angle (% radian)
4
4.5
5
Figure 5-88: Comparison of beam flange rotations in Models SH-EC01, BX-CP07, BX-CP00,
and WF-CP14
190
5
SH-EC01
BX-CP07
BX-CP00
WF-CP14
Beam web rotation (% radian)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
3.5
3
2.5
2
Story drift angle (% radian)
4
4.5
5
Figure 5-89: Comparison of beam web rotations in Models SH-EC01, BX-CP07, BX-CP00, and
WF-CP14
1.4
Moment at the column face (M col/Mp )
1.2
1
0.8
0.6
0.4
SH-EC01
BX-CF08
BX-CF20
WF-CP14
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
Story drift angle (% radian)
4
4.5
5
Figure 5-90: Comparison of global responses in Models SH-EC01, BX-CF08, BX-CF20, and
WF-CP14
191
5
SH-EC01
BX-CF08
BX-CF20
WF-CP14
Beam flange rotation (% radian)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
3.5
3
2.5
2
Story drift angle (% radian)
4
4.5
5
Figure 5-91: Comparison of beam flange rotations in Models SH-EC01, BX-CF08, BX-CF20,
and WF-CP14
5
SH-EC01
BX-CF08
BX-CF20
WF-CP14
Beam web rotation (% radian)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
Story drift angle (% radian)
4
4.5
5
Figure 5-92: Comparison of beam web rotations in Models SH-EC01, BX-CF08, BX-CF20, and
WF-CP14
192
Figure 5-93: Equivalent plastic strain (PEEQ) distribution on a plastic hinge formed in the box
column connection (Model SH-EC01) at 3-percent drift
Figure 5-94: Equivalent plastic strain (PEEQ) distribution on a plastic hinge formed in the Wshape column connection (Model WF-CP14) at 3-percent drift
193
Boundary point of
column top
Lateral bracing
Lateral bracing
Beam 1
Beam 2
Beam tip displacements
Beam tip displacements
Figure 5-95: Model BX-BI05
194
Box column (BC18×18×257)
1
2
Beam top flange
Beam web
Figure 5-96: Normalized tensile stress (σ22/Fy) distribution at 3-percent drift along the column
web in Model BX-CP05: Uni-directional loading
Box column (BC18×18×257)
1
2
Beam top flange
Beam web
Beam 2
Beam 1
Figure 5-97: Normalized tensile stress (σ22/Fy) distribution at 3-percent drift along the column
web in Model BX-BI05: Bi-axial loading
195
Box column
Beam 1
A
Beam 2
Figure 5-98: Maximum principal stress vectors on the top continuity plate at 3-percent drift, BXBI05
24 ksi
Model SH-EC01
-17 ksi
Continuity
plate
61 ksi
Model BX-CP05
-61 ksi
A
66 ksi
B
Model BX-BI05
PJP weld
-61 ksi
(a) Detail of box column corner
(b) Normal stress distribution along line A-B
Figure 5-99: Normal stress (σ22) distribution along the PJP weld line of column plates
196
Chapter 6. Performance Evaluation of Deep Wshape Column Connections
6.1 Introduction
The following section reports the results of the test on and the numerical simulation of a
deep column connection specimen (EC03) fabricated using a pre-Northridge connection detail.
Global and local response information is presented in Section 6.2. The remainder of the chapter
provides an evaluation of the experimental and analytical data. In particular, the results of a
parametric study on the key deep column connection design variables are presented in Section 6.3.
Section 6.4 provides tentative design guidelines for deep W-shape column connections.
6.2 Performance of Pre-Northridge Connection
A full-scale steel beam-column connection (Specimen EC03) was tested in the Structural
Research Laboratory at the Pacific Earthquake Engineering Research (PEER) Center at the
University of California, Berkeley, on August 22 and 23, 2002.
Selected global and local response data for the specimen are presented in this section.
Global response data in the form of moment-story drift angle and moment-panel zone plastic
rotation relations are presented. Local responses in the beam and column flanges and webs are
reported in terms of strains. The procedure used to calculate the global and local response is
identical with that described in Chapter 5.
197
6.2.1 Cyclic response of Specimen EC03
Specimen EC03 was tested using the loading protocol presented in Section 3.4.3. An
actuator displacement of 41 mm corresponded to a story drift angle of 1-percent in the specimen.
Whitewash paint was applied to the specimen prior to testing to aid in the visual identification of
damage and yielding in the components of the connection.
Specimen response
Yielding of the bottom flange of the beam was observed during the first displacement
excursion to a drift angle of 0.375-percent: see Figure 6-1 for details.
A hairline crack formed in the CJP weld of the beam top flange to the column flange at
the end of the cycles to a story drift angle of 0.375-percent. The crack propagated during the
displacement cycles to a story drift angle of 0.5-percent: see Figure 6-2 for details. The beam top
flange of Specimen EC03 fractured at the story drift angle of 0.58-percent during the first
displacement excursion to a story drift angle of 0.75-percent. Figure 6-3 and Figure 6-4 are
photographs of the fractured top flange. Local buckling of the beam top flange was observed
during the cycles to a drift angle of 1-percent as shown in Figure 6-5, showing that substantial
axial forces were being transmitted across the fractured surfaces.
The beam bottom flange fractured at a story drift angle of 1.38-percent during the first
negative displacement excursion to a story drift angle of 1.50-percent. Figure 6-6 and Figure 6-7
are photographs of the fractured bottom flange. The test was terminated when the six bolts in the
shear tab had fractured, during the first excursion to a story drift angle of 3-percent. Figure 6-8 is
a photograph of the fractured web shear tab at a story drift angle of 3-percent.
Global response
The relation between moment (at the column face) and story drift angle for Specimen
EC03 is presented in Figure 6-9. The positive (tension in the top flange and compression in
198
bottom flange) maximum moment at the column face before the first fracture was 2,582 kN-m
(22,856 kip-in), which is 55 percent of the plastic moment based on the nominal yield strength of
345 MPa (50 ksi) or 48 percent of the plastic moment based on the MTR yield strength of 389
MPa (57 ksi). The negative (compression in the top flange and tension in the bottom flange) peak
moment before the bottom flange fractured was 4,193 kN-m (37,108 kip-in), which is 89 percent
of the plastic moment based on the nominal yield strength of 345 MPa (50 ksi) or 79 percent of
the plastic moment based on the MTR yield strength of 389 MPa (57 ksi).
The peak moment resisted by the shear tab after both flanges had fractured was 1,064 kNm (9,415 kip-in), which is 23 percent of the plastic moment of the connection based on the
nominal yield strength, and 3.2 times larger than the plastic moment of the shear tab alone based
on a nominal yield strength (for the tab) of 248 MPa (36 ksi). Similar to Specimens EC01 and
EC02, this relatively large residual strength is developed by the couple between the compressive
force transferred across one of the fractured beam flanges and a resultant tensile force carried by
the bolts of the shear tab.
The relation between the moment and the plastic deformation in the panel zone is
presented in Figure 6-10. The relative stiffness and strength of the deep column were extremely
high and the panel-zone and column deformations were very small.
Local response
Figure 6-11 shows the maximum tensile strain profiles on the beam top flange during the
each drift cycle. This strain distribution was recorded by strain gages attached on the top surface
of the top flange along a line at a distance of 51 mm (2 in.) from the column face during the
positive loading half-cycle (producing tension in the top flange). The strain was normalized by an
assumed yield strain of 0.002. The strains were uniform across the width of the beam, which is an
expected result given the use of a W-shape column with thick continuity plates. Note that the
maximum strain before fracture (0.5-percent story drift) is less than the yield strain.
199
The shear strain profiles in the beam web produced by positive loading half-cycle are
shown in Figure 6-12. The shear strains were recorded using three rosette strain gages attached to
the web along a line at a distance of 178 mm (7 in.) from the column face. The shear strains are
higher near the flanges and lower at the mid-height of the web, an observation identical to those
for Specimens EC01 and EC02 but which contradicts the typical beam-theory assumption as
discussed by Lee et al. (1997).
6.2.2 Numerical simulation of the test
A numerical model for the tested specimen was prepared after the test was completed;
details are provided in Chapter 4. This finite element model was analyzed by applying monotonic
loading as discussed in Section 4.3.3. The expected global response of the test specimen and the
states of stress and strain in the critical regions of the model are presented in this section.
Global response
The beam moment-story drift angle response of the finite element model of Specimen
EC03 (Model SH-EC03) is presented in Figure 6-13. The cyclic response of the test specimen is
also shown for the purpose of comparison. Yielding, characterized by a change in model stiffness,
starts at approximately 1-percent story drift angle for the analytical model. The peak resistance in
the finite element model was attained at slightly more than 3-percent story drift. Beyond this drift
angle, local buckling of the beam flange and web results in a loss of strength and stiffness. Since
the finite element model was not capable of predicting fracture, local responses of the analytical
model are reported at a story drift angle of 0.5-percent in the following sections: the story drift
angle associated with fracture of the test specimen.
200
Shear transfer
Figure 6-14 shows the distribution of von Mises stress in the beam web and the panel
zone at 0.5-percent story drift angle in Model SH-EC03. Even though a hairline crack in the CJP
weld of the beam top flange was formed during 0.375-percent story drift cycle, both the specimen
and the finite element model were still elastic at this drift level. The value of von Mises stress in
the web are large (and similar to those recorded in the beam flange) near the weld access hole.
Table 6-1 shows the distribution of shear force in the web and both flanges of the beam at
four cross-sections located at increasing distance from the column face. The shear force
transferred to the column via the beam flanges is quite high: 38 percent in Model SH-EC03 at a
cross-section 10 mm (0.4 in) away from the column face. In addition to producing a complex
state of stress in the flanges, such shear forces cause local bending of the flanges in the access
hole region. Note that the distribution of the shear force in the beam cross section follows the
beam theory at a cross section 460 mm (18.4 in), or one-half of beam depth, away from the
column face. Thus, only the connection region of the beam is affected by the connection
boundary conditions.
Table 6-1: Distribution of shear force in beam flanges and beam web at 0.5-percent story drift
Distance from column face (mm)
SH Model
10
25
180
460
% shear in web
62
65
96
96
% shear in flanges
38
35
4
4
EC03
Local response
The distributions of axial stress S11 (the 1-direction lies along the longitudinal axis of the
beam) on the upper surface of the beam top flanges and top surface of the continuity plates in
Model SH-EC03 are presented in Figure 6-15 at 0.5-percent story drift angle. The highly stressed
201
region in the analytical model corresponds to the location of the cracks observed just before
fracture of beam flanges in the test. The stress in Model SH-EC03 is maximized in the middle of
beam flange while the stresses at the flange edges are relatively small. Such a stress distribution is
a consequence of the location of the column web.
The fracture indices for Model SH-EC03 along the upper surface of the beam top flange,
along the lines defined in Figure 5-35 are presented in Figure 6-16. The Mises Index (MI)
increases near the column flange. The maximum value of Mises Index is approximately 1,
suggesting that yielding should occur. The maximum value in Model SH-EC03 is located in the
middle of beam flanges near the column face.
The Pressure Index (PI) shows high values near the column flange. Note that hydrostatic
pressure was defined as positive in compression, thus giving the values of Pressure Index in the
tension flange negative signs. The absolute value of Pressure Index are smaller than 0.5 and
larger than 0.1 for all models. The maximum Pressure Index in Model SH-EC03 is located in the
middle of the beam flange. The maximum value of the Triaxiality Index (TI) in the specimen is
approximately 0.47.
6.3 Evaluation of Response Data
This section serves to integrate the results of experimental studies of Section 6.2 and the
findings from the theoretical studies in Chapter 2. The following section describes the out-ofplane deformation of the deep column connection and their related design variables. Vulnerability
to brittle fracture of the welded joints and post-fracture behavior of the deep W-shape column
connection specimen are discussed in the Sections 6.3.2. An evaluation on post-fracture
connection stiffness is presented in Section 6.3.3. Sections 6.3.3 through 6.3.6 present and
evaluate the response of the analytical models in terms of design variables, namely, column
202
boundary condition (Section 6.3.3), connection type (Section 6.3.5), and beam lateral bracing
(Section 6.3.6).
6.3.1 Analysis parameters
The depth of a W-shape column in Specimen EC03 is larger than the limit set on column
depth in the qualified steel moment connections in FEMA-350 (2000). Deep columns tend to
twist because the beam flange force is eccentric to the column axis. Such twisting can lead to
large strain demands along the k-line of a W-shape column and can cause fracture as observed in
a test conducted at University of California at San Diego (Chi and Uang 2002; Barsom and
Pellegrino 2000). Furthermore, initial twisting of the column can be exacerbated by high axial
load, and could result in column lateral-torsional buckling over several stories. The likelihood of
this occurring depends on the beam and column geometry parameters as well as other design
variables in the deep column connections.
Figure 6-17 shows the plan view of the deformed shape of a beam-column connection,
where the beam bottom flange is subjected to compression due to plastic moments developed in
the beam. Lateral-torsional buckling of a beam could lead to out-of-plane deformation in the
connection if the connection is not braced. Points A, B, C, and D in this figure corresponds to the
location of the far flange of the column, near flange of the column, maximum lateral deflection,
and the brace point on the top beam flange, respectively. Note that the bottom flange might not be
restrained at point D. Due to the lateral movement of the beam flange, a force component is
developed in the direction perpendicular to the longitudinal axis of the beam. In this figure, ex is a
distance from the face of a column to the point of maximum beam lateral deflection; ey is a
magnitude of the beam lateral deflection; θc is an angle of column twist at the level of the beam
bottom flange; θb is the inclined angle of the beam flange; and Fflange is a flange compression
force developed in the plastic hinge. The torque imposed on the column is (Chi and Uang 2002):
203
Tcol = F flange [(e x + Dc / 2) cos θ b + e y sin θ b ]
( 6-1 )
The column boundary condition, connection type, and beam lateral bracing were selected
as parameters varied in the analytical models for this study. The information on the effects of the
beam and column geometry parameters can be found in the literature (Chi and Uang 2002,
Stojadinovic 2003). Model DC-UR00 prepared for the study is identical to Model SH-EC03
except for the design of the beam lateral bracing. Lateral bracing for the beam bottom flange is
not included in this mode (see Figure 6-18). In all cases, the lateral movement of the beam top
flange is restrained at the brace point. The analytical models are summarized in Table 6-2.
Table 6-2: Analytical models for the deep column connection
Model
Column boundary conditions
Hc
1
DC-UR00
1.0 Hs
DC-URWP
DC-URFH
2.0 Hs
Bending
RollerPin
2
3
Torsion
Connection
type
Pin-Pin
NA5
Fix-Fix
DC-FF00
Free flange
DC-CP10
0
Unreinforced
RBS
1.0 Hs
Brace
location4
Fix-Fix
DC-RB00
DC-CP00
Brace
stiffness
RollerPin
Fix-Fix
1.0 βbr
Cover plate
1,457 mm
DC-CPBR
Infinity
DC-CPNH
1.
2.
3.
4.
5.
787 mm
Hc is the column height in the connection model; Hs is the story height.
Roller: UX = UY = 0; Pin: UX = UY = UZ =0; Fix: UX = UY = UZ = RX = RY = RZ = 0.
Fix: φ = 0, dφ/dz = 0; Pin: φ = 0, d2φ/dz2 = 0; φ is an angle of column twist.
Distance from the column face to the brace point of the beam bottom flange.
Not applicable.
The connection sub-assemblage shown in Figure 6-19 was used for the parametric
analysis of steel moment connections. This connection sub-assemblage assumes that in-plane
boundary conditions can be defined at the inflection points of the column. However, out-of-plane
204
boundary condition cannot be specified at these locations. The top and bottom ends of the column
are the appropriate locations to define the out-of-plane boundary conditions. Warping restraint at
the support is also major consideration for torsional behavior (Pi and Trahair 2000). Thus, such
torsional boundary conditions and column height are analysis parameters in this study. The
torsionally fixed end neither twists nor warps, while the torsionally pinned end cannot twist (φ = 0)
but can warp (φ˝ = 0) (AISC 1983).
The out-of-plane response of deep column connections can be affected by the type of
moment connection. Three types of the moment connection, Reduced Beam Section (RBS),
Welded Cover Plated Flange (WCPF), and Free Flange (FF) connections are modeled as shown
in Figure 6-20. The location and size of reduced beam flange in RBS, size of shear tab and weld
access hole in FF, and size of cover plate in WCPF are selected so that the differences in the
plastic hinge location in each connection are minimal.
The cover-plate connection model is used to investigate the effects of beam lateral
bracing, because it is more vulnerable to column twisting than the unreinforced connection since
the hinge is relocated away from the column face. The lateral movement of the beam bottom
flange is prevented at the location brace points in the test setup for Specimens EC02 and EC03:
see Figure 3-15. The lateral bracing near the actuators and at the mid-span of the beam are
modeled by imposing the displacement boundary condition such that the lateral movements at the
brace points in the beam are prevented (UY = 0). For the lateral bracing of the beam bottom flange,
a boundary condition with a finite spring constant was included in the model. The minimum
required brace stiffness for nodal bracing, βbr, is used to model such boundary condition
following the equation given in AISC LRFD Manual (AISC 2001):
βbr =
10 M u Cd
φ Lbr ho
( 6-2 )
where, φ = 0.75; Mu = required flexural strength; ho = distance between the flange centroids; Cd =
1.0 for bending in single curvature; and Lbr = distance between braces.
205
The location of the lateral bracing can also affect the response of the model (Nakashima
et al. 2002). A model in which the brace point is located near the beam plastic hinge is included
in the study to investigate the effect of the brace location on the connection response.
6.3.2 Welded joints
The likely location of brittle fracture in Specimen EC03 was identified in the numerical
simulation study (Section 6.2). The location of the crack observed before fracture in the test of
Specimen EC03 coincides with the highly stressed region identified in the numerical simulation.
However, because of the limitations in the shell element formulation, such models cannot provide
sufficient information on the local stress and stain distribution along the beam flange thickness,
which is important to evaluate the fracture vulnerability of the welded joint. Thus, the solid
element model described in Section 4.3.1, Model SOL-EC03, is employed to investigate the
cause of brittle fracture of the tested specimen.
In the following discussion, response data are presented at three levels of inter-story drift:
0.5-percent (elastic response); 0.58-percent (the drift level corresponding to brittle fracture in
Specimen EC03); and 2-percent (inelastic response of the numerical model). Data are not
presented for story drifts greater than 2-percent because geometric instabilities at such high story
drift render the solid element model inaccurate.
The response of the solid element model is described below using fracture indices
presented in Section 2.2.3. ABAQUS data are reported for the cross section of the beam flange
defined in Figure 5-39. Plane A is the vertical plane of the beam flange at the face of the column.
Plane B is the vertical plane at the toe of the weld access hole. Model SOL-EC03 has 6 elements
through the thickness of the beam flange. Numbering of the layers that define the surfaces of the
elements, starts from the bottom surface of the beam flange and increases sequentially through
the flange thickness.
206
Fracture indices of SOL-EC03
Figure 6-21, Figure 6-22, and Figure 6-23 present the distributions of Maximum Principal
Index (MPI), Mises Index (MI), and Pressure Index (PI), respectively, across the width of the
beam flange at the face of the column (Plane A) at story drifts of 0.5- and 2-percent. At 0.5percent story drift, the distribution of Pressure Index and Mises Index are similar to that of
Maximum Principal Index. The indices are maximized in the middle of the beam flange on the
bottom surface (Layer 1). As the drift increases, the distributions of all the indices on the bottom
surface are relatively uniform while those of the Maximum Principal Index and Pressure Index on
the top surface are small at the center but larger at the both edges of the beam flange.
Figure 6-24 and Figure 6-25 present the distributions of Triaxiality Index and Rupture
Index, respectively, across the width of the beam flange at the face of the column (Plane A) at
story drifts of 0.5- and 2-percent. At 0.5-percent story drift, the values of Triaxiality Index in the
middle layers (Layers 2, 3, 4, and 5) are higher than those in the bottom layer and the maximum
value is -1.0: a value can trigger brittle fracture. Rupture Index at this drift is localized in the
middle beam flange and its magnitude is very small. Thus, as soon as the initial crack induced by
high principal stress grows into the upper middle layers, rapid crack propagation will occur.
Figure 6-26, Figure 6-27, Figure 6-28, Figure 6-29, and Figure 6-30 present the
distributions of Maximum Principal Index (MPI), Mises Index (MI), Pressure Index (PI),
Triaxiality Index (TI), and Rupture Index (RI), respectively, across the width of the beam flange
at the toe of the weld access hole (Plane B) at story drifts of 0.5- and 2-percent. At 0.5-percent
story drift, brittle fracture should not occur in this region because the values of Maximum
Principal Index and Triaxiality Index are lower than the value that should trigger brittle fracture
in the connection. At 2-percent story drift, the high value of Rupture Index could lead to ductile
fracture but it is lower than that of other test specimens.
207
Table 6-3 presents the summary of the response indices in Model SOL-EC03 at 0.5- and
2-percent story drift. The maximum values of Maximum Principal Index, Mises Index, Pressure
Index, Triaxiality Index, and Rupture Index are greater at the column face than at the toe of the
weld access hole at 0.5-percent story drift. The maximum values of Mises Index and Rupture
Index at the toe of the weld access hole are slightly higher than those at the column face, while
the maximum values of other indices at the location are lower than those at the column face.
In Specimen EC03, Plane A is the location of the CJP welds where E70T-4 electrodes
were used to join the beam flanges to the column flange. It is well known that the CJP welds
using E70T-4 electrodes have low fracture toughness (Tide 1998; FEMA 2000a). Brittle crack
propagation initiated at the column face during the test, likely because the fracture strength at
Plane A is much lower than that at Plane B while the values of Maximum Principal Index and
Triaxiality Index at 0.5-percent story drift are higher at Plane A than at Plane B. Rupture Index at
the toe of the weld access hole at Plane B is slightly higher than at Plane A at 2-percent story drift.
If notch-tough electrodes (CVN greater than 27 J at 21 °C or 20 ft-lbf at 70 °F, AISC 2002) were
used for the CJP welds, brittle fracture at Plane A might be prevented. Instead, ductile fracture
could initiate at the locations where Rupture Index is high.
Table 6-3: Maximum values of response indices in Model SOL-EC03
Column face (Plane A)
Toe of the weld access hole (Plane B)
Drift
MPI
MI
PI
TI
RI
MPI
MI
PI
TI
RI
0.5 %
1.36
1.00
-0.70
-1.01
0.004
0.99
0.84
-0.43
-0.51
0
2.0 %
1.56
1.11
-0.89
-0.80
0.12
1.48
1.14
-0.75
-0.66
0.13
Local response at fracture
The sizes of members and lengths of beams in Specimens EC01, EC02, and EC03
differed. Thus, stress and strain states at a fixed level for the specimens cannot be directly
208
compared. For the purpose of comparison, story drift angles at the first brittle fracture of each
specimen are selected as reference drifts. The story drifts at fracture were 0.78-percent in
Specimen EC01, 0.59-percent in Specimen EC02, and 0.58-percent in Specimen EC03.
Figure 6-31, Figure 6-32, and Figure 6-33 show the contours of Maximum Principal
Index, equivalent plastic strain (PEEQ), and Pressure Index of Specimen EC03, respectively, at
the story drift of 0.58-percent. The Maximum Principal Index is 1.42 (corresponding to 544 MPa
or 78.8 ksi) at Point A, 1.32 (505 MPa or 73.2 ksi) at Point B, and 1.01 (385 MPa or 56.1 ksi) at
Point C. The equivalent plastic strain is 0.002 at Point A and zero at Point C. The Pressure Index
is -0.66 (-254 MPa or -37.0 ksi) at Point D, -0.56 (-215 MPa or -31.1 ksi) at Point E, and -0.38 (147 MPa or -21.4 ksi) at Point F. The Triaxiality Index at those points (Points D, E, and F) are 0.66, -0.72, and -0.59, respectively, indicating that triaxiality of the middle of beam flange is
higher than that at the beam edge.
Table 6-4: Summary information of stress and strain states for Specimens EC01, EC02, and EC03
Point
Story drift
%
EC01
0.78
EC02
0.59
EC03
0.58
Maximum principal
stress
A
B
C
Hydrostatic stress
D
E
F
MPa
MPa
MPa
MPa
MPa
MPa
ksi
ksi
ksi
ksi
ksi
ksi
654
629
614
-319
-295
-298
95.8
91.2
89.0
-46.3
-42.8
-43.2
564
535
507
-304
-261
-247
79.2
77.6
73.6
-44.1
-37.9
-35.9
544
505
385
-254
-215
-147
78.8
73.2
56.1
-37.0
-31.1
-21.4
PEEQ
A
C
%
%
0.3
0.5
0.1
0.3
0.2
0
Table 6-4 presents the summary information of stress and strain at fracture of Specimens
EC01, EC02, and EC03, respectively, at each data report point. The principal stresses at fracture
of Specimens EC02 and EC03 are lower than that of Specimen EC01. The uniform distribution of
the critical stress and high triaxiality in the CJP region likely caused the sudden fracture of
209
Specimen EC02 without the formation of any noticeable initial crack. The maximum principal
stresses of Specimen EC03 are concentrated in the middle of the beam flange. Such a stress
concentration and welding-induced residual stress likely contributed to the initial crack observed
during 0.375-percent story drift cycles.
6.3.3 Post-fracture connection stiffness
Figure 6-34 presents a classification of the connection stiffness (AISC 2002). Momentrotation curves from the test and numerical simulation are also plotted in this figure. Moments are
computed at a column centerline and normalized by beam stiffness as in Figure 5-74 and Figure
5-75. Nominal beam plastic moments are also shown in those figures.
Before top flange fracture, the Specimen EC03 connection stiffness ratio is 15. The
bottom flange of this specimen did not fracture during several displacement cycles after the top
flange fracture. The connection stiffness ratio is 14 under the negative half-cycles (compression
in top flange and tension in bottom flange) before bottom flange fracture while it is 2 under
positive half-cycles. After bottom flange fracture, the connection stiffness ratio is 2 under
negative half-cycles.
Binding of beam flange on the column can provide the connection stiffness comparable
to an undamaged connection. Even though a welded steel moment connection to W-shape column
is considered to be a fully-restrained connection, connection stiffness can be lower than the one
specified in AISC LRFD Manual (AISC 2001) because of the effects by column deformation.
Note that the connection stiffness ratio of the stiff rectangular box column connection (Specimen
EC02) was 18. Therefore, researches are required to define a more accurate connection stiffness
criterion for welded steel moment connections that includes the effects of column deformation.
210
6.3.4 Column boundary condition
The differential equation for torsion of a W-shape member is given by Salmon and
Johnson (1995) as:
dφ
d 3φ
M z = M s + M w = GJ
− ECw 3
dz
dz
( 6-3 )
where, Mz is the total torsional moment composed of the sum of the pure torsional moment
(Saint-Venant torsion) Ms and the warping torsion Mw, J is the torsional constant, and Cw is the
warping constant. By solving the above equation with given boundary conditions, one can obtain
the twist angle of the column subjected to a torque. For the same column shape and torque, the
twist angle of the column is dependent on the boundary conditions and column length.
Figure 6-35 presents the relationship between moment at the column face versus story
drift angle for Models DC-UR00, DC-URWP, and DC-URFH Moments are normalized by the
nominal plastic moment of the beam. The global responses in Models DC-UR00 and DC-URWP
are identical, indicating that the torsional boundary condition may not affect the in-plane response
of the connection. The global response in Model DC-URFH, which has a column length of twice
the story height, is slightly different from that in Model DC-UR00 with a column length equal to
story height. The reduced in-plane column stiffness due to the increased length provides the
difference in the elastic range of the responses but the difference in the ultimate strength of the
connections is negligible. Note that ultimate strength of the connection is determined primarily by
the plastic moment capacity of the beam.
The angles of column twist (θc in Figure 6-17) along the bottom half of the column length
in Models DC-UR00, DC-URWP, and DC-URFH are plotted in Figure 6-36, at 4-percent story
drift. The column twist angle increases significantly if the warping restraint at the both ends of
the column is not included. The twist angle at the bottom flange level (BF in the figure) of the
column is 0.15-percent radian in Model DC-UR00 and 0.53-percent radian in Model DC-URWP.
211
The twist angle of the connection with torsionally pinned boundaries is 3.7 times larger than that
with torsionally fixed boundaries.
Because the degree of column twists is much less than that of inclined angle of beam
flanges (see Figure 6-38), the applied torques are the same for both models with the column
length of a story height (Models DC-UR00 and DC-URWP), and their distribution along the
column height are similar with each other. Table 6-5 presents torque reaction of each model at 4percent story drift. The reaction torque recorded at the column end (IP in the figure) in Model
DC-URWP is 1.17 times larger than that in Model DC-UR00, indicating that the torsional
boundary condition may not affect the torsional shear distribution in the column. However, the
distribution of the torsional moment will be substantially changed if the column length increases.
The reaction torque recorded at the column end (BC in the figure) in Model DC-URFH is 56
percent of that in Model DC-UR00. The torsional moment at the top flange level can be
computed from the torsional moment equilibrium (Tcol = Ttop + Tbot: see Figure 6-19). Thus, the
torsional moment in the upper part of the column (panel zone) increases more than that in Model
DC-UR00 and induces high warping stress that might cause fracture along the k-line (Barsom and
Pellegrino 2000; Chi and Uang 2002).
Table 6-5: Torque reactions at 4-percent story drift
DC-UR00
DC-URWP
DC-URFH
Model
Torque reaction, Tbot
kN·m
kips·in
kN·m
kips·in
kN·m
kips·in
29.5
262
34.6
306
16.7
148
6.3.5 Connection type
Specimen EC03, a pre-Northridge steel moment connection, failed by brittle fracture in
the CJP welds at 0.58-percent story drift. By modifying the connection detail, post-Northridge
steel moment connections (FEMA 2000a), such as Welded Unreinforced Flange/Welded-web
212
(WUF-W), Free Flange (FF), Reduced Beam Section (RBS), Welded Cover Plated Flange
(WCPF), can prevent brittle fracture and increase their rotation capacity more than that of the preNorthridge connection. Even though brittle fracture is controlled in the pre-qualified (postNorthridge) connection, the rotation capacity of the connection is limited by ductile failure modes.
Stojadinovic (2003) classified the failure mode of pre-qualified US connections into three
categories; beam instability, lateral-torsional buckling of the column, and low-cycle connection
fatigue. Column twisting and its subsequent lateral-torsional buckling can occur in a deep Wshape column without lateral restraints.
Figure 6-37 presents the relationship between moment at the column face versus story
drift angle for Models DC-UR00, DC-RB00, DC-FF00, and DC-CP00. Moments are normalized
by the nominal plastic moment of the beam. The maximum resistances in Models DC-CP00 and
DC-FF00 are 6 percent higher than that in Model DC-UR00 because of the increased strength due
to cover plates and a thick shear tab, respectively. The rate of strength degradation after peak
resistance of the cover-plate connection (Model DC-CP00) is more rapid than that of the free
flange connection (Model DC-FF00), indicating that the amplitude of flange local buckling in
Model DC-CP00 is larger than that in Model DC-FF00. The peak resistance of the reduced beam
section connection (Model DC-RB00) is 79 percent of that in Model DC-UR00 because the
flange area at a plastic hinge in Model DC-RB00 is smaller than that in Model DC-UR00. The
strength degradation rate after peak resistance in Model DC-RB00 is same as that in Model DCCP00 before 4-percent story drift. Beyond 4-percent story drift, the strength degradation in Model
DC-RB00 is faster than that in Model DC-CP00 due to the excessive lateral-torsional buckling of
the beam.
The lateral displacements at each data report point (see Figure 6-17) in Models DC-UR00,
DC-RB00, DC-FF00, and DC-CP00, at 4-percent story drift are plotted in Figure 6-38. The lateral
displacements, δLAT, are normalized using the beam flange width, bf. The distance from the
column face, x, is normalized by the beam depth, Db. The maximum beam lateral displacements
213
in Models DC-RB00 and DC-CP00 are much higher than those in Models DC-UR00 and DCFF00. Because the amplitudes of flange local buckling in the reduced beam section and the coverplate connection are larger than that of the unreinforced connection, the effective in-plane
stiffness will be reduced in such connections, which leads to the large lateral deflection of the
beam flange. The column twisting angle in Model DC-CP00 is larger than that in Model DCRB00. Since the flange force developed in the cover-plate connection is larger than that in the
reduced beam section connection, the torque applied to the column in Model DC-CP00 is greater
than that in Model DC-RB00, which leads the larger column twisting. The maximum lateral
deflection of the free flange connection (Model DC-FF00) is smaller than that in Model DCUR00. In the free flange connection, the shear tab carries a large portion of the moment at the
column face. Thus, the flange force in the free flange connection is reduced and the lateral beam
deflection also decreases.
6.3.6 Beam lateral bracing
Column twisting induces large shear stresses along the column k-line inside the panel
zone where Saint-Venant and warping torsions are highly restrained. Lateral bracing of the beam
can reduce such column twisting by limiting the amplitude of the lateral deflection of a beam
flange, which causes the eccentricity for the flange force. Figure 6-39 shows the connection detail
of the beam lateral bracing in Building CT-15. A fly-brace spans between the bottom flange of
the (seismic) frame girder and the top flange of the adjacent (gravity) beam. The distance between
the seismic girder and the gravity beam in the building was 2,286 mm (90 in.).
Two lateral braces included in Model DC-CP10 are shown in Figure 6-40. A truss
element is used to model the brace and connects a brace point at the beam bottom flange and a
boundary node located in the horizontal plane of the flange. The distance from the column face to
the brace point is 1,457 mm (57.4 in.) in Models DC-CP10 and DC-CPBR and 787 mm (31 in.)
in Model DC-CPNH. The area of each brace corresponds to half of the area required to achieve
214
the brace stiffness specified in AISC LRFD Manual (AISC 2001). These braces are assumed to be
made of Grade 50 steel (Fy = 222 MPa or 50 ksi).
Figure 6-41 presents the relationship between moment at the column face versus story
drift angle for Models DC-CP00, DC-CP10, DC-CPBR, and DC-CPNH. Moments are
normalized using the nominal plastic moment of the beam. The difference between the global
responses in Models DC-CP10 and DC-CPBR is negligible, indicating that the stiffness of a brace
does not affect the global response of the connection as long as it is greater than the limits in the
code. When the lateral brace is not used (Model DC-CP00), the resistance of the connection drops
below than that of the braced connection, albeit a small percentage, at the story drift greater than
3-percent. The increased amplitude of the beam flange deflection due to lateral-torsional buckling
is the cause of the strength degradation. Moving the brace point closer to the beam plastic hinge
(Model DC-CPNH) increases the connection resistance slightly after 3-percent story drift.
The largest difference in the global responses of each model is only 5 percent. However
the column twisting and the brace forces are greatly influenced by the stiffness and location of the
brace. Figure 6-42 presents the relationship between the column twist angle at the level of the
beam bottom flange versus story drift angle for Models DC-CP00, DC-CP10, DC-CPBR, and
DC-CPNH. Peak angles of column twist are maximized in Model DC-CP00 and minimized in
Model DC-NH00. The peak twist angle in Model DC-CPBR is 64 percent of that in Model DCCP00, indicating that lateral braces can effectively reduce the degree of column twisting. When
the flexible lateral bracing (Model DC-CP10) is used to restrain the lateral moment of the brace
point in the beam, the peak twist angle is 16 percent lower than that of the connection using the
rigid lateral bracing (Model DC-CPBR). In general, flexible lateral bracing increases the column
twist angle (Ales and Yura 1993) because the movement of the brace point in the beam flange is
not sufficiently restrained and increases the eccentricity of the beam flange force. However, in
this analysis, the column twist angle for rigid lateral bracing is larger than that for flexible lateral
bracing. The reason for this occurring is due to the difference in modeling of lateral bracing.
215
Because the vertical and longitudinal movement of the brace point is also restrained by the
flexible lateral bracing, it changes the mode shape and amplitude of flange local buckling from
those by rigid lateral bracing, and makes such difference.
It is important to design a lateral brace to have enough strength as well as stiffness to
control excessive column twist (Yura 1993, 1995). Figure 6-43 presents the relationship between
the total reaction at both boundaries of the braces in the lateral direction (Y-axis in Figure 6-40)
versus story drift angle for Models DC-CP00, DC-CP10, DC-CPBR, and DC-CPNH. The
reactions are normalized by the nominal squash load of the beam flange, Py (= Abf × Fy). The
brace reaction is maximized when the rigid bracing condition (Model DC-CPBR) is used. The
maximum reaction of the connection using the flexible braces (Model DC-CP10) is 80 percent of
that in Model DC-CPBR. As the distance between the brace and the beam plastic hinge decreases,
the brace reaction force decreases. The maximum reaction in Model DC-CPNH is 32 percent of
that in Model DC-CPBR. The drift at which the brace forces increase are different depending on
the models: 0.5-percent story drift for Model DC-CP10, 1-percent story drift for Model DCCPBR, and 3-percent story drift for Model DC-CPNH. As the distance from the brace point to the
plastic hinge is reduced, lateral-torsional buckling of the beam is delayed and the column twist is
also reduced.
Figure 6-44 presents the relationship between the story drift angles versus the member
forces of in each brace in Model DC-CP10. The total lateral reactions at the brace boundaries are
also plotted. Brace forces are normalized by the nominal squash load of the beam flange.
Negative value of brace forces indicates that the brace is in compression. Note that the inability to
resist the compression force due to brace buckling is not considered. The brace force ratio at 5percent story drift is 0.64 for Brace 1 and 0.36 for Brace 2. The brace force in the compression
(Brace 2) is 44 percent less than the brace force in the tension (Brace 1). Any movement of the
brace point in the directions (X- and Z- in Figure 6-40) perpendicular to the longitudinal axis of
the braces (Y-axis) introduces tension in the brace while the movement along the brace axis
216
induces compression in one brace and tension in the other. Thus, superposing these force
components give a rise to the difference in the brace forces. Table 6-6 presents information on the
displacement of the brace point in the global coordinate system and its contribution to the
member force in each horizontal brace, at 4-percent story drift. Displacement components
perpendicular to the longitudinal axis of the brace are much higher than those parallel to the brace
axis while their contribution to the member force are smaller than those parallel to the
longitudinal axes of the braces.
Table 6-6: Contribution of each displacement component in the brace force
Brace 1
Brace 2
Direction
X-
Y-
Z-
Total
X-
Y-
Z-
Total
Displacement1
-0.44
-0.04
-1.0
NA.
-0.44
-0.04
-1.0
NA.
Force2
0.04
0.75
0.21
1.0
0.04
-0.75
0.21
-0.50
1.
2.
Normalized using the magnitude of the vertical displacement of the brace point, UZ = 52.8 mm (2.1
in.).
Contribution by corresponding displacement, and is normalized using the member force of Brace 1,
50.0 kN (11.3 kips).
Depending on the bracing detail, lateral braces restrain not only the lateral movement of
the beam but also the vertical movement of the beam (Lay and Galambos 1966). In the case of
horizontal bracing discussed above, the contribution to the brace force from beam vertical and
longitudinal displacement is not significant, but can be substantial in the diagonal bracing shown
in Figure 6-39. Under the assumption that the displacement of the brace point is identical with
that in Model DC-CP10, the force in the diagonal brace can be computed from the geometric
relation shown in Figure 6-45. Table 6-7 presents information on the displacement of the brace
point in the global coordinate system and its contribution to the member force in each diagonal
brace, at 4-percent story drift. In the diagonal brace of Figure 6-39, the maximum brace force is 7
times larger than that of the horizontal brace and 5 times larger than the nominal yield strength of
217
the brace, Py,br (= Abr × Fy,br). In these instances, the brace will yield or buckle and no longer
restrain the lateral movement of the beam bottom flange.
Table 6-7: Contribution of each displacement component in the member force of diagonal bracing
Brace 1
Brace 2
Direction
X-
Y-
Z-
Total
X-
Y-
Z-
Total
Displacement1
-0.44
-0.04
-1.0
NA.
-0.44
-0.04
-1.0
NA.
Force2
0.04
0.66
6.4
7.1
0.04
-0.66
6.4
5.8
1.
2.
Normalized using the magnitude of the vertical displacement of the brace point, UZ = 52.8 mm (2.1
in.).
Contribution by corresponding displacement, and is normalized using the member force of Brace 1,
50.0 kN (11.3 kips).
The brace discussed above was nodal bracing that controls the movement at a particular
brace point only. Because of large in-plane stiffness of the floor slab attached to the top flange of
the gravity beam where the brace boundary is located, the floor slab can prevent any movement
of the brace boundary in the plane of the floor slab (Civjan et al. 2001). However the movement
of the brace point in vertical direction (Z-axis) can occur due to the flexibility of the floor slab
and gravity beam. Thus, the high force contribution due to the vertical movement of a brace point
may be lessened if the flexibility at the brace boundary is considered. Analysis of more complex
model that includes the three dimensional frame structure is needed to attain this reduction in
brace force.
6.4 Design Guidelines for Deep W-shape Column
Connections
This section outlines design and upgrade guidelines for welded steel moment connections
to deep W-shape columns. These preliminary design and upgrade guidelines are based on the
results of experimental and analytical investigations presented in this study. Thus, these
guidelines may not be applicable to the connection comprising member size and materials other
218
than the ones used in tests conducted in this study. Design guidelines for fully restrained (FR)
moment connection specification in FEMA-350 documents (FEMA 2000a) and AISC Seismic
Provisions (AISC 2002) take precedence over these recommendations. The following subsection
provides additional guidelines for design of lateral bracing. The remainder of this section
discusses upgrading design strategy for pre-Northridge deep W-shape column connections.
6.4.1 Beam lateral bracing
Design of horizontal braces should be considered, using AISC Seismic Provisions (AISC
2002). Design of diagonal braces should account for brace connection flexibility as well as the
difference of vertical deflections of the brace connection points. More research is needed to
evaluate the effect of vertical deflection on brace design force.
6.4.2 Connection upgrade
Lateral deflection of the beam flange in beam plastic hinges is larger when the plastic
hinge forms further away from the column face. The magnitude of column torque is directly
related to the magnitude of lateral beam flange deflection. Therefore, bracing the beam as close to
the expected location the plastic hinge is recommended and column lateral bracing (Helwig and
Yura 1999) or torsional strengthening may be required.
219
Figure 6-1: Whitewash flaking during the 0.375-percent drift cycle
Figure 6-2: Crack in top CJP weld during the 0.5-percent drift cycles
220
Figure 6-3: Beam top flange fracture during the 0.75-percent drift cycle
Figure 6-4: Fracture surface of the beam top flange
221
Figure 6-5: Beam top flange local buckling during the 1-percent drift cycle
Figure 6-6: Beam bottom flange fracture during the 1.5-percent drift cycle
222
Figure 6-7: Fracture surface of the beam bottom flange
Figure 6-8: Bolt failure during the 3-percent drift
223
Moment at the column face (×1000 k-in)
40
30
Top flange fracture
Shear failure of bolts
near top flange
20
10
0
-10
Shear failure of bolts
near bottom flange
-20
-30
Bottom flange fracture
-40
-5
-4
-3
0
1
2
-2
-1
Story drift angle (% radian)
3
4
5
Figure 6-9: Moment at the column face versus story drift angle
Moment at the column face (×1000 k-in)
40
30
20
10
0
-10
-20
-30
-40
-5
-4
-3
-2
-1
0
1
2
Panel zone plastic rotation (% rad)
3
4
5
Figure 6-10: Moment at the column face versus panel zone plastic rotation
224
1
0.375% drift
0.500% drift
Nomalized distance from beam web
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.2
0.4
0.6
0.8
1
1.2
Normalized peak strain profile on top flange (ε /ε y)
1.4
Figure 6-11: Beam top flange tensile strain profiles
Nomalized distance from beam mid-depth
1
0.375% drift
0.500% drift
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.2
0.4
0.6
0.8
1
1.2
Normalized peak shear strain profile in web (γ/γy)
Figure 6-12: Beam web shear strain profiles
225
1.4
Moment at the column face (×1000 k-in)
60
Analysis
Experiment
50
40
30
20
10
0
0
0.5
1
1.5
2
2.5
3
3.5
Story drift angle (% radian)
4
4.5
5
Figure 6-13: Moment-drift relations for analysis and experiment in Model SH-EC03
Column
Beam
(ksi)
Figure 6-14: Von Mises stress distribution in the panel zone and the beam web at the 0.5-percent
story drift in Model SH-EC03
226
(ksi)
Beam
Column
Figure 6-15: Normal stress distribution along the top continuity plate and beam top flange at the
0.5-percent story drift in Model SH-EC03
227
1
0.8
Line
Line
Line
Line
A
B
C
D
Line
Line
Line
Line
A
B
C
D
Line
Line
Line
Line
A
B
C
D
0.6
0.4
0.2
0
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
a. Mises Index
-0.5
-0.4
-0.3
-0.2
-0.1
0
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
b. Pressure Index
-0.5
-0.4
-0.3
-0.2
-0.1
0
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
c. Triaxiality Index
Normalized distance from beam web centerline
Figure 6-16: Stress and fracture indices along the upper surface of beam top flange at the 0.5percent story drift in Model SH-EC03
228
y
ex
Dc
θb
ey
D
beam flange
Max lateral
Near flange
column
Far flange
Fflange
x
Top brace
A θc
B
C
Figure 6-17: Out-of-plane deformation of a beam column connection
Boundary point for column top
Hc
Lateral bracing for beam top flange
Lateral bracing for
actuator
No lateral
bracing for beam
bottom flange
Boundary point
for column bottom
Beam tip displacements
Figure 6-18: Model DC-UR00
229
Z
Lb/2
X
Tcol
Hs
P, Δ
Tbot
inflection point
Figure 6-19: Sub-assemblage for connection model
(a) Plan view of Reduced Beam Section connection (DC-RB00)
(b) Plan view of Welded Cover Plated Flange connection (DC-CP00)
(c) Side view of Free Flange connection (DC-FF00)
Figure 6-20: Meshing details of post-Northridge connection models
230
Hc
beam
column
Ttop
1.6
1.6
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0.5
0
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 6-21: Maximum Principal Index in Model SOL-EC03 beam flange at column face, Plane
A
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0
0.5
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0
0.5
Normalized distance, y/bf
(b) 2.0% drift
Figure 6-22: Mises Index in Model SOL-EC03 beam flange at column face, Plane A
231
-1
-1
-0.8
-0.8
-0.6
-0.6
-0.4
-0.4
-0.2
-0.2
0
0
-0.5
0.5
0
Normalized distance, y/bf
-0.5
(a) 0.5% drift
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 6-23: Pressure Index in Model SOL-EC03 beam flange at column face, Plane A
-2
-2
-1.5
-1.5
-1
-1
-0.5
-0.5
0
0
-0.5
0
0.5
Normalized distance, y/bf
-0.5
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0
0.5
Normalized distance, y/bf
(b) 2.0% drift
Figure 6-24: Triaxiality Index in Model SOL-EC03 beam flange at column face, Plane A
232
0.2
0.15
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.2
0.15
0.1
0.1
0.05
0.05
0
-0.5
0
-0.5
0.5
0
Normalized distance, y/bf
(a) 0.5% drift
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 6-25: Rupture Index in Model SOL-EC03 beam flange at column face, Plane A
1.6
1.6
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0
0.5
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0
0.5
Normalized distance, y/bf
(b) 2.0% drift
Figure 6-26: Maximum Principal Index in Model SOL-EC03 beam flange at weld access hole,
Plane B
233
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-0.5
0
-0.5
0.5
0
Normalized distance, y/bf
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 6-27: Mises Index in Model SOL-EC03 beam flange at weld access hole, Plane B
-1
-0.8
-0.6
-1
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
-0.8
-0.6
-0.4
-0.4
-0.2
-0.2
0
0
-0.5
0
0.5
Normalized distance, y/bf
-0.5
(a) 0.5% drift
0
0.5
Normalized distance, y/bf
(b) 2.0% drift
Figure 6-28: Pressure Index in Model SOL-EC03 beam flange at weld access hole, Plane B
234
-2
-2
-1.5
-1.5
-1
-1
-0.5
-0.5
0
0
-0.5
0.5
0
Normalized distance, y/bf
-0.5
(a) 0.5% drift
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.5
0
Normalized distance, y/bf
(b) 2.0% drift
Figure 6-29: Triaxiality Index in Model SOL-EC03 beam flange at weld access hole, Plane B
0.2
0.15
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
0.2
0.15
0.1
0.1
0.05
0.05
0
-0.5
0
-0.5
0
0.5
Normalized distance, y/bf
(a) 0.5% drift
0
0.5
Normalized distance, y/bf
(b) 2.0% drift
Figure 6-30: Rupture Index in Model SOL-EC03 beam flange at weld access hole, Plane B
235
C
B
A
Figure 6-31: Normalized maximum principal stress (MPI) distribution on the interface of the
beam flange in Model SOL-EC03 at 0.58-percent story drift
C
A
Figure 6-32: Equivalent plastic strain (PEEQ) distribution on the interface of the beam flange in
Model SOL-EC03 at 0.58-percent story drift
236
F
E
D
Figure 6-33: Normalized hydrostatic stress (PI) distribution on the interface of the beam flange in
Model SOL-EC03 at 0.58-percent story drift
25
20
Model SH-EC03
Specimen EC03
FR
15
(%)
beam
/EI
5
Simple
0
floor
4ML
PR
10
-5
Simple
4 M p , beam L floor
-10
(%)
EI beam
PR
-15
-20
-25
-4
FR
-3
-2
-1
0
1
Story drift angle (% radian)
2
Figure 6-34: Connection stiffness in Specimen EC03
237
3
4
1.4
Moment at the column face (M col/Mp )
1.2
1
0.8
0.6
0.4
DC-UR00
DC-URWP
DC-URFH
0.2
0
0
1
0.5
1.5
3.5
3
2.5
2
Story drift angle (% radian)
4.5
4
5
Figure 6-35: Comparison of global responses in Models DC-UR00, DC-URWP, and DC-URFH
1.0
BF
Column height (Z/Hs)
0.8
0.6
IP
0.4
0.2
BC
DC-UR00
DC-URWP
DC-URFH
0
0.1
0.2
0.3
0.4
Angle of column twist (% radian)
0.5
0.6
Figure 6-36: Comparison of twist angles in Models DC-UR00, DC-URWP, and DC-URFH along
the column height at 4-percent story drift
238
1.4
Moment at the column face (M col/Mp )
1.2
1
0.8
0.6
0.4
DC-UR00
DC-RB00
DC-FF00
DC-CP00
0.2
0
0
0.5
1
1.5
3.5
3
2.5
2
Story drift angle (% radian)
4
4.5
5
Figure 6-37: Comparison of global responses in Models DC-UR00, DC-RB00, DC-FF00, and
DC-CP00
Out-of-plane displacment (δLAT /bf)
0.1
0.08
DC-UR00
DC-RB00
DC-FF00
DC-CP00
0.06
0.04
0.02
0
-0.02
"A"
-0.5
"B"
0.5 "C"
1.0
Distance from the column face (x/Db)
"D"
Figure 6-38: Comparison of out-of-plane displacements in Models DC-UR00, DC-RB00, DCFF00, and DC-CP00 at 4-percent story drift
239
Figure 6-39: Connection detail of lateral beam braces in Building CT-15 (Design Documents
1990)
Column
Brace 2
Brace 1
Beam
RZ,BR2
RZ,BR1
RY,BR2
RY,BR1
2286 mm (90 in.)
Hinges
Figure 6-40: Lateral braces in Model DC-CP10
240
1.4
Moment at the column face (M col/Mp )
1.2
1
0.8
0.6
0.4
DC-CP00
DC-CP10
DC-CPBR
DC-CPNH
0.2
0
0
0.5
1
1.5
3.5
3
2.5
2
Story drift angle (% radian)
4
4.5
5
Figure 6-41: Comparison of global responses in Models DC-CP00, DC-CP10, DC-CPBR, and
DC-CPNH
0.4
DC-CP00
DC-CP10
DC-CPBR
DC-CPNH
Angle of column twist (% radian)
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
0
0.5
1
1.5
2
2.5
3
3.5
Story drift angle (% radian)
4
4.5
5
Figure 6-42: Comparison of column twist at the level of the beam bottom flange in Models DCCP00, DC-CP10, DC-CPBR, and DC-CPNH
241
0.06
DC-CP00
DC-CP10
DC-CPBR
DC-CPNH
Lateral reaction (RY/Py,flange)
0.05
0.04
0.03
0.02
0.01
0
0
0.5
1
1.5
3.5
3
2.5
2
Story drift angle (% radian)
4
4.5
5
Figure 6-43: Comparison of lateral reaction at the brace point in Models DC-CP00, DC-CP10,
DC-CPBR, and DC-CPNH
Total lateral reaction
Member force in Brace 1
Member force in Brace 2
Normalized force (P/Py,flange)
0.04
0.03
0.02
0.01
0
-0.01
-0.02
0
0.5
1
1.5
2
2.5
3
3.5
Story drift angle (% radian)
4
4.5
5
Figure 6-44: Comparison of lateral reaction and member forces in Brace 1 and Brace 2
242
L = 2,286 mm (90 in.)
Db = 914 mm (36 in.)
Abr = area of brace
Lbr = length of brace
Brace
E = Young’s modulus
Beam
Brace boundary
Δbr,Z = elongation due to UZ
Fbr,Z = force due to UZ
Brace point
=
Lbr
Vertical deflection
UZ = 52.8 mm (2.1 in.)
∆ br , Z =
=
Fbr , Z
L2 + Db2
L2 + ( Db + U Z ) 2 − L2br
E × Abr
∆ br , Z
Lbr
Figure 6-45: Computation of the brace force contribution by vertical deflection of beam
243
Chapter 7. Summary and Conclusions
7.1 Summary
FEMA-350 connections are pre-qualified only for W12 and W14 columns. There is not
enough test data upon which to base a performance evaluation or develop retrofit solutions for
moment connections to box columns or deep W-shape columns. The main objectives of this study
are to investigate the seismic performance, identify the key design variables, and to present
design recommendations for welded steel moment connections to box columns or to deep Wshape columns. To achieve the objectives three phases of work were conducted: theoretical
studies to identify factors influencing connection ductility, physical and numerical investigations
on the seismic performance of pre-Northridge connections, and parametric studies on connections
to box or deep W-shape columns.
In the theoretical studies, three factors influencing connection ductility were identified:
brittle fracture, inelastic instability, and residual rotation capacity. Models to evaluate these
factors were suggested. The metallurgical characteristics of fracture were studied first, and the
effects of deformation restraint on metal fracture were investigated using a simple analytical
model and finite element models. Existing methods to assess the potential of fracture were
reviewed. A procedure to identify the likelihood of brittle fracture of the weld in the absence of
defects was proposed. The results of previous research were investigated to study the inelastic
instability of the welded steel moment connections. The classical theories on inelastic instability
in beams, flange local buckling, web local buckling, and lateral-torsional buckling, were
summarized. A model for strength degradation was suggested using the amplitude of local flange
buckling as a key variable. Damage to shear tabs was investigated to gage the residual strength of
244
flange fractured connections. A simple design approach for shear tabs in moment connections
was suggested on the basis of the results of cyclic nonlinear finite element analysis.
In the experimental studies, three beam-column connections from an existing building
designed and built before the 1994 Northridge earthquake were selected as test specimens. These
specimens were constructed using pre-Northridge connection details and welding procedures. A
test fixture was designed and constructed to accommodate all three specimens in a horizontal
plane. The test fixture included two lateral-restraint frames that served to replicate the restraint
provided to the beams in the field. A cyclic displacement history was applied at the tip of the
beam following the AISC prequalification test procedure. Tests were continued until the beam
section had completely separated from the column. The observed performance of these
connections was poor.
In parallel with the test program, the connections were analyzed using nonlinear finite
element techniques. These analytical models were used to augment and interpret the test results.
The causes of brittle fracture in the test specimens were investigated using solid finite element
analysis and the models proposed in the first part of this thesis. The key design variables were
identified as: column shapes, continuity plate strength, column plates stiffness, and loading
directions for box column connections; and column boundary conditions, connection types, and
beam lateral bracing for deep W-shape column connections. A series of parametric finite element
studies for these design variables were conducted to formulate tentative design recommendations.
7.2 Conclusions
In modern construction heavy W-shape beams, deep W-shape columns, and column
shapes other than the traditional W-shape are often preferred as a component of a welded steel
moment frames because moment-resisting frames designed with such component can provide
better drift control and can be somewhat more economical. A comprehensive series of pre245
qualification tests is now mandatory for all connections that fall outside the prequalified
connection parameter space evaluated to date. Full-scale connection tests and finite element
analyses can be used to expand the parameter space. This research project involved integrated
experimental and analytical studies for welded steel moment connections to box or deep W-shape
columns for the purpose of expanding the prequalified connection parameter space. The key
conclusions from the studies reported in this thesis are:
Factors influencing connection ductility
1. Stress concentrations due to end effects in the CJP welds between a beam flange and column
can cause microcracking when the maximum principal stresses exceed the tensile strength of
the material. Due to the microcracking, an initial crack might form without any apparent weld
defect. High stress triaxiality is such a sufficient condition for brittle fracture initiation. When
the driving force at the crack tip exceeds the fracture resistance of the material under the high
stress triaxiality, brittle fracture may occur.
2. The location, size, and propagation of initial cracks induced by high principal stresses can be
predicted using a new principal stress model proposed in this thesis. The observed locations
of cracks in the test specimens matched closely with the regions subjected to high tensile
principal stress. Stress intensity factors at a crack tip were computed using the crack size
predicted by the proposed model. A critical magnitude of stress intensity factor that could
trigger brittle fracture in low notch-tough weld metal was identified in Section 5.3.2. The
direction of crack propagation was perpendicular to the axis of maximum principal stress.
3. Brittle fracture in CJP welds of beam flanges can be prevented by using high toughness-rated
weld metal, by using pre-qualified connection detail, and by reinforcing the fracture critical
region with weld overlays.
4. Under moment gradient in a steel W-shape beam, flange local buckling triggers web local
buckling and lateral-torsional buckling. Such buckling also leads to strength degradation in
246
the moment connection because the flange subjected to high amplitude local buckling cannot
transmit the compression force due to local P-delta effects.
5. The amplitudes of flange local buckling are affected by the slenderness ratio of each
component in the W-shape and the type of moment connection. Highly slender components
and connection details in which a plastic hinge is located further away from the column face
increase the buckling amplitude and lead to rapid degradation in the strength of the
connection. Additional research to correlate AISC Seismic Provisions (AISC 2002) on
slenderness limits and rate of strength degradation is needed.
6. Because the three buckling modes (flange local buckling, web local buckling, and lateraltorsional buckling) are interrelated, control of one buckling mode affects the buckling
amplitudes of the other buckling modes. Therefore, increasing the web slenderness ratio or
bracing the lateral movement of beam flanges can reduce the amplitude of flange local
buckling, and delay the loss of strength of the connection.
7. The shear tab connection is the final line of defense against progressive collapse of momentresisting frames. Even if the flange fractures, the shear tab connection can still resist gravity
loads and a limited amount of lateral loads, albeit with a significantly reduced lateral stiffness.
Rotation capacity of a post-fracture moment connection is limited by net section fracture of
shear tab and fracture of shear tab bolts. Ductile detailing of shear tab connection components
may slightly improve the residual rotation capacity of a connection.
Performance of pre-Northridge connections
8. None of the three tested full-scale connections exhibited any plastic rotation in either the
beams or the panel zone. The story drift angles associated with beam flange fracture were
substantially less than 1 percent. This observation can be attributed to a number of factors
including the large size and depth of the beams, the use of non-toughness rated weld metal,
and sub-optimal weld access hole details. The three connection evaluated in the experimental
247
program are at least as vulnerable to earthquake shaking as the pre-Northridge connections
tested within the SAC Joint Venture Steel Project.
9. Maximum tensile principal stresses exceeding material tensile strength were identified using
a finite element model at the crack location of the tested specimens at drift levels
corresponding to flange fracture in the tests. Stress triaxiality in front of the crack location
was high enough to delay yielding. Computed stress intensity factors at the crack tip were
large enough to cause brittle crack propagation.
10. The residual strength of the beam-column connections immediately following fracture of both
beam flanges ranged between 22 percent and 45 percent of the plastic moment of the beam
section. The residual strength degraded with repeated cycling. Flange fracture significantly
reduced the lateral stiffness of the connection. After fracture the connections were no longer
fully-restrained. Instead, these can be classified as pinned using the AISC LRFD
methodology (AISC 2001). The story drift angle at which the residual strength of the
connections was completely lost ranged between 3 and 4 percent. Loss of residual strength in
these connections was associated with fracture of the shear tab or bolts. Such fracture may
lead to the loss of gravity load-carrying capacity of the beam that may initiate progressive
frame collapse.
Box column connections
11. The force transfer mechanism in box column connections is different from that in traditional
W-shape column connections. Most of beam flange force is transmitted to the column web
plates through continuity plates in the box column connection, whereas the flange forces are
transmitted to the column web directly or through a part of the continuity plate in the Wshape column connection.
12. Because the continuity plate transmits the beam flange force to the box column, its strength
and stiffness affect the global response as well as local response of a box column connection.
248
The strength and stiffness of the connection decrease as the thickness of the continuity plate
decreases. Local yielding or plastic buckling of a continuity plate leads to further losses in
strength and stiffness. If the continuity plate is too thin or is not installed, the connection may
not be stiff enough to qualify as a rigid connection. Continuity plates thicker than the beam
flange will prevent local yielding and plastic buckling and produce a rigid connection.
13. As the thickness of a continuity plate decreases the out-of-plane bending stiffness of the
column flange plates increasingly impacts the response of a box column connection. Local
bending of the column flange plate causes beam web rotation and accommodates most of the
connection rotation. Consequently, a plastic hinge will not develop in the beam. Instead, the
plastic hinge forms partially inside the box column, moving the theoretical center of
connection rotation closer to the column centerline. If the column flange plate is thicker than
the thickness associated with yielding in the column flange plate (Section 5.4.2), the moment
capacity of the connection will match that of W-shape column connections.
14. As long as the continuity plate in box column connection is thicker than the largest framing
beam flange thickness, the local and global response of the connection are not affected
substantially by biaxial loading. However, if the thickness of the continuity plates is not
sufficient, local deformation and tensile stresses in the corner of the connection increase in
magnitude and may lead to brittle fracture in the welds joining the column plates. Reinforcing
the reentrant corner of a box column with notch-tough fillet weld may reduce the potential of
brittle fracture in that region.
15. Damage inside a box column cannot be easily inspected and repaired. Therefore, continuity
plates, column plates, and box column welds should be carefully designed and detailed to
prevent such damage. It is also recommended to use notch-tough weld metal and good
welding procedure.
249
Deep column connections
16. Deep columns tend to twist because the beam flange force becomes eccentric to the column
axis after local or lateral-torsional buckling occurs in the beam plastic hinge. Such twisting
can lead to large strain demands along the k-line of a W-shape column and can cause fracture.
Furthermore, initial twisting of the column can be exacerbated by high axial loads, and could
result in column lateral-torsional buckling over several stories. The likelihood of this
occurring depends on the beam and column geometry, bracing provided as floor diaphragms,
as well as other design variables in the deep column connections.
17. The out-of-plane deformation of deep column connections depends on the torsional boundary
condition on the column. The assumed boundary condition affects the angle of twist in the
column but does not change the torque distribution along the height of the column: column
height variation significantly changes the torque distribution and column twisting. For
example, a large torque inducing high warping and causing fracture along the k-line develops
in the panel zone of the connection modeled with a full-height column above and below it.
The current practice of using the column mid-height inflection point as a boundary for a
connection subassembly may underestimate such warping stresses in deep column
connections. More research of this issue is needed.
18. The out-of-plane response of deep column connections is affected by the type of moment
connection. Maximum beam lateral displacement of Reduced Beam Section and Cover Plate
connections are much higher than those of Unreinforced and Free Flange connections,
because the lateral stiffness of the beam flange is reduced due to either high amplitude flange
local buckling or a reduced beam area. The large out-of-plane displacement of the beam
flange can lead to excessive column twisting. To prevent column twisting, lateral bracing
may be required for a connection in which in-plane stiffness of the beam flange is small or
the amplitude of flange local buckling is anticipated to be high.
250
19. The bracing force is affected by the location, stiffness, and configuration of the lateral beam
brace. Beam lateral bracing close to the beam plastic hinge is most effective because it
reduces the column twist angle and brace force. The stiffness of a brace does not change the
response of the connection compared to that using a rigid lateral restraint in a finite element
model, as long as the brace is stiffer than that required by the AISC LRFD Manual (AISC
2001).
20. The force developed in a horizontal lateral brace is caused by restraining the lateral
movement of a beam flange while that in the diagonal brace is caused primarily by restraining
the vertical movement of the beam. In service, the brace force in the diagonal brace may not
be large as that computed by the numerical model due to the flexibility of the floor slab and
adjacent gravity beam to which the brace is attached. However it is possible that the brace
force may exceed the strength required in the AISC LRFD Manual (AISC 2001). In such a
case, the brace may no longer restrain the lateral movement of the beam flange. Analysis of a
significantly more complex model, which includes the floor slab and gravity beams, is
required to refine these studies further.
251
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