10NCEE
Tenth U.S. National Conference on Earthquake Engineering
Frontiers of Earthquake Engineering
July 21-25, 2014
Anchorage, Alaska
A MODEL FOR PREDICTING PANEL ZONE
DEFORMATION CAPACITY IN
REHABILITATED STEEL MOMENT
CONNECTIONS
Dong-Won Kim1, Chia-Ming Uang2, and Colin Blaney3
ABSTRACT
Three full-scale specimens that simulated rehabilitated pre-Northridge steel moment connections
were tested to failure. A Kaiser Bolted Bracket (KBB) was used on the beam bottom flange for
all specimens, but different rehabilitation schemes [KBB, complete-joint-penetration (CJP)
replacement weld, or welded double-tee bracket with CJP replacement weld] were used for the
beam top flange. Test results showed that the proposed rehabilitation schemes adequately
protected the pre-Northridge moment connections to an acceptable story drift angle. Large panel
zone deformation with significant yielding occurred in all specimens. An analytical model was
developed to predict the panel zone deformation capacity and the associated strength. In the
proposed model, it was postulated that the notch-tough CJP welds located at the column kinking
locations would fracture when the column flange was fully yielded there; this limit state was
used to define the ultimate deformation capacity of the panel zone. The proposed model not only
correlated very well with the test results but also showed that the deformation capacity is a
function of db/tcf, where db is the beam depth, and tcf is the column flange thickness. The effect of
column axial load on the panel zone shear deformation was also considered in the model.
1
Ph.D Candidate, Dept. of Structural Engineering, University of California, San Diego, La Jolla, CA 92092
Professor, Dept. of Structural Engineering, University of California, San Diego, La Jolla, CA 92092
3
Executive Principal, ZFA Structural Engineers, San Francisco, CA 94104
2
Kim DW, Blaney C, Uang, CM. A Model for Predicting Panel Zone Deformation Capacity in Rehabilitated Steel
Moment Connections. Proceedings of the 10th National Conference on Earthquake Engineering, Earthquake
Engineering Research Institute, Anchorage, AK, 2014.
A Model for Predicting Panel Zone Deformation Capacity in
Rehabilitated Steel Moment Connections
Dong-Won Kim1, Chia-Ming Uang2, and Colin Blaney3
ABSTRACT
Three full-scale specimens that simulated rehabilitated pre-Northridge steel moment connections
were tested to failure. A Kaiser Bolted Bracket (KBB) was used on the beam bottom flange for all
specimens, but different rehabilitation schemes [KBB, complete-joint-penetration (CJP)
replacement weld, or welded double-tee bracket with CJP replacement weld] were used for the
beam top flange. Test results showed that the proposed rehabilitation schemes adequately
protected the pre-Northridge moment connections to an acceptable story drift angle. Large panel
zone deformation with significant yielding occurred in all specimens. An analytical model was
developed to predict the panel zone deformation capacity and the associated strength. In the
proposed model, it was postulated that the notch-tough CJP welds located at the column kinking
locations would fracture when the column flange was fully yielded there; this limit state was used
to define the ultimate deformation capacity of the panel zone. The proposed model not only
correlated very well with the test results but also showed that the deformation capacity is a
function of db/tcf, where db is the beam depth, and tcf is the column flange thickness. The effect of
column axial load on the panel zone shear deformation was also considered in the model.
Introduction
Rehabilitation of pre-Northridge steel moment connections to avoid brittle fracture in the
beam flange weld joints is a challenging task to design engineers. Designed before PreNorthridge earthquake, it is also not uncommon that very weak panel zone exists in these
connections.
To support the seismic rehabilitation of a steel moment frame building constructed before
1994, three full-scale specimens were tested. Test results showed that panel zone yielding was
the primary source of energy dissipation. Two specimens eventually experienced fracture at the
notch-tough CJP welds at the column kink locations due to excessive panel zone deformation.
This motivated the development of a procedure to predict the ultimate panel zone deformation
capacity beyond which beam flange CJP weld fracture is imminent.
1
Ph.D Candidate, Dept. of Structural Engineering, University of California, San Diego, La Jolla, CA 92092
Professor, Dept. of Structural Engineering, University of California, San Diego, La Jolla, CA 92092
3
Executive Principal, ZFA Structural Engineers, San Francisco, CA 94104
2
Kim DW, Blaney C, Uang, CM. A Model for Predicting Panel Zone Deformation Capacity in Rehabilitated Steel
Moment Connections. Proceedings of the 10th National Conference on Earthquake Engineering, Earthquake
Engineering Research Institute, Anchorage, AK, 2014.
Test Program
Test Specimens
Three nominally identical pre-Northridge moment connections with a W36150 beam
and a W14193 column were rehabilitated and tested. As a rehabilitation scheme, a Kaiser
Bolted Bracket (KBB) was used on the beam bottom flange for all specimens, but different
rehabilitation schemes were used to strengthen the beam top flange; this included the use of
another KBB for Specimen 1, a notch-tough complete-joint-penetration (CJP) beam flange
replacement groove weld for Specimen 2, as well as a welded double-tee bracket and a
replacement weld for Specimen 3 [4, 9]. Table 1 shows the mechanical properties of the
materials obtained from tensile coupon tests for the specimens.
Table 1.
Steel Mechanical Properties
Component
Yield Stress
(MPa)
Tensile Strength
(MPa)
Elongation*
(%)
Beam Flange (W36×150)
425
523
33
Column Flange (W14×193)
* based on a 51-mm gage length
428
555
31.5
Fig. 1 shows the test setup. A corbel was bolted to the end of the beam and attached to
two 980-kN hydraulic actuators. With some minor modification, the loading sequence specified
in Appendix S6.2 of AISC 341-10 [1] for beam-to-column moment connection test was used.
Since the target story drift for this rehabilitation project was 3.5% story drift, the AISC loading
protocol was modified to include two additional cycles at 3.5% story drift.
Bracing
Bracing
Location A Location B
2,286
Column
(W14x193)
Corbel
Beam
(W36x150)
Two 980-kN
Hydraulic
Actuators
2,286
4,420
Figure 1.
Test Setup (Specimen 3)
Units: mm
Test Results
Significant shear yielding in the panel zone was observed in all three specimens. The
KBBs remained intact and showed no sign of yielding or damage. For Specimen 1, the double
KBBs forced beam plastic hinging in the form of flange and web local buckling as well as
lateral-torsional buckling near the tip of the KBBs.
Specimen 2 experienced significant yielding in the panel zone, but the extent of beam
plastic hinging was very limited with no sign of buckling. After completing one cycle at 4%
story drift, fracture of beam top flange at the replacement weld occurred during the second cycle.
The behavior of Specimen 3 was similar to that of Specimen 2, i.e., inelastic action occurred
mainly in the panel zone. The CJP weld connecting the horizontal plate of the double-tee bracket
to the column flange started to fracture at 4% story drift. Brittle fracture occurred during the
cycle of 4.5% story drift (see Fig. 2).
Applied Load (kN)
1500
-6
-4
Story Drift Ratio (%)
-2
0
2
4
6
1000
500
0
-500
-1000
-1500
-300
Fracture
-200 -100
0
100 200
Beam Tip Displacement (mm)
300
(a)
Applied Load (kN)
1500
-6
-4
Story Drift Ratio (%)
-2
0
2
4
6
1000
500
0
-500
-1000
-1500
-300
Fracture
-200 -100
0
100 200
Beam Tip Displacement (mm)
300
(b)
Figure 2.
Test Results: (a) Specimen 2; (b) Specimen 3
Effective Depth of Extended Panel Zone in Rehabilitated Steel Moment Connection
Large panel zone deformation caused the column flange to kink at four corners of the
panel zone. With the addition of KBBs and double-tee bracket, the panel zone was extended in
depth. AISC 358 [2] defines the effective depth, d eff , of the extended panel zone as the centroid
distance between column bolt groups in the KBBs. Generalizing the AISC definition to
Specimens 2 and 3, the definition of d eff is shown in the Fig. 3.
CJP Weld and Panel
Zone Kink Location
CJP Weld and Panel
Zone Kink Location
deff
deff
(a)
Figure 3.
4000
(b)
Effective Depth of Extended Panel Zone: (a) Specimen 2; (b) Specimen 3
-10
Normalized Shear Deformation, y
-5
0
5
10
4000
Shear Force (kN)
Shear Force (kN)
Normalized Shear Deformation, y
-5
0
5
2000
1000
0
-1000
-2000
2000
1000
0
-1000
-2000
-3000
-3000
-0.02
0.0
0.01
0.03
Panel Zone Shear Deformation (rad.)
-4000
-0.04
-0.02
0.0
0.01
0.03
Panel Zone Shear Deformation (rad.)
(a)
Figure 4.
10
3000
3000
-4000
-0.04
-10
(b)
Cyclic Response of Extended Panel Zone: (a) Specimen 2; (b) Specimen 3
The shear in the extended panel zone can be computed as follows:
Mf
V 
 Vc
(1)
0.95d eff
where Mf = moment at the face of column, and Vc = shear in the column. The cyclic responses of
the extended panel zones for Specimens 2 and 3 are presented in Fig. 4.
Panel Zone Shear Deformation Capacity
Panel zone behavior was extensively researched [5, 6, 7, 8, 10, and 11]. However, past
research was mainly focused on the strength, not the ultimate deformation capacity beyond
which excessive kinking in the column flanges would cause fracture of the beam flange CJP
welds.
It was obvious from Fig. 4 that a panel zone could deform to a deformation level much
higher than 4γy, a deformation level corresponding to the panel zone strength in AISC 360 [3].
But excessive deformation could cause fracture in the beam flange-to-column flange CJP weld.
To predict the panel zone deformation and the associated strength, an alternative model is
developed. The panel zone behavior is established by superimposing the responses of the column
web and flanges (see Fig. 5). The web area is taken as 0.95dctcw. Therefore, the shear yield
strength of the column web is
(2)
Vcw, y  0.6 Fy 0.95d c t cw 
With  y  0.6 Fy / G , the elastic shear stiffness of the column web is:
K cw 
Vcw, y
y
 0.95d c t cw G
(3)
Since strain hardening generally exists for the steel grades ( Fy  345 MPa) permitted in
AISC 341-10 [1], a shear strain hardening ratio of 0.03 is considered as shown in Fig. 5(a). The
strain hardening ratio of 0.03 is based on monotonic torsional coupon test results conducted by
Slutter [12].
Since each column flange in the panel zone region would bend about its weak axis in
reverse curvature, the model in Fig. 6(a) is used to consider the contribution from column
flanges. It is idealized that each column flange will deform elastically until the plastic moment of
the column flange is reached:
 bcf t cf 2 
F
(4)
M p ,cf  
 4  yc


The associated panel zone deformation, which is the chord angle in Fig. 6(b), corresponds
to γpz in Figure 5. It is postulated that γpz can be defined as the plastic deformation capacity of the
panel zone beyond which the notch-tough CJP weld at the kink locations is prone to fracture.
This postulation is to be verified by test data. The derivation of γpz follows.
Vcw
Vcw
Vcw, y
V pz
Vcf
0.03K cw
Kcw  0.95dctcwG
y
 pz
(a)
Figure 5.
V pz
+ V
p ,cf

=
2Kcf
y
 pz
(b)

Vy
y
 pz

(c)
Superposition of Proposed Shear Strength Components: (a) Column Web Panel Zone
Response; (b) Response of Two Column Flanges; (c) Superposition
Mp , cf
Mp , cf
0.95d b
2
pz
0.95d b
pz

Vp , cf 
2 Mp , cf
0.95db

Moment Diagram
(b)
0.95d c
(a)
Figure 6.
Panel Zone Model: (a) Panel Zone Deformation; (b) Mathematical Model
Consider one fix-ended “column-flange flexural member” with a span of 0.95db and a
depth of tcf (see Fig. 6). The shearing effect of this flexural member can be significant when the
span (= 0.95db) is small and the column flange (tcf) is thick. Applying elastic beam theory, the
mid-span deflection when the fixed-end moment reaches Mp,cf is:
3
1  M p ,cf  0.95d b 
1  M p ,cf  0.95d b 

 





GAs ,cf  0.95d b / 2 2 
3EI cf  0.95d b / 2 2 
 d 2
 M p ,cf
 2
 M p ,cf
  b 2  3.12

 3.12
1.11t cf
 Ebcf t cf 1.11
 Ebcf t cf
3
where Icf (= bcf t cf / 12 ) and As ,cf
(5)
(= 5bcf t cf / 6 ) are the moment of inertia and shear area of one
column flange, respectively. In the above equation, the coefficient  is the related span-depth
ratio of the column-flange flexural member:
  d b / t cf
(6)
The first term on the right-hand side in Eq. 5 is the flexural component and the second term is the
shearing component. Dividing  by 0.95d b / 2 and simplifying gives the ultimate deformation
capacity of the panel zone (see Fig. 6):
0.475Fyc 
3.45 
(7)
 pz 

 
E
 

The elastic stiffness of one column flange is
V p ,cf
2M p ,cf
1.11Ebcf t cf
(8)

 2
K cf 
 pz
0.95d b  pz
  3.45
The total elastic stiffness for both column flanges is 2 K cf , as shown in Fig. 5(b). Therefore, the
total panel zone shear strength in the elastic range is
when 0     y
V pz  K cw  2 K cf  
(9)
When  y     pz , the components of panel zone shear strength due to column web and two
column flanges are [see Fig. 5(a)]
(10)
Vcw  Vcw, y  0.03K cw    y 
Vcf  2 K cf 
(11)
(12)
4000
4000
3500
3500
Shear Force (kN)
Shear Force (kN)
Therefore, the total panel zone shear strength is
when  y     pz
V pz  Vcw  Vcf
3000
2500
pz/y
2000
(= 8.99)
1500
Test
Proposed
AISC
1000
500
0
0
2
4
6
8
10
Normalized Shear Deformation, y
Figure 7.
3000
2500
pz/y
2000
(= 10.04)
1500
1000
Test
Proposed
AISC
500
12
0
0
2
4
6
8
10
12
Normalized Shear Deformation, y
(a)
(b)
Comparison of panel zone responses: (a) Specimen 2; (b) Specimen 3
Based on Eqs. 9 and 12 and replacing d b with d eff , the predicted panel zone responses
for Specimens 2 and 3 up to γpz are shown in Fig. 7. The predicted panel zone behaviors
reasonably match well. The ratios between the predicted and experimental panel zone ultimate
deformations are 1.02 and 0.94 for Specimens 2 and 3, respectively.
Normalizing the panel zone ultimate deformation capacity,  pz , in Eq. 7 by  y (=
0.6Fy/G) gives the following:
 pz
3.45 

(13)
 0.30  

y
 

Fig. 8 shows the variation of the normalized panel zone ultimate deformation with respect to 
(= db/tcf). It is shown that the AISC assumed panel zone deformation capacity (4γy) can be very
conservative for a high db/tcf ratio. When the db/tcf ratio is low (i.e., a shallow beam connected to
a thick column flange), on the other hand, the panel zone deformation can be lower than 4γy.
Therefore, column flanges at kink locations would yield early when db/tcf is low, which makes
the beam flange-to-column flange CJP welds more prone to fracture at a low panel zone
deformation (  4 y ).
Normalized Panel Zone
Deformation, pz/y
20
15
Eq. (13)
10
5
0
Figure 8.
AISC (4y)
0
10
20
30
(= db/tcf)
40
50
Relationship between Panel Zone Ultimate Deformation Capacity and 
Panel Zone Deformation, ‫׳‬pz
0.05
Figure 9.
P/2Py,cf = 0
P/2Py,cf = 0.25
P/2Py,cf = 0.5
P/2Py,cf = 0.75
0.04
0.03
0.02
0.01
0.0
0
10
20
30
40
50
Column Flange Span-Depth Ratio, (= db/tcf)
Effect of Column Axial Load on Panel Zone Shear Deformation Capacity (A992 Steel)
Effect of Column Axial Force
With the presence of an axial load, Krawinkler et al. [7] reported that column flanges
carry all the axial load after the panel zone web has completely yielded. This is also the basis of
the panel zone design shear strength with high axial load in AISC 360-10 [2]. Based on the same
assumption, one can derive the reduced moment capacity of one column flange as
  P 2 
 
(14)
M p ,cf  M p ,cf 1  
  2 Py ,cf  


Therefore, the corresponding shear of one column-flange flexural member in Fig. 6 is
  P 2 
2M p ,cf
 
V p,cf 
(15)
 V p ,cf 1  
0.95d b
  2 Py ,cf  


Following the similar procedure described in Eqs. 5 and 7, the reduced plastic shear deformation
can be derived by replacing M p ,cf and V p ,cf by M p ,cf and V p,cf :
2
  P 2 
0.475Fyc 
3.45    P  
 
(16)
  pz 1  
 pz 
 
 1
E
    2 Py ,cf  
  2 Py ,cf  





Fig. 9 shows the effect of column axial load on the panel zone ultimate deformation capacity.
The associated panel zone shear strength at  pz is established as follows. The component
of panel zone shear strength due to column web from Eq. 10 can be approximated as
Vcw  Vcw, y  0.03K cw  pz   y 
From Eq. 15, the component of the panel zone shear strength due to two column flanges is
  P 2 
 
Vcf  2V p,cf  2V p ,cf 1  
  2 Py ,cf  


Therefore, the total panel zone shear strength is
V pz  Vcw  Vcf
(17)
(18)
(19)
Fig. 10 shows example plots of the panel zone axial-shear interaction curves. A
W36×150 beam with three different W14 column sections in Fig. 10(a) and W36 column
sections in Fig. 10(b) are considered. It is observed that axial load has a significant effect on the
panel zone deformation capacity than on the shear strength. Since the interaction between axial
load and panel zone shear strength is relatively weak, the axial load effect can be ignored for
simplicity when P / 2 Py ,cf  0.6 (or P / Py ,cf  1.2 )..
1.0
Normalized Panel Zone
Shear Strength, V’pz /Vpz
Normalized Panel Zone
Shear Strength, V’pz /Vpz
1.0
0.8
0.6
0.4
W14X109
Column
W14X109
Column
W14X193
Column
W14X193
Column
W14X370
Column
W14X370
Column
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.8
0.6
0.4
0.0
0.0
Normalized Axial Load, P/2Py,cf
(a)
Figure 10.
W36X210
Column
W36X210
Column
W36X231
Column
W36X231
Column
W36X361
Column
W36X361
Column
0.2
0.2
0.4
0.6
0.8
1.0
Normalized Axial Load, P/2Py,cf
(b)
Interaction of Shear and Axial Force: (a) W14 Columns; (b) W36 Columns
Summary and Conclusions
An analytical model was developed to predict the panel zone ultimate deformation
capacity and the associated strength in rehabilitated steel moment connections; the ultimate
deformation was defined as that beyond which excessive kinking in the column flanges would
cause weld fracture in the beam CJP welds. The effect of column axial load was also included in
the formulation. The conclusions are summarized as follows.
(1)
The proposed model (see Eqs. 7 and 13) showed that the ultimate deformation
capacity is a function of db/tcf. The low db/tcf ratio (i.e., a shallow beam connected to a column
with thick flanges) may result in earlier yielding of the column flanges at the kink location and
makes the CJP welds more vulnerable to fracture.
(2)
The column axial load effect on the panel zone ultimate deformation capacity can
be significant (see Eq. 16). But the effect on shear strength is relatively insignificant (see Fig. 10)
and can be ignored when the column axial load is less than 1.2 times the yield force of one
column flange.
Acknowledgements
This project was sponsored by Civic Facilities Division of the City of Fremont.
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