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A phenomenological component-based model to simulate seismic
behavior of bolted extended end-plate connections
Pu Yang a, Matthew R. Eatherton b,
a College of Civil Engineering, Chongqing University, Chongqing 400045, PR Chinab Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg 24060, VA, USA
a r t i c l e i n f o
Article history:
Received 5 August 2013
Revised 16 May 2014
Accepted 17 May 2014
Keywords:
Component-based model
Phenomenological model
End-plate connections
Seismic behavior
Moment-resisting connections
Computational simulation
a b s t r a c t
In order to investigate seismic behavior of bolted extended end-plate connections, a phenomenological
component-based model with several separated springs is presented where the constitutive relationships
for individual components are determined using material and geometric properties. Analytical results
using the developed model were compared with experimental data from full-scale moment connection
tests including global load versus displacement and local response of beam hinge, panel zone and other
components. The effectiveness of the model was demonstrated by these comparisons. The model is then
leveraged to study the influence of design decisions such as weak columns and bolt pretension. The
analytical results indicate that bolt pretension and related connection slip can significantly affect the
seismic behavior of the end-plate and column flange and thus their inclusion in the proposed model is
validated.
2014 Elsevier Ltd. All rights reserved.
1. Introduction
Steel end-plate moment connections are an important connec-
tion type used in many buildings in seismic regions. There have
been numerous previous experimental programs investigating
the behavior of end-plate moment connections subjected to
monotonic and cyclic loading and similarly, a range of computa-
tional models and analytical expressions have been developed to
simulate their behavior. High fidelity three dimensional finite
element (FE) models are presented in the literature that can cap-
ture monotonic and cyclic response of end plate connections in
small subassemblages such as those tested in the lab. On the other
hand, analytical expressions and simplified component models
have been developed to model the behavior of end plate connec-
tions subjected to monotonically increasing moment. Although
these models allow computationally efficient analysis of end plate
moment frames, they are typically not capable of capturing the
seismic response of a frame subjected to inelastic cycles.
In the context of modern earthquake engineering which focuses
on probabilistic evaluation of seismic performance, computation-
ally efficient numerical models of seismic resisting systems are
critical. For example, evaluating the suitability of seismic perfor-
mance factors such as the response modification factor, R, used
in current United States building codes, often requires thousands
of response history analyses on archetype buildings[1]. Similarly,
performance based earthquake engineering design of new
buildings[2]and retrofit of existing buildings[3]requires numer-
ous response history analyses to verify seismic performance and in
some cases iterate on the structural configuration and details. Con-
ducting these types of studies using three dimensional FE models is
not feasible making cyclic component models necessary.
A brief overview of the types of models available in the litera-
ture is provided here although more thorough background on
end plate modeling is provided elsewhere [4]. A number of the
models developed in the literature are constructed and calibrated
for flush end plates or end plates that are extended only on one
side that do not conform to prequalified seismic extended end
plate connections in the United States[5]. Furthermore, as noted
below, the studies are almost exclusively developed for monotonic
loading only.
There have been a number of previous studies that created
detailed three dimensional finite element (FE) models of end plate
connections with continuum elements, contact, bolt pretension,
and more [610]. These models have been shown to accurately
capture the behavior of a wide range of end plate moment
connections to different loading scenarios.
In an effort to create simplified models, researchers have
developed analytical equations to model moment rotation
behavior of flush end plate connections [11,12], and extended
http://dx.doi.org/10.1016/j.engstruct.2014.05.023
0141-0296/ 2014 Elsevier Ltd. All rights reserved.
Corresponding author. Tel./fax: +1 540 231 4559.
E-mail address:[email protected](M.R. Eatherton).
Engineering Structures 75 (2014) 1126
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end plate connections [7,12,1316]. Several of these models
analytically decompose the connection into components and thensum up their moment-rotation behavior. In effect, these models
can be considered as a component model with a single rotational
spring at the intersection of the beam and columns. Some
researchers have even extended the analytical equations to work
for cyclic loading[17,18].
Another approach is to explicitly model each component of the
end-plate connection as a discrete spring. Anderson and Najafi [19]
developed a simplified component model to capture monotonic
behavior of extended end plate connections with a composite slab.
Assemblies included a few springs that lumped end plate behavior
in with beam flange and column behavior. More recently,
component models have been developed for flush end plates with
composite slabs [20], extended end plate connections [21],
extended end plate models capable of capturing ultimate rotationand ductility [22], and end plate connection models capable of
capturing flexure-axial interaction [4]. However, all of thesecomponent models were constructed and calibrated to work for
monotonic loading only.
There has also been substantial work on component modeling
of end plate connections subjected to elevated temperature. These
vary in complexity and can capture behavior of short end plates
[23], and full depth end plates[2426], but similarly are calibrated
for monotonic behavior and do not capture cyclic behavior.
Considerably fewer examples of component models exist capa-
ble of modeling cyclic behavior of semi-rigid steel connections.
Rassati et al. [27] developed a component model for a partially
restrained composite connection with bottom seat angles and
composite concrete slab. Kim et al. [28] developed a component
model to capture the behavior of top and seat angle connections
with double angle web connection to column.In this paper, a phenomenological component-based model is
developed to simulate cyclic behavior of bolted extended end-plate
connections. Bilinear or tri-linear constitutive relationships based
on material and geometric properties of the connection are used
to represent the behavior of connection components. The connec-
tion is decomposed into components related to the deformation
of the column flange, column web, end-plate, panel zone, and a slip
model is used to simulate the relative slippage between end-plate
and column flange. The model is built based on connection
geometry and material properties and thus does not require
calibration. The proposed model is developed and then applied to
specific connection configurations, subjected to cyclic loading,
and evaluated against experimental results.
2. Phenomenological component-based model
2.1. Identification of key deformation sources and model description
The key components which contribute to the deformation of
steel bolted extended end-plate connections are shown in Fig. 1
and include, going from left to right: (1) shear deformation of col-
umn web including consideration of continuity and doubler plates;
(2) compression of the column web; (3) bending of the column
flange; (4) vertical slip between the end-plate and column flange;
(5) bending of the extended end-plate in association with elonga-
tion of the bolts in tension; and (6) inelastic deformations of the
beam in the plastic hinge region. These deformation sources and
the proposed phenomenological component-based model areshown inFig. 1.
Fig. 1. An extended end-plate connection and analytical model.
Fig. 2. Constitutive relationship of components.
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The component-based model was implemented in the Open-
Sees software [29]. Nonlinear springs are used to simulate the
behavior of each of the key components of the connection listed
above. The column panel zone is simulated with four rigid bars
pin connected at the corners with a nonlinear rotational spring at
one corner as developed by Krawinkler [30]. The deformation of
the column web, end plate slip, column flange bending, and end
plate bending were implemented as zero length springs at theheight of the top and bottom flanges of the beam. The beam plastic
hinge is implemented as a nonlinear rotational spring using the
Ibarra-Krawinkler deteriorating hysteretic model[31]as described
further in the next section. The columns were modeled using non-
linear fiber elements with 10 fibers per web and flange. The beam
was modeled using elastic beam-column elements outside the
plastic hinge region.
2.2. Constitutive relationships of each component
Models for many of the components of the extended end-plate
connection have been developed by others for either nonend-plate
type moment connections, or for monotonic loading as described
previously. In this section, the constitutive relationship and cyclic
behavior of each component are discussed as they apply to the
component-based model of the end-plate connection.
For typical moment frames, shear deformation of the panel zone
can be non-negligible [32]. The panel zone model developed by
Krawinkler [30] which uses a tri-linear shear force versus shear
distortion relationship shown in Fig. 2 a has been shown to
accurately capture panel zone shear deformations. The control
values for panel zone shear yield, Vy, and shear distortion at shear
yield, cy, [30]are given as follows:
VyFycAeffffiffiffi3
p 0:55Fycdctcw 1
cy Fyc
ffiffiffi3p G
2
where Fycis the column yield strength, Aeffis the effective shear
area, dcis the column depth, tcw is the column web thickness, and
G is the shear modulus of steel. The full plastic shear resistance,
Vp, and related shear distortion of the joint, cp, are estimated using
the following equation:
VpVy 1 3KpKe
0:55Fycdctcw 1
3:45bcft2
cf
dbdctcw
! 3
cp4cy 4whereKe, andKpare the elastic and post-yield stiffness of the panel
zone, respectively,tcfand bcf are the column flange width and thick-
ness, respectively, anddb is the depth of the beam. Since the panel
zone shear resistance is modeled using one rotational spring in an
assembly of rigid elements, the rotational spring moment is merely
the shear force,V, multiplied by the beam depth, dband the spring
rotation is equal to the panel shear deformation, c.
The column web bending model is based on work by Yee and
Melchers [16], using a bilinear forcedeformation relationship as
shown inFig. 2b. The yield compression force,Fcwy, initial stiffness,
Kcw, and post-yield stiffness, Kcwp, are calculated by Eqs. 57
respectively.
FcwyFyctcwbeff;cw 5
Kcw Etcw1m2 6
KcwpEtcw2:45
1
m2
2:45 Kcw 7
beff;cwtbfl 2tep5k 8where, beff,cw is the effective depth of the column web given by
Eq.(8), E is the modulus of elasticity of steel (taken as 200 GPa), t
is the Poissons ratio for steel (taken as 0.3), tbf is the beam flange
thickness,lis total fillet weld thickness from the beam to end plate,
andk is the distance from the edge of column flange to the root of
the column web fillet. The model is intended to capture local defor-
mations due to column web crippling. Since these types of deforma-tions only occur when the web is subjected to compression, the
component spring is defined to have large stiffness in tension.
On the other hand, the complimentary deformations of the col-
umn flange and end-plate as subjected to tension are defined to
have an elasticplastic forcedeformation relationship as shown
in Fig. 2c with near rigid response in compression. The column
flange yield force,Fcfy, end plate yield force, Fepy, and related initial
stiffnesses,KcfandKep, are determined using the following equa-
tions from Yee and Melchers[16].
Fcfy1Fyct2cf 3:14 0:5C
mn
4FubAbnmn 9
Fcfy2
Fyct2
cf 3:14
2nCdbh
m 10
where m is the distance from the bolt to the column web,
m= (Atcw)/2, n is the distance from the bolt to the edge of the
column flange, n = (bcfA)/2, A is the horizontal bolt gage, C is the
vertical bolt spacing (assuming one row of bolts on each side of
the flange), Fub is the ultimate stress of the bolts, Ab is the area of
one bolt, anddbh is the bolt hole diameter.
FcfyminFcfy1; Fcfy2 11
FepyFypt2ep2bep
Ctbf 2l 2p
Atbw2l
12
whereFypis the yield strength of the end plate, p = 0.6(dbtbf),bepis
the width of the end plate, tepis the thickness of the end plate, and
tbw is the thickness of the beam web.
Kcf 8EZcf 1q3acf 4a3cf
h i 13
Kep 8EZep 1q 3aep4a3ep
h i 14whereZep
l3ep
wept3ep
,Zcf l3cf
wcft3cf
, and
aep11:5aep2a3ep; aep26a2ep8a3ep 15
acf11:5acf 2a3cf; acf26a2cf 8a3cf 16
lep2ab; aep alep
; wepbep2
17
where a is the distance from the edge of the end-plate to the bolt
centerline, b is the distance from the bolt centerline to the face of
the beam flange, andbepis the width off the end-plate. These equa-
tions are based on a T-stub model in whichlepandlcfare the effec-
tive lengths of the T-stub for the end plate and column respectively.
For stiffened connections:
lcf lep; acf alcf
; wcf bcf2
18
For unstiffened connections:
lcf bcftcw; acfbcf
A
2lcf;
wcf abtbf2 19
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For pretensioned bolts, the effect of bolt force on joint stiffness,
q, is given by:
q Zepaep1Zcfaep2Zepacf1Zcfacf2 k2k3
2Ab k2k3 20
where k2= ls+ 1.43lt+ 0.91ln+ 0.4lw,lsis the length from the base ofthe bolt head to the threads, l tis the length of threads below the
surface of theend-plate or column flange, lnis the thickness (height)
of the nut, and lwis two times the thickness of an individual washer.
k3teptcf
5 21
For snug-tightened bolts, the effect of bolt force on joint stiff-
ness,q, is given by:
q
Zepaep1
Zcfaep2
Zepacf1Zcfacf2 k12k42Ab 22
Table 1
Measured connection dimensions (mm).
Specimen
Number
Column Beam End-plate Dimension (mm) Bolt
tep bep A C a b dbo (mm) T1(kN)
1, 2, 5 W14 257 with 12 mm doubler plates each
side
W24 62, RBS 34.9 254.0 127.0 119.8 44.5 52.4 34.9 533.4
3, 4 W24 62, No RBS
10 W36 150, No RBS 38.1 355.6 127.0 119.1 47.6 47.6 34.9 533.4
ES-1-1/2-24a* dc= 508,tcw= 9.5, bcf= 203.2,tcf= 12.7 db= 609.6,tbw= 6.35, bbf= 203.2,
tbf= 9.5
12.7 203.2 82.5 92.1 47.6 41.3 25.4 226.8
M2 W12 96 with 12.7mm doubler plates W18 65 15.9 230.0 125.0 164 60.0 99.4 25.4 226.8
* With continuity and stiffened extended end-plate.
Fig. 3. Moment connection configuration and loading protocol, (* values in (parentheses) are for Specimen ES-1-1/2-24a and values in [brackets] are for Specimen M2).
LVDT Lin.Variable Diff.Transformer
SP String PotentiometerInc - Inclinometer
(e) Instrumentation Plan
for Specimens 1-10
Fig. 4. Connection details and instrumentation plan all (all units in mm).
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wherek1= ls+ 1.43lt+ 0.71ln
k40:1ln0:2lw 23The model is based on a four bolt extended end plate connec-
tion (four bolts around the tension flange) so the maximum flange
force, Fbo, [15] is given by Eq. (24), where, Fybis yield strength of the
bolt, and cb is the bolt force prying factor taken to be, cb= 1.33.
However, modifications of this model for use with eight bolt
connections are discussed and validated later in this paper. The
yield deformation of the column flange and end plate can obtained
as given in Eq.(25).
Fbo4FybAbcb
24
DepyFepyKep
; DcfyFcfyKcf
25
The vertical slip mechanism between end-plate and column
flange has three idealized stages shown in Fig. 2d, which are
pre-slip, slipping and bearing. The spring is given a large initial
stiffness such that the deformation in the pre-slip stage may be
neglected. Slip occurs when the friction force, Fslip, is attained and
then maintained during slip displacement. After the bolts engagethe plies in bearing, the bearing force increases proportionally with
displacement. This model is similar to the one proposed by Kim
et al. [28], but adds a final branch in which the connection fails
in either bolt shear or bearing. The control values for the model
are given as follows:
FsliplmboT1 26
Dslipdbhdbo2
27
Fs&bminfFshear; Fbearingg 28
kbearing 120Fytpmind0:8bo 29where,Fslip is slip force, lis friction coefficient which is taken as 0.3
for clean mill scale steel surfaces in current AISC specifications [33],
mbo is number of bolts, T1 is the bolt pretension, (Fytp)min is
minimum yield stress times thickness between the end-plate and
column flange, Fshear and Fbearing is shear strength of bolts and
bearing strength at bolts holes, respectively.
The plastic hinge is modeled using the modified Ibarra
Krawinkler deteriorating hysteretic model [34]. The parameters
for the degrading hysteretic spring were taken from Lignos and
Krawinkler [35]and implemented with the Bilin hysteretic modelavailable in OpenSees[29]. Since the hysteretic model and related
(b) Specimen 2(a) Specimen 1
(c) Specimen 3 (d) Specimen 4
(f) Specimen 10
-0.2 -0.1 0 0.1 0.2
-100
-50
0
50
100
Displacement (m)
Force(kN)
Experimental
Analytical
-0.2 -0.1 0 0.1 0.2
-100
-50
0
50
100
Displacement (m)
Force(kN)
Experimental
Analytical
-0.2 -0.1 0 0.1 0.2
-100
0
100
Displacement (m)
Force(kN)
Experimental
Analytical
-0.2 -0.1 0 0.1 0.2-200
-100
0
100
200
Displacement (m)
Force(kN)
Experimental
Analytical
-0.2 -0.1 0 0.1 0.2
-100
-50
0
50
100
Displacement (m)
Force(kN)
Experimental
Analytical
-0.2 -0.1 0 0.1 0.2
-500
0
500
Displacement (m)
Force(kN)
Experimental
Analytical
(e) Specimen 5
Fig. 5. Comparison of hysteresis loops.
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parameters are documented well in the literature [34,35], further
details are not repeated here.
Thus, the proposed component-based model of the extended
end plate connection is shown in Fig. 1b, in which the spring
moments and forces Mpz,Ffrict,Fcw, Fcf, andFep, andMph, represents
the nonlinear force or moment associated with shear deformation
of panel zone, slip and bearing of bolts, compression deformation
of column web, deformation of column flange, deformation of the
end-plate, and plastic hinge rotation, respectively.
3. Validation of the modeling with experimental results
3.1. Description of experimental program
The computational model is validated against seven experimen-
tal tests including six recent full-scale extended end-plate
beam-column connections and one full-scale connection test with
thinner end plate found in the literature. Information about the
seven specimens is included in Table 1, the connection geometry
is shown inFig. 4ad, and the layout of instrumentation is given
inFig. 4e.
The experimental configuration for the set of six full-scale tests[36] used the same column for all tests with removable
cantilevered beams connected to the column using prequalified
bolted end-plate connections in accordance with AISC 358-10[5]
as shown inFig. 4a and c. All specimens were subjected to a dis-
placement protocol consistent with connection qualification
requirements provided in AISC 341 Chapter K [37]and shown in
Fig. 3b. All bolts were ASTM A490 high-strength structural bolts
fully pretensioned using direct tension indicator washers at the
end plate connections. The column and beam were A992 steel
and the rest of the plates were fabricated from A572 Grade 50steel. From three coupon tests for each beam size, the average yield
stress was 363 MPa for the W24 62 specimens and 372 MPa for
the W36 150 specimens.
Specimens 1, 2, and 5 had reduced beam section (RBS) as shown
inFig. 4b. Although it is not typical to include an RBS with the
prequalified extended end plate connection, the specimens
included both to provide the opportunity to study the behavior
of the RBS plastic hinge behavior while reusing the column. Param-
eters for calibrating the plastic hinge rotational spring are given in
[35]for RBS connections.
Specimen 10 was an eight bolt stiffened extended end plate
connection A method for idealizing the connection as an equivalent
four bolt unstiffened extended end plate connection is used as
follows. The value of flange force, Fbo, is assumed as two times asvalue determined by Eq.(24)to account for twice as many bolts.
0 20000 40000 60000
-0.05
0
0.05
Experimental steps
Rotation(rad)
Experimental
Analytical
0 20000 40000 60000
-0.04
-0.02
0
0.02
0.04
Experimental steps
Rotation(rad)
Experimental
Analytical
0 20000 40000 60000
-0.04
-0.02
0
0.02
0.04
Experimental steps
Rotation(rad)
Experimental
Analytical
0 20000 40000 60000
-0.04
-0.02
0
0.02
0.04
Experimental steps
Rotation(rad)
Experimental
Analytical
0 20000 40000 60000
-0.04
-0.02
0
0.02
0.04
Experimental steps
Rotation(rad)
Experimental
Analytical
0 20000 40000 60000 80000
-0.04
-0.02
0
0.02
0.04
Experimental steps
Rotation(rad)
Experimental
Analytical
(e) Specimen 5 (f) Specimen 10
(c) Specimen 3 (d) Specimen 4
(b) Specimen 2(a) Specimen 1
Fig. 6. Comparison of beam hinge rotation.
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Parameter,b, was taken as the distance from the first bolt center-
line to the face of beam flange, while parameter, a, is assumed as
half the distance between bolt rows on the outside of the beam
flange. This specimen is included in this study as a preliminary
effort to assess whether the proposed component model might
be applied to eight bolt stiffened connections.
In order to validate the proposed component model against
connections with thinner end-plate, column flanges, and column
web, two additional tests with bolted stiffened extended end-platefrom the literature have been investigated[38,39]. The loading
protocol for the specimen designated as ES-1-1/2-24a [38] was
the same as given in Fig. 3b whereas the M2 specimen [39]
followed the ATC 24 loading protocol (see [39] for details). The
bolts were ASTM A325 high-strength structural bolts and all
components were fabricated from A572 Grade 50 steel plate. From
coupon tests, the average yield stress of the end plate steel was
421 MPa and 322 MPa for ES-1-1/2-24a and M2 respectively.
The instrumentation plan for Specimens 110 as shown in
Fig. 4e was sufficient to decompose the story drift into different
components such as panel zone shear, end plate deformation,
and plastic hinge rotation[35]. The instrumentation for specimen
ES-1-1/2-24a included global moment and rotation measurements
as well as displacement transducers measuring the separation ofthe end plate from the column [38]. The only data for specimen
M2 provided in the literature was the end plate rotation and
related moment[39].
3.2. Comparison of analysis and experimental results
In order to validate the proposed component-based end plate
connection model, the experimental response of the above
described specimens are compared to model predictions including
global response and the contribution of each component tomoment-rotation. The model described in Section 2 and shown
inFig. 1b was implemented in OpenSees[29]with the geometry
given inTable 1andFig. 4, and material properties given above.
Fig. 5 shows the overall applied force versus vertical displace-
ment relationship for Specimens 1, 2, 3, 4, 5, and 10. It is shown
that the analytical hysteresis loops match the test results closely,
especially the forces at peak displacement in each cycle (average
error of 6% for the set). For these specimens, the strength is primar-
ily governed by the plastic hinge behavior and as such the accuracy
of the backbone and strength degradation is largely attributed to
the plastic hinge spring modeled using parameters from Lignos
and Krawinkler[35]. Additionally, the stiffnesses of the specimens
in both the elastic and inelastic range are all quite close to the test
results. This suggests that the flexibility of the connection made upof the assembly of springs in the component model can accurately
0 20000 40000 60000
-0.001
-0.0005
0
0.0005
D
istortion(rad)
Experimental steps
Experimental
Analytical
0 20000 40000 60000
-0.001
-0.0005
0
0.0005
Distortion(rad)
Experimental steps
Experimental
Analytical
0 20000 40000 60000
-0.001
-0.0005
0
0.0005
0.001
0.0015
Distortion(rad)
Experimental steps
Experimental
Analytical
0 20000 40000 60000
-0.001
0
0.001
Distortion(rad)
Experimental steps
Experimental
Analytical
0 20000 40000 60000-0.001
-0.0005
0
0.0005
0.001
Distortion(rad)
Experimental steps
Experimental
Analytical
0 10,000 20,000 30,000 40,000
-0.006
-0.004
-0.002
Distortion(rad)
Experimental steps
Experimental
Analytical
(e) Specimen 5 (f) Specimen 10
(c) Specimen 3 (d) Specimen 4
(b) Specimen 2(a) Specimen 1
Fig. 7. Comparison of shear distortion of panel zone.
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capture the stiffness of the overall connection. The component-
based model is shown to generally predict the overall hysteretic
behavior accurately.
The response of individual components such as the plastic
hinge, end-plate, column flange, column web, and panel zone are
investigated individually and compared with experimental data.
The comparisons of analytical and experimental rotation of thebeam plastic hinge in each loading step are shown in Fig. 6. As
mentioned previously, the beam plastic hinge contributed the
majority of the deformation in these specimens and the proposed
model is shown to capture the amount of deformation due to the
plastic hinge well. On average, the model predicted the amount
of plastic hinge rotation during the 0.1 m and 0.2 m drift cycles
within 12% of the experimental value. The ability of the proposed
model to capture the plastic hinge deformation is due in part tothe ability of the plastic hinge model[35]to capture the strength
0 20,000 40,000 60,000-0.002
0
0.002
0.004
0.006
Experimental steps
Rotation(rad)
Experimental
Analytical
0 20,000 40,000 60,000
-0.0005
0
0.0005
0.001
0.0015
0.002
Experimental steps
Rotation(rad)
Experimental
Analytical
0 20,000 40,000 60,000-0.003
-0.002
-0.001
0
0.001
0.002
Experimental steps
Rotation(rad)
Experimental
Analytical
0 20,000 40,000 60,000
-0.001
0
0.001
0.002
Experimental steps
Rotation(rad)
Experimental
Analytical
0 20,000 40,000 60,000
-0.0005
0
0.0005
0.001
0.0015
Experimental steps
Rotation(rad)
Experimental
Analytical
0 20,000 40,000 60,000 80,000
-0.004
-0.002
0
0.002
Experimental steps
Rotation(rad)
Experimental
Analytical
(e) Specimen 5 (f) Specimen 10
(c) Specimen 3 (d) Specimen 4
(b) Specimen 2(a) Specimen 1
Fig. 8. Comparison of end-plate rotation.
-0.0008 -0.0006 -0.0004 -0.0002 0
-4000
-2000
0
2000
4000
Deformation (m)
Force(kN)
-0.005 0 0.005
-50,000
0
50,000
Distortion (rad)
ShearForce(kN)
(a) Column web (b) Panel zone
Fig. 9. Force vs. deformation of Specimen 10.
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contributing to total response as shown inFig. 10. This is expected
for prequalified moment connections designed in accordance with
AISC 358-10[5]. It is shown that these contributions are changing
during the displacement history as deformations shift from elastic
to inelastic. The contribution of the plastic hinge was about 30%
and 22% for Specimens 15 and 10, respectively while the in the
elastic range. When the beam entered the inelastic range, the plas-tic hinge contribution increased sharply from 30% to almost 100%.
The component model is shown to capture this trend.
Fig. 11 shows the percent contribution of the panel zone to total
story drift at each cycle peak which demonstrates that similar to
the other contributions, the portion of story drift due to panel zone
shear remains fairly constant while the plastic hinge is elastic.
When the plastic hinge region becomes inelastic and the plasticity
starts spreading, the panel zone contribution drops quickly from
about 7% to lower than 2% for Specimen 15, and from about
15% to 5% for Specimen 10.
Fig. 12shows the contribution of the end-plate deformation to
total story drift at each cycle peak. The end plate contribution
varies more during the elastic cycles than the other components
ranging between 0% and 36% for some specimens with the compu-tational model predicting constant values between 3% and 12%.
When the beam begins to yield, the end-plate contribution pre-
dicted in the component model drops quickly from about 4% to
1% for Specimen 15, from about 12% to 3% for Specimen 10. While
the experimental data is generally similar, as discussed previously,
the measurement of end plate rotation in the experiments was a
rough approximation using the difference of two inclinometer
rotations and thus does not capture the end plate rotation by itself.Specimens ES-1-1/2-24a[38]and M2[39]were to examine the
accuracy of the model for thinner end plates, column flanges and
column webs. Both the global moment-rotation response and local
end-plate separation response were provided in Ryan [38]. Similar
to previously described specimens, the connection was modeled in
Opensees[29]with the geometry given inTable 1andFig. 4,and
material properties given in the previous section. Some simplifying
assumptions were required such as neglecting the stiffener on the
extended end-plate of ES-1-1/2-24a in the analytical model and
neglecting column web deformation because continuity plates
are provided in the column web.
Fig. 13a illustrates the global response of Specimen ES-1-1/2-
24a. In this test, inelasticity was concentrated in the end-plate
and column flange components while all other componentsincluding the plastic hinge remained elastic. The experimental
0 20 40 600
2
4
6
8
No. of peak points
P
ercentage(%)
Analytical
Experimental
0 10 20 30 40 500
2
4
6
8
10
No. of peak points
P
ercentage(%)
Analytical
Experimental
0 20 40 600
2
4
6
8
10
No. of peak points
Percentage(%)
Analytical
Experimental
0 20 40 600
2
4
6
8
10
No. of peak points
Percentage(%)
Analytical
Experimental
0 20 40 600
2
4
6
8
No. of peak points
Percentage(%)
Analytical
Experimental
0 20 40 600
5
10
15
20
25
No. of peak points
Percentage(%)
Analytical
Experimental
(e) Specimen 5 (f) Specimen 10
(c) Specimen 3 (d) Specimen 4
(b) Specimen 2(a) Specimen 1
Fig. 11. Contribution of Panel Zone at each peak point.
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moment vs. total rotation is compared with the results from the
proposed model as shown inFig. 13a and it is found that although
the proposed model does not simulate the pinched response of a
thin end-plate going through large deformations, the stiffness
and strength of the connection are generally captured. The
analytical model is shown to idealize the pinched behavior of theconnection as elastic with linear hardening.
The comparison of moment at end-plate vs. end-plate separa-
tion at the bottom of beam flange is shown in Fig. 13b and sheds
light on the difference between the hysteretic behavior of the
experiment and model. When the end plate is compressed toward
the column flange, the end plate deforms inelastically in a gradual
manner as opposed to the model which predicts sharp changesbetween elastic and inelastic behavior. Some of the difference is
0 20 40 600
2
4
6
8
No. of peak points
P
ercentage(%)
Analytical
Experimental
0 20 40 600
5
10
15
No. of peak points
Percentage(%)
Analytical
Experimental
0 20 40 600
5
10
15
No. of peak points
P
ercentage(%)
Analytical
Experimental
0 20 40 600
5
10
15
No. of peak points
Percentage(%)
Analytical
Experimental
0 20 40 600
2
4
6
8
No. of peak points
Percentage(%)
Analytical
Experimental
0 20 40 600
10
20
30
40
No. of peak points
Percentage(%)
Analytical
Experimental
(e) Specimen 5 (f) Specimen 10
(c) Specimen 3 (d) Specimen 4
(b) Specimen 2(a) Specimen 1
Fig. 12. Contribution of end-plate at each peak point.
-0.02 -0.01 0 0.01 0.02-600
-400
-200
0
200
400
600
Total Rotation (rad)
Moment(kN-m)
Experimental
Analytical
-0.005 0 0.005 0 .01 -0.005 0
-500
0
500
End-plate Separation (m)
Moment(kN-m)
Experimental
Analytical
(b) Moment vs. End-plate Separation(a) Moment vs. Rotation
Fig. 13. Comparison of specimen ES-1-1/2-24a fortunately (Experimental Response Adapted from Ryan [38]).
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also attributed to the simplifying assumptions made in the model
as described above.
Specimen M2 had wider spacing of bolts on either side of the
flange and was subjected to considerably larger rotations. As
shown in Fig. 14, the end plate underwent geometric hardening
as the end plate tension force resistance shifted to a catenary
mechanism rather than being related to end plate moment capac-
ity as was assumed in the equations presented in Section 2.2 based
on Yee and Melchers[16]. Pinching of the hysteretic shape similar
to Specimen ES-1-1/2-24a was noted in the response of Specimen
M2 which is likely due to similar reasons as identified above
related toFig. 13b. Based on an examination of the responses for
Specimen ES-1-1/2-24a and M2, it is concluded that improvementsto the end plate analytical component response are warranted by
implementing a pinching hysteretic shape with cyclic strength
degradation that also captures geometric hardening due to cate-
nary action. Because of the limited data available in the literature,
this future research will likely need to be conducted in association
with additional cyclic tests on thin extended end plate connections
to provide sufficient data to calibrate such an end plate
component.
4. Parameters study and discussion
Several key aspects of the proposed component model were
examined and validated in the previous section. In this section,
the model is used to examine the sensitivity of the proposed model
-0.04 -0.02 0 0.02 0.04-500
0
500
End-plate Rotation (rad)
Mom
ent(kN-m)
Experimental
Analytical
Fig. 14. Comparison of specimen M2 (Experimental Response Adapted from Adey
et al.[39]).
Table 2
Comparison of parameters between Specimen 1 and Example 1 (mm).
Parameters Specimen 3 Example 1
Column section W14
257 W14
82End plate thickness, tep 34.9 25.4
Bolt diameter, dbo 34.9 28.6
Vertical distance between bottom flange
and outer bolt, a
52.4 44.4
Vertical bolt edge distance on plate, b 44.4 38.1
-0.2 -0.1 0 0.1 0.2-200
-100
0
100
200
Displacement (m)
F
orce(kN)
Example 1
Specimen 3
Fig. 15. Comparison of overall force versus displacement of Example 1 and
Specimen 3.
-0.8 -0.6 -0.4 -0.2 0
-1000
0
1000
2000
Deformation (mm)
Compressionforce(kN)
0 2 4 6 8 10
-1500
-1000
-500
0
500
1000
1500
Deformation (mm)
Tensionforce(kN)
-0.2 0 0.2
-1000
-500
0
500
1000
Distortion (mm)
Shearforce(kN)
0 1000 2000 3000 4000 50000
10
20
30
40
Steps
Percentage/%
Beam Hinge
Panel Zone
Column Web
End-plate
Fig. 16. Forcedeformation relationship of each component of Example 1.
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to variations in the input parameters. To this end, an example was
designed for comparison with Specimen 3 as shown in Table 2 with
all other variables and geometry identical to Specimen 3. The pur-
pose of Example 1 is to examine the effect of a weaker column and
less conservative end plate on connection behavior.
4.1. Comparing behavior of specimens with different configuration
The overall force versus displacement of Example 1 was
compared with that of Specimen 3 as shown in Fig. 15. Due primar-
ily to the change in column section and end plate, the initial elastic
stiffness of Example 1 is noticeably lower than Specimen 3 and
inelastic behavior in the end plate and column begins before
inelasticity in the plastic hinge, although the ultimate strength isalmost same. The resulting hysteretic shapes are significantly
different between the two cases.
For Specimen 3, plastic deformation concentrates at the beam
hinge while other components remain elastic during the entire
loading sequence as shown in Figs. 10c, 11c, and 12c. However,
for Example 1, the column web, panel zone and end-plate yielded
under compression, shear and tension force, respectively, while the
beam stayed elastic as shown inFig. 16. It was found that the con-
tribution of the beam hinge to total story drift decreased from 25%
during the elastic regime to 10% after inelasticity initiated, while
the contribution of the panel zone and end-plate to total rotation
increased from 15% to 30%, and 4% to 40%, respectively. The contri-
bution of the column web to story drift remained fairly constant
and relatively small.
4.2. Effect of bolt pretension
Bolts that are part of the seismic force resisting system are gen-
erally supposed to be fully pretensioned [37]. However, the effect
of bolt pretension can be examined through the use of the pro-
posed model to determine the effect of slip between the end plate
and the column flange. Two levels of pretension are considered
including snug-tight and fully pretensioned. The minimum clamp-
ing force of a fully pretensioned bolt is specified in the RCSC spec-
ifications[40], while the clamping force of a snug-tightened bolt is
assumed to be 10% of pretensioned bolt force as given in Table 3.
Fig. 17shows the comparison of loaddisplacement behavior of
beam-to-column joints with snug-tightened and pretensioned
bolts. The stiffness of Specimen 3 with pretensioned bolts is
slightly higher than that with snug-tightened bolts during cyclic
loading. This difference in stiffness demonstrates that the compo-nent model captures the effect of bolt pretension on end-plate
stiffness and column flange stiffness according to Eq. (13), (14).
Bolt slip was shown to occur when the vertical shear at the end
plate interface exceeded the slip force with snug-tightened bolts.
Since the slip force was ten times larger for the pretensioned bolts,
the vertical force was not close to that required to cause slip in the
pretensioned connection as shown inFig. 18.
The effect of bolt slip on shear distortion of the panel zone is
demonstrated in Fig. 19 by comparing the models with preten-
Table 3
Clamping force per bolt, T1(unit: kN).
Name Pretensioned bolt Snug-tightened bolt
Specimen 3 533 53.3
Example1 356 35.6
(a) Specimen 3 (b) Example1
-0.2 -0.1 0 0.1 0.2-200
-150
-100
-50
0
50
100
150
200
Displacement (m)
Force(kN)
Pretensioned
Snug-tightened
-0.2 -0.1 0 0.1 0.2-200
-150
-100
-50
0
50
100
150
200
Displacement (m)
Force(kN)
Pretensioned
Snug-tightened
Fig. 17. Effect of bolt pretension on loaddisplacement behavior.
(a) Specimen 3 (b) Example 1
-0.001 -0.0005 0-100
-50
0
50
100
Vertical displacement (m)
Force(kN)
Pretensioned
Snug-tightened
-0.001 -0.0005 0-100
-50
0
50
100
Vertical displacement (m)
Force(kN)
Pretensioned
Snug-tightened
Fig. 18. Comparison of slip force vs. displacement.
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(a) Specimen 3 (b) Example 1
-0.002 -0.001 0 0.001 0.002-1500
-1000
-500
0
500
1000
1500
Distortion (rad)
Force(kN)
Pretensioned
Snug-tightened
-0.01 -0.005 0 0.005 0.01
-1000
-500
0
500
1000
Distortion (rad)
Force(kN)
Pretensioned
Snug-tightened
Fig. 19. Comparison of shear force vs. distortion of panel zone.
(a) Specimen 3 (b) Example 1
0 5000 10000 15000-0.04
-0.02
0
0.02
0.04
Loading step
Rotat
ion(rad)
Pretensioned
Snug-tightened
0 5,000 10,000 15,000 20,000 25,000-0.01
-0.005
0
0.005
0.01
-0.01
-0.005
Loading step
Rotation(rad)
Pretensioned
Snug-tightened
0 5000 10000 15000
1.01
1.02
1.03
1.04
1.05
1.06
Loading step
Ratio
0 5,000 10,000 15,000 20,000 25,000
1.01
1.02
1.03
1.04
Loading step
Ratio
Fig. 20. Comparison of rotation history of plastic beam hinge.
(a) Specimen 3 (b) Example 1
0 5000 10000 15000-0.0002
-0.00015
-0.0001
-0.00005
0
Steps
Displacement(m)
Pretensioned
Snug-tightened
0 5,000 10,000 15,000 20,000 25,000-0.0008
-0.0006
-0.0004
-0.0002
0
Steps
Displacement(m)
Pretensioned
Snug-tightened
0 5000 10000 15000
1
1.01
1.02
1.03
Loading step
Ratio
0 5,000 10,000 15,000 20,000 25,0001
1.02
1.04
1.06
1.08
Loading step
Ratio
Fig. 21. Comparison of displacement history of column web.
24 P. Yang, M.R. Eatherton/ Engineering Structures 75 (2014) 1126
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sioned and snug tightened bolts. For Specimen 3, the panel zone is
elastic during cyclic loading and the bolt pretension has negligible
effect. Conversely, Fig. 19 shows that Example 1 shows a significant
change in the inelastic deformation of the panel zone as the result
of bolt slip.
The displacement history of the beam plastic hinge component
is investigated inFig. 20. A bolt pretension effect ratio is defined as
the ratio of component response with snug-tightened bolts at each
cycle peak to the response with pretensioned bolts at the same
peak. Fig. 20shows that the value of bolt pretension effect ratioranged from 1.02 to 1.06 and 1.01 to 1.04 for Specimen 3 and
Example1 respectively. Fig. 21 shows the column web displace-
ment history and bolt pretension effect ratio with different bolt
type. It was found that the value of the ratio for column web
displacement ranged from 0.96 to 0.93 and 0.95 to 1.18 for
Specimen 3 and Example 1 respectively.
Fig. 22 presents the end-plate displacement history for snug-
tight and fully pretensioned bolts along with the bolt pretension
effect ratio. It was found that the value of the ratio for end-plate
displacement ranged from 0.93 to 0.96 and 0.95 to 1.16 for Speci-
men 3 and Example 1, respectively with trends that were quite
similar to column web displacement.
From the above results, the bolt pretension is found to primarily
affect the response of the end-plate and column flange among allcomponents included in the model. Its effect for Example 1 was
much more than Specimen 3, implying that the effect of bolt slip
is more significant in the presence of a weaker column and end
plate. Thus the effect of bolt pretension and connection slip should
be considered for moment frames with relatively weak connec-
tions. Furthermore neglecting the effect of bolt slip in connections
with snug tight bolts, while not significantly effecting the overall
load-deformation response of the frame, can cause as much as
18% error in component deformations as discussed with the bolt
pretension effect ratio.
5. Conclusions
A phenomenological component-based model was proposed tosimulate the cyclic behavior of bolted extended end-plate connec-
tions utilizing five separate springs to represent the nonlinear
response of the column panel zone undergoing shear distortion,
column web undergoing web crippling, column flange bending,
end-plate bending, end plate slip relative to the column flange,
and beam plastic hinge rotation. The behavior of each component
was defined based on or adapted from research on similar connec-
tions found in the literature.
Six full-scale experiments were conducted with sufficient
instrumentation to decompose the deformation of the key compo-
nents. The six test specimens were modeled using the proposedmethod as subjected to the same reversed cyclic loading used in
the experiments. Furthermore a test specimen found in the litera-
ture with thin end plate, column flange, and column web was used
to validate the behavior of the model with large displacement con-
tributions from column and end plate deformations.
The simulation results were compared with test data including
a discussion of the ability of the model to capture global moment
rotation response of the connection and the ability of the model
to capture the deformation of each individual component. The
accuracy of the modeling approach was explored and suggestions
for future research to improve the model were presented. The
resulting component model represents a computationally efficient
validated modeling approach for end plate moment connections
subjected to seismic loading.The model was then extended to examine the sensitivity of the
model behavior to connection geometry. An example configuration
was developed similar to one of the test specimens but with
weaker column and end plate. Analysis of the resulting global
and local response showed that to capture the load-deformation
response of connections in which column and end plate deforma-
tions are prevalent, it is critical to use a model like the one
proposed herein that captures the deformation contributions from
the key components.
The effect of snug-tightened versus fully pretensioned bolts was
also investigated using the proposed model to examine the effect
of end plate slip on connection behavior and determine whether
the end plate slip component springs are necessary in the proposed
model. The results show that slip of the end plate can have a
noticeable effect (as much as 18%) on the deformation of individual
(a) Specimen 3 (b) Example 1
0 5000 10000 15000
0
0.001
0.002
0.003
0.004
Steps
D
isplacement(m)
Pretensioned
Snug-tightened
0 5,000 10,000 15,000 20,000 25,000
0
0.002
0.004
0.006
0.008
0.01
Steps
D
isplacement(m)
Pretensioned
Snug-tightened
0 5000 10000 150000.93
0.935
0.94
0.945
0.95
0.955
0.96
Loading step
Ratio
0 5,000 10,000 15,000 20,000 25,0000.95
1
1.05
1.1
1.15
1.2
Loading step
Ratio
Fig. 22. Comparison of displacement history of end-plate.
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