a phenomenological component-based model to simulate seismic

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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.

12 P. Yang, M.R. Eatherton/ Engineering Structures 75 (2014) 1126


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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

P. Yang, M.R. Eatherton/ Engineering Structures 75 (2014) 1126 13
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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



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




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




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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10/16

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




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




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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-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.


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.


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.



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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


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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a phenomenological component-based model to simulate seismic

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