prediction of cyclic behavior of wuf-w connections...

www.springer.com/journal/13296

International Journal of Steel Structures 16(4): 1197-1208 (2016)

DOI 10.1007/s13296-016-0057-0

ISSN 1598-2351 (Print)

ISSN 2093-6311 (Online)

Prediction of Cyclic Behavior of WUF-W Connections with

Various Weld Access Hole Configurations Using Nonlinear FEA

Sang Whan Han*, Nam Hun Kim, and Soon Wook Cho

Department of Architectural Engineering, Hanyang University, Seoul 133-1791, Korea

Abstract

The welded unreinforced flange-welded web (WUF-W) moment connection is one of seven prequalified connections for thespecial moment frames (SMF) specified in AISC 358-10. Previous studies reported that some WUF-W connections with a steepaccess hole slope failed before completing a loading cycle of 4% drift ratio. For investigating in detail the effect of access holegeometry including access hole slopes on the connection behavior, experimental tests require excessive costs and effortsbecause there are the large number of combinations of configuration parameters for access hole geometry. In this study, thecyclic behavior of WUF-W connections is evaluated using three-dimensional nonlinear finite element (FE) analyses with anadequate solid element and failure index. Based on the results of FEA, the effect of configuration parameters on the connectionbehavior is investigated.

Keywords: cyclic behavior, moment connection, finite element analysis, access hole, failure index, special moment frame

1. Introduction

In AISC 358-10 (2010), seven prequalified connections

are specified for special moment frames (SMF). The

welded unreinforced flange-welded web (WUF-W) moment

connection is one of the permitted SMF connections,

which is an all-welded moment connection as shown Fig

1. According to the commentary of AISC 358-10, the

prequalification of the WUF-W moment connection is

based on the results of two major research programs

conducted at Leigh University and the University of

Minnesota. These experimental research program (Ricles

et al., 2000, 2002; Lee et al., 2005a, b) reported that

WUF-W connections had deformation capacities significantly

larger than 4% drift ratio, satisfying the requirements for

SMF connections specified in AISC 341-10 (2010). Finite

element studies were also conducted for developing the

special seismic weld access hole and the details of the

web connection (Lu et al., 2000; Mao et al., 2001; El-

Tawil et al., 1998).

Recently, Han et al. (2014) also conducted experimental

tests for WUF-W connections. It was reported that some

WUF-W connections with a beam depth of 890 mm

experienced brittle failure and did not satisfy the requirements

forSMF connections even though the connections were

designed and detailed according to AISC 341-10 and

AISC 358-10. It was suspected that the main cause of

premature failure in WUF-W connections was the access

hole slope. Steep access hole slopes was used in Han et

al. (2014), which was 21º. AWS D1.8/D1.8M (2009)

specifies that the angle of access hole slope should be less

than 25º.

For investigating the effect access hole geometry on the

cyclic behavior of WUF-W connections, it is difficult to

conduct experimental tests due to excessive costs and

efforts. Instead, finite element analyses can be used, which

provide detailed stress and strain information at critical

regions in WUF-W connections. In this study a three-

dimensional (3D) nonlinear finite element analyses (FEA)

are conducted to simulate the cyclic curves of WUF-W

connections with various access hole geometries. Based

on FEA results, this study evaluates the effect of the

configuration parameter of access holes on connection

behavior. For this purpose, a proper solid element is

proposed considering computation stability, accuracy and

convergence. In order to predict the incidence of connection

fracture, this study also proposes a proper failure index.

Received January 30, 2016; accepted June 28, 2016;published online December 31, 2016© KSSC and Springer 2016

*Corresponding authorTel: +82-2-2220-1715, Fax: +82-2-2291-1716E-mail: [email protected]

1198 Sang Whan Han et al. / International Journal of Steel Structures, 16(4), 1197-1208, 2016

2. Comparison between Cyclic Curves of WUF-W Connections with Different Access Hole Geometries

In order to compare the cyclic behaviors of WUF-W

connections specimens with different access hole geometries,

this study considers two code-compliant WUF-W connection

specimens, T5 and D900-S, which were tested by Ricles

et al. (2002) and Han et al. (2014).

Figure 2(a) shows the cyclic curve for specimen T5

with a strong panel zone. The beam and column for

specimen T5 were A572 Grade 50 W36×150 (a depth of

beam=920 mm) and W14x311 sections, respectively, and

the moment strength ratio of panel zone to beam (Mpz/Mp)

was 1.55. This specimen exhibited stable cyclic behavior

and sustained cyclic 3loading until a drift ratio was 6%.

For specimen D900-S with a beam depth of 890 mm,

cyclic curves are presented in Fig. 2(b). The details for

specimen D900-S is shown in Fig. 1(a). Specimen D900-

S failed before completing one loading cycle at 4% drift

ratio, which did not satisfy the requirement for SMF

connections. It is noted that the main difference between

specimens T5 and D900-S was access geometry. Particularly,

the access hole slopes of those specimens are 13º and 21º,

respectively. Table 1 summarizes five configuration para-

meters for access hole geometry and corresponding

values for specimens T5 and D900-S.

Figure 1. WUF-W connection details.

Figure 2. Cyclic curves for specimens T1 and D900-S.

Prediction of Cyclic Behavior of WUF-W Connections with Various Weld Access Hole Configurations Using Nonlinear FEA 1199

3. Three Dimensional Finite Element Analyses

For investigating the effect of access hole geometry on

the cyclic behavior of WUF-W connections, this study

simulates the cyclic behavior of WUF-W connections via

3D nonlinear FEA with a proper FE model. Since it is

complex to predict the incidence of connection fracture

using FE model alone, a proper index is proposed.

In order to simulatethe cyclic responses in plastic ranges

with FEA, a proper FE software should be chosen. The

plasticity models included in software ABAQUS (Hibbitt

et al., 2011) are incremental theories in which the

mechanical strain rate is decomposed into an elastic part

and a plastic (inelastic) part, which are considered to be

sufficient for the analysis of WUF-W connections.

Incremental plasticity models are usually formulated in

terms of following three rules: (1) A yield surface, which

generalizes the concept of “yield load” into a test function

that can be used to determine if the material responds

purely elastically at a particular state of stress, (2) A flow

rule, which defines the inelastic deformation that occurs

if the material point is no longer responding purely elastically,

and (3) Evolution laws that define the hardening-theway

in which the yield and flow definitions change as inelastic

deformation occurs. Since such functions provided in the

software are considered to be sufficient for simulating the

cyclic behavior of WUF-W connections, this study uses

software ABAQUS. This software provides various solid

brick elements for nonlinear 3D FEA. In order to obtain

accurate FEA results, an accurate element should be used.

3.1. Selection of a proper brick solid element

In ABAQUS, many brick elements are available: the

regular brick element with standard integration (C3D8,

C3D20), the brick element with an incompatible deformation

mode (C3D8I, C3D20I), and the brick element with

reduced integration (C3D8R, C3D20R). Element C3D8 is

the first order fully integrated element, which overestimates

stiffness significantly due to shear lockingproblem in this

element. The first order integrated element C3D8I with

incompatible modes was developed to reduce the problem

arisen by using element C3D8,but shear locking could not

be removed completely. Element C3D8R is the first-order

reduced-integration element that eliminates shear locking

so that this element can be used for modeling a member

dominated by flexure. Since element C3D8R requires

reduced integration, this element requires less computation

than elements C3D8 and C3D8I. Elements C3D20 and

C3D20R second order full and reduced solid elements.

Since these elements use more integration points than

first order solid elements, the results of FEAare more

accurate than those with the first order elements. However,

the second order elements require large computational

efforts, which become more excessive with increasing the

number of meshes.

In order to select a proper element for WUF-W

connections, specimen D900-S is used for FE models. A

lower portion of the connection is tested as shown in Fig.

3. The support conditions for all boundaries are assumed

to be fixed. The tensile force is applied to the beam

flange. The components of the connection are divided

into four different layers of elements through their

thickness (Fig. 3).

Figure 4(a) shows computing time required in FEA

with each type of element normalized by that required in

FEA with element C3D20 and six layers of elements

through the thickness of components. As expected,

element C3D20 requires the most computing time among

the elements whereas the computing time required using

element C3D8R is the least. In Fig. 4(b), the distribution

Table 1. Configuration parameters for weld access holesfor specimens T5 and D900-S

(a) T5 (b) D900-S

Specimen T (mm) R (mm) S (o) H (mm) L (mm)

T5 79 10 13 19.1 25.4

D900-S 69 10 21 23 23

Figure 3. FE model for lower portion of WUF-W connections.


of von Mises stress is plotted within the region of stress

larger than 85% of the maximum stress for element

C3D20. It is noted that the maximum stresses obtained

using different elements are similar irrespective of element

types. This study assumes that the stress distribution obtained

using element C3D20 is accurate. As shown in Fig. 4(b),

element C3D8R produces a stress distribution that best

matches the stress distribution obtained using element

C3D20. Thus, considering the computational efficiency

and accuracy, this study uses element C3D8R for modeling

WUF-W connections.

3.2. Minimum layers of elements for accurate results

It is important to determine the optimal number of layers

of elements for FEA because computing time increases

with increasing the number of layers. FEA are repeatedly

conducted with increasing the number of layers until

convergence is achieved. Figure 5 shows the von Mises

stress normalized by the maximum stress obtained with

single layer of elements (Fig. 3(a)). Figure 5(b) shows the

trend of error (%) associated with the stress obtained with

different element layers. The error is defined as the

difference between stresses obtained using multi-layers of

elements (σn) and single layer of element (σ1) normalized

by σ1[=(σn−σ1)/σ1×100]. It is observed that the stress

distribution obtained with four layers of elements is close

to that obtained with six layers of elements. The error

associated with four layers of elements is only 6.5%,

indicating that the FEA results converges when the number

of layers equal to or greater than 4. Thus, this study

divides the thickness of components into four layers as

shown in Fig. 3(c).

4. Simulating Cyclic Curves Using Finite Element Analyses for WUF-W Connections

The cyclic behavior of WUF-W connections with different

access holes are simulated via 3D nonlinear FEA with

element C3D8R. Specimens D900-S and T5 are considered

in this study. Figure 6 shows the test setup and FE model

for specimens D900-S and T5. The loading histories,

support conditions and locations of lateral supports used

in FE models are kept the same as those used in the tests.

It is observed that the lateral loading was applied at the

end of the upper column for specimen T5 whereas the

lateral load for specimen D900-S was applied at the end

of beam. The same displacement controlled cyclic

loadings are applied to the specimens as used in the tests.

4.1. Material models

In order to simulate the cyclic behavior of WUF-W

connections via FEA, cyclic coupon tests results are

required. Since previous studies did not provide cyclic

Figure 4. Computing time and distribution of von Mises stress according to different types of elements.

Figure 5. Distribution of von Mises stress according to the layers of elements.


coupon test results, this study adopts cyclic coupon test

results for steel grades A36 and A572-GR50 conducted

by Kauffman et al. (1999). Steel grades SS400 (Fy=245

MPa and Fu=400 MPa) and SM490 (Fy=325 MPa and

Fu=490 MPa) used for beams and columns of specimen

D900-S have similar mechanical properties with steel

grades A36 and A572-GR50 (Fy=345 MPa and Fu=450

MPa), respectively. Thus, cyclic coupon test results for

A36 and SM 490 conducted by Kauffman et al. (1999)

are used to define the cyclic material properties for

specimen D900-S, which are shown in Fig. 7.

In order to define the cyclic stress-strain relationship (f

and ε),the modified Ramberg-Osgood equation is used

[Eq. (1)]. Coefficients A, B, and C for the equation are

determined using a trial-and-error procedure. Coefficients

A, B, and C for A36 (SS400) are 0.0001, 220 and 2.4,

respectively, whereas for A572-GR50 (SM 490), they are

0.0001, 270 and 2.4, respectively.

(1)

where E is the elastic modulus and Fu is the ultimate

stress. In Fig. 7, the stress-strain curve for the 1st half

cycle is calculated using Eq. (1) and plotted with thick

dotted lines, which is only required for FE modelingin

software ABAQUS. It is observed that the dotted lines

accurately match the 1st half cycle of the cyclic curves.

The stress strain curve obtained from uniaxial coupon

tests for steel grades SS400 and SM 490 is also plotted

with thin dotted lines, which matches the uniaxial stress-

strain curves for steel grades A36 and A572GR50,

respectively.

4.2. Consideration of shear tabs in FE models

To investigate the effect of shear tab modeling on the

results of FEA, specimen D900-S is modeled with and

without considering shear tabs. Figure 8 shows the FE

model used for WUF-W connections with and without

shear tabs. Figure 9 shows the cyclic curves simulated via

FEA with and without considering shear tabs. In this figure,

cyclic curves obtained from the test are also included. It

is observed that the cyclic curves simulated using FE

f Eε A1 A–

1 Bε( )C+{ }1 C⁄

----------------------------------+= fu≤

Figure 6. FE models for specimens T5 and D900-S.


models match the actual cyclic curve irrespective of shear

tab modeling. The initial stiffness and maximum forces of

the specimen are summarized in Table 2. Comparing the

results between test and analysis results, the FE model

without considering shear tabs produced less accurate

results than the FE model with considering shear tables,

but the difference between theresults is small. The cumulative

dissipated energy is also calculated from the cyclic curves

and plotted in Fig. 10. The similar observation is made

for cumulative dissipated energy. In order to conduct

FEA with more computational efficiency, this study

Figure 7. Cyclic stress-strain curves (Kaufmann et al., 1999) for A36 steel and calculated stress-strain curve.

Figure 9. Cyclic curves obtained using FE models with and without shear tabs.

Table 2. Initial stiffness and maximum shear forces

Test resultsFEA without

considering shear tabsFEA with

considering shear tabs FEA

Initial Stiffness (kN/mm) 27.74 27.46 29.03

Maximum shear force (kN) 1220.4 1151.5 1087.2

Figure 8. FE model with shear tabs.

Figure 10. Cumulative dissipated energies obtained fromtests and analyses.


constructs FE models for WUF-W connections without

considering shear tabs.

4.3. Cyclic curves simulated using FEA

To verify the accuracy of the FE model used in this

study, cyclic curves obtained from FEA are compared

with those obtained from tests. For this purpose, tested

WUF-W connection specimens are collected, which are

summarized in Table 3.

Figure 11 shows the actual and simulated cyclic curves

for collected specimens. The cyclic curves simulated with

FEA match those obtained from experimental tests. In

Fig. 12, cumulative energies dissipated byspecimens T1

and T5 are also plotted according to drift ratios. It is

observed that cumulative dissipated energies calculated

using FEA results agrees well with those using test

results.

This study also compares the distributions of strain for

specimens D900-S and D700-S obtained from FEA with

those obtained viastrain gauges during the test. Figure 13

shows the strain distribution. The locations of gauges are

also shown in Fig. 13(a). It is observed that FEA produces

accurate strain distributions for WUF-W connections.

5. Determination of Proper Failure Index for Predicting Connection Fracture

The incidence of fracture in members can be accurately

predicted using comprehensive fracture mechanics. However,

it is complex to construct an explicit model for predicting

the incidence of fracture using fracture mechanics, particularly

for members with complex configurations such as WUF-

W connections. In this study, cracks are not explicitly

modeled to predict the behavior and strengthof solids

having crack propagation using fracture mechanics. To

evaluate and compare WUF-W connections with various

access hole configurations for ductile fracture potential,

several indices were considered and computed near access

holes in WUF-W connections such as PEEQ index, von

Mises stress index, triaxiality ratio, and rupture index.

Then, the most proper index is chosen and used for

predicting the incidence of connection fracture. Equations

for above mentioned indices are briefly addressed as

follows.

Von Mises Stress Index (MSI) is defined as the ratio of

Von Mises stress (σeff) to the yield stress (σy) [Eq, (2)].

MSI=σeff/σy (2)

(3)

S ij=σ ij+σmδ ij

where S ij is the deviatoric stress components of global

coordinates, (i, j) and δ ij is the Kronecker delta.

PEEQ Index (PI) is calculated with effective plastic

strain (PEEQ) and yield strain (εy) using Eq. (4). The

local ductility can be accurately predicted using PI.

PEEQ Index=PEEQ/εy (4)

(5)

where is the plastic strain of global coordinates, (i, j).

Rupture Index (RI) is defined as the ratio of PEEQ

index to ductile fracture strain ε f multiplied by the

material constant α as follows.

Rupture Index (RI)= = (6)

σeff

2

3---SijSij=

PEEQ2

3---εij

pεijp

=

εijp

aPEEQ εy⁄

εf

----------------------PEEQ εy⁄

exp 1.5σm

σeff

--------–⎝ ⎠⎛ ⎞

---------------------------------

Table 3. Collected WUF-W connection specimens

Reference Specimen Connection typeColumn size, (Fy · Fu) MPa

Mpz/Mp

+ l/d++

Beam size, (Fy · Fu) MPa

Han et al.(2014)

D900-SWUF-WExterior

H458×417×30×50, (364.2,534.7)1.56 7.75

H890×299×15×23, (340.1,481.5)

D900-BWUF-WExterior

H458×417×30×50, (364.5,537)1.56 7.75

H890×299×15×23, (334.6,481.2)

D700-SWUF-WExterior

H428×407×20×35, (344.4,535.2)1.64 9.97

H692×300×13×20, (344.8,506.3)

D700-BWUF-WExterior

H428×407×20×35, (310.6,540.5)1.64 9.97

H692×300×13×20, (340.2,499.3)

Ricles et al. (2000)

T1WUF-WExterior

W14×311, (372.1,489.2)1.09 9.84

W36×150, (385.8,502.9)

T5WUF-WExterior

W14×311, (372.1,489.2)1.55 9.84

W36×150, (385.8,502.9)

+Mpz/Mp: the ratio of moment strength of panel zone to that of beam, ++l/d: span-to-depth ratio of beam


Figure 11. Comparison between Cyclic curves obtained from tests and FEA.

Figure 12. Cumulative dissipated energies for specimens T1 and T5.

Figure 13. Distribution of strains from tests and FEA.


(7)

(8)

(9)

where σm is the hydrostatic stress.

Triaxiality Ratio (TR) can be calculated using Eq. (10).

TR=σm/σeff (10)

Using the above equations, indices for fractured connection

specimens (Table 1) are estimated with FEA results from

the first to the last loading cycles. Since all fractured

specimens experienced beam flange fracture within aregion

ranging from access hole toe to column face, indices are

calculated in this region. Figure 14 shows the calculated

values foreach index according to drift ratios. It is noted

that RI and PI becomes larger with an increase in drift

ratio whereas TR and MSI increase according to a drift

ratio, approximately up to 1%, but after 1% drift ratio,

they are almost constant irrespective of drift ratios.

Table 4 summarizes the values of indices corresponding

to connection fracture. The coefficient of variations of

MSI, PI, RI, and TR for fractured WUF-W connection

specimens are 0.136, 0.227, 0.058 and 0.312, respectively.

It is noted that the variation of RI corresponding to

connection fracture is the smallest among the indices.

Thus, RI can be used to predict the incidence of connection

fracture with little variability. In this study, it is assumed

that a limiting value of RI is assumed as 1179, which is

the mean value of RI. Thus, when cyclic curves are

simulated using FEA for WUF-W connections, analyses

are conducted until RI becomes 1179.

6. Evaluation of Access hole Geometry on Connection Behavior

Since accurate FE model and failure index are esta-

blished, the cyclic behavior of WUF-W connections with

various access hole configurations can be accurately predicted.

As summarized in Table 3, there are five configuration

parameters: thelength of the flat portion (L), radius of

access hole (R), access hole height (H), access hole slope

(S) and overall length (T). This study assumes that R is

assumed to be 10 mm, for simplicity. Since L and T are

dependent parameters, only L is considered as a variable.

Thus, this study considers T, L and S as variables. In

AWS D1.8/D1.8M, permissible ranges for T and L are

specified as 64-80 mm and 17.3-34.5 mm, respectively,

whereas for assess hole slopes, only the maximum value

is specified as 25o.

Figure 15 shows the von Mises stress of five WUF-W

connections at a drift ratio of 3%. These specimens are

identical with specimen D900-S except for the access

hole geometry. This figure shows that von Mises stress

near access holes varies according to access hole geometry.

Specimen D900-L18-S13-T74 had an access hole with

L of 18 mm, S of 13o and T of 74 mm whereas specimen

D900-L18-S25-T74 had the same access hole geometry

εf aexp 1.5σm

σeff

--------–⎝ ⎠⎛ ⎞=

σm

1

3---trace σij( )–=

σeff

2

3---SijSij=

Figure 14. Failure indices for WUF-W connections


as specimen D900-L18-S13-T74 except for access hole

slope (S=25o). The stress distributions of the two specimens

are plotted in Fig. 15(a) and (b). In the specimen with S

of 13o, maximum stress is measured within the circular

region of the access hole whereas the maximum stress of

the specimen with S of 21o occurs at the access hole toe.

Therefore, the location of maximum stress and stress

distribution vary according to access hole slope.

In Figs. 15(a) and 15(c), stress distributions are plotted

according to different lengths of the flat portion (L).

Specimens D900-L18-S13-T74 and D900-L34-S13-T74

had the length of the flat portion (L) of 18 and 34 mm,

respectively. Both specimens had the same S and T, which

are 13o and 74 mm, respectively. This figure shows that the

location of the maximum stress migrates downward within

the circular region of the access hole with increasing L.

Table 4. Vales of indices corresponding to connection fracture

Specimens MSI PI TR RI

D700-B 1.41 538 0.557 1299

D700-S 1.11 439 0.680 1223

D900-B 1.17 289 0.922 1096

D900-S 1.37 398 0.880 1146

T1 1.53 415 0.355 1121

T5 1.65 277 0.502 1190

Mean 1.37 392.5 0.65 1179

STD 0.19 89 0.20 68.07

COV 0.136 0.227 0.312 0.058

Figure 16. Cyclic curves of WUF- W connections with different access hole slopes.

Figure 15. von Mises stress near access hole for WUF-W connections.


The effect of overall length (T) on stress distribution is

also investigated. Figures 15(d) and 15(e) show the stress

distributions in the specimens with T of 64 and 80 mm,

respectively (D900-L34-S13-T64 and D900-L34-S13-T80).

Unlike S and L, Tdoes not affect the location of maximum

stress and stress distribution.

This study also simulates cyclic curves for specimens

D900-L18-S13-T74 and D900-L34-S13-T74, which have

different access hole slopes. During the FEA, connection

fracture is monitored with rupture index. Figure 16 shows

the simulated cyclic curves. Connection fracture was denoted

by symbol ‘x’. It is shown that specimens D900-L18-

S13-T74 withstands cyclic loading with a drift ratio

greater than 4%, whereas specimen D900-L34-S25-T74

failed prior to a drift ratio of 4%. This indicates that the

range of access hole slope specified in AWSD 1.8/D1.8M

should be modified to improve the cyclic behavior of

WUF-W connections.

7. Conclusions

This study conducted nonlinear 3D FEA to simulate the

cyclic curves for WUF-W connections. For computational

accuracy, stability and convergence, adequate solid element

was proposed for FEA, which is element C3D8R. In order

to improve the computational accuracy, each component

of WUF-W connections was divided into four layers

through the thickness of components. The minimum number

of the layers was determined as 4, which was obtained by

conducting repeated FEA with increasing layers of elements

until convergence was achieved. Using the proposed FE

model, the cyclic curves of six tested specimens were

accurately simulated. In order to predict the incidence of

connection fracture with FEA results, this study adopted

rupture index. This study showed that the incidence of

fractures in eight fractured WUF-W connection specimens

were predicted with rupture index with little variation.

Based on FEA results with rupture index, it is also shown

that the cyclic behavior of WUF-W connections was strongly

affected by access hole geometry. The distribution of

strains and stress near access holesare significantly varied

according to the change in access hole geometry. Even

though the configuration parameters of access holes were

selected within ranges permitted in in AWS D1.8/D1.8M,

this study showed that some connections did not satisfy

the requirements specified in AISC 341-10.

Acknowledgments

The research was supported by grants from the National

Research Foundation of Korea (No. 2015R1A2A1A1505

5248).

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prediction of cyclic behavior of wuf-w connections...

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