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Journal of Constructional Steel Research 63 (2007) 751–765 www.elsevier.com/locate/jcsr Cyclic loading behavior of EBF links constructed of ASTM A992 steel Taichiro Okazaki a,* , Michael D. Engelhardt b a Department of Civil Engineering, University of Minnesota, Minneapolis, MN, 55455-0116, USA b Department of Civil, Architectural, and Environmental Engineering, University of Texas at Austin, Austin, TX 78712-0275, USA Received 4 May 2006; accepted 8 August 2006 Abstract Cyclic loading tests were conducted to study the behavior of link beams in steel eccentrically braced frames. A total of thirty-seven link specimens were constructed from five different wide-flange sections, all of ASTM A992 steel, with link length varying from short shear yielding links to long flexure yielding links. The occurrence of web fracture in shear yielding link specimens led to further study on the cause of these fractures. Since the link web fracture appeared to be a phenomenon unique to modern rolled shapes, the potential role of material properties on these fractures is discussed. Based on the test data, a change in the flange slenderness limit is proposed. The link overstrength factor of 1.5, as assumed in the current U.S. code provisions, appears to be reasonable. The cyclic loading history used for testing was found to significantly affect link performance. Test observations also suggest new techniques for link stiffener design and detailing for link-to-column connections. c 2006 Elsevier Ltd. All rights reserved. Keywords: Cyclic tests; Steel structures; Seismic design; Flange slenderness ratio; Loading history; Fracture; k-area; Eccentrically braced frame 1. Introduction The design intent for a seismic-resistant steel Eccentrically Braced Frame (EBF) is that inelastic action under strong earthquake motion is restricted primarily to the links. Therefore, the EBF design procedure prescribed in the 2005 AISC Seismic Provisions for Structural Steel Buildings [1] relies on an understanding of link behavior under severe cyclic loading. The AISC Seismic Provisions contain U.S. building code rules for detailing steel structures, including EBFs, for seismic resistance. The current building code rules for EBFs in the AISC Seismic Provisions, including link design, link rotation limits, and link overstrength factors, were developed from rather extensive experimental studies conducted almost exclusively on wide-flange shapes of ASTM A36 steel [2]. However, structural steel shapes most commonly used in the U.S. today are produced according to the newer ASTM A992 standard, which provides for a higher yield and tensile strength than A36 steel. The move to A992 steel raised concerns regarding the appropriateness of the flange width–thickness limits for EBF * Corresponding author. Tel.: +1 612 626 0331; fax: +1 612 626 7750. E-mail address: [email protected] (T. Okazaki). link sections. A limit of 0.30( E / F y ) 1/2 was traditionally specified for the flange width–thickness ratio of EBF links. This flange slenderness ratio corresponds to 8.5 for A36 steel (with minimum specified yield strength of F y = 250 MPa) and 7.2 for A992 steel (minimum specified F y = 345 MPa). A number of rolled wide-flange shapes meet the flange slenderness limit of 8.5 but do not meet the limit of 7.2, and thus are disqualified from use as EBF links by the traditional flange slenderness limit. Meanwhile, the effect of flange slenderness ratio on link behavior has not been explicitly addressed in previous research. A secondary concern was the appropriateness of link overstrength factors used in the capacity design procedure for EBFs. Link overstrength is defined as the maximum shear force developed in the link divided by the plastic shear strength of the link. While the 2005 AISC Seismic Provisions implicitly assume a link overstrength factor of 1.5, recent tests on large built-up shear links for use in bridge applications showed overstrength factors of nearly 2 [3,4]. This has led to concerns that current overstrength factors may be unconservative, particularly for shapes with heavy flanges, where shear resistance of the flanges contributes significantly to overstrength. An experimental research program was conducted at the University of Texas at Austin. The initial objective for this program was to examine flange buckling and overstrength in 0143-974X/$ - see front matter c 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2006.08.004

Transcript of 1-s2.0-S0143974X06001787-main.pdf

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Journal of Constructional Steel Research 63 (2007) 751–765www.elsevier.com/locate/jcsr

Cyclic loading behavior of EBF links constructed of ASTM A992 steel

Taichiro Okazakia,∗, Michael D. Engelhardtb

a Department of Civil Engineering, University of Minnesota, Minneapolis, MN, 55455-0116, USAb Department of Civil, Architectural, and Environmental Engineering, University of Texas at Austin, Austin, TX 78712-0275, USA

Received 4 May 2006; accepted 8 August 2006

Abstract

Cyclic loading tests were conducted to study the behavior of link beams in steel eccentrically braced frames. A total of thirty-seven linkspecimens were constructed from five different wide-flange sections, all of ASTM A992 steel, with link length varying from short shear yieldinglinks to long flexure yielding links. The occurrence of web fracture in shear yielding link specimens led to further study on the cause of thesefractures. Since the link web fracture appeared to be a phenomenon unique to modern rolled shapes, the potential role of material properties onthese fractures is discussed. Based on the test data, a change in the flange slenderness limit is proposed. The link overstrength factor of 1.5, asassumed in the current U.S. code provisions, appears to be reasonable. The cyclic loading history used for testing was found to significantly affectlink performance. Test observations also suggest new techniques for link stiffener design and detailing for link-to-column connections.c© 2006 Elsevier Ltd. All rights reserved.

Keywords: Cyclic tests; Steel structures; Seismic design; Flange slenderness ratio; Loading history; Fracture; k-area; Eccentrically braced frame

1. Introduction

The design intent for a seismic-resistant steel EccentricallyBraced Frame (EBF) is that inelastic action under strongearthquake motion is restricted primarily to the links. Therefore,the EBF design procedure prescribed in the 2005 AISC SeismicProvisions for Structural Steel Buildings [1] relies on anunderstanding of link behavior under severe cyclic loading.The AISC Seismic Provisions contain U.S. building code rulesfor detailing steel structures, including EBFs, for seismicresistance. The current building code rules for EBFs in the AISCSeismic Provisions, including link design, link rotation limits,and link overstrength factors, were developed from ratherextensive experimental studies conducted almost exclusivelyon wide-flange shapes of ASTM A36 steel [2]. However,structural steel shapes most commonly used in the U.S. todayare produced according to the newer ASTM A992 standard,which provides for a higher yield and tensile strength than A36steel.

The move to A992 steel raised concerns regarding theappropriateness of the flange width–thickness limits for EBF

∗ Corresponding author. Tel.: +1 612 626 0331; fax: +1 612 626 7750.E-mail address: [email protected] (T. Okazaki).

0143-974X/$ - see front matter c© 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2006.08.004

link sections. A limit of 0.30(E/Fy)1/2 was traditionally

specified for the flange width–thickness ratio of EBF links.This flange slenderness ratio corresponds to 8.5 for A36 steel(with minimum specified yield strength of Fy = 250 MPa)and 7.2 for A992 steel (minimum specified Fy = 345 MPa).A number of rolled wide-flange shapes meet the flangeslenderness limit of 8.5 but do not meet the limit of 7.2,and thus are disqualified from use as EBF links by thetraditional flange slenderness limit. Meanwhile, the effect offlange slenderness ratio on link behavior has not been explicitlyaddressed in previous research. A secondary concern was theappropriateness of link overstrength factors used in the capacitydesign procedure for EBFs. Link overstrength is defined asthe maximum shear force developed in the link divided bythe plastic shear strength of the link. While the 2005 AISCSeismic Provisions implicitly assume a link overstrength factorof 1.5, recent tests on large built-up shear links for use in bridgeapplications showed overstrength factors of nearly 2 [3,4].This has led to concerns that current overstrength factors maybe unconservative, particularly for shapes with heavy flanges,where shear resistance of the flanges contributes significantlyto overstrength.

An experimental research program was conducted at theUniversity of Texas at Austin. The initial objective for thisprogram was to examine flange buckling and overstrength in

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Fig. 1. Test setup: (a) energy dissipation mechanism of EBF; (b) schematicrepresentation of test setup; and (c) details and dimensions.

links constructed of A992 steel. Link specimens with varioussections and lengths were tested for this purpose. As discussedlater, many of these initial specimens failed prematurely dueto fracture of the link web. This type of failure mode wasnot typically reported in earlier tests [5–7], and thus motivatedfurther testing to investigate the cause of the link web fracture.

Failure of the initial specimens to meet rotation requirementsled to questions concerning the loading protocol for testing EBFlinks specified in the 2002 AISC Seismic Provisions [8]. A totalof thirty-seven link specimens were tested during the course ofthis investigation. In the rest of this paper, the test specimensand test procedure is discussed, followed by an overview of testresults. Key observations pertaining to loading history, link webfracture, and link end welds are discussed. The test data is usedto evaluate the flange slenderness limit, inelastic rotation limit,and overstrength factor for EBF links prescribed in the 2005AISC Seismic Provisions [1]. Suggestions on new techniquesfor link stiffener design and new detailing for link-to-columnconnections are made. While some results from the researchprogram have been discussed in a previous publication by theauthors [9], these results are also mentioned in this paper forcompleteness.

2. Experimental program

2.1. Test setup

A test setup was devised to reproduce the force anddeformation environment imposed on a link in an EBF withone end of the link attached to a column, as shown in Fig. 1(a).Fig. 1(b) illustrates that the kinematics of the test setup followsthe energy dissipation mechanism of the EBF. Full details anddimensions of the test setup are shown in Fig. 1(c). The linklength is indicated in the figures by the letter e. The linkspecimens were welded to heavy end plates at each end, asshown in Fig. 2. The end plates were, in turn, bolted into thesetup, between the vertical column and horizontal beam.

Fig. 2. Details of selected link specimens.

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Table 1Test section properties

Section Fy (MPa) Fu (MPa) b f /2t f

Flange Web Flange Web Nominal Actual

W10×19 367 405 509 531 5.1 5.2W10×33 356 382 507 503 9.1 9.2W10×33 (A) 374 365 520 503 9.1 9.6W10×33 (B) 379 402 518 530 9.1 9.2W10×33 (C) 374 367 518 503 9.1 9.6W16×36 362 392 534 565 8.1 7.1W10×68 319 404 479 531 6.6 6.6W18×40 352 393 499 527 5.7 6.1

Note: The tabulated Fy is a static yield stress value, measured with thetest machine cross-heads stationary. The tabulated Fu is a dynamic ultimatestrength, measured with the test machine cross-heads in motion.

2.2. Test specimens

Five different wide-flange shapes were used to constructthe test specimens. All sections were of ASTM A992 steel.The actual measured yield and ultimate strength values arelisted in Table 1 for samples taken from the edges of theflanges and from mid-depth of the web. The link sections hada range of flange width–thickness ratios, b f /2t f , to study theeffect of flange slenderness on link behavior. The W10×19,W10×68, and W18×40 sections satisfied the seismicallycompact limit [1] for flanges of 0.30(E/Fy)

1/2 (=7.2 forFy = 345 MPa). The W10×33 was chosen specifically becauseits flange slenderness exceeds the seismically compact limitand is at the compact limit [10] of 0.38(E/Fy)

1/2 (=9.2 forFy = 345 MPa). The flange slenderness of the W16×36, basedon the actual measured dimensions, was substantially smallerthan the nominal slenderness so that this section satisfied theseismically compact limit. Another consideration for selectingthe test sections was to study the link overstrength for sectionswith large ratios of flange to web area. This was based on aconcern that heavy flanges can contribute substantially to theshear capacity of the section, and therefore generate high levelsof overstrength. The W10×68 section was chosen specificallyto investigate this issue. The ratio of the area of one flange tothe area of the web, for the W10×68, is approximately 2, whichis near an upper bound for rolled wide-flange shapes normallyused as links.

Table 2 provides a listing of all link test specimens. Arange of link lengths were tested, from short shear yieldinglinks to long flexural yielding links. Links with a length lessthan 1.6Mp/Vp are dominated by shear yielding, whereasthose longer than 2.6Mp/Vp are dominated by flexuralyielding [1]. Between these limits, link inelastic response isheavily influenced by both shear and flexure. The link lengthparameter, e/(Mp/Vp), listed in Table 2, was evaluated basedon the measured section dimensions and the measured yieldstrength values.

Fig. 2 shows schematic views of specimens with variousstiffener details. The stiffener locations are listed in Table 2.As indicated in the table, the thirty-seven link specimens arecategorized into three groups. All specimens in Groups I andII were provided with intermediate stiffeners according to the

2005 AISC Seismic Provisions. As illustrated in Fig. 2 forSpecimens 4A, 4B, and 4C, stiffeners were provided on onlyone side of the web, as permitted by the Provisions for linksections with a depth less than 635 mm. The stiffeners werefull depth, welded to the web and to both flanges using filletwelds. The specimens in Group III, which were all identical insection and length, were provided with varying stiffener details.Specimens S1 through S3 had full depth one-sided stiffeners,similar to specimens in Groups I and II. Specimens S4, S6, andS9 had full depth stiffeners at both sides of the web, weldedto the web and to both flanges. Specimens S5, S7, S8, andS10 did not meet the stiffener requirements in the Provisions.Specimens S5 and S8 had stiffeners at both sides of the web,welded only to the flanges and not to the web. Specimen S7had one-sided stiffeners welded only to the web and not tothe flanges. The spacing of stiffeners in Specimen S10 did notmeet the stiffener spacing requirement in the Provisions. Thestiffeners for Specimens S6 and S9 were welded to the weband flanges using a self-shielded flux core arc welding (FCAW)process with an E70T-6 electrode. In the remaining thirty-fivespecimens, the stiffeners were welded to the web and/or flangesusing a shielded metal arc welding (SMAW) process with anE7018 electrode.

2.3. Loading protocol

Four different cyclic loading protocols, as shown in Fig. 3,were used in the tests. As indicated in the figure, the fourprotocols are referred to in this paper as the old-AISC, revised,severe, and random loading protocols. Each loading protocolcontrols the link rotation angle, γ , which is computed as therelative displacement of one end of the link compared to theother, divided by the link length.

After several initial elastic cycles, the old-AISC loadingprotocol (Old) requires increasing the applied link rotation inincrements of 0.01 rad, with two cycles of loading appliedat each increment of rotation. The severe loading protocol(SEV) was identical to the old-AISC protocol, except thatfour cycles of loading, instead of two cycles, were requiredat each increment of rotation. This protocol was intended topromote low cycle fatigue and premature failure of the linkspecimen. The Revised Loading Protocol (RLP) requires that,after completing the loading cycle at a link rotation of 0.05 rad,the link rotation be increased in increments of 0.02 rad, withone cycle of loading applied at each increment of rotation.The old-AISC protocol was specified in the previous, 2002AISC Seismic Provisions as the loading protocol for testingEBF links. However, the old-AISC protocol is replaced by therevised protocol in the current, 2005 AISC Seismic Provisions.As discussed later, the revised protocol is believed to be morerepresentative of demands caused by actual earthquake groundmotion than the old-AISC protocol. Except for Specimen9-RLP, the revised protocol used in this study included twoloading cycles at a link rotation of 0.02 rad, instead of fourloading cycles required in the 2005 AISC Seismic Provisions.It is believed that the lack of these small amplitude cycles hadlimited influence on the overall performance of the specimen.

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Table 2Test specimens

Group Specimen Section Link length Intermediate stiffeners Loading protocole (mm) e/(Mp/Vp)

I

1A W10×19 584 1.73 3@146 mm Old1B W10×19 584 1.73 3@146 mm Old1C W10×19 584 1.73 3@146 mm Old2 W10×19 762 2.25 4@152 mm Old3 W10×19 1219 3.61 152 mm from each end Old4A W10×33 584 1.04 3@146 mma Old4B W10×33 584 1.04 3@146 mma Old4C W10×33 584 1.04 3@146 mma Old5 W10×33 930 1.65 5@156 mm Old6A W10×33 1219 2.16 4@244 mm Old6B W10×33 1219 2.16 4@244 mm Old7 W10×33 1854 3.29 305 mm from each end Old8 W16×36 930 1.49 6@133 mm Old9 W16×36 1219 1.95 5@203 mm Old10 W10×68 930 1.25 2@305 mm Old11 W10×68 1219 1.64 3@305 mm Old12 W18×40 584 1.02 3@146 mm Old

II

4A-RLP W10×33 584 1.04 3@146 mma RLP4C-RLP W10×33 584 1.04 3@146 mma RLP8-RLP W16×36 930 1.49 6@133 mm RLP9-RLP W16×36 1219 1.95 5@203 mm RLP10-RLP W10×68 930 1.25 2@305 mm RLP11-RLP W10×68 1219 1.64 3@305 mm RLP12-RLP W18×40 584 1.02 3@146 mm RLP12-MON W18×40 584 1.02 3@146 mm MON12-SEV W18×40 584 1.02 3@146 mm SEV12-RAN W18×40 584 1.02 3@146 mm RAN

III

S1 W10×33 (A) 584 1.01 3@146 mma SEVS2 W10×33 (B) 584 0.99 3@146 mma SEVS3 W10×33 (C) 584 0.99 3@146 mma SEVS4 W10×33 (B) 584 0.99 3@146 mma SEVS5 W10×33 (B) 584 0.99 3@146 mma,b SEVS6 W10×33 (B) 584 0.99 3@146 mma SEVS7 W10×33 (B) 584 0.99 3@146 mma,b SEVS8 W10×33 (B) 584 0.99 3@146 mma,b RLPS9 W10×33 (B) 584 0.99 3@146 mma RLPS10 W10×33 (B) 584 0.99 2@195 mma,b RLP

a See Fig. 2 for stiffener details.b Violates the stiffener requirements in the 2005 AISC Seismic Provisions.

Finally, the random loading protocol (RAN) was a randomlygenerated sequence which imposes large rotations in bothloading directions during early loading cycles.

As indicated in Table 2, the seventeen specimens in Group Iwere tested using the old-AISC protocol. The ten specimens inGroup II were tested using various loading histories, includingmonotonic loading (MON). The ten specimens in Group IIIused either the severe protocol or the revised protocol.

3. Test results

Acceptance criteria for links are defined in the 2005 AISCSeismic Provisions based on inelastic rotation. The inelasticrotation, γp, is evaluated by removing the contributions ofelastic response from the link rotation, γ . The Provisionsspecify shear yielding links (e ≤ 1.6Mp/Vp) should be capableof developing an inelastic rotation of 0.08 rad, whereas flexuralyielding links (e ≥ 2.6Mp/Vp) should be capable of an

inelastic rotation of 0.02 rad. The required inelastic rotationof intermediate length links (1.6Mp/Vp < e < 2.6Mp/Vp)

is determined by linear interpolation between 0.08 and 0.02rad. The inelastic rotation capacity of the link specimens wasdefined per the 2005 AISC Seismic Provisions, as the maximumlevel of inelastic rotation sustained for at least one full cycleof loading prior to the link shear strength dropping below thenominal link shear strength. Here, the nominal strength wasevaluated based on the nominal section dimensions and a yieldstrength of Fy = 345 MPa.

Table 3 summarizes results for each of the link specimenstested in this program. The table lists the actual inelasticrotation achieved by the specimen, along with the inelasticrotation required by the 2005 AISC Seismic Provisions. Alsolisted is a brief description of the controlling failure modefor each specimen. Detailed descriptions of individual testscan be found in Arce [11] (for all specimens in Group Iexcept Specimen 12), Ryu [12] (Specimen 12 and all specimens

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Fig. 3. Loading protocols.

Fig. 4. Response of Specimen 4A.

in Group II except Specimen 9-RLP), and Galvez [13] (allspecimens in Group III).

Specimens 1A, 1B, and 6A failed prematurely due tofractures at the fillet welds connecting the link flanges to theend plates. These failures are considered an artifact of thetest setup, as the link end connections used for the specimenswere not representative of typical link end connection detailsused in actual EBFs. Details of the fracture in the link endwelds and their implications will be discussed later in thispaper. Meanwhile, these specimens will be excluded from thediscussion of link behavior. Excluding Specimens 1A, 1B,and 6A, there are thirty-four remaining specimens that werenot affected by failures at the link end connections, and cantherefore be considered as providing valid fundamental data onthe behavior of links.

A notable feature of the tests was that specimens with lengthe < 1.7Mp/Vp typically exhibited link web fracture as thecontrolling failure mode. The link web fractures initiated at thetop and bottom ends of the link web stiffeners, at the pointof termination of the fillet welds connecting the stiffeners tothe link web. These fractures often propagated in a horizontaldirection, running parallel to the flanges. Ultimately, the growthof these cracks led to a drastic reduction of the link shearresistance. Specimen 4A provides an example of a specimenthat failed due to this type of fracture. Fig. 4 shows thehysteretic response of this specimen and Fig. 5 shows thespecimen after testing. Fractures running across the top andbottom of the link web are visible in this photo. The link webfractures limited the inelastic rotation capacity of Specimen 4Ato γp = 0.06 rad, falling short of the 0.08 rad required by the

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Table 3Test results

Specimen γp (rad) Observed failure modeRequired Test

1A 0.072 0.042 Fracture at link end plate connection1B 0.072 0.060 Fracture at link end plate connection1C 0.072 0.081 Flange and web buckling followed by fracture in web2 0.042 0.070 Flange and web buckling followed by fracture in flange near link end3 0.02 0.041 Flange and web buckling followed by fracture in flange near link end4A 0.08 0.061 Fracture of web at stiffener weld4B 0.08 0.071 Fracture of web at stiffener weld4C 0.08 0.080 Fracture of web at stiffener weld5 0.077 0.067 Fracture of web at stiffener weld6A 0.046 0.047 Fracture at link end plate connection6B 0.046 0.047 Flange and web buckling followed by fracture in web7 0.02 0.037 Flange, web, and lateral torsional buckling8 0.08 0.077 Flange and web buckling followed by fracture in web at stiffener weld9 0.059 0.048 Flange and web buckling10 0.08 0.073 Fracture of web at stiffener weld11 0.078 0.068 Fracture of web at stiffener weld12 0.08 0.091 Fracture of web at stiffener weld accompanied by web buckling4A-RLP 0.08 0.12 Fracture of web at stiffener weld4C-RLP 0.08 0.12 Fracture of web at stiffener weld8-RLP 0.08 0.117 Flange and web buckling followed by fracture in web at stiffener weld9-RLP 0.059 0.058 Flange and web buckling10-RLP 0.08 0.113 Fracture of web at stiffener weld possibly caused by inadequately small fillet weld size11-RLP 0.078 0.087 Fracture of web at stiffener weld; link rotation limited by ram stroke12-RLP 0.08 0.119 Fracture of web at stiffener weld accompanied by web buckling12-MON 0.08 >0.34 Web buckling12-SEV 0.08 0.072 Fracture of web at stiffener weld12-RAN 0.08 0.125 Web buckling followed by fracture of web at stiffener weldS1 0.08 0.062 Fracture of web at stiffener weldS2 0.08 0.061 Fracture of web at stiffener weldS3 0.08 0.072 Fracture of web at stiffener weldS4 0.08 0.061 Fracture of web at stiffener weldS5 0.08 0.071 Web buckling followed by fracture of webS6 0.08 0.051 Fracture of web at stiffener weldS7 0.08 0.051 Fracture of web at stiffener weld promoted by web bucklingS8 0.08 0.122 Web buckling followed by fracture of webS9 0.08 0.101 Fracture of web at stiffener weldS10 0.08 0.121 Fracture of web at stiffener weld and web buckling

2005 AISC Seismic Provisions. In fact, the majority of shearlink specimens in Group I, tested with the old-AISC loadingprotocol, failed to achieve their required inelastic link rotationsdue to this type of fracture. The majority of the twenty-sevenspecimens with length e < 1.7Mp/Vp were controlled by linkweb fracture. The only exceptions were Specimen 12-MON,which was tested with monotonic loading, and Specimens S5and S8, which did not have the stiffeners welded to the linkweb.

Specimens 9 and 9-RLP were identical specimens withan intermediate length of e = 2.0Mp/Vp, tested with theold-AISC protocol and revised protocol, respectively. Bothspecimens failed before achieving the rotation requirement,due to strength degradation associated with severe flangeand web buckling in the end panels. The link web fracturesdiscussed above were not observed in these specimens. Fig. 6shows the hysteretic response of Specimen 9-RLP and Fig. 7shows the specimen after testing. The photo shows substantialconcentration of deformation in the end panels, where thesection was severely distorted due to combined flange and web

Fig. 5. Specimen 4A after testing.

buckling. Significant yielding is visible in the link web panelsbesides the end panels. The development of local buckling ledto the gradual strength degradation shown in Fig. 6.

Besides Specimens 9 and 9-RLP, six other specimens hadlonger links in the intermediate and flexure yielding range of

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Fig. 6. Response of Specimen 9-RLP.

Fig. 7. Specimen 9-RLP after testing.

1.7Mp/Vp < e ≤ 3.6Mp/Vp. These specimens, all testedwith the old-AISC loading protocol, successfully achievedtheir required link rotations, and ultimately failed due tocombinations of severe flange buckling, web buckling, and insome cases, lateral torsional bucking. The link web fractureexhibited by short links was not observed in these specimens.Overall, the behavior of longer links (1.7Mp/Vp < e ≤

3.6Mp/Vp) was very similar to that reported in earlier tests,for example in Engelhardt and Popov [14].

4. Loading protocol

A large number of test specimens in Group I failedprematurely, before achieving their required rotation levels.Most of these specimens met all link design requirements, andwere tested with the old-AISC loading protocol specified in the2002 AISC Seismic Provisions. After observing these results,Richards and Uang [15] noted that the typical loading historiesused in shear link tests conducted in the 1970s and 1980sintroduced a significantly smaller number of inelastic loadingcycles compared to the old-AISC loading protocol used for thetests in Group I. Further, there appeared to be no rational basisfor the old-AISC loading protocol. Consequently, Richards andUang [16,17] developed a revised loading protocol for testing

EBF links, which was then used for selected specimens inGroups II and III. The revised loading protocol was developedusing a methodology similar to that used for moment frameconnection testing, developed under the FEMA/SAC programby Krawinkler et al. [18].

Seven of the specimens in Group I that failed to meet theirinelastic rotation requirements were duplicated and retestedusing the revised loading protocol developed by Richardsand Uang [16,17]. Among the seven specimens, the sixshorter specimens with length e < 1.7Mp/Vp achieved linkrotations well in excess of the required level. As indicatedby the data in Table 3, these specimens developed inelasticrotations of 10–50% greater than the level required in the 2005AISC Seismic Provisions. The inelastic rotation developed bySpecimen 11-RLP was limited due to limitations in the strokeof the loading ram. Nonetheless, this specimen developed aninelastic rotation exceeding the required level.

However, one specimen tested with the revised loadingprotocol, 9-RLP, failed to significantly exceed the requiredrotation. After completing a full cycle at γp = ±0.058 rad,this intermediate link specimen lost its strength during thefollowing loading cycle of roughly γp = ±0.08 rad dueto severe flange and web buckling. Consequently, althoughSpecimen 9-RLP achieved a 20% greater rotation comparedto Specimen 9, which was tested with the old-AISC loadingprotocol, Specimen 9-RLP still failed to meet the requiredinelastic rotation of γp = 0.059 rad. However, the specimenretained a shear strength of 120% of its nominal shear strengthat γp = ±0.058 rad, and the following strength degradationwas rather gradual. As indicated in Fig. 6, the backbonecurve connecting the maximum rotation points at each rotationincrement exceed the nominal shear strength up to γp =

±0.07 rad, which is beyond the required γp = 0.059 rad.Therefore, since Specimen 9-RLP failed to meet the rigorousinelastic rotation requirement by such a small margin, andmaintained appreciable strength during rotations beyond therequired inelastic rotation, this specimen is considered aseffectively satisfying the rotation requirements of the 2005AISC Seismic Provisions.

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Fig. 8. Response of Specimen 4A-RLP.

Fig. 9. Specimen 4A-RLP after testing.

To illustrate the effect of loading protocol, Fig. 4 showsthe hysteretic response of Specimen 4A, which was testedusing the old-AISC loading protocol. In comparison, Fig. 8shows the hysteretic response of Specimen 4A-RLP, which wasnominally identical to Specimen 4A, except that 4A-RLP wastested using the revised loading protocol. Specimen 4A-RLPdeveloped an inelastic rotation capacity of γp = 0.12 rad,as compared to γp = 0.061 rad for Specimen 4A. Fig. 9 isa photo of Specimen 4A-RLP after testing, showing the linkweb fractures that ultimately caused failure of this specimen.This failure mode is very similar to that observed in Specimen4A, shown in Fig. 5. In general, whereas the change from theold-AISC protocol to the revised protocol led to an increasein link rotation capacity on the order of 20–100%, it did notsignificantly change the controlling failure mode for the link.Links that failed due to fracture of the link web under the old-AISC protocol still failed by fracture of the link web under therevised protocol.

In order to further investigate the effect of loading history onlink behavior, four replicates of Specimen 12 were fabricatedand tested with different loading histories. In addition to therevised loading protocol discussed above (Specimen 12-RLP),three other duplicate specimens were subjected to monotonicloading (12-MON), the severe loading protocol (12-SEV),

and random loading protocol (12-RAN). Specimen 12-MONachieved an inelastic rotation larger than 0.34 rad, which ismore than four times the 0.08 rad required in the 2005 AISCSeismic Provisions. An earlier monotonic loading test by Kasaiand Popov [7] also showed a shear link specimen developingγp = 0.19 rad. These test results demonstrate the ability of EBFlinks to withstand very large single excursion deformations,such as those imposed by large near-fault earthquake groundmotions. The inelastic rotations achieved in the five tests on thereplicates of Specimen 12 were strongly related to the imposedloading history. The inelastic rotation capacities increased fromSpecimen 12-SEV (γp = 0.072 rad), to 12 (γp = 0.091 rad),to 12-RLP (γp = 0.119 rad), to 12-RAN (γp = 0.125 rad),and finally, to 12-MON (γp > 0.34 rad, one direction only).Specimens 12, 12-RLP, 12-SEV, and 12-RAN all failed due tolink web fracture initiating at the termination of stiffener tolink web welds. Specimen 12-MON failed due to severe webbuckling and distortion of the link. Although web fracture wasobserved at the stiffener weld terminations, web buckling wasthe primary cause of strength loss. Specimen 12-RAN showedstrength degradation due to web buckling before developmentof significant link web fracture. These observations suggest thatlink web fracture is related to low cycle fatigue effects, andif very large rotations are imposed at an early loading stage,significant web buckling can precede the occurrence of link webfracture.

As illustrated by the discussion above, the loading protocolused to test link specimens has a very large effect on theinelastic rotation capacity achieved by the link. Links testedwith the revised loading protocol achieved inelastic rotationsthat were from 20 to 100% greater than links tested with theold-AISC protocol. The average increase in inelastic rotationusing the revised protocol over using the old-AISC protocolwas 47%. Since the loading protocol has such a large effecton link test results, it is important that loading protocols beselected that realistically reflect link demands under actualearthquake loading, as represented by the revised loadingprotocol developed by Richards and Uang [16,17].

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5. Link web fracture

The majority of specimens in the length range of e <

1.7Mp/Vp developed web fractures at the ends of stiffener tolink web welds, prior to the occurrence of any web buckling, oronly after very mild buckling, as exhibited by Specimen 4A (seeFig. 5). However, this type of link web fracture was not reportedin earlier tests, for example in Hjelmstad and Popov [5], andMalley and Popov [6]. While fractures of the link web werereported in these past tests, those fractures occurred only afterthe web had undergone severe buckling, with fracture initiationoccurring at locations of large localized bucking deformations.An exception is a recent test by McDaniel et al. [4] on avery large built-up link section tested for use in the new eastspan of the San Francisco–Oakland Bay Bridge. In this test,a fracture initiated at the termination of a stiffener weld priorto web buckling, although the fracture propagated diagonallyacross the web, compared to the horizontal fracture propagationobserved in Specimen 4A. Analysis of the failure [4] suggestedthat the fracture was caused by a stress concentration at the endof the stiffener weld, because the stiffener was terminated tooclose to the flange-to-web groove weld of the built-up section.

The occurrence of pre-bucking web fracture as thecontrolling failure mode for shear links was not typicallyobserved in the extensive link testing programs conducted inthe 1980s, which formed the basis for EBF detailing rulesin the AISC Seismic Provisions. Consequently, links tested inthis current program exhibited fundamentally different failuremechanisms from many links tested in earlier programs.Richards and Uang [15] noted three significant differencesbetween recent and earlier link tests. These differences werein: (a) cyclic loading history; (b) stiffener details; and (c) linkmaterial. Tests in Groups II and III were conducted to furtherstudy the effect of these three factors, and to further examinethe cause of the link web fracture.

5.1. Loading protocol

An initial concern after completing the tests in Group Iwas that the majority of shear yielding links failed due to linkweb fracture before achieving the required inelastic rotationof γp = 0.08 rad. As discussed earlier, this concern led toquestions regarding the loading protocol provided in the 2002AISC Seismic Provisions, and the development of the revisedloading protocol by Richards and Uang [16,17]. Six shearyielding links were duplicated and retested using the revisedloading protocol. Since all six specimens (4A-RLP, 4C-RLP,8-RLP, 10-RLP, 11-RLP, and 12-RLP) significantly exceededthe required γp = 0.08 rad, concerns regarding the ability ofshear links to provide adequate inelastic rotation capacity werelargely alleviated.

The shear yielding links tested in this program consistentlyfailed by link web fracture, regardless of the loading protocol.The only exceptions were Specimens 12-MON, S5, and S8.While the monotonically loaded Specimen 12-MON failed dueto web buckling, the web buckling was not evident until thespecimen reached a very large rotation of γp = 0.2 rad. The

failure modes of Specimens S5 and S8 were associated withthe unique stiffener details used for these specimens, in thatthe stiffeners were not welded to the link web. These uniquespecimens aside, all other test results indicate that the loadinghistory has little influence on the link web fracture. That is,regardless of loading protocol, the shear links tested in thisprogram consistently exhibited web fracture as the controllingfailure mode.

5.2. Stiffener details

The first specimen in this program to exhibit a horizontalweb fracture initiating at the end of a stiffener weld wasSpecimen 4A. Following this failure, and based on therecommendations by McDaniel et al. [4], the stiffener weldswere terminated at a larger distance from the flange in thesubsequent Specimens 4B and 4C. In going from Specimens4A to 4B, and then to 4C, the termination of the stiffenerweld was moved progressively further from the flange (seeFig. 2). In Specimen 4C, the stiffener welds were terminated adistance of approximately five times the web thickness from the“k-line” of the section. The k-line is the location where the webmeets the flange–web fillet. The test results (see Table 3) showthat larger inelastic rotations were achieved as the stiffenerwelds were moved further from the k-line. However, even forSpecimen 4C, which had the stiffener welds terminated quitea large distance from the k-line, the horizontal fractures stillultimately developed. Thus, while moving the stiffener weldsfurther from the k-line was beneficial, it did not eliminate theoccurrence of link web fracture.

Although moving the stiffener weld termination further fromthe k-line resulted in higher inelastic rotations prior to linkweb fracture, all shear link specimens tested with the revisedloading protocol developed the required inelastic rotation of0.08 rad. That is, even specimens where the stiffener weldtermination was relatively close to the k-line (Specimen 4A-RLP for example) still developed 0.08 rad inelastic rotation.Therefore, providing a generous distance between the k-lineand the stiffener weld termination, while beneficial, may notbe essential for satisfactory link performance. Nonetheless,due to the beneficial higher inelastic rotations, terminatingthe stiffener welds a generous distance from the k-line isrecommended. Based on this test program, a distance of fivetimes the link web thickness from the k-line of the link sectionto the stiffener weld termination is suggested as a reasonablebasis for design.

As noted by Richards and Uang [15], a large number ofearlier link tests were conducted to investigate stiffener designcriteria, and as such, the majority of these specimens didnot satisfy the current stiffener design criteria. As discussedabove, the link web fracture observed in Groups I and II testswas not reported previously with the exception of McDanielet al. [4], which also followed the current stiffener designcriteria. Therefore, it was speculated that the preclusion ofweb buckling shifts the critical failure mode to one controlledby fracture at the location of high restraints due to low cyclefatigue. In order to investigate the relation between stiffener

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details and link web fracture, and to identify details thatdelay link web fracture, specimens in Group III were testedwith various stiffener details. Specimens S4 through S10 wereprovided with non-typical stiffener details, some of whichviolate requirements in the 2005 AISC Seismic Provisions.These specimens were constructed of the same material asSpecimen S2, which conformed to the stiffener requirementsin the Provisions. The severe loading protocol was used forSpecimens S4 through S7 in order to promote prematurelink web fracture. Further, the specimens had stiffener weldsterminated close to the k-line of the section (see Fig. 2) in orderto draw higher stresses and strains near the k-area, where rolledshapes can have locally degraded material properties.

Specimen S4 had full depth stiffeners on both sides of theweb, welded to both flanges and to the web. This arrangementwas expected to elevate the local restraint near the k-areacompared to the standard arrangement as in Specimens S2, andconsequently, promote link web fracture. However, SpecimenS4 sustained one more loading cycle than Specimen S2 beforefailing by link web fracture. Therefore, two-sided fully weldedstiffeners were no more detrimental to the occurrence of webfracture than one-sided stiffeners. Specimen S6 had the samestiffener arrangement as Specimen S4, but used a differentwelding process to weld the stiffeners to the link flanges andweb. Specimen S4, which used the shielded metal arc welding(SMAW) process with an E7018 electrode, achieved greaterrotation and survived four-and-one-half more loading cyclesthan Specimen S6, which used the self shielded flux cored arcwelding (FCAW) process with an E70T-6 electrode. The lowerfracture toughness and higher heat input of the FCAW processmay have caused the degraded performance of Specimen S6compared to Specimen S4.

Specimen S5 was provided with unconventional linkstiffener detailing. This specimen had full depth stiffeners onboth sides of the web, but these stiffeners were welded onlyto the flanges and not to the web. Eliminating the stiffenerto link web weld was expected to avoid the occurrence offracture in the k-area of the link web. In the absence of stiffenerto link web welds, it was expected that restraint against linkweb buckling would be achieved by “sandwiching” the linkweb between stiffeners on opposite sides of the web. Unlikespecimens with fully welded stiffeners, Specimen S5 exhibitednotable web buckling starting from early inelastic loadingcycles. Although no fracture occurred near the k-area of thesection, this specimen ultimately fractured at a location ofconcentrated buckling deformation, where the link web wasrubbing against the stiffener. Specimen S5, which had stiffenerswelded to the link flanges only, completed three more loadingcycles and achieved a larger inelastic rotation than SpecimenS2, which was provided with conventional stiffener detailing.This approach of sandwiching the link web between stiffenerswithout applying welds to the web can provide excellent cyclicperformance, and merits further investigation.

Specimen S7 was also provided with unconventionalstiffener detailing. For this specimen, partial depth stiffenerswere provided on only one side of the web, and were weldedonly to the web and not to the flanges. This arrangement

was expected to reduce the local restraint near the k-area,although it was questionable whether the stiffeners wouldprovide sufficient buckling restraint for the web. Specimen S7developed a smaller inelastic rotation than Specimen S2, andfailed due to web fracture at the termination of stiffener welds.Buckling deformation of the web concentrated near the verticalends of the stiffeners, and eventually caused fracture of the web.Therefore, eliminating the connections of the stiffeners to theflanges was not beneficial for mitigating fracture developmentin the web.

Specimens S5 and S6 were duplicated and retested usingthe revised loading protocol. These two specimens, designatedrespectively as S8 and S9, developed inelastic rotations muchgreater than the required 0.08 rad. The failure modes weresimilar to the failure modes of Specimens S5 and S6. Theseresults suggest that the two-sided stiffeners, whether welded ornot welded to the link web, are effective arrangements to controllink rotation capacity.

Specimen S10 was provided with fewer stiffeners (i.e., largerstiffener spacing) than required in the 2005 AISC SeismicProvisions. Under the revised loading protocol, this specimendeveloped an inelastic rotation much greater than the required0.08 rad, and failed due to fracture of the link web. Although thespecimen exhibited strength degradation caused by substantialweb buckling, Specimen S10 ultimately failed due to link webfracture. This test result suggests that the shear link stiffenerspacing requirement in the Provisions is conservative. Furtherresearch may be beneficial to determine if a relaxation in thestiffener spacing criteria is justified.

Based on the above observations for Specimen S10, the linkweb fractures which were observed in the current tests, but notreported from earlier tests, do not appear to be the result of thestiffener spacing criteria in the Provisions. Alternative stiffenerdesigns which are not currently permitted by the Provisions,such as the sandwiching stiffeners used in Specimens S5 andS8, may be effective for link detailing. As demonstrated bythe comparison between Specimens S4 and S6, the weldingprocess used for the stiffener to web weld may have a significantinfluence on the link web fracture.

5.3. Material properties

The proximity of the link web fractures in many of thetest specimens to the k-line of the section suggests thatmaterial properties in the k-area may have played a role inthese fractures. The commentary on the 2005 AISC SeismicProvisions discusses that the steel in the k-area of rolled wide-flange shapes (the region where the web meets the flange) canexhibit high hardness and be prone to fracture.

In order to investigate the effect of material properties onlink behavior, specimens of identical geometry, Specimens S1,S2, and S3, were constructed from W10×33 shapes producedby three different mills. The three steels are indicated in Table 1as (A), (B), and (C). Sample ASTM Rockwell B hardnessmeasures taken along the web-centerlines for the three steelsections are shown in Fig. 10(a). While all three sections shownotably higher hardness values near the k-area of the section,

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Fig. 10. Material properties measured for W10×33 sections: (a) hardnessmeasures along web centerline of link section; and (b) tension coupon testresults for Steel (C).

Steel (A) shows the highest peak hardness value, while Steel(B) shows somewhat lower hardness values. The peak valueis seen at a distance of 20–25 mm from the outer face ofthe flange, at the k-line of the section. Tension coupons weretaken from the location of the web indicated in Fig. 10(a). ForSteels (A) and (C), the coupons taken from the k-area showed25–35% higher tensile strength and a two-thirds reduction inelongation compared to the coupon taken from the mid-depthof the web. For Steel (B), the coupons taken from the k-areashowed a 5% higher tensile strength and one-third reduction inelongation compared to the coupon taken from the mid-depthof the web. Fig. 10(b) shows the tensile coupon test resultsfor Steel (C), comparing three coupons taken from the edgeof the flange, mid-depth of the web, and k-area of the section.The figure illustrates the significantly higher tensile strengthand reduced elongation of the coupon taken from the k-area.Elevated hardness values, elevated tensile strength, and reducedductility is characteristic of the k-area of roller straightenedshapes [19], and was observed in all sections used for the linkspecimens in this study with the exception of the W10×19.

For specimens in Group III, the stiffener weld wasterminated within the region of elevated hardness values, asindicated in Fig. 10(a), so that the degraded material propertieswould influence their performance. The notable difference inthe k-area material properties was expected to cause varying

performance between the three specimens, S1, S2, and S3. Dueto the higher hardness and lower elongation in their k-areas,Specimen S1 (Steel (A)) and S3 (Steel (C)) were expectedto exhibit a smaller rotation capacity compared to SpecimenS2 (Steel (B)). However, the overall performance of the threespecimens was quite similar, with Specimen S3 completingthree more loading cycles than Specimens S1 and S2. All threespecimens failed by fracture of the link web initiating at thestiffener weld terminations. While these test results indicate thatthe steel material can influence link performance, the resultsdo not clarify the correlation between the reduced materialductility in the k-area and the occurrence of link web fracture.It is possible that the difference in k-area material propertiesbetween the three steels, which were all A992 steel, wasinsufficient to clearly highlight the influence of k-area materialproperties.

A rather large number of tests in this program indicate thatthe loading history and stiffener details do not change the failuremode of shear links from that controlled by link web fractureto a different failure mode. However, the relation between thematerial properties and the link web fracture is less clear. It issuggested that further studies be conducted to clarify the effectof material properties, specifically the properties in the k-area,on link web fracture.

6. Link end welds

The link specimens tested in this program were welded toheavy end plates, which in turn were bolted into the test setupshown in Fig. 1. Studying the behavior of connections betweenthe link and surrounding members was not an objective ofthis research program. Consequently, the end plate connectiondetails used in these tests were not intended to representrealistic link end conditions. Rather, the end plate detail wasdevised to preclude failure at the link ends, and thereby topermit study of link behavior. Nonetheless, the results of thistest program provide some useful insights into potentiallyeffective link-to-column connection details.

As discussed earlier, Specimens 1A, 1B, and 6A failedprematurely due to fracture of a fillet weld connecting the linkflange to the end plate. The fracture of the end plate weldsoccurred either in the throat of the weld, or in the link flangebase metal near the weld–base metal interface. Similar fractureswere reported in tests by Kasai and Popov [7] and Ramadanand Ghobarah [20]. In order to avoid these fractures, in laterspecimens, the leg size of the fillet welds was increased to one-and-one-half times the link flange or web thickness (see Fig. 2).Further, weld tabs were used at the edges of the flanges, asshown in Fig. 11, to avoid introducing undercuts or weld defectsat these edges. With the exception of Specimen 1A, which usedthe FCAW process with an E70T-6 electrode, the fillet weldswere made using the SMAW process with an E7018 electrode.Instead of using fillet welds, the 20 mm-thick flanges of theW10×68 links were connected to the end plates with partialpenetration groove welds (groove depth of 14 mm), reinforcedat the root side of the weld by fillet welds with a leg size equalto the flange thickness.

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Fig. 11. Typical end plate weld.

The improved end plate welds shown in Fig. 11 were usedat both ends of thirty-one link specimens. No damage in theend plate welds was observed in any of these specimens.Therefore, although the thickness of the end plates of 50 mm(three to five times the thickness of the link flange) may beunrealistic for practical application, the end plate connectionsused in these tests are promising for application to link-to-column connections. Research is continuing by the authors todevelop practical link-to-column connection details.

7. Design implications

7.1. Link flange slenderness limit

A basic objective of this research program was to study theeffect of flange slenderness on link behavior. More specifically,the objective was to determine if the flange slenderness limit,b f /2t f , for link flanges can be increased from the seismicallycompact limit of 0.30(E/Fy)

1/2 to the compact limit of0.38(E/Fy)

1/2. In this test program, the flange slendernessof the W10×33 was very close to 0.38(E/Fy)

1/2 for Fy =

345 MPa. Specimens with W10×33 sections were testedover a range of lengths varying from 1.0 to 3.6Mp/Vp,covering a wide range of link behaviors ranging from shear toflexural dominated response. The longer W10×33 specimens(Specimens 6B and 7) performed very well. These specimensexhibited flange buckling, but significantly exceeded theirrequired rotation levels before link strength dropped belowthe defined failure threshold. The shorter W10×33 specimenstested using the old-AISC loading protocol (Specimens 4Ato 4C and 5) did not achieve their required rotations dueto premature web fractures. However, when retested usingthe more realistic revised loading protocol, short W10×33specimens (Specimens 4A-RLP and 4C-RLP) significantlyexceeded their required rotation. Similar results were obtainedfrom Specimens S1 through S10. Therefore, data from theW10×33 test specimens suggest that the compact limit forflange slenderness is adequate for links of all practical lengths.Companion finite element simulations of EBF links by Richards

and Uang [15], calibrated to the results of these tests, andextended to a wider range of link parameters, also support theuse of the compact limit for all link lengths.

The specimens constructed with W16×36 sections alsoprovide useful data on flange slenderness effects. Based onnominal section dimensions, the flange slenderness of theW16×36 falls between the seismically compact limit and thecompact limit. However, based on measured dimensions, theactual flange slenderness was smaller than the nominal value,and fell just within the seismically compact limit. The failuremode of Specimens 8 and 8-RLP, which were W16×36 linkswith a length of e = 1.5Mp/Vp, was unique comparedwith other shear yielding links. The specimens developedsignificant flange and web buckling at both ends of the link,and ultimately failed by web fracture at the link end panels.Although the flange and web buckling did not directly causestrength degradation, it appeared that the severe web bucklingtriggered rapid growth of the web crack. Specimens 9 and9-RLP, which were W16×36 links with a length of e =

2.0Mp/Vp, failed due to strength degradation associated withcombined flange and web buckling in the link end panels.Between the two W16×36 links tested using the revisedloading protocol, Specimen 8-RLP significantly exceeded therequired rotation, while Specimen 9-RLP only barely met therotation requirement, as discussed earlier. The tendency oflocal buckling in the W16×36 sections suggests caution inpermitting the compact limit of 0.38(E/Fy)

1/2 for the flangesof longer flexure dominated links. The strength degradationin the W16×36 links appeared to result from flange–webinteraction, and further studies of such interaction are needed.

There is strong and consistent evidence from the results ofthis testing program, results from analytical studies [15], as wellas results from previous tests [7], to support the less stringentlimit of 0.30(E/Fy)

1/2 for shear yielding links. For longerlinks (e > 1.6Mp/Vp), the evidence on flange slendernesseffects on link rotation capacity is not as clear. A number oflonger link specimens with a flange slenderness at the limitof 0.38(E/Fy)

1/2 provided excellent performance, achievinginelastic rotations well beyond the required levels. However,rather short specimens (e = 1.5 and 2.0Mp/Vp) constructedwith the W16×36 section showed a notable tendency for flangebuckling. Since the flange slenderness of the W16×36 waswithin the limit of 0.30(E/Fy)

1/2, it is unclear if the flangeslenderness limit for links dominated by flexure could berelaxed to 0.38(E/Fy)

1/2. Based on this research and others,the flange slenderness limit for shear links (e ≤ 1.6Mp/Vp)

has been relaxed to 0.38(E/Fy)1/2 in the 2005 AISC Seismic

Provisions.

7.2. Inelastic rotation limit

The loading protocol used for testing has a very significanteffect on the performance of link specimens. This can be seenin Fig. 12(a), which compares the inelastic rotation measuredfor all twenty-four shear yielding links tested in this program.Although the data is skewed by the large number of W10×33links (fifteen specimens) and W18×40 links (five specimens),

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Fig. 12. Performance of shear yielding links: (a) inelastic rotation; and (b) overstrength factor.

each of identical length, the figure indicates the inelasticrotation is significantly affected by the loading protocol usedfor testing. The average inelastic rotation was 0.075 rad for thesix specimens tested with the old-AISC protocol, 0.117 rad forthe eight specimens tested with the revised protocol, and 0.062rad for the eight specimens tested with the severe protocol.While the influence of link section geometry, material, andstiffener details may also be recognized from the figure, theinfluence of loading protocol is dominant over these secondaryfactors. The data in Fig. 12(a) emphasize the importance ofchoosing a loading protocol that realistically reflects expectedearthquake demands, such as the revised loading protocol forEBF links developed by Richards and Uang [16,17]. Thisrevised loading protocol has been adopted by the 2005 AISCSeismic Provisions [1].

All shear yielding links tested in this program with therevised loading protocol consistently exceeded the requiredinelastic rotation of γp = 0.08 rad. With the exceptionof Specimen 9, the intermediate and flexural yielding links,tested with the old-AISC protocol, met their inelastic rotationrequirements. Specimen 9-RLP, which was a duplicate ofSpecimen 9, tested with the revised protocol, exceeded itsrequired rotation. Analysis by Richards and Uang [17] suggeststhat while the old-AISC protocol was overly conservative for

shear yielding links, it was adequate for flexure yielding links.Therefore, data from the current project suggest that linksdesigned according to the 2005 AISC Seismic Provisions wouldreliably develop the prescribed inelastic rotation.

7.3. Link overstrength

The link overstrength values evaluated for each specimenare presented in Table 4. This table lists the ratio Vmax/Vn ,where Vmax is the largest shear force measured in a test. Vnis the plastic strength of the link, and was calculated perthe 2005 AISC Seismic Provisions as the smaller of Vp or2Mp/e, where Vp and Mp were computed using the actualmeasured dimensions and actual measured yield strengths ofthe test sections. As indicated in Figs. 4, 6 and 8, the measuredvalue of Vn was typically equal to or somewhat larger than itsnominal value (based on nominal dimensions and nominal yieldstrength).

The overstrength tended to be greater for shorter links oflengths between 1.0 and 1.7Mp/Vp, compared to longer linkswith a length greater than 1.7Mp/Vp. The average overstrengthfor these shorter link specimens was 1.41, with a variation from1.25 to 1.62. The average overstrength for the longer specimens(e > 1.7Mp/Vp) was 1.20, with a variation from 1.05 to 1.27.

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Table 4Specimen overstrength

Specimen Vmax/Vp Specimen Vmax/Vp

1A 1.20 4A-RLP 1.451B 1.20 4C-RLP 1.471C 1.23 8-RLP 1.372 1.24 9-RLP 1.053 1.26 10-RLP 1.474A 1.40 11-RLP 1.424B 1.42 12-RLP 1.444C 1.41 12-MON 1.595 1.34 12-SEV 1.366A 1.21 12-RAN 1.626B 1.21 S1 1.497 1.27 S2 1.298 1.35 S3 1.569 1.11 S4 1.3710 1.44 S5 1.2511 1.42 S6 1.3212 1.40 S7 1.28

S8 1.27S9 1.43S10 1.36

Fig. 12(b) compares the overstrength factor measured forall shear yielding links tested in this program. The averagelink overstrength was 1.41 for the specimens tested withthe old-AISC protocol, 1.41 for the specimens tested withthe revised protocol, and 1.37 for the specimens tested withthe severe protocol. Specimens 12 and 12-RLP, 12-SEV,12-MON, and 12-RAN were subjected to various differentloading histories. Specimen 12-SEV, which was subjected toa large number of inelastic loading cycles before failing at arotation of γp = 0.072 rad, developed an overstrength of1.36, whereas the monotonically loaded Specimen 12-MONachieved an overstrength of 1.59 at a rotation of roughly γp =

0.21 rad. Comparing the seven identical specimens (five ofwhich are shear yielding links) tested with both the old-AISCand revised loading protocol, the overstrength was 1.36 for thespecimens tested with the old-AISC protocol, and 1.38 for thespecimens tested with the revised protocol. The data suggestthat the loading protocol has a more limited influence on linkoverstrength than on link rotation.

Specimens 10, 11, 10-RLP, and 11-RLP were made of theW10×68 section, which had a high ratio of flange to web area.These specimens were expected to develop shear resistance inthe flanges, and therefore, greater overstrength compared tothe other specimens. However, these specimens did not showunusually large values of link overstrength compared to othershear link specimens.

A notably large variation in overstrength values is seenbetween Specimens S1, S2, and S3. These three specimenswere W10×33 links of identical length, tested with the severeloading protocol, but constructed from different steels (seeTable 1 and Fig. 10). The higher overstrength values ofSpecimens S1 and S3 compared to Specimen S2 may bepartly due to the significantly higher tensile strength measuredin the k-area of the section, which was not accounted forin evaluating the nominal shear strength. However, since the

k-area would represent a smaller fraction of the web depth,the higher strength in the k-area should have a more limitedinfluence on the overstrength factor of deeper sections. The datafor Specimens S2 and S4 through S7, which were constructedfrom the same steel but provided with different stiffener details,suggest that the stiffener details have little influence on theoverstrength factor.

While the test data suggest smaller overstrength factorsfor longer links in the length range of e > 1.7Mp/Vp, theW16×36 links showed especially low overstrength values. Theoverstrength values for Specimens 9 and 9-RLP, both with alength of e = 2.0Mp/Vp, were 1.11 and 1.05, respectively.Combined flange and web buckling caused drastic strengthdegradation in these specimens. In fact, links with a lengthnear e = 2.0Mp/Vp are expected to experience significantshear-flexure interaction [14], and thus, the inelastic strengthas defined by the 2005 AISC Seismic Provisions is likelyto be conservative for these links. The occurrence of localbuckling and overestimation of the inelastic strength were thelikely reasons for the particularly low overstrength values forSpecimens 9 and 9-RLP.

8. Conclusions

This paper summarized an experimental program on thecyclic loading behavior of EBF links made of ASTM A992steel. The test results provide data pertaining to a wide range ofdesign issues for EBFs including the flange slenderness limits,overstrength factors, and stiffener design for links.

Results of this test program clearly show that the loadingprotocol used to test EBF links has a very large effect onthe inelastic rotation achieved by the links. Since the loadingprotocol has such a large effect on link test results, it isimportant that loading protocols realistically reflect demandscaused by actual earthquake loading. Such a loading protocolfor EBF links was recently developed by Richards andUang [16,17], and has been adopted by the 2005 AISC SeismicProvisions.

A number of shear yielding links tested in this programfailed due to fracture of the link web. These fractures initiated atterminations of stiffener to link web fillet welds and ultimatelycaused rapid strength degradation. This type of link webfracture has not typically been observed in earlier link testsreported in the literature. Observations from this programsuggest that the loading history and stiffener arrangement havelimited influence on the link web fracture. Further investigationis recommended to study the effect of material properties in thek-area on the occurrence of the link web fracture.

Link web fracture can be delayed and link rotation capacitycan be enhanced by altering the stiffener details. One method isto increase the distance from the k-line of the rolled link sectionto the termination of the stiffener to link web fillet weld. Basedon the test results, it is recommended that stiffener welds beterminated a distance of at least five times the web thicknessfrom the k-line of the link section. Another method to delay webfracture is to restrain both sides of the link web using stiffenerswithout placing welds directly to the web. The stiffeners are

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welded only to the flanges and not to the web. This technique,while promising, requires further investigation.

Test data from this program indicate that the flangeslenderness limit of shear yielding links (e ≤ 1.6Mp/Vp) canbe relaxed to the compact limit of 0.38(E/Fy)

1/2. For longerlinks (e > 1.6Mp/Vp), it is recommended that the flangeslenderness limit be maintained at the seismically compactlimit of 0.30(E/Fy)

1/2, pending further study of the effects ofshear-flexure interaction on local buckling. All link specimensconforming to these flange slenderness limits were capableof achieving the inelastic rotations required in the 2005 AISCSeismic Provisions.

The ASTM A992 rolled wide-flange links tested in thisprogram exhibited overstrength factors ranging from 1.05 to1.62, with an overall average of 1.35. Sections with highratios of flange to web areas did not exhibit unusually highoverstrength factors, at least within the range of flange toweb area ratios typical of rolled wide-flange shapes. Theoverstrength factor of 1.5, which forms the basis for thecapacity design procedure in the 2005 AISC Seismic Provisions,appears reasonable for links constructed of typical rolledshapes. However, based on experimental and analytical resultsreported by others, a higher overstrength factor may beappropriate for short links constructed of built-up shapes withheavy flanges [15].

As a closing remark, the large number of tests conducted inthis research program suggests that EBF links constructed ofASTM A992 steel and designed according to the 2005 AISCSeismic Provisions perform well, and meet the performancerequirements of the 2005 AISC Seismic Provisions.

Acknowledgements

The writers gratefully acknowledge primary fundingprovided for this project by the American Institute of SteelConstruction (AISC) and the National Science Foundation(Grant No. CMS-0000031). The first author expresses gratitudefor sponsorship provided by the Twenty-First Century Centerof Excellence Program awarded to the Tokyo Institute ofTechnology, Japan. The tests discussed herein were conductedas Masters’ thesis work by former students at the Universityof Texas at Austin, Gabriela Arce, Han-Choul Ryu, and PedroGalvez. The writers would like to particularly thank TomSchlafly of AISC for his support and assistance throughoutthis project. The writers thank Chia-Ming Uang, Paul Richards,James Malley, Subhash Goel, and Tom Sabol for theirassistance and advice on this study.

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