Journal of Constructional Steel Research 103 (2014) 179–189

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Journal of Constructional Steel Research

Experimental study of ring-shaped steel plate shear walls

Natalia Egorova, Matthew R. Eatherton ⁎, Abhilasha MauryaVirginia Tech, Blacksburg, VA, USA 24060

⁎ Corresponding author at: 200 Patton Hall, Blacksburg231 4559.

E-mail addresses: natalya1@vt.edu (N. Egorova), meatabhilasha.maurya@vt.edu (A. Maurya).

http://dx.doi.org/10.1016/j.jcsr.2014.09.0020143-974X/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 2 February 2014Accepted 2 September 2014Available online xxxx

Keywords:Steel plate shear wallRing shapeHysteretic behaviorPlate bucklingSeismic designExperimentation

A new type of steel plate shear wall (SPSW) has been developed which resists out-of-plane buckling. The ring-shaped steel plate shear wall (RS-SPSW) includes a steel web plate that is cut with a pattern of holes leavingring-shaped portions of steel connected by diagonal links. The ring shape resists out-of-plane buckling throughthe mechanics of how a circular ring deforms into an ellipse. It is shown that the ring’s compression diagonalwill shorten a similar amount as the tension diagonal elongates, essentially eliminating the slack in the directionperpendicular to the tension field. Because of the unique features of the ring’s mode of distortion, the load-deformation response of the resulting RS-SPSW system can exhibit full hysteretic behavior and possess greatlyimproved stiffness relative to thin unstiffened SPSW. The concept has been validated through testing on sevenapproximately 1 m × 1 m RS-SPSW panels and compared to the experimental response of a solid plate panel.General conclusions about the influence of different geometric parameters on plate behavior aremade includinglimits on geometry that produce desirable hysteretic response.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Steel plate shear walls (SPSW) are an attractive option for earth-quake engineering design for a variety of reasons including reducedcost, less invasive construction, and small architectural wall thicknessrelative to concrete shear walls as well as increased speed of construc-tion and efficient use of slender wall elements (see [1] for a summary).In the past few decades, a significant number of computational andexperimental research programs have been conducted on SPSW andthey have been implemented in buildings located in the USA, Canada,Japan and elsewhere. Even though SPSWs have been used in practice,there are several challenges associated with the design, construction,and behavior of SPSW that limit their use.

The key components of a typical SPSW (see Fig. 1a) are a thin webplate, beams which are referred to as horizontal boundary elements,and columns also referred to as vertical boundary elements. The webplate resists horizontal story shear through tension field action ofthe web plate and dissipates seismic energy as the web plate yieldsalong the inclined tension field direction (e.g. [2]). Although SPSW candevelop significant post-buckling shear capacity, the web plate bucklesat small shear force which may even occur during large wind loads.Buckling of the SPSW leads to significant loss of stiffness and a pinchedhysteretic behavior (e.g. [3]). Tomitigate the negative effects associated

, VA, USA, 24060. Tel.: +1 540

her@vt.edu (M.R. Eatherton),

with SPSW web plate buckling, a surrounding moment frame is re-quired in the U.S. building codes [4].

The ring-shaped steel plate shear wall (RS-SPSW) (see Fig. 1b) in-cludes a unique pattern of cutouts leaving ring shapes that can mitigateplate buckling by the mechanics of how a circle deforms into an ellipse.The mechanics of the systemwere explored byMaurya et al. [5] includ-ing computational simulation of a set of RS-SPSW panels [6]. It wasfound that the RS-SPSW system has substantially improved stiffnessand energy dissipation characteristics as compared to conventionalSPSW.

The objective of this paper is to verify the RS-SPSW theoretical con-cepts through an experimental program. Furthermore, different configu-rations including plate thickness, number of rings, and ring geometrywere chosen to study the effect of design variables on RS-SPSWbehavior,identify potential bucklingmodes, provide data for validation/calibrationof computational models by others, compare measured shear capacitywith theoretical strength predications, and to explore which combina-tions of design variables produce desirable hysteretic response.

To serve these goals, eight specimens were designed, fabricated andsubjected to reversed cyclic shear deformations. This paper describesthe basic concepts related to the RS-SPSW system, the experimentalsetup and displacement protocol, as well as presenting the results andanalyzing the implications of the results for use of this system inpractice.

2. Background and RS-SPSW concept

A large number of small and large scale experiments have been per-formed on steel plate shear wall panels (see [1] for a summary). Of

Moment Connec�ons with Seismic Detailing and Field Welding

Thin Web Plate (Typically Between 1.7 mm to 7 mm) Buckles When Subjected to Small Shear

Fish Plates

Boundary Elements Designed to Resist Large Inward Pull of Web Plate Fully Yielding in Tension Field

Simple Shear Connec�ons Between Horizontal and Ver�cal Boundary Elements

Web Plate with Ring Shaped Cutouts Resists Out-of-Plane Buckling

Fish Plates

Diagonal Links Between Rings

(a) Conven�onal Steel Plate Shear Wall (SPSW) (b) Ring-Shaped Steel Plate Shear Wall (RS-SPSW)

Tension Field

Horizontal Boundary ElementsstnemelE

yradnuoBlacitreV

RingLink

Fig. 1. Conventional and ring-shaped steel plate shear walls.

180 N. Egorova et al. / Journal of Constructional Steel Research 103 (2014) 179–189

particular interest are tests on specimens with thin web plates, such asthe web plates as thin as 1.6 mm suggested for upper floors in designexamples [1]. It has been shown in tests that thin 1.0 mm web platesact similar to 25mmx50mmtension only braceswith negligible lateralresistance provided by the web plate during load reversal [7]. Therehave been a number of attempts to improve the performance of SPSWincluding use of low yield strength steel [8], corrugated steel panels(e.g. [9]), and perforated steel plate shear walls [8]. The perforatedSPSW include a regular pattern of circular holes cut in the web plateand are allowed in current U.S. building codes [4]. However, perforatedSPSW also develop early buckling and have limited design flexibilitybecause the ductile mechanism still depends on tension field actionand yielding of the web plate along tension diagonals.

On the other hand, ring shapes have been used in seismic systems todissipate seismic energy without buckling. Tyler [10] describes tests ona yielding frame that dissipates energy through the yielding of roundbars that are oriented in a circular or rectangular shape and connectedto the four corners of a steel frame with diagonal braces. When thesteel frame was subjected to lateral loading, this device deformed insuch a way as to eliminate slack in the braces and thus exhibited signif-icant energy dissipation, even during load reversal. Ciampi et al. [11]proposed a similar class of hysteretic deviceswith rectangular geometrysuspended in a steel frame with diagonal tension braces to the fourcorners. A modified version of the device was incorporated in one ofthe buildings of the Laboratories of the National Research Council inFrascati, Italy [11].

The RS-SPSW system proposed herein also uses the ring shape toresist buckling. To demonstrate this concept, a single ring is consideredas shown in Fig. 2a. The perimeter of the ring, Pcircle, is given in Eq. (1)where r is the centerline radius of the ring.

Pcircle ¼ 2πr ð1Þ

δ2δ1

δ2

δ

(a) Ring (b) Solid Plate

Fig. 2.Mechanics of ring shap

The application of a diagonal tension force transforms the circle intoan ellipse as shown in Fig. 2a. The perimeter of the ellipse is approxi-mately given by Eq (2) as a function of the elongation of the circle inthe longitudinal tension direction, δ1, and its shortening in the trans-verse direction, δ2. A relationship between δ1 and δ2 can then be foundby setting theperimeter of the circle equal to the perimeter of the ellipseas given in Eq. (3) assuming the circle does not undergo any axialstretching.

Pellipse ≈ 2π

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir þ δ1ð Þ2 þ r−δ2ð Þ2

2

sð2Þ

δ2 ¼ r−12

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4r2−4δ21−8rδ1

qð3Þ

A plot of the relationship between the longitudinal elongation, δ1,and the transverse shortening, δ2 is shown in Fig. 2c for an arbitraryvalue of the ring radius. It is shown in Fig. 2c that the longitudinal elon-gation and transverse shortening are approximately equal for values ofdeformation that are small relative to the ring radius. Conversely, a solidsquare steel cube undergoing small uniaxial elongation will contract inthe transverse directions, δ2, by an amount equal to the Poisson's ratio(0.3 for steel)multiplied by the longitudinal elongation, δ1. In the inelas-tic range, this ratio increases toward 0.5 for constant volume deforma-tion. If shear buckling of a thin unstiffened SPSW is conceptuallyviewed as occurring when there is excess material along the compres-sion diagonal, then the shaded region of Fig. 2c represents configura-tions prone to buckling. Unlike the solid plate, the ring shape removesthe slack in the compression diagonal direction and therefore reducesout-of-plane buckling.

Afinite element (FE) computational studywaspreviously conductedto study the RS-SPSW concept [6]. Shell elementmodelswere usedwith

1

Ring

SolidPlate

Excess material in transverse direc�on :

Prone to buckling

No slack in the

transverse direc�on

δ1

δ2

(c) Rela�onship Between δ1and δ2

e resistance to buckling.

MTS Model 243.60 Hydraulic Actuator

2 - L8x4x7/16

864 mm

1168

mm

2 - L8x4x7/16

W12

x26

W12

x26

2 – L6x3-1/2 x ½Both Sides

Shear Panel Specimen

762

mm

762 mm

Fully Pretensioned 19 mm A325 Bolts Typical

Fig. 4. Side view of the experimental setup.

181N. Egorova et al. / Journal of Constructional Steel Research 103 (2014) 179–189

geometrically nonlinear analysis to capture buckling. It was foundthat RS-SPSW were capable of reducing and in some cases preventingbuckling. The panels demonstrated significant improvement in energydissipation and stiffness compared to solid panel SPSWs and the addi-tional geometric parameters suggested promise in allowing responseparameters to be individually tuned for project specific conditions.Two potential buckling modes were identified including global shearbuckling similar to tension field buckling of a solid plate, and lateraltorsional buckling of individual rings.

Analytical expressions for RS-SPSW shear strength were derivedusing plastic mechanism analysis [12]. Interaction between axial forcesand flexure were neglected because the effects were generally foundto be small [6]. The first mechanism considered (shown in Fig. 3b),assumes four plastic hinges will form at the intersection of the ring cen-terline and the centerline of the links connecting the rings. However,since the links have a discrete width, the plastic hinges are forced tooccur at the edges of the link as shown in Mechanism 2 (Fig. 3c). Simi-larly, Mechanism 3 (Fig. 3d) assumes the plastic hinges form at theedges of the link, but the ring undergoes a shear deformation ratherthan elongation along the diagonal.

The shear loads (horizontal component of the diagonal force) associ-atedwith eachmechanismwere derived inMaurya [6] and are given byEq. (5) for Mechanism 1 and Eq. (6) for Mechanism 2 and 3 whichresulted in the same shear capacity. Both equations were based on thegeometry of the ring shown in Fig. 5a including the centerline radius,R, the ring width, wc, the link width, wL, and the plate thickness, tw.The plastic moment capacity, Mp, is given by Eq. (4) as a function ofthe plate yield strength, Fy. The shear capacity of a solid unstiffenedsteel plate shear wall, Qsolid, as derived in multiple references (e.g. [1]),is provided in Eq. (7), and is a function of the web plate clear width,Lcf, and the tension field angle, α.

Mp ¼ w2c tw4

Fy ð4Þ

Q1 ¼ 2ffiffiffi2

pMp

Rð5Þ

Q2 ¼ Q3 ¼ 2ffiffiffi2

pMp

R−wL

2

ð6Þ

QSolid ¼ 0:5FytwLcf sin 2αð Þ ð7Þ

The application of the RS-SPSW to six-story prototype structure wasinvestigated [13] including schematic design, fabrication issues, cost

ab

c

de

f gh

i

jk

l b

eh

k

R

Plas�c Strength, Mp

(a) Ring Geometry (b) Mechanism 1

Loca�on of Plas�c HingeswL

Q1diag

Q

wc

Ro

Thickness, tw

Fig. 3. Plastic mechanism analysis to determi

comparison, and performance evaluation compared to conventionalSPSW. The economic analysis showed comparable cost between a RS-SPSW and conventional SPSW because the RS-SPSW does not requiremoment connections at the beam-to-columnconnections. Furthermore,machine shopswith large waterjet cutting tables were found capable offabricating the RS-SPSWwebplates suggesting that the RS-SPSW can befabricated and erected in practice.

3. Design of experimental study

A series of experiments were conducted at the Thomas M. MurrayStructural Engineering Laboratory at Virginia Tech to validate the RS-SPSW concept, investigate the cyclic hysteretic behavior of these panels,evaluate the effectiveness of a derived strength equation, and study thepotential buckling modes associated with these plate configurations.The tests were performed on plates that were approximately onemeter square which was large enough to test rings that might be usedin full-scale structures.

3.1. Test setup and loading protocol

The test setup shown in Fig. 4 was designed to apply shear deforma-tions to the steel plate specimens. The free end shown on the left ofFig. 4 was displaced up and down using anMTSModel 243.60 hydraulicactuator with force capacity of 650 kN and 1015 kN in tension and

1

(c) Mechanism 2

a

c

df

g

i

j

l

Q2diag

Q2

c

d i

j

(d) Mechanism 3

Q3

Q3

ne shear yield capacity of the RS-SPSW.

Table 1Displacement protocol.

Level Target sheardisplacement, δ

Target sheardisplacement,δ (mm)

Target sheardistortion angle,δ/a, %

Numberof cycles

1 0.5 δy 2.2 0.25 32 0.75 δy 3.2 0.37 33 1.0 δy 4.3 0.5 34 2 δy 8.6 1.0 35 3 δy 13.0 1.5 36 4 δy 17.3 2.0 27 5 δy 21.6 2.5 28 6 δy 25.9 3.0 29 8 δy 34.5 4.0 210 10 δy 43.2 5.0 211 12 δy 51.8 6.0 212 16 δy 69.1 8.0 213 20 δy 86.4 10 2

182 N. Egorova et al. / Journal of Constructional Steel Research 103 (2014) 179–189

compression respectively. The fixed end, shown on the right of Fig. 4,was anchored to the strong floor. The web plate was sandwichedbetween angles in a slip critical connection along all four edges. Thedouble-angle boundary elements at the top and bottom were attachedto the vertical elements using 50 mm diameter steel pins and as suchheld a constant distance between the pins creating a slight arc motionof the free side. The steel plate specimens were bolted to the testframe to allow testing of multiple specimens with the same testing rigalthough boundary connections in practice could be welded. Out-of-plane lateral bracing was provided for the actuator and at the middleof the free end vertical element. The fixed side of the SPSW panel wasrestrained from out-of-plane motion by minor axis flexural rigidity ofthe reaction frame and its connection to the strong floor.

The ATC-24 loading protocol [14] was adopted assuming a shear dis-tortion angle at yield, δy/a= 0.5%, to allow a consistent loading protocolfor all specimens where, a, is the horizontal distance between pins, a =864 mm. The target displacements, number of cycles, and shear distor-tion for each displacement level is given in Table 1. The actuator wasdisplacement-controlled to apply the target displacements, but afterSpecimen 1, the applied actuator displacements were amplified by 1.3relative to those listed in Table 1 to better obtain the target shear

Actuator Load Cell and LVDT

SP 1

SP 4

SP 2 SP 3

SP = String Poten�ometer

Photogrammetry Targets on Back

Side

(a) Instrumentation Plan

Fig. 5. Instrumentation plan and photograph of test setup. (

deformation of the specimen in the presence of elastic reaction framedeformations. The displacement rate was held constant throughoutthe loading at 25 mm/min.

3.2. Instrumentation

The instrumentation plan is shown in Fig. 5a including the actuatorLVDT with 508 mm range and load cell with 105 kN capacity. FourCelesco PT101 string potentiometers with 254 mm range were used tomeasure the in-plane displacements of the test specimen and setup.String potentiometer 1 shown in Fig. 5a measured the vertical displace-ment of the frame free end which differed slightly compared to theactuator LVDT due to elastic deformations in the steel frame supportingthe actuator. The displacements measured using string potentiometers2, 3, and 4 were used to compute the shear distortion angle of theweb plate. The lengths of three lines were found as the string potenti-ometer displacements added to themeasured initial lengths. Geometriclaws were used to calculate the shear angle at each time step assumingthat the axial deformation of the vertical element was negligible. Thecomputed shear angles at the left and right of the specimen were thenaveraged to produce the values reported in the results section.

Photogrammetry was used to measure the out-of-plane displace-ment pattern of the web plates using a NIKON D7000 camera withNIKKON 20mm, f/2.8 fixed focal length lens and 16.2megapixel resolu-tion in association with the PhotoModeler software [15]. With the pro-cedures used in this study (see [16]), the error is estimated to be within0.05 mm based on previous testing [17]. The photogrammetry proce-dure was conducted before the test and at four times during each testto measure the initial imperfection profile, buckling mode shapes ofthe RS-SPSW, identify the onset of buckling, and quantify the magni-tudes of out-of-plane displacements. The photogrammetry targetswere typically placed around the inside and outside perimeter of therings and along the edges of the links connecting the rings.

3.3. Specimens design and fabrication

Eight specimens, described in Table 2 and shown in Fig. 6, were test-ed to study the influence of geometric design parameters on the cyclicbehavior. Some of the basic dimensions are defined graphically in

(b) Photograph of Test Setup

a) Instrumentation plan. (b) Photograph of test setup.

Table 2Test matrix.

Basic dimensions Nondimensional ratios

Test # Specimen Name tw (mm) R0 (mm) wc (mm) wL (mm) N atw

R0

tw

wc

tw

1 2-13-1 12.7 150 56 56.1 2 68 11.8 4.42 Solid Plate 1.9 - - - - 455 - -3 1-13-1 12.7 300 112 112 1 68 23.6 8.84 3-13-1 12.7 100 37.3 37.3 3 68 7.9 2.95 2-6-0.81 6.4 150 45.7 56.1 2 136 23.6 7.26 2-6-1 6.4 150 56.1 56.1 2 136 23.6 8.87 3-6-1 6.4 100 37.3 37.3 3 136 15.7 5.88 3-10-1 9.5 100 37.3 37.3 3 91 10.5 3.9

tw = Plate thickness, Ro = outside ring radius, wc = width of the ring.wL = Width of the link, and N = Number of rings per row.Specimen name is defined as: N − tw − wc/wL.

183N. Egorova et al. / Journal of Constructional Steel Research 103 (2014) 179–189

Fig. 6 and include the panel thickness, tw, outside ring radius, Ro, widthof the circular ring, wc, width of the link, wL, number of rings per row,N, and least pin-to-pin dimension of the plate, a=864mm. In the pre-vious computational study [6], three nondimensional slenderness ratioswere proposed to be related to buckling. Global shear buckling wasshown to be related to plate slenderness, a/tw. Lateral torsional bucklingof the rings was associated with two ring slenderness parameters, Ro/twand wc/tw. The computational study found that the corners where therings and links converged resulted in a substantial stress concentration[6]. Based on a set of models with various fillet radius, a fillet radiusequal to 20% of the outer ring radius, Ro, was found tomitigate the stressconcentration and was thus used for all specimens.

Specimens 3-13-1, 2-13-1, and 3-10-1 were designed with smallglobal slenderness, a/tw, and ring slenderness parameters, Ro/tw andwc/tw, to demonstrate the least amount of buckling andmost full hyster-etic response. Specimens such as 3-6-1 possess larger global slender-ness with relatively small ring slenderness which was expected to

Radius of All Fillets is 20% of Ro Typical

127 mm Radius

(a) Specimens 4, 7, 8 (b) Specimens 1, 5, 6

(c) Specimen 3 (d) Specimen 2

Rowc

wL

356 mm

711 mm Typical

711

mm

Typ

ical237 mm

356

mm

237

mm

Fig. 6. Test specimen geometry.

undergo global shear buckling. Conversely, specimens such as 1-13-1have large ring slenderness and small global slenderness and are thusdesigned to develop lateral torsional buckling of the ring. Specimenswere cut using a waterjet cutting machine with the highest quality cut-ting (see Fig. 7).

A solid plate specimen with thickness, tw =1.9 mmwas consideredrepresentative of thinner SPSW web plates used in practice. This solidplate specimen thickness was selected to have similar shear strengthas the RS-SPSW specimens. Solid plate specimens with the same thick-ness as the RS-SPSW specimens were not selected because their shearstrength would have been almost an order of magnitude greater andthus would not be reasonable in practical SPSW applications.

Three tension coupon tests were conducted in accordance withASTMA370-07a [18] on each plate thickness with the resulting averagematerial properties summarized in Table 3. All plates of a given thick-ness were obtained from the same heat.

4. Results and discussion

The results of the eight shear panel tests are presented in this sectionstarting with the solid plate specimen for context, the RS-SPSW thatdevelop plastic hinges in the rings prior to buckling, shear buckling ofthe RS-SPSW panels, and lateral torsional buckling. The section endswith a discussion of fracture potential, energy dissipation, and the accu-racy of the shear strength prediction equation.

4.1. Solid plate behavior

The cyclic shear load vs. shear distortion angle behavior of the solidplate is shown for the small cycles in Fig. 8a and for larger cycles inFig. 8b. It is noted that although the actuator displacement history was

Fig. 7. Close-up photograph of smooth cut surface obtained using water jet cutting(photogrammetry targets also shown).

Table 3Material properties based on tension coupon tests.

Plate thickness(mm)

Modulus of elasticity(GPa)

Yield strength(MPa)

Ultimate strength(MPa)

13 210 331 4001.9 200 296 3656.4 210 317 4839.5 203 296 434

184 N. Egorova et al. / Journal of Constructional Steel Research 103 (2014) 179–189

symmetrically applied, the shear distortion of the specimen was notfully symmetric because of uneven deformations in the reaction frame.

As expected, the thin solid panel exhibited a large stiffness ofapproximately 5300 kN/% during several small displacement cyclesprior to shear buckling. A distinct change in stiffness occurred at ap-proximately 100 kN (approximately 50% of the shear yield force), afterwhich a tension field was observed to develop. The unloading stiffnesswas found to be approximately 650 kN/% which may be representativeof the stiffness of the panel when the tension field is fully engaged. Thestiffness dropped even further during load reversal. As shown in Fig. 8b,the secant stiffness of the solid panel during load reversal becomesnegative as the previous tension diagonal is subjected to compressionand undergoes buckling instability. Although the specimen continuedto resist approximately 25% of the specimen shear yield force duringreloading, the secant stiffness was nearly zero until the tension fieldengaged in the opposing direction. The resulting hysteretic behaviorwas similar in character to tension-only bracing with highly pinchedhysteresis and negligible stiffness during load reversal. The energy dis-sipation during the 4% drift cycle was computed, Ed, and found to be44% of the energy that would be dissipated by an equivalent elasticperfectly plastic system with the same peak shear force, EEPP.

Even at 0.5% shear distortion angle, the shear buckling was welldefined as shown in Fig. 9a and visually observable. Five buckling halfwaves formed at an approximately 40° angle relative to horizontalwith a peak amplitude of 0.75 cm. A photograph of the buckled shapeat 5% shear distortion angle is shown in Fig. 9b at which point thephotogrammetry measurements found that the peak to peak bucklingamplitude had grown to approximately 6 cm.

For clarity, Fig. 8b shows data only up to 5% shear distortion angle,although the test was conducted to 8% shear distortion angle (see [16]for details). Tearing of the plate started at 6% drift at the bottom rightcorner and propagated during each subsequent cycle. Tearing alsodeveloped at a sharp fold on the interior of the plate as well as smalltearing at the other three corners. At large deformation angles, thebolts designed to be slip critical started to slip and bearing and tearout type failures occurred at the bolt holes. During the 8% drift cycle,the tear along the bottom of the plate propagated substantially contrib-uting to a significant loss in shear strength.

(a) Initial Buckling Response

Fig. 8. Hysteretic behavior of the solid plate specimen. (a) Initia

4.2. Plastic hinging RS-SPSW

As discussed in a previous section, the intent of the ring shapes is toremain relatively planar while the ring is inelastically stretched into anellipse. As the ring is stretched, the largest moments occur where thering intersects with the link and it is at these locations that a plastichinge was assumed to form in the derivation of the shear strengthequations. Fig. 10a shows the load-deformation response of specimen3-13-1 which remained relatively planar as the rings underwent plastichinging. The stable and full hysteretic behavior is similar in character tosystems in which buckling is restrained (e.g. buckling restrainedbraces). The stiffness of approximately 1300 kN/% remained fairlyconstant throughout the test. Photogrammetry data showed the plateremained relatively flat (5 mm out-of-plane displacement) throughthe 1.5% shear distortion angle cycles and by the 3% shear distortionangle cycle, the plate developed a concave deformed shape with a3 cmamplitude although nodefined tensionfield diagonals had formed.The test was stopped after the first cycle at 3% shear distortion angledue to a fracture in the reaction frame. The W12x26 vertical memberattached to the strong floor experienced a fracture through the flangeat the top pin connection, but was subsequently repaired and strength-ened for testing of the rest of the specimens.

Specimens 2-13-1 and 3-10-1 with load-deformation behaviorshown in Fig. 10b and c, developed similar full hysteretic behaviorat the beginning of the test. The energy dissipation during the4% drift cycle, Ed, was found to be 79% and 71% of the energy thatwould be dissipated by an equivalent elastic perfectly plastic systemwith the same peak shear force, EEPP, for specimens 2-13-1 and 3-10-1 respectively. Fig. 13d shows that the inelastic regions, identi-fied by areas on the specimen where whitewash had flaked off,were concentrated at the intersection of the ring and the link, thusconfirming the locations of plastic hinging assumed in the plasticmechanism model.

Specimen 2-13-1 retained full hysteretic behavior until shear buck-ling occurred during the 4% shear distortion cycles. Specimen 3-10-1started to experience strength degradation associated with shear buck-ling during cycles between -2.1% and 3.7%, or 3% average shear distor-tion angle. As shown in Fig. 10b and c, the strength degradation due toshear buckling occurred in a gradual manner without a sudden loss ofstrength or stiffness. Testing of specimen 2-13-1was arbitrarily stoppedafter two cycles at 6% shear distortion angle, but specimen 3-10-1 wassubjected to additional cycles up to 8% shear distortion during which afracture developed at an exterior joint between a link and ring (seeFig. 13d). The fracture did not lead to a steep loss of shear strength asthe majority of rings remained intact.

Specimens 3-13-1, 2-13-1, and 3-10-1 all produced cyclic load-deformation response and progression of limit states with beneficialattributes for the seismic resistance of structures. The RS-SPSW con-figurations prevented buckling until 3% to 4% shear distortion which

(b) Behavior up to 5% Distortion Angle

l buckling response. (b) Behavior up to 5% distortion angle.

(a) Buckled Shape at 0.5% Shear Distortion (b) Photograph at 5% Shear Distortion

Fig. 9. Deformed shape of the solid plate specimen. (a) Buckled shape at 0.5% shear distortion. (b) Photograph at 5% shear distortion.

185N. Egorova et al. / Journal of Constructional Steel Research 103 (2014) 179–189

are well above the 2% lateral drifts associated with the design basisearthquake [19]. The stiffness and energy dissipation are shown to bemuch larger than the solid plate SPSW. Furthermore, the shear bucklingthat occurs at large drifts effectively limits the peak shear forces inthe RS-SPSW thereby controlling panel overstrength and reducing thedemands on surrounding framing.

4.3. Global shear buckling of RS-SPSW panels

Global shear buckling is further studied by examining the behaviorof Specimen 3-6-1 which had identical geometry as Specimen 3-10-1and 3-13-1 except that it had a 6.4mmthickness. Fig. 11a shows the ini-tial behavior of Specimen 3-6-1 exhibited full hysteretic behavior up tocycles between −1.5% and 2.2% at which time the plate underwent

(a) Hysteretic Behavior of 3-13-1

(c) Hysteretic Behavior of 3-10-1

Fig. 10. Behavior of RS-SPSW capable of developing full plastic hinging of rings. (a) Hysteretic(d) Deformed shape of 3-10-1 at last peak.

shear buckling and the hysteretic behavior became pinched. Fig. 12ashows that the photogrammetry measurements conducted in the fol-lowing cycle at−2% drift captured the buckled shape with one primaryhalf wave, four smaller half waves, and a peak-to-peak amplitude of32 mm.

Unlike Specimens 2-13-1 and 3-10-1 that reached their peak shearforce at 3.1% and 2.1% shear distortion angle respectively, Specimen 3-6-1 reached its peak shear force at 1.3% and the shear strength contin-ued to gradually degrade after shear buckling. The test was continuedto cycles at 9% shear distortion angle as shown in Fig. 11b. As the buck-ling was cyclically and repeatedly reversed, the plate began to formmore sharply folded buckles as shown in Fig. 12b. The buckled shapehad similar number and orientation of the half waves at 6% sheardistortion as previously, but with peak-to-peak amplitude of 57 mm.

(b) Hysteretic Behavior of 2-13-1

(d) Deformed Shape of 3-10-1 at Last Peak

Fracture

behavior of 3-13-1. (b) Hysteretic behavior of 2-13-1. (c) Hysteretic behavior of 3-10-1.

(a) Beginning of the Test (b) Complete Test Data

Fig. 11. Behavior of specimen 3-6-1 demonstrating global shear buckling. (a) Beginning of the test. (b) Complete test data.

186 N. Egorova et al. / Journal of Constructional Steel Research 103 (2014) 179–189

Eventually, the sharp creases in the plate led to tears forming at twolocations at 8% shear distortion angle.

As the rings and links undergo inelastic axial elongations, themech-anism whereby a ring deforming into an ellipse removes slack in thecompression diagonal loses its effectiveness. Just as moment resistingframe connections subjected to large inelastic rotation cycles will even-tually develop local buckles regardless of how compact the beamsection, the RS-SPSW will develop shear buckling if subjected to largeenough cycles regardless of plate slenderness. However, plate slender-ness, defined as the plate dimension divided by the thickness, a/tw,appears to be strongly correlated with the shear distortion angle atbuckling (see Fig. 13). The results suggest that it may be possible tocontrol the shear distortion angle at the onset of buckling by properselection of the global plate slenderness parameter, a/tw. Although it isnecessary to further validate the relationship for a range of full-scaleplate configurations, plates with a plate slenderness, a/tw b100 success-fully limited the shear buckling to occur for drifts larger than the 2%limit associated with the design basis earthquake hazard level [19].

4.4. Lateral torsional buckling of rings

Another important limit state for RS-SPSWs is lateral torsional buck-ling. The hysteretic behavior of Specimen 1-13-1 is shown in Fig. 14awith shear angle defined on the horizontal axis as actuator displace-ment divided by the panel pin to pin width, a = 864 mm. Actuatordisplacement is used for this specimen because of malfunctions in thestring potentiometer system. Specimen 1-13-1 consisted of one largering with the largest values of ring slenderness considered in thisstudy (R0/t = 23.6 and wc/t = 8.8). Based on the load-deformation

(a) -2% Shear Distortion

Fig. 12. Global shear buckling evolution for specimen 3-6

response, it appears that buckling occurred before plastic hingingcould fully develop in the rings. This was further corroborated by thepeak force which was smaller than the computed shear capacity astabulated later in Table 4 and discussed in a subsequent section.

Lateral torsional buckling is characterized by a twisting of the ring asshown in Fig. 14b. Unlike shear buckling panels which can still resistadditional shear force through a tension field type of mechanism, thespecimens that undergo lateral torsional buckling suffer more substan-tial strength degradation. The energy dissipation ratio was found to be,Ed/EEPP =46% approximately equal to that of the solid plate. Because ofthe potential for large strength degradation and loss of energy dissipa-tion ability, the lateral torsional buckling limit state is less desirablethan shear buckling.

Two specimens were designed to explore the intersection betweenthe two bucklingmodes. Specimen 2-6-1 had identical ring slendernessparameters (R0/t=23.6 andwc/t= 8.8) as Specimen 1-13-1 but also alarge panel slenderness, a/tw=136whichwas shown capable of devel-oping shear buckling in specimen 3-6-1 in the previous section. Theshear force vs shear distortion behavior is shown in Fig. 15a to have apeak shear force at 1.0% shear distortion and subsequent strengthdegradation. The degradation in strength and energy dissipation is lesssevere for this panel than Specimen 1-13-1. The results suggest thatthe addition of shear buckling may be beneficial to a lateral torsionalbuckling specimen as the tension field provides amechanism for furthershear force resistance and energy dissipation.

Specimen 2-6-0.81 is identical to specimen 2-6-1 except that thering width is reduced from 56.1 mm to 45.7 mm. A comparison ofFig. 15a and b shows that the narrower ring reduces the effects of lateraltorsional buckling because the disparity between the ring’s major and

(b) -6% Shear Distortion

-1. (a) 2% Shear distortion. (b) 6% Shear distortion.

Fig. 13. Relationship between plate slenderness and the shear distortion angle at whichshear buckling occurs.

187N. Egorova et al. / Journal of Constructional Steel Research 103 (2014) 179–189

minor axis moments of inertia is smaller. As the ring cross section ratio,wc/tw reduces, the lateral torsional buckling, strength degradation, andloss of energy dissipation also reduces.

4.5. Discussion

Results for all specimens are summarized in Table 4. The shearstrength of one ring as calculated by Eq. (6) with measured yieldstrength, Fy, and the inner radius, Ri, substituted for the centerlineradius, R, wasmultiplied by the number of rings in a row to get the com-

(a) Hysteretic Behavior

, δactuator / a

Fig. 14. Behavior of panel undergoing lateral torsional buckling (Specimen

Table 4Summary of specimen behavior.

Test # Specimen Computed shear strength,Q2i (kN)

Measured shear strength,Vy (kN)

Peak fVu (kN

1 2-13-1 286 350 3782 Solid plate Qsolid = 215 200 2343 1-13-1 286 N/A 2714 3-13-1 284 350 4055 2-6-0.81 78 90 1056 2-6-1 137 130 1557 3-6-1 136 130 1718 3-10-1 190 250 302

PH = plastic hinging of ring, GSB = global shear buckling, TFY = yielding along the tension fi

†Shear distortion measurement not available.‡Energy dissipation reported for the 3% shear distortion cycle.

puted shear strength, Q2i. The measured shear yield strength, Vy, wasdefined as the approximate load at which significant nonlinearitybegan occurring. As described previously, the energy dissipation ratiowas computed for the 4% drift cycle as the ratio of the measured dissi-pated hysteretic energy, Ed, to the hysteretic energy that would beabsorbed by an equivalent elastic perfectly plastic system with thesame peak shear strength, EEPP.

Specimens 2-13-1, 3-13-1, and 3-10-1 were determined to havedeveloped plastic hinging of the rings in a previous section. As such,Eq. (6) would be expected to capture the shear yield strength of theseplate specimens. The results of Eq. (6) are reported as calculated usingthe inner ring radius because calculated values using the centerlineradius were overly conservative. Table 4 shows that the larger comput-ed shear strengths using inner ring radius are still only 80% of themeasured shear strength. The capacity equation is based on a plasticmechanism of the ring undergoing idealized displacement, whereasthe actual displacement pattern is more complex andmay include plas-tic hinging of some of the links around the perimeter (see Fig. 10d).More research is warranted to investigate the applicability of theshear strength equation to full-scale RS-SPSW panels, but based on theresults tabulated in Table 4, the shear strength equation appears toproduce conservative values.

The progression of limit states for each specimen is also listed inTable 4. Many of the RS-SPSW specimens subjected to cycles of sheardistortion up to and exceeding 8% experienced ductile tears in therings. The locations of the tears consistently occurred in the cornerrings at the first interior joint between ring and link as shown inFig. 16b. This location is subject to sharp creases in the plate duringload reversals as shown in Fig. 12b. Fig. 16a shows a fracture in the bot-tom right ring of Specimen 2-6-1 in which a fracture initiated at the

(b) Buckled Shape at 7% Shear Angle

1-13-1). (a) Hysteretic behavior. (b) Buckled shape at 7% shear angle.

orce,)

Shear distortionat peak force (%)

Energy dissipation,Ed/EEPP (%)

Limit state progression

3.1 79 PH, GSB at 4%4.5 44 GSB at 0.1%, TFY, DF† 46 LTB without PH3.4 86 ‡ PH, GSB9.0 64 Limited PH, GSB + LTB at 2%, DF1.0 54 GSB + LTB at 1%, DF1.3 64 PH, GSB at 2%, DF2.1 71 PH, GSB at 3%, DF

eld diagonal, LTB = lateral torsional buckling, DF = ductile propagation of a fracture.

(a) Specimen 2-6-1 Wider Ring (b) Specimen 2-6-0.81 Narrower Ring

Fig. 15. Influence of ring width on buckling behavior. (a) Specimen 2-6-1 wider ring. (b) Specimen 2-6-0.81 narrower ring.

188 N. Egorova et al. / Journal of Constructional Steel Research 103 (2014) 179–189

outside of the ring and propagated toward the inside of the ring. Fig. 16bshows a similar fracture initiating at the top of Specimen 2-6-0.81.The initiation occurred at shear distortion angles of 8% or more andpropagation occurred over several cycles. In RS-SPSW panels such asthose shown in Fig. 16 with nine rings, there is substantial built-inredundancy. Even as the fractures initiated and propagated, the effecton the global shear force vs shear distortion behavior was limited.

(a) Specimen 2-6-1 at 10% (b) Typical Fra

Fracture Prone L

Fig. 16. Fracture of RS-SPSW specimens at the corners of the panels. a) Specime

(a) Plate Slenderness

Fig. 17. Influence of geometric parameters on energy dissip

The energy dissipation ratio listed in Table 4 provides a good mea-sure of how full the hysteretic shape was during the 4% shear distortioncycle, and also eludes to the severity of the buckling at that point in thetest. The variation in energy dissipation ability of three RS-SPSW speci-mens with varying plate slenderness ratios and small enough ring slen-derness to prevent lateral torsional buckling is shown in Fig. 17a. Asdiscussed in previous sections, the rings underwent plastic hinging

cture Locations

oca�ons

(c) Specimen 2-6-0.81 at 10%

n 2-6-1 at 10%. (b) Typical fracture locations. (c) Specimen 2-6-0.81 at 10%.

(b) Ring slenderness

ation ratio. (a) Plate slenderness. (b) Ring slenderness.

189N. Egorova et al. / Journal of Constructional Steel Research 103 (2014) 179–189

before undergoing shear buckling and the associated strength degrada-tion and pinching of the hysteretic behavior.

The effect of lateral torsional buckling on the hysteretic shapeand energy dissipation capacity is more dramatic as shown in Fig. 17b.These three specimens had identical plate slenderness, a/tw, so Fig. 17bisolates the effect of lateral torsional buckling. The energy dissipationratio drops from values representing relatively full hysteretic behaviorto values similar to the thin solid plate specimen as the ring slenderness,Ro/tw, is increased from 7.9 to 23.6. Because the degradation in strengthand energy dissipation is so severe for Specimen 1-13-1, it is desirableto limit the ring slenderness below these values.

5. Conclusions

Conventional steel plate shearwalls (SPSW) have small stiffness andenergy dissipation capacity as they act like tension-only bracing aftershear buckling occurs at small shear force.

A ring-shaped steel plate shear wall (RS-SPSW) is proposed thatlimits out of plane buckling by the mechanics of how the circular ringdeforms into an ellipse. An experimental study was conducted oneight approximately 1 m x 1 m shear panels to validate the RS-SPSWand investigate the effect of the geometric parameters on cyclic shearbehavior.

A solid plate specimen was tested to give baseline performance of athin web plate representative of plates used on upper floors of an SPSWbuilding. Shear buckling occurred at a load that was approximately halfthe shear capacity of the panel and a shear distortion angle of 0.1%. Aftershear buckling, the hysteretic behavior became highly pinched andthere was near zero stiffness during load reversal.

In contrast, results from several RS-SPSW specimenswere presenteddemonstrating that they were capable of developing plastic hinging ofthe rings and nearly full hysteretic behavior. Although shear bucklingof the RS-SPSW panels can occur after large inelastic shear distortionangles, the shear distortion angle when shear buckling occurs wasfound to be strongly correlated with plate slenderness defined as thepin to pin dimension divided by the thickness of the plate. It wasfound that specimens with plate slenderness less than 100 were ableto prevent shear buckling for shear distortion angles less than 2% andthe degradation in strength and energy dissipation capacity occurredgradually afterwards.

Specimens experiencing lateral torsional buckling suffered moresevere degradation in strength and energy dissipation. Lateral torsionalbucklingwas found to be related to the ring slenderness defined by twounitless parameters: 1) the outside ring radius divided by the platethickness, and 2) the ring width divided by the plate thickness. Morenarrow rings resisted lateral torsional buckling more than wide ringsbecause the disparity betweenmajor andminor axismoments of inertiawas smaller. Values of outer ring radius divided by plate thickness be-tween 8 and 16were shown to resist lateral torsional buckling whereasspecimens with values equal to 24 experienced severe lateral torsionalbuckling.

An equation for RS-SPSW shear strength was presented based onplastic mechanism analysis and was shown to conservatively result invalues 80% of themeasured shear yield strengths. Furthermodificationsof the strength equation based on a more realistic displacement field

and plastic hinging of some linksmay bewarranted to improve accuracy.Fracture of the RS-SPSW specimens occurred at large shear distortionangles of 8% or more. Fracture is thus considered unlikely for panelsexperiencing typical earthquake drifts. Detailed design procedures thatproduce desirable hysteretic response while preventing undesirablelimit states are being developed as part of future research.

Acknowledgements

This work is supported by the American Institute of Steel Construc-tion through the Milek Faculty Fellowship Program and Virginia Tech.Thanks toMichaelWood, Adam Phillips, Stuart Salmon, and Chris Galitzfor their contribution to this work.

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