Experimental study of perforated yielding shear panel device for passive energy dissipation

Journal of Constructional Steel Research 91 (2013) 14–25

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Journal of Constructional Steel Research

Experimental study of perforated yielding shear panel device for passiveenergy dissipation

Ricky W.K. Chan a,⁎, Faris Albermani b, Sritawat Kitipornchai b

a School of Civil, Environmental and Chemical Engineering, RMIT University, Australiab School of Civil Engineering, The University of Queensland, Australia

⁎ Corresponding author.E-mail address: ricky.chan@rmit.edu.au (R.W.K. Chan)

a b s t r a c t

Article history:Received 11 January 2013Accepted 20 August 2013Available online 24 September 2013

Keywords:Shear panelPerforationEnergy dissipation

This paper describes an investigation into a metallic energy dissipater designed for earthquake risk mitigation ofcivil structures. It is called the Perforated Yielding Shear Panel Device (PYSPD). It comprises of a thin perforateddiaphragm plate welded inside a short length square hollow section. The device is to be connected in the lateralload resisting system of a structure with the diaphragm plate being in the plane of the building frame. It isa displacement-based device in which energy is dissipated through plastic shear deformation of its perforateddiaphragm plate. The PYSPD is a modified version of the previously tested Yielding Shear Panel Device (YSPD).Perforations on the diaphragm plate alleviate demand on supporting elements which reduces undesirable localdeformations near the connections. As a result more stable force-displacement hysteresis is obtained. Threepatterns of perforations are studied. Finite element models confirm that diagonal tension field develops undershearing action but stress patterns are affected by perforations. Two plate slenderness and three perforationpatterns combinations were tested experimentally. Under quasi-static condition, devices with certain plateslenderness produced stable and repeatable force-displacement hysteresis, and achieved large energydissipationcapability. Compared to un-perforated specimens, perforations reduce elastic stiffness and yield strength. Underdesign displacement it produced a stable hysteretic behavior and endured code requirements against low-cyclefatigue.

1. Introduction

Structural vibration control andminimization of damage is a subjectthat has received large attention in earthquake engineering. One prom-isingmethod is to dissipate a portion of input energy from ground shak-ing in a controlled manner. Dissipation of seismic energy by meansof yielding of metals has been widely studied and implementedto mitigate seismic risks in civil structures [1]. Energy imposed on astructure can be dissipated by means of designated passive energydissipaters (PEDs) such that structural responses may be suppressedand damage to structures may be minimized. Under a small to moder-ate seismic event, damaged PEDs can be repaired or replaced, whilethe parent structural system deforms largely within its elastic limits.Under a strong seismic event, damage to the main structure can beminimized and life-safety can be enhanced. Metallic PEDs, developedover the last three decades, remained one of the most popular choicesin seismic activity-prone areas. They are generally inexpensive, easyto maintain, and replacement after moderate seismic events is simple.Various forms of metallic PEDs have been proposed and implemented,such as the hourglass shape ADAS [2], triangular shape TADAS [3],

ights reserved.

brace-type BRB [4] and slit type [5]. Recently, energy dissipation bymeans of shear deformation of steel plate has been studied in largesteel panels [6] and in smaller units in the form of shearing devices[7,8]. These shear panels typically comprise of a thin metal plate sup-ported by a rigid boundary. Upon shear deformation, energy is absorbedby shear yielding of the plate. Plates with large slenderness tend tobuckle out-of-plane and produce pinched hysteresis. The addition oflongitudinal and transverse stiffeners reduces effective slenderness,have been studied experimentally [7] and numerically [9]. In particular,shear yielding of metal plates offer two distinct features compare toflexural and axial yielding: higher initial stiffness and lower yield stress.Typically PED connects with a brace in-series. Devices with high stiff-ness are generally desired to control serviceability deflection of themain structure.Multiple plates are usually required inflexural dampers,such as ADAS, to build up the required stiffness whereas devices whichdeform in shear usually possess sufficient stiffness. The influence of de-vice stiffness and other parameters are studied previously [10,11].

This paper describes an investigation into using shear yieldingof square perforated plate to dissipate energy. By introducing perfo-ration in the plate it reduces the in-plane stiffness of the plate, andsubsequently reduces the deformation demand of the supportingelements. Concerns over stress concentration and the low-cyclefatigue are addressed. Background of the device development willfirst be described, followed by findings from finite element modeling.

Fig. 1. Yielding Shear Panel Device [13]. (a) Elevation (b) Top view (c) Deformed shape.

15R.W.K. Chan et al. / Journal of Constructional Steel Research 91 (2013) 14–25

Experimental investigation focusing on force-displacement hysteresisand energy dissipation will be presented.

2. Literature review

2.1. The Yielding Shear Panel Device

The study of shear buckling of thin plates has been a classical topicin structural mechanics. The attempt to utilize plastic shearing of thinplates to dissipate energy was pioneered by Nakashima et al. [7,8].Their design, called Low-yield Steel Shear Panel, was made of a specialgrade of steel which yields at approximately 120 MPa. Its low yieldstrength makes small slenderness possible and avoids shear buckling.The panel produced very stable hysteresis. However, this special steelgrade is not widely available. The design described in this paper isdeveloped fromapassive seismic damper—Yielding Shear Panel Device(YSPD, see Fig. 1)whichwasfirst investigated byWilliams et al. [12] andChan et al. [13] at the University of Queensland. It comprises of a squaresteel plate welded inside a short length structural hollow section. It is adisplacement-based metallic device which dissipates input energy byshearing action. The device is installed on top of an inverted-V brace,forming a dissipative brace system (Fig. 2). The hollow section providesa continuous support to the diaphragm plate and at the same timeprovides an interface to connect to the main structure. Compare toother existing metallic designs, the YSPD provides significantly higherelastic stiffness which is desirable for stringent drift control. Influence

Fig. 2. YSPD installed on a chevron brace.

of diaphragmplate slenderness ratio, SHS thickness, and support flexibil-ity were studied [12–14] and a retrofit design method for implementingthe YSPD has been recently proposed [15].

Plate slenderness ratio is defined as,

β ¼ dt

� � ffiffiffiffiffif yE

s: ð1Þ

Assuming the diaphragm plate is simply supported by four bound-aries, the theoretical elastic in-plane lateral stiffness of the device kdis given by [13],

kd ¼ Gt ð2Þ

where G is shear modulus and t is the thickness of the diaphragm plate.With von Mises yield criterion and a stocky diaphragm plate the yieldstrength can be taken as the shear yield strength,

Fy ¼f yffiffiffi3

p dt ð3Þ

where d is the width of the steel plate and fy is its tensile yield stress.Consequently, the yield displacement of the device is,

uy ¼Fykd

¼ f ydffiffiffi3

pG: ð4Þ

For a device with a slender diaphragm plate, elastic shear bucklingoccurs prior to yielding (Fig. 3(a)). Upon the critical shear stress τcr,buckling is triggered and a tensile field is developed.

τcr ¼ ksπ2E

12 1−ν2� � td

� �2ð5Þ

Fig. 3. (a) Onset of buckling, (b) post-buckling tension field.

Fig. 4. Perforated YSPD.

16 R.W.K. Chan et al. / Journal of Constructional Steel Research 91 (2013) 14–25

where t, d, E and v are the plate thickness, the width, the Young'sModulus and Poisson's ratio respectively. Once critical shear stress hasreached, a tension field inclines at an angle θ from the horizontalthroughout the plate and is evolved with σty which represents the ten-sion field stress at which yielding occurs. The state of stress in the post-

Fig. 5. Finite element model of (a) Type 1; (b) Type 2; (c) Type 3; (d) mode s

buckled range is shown in Fig. 3(b). The components of critical stressand those of the tension field are super-positioned, and the resultantstresses are [16],

σxx ¼ σ ty sin2θ ð6Þ

hape of Type 1; (e) mode shape of Type 2 and (f) mode shape of Type3.

Table 1FE study of perforated plate.

FE model ID d × d × t(mm)

Perforation type dp(mm)

Ah/Ag kd(kN/mm)

Fy, FEM/Fy

FE-0–0 92 × 92 × 3β = 34.7

0 0 0 141.8 0.72FE-1–3 1 3.0 0.16 134.1 0.65FE-1–5.5 5.5 0.30 115.8 0.58FE-1–7 7.0 0.38 104.5 0.52FE-1–11.5 11.5 0.62 69.3 0.36FE-2–3 2 3.0 0.30 123.4 0.61FE-2–5.5 5.5 0.55 87.2 0.44FE-2–7 7.0 0.70 61.2 0.34FE-3–3 3 3.0 0.23 130.0 0.61FE-3–5.5 5.5 0.42 104.5 0.53FE-3–7 7.0 0.54 87.2 0.46

σyy ¼ σ ty cos2θ ð7Þ

τxy ¼ τyx ¼ τcr þσ ty sin 2θ

2: ð8Þ

The von Mises yield criterion states that

σ xx−σyy

� �2 þ σ2yy þ σ2

xx þ 6τ2xy−2 f 2y ¼ 0: ð9Þ

By substituting Eqs. (6), (7), and (8) into (9), σty can be solved:

3τ2cr þ 3τcrσ ty sin 2θþ σ2ty− f 2y ¼ 0 ð10Þ

The shear strength of the steel plate is then written as

Fu ¼ τxydt ¼ τcr þ12σ ty sin 2θ

� �dt: ð11Þ

YSPD with slender diaphragm plates are prone to out-of-planeshear buckling resulting in a pinched hysteresis response. A devicewith stocky diaphragm plate eliminates buckling but the very high in-plane stiffness of the plate imposes large demand on the supportingSHS. Undesirable damage occurs in SHS near the bolt holes and signifi-cant pinching of the force-displacement hysteresis was observed thathindered energy dissipation. Attempt to increase the SHS stiffness bythickening the connected flange resulted in an increase in load eccen-tricity without significant improvement in hysteretic response stability[13].

2.2. Shear strength of perforated plates

Study on buckling strength of perforated plates were undertakenby many researchers [17,18], driven particularly by the need to reduceweight for ships and aircrafts, and to provide access for services or in-spections. Perforations on civil structures such as in the web of plate-girders are also widely studied [19,20]. Semi-empirical equations cali-brated from experiments and numerical models have been formulated

Table 2Test specimens in experiments.

Specimen ID Perforation type dp(mm)

100-4C-P1 1 5.5 100 × 100 × 4(fy = 414 N/mm2)tSHS = 3.76 mm

100-4C-P2 2 5.5100-4C-P3 3 7.5100-3C-P1 1 5.5100-3C-P2 2 5.5100-3C-P3 3 7.5100-3C-P2-F1 2 5.5100-3C-P2-F2 2 5.5

to obtain buckling strength. On the other hand, the excellent strengthand ductility of steel plate shear walls (SPSWs) have attracted muchattention for its suitability as an earthquake-resistance form of construc-tion. More recently, cyclic responses of perforated SPSWs have beeninvestigated. The main reason of introducing perforation in SPSWs isto allow passage of services, and to alleviate the force exerted on theframe members when the minimum available plate thickness is largerthan the required thickness. Vian et al. [21] tested SPSWs with regularlyspaced holes and reported good strength and ductility. Purba et al.[22] studied numerically and proposed design equations for perforatedSPSWs. Valizadeh et al. [23] performed cyclic experiments on SPSWswith a single circular perforation in the center and reported that stablehysteresis can be obtained up to 6% drift.

3. The perforated YSPD

As discussed in the previous section experimental investigation onYSPD indicated that undesirable deformation near bolted flange con-nection of the SHS has caused pinched and unstable hysteresis for sam-pleswith small plate slenderness. This is due to the fact that the in-planestiffness of the steel diaphragm plate is many times larger than thatof the flexural stiffness of the surrounding SHS. Deformation demandis attracted to the SHS near its connection, rather than shearing in thediaphragm plate. To reduce the in-plane stiffness of the diaphragmplate, patterned perforations are introduced. Three patterns are investi-gated in this paper as shown in Fig. 4. Type 1 consists of 24 holes arrangedin a staggered fashion with six holes along the leading diagonal of theplate. Perforation is not introduced at the center of the diaphragm platefor attachment of a rosette strain gage in the experiments. Type 2 consistsof 48 holes arranged in a rectangular pattern, leaving the center of theplate un-perforated for the same reason. Type 3 consists of 36 holes,grouped into four triangular patterns.

To study their behaviors, a finite element analysis is carried out asdescribed in the next section. Parameters of interests are the reductionin yield strength and in-plane stiffness, stress concentration and theeffect of initial imperfection.

3.1. Finite element study

To build an understanding of a perforated plate subjected to shear,finite element models are developed in ABAQUS. Fig. 5(a) to (c) showthe FE models. The plate dimensions are d × d and thickness t withboundary conditions indicated in the figure. Four-node shell elementswith reduced integration (S4R) are used throughout. Ten FE modelswith perforation diameter dp ranged from 0.03d to 0.12dwere analyzedand their details are listed in Table 1. The following nomenclature isused for the analysis models FE – perforation type – perforation diameter.Convergence study onmesh density is carried out to ensuremesh is suf-ficiently fine. Material properties are assumed to be elastic-perfectly-plastic with yield stress equals 320 N/mm2 with Mises plasticity. Priorto loading, the models are subjected to an initial imperfection withmagnitude equal to w0 = cβ2t in the first plate buckling mode, where

fy.dia(N/mm2)

β Displacement regime

3.78 351.2 28.8 A

2.83 321.3 36.9

Fig. 6. (a) Effect of imperfection; (b) normalized shear strength and (c) effect of perforation ratio.

Fig. 7. Mises stress distribution of (a) FE-1-5.5; (b) FE-2-5.5 and (c) FE-3-5.5 at 0.25%average strain.

c is a scalar coefficient. The dimensions of the FE models are the sameas the physical test specimens given in Table 2.

Fig. 5(d) to (f) show thefirst bucklingmodewhich is similar for Type1 and 2 perforations and consisting of a single out-of-plane bulge.For Type 3 perforation the buckling mode consists of two oppositeout-of-plane bulges.

A sensitivity analysis was first carried out to study the effect of initialimperfection. Model FE-1–5.5 (Type 1 perforation with dp = 5.5 mm)is selected as the base model. Coefficient c ranged from 0.1 to 1.0 wasanalyzed. Normalized shear force F/Fy (where Fy to Eq. (3)) and strainrelationship is plotted in Fig. 6(a). It could be observed that magnitudeof imperfection has a small effect on yield strength. A larger imper-fection magnitude appears to slightly decrease the yield and post-yield strengths. Elastic stiffness, however, appears not being affected.In general the magnitude of imperfection has little influence on theoverall behavior and stress distribution.

A uniform displacement equal to 0.05d was monotonically appliedto edge 2 in the positive x-direction. Normalized shear and averagestrain relationship is plotted in Fig. 6(b). The response of an intactplate (FE-0–0) is also shown for comparison. It can be observed thatall models exhibit a nonlinear response with a smooth transition

between elastic and inelastic regime. They begin to deviate from the ini-tial elastic response between 0.2–0.3% strain. As expected, perforationsreduce elastic stiffness as well as yield strength. Type 2 perforationsshow a more significant decrease in shear strength compare to thoseof Type 1 and 3, due to its higher perforation ratio.

The yield strength Fy is taken as the 0.2% offset yield strength.Fig. 6(c) shows the comparison of normalized yield strengths of modelsplotted against perforation ratio Ah/Ag. The perforation ratio is definedas the total hole-area Ah divided by the gross cross-sectional area Ag,along the leading diagonal of the diaphragm plate as shown in thefigure. An approximately linear relationship can be drawn, indicatingthe strengths of perforated plates are dominated by tension fieldsinclined at 45°. The initial elastic stiffness kd andnormalized yield strengthare tabulated in Table 1.

The von Mises yield criterion stresses of the models are shown inFig. 7. Models with dp =5.5 mm deformed at 0.25% strain are shown.At this strain the model is approaching yield (see Fig. 6(b)) but part ofthe plate is still elastic. Regions approached yield stresses are shownin red color. In the Type 1 model (Fig. 7(a)), stress is high along thetension field diagonally on the plate. Perforations clearly interrupt thestresses. In the compression diagonal stresses are comparatively low.Four corners of the plate are heavily stressed. In the Type 2 model(Fig. 7(b)), stress pattern is very similar to Type 1's except there aremore perforations interrupting the stresses. It is interesting to observethat in the tension field diagonal high stresses are concentrated in nar-row bands connecting holes at 90°. On the other hand, the Type 3modelshows a fairly different stress pattern. High stresses are formed as an X-shape over the un-perforated diagonal bands.

4. Experimental study

4.1. Specimens, test setup and load histories

Fabrication of specimens was performed by a steelwork specialistto industry steelwork practice. 100 × 100 × 4 (D × D × tSHS) squarehollow sections were used with 3 mm and 4 mm (nominal thickness)diaphragm plates. Perforations were drilled manually with a pedestaldrill after the diaphragmplateswerewelded. As oppose to the FEmodels,the center of the plate is not perforated such that rosette gages could beattached. All perforated YSPD samples were fabricated from the samebatch of YSPD samples studied previously [13]. Results of 8 specimenswith 3 different perforation patterns are reported herein. Table 2 showsmeasured dimensions and yield strengths of the test specimens.

Experiments were carried out in the Heavy Structures TestingLaboratory at the City University of Hong Kong. The test setup isshown in Fig. 8. The test rig was designed and fabricated to rest on a40-ton-capacity reaction frame. Strength capacity of the reactionframe, stroke displacement of the actuator, and flexibility of the speci-men dimensions were taken into consideration. The test specimenswere installed between a ground beam and an L-beam and securely fas-tened by four M16 bolts snug tightly on each side. Forced displacementwas applied by an MTS 100 kN capacity computer-controlled actuatorquasi-statically to the specimen via the L-beam. A pantograph systemwith eight pin-ended beams was welded to the right-hand side of theL-beam and fastened to the left column of the reaction frame. Thepantograph allowed vertical movement of the actuator only, and anyin-plane rotation was restrained. Two vertical guides prevented out-of-plane movement of the L-beam. The same setup has been used satis-factorily in experimental investigation of the Steel Slit Damper [5] andYSPD [13]. The centerline of the actuator implied eccentricity in thespecimen and measured 131 mm to the specimen centerline. Similareccentricity may be present in actual inverted-V brace application,although the magnitude would depend on dimensions of connectedelements. This eccentricitywill cause a small global bending in the spec-imen. Displacements were measured independently by three LVDTmarked as 1 to 3 in Fig. 8(a). A free-run of the test setup (i.e. without

ActuatorPantograph system

L-Beam

Ground beam

a) Test setup

b) Overview of test setup with specimen 100-3C-P3 installed

Fig. 8. (a) Test setup. (b) Overview of test setup with specimen 100-3C-P3 installed.

Fig. 9. Displacement regime A.

the specimen installed) was performed, and the results showed thatfriction and the effect of gravity were considered to be negligible. Thesetup was robust and repeatable, and no visible damage occurred afterall of the tests had been carried out.

The following nomenclature is used for the specimen ID: SHS size –diaphragm plate thickness C – perforation type, where the “C” standsfor cyclic test. Six specimens were tested to Displacement regime Ashown in Fig. 9: three repeated cycles at 0.5, 1.5, 3.0, 5.0, 10.0 and20.0 mm. At the end of the 20 mm cycle, force in the actuator wasreleased, leaving the specimen in permanent deformed shape. The lasttwo specimens in Table 2 are tested for their fatigue life under Displace-ment regime B and C. They will be discussed in a later section.

4.2. Tests with displacement regime A

4.2.1. 4 mm plated specimensForce-displacement hysteresis for specimens subjected to Displace-

ment regime A is shown in Fig. 10. The load-displacement curves were

γ (%)

-8 -6 -4 -2 0 2 4 6 8

γ (%)

-8 -6 -4 -2 0 2 4 6 8

γ (%)-8 -6 -4 -2 0 2 4 6 8

-20 -15 -10 -5 0 5 10 15 20

γ (%)-20 -15 -10 -5 0 5 10 15 20

a) 100-4C-P1 b) 100-4C-P2

-15 -10 -5 0 5 10 15 20-1.5

c) 100-4C-P3 d) 100-3C-P1

1e) 100-3C-P2 f) 100-3C-P3

g) 100-3C

Fig. 10. Force-displacement hysteresis for specimens under displacement regime A.

a) 100-4C-P1 b) 100-4C-P2 c) 100-4C-P3

d) 100-3C-P1 e) 100-3C-P2 f) 100-3C-P3

Fig. 11. Specimens after the tests (Displacement regime A).

a) 100-3C-P2-F1 b) 100-3C-P2-F2

Fig. 12. Specimens with 3-mm-thick perforated plates after the extended cyclic tests.

normalized by Eq. (3). Positive force represents downward movementof the actuator. Results of the 4-mm plate perforated specimens(Fig. 10(a)–(c)) generally show unstable behavior. They are character-ized by pinched hysteresis loops near zero displacements. Strengthof the specimen fell significantly below the normalized value of unity.Repeated cycling at the same amplitude shows that force-displacementpaths are not identical, indicating that cumulative plastic deformationhad a detrimental effect on subsequent load cycle. Photographs of thesespecimens after tests are shown in Fig. 11(a)–(c).

No buckling was observed in the 4-mm perforated specimensand nor was there any visible damage on the diaphragm plate. Weldswere also undamaged. It appears that the perforation had little benefi-cial effect on the stability of hysteresis. Visual examination of thesespecimens revealed concentrated plastic deformation around the boltholes on the SHS flanges. This explains the poor hysteresis stability.This also suggests that the perforations in these three specimens wereinsufficient to reduce the in-plane stiffness of the diaphragm plate toalleviate the strength demand on the SHS. A similar problem was ob-served in un-perforated YSPDwith4 mmdiaphragmplates [13]. It shouldbe noted that the tests on specimens 100-4C-P1 and 100-4C-P2 wereterminated at the 10-mm cycles due to their poor performances.

-4 -3 -2 -1 0 1 2 3 4

a) 100-3C-P2-F1

-10 -8 -6 -4 -2 0 2 4 6 8 10

b) 100-3C-P2-F2

γ (%)

Fig. 13. Load-displacement curves under displacement regimes B and C.

Fig. 14. Principle strain angle.

4.2.2. 3 mm plated specimensForce-displacement hysteresis for 3 mmplate specimens are shown

in Fig. 10(d)–(f). They showed much more stable hysteresis loops.Specimen 100-3C-P1 still suffered from noticeable pinching, which indi-cates that the strength demand on the SHS is still overwhelming. The re-sult from an un-perforation 100-3C is shown in Fig. 10(g) for comparison[13]. Compared with the result of 100-3C, of which a distinct yieldstrengthwas hardly identifiable due to the seriously pinched hysteresis,the perforations of 100-3C-P2 and 100-3C-P3 clearly corrected thepinching problem and showed much more stable hysteresis. However,at the 20 mm amplitude fracturing and tearing of the diaphragm platebegan, which caused the force-displacement path to deviate.

Fig. 11(d)–(f) show these specimens after test. As shown in thephotographs they all buckled during the test. The welding along thediaphragm plates remained undamaged. Specimen 100-3C-P1 did notshow any sign of fracture. On specimens 100-3C-P2 and 100-3C-P3,fracture was observed with the tear propagated through the perfora-tions nearest to the connected flanges.

Table 3Summary of selected test results.

Specimen kd(kN/mm)

Fy, exp(kN)

(kN)Fmin

100-4C-P3 23.2 13.8 56.6 −48.4100-3C-P1 25.1 11.0 53.4 −53.3100-3C-P2 18.1 12.7 42.5 −41.7100-3C-P3 19.7 15.5 39.5 −31.9100-3C-P2-F1 18.5 17.6 30.8 −21.7100-3C-P2-F2 21.2 14.6 35.5 −34.5

4.3. Tests with displacement regimes B and C

FE study described in Section 3 showed perforations on steel plateintroduce stress concentration, which would reduce the low-cycle fa-tigue life of the device. To further examine the performance of theperforated specimens under repeated cycles, two different displacementregimes B and C are applied to the specimens. Displacement regime Bcomprised of three repeated cycles at 0.5, 1.0, 3.0 mm amplitude, follow-ed by 20 cycles at 5 mm. Displacement regime C comprised of 3 repeatedcycles at 0.5, 1.0, 3.0 and 5.0 mm, followed by 20 cycles at 10 mm. Inthese tests the 3 mm plate device with Type 2 perforation was used asit dissipated the largest amount of energy under Displacement regime A.

The specimen 100-3C-P1-F1 endured the whole displacementregime B history without any sign of fracture. It did not buckle orshowed any sign of visible damage. Fig. 12(a) showed the specimen atthe end of the test. The normalized force-displacement curve is shownin Fig. 13(a). The hysteresis loops are stable, and there was very minorstrength degradation. It suggests that the specimen performed satis-factorily. The actual displacement at the largest amplitudewith the elas-tic deformation of the support considered was approximately 3.5 mm(γ = 3.5%). The ductility at this amplitude was approximately μ = 4.4.

Specimen 100-3C-P2-F2 was tested under Displacement regime Cwhere a more stringent history of 20 cycles at amplitude of 10 mmwas applied. In the first few cycles of 10 mm amplitude, no plate buck-ling was observed. Out-of-plane buckling gradually appeared, andit became obvious in the seventh cycle. Cracks appeared in the twelfthcycle near the side connected to the ground beam. The crack slowlypropagated through the holes vertically. Strength degradation be-came obvious in the thirteenth cycle. Fig. 12(b) shows this specimenafter the test. The normalized load-displacement curve is shown inFig. 13(b). The actual displacement at the largest amplitude withthe elastic deformation of the support considered was approximately7.5 mm (γ = 7.5%). The ductility at this amplitude was approximatelyμ = 7.9.

Fy, exp/Fy Ω10 Energy dissipated(kJ)

Buckled

0.20 3.58 5.05 No0.23 4.26 6.67 Yes0.26 3.07 6.85 Yes0.32 2.37 5.57 Yes0.36 – 2.76 No0.30 – 9.77 Yes

0 50 100 150 200 250 300 350 4000

Cumulative displacement (mm)

100-4C-P1100-4C-P2100-4C-P3100-3C-P1100-3C-P2100-3C-P3

Fig. 15. Cumulative energy (Displacement regime A).

5. Discussions

5.1. Stiffness and yield strength

Table 3 shows key experimental results. Eq. (2) predicts very highinitial stiffness values for un-perforated plates. This equation ignoresperforations and any flexibility in the plate boundary and supports.On the other hand, the FE models take on the consideration of theperforation but ignore flexibility of the boundary and supports. Theypredict stiffness values which range from 87.2kN/mm to 115.8kN/mm.Comparing to the values in Table 3, measured initial stiffness kd gener-ally fell much below the values predicted. This is mainly due to theflexibility of the boundary SHS and the bolt connections. Other possiblereasons include out-of-plane movement of the specimens and bolt slip-page [13,14]. Since stiffness of passive devices is related to the elasticstiffness of the complete structure, and subsequently affects the dynamicproperties. As a result, stiffness of the proposed device must be experi-mentally obtained such that more reliable values could be used in struc-tural design.

Measured yield (Fy,exp) and ultimate strengths (Fmax and Fmin) arealso tabulated in Table 3. An over-strength factor Ω10, defined as theforce sustained at a shear strain γ = 10%, divided by the experimentalyield strength is also shown. The over-strength factor shows thatsignificant strain hardening is measured. The measured normalizedyield (Fy,exp/Fy) of the 3 mm plated specimens were 0.23–0.36, whichfell below the predicted values of 0.44–0.58 by finite elementmodeling.This is attributed to the plastic deformation of the boundary elements.

5.2. Strain measurement

A rosette gage was attached to the center of each tested specimen tomeasure strain variation on the diaphragmplate. Fig. 14 shows themea-sured principle strain angle with respect to the horizontal of specimen100-3C-P2. It can be observed that early in the test the principle strainangle oscillated between ±45°, indicating close to pure shear behavior.Towards the end of the test the angle began to behave in a less stablemanner. This corresponds to the buckling, fracturing and tearing ofthe diaphragm plate at a large amplitude. It should be noted that inthe first few cycle the principle strain angle did not reach 45°. It wasdue to the limitation of the sampling frequency of instrumentation.

5.3. Energy dissipation

Numerical integration is used to obtain energy dissipationof specimens subjected to Displacement regime A. The results are

shown in Fig. 15. All specimens appeared to dissipate energy at asimilar rate when cumulative displacement was small. As the testsof the 4 mm plated specimens were terminated at an earlier stage,so as their energy curves. Among all specimens tested, specimen100-3C-P2 dissipated the largest amount of energy. At the end ofthe test, it dissipated 6.85 kJ of energy. Specimen 100-3C-P3 dissipatedthe least energy among the 3 mm plated specimens. This result indi-cates that the perforation Type 2 is the best pattern among the patternsinvestigated.

5.4. Low-cycle fatigue life

The ASCE7-10 [24] standard requires a prototype energy dissipatingdevice to endure five repeated cycles at the design earthquake devicedisplacement. From the test in Displacement regime C, the perforatedYSPD specimen 100-3C-P2-F2 passed the code requirement if the designdisplacement is taken to 7.5 mm. Further tests are required, however,to verify the device's performance in a serviceability limit state.

6. Conclusion

An experimental study on a metallic passive energy dissipative de-vice which utilizes plastic shear deformation of perforated diaphragmsteel plate is presented. The device is called Perforated Yielding ShearPanel Device (PYSPD). It is a modification of a previous design YieldingShear Panel Device (YSPD) studied by the authors. It consists of aperforated diaphragm plate welded inside a square hollow section.It dissipates energy by plastic shearing of the plate. Perforations of steelplate alleviate demand on supporting elementswhich reduce undesirablelocal deformations near connections under cyclic loading. Three patternsof perforations are studied usingfinite elementmodeling and experimen-tal tests.

Ten finite element models are developed with perforation sizeswhich ranged from 0.03d to 0.12d, where d is the width of a squarediaphragm plate. The models with imperfection defined by thefirst mode shape are subjected to a monotonic shear displacement.The effect of imperfection is investigated and found that the shearload-displacement relationship is not very sensitive to its magnitude.Diagonal tension field develops and stress patterns are interrupted byperforations and causes stress concentrations. Shear strength decreaseswith increased perforation sizes. The decrease in shear strength isapproximately linear with perforation ratio measured diagonally alongthe plate.

Eight specimens with two different diaphragm plate-to-SHS combi-nations and with three different perforation patterns were fabricatedand tested under cyclic displacements. Six specimens were tested toincreasing amplitudes with three repeated cycles at each amplitude.Two specimens were further tested to illustrate their low-cycle fatiguelife. Major findings are summarized as follows:

1. Perforations in diaphragm plates reduce elastic stiffness and yieldstrength.

2. Perforations in the 3-mm diaphragm plates reduced the demand tothe SHS elements, and amore stable hysteresiswas observed. Identicalperforations on the 4-mm specimen showed no significant improve-ment in hysteresis stability.

3. Perforations in the diaphragm plates attracted stress concentration,and cracks that passed through the holes were identified.

4. Two extended cyclic tests were carried out on a 3 mm plate withType 2 perforation. The specimen did not fail in fewer than 20 cyclesof small displacements (μ = 4.4), but it did fail after 14 cycles of largedisplacements (μ = 7.9). The tests showed the device producedstable hysteretic behavior and endured code requirements againstlow-cycle fatigue.

Acknowledgment

Experiments described in this paperwere supported by RGCGeneralResearch Fund (Project 9041352), Hong Kong. Their financial support isgratefully acknowledged.

References

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Experimental study of perforated yielding shear panel device for passive energy dissipation

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