research article seismic performance of rc beam...

Research ArticleSeismic Performance of RC Beam-ColumnConnections with Continuous Rectangular Spiral TransverseReinforcements for Low Ductility Classes

Mohammadamin Azimi1 Azlan Bin Adnan1 Abdul Rahman Bin Mohd Sam1

Mahmood Md Tahir2 Iman Faridmehr2 and Reza Hodjati2

1 Faculty of Civil Engineering Engineering Seismology and Earthquake Engineering Research (e-SEER)Department of Structure and Materials Universiti Teknologi Malaysia (UTM) 81300 Skudai Johor Bahru Malaysia

2 Faculty of Civil Engineering UTM Construction Research Centre (CRC) Universiti Teknologi Malaysia (UTM)81300 Skudai Johor Bahru Malaysia

Correspondence should be addressed to Mohammadamin Azimi mohammadaminazimiyahoocom

Received 22 May 2014 Accepted 20 July 2014 Published 17 September 2014

Academic Editor Keun Hyeok Yang

Copyright copy 2014 Mohammadamin Azimi et alThis is an open access article distributed under the Creative CommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

The seismic performance of RC columns could be significantly improved by continuous spiral reinforcement as a result ofits adequate ductility and energy dissipation capacity Due to post-earthquake brittle failure observations in beam-columnconnections the seismic behaviour of such connections could greatly be improved by simultaneous application of this methodin both beams and columns In this study a new proposed detail for beam to column connection introduced as ldquotwisted opposingrectangular spiralrdquo was experimentally and numerically investigated and its seismic performance was compared against normalrectangular spiral and conventional shear reinforcement systems In this study three full scale beam to column connections werefirst designed in conformance with Eurocode (EC2-04) for low ductility class connections and then tested by quasistatic cyclicloading recommended by ACI Building Code (ACI 318-02) Next the experimental results were validated by numerical methodsFinally the results revealed that the new proposed connection could improve the ultimate lateral resistance ductility and energydissipation capacity

1 Introduction

Incorporation of continuous spiral reinforcement in circularcross section components such as beams and columns ofRC structures could improve the strength ductility andenergy dissipation capacity of such structural members [1ndash3] The first application of spiral reinforcement as the shearreinforcement to increase the axial behaviour of reinforcedcolumns was first presented by Park in 1975 [1] Similarstudies have been performed by other scientists regardingthe use of continuous spiral shear reinforcement instead ofconventional stirrups hoops and so forth [3 4] In 2004 anew technique based on application of two opposing spirals(cross spirals) was reported by Mander et al [5] where theincrease in the pitch distance of spiral reinforcement did notresult in any reduction in strength or ductility in columnDue

to the wide application of rectangular shape cross sectionsin RC structures incorporation of continuous rectangularreinforcement in RC elements has recently become morepopular Application of rectangular spiral reinforcement inRC beams was first introduced by Saatcioglu and Razvi [2]in an experimental investigation in 2005 Recently there hasbeen an increasing trend of studies regarding the effectivenessof rectangular spiral shear reinforcement on RC structures[6ndash9] In 2011 Sheikh and Toklucu [3] conducted exper-iments on shear behaviour of RC T-beams reinforced byspiral-type wire ropes as internal shear reinforcements Theyconcluded that the maximum load bearing capacity energyabsorption and the ductility of their connections using theproposed method were higher than that of conventionalstirrup shear reinforcement In addition incorporation ofrectangular continuous spiral reinforcement in RC elements

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 802605 12 pageshttpdxdoiorg1011552014802605

2 The Scientific World Journal

H

F

V

S

12057990∘

Sheardiagonal crack

(a) Common closed stirrups

H

F

V

S

120579615∘

Sheardiagonal crack

(b) Rectangular spiral reinforcement

F

VH

S

120579427∘

Shear

diagonal crack

(c) Twisted opposing rectangular spiral

Figure 1 Contribution of the spiral reinforcement on the shear capacity

could improve the seismic performance of the structuralcomponents as well [10 11] Once the ductility and seismicresistance of the structure is considered ACI 318-02 recom-mends that continuous spiral reinforcement be used insteadof conventional shear resistant one [12] A quick review ofthe literature reveals the abundant amount of studies oncontinuous spiral reinforcement in RC elements howeverthere has been little discussion about the use of rectan-gular spiral reinforcement as shear reinforcement in RCelements

Since the spiral reinforcement is extended like an accor-dion it could positively and quickly be tied into place Thisprocedure is more economical in terms of reduction of man-hours cost compared with the installation of the single closedstirrupsMoreover formation of two endhooks for anchoragewill be required for the installation of single closed stirrupsThese two hooks for each closed stirrup impose extra costs onthe contractors due to increased amount of steel used in theirlength On the contrary this extra length of steel will not berequired in spiral reinforcement installation and hence thetotal cost will be reduced as well This benefit will becomemore significant in terms of RC columns where multiplestirrups per cross-section are installed plus the use of steeloverlaps of stirrups [13] Another advantage of application ofspiral reinforcement would be the prevention of immatureshear failure mechanism due to the continuous nature of thespirals Yet limited performance in torsion and questionableshear resistance in cyclic loading are listed as the weak pointsof both rectangular and circular spiral reinforcement

In this study an experimental and numerical investi-gation on the behaviour of low ductility class RC beamto column connections using spiral and conventional shearreinforcement systems under seismic loading simulated byquasistatic cyclic loading was conducted in the Laboratoryof Structures and Materials Universiti Teknologi Malaysia(UTM) Furthermore an advanced rectangular spiral rein-forcement along with a twisted opposing rectangular spiralmade of double rectangular spiral reinforcements having apitch distance twice the pitch distance of spiral reinforce-ments was also tested in this study In the experimental por-tion of the study three full scale beam to column connectionswere first designed in conformance with Eurocode (EC2-04) [14] for low ductility class connections and then testedby quasistatic cyclic loading recommended by ACI BuildingCode (ACI 318-02) [15] In the end the experimental resultswere validated with numerical results obtained from the FESoftware ANSYS

2 Test Program

21 Analytical Predictions The design of reinforced concretebeams is primarily based on flexural and shear strengthOncethe design of a reinforced concrete member is preferredflexure would be the first item to be considered whicheventually leads to the determination of the section sizeand arrangement of reinforcement to provide the requiredresistance for moments However to successfully develop theplastic hinges in beams instead of columns the beam-columnrelationship would be the fundamental function Then thebeams are designed for shear failure which is sudden withno prior warning Hence the shear design must be in away so that the shear strength for every structural memberexceeds the flexural strengthThemechanism of shear failureis a function of the cross-sectional dimensions the shearreinforcement properties of the member and type of loadingNormally formation of the inclined shear cracks initiates atthemiddle height of the beamnear supports at almost 45∘ andextends towards the compression zone Resistance against theshear forces near supports is provided through application ofanchored reinforcement that intersects these diagonal cracksIn practice provision of shear reinforcement is done in threeforms stirrups inclined bent-up bars and a combination ofa system of stirrups and bent-up bars One great advantageof the rectangular spiral reinforcement system would be itsangle that intersects the diagonal shear cracks (Figure 1) Theshear design of structural members is conducted using thefollowing equation (ACI 318-02)

120593119881119899 ge 119881119906 (1)

where 119881119906 = the factored shear force at the section 120593 =strength reduction factor (085 for shear) and Vn = nominalshear strength computed by

119881119899 = 119881119888+ 119881119904 (2)

where 119881119888= nominal shear strength provided by concrete and

119881119904= nominal shear strength provided by shear reinforcement

for inclined stirrups computed by

119881119904=119860119881119891119910119889 (sin120572 + cos120572)119878

(3)

where 119860119881= total cross sectional area of web reinforcement

within a distance 119878 for single loop stirrups and 119860119881= 2119860

119904

119860119904= cross sectional area of the stirrup bar (mm2) 119878 =

center to center spacing of shear reinforcement in a direction

The Scientific World Journal 3

Table 1 Reinforcement details of specimens

Specimen class Beam reinforcement Column reinforcement120588119897

() 1205881015840

119897

() 120588119905

() 120588119905120593

() 120593front (deg) 120593back (deg) 120588119892

() 119870tr

DCL-CONVEN 0359 0359 0108 mdash mdash mdash 141 4349DCL-SINGLE 0359 0359 mdash 0117 68 112 141 4349DCL-DOUBLE 0359 0359 mdash 0139 51 129 141 4349

parallel to the longitudinal reinforcement (mm) 119891119910= yield

strength of web reinforcement steelIt can be inferred from the aforementioned equations

that the shear resistance could be improved by the angle ofshear reinforcement up to 141 times once the angle is 45∘Moreover close installation of stirrups near the high-shearregions in conventional design would lead to congestionnear the supports of the reinforced concrete beams andconsequently increased time and costsThis problem could beeliminated by using rectangular spiral reinforcement whichleads to improved flow of concrete within the member whenit is delivered to the site by a truck mixer

22 Case Studies and Modelling Set Up The case studies ofthis research are composed of three full-scale beam to columnconnections using rectangular cross-section subjected toearthquake loading simulated by quasistatic cyclic loadingThe effectiveness of shear transverse patterns as a funda-mental parameter was investigated in this study The threeshear transverse patterns used in this study are as follows (i)common closed stirrups (DCL-CONVEN) (ii) rectangularspiral reinforcement (DCL-SINGLE) and (iii) twisted oppos-ing rectangular spiral (DCL-DOUBLE) All the specimenswere designed with same dimensions with a column length1200mm and a beam length 600mm and longitudinal rein-forcement designed in conformance with Eurocode (EC2-04) the Appendix Table 3 The rebar 1205936 was used as thetransverse reinforcement with same steel percentage in allspecimens and a distribution following the abovementionedpatterns Furthermore to successfully isolate the low ductilityclass multistorey RC moment resisting frame all specimenswere considered as exterior beam to column connectionsThe longitudinal reinforcement of the tested beams is twolongitudinal bars of diameter 8mm as tension reinforcementand two bars of 8mm as compression reinforcement (21206018 topand 41206018 bottom)The flexural tension reinforcement ratio 120588

119897

and compression reinforcement ratio 1205881015840119897

is calculated usingthe following expressions and summarized in Table 1

120588119897=119860119904119897

119887119889 120588

1015840

119897

=1198601015840

119904119897

119887119889 (4)

where 119887 and 119889 are the width and the effective depth of thecross section of the beam respectively and119860

119904119897and1198601015840

119904119897

are thearea of the tension and the compression steel reinforcementrespectively Table 1 also presents the values of the transversereinforcement ratios 120588

119905and 120588

119905120593 of each beam based on the

following relationships (5) and (6) for stirrups and spiralreinforcement respectively

120588119905=119860119904119905

119887119904(5)

120588119905120593=1198601199041199052

119887119904 sin120593front+1198601199041199052

119887119904 sin120593back (6)

where 119860119904119905= 2(120587(120601

2

119905

4)) is the area of the two-legged stirrupor the two linked spiral reinforcement with diameter 120601

119905 119904 is

the uniform spacing of the shear reinforcement and120593front and120593back are the angles between the front and the back verticallink respectively of the spiral reinforcement and the beamaxis perpendicular to the shear force

Notice that the minimum volumetric ratio of spiralreinforcement was calculated based on following equation inaccordance with ACI 318-08

120588ℎ= 045 (

119860119892

119860119888

minus 1)1198911015840

119888

119891119910ℎ

(7)

where 119860119892 total cross-sectional area of column section

including the shell and the core 119860119888 cross-sectional area of

column core confined by spiral reinforcementThe most important criteria to evaluate RC column

against seismic loading are the ratio of longitudinal steel area119860 st to gross concrete cross section 119860

119892 120588119892 and transverse

reinforcement index119870tr Equation (8) is used to evaluate theabove mentioned parameters in accordance with ACI 318-08

120588119892=119860 st119860119892

119870tr =40119860 tr119878tr119899

(8)

where 119860 tr = area of transverse reinforcement within spacing119904tr that crosses the splitting plane 119904tr = spacing of transversereinforcement 119899 = number of bars or wires being spliced ordeveloped along the plane of splitting

Notice that 119870tr factor shall be lt25 imposed to avoidbrittle failure and ratio of longitudinal bars should be selectedbetween 001 and 008 The geometry and properties of thereinforcements used in this study are listed in Figure 2 andTable 1 respectively

A typical quasistatic cyclic pattern and modelling setupwas prepared for the tests in conformance with ldquoCommentaryonAcceptanceCriteria forMoment Frames Based on StructuralTestingrdquo (ACI T11R-01) [16] Also deformation of the exterior


200

200

1200

260

700

1206016

1206016

21206018

21206018

4120601826

0

Column200

200

160

160

BEAM

21206018

21206018

1206016260

412060181206016260

120

12070

138∘

(a) DCL-CONVEN

260

260

1206016

41206018

21206018

212060181206016

200

160

200

160

Beam

Column

41206018

1206016260

21206018

21206018

1206016260

260

(b) DCL-SINGLE

520

21206018

21206018

41206018

1206016

1206016

520

Column

520

21206018

21206018

41206018

12060165201206016520

1206016520

1206016520

200

200

160

160

Beam

(c) DCL-DOUBLE

Figure 2 Geometry and steel reinforcement of the tested specimens (a) DCL-CONVEN (b) DCL-SINGLE and (c) DCL-DOUBLE


Table 2 Mechanical properties of reinforcing bars

Bar size Bar diameter (mm) Bar area (mm2) Modulus of elasticity (GPa) Yield strength (MP) Yield strain mmmm1205938 85 60 200 450 000221205936 62 30 200 450 00022

beam to column test module is given in Figure 3 Accordingto the figure the broken lines indicate the initial position ofthe connection considering its self-weight only The moduleis pin supported at 119860 and roller supported at 119863 For seismicassessment the column is subjected to the cyclic force HCEthrough the pin at 119862 and hence the specimen deformsaccordingly as indicated by the solid linesThe concept of driftratio is indicated by 120579

The following statements indicate the various measure-ment instruments used for data collection The DEMECMechanical Strain Gauge was hired as an accurate andreliable crack monitoring device at one side of specimensBesides TML Strain Gauges were applied to measure thedegree of deformation resulting from mechanical strain Inorder to record accurate strain values the strain gaugesare supposed to be correctly installed on the predictedplastic hinge locations For the purpose of measuring thelinear displacements linear variable differential transformers(LVDT) were hired in this project therefore three LVDTswith accuracies of 001mm were installed on the preferredlocations to record the beam displacement and deflectionAlso a 250-KN hydraulic pseudodynamic actuator with amaximum piston stroke of 500mm connected to reactingframe was used in this project Finally application of theaxial load on top of the column to simulate gravity wasmonitored by a 50-ton load cell The modelling setup andtesting instruments are shown in Figure 4

23 Loading Protocol The Displacement Control Methodfollowed by the loading sequence recommended by ldquoCom-mentary on Acceptance Criteria for Moment Frames Based onStructural Testingrdquo (ACI T11R-01) provisions was used in thisstudy A series of load steps and the number of cycles foreach one are specified in the ACI Protocol (Figure 5) Eachload step corresponds to a total inter-storey drift angle Theload was incremented in a step by step manner while the datapoints were recorded and photographs were taken at regularintervals at the end of each load step Once the strength of thespecimens reduced to 40 percent of the maximum strengththe load steps were stopped

The hydraulic jack and load cell were positioned verticallyat the tip of the column in order to provide a constantaxial compression force to the column during cyclic testingThe reason of such loading is that the effect of transversereinforcement on the ductility of connections is significantlydependent on the axial load levelThe amount of applied axialload is a function of column axial load capacity limited tothe 70 capacity to avoid the joint failure which may occurdue to high compressive stresses developed in the joint coreAccording to finite element study increasing the column axialload level up to 30 of the column axial capacity resulted inincreasing the average lateral load capacity by approximately

C

A

B D

h

+Δ

minus

HCF

120579

Initial positionFinal position

Drift ratio 120579 = Δh

Figure 3 Deformation of the exterior beam to column test module[16]

24 However in the range of 30 to 70 of the column axialcapacity no significant change in the overall behaviour wasobserved

24 Materials Properties Normal weight and ready mixedconcrete with a maximum aggregate size of 20mmwere usedfor casting and constructing all test specimens Casting of allspecimens was performed in a horizontal layout way fromthe side Then the specimens were cured for seven days aftercasting in the laboratory environment Readymixed concretewas ordered for 28-day concrete compressive strength of30MP Nevertheless the standard cylinder test yielded acompressive strength of 35MP The yield strength and yieldstrain of the reinforcement bar used in this study were450MPa and 00022 respectively according to the results ofthe Universal Test conducted in Laboratory of Structures andMaterials Universiti Teknologi Malaysia (UTM) (Table 2)

25 Numerical Study Procedure To perform the FEA phaseof the study the FE software ANSYS was used to appro-priately simulate the nonlinear behaviour of beam columnconnections Three-dimensional (3D) FEA was preferred totwo-dimensional (2D) ones as a result of its higher accuracyThree techniques exist in modelling the steel reinforcementin the numerical study [3ndash5] which as listed as (i) dis-crete modelling (ii) embedded modelling and (iii) smearedmodelling (Figure 6) In this study discrete modelling wasused to model the steel bars To efficiently describe the


Table 3 Connection design formulas for ductility classes low inEurocode

DCL

Beam

Longitudinal Bars (L)Critical Region Length ℎ

119908

120588min 05119891ctm119891yk 013120588max 004

Transverse bars (w)Outside Critical Regions

Spacing 119904119908

le 075 d120588119908

ge 008(119891ck)12

119891yk

In Critical RegionsSpacing 119904

119908

le mdash119889bw ge 6mm

Column

Longitudinal Bars (L)Critical Region Length mdash120588min 01119873

119889

119860119888

119891yd 02120588max 4Bars per side 2Spacing betweenrestrained bars mdash


119889bw ge 6mm 119889bl4Spacing 119904

119908

le 20119889blmin (ℎ119888

119887119888

) 400mmIn Critical Regions


119908

le mdashwhere 119891ck is characteristic compressive cylinder strength of concrete at 28days119891cd is design value of concrete compressive strength119891ctm is mean valueof axial tensile strength of concrete 119891yk is characteristic yield strength ofreinforcement 119891yd is design yield strength of reinforcement 119891ywd is designyield of shear reinforcement d is effective depth of section 119889bl is longitudinalbar diameter 119889bw is diameter of hoop ℎ

119908is cross-sectional depth of beam

ℎ119888is cross-sectional depth of column in the direction of interest 120576sy119889 is

design value of steel strain at yield 1205830is curvature ductility factor 120588

119908is shear

reinforcement ratio 1205881015840 is compression steel ratio in beams and 1198870is width

(minimum dimension) of confined concrete core (to centreline of hoops)

constitutive behaviour of the reinforcements the isotropicstrain hardening of von Mises yield criterion along with anassociated flow rule were applied The ANSYS options ofldquoseparate link 180 elementsrdquo were used to model the barsThereinforcement modelling for all three specimens is shown inFigure 7

To appropriately model the concrete behaviour theldquoSolid65rdquo element was hired along with application of lin-ear isotropic and multilinear isotropic material propertiesTherefore the vonMises failure criterionwith themultilinearisotropic material was used to properly define the concretefailure [17] The concrete specimens modelled with ANSYSare shown in Figure 8

26 Acceptance Criteria Based on ACI 318-08 According tothe ldquoBuilding Code Requirements for Structural Concreterdquo

ACI 318-08 significant inelastic drift capacity must be pro-vided by the connection through flexural yielding of thebeams and limited yielding of the column and strong column-weak beam theory Hence an inter-storey drift angle of atleast 0035 rad must be sustained by the connection The fol-lowing requirements must be satisfied by the characteristicsof the third complete cycle for cycling at drift ratio of 0035rad

(i) The peak force must be at least 075 119864max(ii) The relative energy dissipation ratio must be at least

18

where 119864max = the maximum lateral resistance of the testspecimen calculated from test results (forces or moments)

3 Test Results and Discussions

The test results are composed of the three following sections(i) hysteresis responses of the specimens (ii) energy dissipa-tion capacity and (iii) beam deflection and crack openingThese test results will be discussed in detail in the followingparagraphs

31 Hysteresis Responses The fundamental parameter forinvestigation of seismic performance is the inter-storey driftangle Based on the data collected by photographic documen-tation data logger and direct observation it was concludedthat initiation and propagation of cracks were observed atthe same storey shear force in all specimens However thespecimens exhibited a different performance after this pointThe efficiency of different transverse shear patterns will bediscussed in the following sections

311 Conventional Specimen A poor performance wasobserved for specimen with conventional stirrups reinforce-ment subjected to cyclic loading While the quasistatic testswere in progress concentration of cracks was observed atthe top and bottom of beam-column joint at an inter-storeydrift ratio of 13 No yielding plateau was indicated bythe hysteresis curves while the response was brittle with animmediate increase in the storeyshear force after attainingthe peak value A severe pinching accompanied by smallenergy absorption was shown by the cyclic loops The initialstiffness was reported to be higher than the stiffness at thebeginning of unloading and reloading loops There was noformation of plastic hinges in the specimen The concretein the joint panel governed the overall behaviour whichwas an indication of the fact that the failure mode ofconnection whether shear or flexural could be identified bythe amount of shear reinforcementTherefore the conclusionis that the failure mode could be classified as joint shearfailure Since the joint shear failure is abrupt and leads topinched hysteresis loops with low energy dissipation it is notdesirable The cyclic relationships between the storey shearforce and the storey drift determined by numerical study andexperimental test are compared in Figure 9 The damagedstate of the specimen after the end of cyclic test along withstress intensity is demonstrated in Figure 10 Finally it was


Actuator Load cell

LVDT

(a)

Actuator

Load cell

Hinged support

Rolled support

LVD

T

LVDT LVDT

Loading

(b)

Figure 4 Real test setup view (a) schematic view (b)

minus4

minus3

minus2

minus1

0

1

2

3

4

02 025 035 05 075 1014

17522

27535

Cycle

s

Drift

ratio

times10

minus2

Figure 5 The cyclic lateral displacement pattern (the loadingprotocol)

concluded that a good correlation existed between the resultsof the numerical model and the experimental test in theoverall cyclic behaviour

312 Rectangular and Twisted Opposing Rectangular SpiralReinforcement Specimens Since a similar behaviour wasobserved by the DCL-SINGLE and DCL-DOUBLE speci-mens they are discussed in the same section Initiation ofthe first diagonal crack was observed in the beam at aninter-storey drift ratio of 05 An X-pattern was formedby these cracks following the alternate load directions Thesize and number of the diagonal cracks in joint cores keptrising until the specimen attained the peak load of almost173 KN at 21 drift ratio for specimen DCL-SINGLE and193 KN at 21 drift ratio for specimen DCL-DOUBLEAfter this cycle there was no crack observation in the beam

however diagonal cracks continued to widen in the jointcore followed by spalling of concrete at the center of thejoint area Extension of concrete spalling throughout a widerjoint area exposing column longitudinal bars occurred at25 drift The 4800120583120576 (microstrain) value recorded bythe strain gauges positioned on appropriate locations wasa sign of strength degradation resulting from yielding oflongitudinal bars which was relevant to the 3 top drift inthe experimental test The failure of both connections wascategorized as ductile flexural failure The wide hysteresisloops were an indication of large energy dissipation inbending mode An acceptable correspondence behaviour isobserved between the experimental results and numericalanalysis of the specimens where this reasonable correlationis highlighted in Figures 11 and 12 Besides the experimentalfailure mode and the equivalent strain distribution at the endof cyclic test are highlighted in Figures 13 and 14 Finally anexperimental comparison between hysteresis performancesof all specimens is shown in Figure 15

32 Energy Dissipation Capacity and Load-Drift EnvelopsThe fundamental parameter in resisting seismic loadingis known to be the energy dissipation capacity In thisstudy energy dissipation of connections in each group wasdetermined using the area enclosed by the lateral load-displacement loops A comparison between the energy dis-sipation capacities of all three connections is depicted inFigure 16 It is evident from the bar graph that a better per-formance in absorbing the cyclic energy was demonstratedby the rectangular spiral reinforcement (DCL-SINGLE) andtwisted opposing rectangular spiral (DCL-DOUBLE) com-pared to the common closed stirrups (DCL-CONVEN)

The shear deformation of beam to column connectionmakes a great contribution to envelope curves in RC frames


Concrete element

Concrete node

Shared node between

concrete and reinforcement

elements

(a)

Concrete elementConcrete node

Reinforcement

Compatible displacements

between concrete and reinforcements

(b)

Concrete Concrete node

Smeared properties of

steel in concrete elements

element

(c)

Figure 6 Reinforcement modelling techniques (a) discrete (b) embedded and (c) smeared [4]

(a) (b) (c)

Figure 7 Definition of reinforcement bars with ldquoLink180 Elementrdquo inANSYS (a)DCL-CONVEN (b)DCL-SINGLE and (c)DCL-DOUBLE

(a) (b) (c)

Figure 8 Concrete element modelling with ANSYS using the element ldquoSolid 65rdquo for (a) DCL-CONVEN (b) DCL-SINGLE and (c) DCL-DOUBLE


minus25minus20minus15minus10minus5

05

10152025

minus004 minus003 minus002 minus001 0 001 002 003 004

Stor

ey sh

ear (

KN)

Storey drift

ExperimentalFinite element

075Emax

Figure 9 An experimental and finite element hysteresis responsecomparison for the DCL-CONVEN specimen

Stress concentrationshear cracks

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

XZ

Y

Figure 10 Stress intensity results and the damaged state at the endof the seismic test for the DCL-CONVEN specimen

The nonlinear behaviour of the tested beam-column joints isreflected in the envelope curves The peak lateral resistancevalues calculated at each level of drift and the correspond-ing drift ratios were incorporated to draw the envelopecurves According to Figure 17 the DCL-SINGLE and DCL-DOUBLE curves are capable of withstanding large driftscompared to DCL-CONVEN due to the impact of the specialshear transverse patterns of the DCL-SINGLE and DCL-DOUBLE specimens Also it is evident that the peak lateralresistances of DCL-SINGLE and DCL-DOUBLE specimensare almost similar

33 Beam Deflection and Crack Opening The overall deflec-tion of the specimens was a function of their shear character-istics A higher deflection was observed for the DCL-SINGLEand DCL-DOUBLE specimens leading to higher impactsand higher absorption of energy It is good to mention thatdeflection measurement was conducted through installationof a vertical LVDT at the bottom of the beams Howeverminor deflections at the ultimate load along with a relativelybrittle failure were observed for the DCL-CONEN specimenIt can be inferred from the results that the deflections and


05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax

Figure 11 An experimental and finite element hysteresis responsecomparison for the DCL-SINGLE specimen


05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax

Figure 12 An experimental and finite element hysteresis responsecomparison for the DCL-DOUBLE specimen

modes of failure of the connections are a function of theappropriate pattern and amount of shear reinforcement Thedrift versus deflection curves for all specimens is shown inFigure 18

Crack opening in RC members is usually accompaniedby shear crack sliding along shear cracks leading to sheartransfer by the aggregate interlock mechanism Shear slidingwhich is related to shear opening is the key factor in frac-turing shear reinforcement particularly under cyclic loadingMoreover the angle between the shear reinforcement andshear cracks significantly affected the diagonal crack open-ings Nevertheless the beam with vertical stirrups showedgreater shear crack widths The crack opening curves for allspecimens are shown in Figure 19

4 Summary and Conclusive Remarks

The seismic performance of a new proposed beam to columnconnection introduced as ldquotwisted opposing rectangularspiral (DCL-DOUBLE)rdquowas experimentally and numerically


Diagonal cracksX pattern plastic hinge

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

X

Z

Y

Figure 13 Stress intensity results and the damaged state at the endof seismic test for the DCL-SINGLE specimen

Diagonal cracks

MN

MX

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

Plastic hinge

X pattern cracksX

Z

Y

Figure 14 Stress intensity results and the damaged state at the endof seismic test for the DCL-DOUBLE specimen


05

10152025


Stor

ey sh

ear (

KN)

Storey drift

DCL-DOUBLEDCL-SINGLEDCL-CONVEN

Figure 15 Experimental comparison of hysteresis performance ofall three specimens

compared against rectangular spiral (DCL-SINGLE) andconventional (DCL-CONVEN) shear reinforcement systemsin this study The fundamental acceptance criteria selectedfor seismic assessment of the connections in this study wasin conformance with ACI 318-08 The main findings of this

100

507

572

0

100

200

300

400

500

600

Ener

gy d

issip

iatio

n (

)

DCL-CONVENDCL-SINGLEDCL-DOUBLE

Figure 16 An energy dissipation capacity comparison for the DCLgroup


05

10152025


Stor

ey sh

ear (

KN)

Storey drift


Figure 17 Envelop curves for comparing themaximum load in eachcycle for the DCL group

research based on the numerical and experimental results arelisted as follows

(i) The failure modes of RC beam to column connec-tions whether ductile flexural failure or joint shearfailure were affected by the angle between the shearreinforcement and shear cracks Hence a highercapacity of connected beam was developed by theDCL-DOUBLE and DCL-SINGLE specimens com-pared to that of the conventional (DCL-CONVEN)shear reinforcement system

(ii) A 35 drift angle was achieved by both the DCL-DOUBLE and DCL-SINGLE specimens with relativeenergy dissipation not lesser than 18 In other wordsalthough the original design of the rectangular spiral


minus7

minus5

minus3

minus1

1

3

5

7

minus003 minus002 minus001 0 001 002 003

Beam

defl

ectio

n (m

m)

Storey drift


Figure 18 The drift versus beam deflection curves for both loadingdirections positive and negative for the DCL group

0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift

DCL-CONVEN + DCL-CONVEN minusDCL-SINGLE + DCL-SINGLE minusDCL-DOUBLE + DCL-DOUBLE minus

Figure 19 Crack opening curves for the DCL group in the criticalzone for both loading directions positive and negative for the DCLgroup

reinforcement specimens was nonseismic they even-tually met the seismic requirements

(iii) A higher energy dissipation capacity was demon-strated by the DCL-DOUBLE specimen comparedto that of the DCL-SINGLE one This higher energydissipation capacity is attributed to the existenceof double spiral transverse reinforcements in eachsection of the beam to column connection whichresist efficiency to cyclic loading

(iv) The shear transverse pattern significantly influencedthe overall deflection and crack opening of the spec-imens A significant deflection will be provided bythe rectangular spiral reinforcement which results inhigher ductility Furthermore a widespread crack dis-tribution was observed for both the DCL-DOUBLEand DCL-SINGLE specimens compared to that of theDCL-CONVEN one

Appendix

See Table 3

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This project was funded by a research grant provided bythe Malaysian government under the supervision of Uni-versiti Teknologi Malaysia (UTM) Any opinions findingsand conclusions expressed in this paper are those of theauthors Moreover all nine full-scale beam-column connec-tion prototypeswere constructed and tested in the Laboratoryof Structures and Materials Universiti Teknologi Malaysia(UTM)

References

[1] R P T Park Reinforced Concrete Structures JohnWiley amp Sons1975

[2] M Saatcioglu and S R Razvi ldquoStrength and ductility ofconfined concreterdquo Journal of structural engineering New Yorkvol 118 no 6 pp 1590ndash1607 1992

[3] S A Sheikh and M T Toklucu ldquoReinforced concrete columnsconfined by circular spirals and hoopsrdquo ACI Structural Journalvol 90 no 5 pp 542ndash553 1993

[4] A Considere Experimental Researches on Reinforced Concretetranslated by L S Moisseiff McGraw Publishing CompanyNew York NY USA 1903

[5] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[6] C G Karayannis and C E Chalioris ldquoShear tests of reinforcedconcrete beams with continuous rectangular spiral reinforce-mentrdquo Construction and Building Materials vol 46 pp 86ndash972013

[7] ACI Committee 318 ldquoBuilding code requirements for struc-tural concreterdquo American Concrete Institute Farmington HillsDetroit Mich USA 2002

[8] A G Tsonos ldquoCyclic load behavior of reinforced concretebeam-column subassemblages of modern structuresrdquo ACIStructural Journal vol 104 no 4 pp 468ndash478 2007

[9] C Karayannis and G Sirkelis ldquoResponse of columns andjoints with spiral shear reinforcementrdquo WIT Transactions onModelling and Simulation vol 41 pp 455ndash463 2005

[10] C Karayannis G Sirkelis and P Mavroeidis ldquoImprovementof seismic capacity of external beam-column joints usingrectangular spiral shear reinforcementrdquo in Proceedings of the5th Conference on Earthquake Resistant Engineering Structures(ERES rsquo05) pp 147ndash156 Skiathos Greece 2005

[11] C G Karayannis C E Chalioris and P D MavroeidisldquoShear capacity of RC rectangular beams with continuous spiraltransversal reinforcementrdquoWIT Transactions on Modelling andSimulation vol 41 pp 379ndash386 2005

[12] K-H Yang G-H Kim and H-S Yang ldquoShear behaviorof continuous reinforced concrete T-beams using wire rope


as internal shear reinforcementrdquo Construction and BuildingMaterials vol 25 no 2 pp 911ndash918 2011

[13] P D Zararis ldquoShear strength and minimum shear reinforce-ment of reinforced concrete slender beamsrdquo ACI StructuralJournal vol 100 no 2 pp 203ndash214 2003

[14] C E Chalioris ldquoSteel fibrous RC beams subjected to cyclicdeformations under predominant shearrdquo Engineering Struc-tures vol 49 pp 104ndash118 2013

[15] C E Chalioris and C G Karayannis ldquoEffectiveness of the useof steel fibres on the torsional behaviour of flanged concretebeamsrdquo Cement and Concrete Composites vol 31 no 5 pp 331ndash341 2009

[16] C G Karayannis and G M Sirkelis ldquoSeismic behaviour ofreinforced concrete columns with rectangular spiral shear rein-forcementrdquo in Proceedings of the 3rd International Conferenceon Construction in the 21st Century (CITC rsquo05) AdvancingEngineering Management and Technology Athens Greece2005

[17] CEN ldquoEurocode 2 Design of concrete structuresmdashpart 1ndash1general rules and rules for buildingsrdquo EN 1992-1-12004E 2004

International Journal of

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RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



H

F

V

S

12057990∘

Sheardiagonal crack

(a) Common closed stirrups

H

F

V

S

120579615∘

Sheardiagonal crack

(b) Rectangular spiral reinforcement

F

VH

S

120579427∘

Shear

diagonal crack

(c) Twisted opposing rectangular spiral

Figure 1 Contribution of the spiral reinforcement on the shear capacity

could improve the seismic performance of the structuralcomponents as well [10 11] Once the ductility and seismicresistance of the structure is considered ACI 318-02 recom-mends that continuous spiral reinforcement be used insteadof conventional shear resistant one [12] A quick review ofthe literature reveals the abundant amount of studies oncontinuous spiral reinforcement in RC elements howeverthere has been little discussion about the use of rectan-gular spiral reinforcement as shear reinforcement in RCelements

Since the spiral reinforcement is extended like an accor-dion it could positively and quickly be tied into place Thisprocedure is more economical in terms of reduction of man-hours cost compared with the installation of the single closedstirrupsMoreover formation of two endhooks for anchoragewill be required for the installation of single closed stirrupsThese two hooks for each closed stirrup impose extra costs onthe contractors due to increased amount of steel used in theirlength On the contrary this extra length of steel will not berequired in spiral reinforcement installation and hence thetotal cost will be reduced as well This benefit will becomemore significant in terms of RC columns where multiplestirrups per cross-section are installed plus the use of steeloverlaps of stirrups [13] Another advantage of application ofspiral reinforcement would be the prevention of immatureshear failure mechanism due to the continuous nature of thespirals Yet limited performance in torsion and questionableshear resistance in cyclic loading are listed as the weak pointsof both rectangular and circular spiral reinforcement

In this study an experimental and numerical investi-gation on the behaviour of low ductility class RC beamto column connections using spiral and conventional shearreinforcement systems under seismic loading simulated byquasistatic cyclic loading was conducted in the Laboratoryof Structures and Materials Universiti Teknologi Malaysia(UTM) Furthermore an advanced rectangular spiral rein-forcement along with a twisted opposing rectangular spiralmade of double rectangular spiral reinforcements having apitch distance twice the pitch distance of spiral reinforce-ments was also tested in this study In the experimental por-tion of the study three full scale beam to column connectionswere first designed in conformance with Eurocode (EC2-04) [14] for low ductility class connections and then testedby quasistatic cyclic loading recommended by ACI BuildingCode (ACI 318-02) [15] In the end the experimental resultswere validated with numerical results obtained from the FESoftware ANSYS

2 Test Program

21 Analytical Predictions The design of reinforced concretebeams is primarily based on flexural and shear strengthOncethe design of a reinforced concrete member is preferredflexure would be the first item to be considered whicheventually leads to the determination of the section sizeand arrangement of reinforcement to provide the requiredresistance for moments However to successfully develop theplastic hinges in beams instead of columns the beam-columnrelationship would be the fundamental function Then thebeams are designed for shear failure which is sudden withno prior warning Hence the shear design must be in away so that the shear strength for every structural memberexceeds the flexural strengthThemechanism of shear failureis a function of the cross-sectional dimensions the shearreinforcement properties of the member and type of loadingNormally formation of the inclined shear cracks initiates atthemiddle height of the beamnear supports at almost 45∘ andextends towards the compression zone Resistance against theshear forces near supports is provided through application ofanchored reinforcement that intersects these diagonal cracksIn practice provision of shear reinforcement is done in threeforms stirrups inclined bent-up bars and a combination ofa system of stirrups and bent-up bars One great advantageof the rectangular spiral reinforcement system would be itsangle that intersects the diagonal shear cracks (Figure 1) Theshear design of structural members is conducted using thefollowing equation (ACI 318-02)

120593119881119899 ge 119881119906 (1)

where 119881119906 = the factored shear force at the section 120593 =strength reduction factor (085 for shear) and Vn = nominalshear strength computed by

119881119899 = 119881119888+ 119881119904 (2)

where 119881119888= nominal shear strength provided by concrete and

119881119904= nominal shear strength provided by shear reinforcement

for inclined stirrups computed by

119881119904=119860119881119891119910119889 (sin120572 + cos120572)119878

(3)

where 119860119881= total cross sectional area of web reinforcement

within a distance 119878 for single loop stirrups and 119860119881= 2119860

119904

119860119904= cross sectional area of the stirrup bar (mm2) 119878 =

center to center spacing of shear reinforcement in a direction




() 1205881015840

119897

() 120588119905

() 120588119905120593


() 119870tr






119897



120588119897=119860119904119897

119887119889 120588

1015840

119897

=1198601015840

119904119897

119887119889 (4)


119904119897and1198601015840

119904119897


119905and 120588



120588119905=119860119904119905

119887119904(5)

120588119905120593=1198601199041199052

119887119904 sin120593front+1198601199041199052

119887119904 sin120593back (6)

where 119860119904119905= 2(120587(120601

2

119905


119905 119904 is



120588ℎ= 045 (

119860119892

119860119888

minus 1)1198911015840

119888

119891119910ℎ

(7)





119892 120588119892 and transverse


120588119892=119860 st119860119892

119870tr =40119860 tr119878tr119899

(8)





200

200

1200

260

700

1206016

1206016

21206018

21206018

4120601826

0

Column200

200

160

160

BEAM

21206018

21206018

1206016260

412060181206016260

120

12070

138∘

(a) DCL-CONVEN

260

260

1206016

41206018

21206018

212060181206016

200

160

200

160

Beam

Column

41206018

1206016260

21206018

21206018

1206016260

260

(b) DCL-SINGLE

520

21206018

21206018

41206018

1206016

1206016

520

Column

520

21206018

21206018

41206018

12060165201206016520

1206016520

1206016520

200

200

160

160

Beam

(c) DCL-DOUBLE









C

A

B D

h

+Δ

minus

HCF

120579









DCL

Beam


119908

120588min 05119891ctm119891yk 013120588max 004


Spacing 119904119908

le 075 d120588119908

ge 008(119891ck)12

119891yk


119908


Column


119889

119860119888




119908

le 20119889blmin (ℎ119888

119887119888



119908





119908is shear








18







Actuator Load cell

LVDT

(a)

Actuator

Load cell

Hinged support

Rolled support

LVD

T

LVDT LVDT

Loading

(b)


minus4

minus3

minus2

minus1

0

1

2

3

4

02 025 035 05 075 1014

17522

27535

Cycle

s

Drift

ratio

times10

minus2








Concrete element

Concrete node

Shared node between


elements

(a)


Reinforcement



(b)




element

(c)


(a) (b) (c)


(a) (b) (c)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

XZ

Y





05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax








2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

X

Z

Y


Diagonal cracks

MN

MX

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

Plastic hinge

X pattern cracksX

Z

Y



05

10152025


Stor

ey sh

ear (

KN)

Storey drift




100

507

572

0

100

200

300

400

500

600

Ener

gy d

issip

iatio

n (

)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift







minus7

minus5

minus3

minus1

1

3

5

7


Beam

defl

ectio

n (m

m)

Storey drift



0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift






Appendix

See Table 3



Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












() 1205881015840

119897

() 120588119905

() 120588119905120593


() 119870tr






119897



120588119897=119860119904119897

119887119889 120588

1015840

119897

=1198601015840

119904119897

119887119889 (4)


119904119897and1198601015840

119904119897


119905and 120588



120588119905=119860119904119905

119887119904(5)

120588119905120593=1198601199041199052

119887119904 sin120593front+1198601199041199052

119887119904 sin120593back (6)

where 119860119904119905= 2(120587(120601

2

119905


119905 119904 is



120588ℎ= 045 (

119860119892

119860119888

minus 1)1198911015840

119888

119891119910ℎ

(7)





119892 120588119892 and transverse


120588119892=119860 st119860119892

119870tr =40119860 tr119878tr119899

(8)





200

200

1200

260

700

1206016

1206016

21206018

21206018

4120601826

0

Column200

200

160

160

BEAM

21206018

21206018

1206016260

412060181206016260

120

12070

138∘

(a) DCL-CONVEN

260

260

1206016

41206018

21206018

212060181206016

200

160

200

160

Beam

Column

41206018

1206016260

21206018

21206018

1206016260

260

(b) DCL-SINGLE

520

21206018

21206018

41206018

1206016

1206016

520

Column

520

21206018

21206018

41206018

12060165201206016520

1206016520

1206016520

200

200

160

160

Beam

(c) DCL-DOUBLE









C

A

B D

h

+Δ

minus

HCF

120579









DCL

Beam


119908

120588min 05119891ctm119891yk 013120588max 004


Spacing 119904119908

le 075 d120588119908

ge 008(119891ck)12

119891yk


119908


Column


119889

119860119888




119908

le 20119889blmin (ℎ119888

119887119888



119908





119908is shear








18







Actuator Load cell

LVDT

(a)

Actuator

Load cell

Hinged support

Rolled support

LVD

T

LVDT LVDT

Loading

(b)


minus4

minus3

minus2

minus1

0

1

2

3

4

02 025 035 05 075 1014

17522

27535

Cycle

s

Drift

ratio

times10

minus2








Concrete element

Concrete node

Shared node between


elements

(a)


Reinforcement



(b)




element

(c)


(a) (b) (c)


(a) (b) (c)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

XZ

Y





05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax








2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

X

Z

Y


Diagonal cracks

MN

MX

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

Plastic hinge

X pattern cracksX

Z

Y



05

10152025


Stor

ey sh

ear (

KN)

Storey drift




100

507

572

0

100

200

300

400

500

600

Ener

gy d

issip

iatio

n (

)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift







minus7

minus5

minus3

minus1

1

3

5

7


Beam

defl

ectio

n (m

m)

Storey drift



0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift






Appendix

See Table 3



Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










200

200

1200

260

700

1206016

1206016

21206018

21206018

4120601826

0

Column200

200

160

160

BEAM

21206018

21206018

1206016260

412060181206016260

120

12070

138∘

(a) DCL-CONVEN

260

260

1206016

41206018

21206018

212060181206016

200

160

200

160

Beam

Column

41206018

1206016260

21206018

21206018

1206016260

260

(b) DCL-SINGLE

520

21206018

21206018

41206018

1206016

1206016

520

Column

520

21206018

21206018

41206018

12060165201206016520

1206016520

1206016520

200

200

160

160

Beam

(c) DCL-DOUBLE









C

A

B D

h

+Δ

minus

HCF

120579









DCL

Beam


119908

120588min 05119891ctm119891yk 013120588max 004


Spacing 119904119908

le 075 d120588119908

ge 008(119891ck)12

119891yk


119908


Column


119889

119860119888




119908

le 20119889blmin (ℎ119888

119887119888



119908





119908is shear








18







Actuator Load cell

LVDT

(a)

Actuator

Load cell

Hinged support

Rolled support

LVD

T

LVDT LVDT

Loading

(b)


minus4

minus3

minus2

minus1

0

1

2

3

4

02 025 035 05 075 1014

17522

27535

Cycle

s

Drift

ratio

times10

minus2








Concrete element

Concrete node

Shared node between


elements

(a)


Reinforcement



(b)




element

(c)


(a) (b) (c)


(a) (b) (c)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

XZ

Y





05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax








2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

X

Z

Y


Diagonal cracks

MN

MX

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

Plastic hinge

X pattern cracksX

Z

Y



05

10152025


Stor

ey sh

ear (

KN)

Storey drift




100

507

572

0

100

200

300

400

500

600

Ener

gy d

issip

iatio

n (

)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift







minus7

minus5

minus3

minus1

1

3

5

7


Beam

defl

ectio

n (m

m)

Storey drift



0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift






Appendix

See Table 3



Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















C

A

B D

h

+Δ

minus

HCF

120579









DCL

Beam


119908

120588min 05119891ctm119891yk 013120588max 004


Spacing 119904119908

le 075 d120588119908

ge 008(119891ck)12

119891yk


119908


Column


119889

119860119888




119908

le 20119889blmin (ℎ119888

119887119888



119908





119908is shear








18







Actuator Load cell

LVDT

(a)

Actuator

Load cell

Hinged support

Rolled support

LVD

T

LVDT LVDT

Loading

(b)


minus4

minus3

minus2

minus1

0

1

2

3

4

02 025 035 05 075 1014

17522

27535

Cycle

s

Drift

ratio

times10

minus2








Concrete element

Concrete node

Shared node between


elements

(a)


Reinforcement



(b)




element

(c)


(a) (b) (c)


(a) (b) (c)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

XZ

Y





05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax








2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

X

Z

Y


Diagonal cracks

MN

MX

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

Plastic hinge

X pattern cracksX

Z

Y



05

10152025


Stor

ey sh

ear (

KN)

Storey drift




100

507

572

0

100

200

300

400

500

600

Ener

gy d

issip

iatio

n (

)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift







minus7

minus5

minus3

minus1

1

3

5

7


Beam

defl

ectio

n (m

m)

Storey drift



0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift






Appendix

See Table 3



Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











DCL

Beam


119908

120588min 05119891ctm119891yk 013120588max 004


Spacing 119904119908

le 075 d120588119908

ge 008(119891ck)12

119891yk


119908


Column


119889

119860119888




119908

le 20119889blmin (ℎ119888

119887119888



119908





119908is shear








18







Actuator Load cell

LVDT

(a)

Actuator

Load cell

Hinged support

Rolled support

LVD

T

LVDT LVDT

Loading

(b)


minus4

minus3

minus2

minus1

0

1

2

3

4

02 025 035 05 075 1014

17522

27535

Cycle

s

Drift

ratio

times10

minus2








Concrete element

Concrete node

Shared node between


elements

(a)


Reinforcement



(b)




element

(c)


(a) (b) (c)


(a) (b) (c)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

XZ

Y





05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax








2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

X

Z

Y


Diagonal cracks

MN

MX

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

Plastic hinge

X pattern cracksX

Z

Y



05

10152025


Stor

ey sh

ear (

KN)

Storey drift




100

507

572

0

100

200

300

400

500

600

Ener

gy d

issip

iatio

n (

)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift







minus7

minus5

minus3

minus1

1

3

5

7


Beam

defl

ectio

n (m

m)

Storey drift



0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift






Appendix

See Table 3



Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Actuator Load cell

LVDT

(a)

Actuator

Load cell

Hinged support

Rolled support

LVD

T

LVDT LVDT

Loading

(b)


minus4

minus3

minus2

minus1

0

1

2

3

4

02 025 035 05 075 1014

17522

27535

Cycle

s

Drift

ratio

times10

minus2








Concrete element

Concrete node

Shared node between


elements

(a)


Reinforcement



(b)




element

(c)


(a) (b) (c)


(a) (b) (c)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

XZ

Y





05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax








2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

X

Z

Y


Diagonal cracks

MN

MX

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

Plastic hinge

X pattern cracksX

Z

Y



05

10152025


Stor

ey sh

ear (

KN)

Storey drift




100

507

572

0

100

200

300

400

500

600

Ener

gy d

issip

iatio

n (

)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift







minus7

minus5

minus3

minus1

1

3

5

7


Beam

defl

ectio

n (m

m)

Storey drift



0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift






Appendix

See Table 3



Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Concrete element

Concrete node

Shared node between


elements

(a)


Reinforcement



(b)




element

(c)


(a) (b) (c)


(a) (b) (c)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

XZ

Y





05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax








2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

X

Z

Y


Diagonal cracks

MN

MX

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

Plastic hinge

X pattern cracksX

Z

Y



05

10152025


Stor

ey sh

ear (

KN)

Storey drift




100

507

572

0

100

200

300

400

500

600

Ener

gy d

issip

iatio

n (

)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift







minus7

minus5

minus3

minus1

1

3

5

7


Beam

defl

ectio

n (m

m)

Storey drift



0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift






Appendix

See Table 3



Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

XZ

Y





05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax



05

10152025


Stor

ey sh

ear (

KN)

Storey drift


075Emax








2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

X

Z

Y


Diagonal cracks

MN

MX

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

Plastic hinge

X pattern cracksX

Z

Y



05

10152025


Stor

ey sh

ear (

KN)

Storey drift




100

507

572

0

100

200

300

400

500

600

Ener

gy d

issip

iatio

n (

)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift







minus7

minus5

minus3

minus1

1

3

5

7


Beam

defl

ectio

n (m

m)

Storey drift



0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift






Appendix

See Table 3



Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

MN

MX

X

Z

Y


Diagonal cracks

MN

MX

2600

56

1923

36

2872

04

3820

72

4769

40

5718

08

6666

76

7615

44

8564

12

9746

85

Plastic hinge

X pattern cracksX

Z

Y



05

10152025


Stor

ey sh

ear (

KN)

Storey drift




100

507

572

0

100

200

300

400

500

600

Ener

gy d

issip

iatio

n (

)




05

10152025


Stor

ey sh

ear (

KN)

Storey drift







minus7

minus5

minus3

minus1

1

3

5

7


Beam

defl

ectio

n (m

m)

Storey drift



0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift






Appendix

See Table 3



Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus7

minus5

minus3

minus1

1

3

5

7


Beam

defl

ectio

n (m

m)

Storey drift



0

2

4

6

8

10

12

14


Crac

k op

enni

ng (m

m)

Storey drift






Appendix

See Table 3



Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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